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Library of Congress Cataloging-in-Publication Data
Computational systems biology (Kriete)
Computational systems biology / edited by Andres Kriete, Roland Eils. -- Second edition.
p. ; cm.
Includes bibliographical references and indexes.
ISBN 978-0-12-405926-9 (alk. paper)
I. Kriete, Andres, editor of compilation. II. Eils, Roland, editor of compilation. III. Title.
[DNLM: 1. Computational Biology. 2. Systems Biology. QU 26.5]
QH324.2
570.1’13--dc23
2013045039
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
ISBN: 978-0-12-405926-9
For information on all Academic Press publications
visit our website at store.elsevier.com
Printed in the United States of America
14 15 10 9 8 7 6 5 4 3 2 1](https://image.slidesharecdn.com/26816717-250512175734-af7d3724/85/Full-Computational-Systems-Biology-Second-Edition-2da-Roland-Eils-8-320.jpg)
![8 Robustness and fragility and application to the cell cycle 37
Figure 3.3 shows that the three couples of Clb cyclins (Clb5,6, Clb3,4, and Clb1,2) undergo
waves with amplitudes at different times. We shall first focus on the Clb5/6 couple and on the
onset and the decay of the peak of their level. Figure 3.2 shows that Clb5/6 has a maximum
at t = 23 and that at t = 8 it is hallway reaching that maximum and at t = 31.5 it is again half-
way down. We computed the time-control coefficient Tc at those times, and this amounted to
0.87 and −4.57, respectively. We also computed the robustness R (defined as the inverse of the
time-control coefficients) of the amplitude of Clb5/6 at the two halfway time points. We first
computed the robustness of the Clb5/6 amplitude exercised by all processes in the network
when perturbed simultaneously and equally in the same direction. The corresponding robust-
nesses were 1.14849 and 0.21881 (see Table 3.1).
Quinton-Tulloch et al. (2013) identified the inverse of the robustness with fragility, which
in turn is equal to the control coefficient. As a consequence the above (Equation 3.10):
can be reformulated as:
For this case of equal perturbations of all processes amounts to:
And the same for the other time point analyzed. The last two columns in Table 3.1 confirms
this computationally.
For the onset of the peak the time-control coefficient is positive. Hence the positive robust-
nesses must be smaller (typically those with respect to kinases perturbations) than the robust-
nesses with respect to the phosphatases (which are not considered explicitly in the system
yet). For the decay of the peak, the inverse should be true.
(3.10)
n
j=1
CXk
ej
(t) = CXk
t (t)
(3.22)
n
j=1
1
ReXk
ej
(t)
= CXk
t (t)
(3.23)
n
j=1
1
ℜXk
total for equal(t 1
2on
)
= CXk
t (t 1
2on
)
0 10 20 30 40 50 60
0
0.3
0.6
0.9
1.2
Time
Clb3,4
Clb5,6
Clb1,2
[Clb]
FIGURE 3.3 Computational time course of Clb cyclins couples over time.](https://image.slidesharecdn.com/26816717-250512175734-af7d3724/85/Full-Computational-Systems-Biology-Second-Edition-2da-Roland-Eils-48-320.jpg)
![38 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS
9 PERFECT ADAPTATION AND INTEGRAL CONTROL IN
METABOLISM
Biochemical reaction networks can exhibit properties similar to those of control system
structures in control engineering, but are they identical? The robustness of cellular adapta-
tion to environmental conditions is often related to negative feedback control structures. For
example, robust adaptations in a bacterial chemotaxis signaling network, in mammalian iron
and calcium homeostasis, and in yeast osmoregulation have been interpreted as integral feed-
back control systems (Yi et al. 2000; El-Samad et al. 2002; Ni et al. 2009; Muzzey et al. 2009).
A recent study identified the three different types of control structures used in control engi-
neering, i.e. proportional, integral, and derivative feedback control, in regulations of energy
metabolism (Cloutier and Wellstead 2010). In addition, specific nonlinear dynamics in signal-
ing networks, such as oscillation or bi-stability, can be induced by positive feedback loops.
Feed-forward control structures are also observed in gene regulatory networks (Mangan and
Alon 2003), as well as in the regulation of glycolytic intermediates (Bali and Thomas 2001).
Regulation in living cells tends to occur at multiple levels simultaneously with a hierarchi-
cal structure (Westerhoff 2008). In a metabolic network the regulation of a reaction rate can be
TABLE 3.1 Calculation of time-control coefficient and robustness for Clb cyclins couples.
Clb5,6 α(5,6) β(5,6)
Max [5,6] Time Max [5,6]/2 t1/2 α(5,6) Max [5,6] Time Max [5,6]/2 t1/2 β(5,6)
1,41473 23 0,707365 8 0,076988 1,41473 23 0,789371 31,5 0,11453
Clb3,4 α(3,4) β(3,4)
Max [3,4] Time Max [3,4]/2 t1/2 α(3,4) Max [3,4] Time Max [3,4]/2 t1/2 β(3,4)
0,959239 30 0,4796195 19,5 0,023046 0,959239 30 0,60479 37 0,05489
Clb1,2 α(1,2) β(1,2)
Max [1,2] Time Max [1,2]/2 t1/2 α(1,2) Max [1,2] Time Max [1,2]/2 t1/2 β(1,2)
1,1148 34 0,5574 27 0,094539 1,1148 34 0,780522 41,5 0,049
Tcα Tcβ Rα Rβ 1/Rα 1/Rβ
Tcα(5,6) Tcβ(5,6) Rα(5,6) Rβ(5,6) Rα(5,6) Rβ(5,6)
0,87071 4,57023 1,14849 0,21881 0,87071 4,57023
Tcα(3,4) Tcβ(3,4) Rα(3,4) Rβ(3,4) Rα(3,4) Rβ(3,4)
0,937 3,358332 1,06723 0,29777 0,937 3,35833
Tcα(1,2) Tcβ(1,2) Rα(1,2) Rβ(1,2) Rα(1,2) Rβ(1,2)
4,57937 2,605393 0,21837 0,38382 4,57937 2,60539](https://image.slidesharecdn.com/26816717-250512175734-af7d3724/85/Full-Computational-Systems-Biology-Second-Edition-2da-Roland-Eils-49-320.jpg)
![9 Perfect adaptation and integral control in metabolism 39
achieved by the modulation of (i) enzyme activity (through a substrate or product effect,
through a different metabolite competing with the substrate for its binding site or through an
allosteric effect), i.e. metabolic regulation, of (ii) enzyme covalent modification status as end-
effect of a signal transduction pathway, or of (iii) enzyme concentration via gene expression,
i.e. gene-expression regulation. Such multiple-level regulations correspond to different con-
trol loops in a control system. This may ensure the robustness versus perturbations at various
frequencies. In engineering, an airplane wing has to be robust at high frequencies of varia-
tions of air pressures, as well as with respect to low frequency perturbations. In order to
achieve this combined robustness, different control loops have to be put in place simultane-
ously, although a trade-off limits what one can do, in the sense that increased robustness at
one frequency comes at reduced robustness at a different frequency (Csete and Doyle 2002).
In systems biology, this can be illustrated through the end product feedback regulations
(Goelzer et al. 2008). If the flux demand on the end product module increases rapidly, the
concentration of the end product decreases rapidly. Often as a result of the allosteric effect of
the penultimate metabolite directly on the first enzyme, the activity of that first enzyme
increase quickly too. This metabolic control of enzyme activity is a fast actuator of the system.
However, if there is a further increase in the flux demand, the first enzyme may “lose” its
regulatory capacity since its activity may be approaching its maximum capacity (kcat). At this
stage, the system has a second “adaptation” which is slow (because the cell has to produce
enzyme) but leads to increase in the concentration of the first enzyme, which then decreases
the direct stimulation of the catalytic activity of the first enzyme. The regulation of the first
enzyme is then bi-functional in dynamic terms (Csete and Doyle 2002): The metabolic regula-
tion rapidly buffers against high frequency perturbations but possibly with small amplitude
or capability, while the gene-expression regulation is slow to adapt but may be able to reject
very large constant perturbations (Ter Kuile and Westerhoff 2001).
When interpreting metabolic and gene-expression regulation separately as specific control
system structures, we identify the former more as a “proportional control” action (El-Samad
et al. 2002; Yi et al. 2000) with limited range, and the latter more as an “integral control” action
with potentially a wider range and acting more slowly. Mechanisms of integral control can
lead to zero steady-state errors of the “controlled variable,” which is not possible with pro-
portional control mechanisms. In the latter case, the perturbation of the controlled variable
has to persist for the regulation as the homeostatic regulation is proportional to the perturba-
tion of the controlled variable (the error function). The mechanism that operates in the former
case is known as “perfect adaptation” in biology when the network becomes completely
robust to the environmental perturbations: here the regulation is proportional to the time
integral of the error function, which persists when the error function has returned to zero. The
proportional control can often provide fast control response but the corresponding adapta-
tion would be imperfect with nonzero steady state errors.
The control engineering interpretations may be mapped onto Metabolic Control Analysis
(MCA) and Hierarchical Control Analysis (HCA) (Westerhoff et al. 1990, 2009), respectively.
The relatively fast metabolic regulation (proportional control) is related to the direct “elastici-
ties” of MCA, while the slow gene-expression regulation (integral control) corresponds to the
indirect “elasticities” of HCA.
Let us consider the example illustrated in Figure 3.4, which is a two-step pathway with
intermediate ATP at an ADP concentration, [ATP] = C-[ADP] and with the gene expression of](https://image.slidesharecdn.com/26816717-250512175734-af7d3724/85/Full-Computational-Systems-Biology-Second-Edition-2da-Roland-Eils-50-320.jpg)
![40 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS
the first enzyme (E = Es) being increased in proportion to the concentration of ADP, which is
a gene-expression regulation. The moiety conservation sum C is the sum of the concentra-
tions of ATP and ADP and constant here because the reactions only convert the one into the
other. The two-step pathway (s and d) represent supply and demand parts of a metabolic
pathway (Hofmeyr 1995), and metabolic regulation is assumed to be part of these processes.
The dynamics of ADP and enzyme E can be described by simple kinetics:
where the degradation of E is assumed to be a mixture of zero and first order processes. The
closed-loop control system structure of the pathway can be represented in Figure 3.5.
From the control system diagram, it can be noted that the ADP concentration is the con-
trolled variable; enzyme concentration E is a control output (the manipulation variable) of the
(3.24)
d[ADP]
dt
= −ks·E·[ADP] + kd·(C − [ADP])
(3.25)
dE
dt
= ka·[ADP] − kb·E − k0
FIGURE 3.4 Illustration of ATP energy metabolism in a two-step pathway with gene-expression regulation.
FIGURE 3.5 Control system structure of ATP energy metabolism.](https://image.slidesharecdn.com/26816717-250512175734-af7d3724/85/Full-Computational-Systems-Biology-Second-Edition-2da-Roland-Eils-51-320.jpg)
![9 Perfect adaptation and integral control in metabolism 41
gene-expression regulation control loop. When the degradation of enzyme is only zero order
in terms of E (with kb = 0), the gene-expression regulation becomes an ideal integral control
loop, and the metabolic network can exhibit robust perfect adaptation to the external or para-
metric perturbations: Equation 3.25 set to zero then determines the steady level of ADP and
Equation 3.24 set to zero the level of the enzyme E. This only happens when the cell popula-
tion is in stationary phase, because in a dividing cell population, the enzyme level per cell
would decay in a quasi first-order process. The zero order degradation rate k0 can be treated
as a reference signal to the system. The metabolic regulation is included as a part of the ADP
kinetic process.
Such a control engineering insight is consistent with classical kinetic analysis and meta-
bolic control analysis. By considering a small perturbation of kd from its steady-state value (δkd
with δ denoting the small deviation), and reformulating the kinetics of dADP/dt and dE/dt, we
have
where the subscript ss denotes the steady state value. We recognize on the right-hand side
first a proportional response term, then an integral response term, and then the perturbation
term. The proportional response corresponds to the direct “elasticity” of the supply and
demand reactions with respect to ADP, which is a metabolic and instantaneous regulation.
The integral response is related to the protein synthesis and degradation and thus to the gene-
expression regulation. If kb = 0, the second term corresponds to an ideal integral action. By
further removing the time dependence of the change in ADP using the steady state condi-
tions, the classical metabolic control coefficients, i.e. the control of the enzyme level by the
demand reaction, and the flux control coefficient, can be obtained:
Both the control of enzyme level and the control of demand flux by the perturbation are
equal to 1 minus a hyperbolic function of kb. For an ideal integral control scenario with kb = 0
the enzyme concentration E perfectly tracks the activity of the pathway degrading ATP, and
CE
kd
= 1. More importantly, the pathway flux perfectly tracks the perturbation in the demand
flux and CJ
kd
= 1. The control of kd on ADP is zero (Using Equation 3.25 with zero change in
enzyme and zero kb). This is the case of robust perfect adaptation. For other cases when kb ≠
0, the adaptation of the pathway to the perturbation will not be perfect. Also the robustness
coefficient as defined by Quinton-Tulloch et al. (2013) can be expressed
(3.26)
dδADP
dt
= −(ks · Ess + kd) · δADP − ks · ADPss
·
∞
0
(ka · δADP − kb · δE) · dt + (C − ADP) · δkd
(3.27)
CE
kd
=
δ ln E
δ ln kd
= 1 −
1
1 + ks·([ADP]ss)2
kd·C
·ka
kb
CJ
kd
=
δ ln J
δ ln kd
= 1 −
[ADP]ss/C
1 + ks·([ADP]ss)2
kd·C
·ka
kb
(3.28)
ℜADP
kd
=
1
∂ ln[ADP]ss
∂ ln kd
=
kd · C + ks · ([ADP]ss)2
· ka
kb
(C − [ADP]ss) · kd](https://image.slidesharecdn.com/26816717-250512175734-af7d3724/85/Full-Computational-Systems-Biology-Second-Edition-2da-Roland-Eils-52-320.jpg)
![25th (THE KING’S
ROYAL RIFLE
CORPS)
defeated at Stormberg on December the 12th, where it was
mentioned for its gallant conduct in covering the retreat. The
Company was then attached to French’s Cavalry Division, and was at
the battle of Paardeburg, where Captain Dewar was killed, and was
also present at the surrender of Cronje on the 27th of February,
Majuba Day. It then rejoined the 1st M.I.; and took part in the battles
of Poplar Grove and Driefontein, and the entry into Bloemfontein
(10th of March). It was at the surprise of Broadwood’s Calvary
Brigade at Sannah’s Post (31st of March), where it behaved with
conspicuous gallantry, and it was at the relief of Wepener, and in the
fighting near Thabanchu.
The 1st M.I. were then allotted to Alderson’s Brigade with
Hutton’s[78]
Mounted Troops, and took part in Lord Roberts’ advance
upon Pretoria on the 2nd May.
The Company, therefore, was present in the actions of Brandfort,
Vet River, Sand River, Kroonstadt, the Vaal River (27th of May), the
battle of Doornkop, near Johannesburg (28th–29th of May), the
actions at Kalkhoevel Defile, Six Mile Spruit (4th of June), and the
entry into Pretoria (5th of June). It was similarly engaged at the
battle of Diamond Hill (11th of June); in the fighting south-east of
Pretoria and at the action of Rietvlei (July the 16th); in the advance
to and operations round Middelburg; in the battle of Belfast (24th of
August, 1900); and in the march east from Dalmanutha, including
the assault of the almost impregnable position of Kaapsche Hoop
during the night of the 12th–13th of September.
From this time till the end of the war this Company was
continually marching and fighting in the Orange River Colony and
Cape Colony, pursuing De Wet, back again in the Transvaal, in
countless forays and skirmishes, in the saddle night and day. When
peace was declared it was at Vereeniging, whence it marched to
Harrismith, and was absorbed into the Rifle Battalion of M.I. formed
at that place.
The 4th Battalion also sent out two complete companies from Cork
early in 1901, which were employed in the Transvaal, and
subsequently joined the 25th M.I. in October of that year (see
below).
On October the 18th, 1901, a complete
Battalion of Mounted Infantry[79]
was](https://image.slidesharecdn.com/26816717-250512175734-af7d3724/85/Full-Computational-Systems-Biology-Second-Edition-2da-Roland-Eils-57-320.jpg)
![MOUNTED
INFANTRY
BATTALION.
formed from the Regiment—an unique
distinction—and consisted of:—
No. 1 Company 1st Battalion.
No. 2 Company 4th Battalion.
No. 3 Company 3rd Battalion.
No. 4 Company 4th Battalion.
The Battalion was concentrated at Middelburg in the Transvaal,
and was placed under the command of Major C. L. E. Robertson-
Eustace[80]
until January, 1902, when he was succeeded by Major W.
S. Kays.[81]
The Battalion thus organised was composed of officers and
riflemen who had been in the field from the beginning of the war,
and were therefore tried and experienced soldiers. It joined
Benson’s[82]
column at Middelburg, a column of which it was said
that no Dutchman dared sleep within thirty miles of its bivouac. The
ceaseless activity and success of Benson eventually decided Louis
Botha, the Boer Commander-in-Chief, to make a determined attempt
to destroy his force. To achieve this purpose he collected nearly 2000
men, and by a skilful combination of his troops attacked the column
while on the march near Bakenlaagte upon the 30th of October. By a
rapid charge he overwhelmed the rear guard, captured two guns,
killed Benson, and surrounded the column, but was eventually
beaten off. The 25th M.I. fought with a stubborn courage, and by
their sturdy gallantry kept the Boers at bay and gloriously upheld the
traditions of the Regiment, losing in the action eleven men killed,
five officers and forty-five men wounded.
Thus—stoutly fought out on both sides by mounted troops of this
especial type—ended a fight which has been described as unique in
the annals of war.[83]
The spirit of the Riflemen will best be
understood from the lips of one of the wounded in this gallant fight,
who remarked that “they were content if they had done their duty,
and felt rewarded if their Regiment thought well of them.”
The Mounted Infantry Battalion of the Regiment ended its short
but brilliant career by taking part in all the great “drives” in the E.
Transvaal and N.E. of the Orange Free State, and was finally at
Greylingstad when peace was declared on the 1st June, 1902.](https://image.slidesharecdn.com/26816717-250512175734-af7d3724/85/Full-Computational-Systems-Biology-Second-Edition-2da-Roland-Eils-58-320.jpg)
![RIFLE DEPOT.
Rifle Depot.
The Depot, under the command of
Colonel Horatio Mends, was at Gosport
throughout the war. A narrative of the work of the Regiment at this
strenuous period would not be complete without grateful reference
to the splendid service of administration, training, and equipment,
so devotedly performed by the Colonel Commandant, his Staff, and
the Company officers generally of the Rifle Depot.
The Adjutant was five times changed, but the Quarter-Master,
Major Riley,[84]
remained constant to his difficult duties throughout
the whole of this trying ordeal.
It is stated that 4470 recruits joined the Depot, were trained, and
passed to the various Battalions, while many thousands of Reservists
were mobilized, equipped, clothed, and drafted for duty.
The work of discharge at the end of the war was not less severe,
but there is no record of failure or of breakdown, and the success of
the admirable system of administration was universally
acknowledged.[85]
The Rifle Depot was moved back to Winchester on the 29th of
March, 1903, after nine years of exile at Gosport caused by the re-
building of the Barracks which had been destroyed by fire.](https://image.slidesharecdn.com/26816717-250512175734-af7d3724/85/Full-Computational-Systems-Biology-Second-Edition-2da-Roland-Eils-59-320.jpg)
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- 7. COMPUTATIONAL SYSTEMS BIOLOGY SECOND EDITION Edited by Roland Eils Andres Kriete AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Academic Press is an imprint of Elsevier
- 8. Academic Press is an imprint of Elsevier 525 B Street, Suite 1800, San Diego, CA 92101-4495, USA 225 Wyman Street, Waltham, MA 02451, USA The Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, UK 32 Jamestown Road, London, NW1 7BY, UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands Copyright © 2014, 2006 Elsevier, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher. Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: permissions@elsevier.com. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier. com/locate/permissions, and selecting Obtaining permission to use Elsevier material. Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made. Library of Congress Cataloging-in-Publication Data Computational systems biology (Kriete) Computational systems biology / edited by Andres Kriete, Roland Eils. -- Second edition. p. ; cm. Includes bibliographical references and indexes. ISBN 978-0-12-405926-9 (alk. paper) I. Kriete, Andres, editor of compilation. II. Eils, Roland, editor of compilation. III. Title. [DNLM: 1. Computational Biology. 2. Systems Biology. QU 26.5] QH324.2 570.1’13--dc23 2013045039 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN: 978-0-12-405926-9 For information on all Academic Press publications visit our website at store.elsevier.com Printed in the United States of America 14 15 10 9 8 7 6 5 4 3 2 1
- 9. ix Frédéric Crémazy Department of Synthetic Systems Biology and Nuclear Organization, Swammerdam Institute for Life Sciences, University of Amsterdam, Amsterdam, The Netherlands Matteo Barberis Department of Synthetic Systems Biology and Nuclear Organization, Swam merdam Institute for Life Sciences, University of Amsterdam, Amsterdam, The Netherlands Chapter 4 Ursula Klingmüller, Marcel Schilling, Sonja Depner, Lorenza A. D’Alessandro Division Systems Biology of Signal Transduction, German Cancer Research Center (DKFZ), Heidelberg, Germany Chapter 5 Christina Kiel EMBL/CRG Systems Biology Research Unit, Centre for Genomic Regulation (CRG), Barcelona, Spain Universitat Pompeu Fabra (UPF), Barcelona, Spain Luis Serrano EMBL/CRG Systems Biology Re search Unit, Centre for Genomic Regulation (CRG), Barcelona, Spain Universitat Pompeu Fabra (UPF), Barcelona, Spain ICREA, Barcelona, Spain Chapter 6 Seiya Imoto Human Genome Center, Institute of Medical Science, The University of Tokyo, Minatoku, Tokyo, Japan Hiroshi Matsuno Faculty of Science, Yamaguchi University, Yoshida, Yamaguchi, Japan Satoru Miyano Human Genome Center, Insti tute of Medical Science, The University of Tokyo, Minatoku, Tokyo, Japan Chapter 1 Roland Eils Division of Theoretical Bio informatics(B080),GermanCancerResearch Center (DKFZ), Heidelberg, Germany Department for Bioinformatics and Func tional Genomics, Institute for Pharmacy and Molecular Biotechnology (IPMB) and BioQuant, Heidelberg University, Heidelberg, Germany Andres Kriete School of Biomedical Engineering, Science and Health Systems, Drexel University, Philadelphia, PA, USA Chapter 2 Robert B. Russell, Gordana Apic, Olga Kalinina, Leonardo Trabuco, Matthew J. Betts, Qianhao Lu CellNetworks, University of Heidelberg, Heidelberg, Germany Chapter 3 Hans V. Westerhoff Department of Synthetic Systems Biology and Nuclear Organization, Swammerdam Institute for Life Sciences, University of Amsterdam, Amsterdam, The Netherlands Department of Molecular Cell Physiology, Faculty of Earth and Life Sciences, VU University Amsterdam, The Netherlands Manchester Centre for Integrative Systems Bio logy (MCISB), Manchester, UK Fei He Manchester Centre for Integrative Systems Biology (MCISB), Manchester, UK Department of Automatic Control and systems Engineering, The University of Sheffield, Sheffield, UK EttoreMurabito ManchesterCentreforIntegrative Systems Biology (MCISB), Manchester, UK Contributors
- 10. x CONTRIBUTORS Chapter 11 Reinhard Laubenbacher Virginia Bioinformatics Institute, Virginia Tech, Blacksburg VA, USA Pedro Mendes Virginia Bioinformatics Institute, Virginia Tech, Blacksburg VA, USA School of Computer Science, The University of Manchester, Manchester, UK Chapter 12 Joseph Xu Zhou, Xiaojie Qiu, Aymeric Fouquier d’Herouel, Sui Huang Institute for Systems Biology, Seattle, WA, USA Chapter 13 John Cole, Mike J. Hallock, Piyush Labhsetwar, Joseph R. Peterson, John E. Stone, Zaida Luthey-Schulten University of Illinois at Urbana-Champaign, USA Chapter 14 Jean-Luc Bouchot Department of Mathematics, Drexel University, PA, Philadelphia, USA William L. Trimble Institute for Genomics and SystemsBiology,ArgonneNationalLaboratory, University of Chicago, Chicago, IL, USA Gregory Ditzler Department of Electrical and Computer Engineering, Drexel University, PA, Philadelphia, USA Yemin Lan School of Biomedical Engineering, Science and Health, Drexel University, PA, Philadelphia, USA Steve Essinger Department of Electrical and Com puter Engineering, Drexel University, PA, Philadelphia, USA Gail Rosen Department of Electrical and Com puter Engineering, Drexel University, PA, Philadelphia, USA Chapter 15 Helder I Nakaya Department of Pathology, Emory University, Atlanta, GA, USA Vaccine Research Center, Emory University, Atlanta, GA, USA Chapter 7 Hong-Wu Ma Tianjin Institute of Industrial Bio technology, Chinese Academy of Sciences, Tianjin, P.R. China School of Informatics, University of Edinburgh, Edinburgh, UK An-Ping Zeng Institute of Bioprocess and Bio systems Engineering, Hamburg University of Technology, Denickestrasse, Germany Chapter 8 Stanley Gu Department of Bioengineering, Uni versity of Washington, Seattle, WA, USA Herbert Sauro Department of Bioengineering, University of Washington, Seattle, WA, USA Chapter 9 Juergen Eils Division of Theoretical Bioinformat ics, German Cancer Research Center (DKFZ), Heidelberg, Germany Elena Herzog Division of Theoretical Bioinformat ics, German Cancer Research Center (DKFZ), Heidelberg, Germany Baerbel Felder Division of Theoretical Bioinforma tics, German Cancer Research Center (DKFZ), Heidelberg, Germany Department for Bioin formatics and Functional Genomics, Institute for Pharmacy and MolecularBiotechnology(IPMB)andBioQuant, Heidelberg University, Heidelberg, Germany Christian Lawerenz Division of Theoretical Bio informatics, German Cancer Research Center (DKFZ), Heidelberg, Germany Roland Eils Division of Theoretical Bioinformat ics, German Cancer Research Center (DKFZ), Heidelberg, Germany Department for Bioinformatics and Functional Genomics, Institute for Pharmacy and Molec ular Biotechnology (IPMB) and BioQuant, Heidelberg University, Heidelberg, Germany Chapter 10 Jean-Christophe Leloup, Didier Gonze, Albert Goldbeter UnitédeChronobiologiethéorique, Faculté des Sciences, Université Libre de Bru xelles, Campus Plaine, Brussels, Belgium x
- 11. xi CONTRIBUTORS Chapter 18 Hang Chang, Gerald V. Fontenay, Cemal Bilgin, Bahram Parvin Life Sciences Division, Law rence Berkeley National Laboratory, Berkeley, CA, USA Alexander Borowsky Center for Comparative Medicine, University of California, Davis, CA, USA. Paul Spellman Department of Biomedical Engi neering, Oregon Health Sciences Univer sity, Portland, Oregon, USA Chapter 19 Stefan M. Kallenberger Department for Bio informatics and Functional Genomics, Divi sion of Theoretical Bioinformatics, German Cancer Research Center (DKFZ), Institute for Pharmacy and Molecular Biotechnology (IPMB) and BioQuant, Heidelberg University, Heidelberg, Germany Stefan Legewie Institute of Molecular Biology, Mainz, Germany Roland Eils Department for Bioinformatics and Functional Genomics, Division of Theoretical Bioinformatics, German Cancer Research Center (DKFZ), Institute for Pharmacy and Molecular Biotechnology (IPMB) and Bio Quant, Heidelberg University, Heidelberg, Germany Department of Clinical Analyses and Toxicology, University of Sao Paulo, Sao Paulo, SP, Brazil Chapter 16 Julien Delile Institut des Systèmes Complexes Paris Ile-de-France (ISC-PIF), CNRS, Paris, France Neurobiology and Development Lab, Terrasse, Gif-sur-Yvette Cedex, France René Doursat Institut des Systèmes Com plexes Paris Ile-de-France (ISC-PIF), CNRS, Paris, France School of Biomedical Engineering, Drexel Uni versity, Philadelphia, PA, USA Nadine Peyriéras Neurobiology and Develop ment Lab, Terrasse, Gif-sur-Yvette Cedex, France Chapter 17 Andres Kriete School of Biomedical Engineering, Science and Health Systems, Drexel Univer sity, Bossone Research Center, Philadelphia, PA, USA Mathieu Cloutier GERAD and Department of Chemical Engineering, Ecole Polytechnique de Montreal, Montreal, QC, Canada xi
- 12. xiii in this area. If compared to the first edition published in 2005, the second edition has been specifically extended to reflect new frontiers of systems biology, including modeling of whole cells, studies of embryonic development, the immune systems, as well as aging and cancer. As in the previous edition, basics of informa- tion and data integration technologies, standards, modeling of gene, signaling and metabolic networks remain comprehensively covered. Contributions have been selected and compiled to introduce the different meth- ods, including methods dissecting biological complexity, modeling of dynamical proper- ties, and biocomputational perspectives. Beside the primary authors and their respective teams who have dedicated their time to contribute to this book, the editors would like to thank numerous reviewers of individual chapters, but in particular Jan Eufinger for support of the editorial work. It is often mentioned that biological sys- tems in its entirety present more than a sum of its parts. To this extent, we hope that the chapters selected for this book not only give a contemporary and comprehensive over- look about the recent developments, but that this volume advances the field and encour- ages new strategies, interdisciplinary coop- eration, and research activities. Roland Eils and Andres Kriete Heidelberg and Philadelphia, September 2013 Computational systems biology, a term coined by Kitano in 2002, is a field that aims at a system-level understanding by modeling and analyzing biological data using computation. It is increasingly recognized that living system cannot be understood by studying individual parts, while the list of molecular components in biology is ever growing, accelerated by genome sequencing and high-throughput omics techniques. Under the guiding vision of systems biology, sophisticated computational methods help to study the interconnection of parts in order to unravel complex and net- worked biological phenomena, from protein interactions, pathways, networks, to whole cells and multicellular complexes. Rather than performing experimental observations alone, systems biology generates knowledge and understanding by entering a cycle of model construction, quantitative simulations, and experimental validation of model predic- tions, whereby a formal reasoning becomes key. This requires a collaborative input of experimental and theoretical biologists work- ing together with system analysts, computer scientists, mathematicians, bioengineers, physicists, as well as physicians to contend creatively with the hierarchical and nonlinear nature of cellular systems. This book has a distinct focus on computa- tional and engineering methods related to sys- tems biology. As such, it presents a timely, multi-authored compendium representing state-of-the-art computational technologies, standards, concepts, and methods developed Preface
- 13. 1 © 2014 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/B978-0-12-405926-9.00001-0 Computational Systems Biology, Second Edition 1 Introducing Computational Systems Biology Roland Eilsa,b , Andres Krietec a Division of Theoretical Bioinformatics (B080), German Cancer Research Center (DKFZ), Heidelberg, Germany b Department for Bioinformatics and Functional Genomics, Institute for Pharmacy and Molecular Biotechnology (IPMB) and BioQuant, Heidelberg University, Heidelberg, Germany c School of Biomedical Engineering, Science and Health Systems, Drexel University, Philadelphia, PA, USA C H A P T E R C O N T E N T S 1 Prologue 1 2 Overview of the content 4 3 Outlook 6 References 7 We need to turn data into knowledge and we need a framework to do so. S. Brenner, 2002. 1 PROLOGUE The multitude of the computational tools needed for systems biology research can roughly be classified into two categories: system identification and behavior analysis (Kitano 2001). In molecular biology, system identification amounts to identifying the regulatory relation- ships between genes, proteins, and small molecules, as well as their inherent dynamics hid- den in the specific kinetic and binding parameters. System identification is arguably one of the most complicated problems in science. While behavior analysis is solely performed on a model, model construction is a process tightly connected to reality but part of an iterative process between data analysis, simulation, and experimental validation (Figure 1.1). A typical
- 14. 2 1. Introducing Computational Systems Biology modeling cycle begins with a reductionist approach, creating the simplest possible model. The modeling process generates an understanding of the underlying structures, and components are represented graphically with increasing level of formalization, until they can be converted into a mathematical representation. The minimal model then grows in complexity, driven by new hypotheses that may not have been apparent from the phenomenological descriptions. Then, an experiment is designed using the biological system to test whether the model predic- tions agree with the experimental observations of the system behavior. The constitutive model parameters may be measured directly or may be inferred during this validation process, how- ever, the propagation of errors through these parameters present significant challenges for the modeler. If data and predictions agree, a new experiment is designed and performed. This pro- cess continues until sufficient experimental evidence in favor of the model is collected. Once the system has been identified and a model constructed, the system behavior can be studied, for instance, by numerical integration or sensitivity analysis against external perturbations. Although the iterative process is well defined, the amount of data to be merged into this process can be immense. The human genome project is one of the hallmarks indicating a turn from a reductionistic approach in studying biological systems at increasing level, into a dis- covery process using high-throughput techniques (Figure 1.2). Ongoing research increases the wealth of contemporary biological information residing in some thousand public databases providing descriptive genomics, proteomics and enzyme information, gene expression, gene variants and gene ontologies. Refined explorative tools, such as new deep sequencing, along with the emergence of new specialized -omics (metabolomics, lipidomics, pharmacogenom- ics) and phenotyping techniques, constantly feed into this data pool and accelerate its growth. Given the enormous and heterogeneous amount of data, computational tools have become indispensable to mine, analyze, and connect such information. The aggregate of statistical FIGURE 1.1 Key to systems biology is an iterative cycle of experimentation, model building, simulation and validation.
- 15. 1 Prologue 3 bioinformatics tools to collect, store, retrieve, visualize, and analyze complex biological data has repeatedly proven useful in biological decision support and discovery. Deciphering the basic building blocks of life is a necessary step in biological research, but provides only lim- ited knowledge in terms of understanding and predictability. In the early stages the human genome project stirred the public expectation for a rapid increase in the deciphering of dis- ease mechanisms, more effective drug development and cure. However, it is well recognized that the battery of mechanisms involved in the proliferation of complex diseases like cancer, chronic diseases, or the development of dementias cannot be understood solely on the basis of knowing all its molecular components. As a consequence, a lack of system level understanding of cellular dynamics has prevented a substantial increase in the number of new drugs available for treatment, drug efficacy, or eradication of any specific diseases. In contrast, pharmaceutical companies are currently lack- ing criteria to select the most valuable targets, R&D expenses skyrocket, and new drugs rarely hit the market and often fail in clinical trials, while physicians face an increasing wealth of information that needs to be interpreted intelligently and holistically. Analysis of this dilemma reveals primary difficulties due to the enormous biomolecular complexity, structural and functional unknowns in a large portion of gene products and a lack of understanding of how the concert of molecular activities transfers into physiological alterations and disease. It has been long recognized that the understanding of cells as open systems, interacting with the environment, performing tasks and sustain homeostasis, or bet- ter homeodynamics (Yates 1992), requires the development of foundations for a general sys- tems theory that started with the seminal work of Bertalanffy (Von Bertalanffy 1969). FIGURE 1.2 By the evolution of scientific disciplines in biology over time, ever-smaller structures have come into focus and more detailed questions have been asked. With the availability of high-throughput sequencing techniques in genetics a turning point was reached at the molecular basis of life. The frontiers of research extended to hypothesis- free data acquisition of biological entities, with genomics becoming the first in a growing series of “-omics” disci- plines. Although functional genomics and proteomics are far from being completed, “omics” -type approaches addressing the phenotypical cellular, tissue and physiological levels constitute themselves as new scientific disci- plines, filling up an otherwise sparse data space. Computational systems biology provides methodologies to com- bine, model, and simulate entities on diverse (horizontal) levels of biological organization, such as gene regulatory and protein networks, and between these levels by using multiscale (vertical) approaches.
- 16. 4 1. Introducing Computational Systems Biology It appears that with the ever increasing quality and quantity of molecular data, mathematical models of biological processes are even more in demand. For instance, an envisioned blue- print of complex diseases will not solely consist of descriptive flowcharts as widely found in scientific literature or in genomic databases. They should rather be based on predictive, rigor- ously quantitative data-based mathematical models of metabolic pathways, signal transduc- tion cascades, cell-cell communication, etc. The general focus of biomedical research on complex diseases needs to change from a primarily steady-state analysis at the molecular level to a systems biology level capturing the characteristic dynamic behavior. Such biosimu- lation concepts will continue to transform current diagnostic and therapeutic approaches to medicine. 2 OVERVIEW OF THE CONTENT This completely revised, second edition of this book presents examples selected from an increasingly diverse field of activities, covering basic key methods, development of tools, and recent applications in many complex areas of computational systems biology. In the follow- ing, we will broadly review the content of the chapters as they appear in this book, along with specific introductions and outlooks. The first section of this book introduces essential foundations of systems biology, princi- ples of network reconstruction based on high-throughput data with the help of engineering principles such as control theory. Robert B. Russell, Gordana Apic, Olga Kalinina, Leonardo Trabuco, Matthew J. Betts, and Qianhao Lu provide an introduction (Chapter 2) on “Structural Systems Biology: modeling interactions and networks for systems studies.” Molecular mechanisms provide the most detailed level for a mechanistic understanding of biological complexity. The current challenges of a structural systems biology are to integrate, utilize, and extend such knowledge in conjunction with high-throughput studies. Understanding the mechanistic consequences of multiple alterations in DNA variants, protein structures, and folding are key tasks of structural bioinformatics. Principles of protein interactions in pathways and networks are introduced by Hans V. Westerhoff, Fei He, Ettore Murabito, Frédéric Crémazy, and Matteo Barberis in Chapter 3. Their contribution is entitled “Understanding principles of the dynamic biochemical networks of life through systems biology” and discusses a number of basic, more recent and upcoming discover- ies of network principles. The contributors review analytical procedures from flux balance in metabolic networks to measures of robustness. In Chapter 4, Ursula Klingmüller, Marcel Schilling, Sonja Depner, and Lorenza A. D‘Alessandro review the “Biological foundations of signal transduction and aberrations in disease.” Signaling pathways process the external signals through complex cellular networks that reg- ulate biological functions in a context-dependent manner. The authors identify the underly- ing biological mechanisms influential for signal transduction and introduce the mathematical tools essential to model signaling pathways and their disease aberrations in a quantitative fashion. Further acceleration of progress in pathway reconstruction and analysis is contingent on the solution of many complexities and new requirements, revolving around the question of how high-throughput experimental techniques can help to accelerate reconstruction and
- 17. 2 Overview of the content 5 simulation of signaling pathways. This is the theme of the review in Chapter 5 by Christina Kiel and Luis Serrano on the “Complexities underlying a quantitative systems analysis of signaling networks.” Chapter 6 by Seiya Imoto, Hiroshi Matsuno, Satoru Miyano presents “Gene net- works: estimation, modeling and simulation.” The authors describe how gene networks can be reconstructed from microarray gene expression data, which is a contemporary problem. They also introduce software tools for modeling and simulating gene networks, which is based on the concept of Petri nets. The authors demonstrate the utility for the modeling and simulation of the gene network for controlling circadian rhythms. Section 2 provides an overview of methods, mathematical tools, and examples for model- ing approaches of dynamic systems. “Standards, platforms, and applications,” as presented by Herbert Sauro and Stanley Gu in Chapter 8, reviews the trends in developing standards indic- ative of increasing cooperation within the systems biology community, which emerged in recent years permitting collaborative projects and exchange of models between different soft- ware tools. “Databases for systems biology,” as reviewed in Chapter 9 by Juergen Eils, Elena Herzog, Baerbel Felder, Christian Lawerenz and Roland Eils provide approaches to integrate information about the responses of biological system to genetic or environmental perturba- tions. As researchers try to solve biological problems at the level of entire systems, the very nature of this approach requires the integration of highly divergent data types, and a tight coupling of three general areas of data generated in systems biology: experimental data, ele- ments of biological systems, and mathematical models with the derived simulations. Chapter 10 builds on a classical mathematical modeling approach to study patterns of dynamic behav- iors in biological systems. “Computational models for circadian rhythms - deterministic versus sto- chastic approaches,” Jean-Christophe Leloup, Didier Gonze and Albert Goldbeter demonstrates how feedback loops give rise to oscillatory behavior and how several results can be obtained in models which possess a minimum degree of complexity. Circadian rhythms provide a par- ticular interesting case-study for showing how computational models can be used to address a wide range of issues extending from molecular mechanism to physiological disorders. Reinhard Laubenbacher and Pedro Mendes review “Top-down dynamical modeling of molecu- lar regulatory networks,” Chapter 11. The modeling framework discussed in this chapter con- siders mathematical methods addressing time-discrete dynamical systems over a finite state set applied to decipher gene regulatory networks from experimental data sets. The assump- tions of final systems states are not only a useful modeling concept, but also serve an explana- tion of fundamental organization of cellular complexities. Chapter 12, entitled “Multistability and multicellularity: cell fates as high-dimensional attractors of gene regulatory networks,” by Joseph X. Zhou and Sui Huang, investigates how the high number of combinatorially possible expression configurations collapses into a few configurations characteristic of observable cell fates. These fates are proposed to be high-dimensional attractors in gene activity state space, and may help to achieve one of the most desirable goal of computational systems biology, which is the development of whole cell models. In Chapter 13 John Cole, Mike J. Hallock, Piyush Labhsetwar, Joseph R. Peterson, John E. Stone, and Zaida Luthey-Schulten review “Whole cell modeling strategies for single cells and microbial colonies,” taking into account spatial and time-related heterogeneities such as short-term and long-term stochastic fluctuations. Section 3 of this book is dedicated to emerging systems biology application including mod- eling of complex systems and phenotypes in development, aging, health, and disease. In Chapter 14, Jean-Luc Bouchot, William Trimble, Gregory Ditzler, Yemin Lan, Steve Essinger,
- 18. 6 1. Introducing Computational Systems Biology and Gail Rosen introduce “Advances in machine learning for processing and comparison of metage- nomic data.” The study of nucleic acid samples from different parts of the environment, reflect- ing the microbiome, has strongly developed in the last years and has become one of the sustained biocomputational endeavors. Identification, classification, and visualization via sophisticated computational methods are indispensable in this area. Similarly, the decipher- ing immune system has to deal with a large amount of data generated from high-throughput techniques reflecting the inherent complexity of the immune system. Helder I. Nakaya, in Chapter 15, reports on “Applying systems biology to understand the immune response to infection and vaccination.” This chapter highlights recent advances and shows how systems biology can be applied to unravel novel key molecular mechanisms of immunity. Rene Doursat, Julien Delile, and Nadine Peyrieras present “Cell behavior to tissue deforma- tion: computational modeling and simulation of early animal embryogenesis,” Chapter 16. They pro- pose a theoretical, yet realistic agent-based model and simulation platform of animal embryogenesis, to study the dynamics on multiple levels of biological organization. This con- tribution is an example demonstrating the value of systems biology in integrating the differ- ent phenomena involved to study complex biological process. In Chapter 17, Andres Kriete and Mathieu Cloutier present “Developing a systems biology of aging.” The contribution reviews modeling of proximal mechanisms of aging occurring in pathways, networks, and multicel- lular systems, as demonstrated for Parkinson’s disease. In addition, the authors reflect on evolutionary aspect of aging as a robustness tradeoff in complex biological designs. In Chapter 18, Hang Chang, Gerald V Fontenay, Ju Han, Nandita Nayak, Alexander Borowsky, Paul Spellman, and Bahram Parvin present image-based phenotyping strategies to classify cancer phenotypes on the tissue level, entitled “Morphometric analysis of tissue het- erogeneity in Glioblastoma Multiforme.” Such work allows to associate morphological heteroge- neities of cancer subtypes with molecular information to improve prognosis. In terms of a multiscale modeling approach the assessment of phenotypical changes, in cancer as well as in other diseases, will help to build bridges toward new spatiotemporal modeling approaches. Stefan M. Kallenberger, Stefan Legewie, and Roland Eils demonstrate “Applications in cancer research: mathematical models of apoptosis” in Chapter 19. Their contribution is focused on the mathematical modeling of cell fate decisions and its dysregulation of cell death, contributing to one of the ramifications of the complexities in cancer biology. 3 OUTLOOK It is commonly recognized that biological multiplicity is due to progressive evolution that brought along an increasing complexity of cells and organisms over time (Adami et al. 2000). This judgement coincides with the notion that greater complexity is “better” in terms of com- plex adaptive systems and ability for self-organization, hence robustness (Csete and Doyle 2002 Kitano 2004). Analyzing or “reverse” engineering of this complexity and integrating results of today’s scientific technologies responsible for the ubiquitous data overload are an essential part of systems biology. The goals are to conceptualize, abstract basic principles, and model biological structures from molecular to higher level of organization like cells, tissues, and organs, in order to provide insight and knowledge. The initial transition requires data
- 19. REFERENCES 7 cleansing and data coherency, but turning information into knowledge requires interpret- ing what the data actually means. Systems biology addresses this need by the development and analysis of high-resolution quantitative models that recapitulate, but more importantly predict cellular behavior in time and space and to determine physiology from the underlying molecular and cellular capacities on a multiscale (Dada and Mendes 2011). Once established, such models are indicators to the detailed understanding of biological function, the diagnosis of diseases, the identification and validation of therapeutic targets, and the design of drugs and drug therapies. Experimental techniques yielding quantitative genomic, proteomic, and metabolomic data needed for the development of such models are becoming increasingly common. Computer representations describing the underlying mechanisms may not always be able to provide complete accuracy due to limited computational, experimental, and methodical resources. Increase in data quality and coherence, availability within integrated databases or approaches that can manage experimental variability, are less considered but may be as essen- tial for robust growth of biological knowledge. Still, the enormous complexity of biological systems has given rise to additional cautionary remarks. First, it may well be that our models and future super-models correctly predict experimental observations, but may still prevent a deeper understanding due to complexities, non-linearities, or stochastic phenomena. This notion may initially sound quite disappointing, but is a daily experience of all those who employ modeling and simulations of large-scale phenomena. Yet, it shows the relevance of computational approaches in this area, and suggestions to link biological with computational problem solving has been suggested (Navlakha and Bar-Joseph 2011). Systems biology should follow strict standards and conventions, and progress in theory and computational approaches will always demand new models that can provide new insights if applied to an existing body of information. Many areas, including cancer model- ing, have demonstrated how models evolve over many cycles of investigation and refinement (Byrne 2010). Once established, new models can be reimplemented into existing platforms to be more broadly available. In the long run, the aim is to develop user-friendly, scalable and open-ended platforms that also handle methods for behavior analysis and model-based dis- ease diagnosis, and support scientists in their every-day practice of decision-making and bio- logical inquiry, as well as physicians in clinical decision support. Systems biology has risen out of consensus in the scientific community, initially driven by visionary scientific entrepreneurs. Now, as its strength becomes obvious, it is recognized as a rapidly evolving mainstream endeavor, which requires specific educational curricula and col- laboration among computational scientists, experimental and theoretical biologists, control and systems engineers, as well as practitioners in drug development and clinical research. These collaborative ties will move this field forwards toward a formal, quantitative, and pre- dictive framework of biology. References Adami, C., Ofria, C., and Collier, T. C. (2000). Evolution of biological complexity. Proc Natl Acad Sci USA 97:4463–4468. Byrne, H. M. (2010). Dissecting cancer through mathematics: From the cell to the animal model. Nat Rev Cancer 10:221–230.
- 20. 8 1. Introducing Computational Systems Biology Csete, M. E., and Doyle, J. C. (2002). Reverse engineering of biological complexity. Science 295:1664–1669. Dada, J. O., and Mendes, P. (2011). Multi-scale modelling and simulation in systems biology. Integr Biol (Camb) 3:86–96. Kitano, H. (2001). Foundations of Systems Biology. MIT-Press. Kitano, H. (2004). Biological Robustness. Nat Rev Genet 5:826–837. Navlakha, S., and Bar-Joseph, Z. (2011). Algorithms in nature: The convergence of systems biology and computa- tional thinking. Mol Syst Biol 7:546. Von Bertalanffy, L. (1969). General Systems Theory. George Brazillar Inc. Yates, F. E. (1992). Order and complexity in dynamical systems: Homeodynamics as a generalized mechanics for biol- ogy. Math and Comput Model 19:49–74.
- 21. 9 © 2014 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/B978-0-12-405926-9.00002-2 Computational Systems Biology, Second Edition 2 Structural Systems Biology: Modeling Interactions and Networks for Systems Studies Robert B. Russell, Gordana Apic, Olga Kalinina, Leonardo Trabuco, Matthew J. Betts, Qianhao Lu CellNetworks, University of Heidelberg, Heidelberg, Germany C H A P T E R C o n t e n t s 1 Introduction 10 2 A brief history of structural bioinformatics 10 3 Structural analysis of interaction data 11 4 Other interaction types 13 5 Systems biology applications 13 6 New datasets-specific protein sites 14 7 Current and future needs 14 8 Concluding remarks 16 References 16 Abstract The best understanding of complex biological systems ultimately comes from details of the underlying atomic structures within it. In the absence of known structures of all protein complexes and interactions in a system, structural bioinformatics or modeling fill an important niche in providing predicted mechanistic information which can guide experiments, aid the interpretation of high-throughput datasets and help provide key details to model biological systems. This introductory review discusses the current state of this field and suggests how current datasets in systems studies can profit from a better integration of predicted or known structural information.
- 22. 10 2. STRUCTURAL SYSTEMS BIOLOGY: MODELING INTERACTIONS AND NETWORKS 1 INTRODUCTION We are clearly today in the era of high-throughput biology. In every area of biology— from plant sciences to human health—one increasingly sees systematic screens that identify hundreds or thousands of molecules regulated or changed in response to some stimulus or perturbation. More than ever there is a need to understand what such large sets of molecules mean when identified together in terms of system functions, and to use these data to suggest therapies, vaccines, diagnostics, herbicides, etc. Invariably scientists wish to use the results from high-throughput experiments to unlock the underlying biological mechanism. The molecular mechanism—in the broadest sense— ultimately provides the details that give a deeper understanding of a biological process, or suggest means to perturb a system with small molecules or other agents. To address this, many efforts have been undertaken to capture systematically all of the mechanistic detail that has been captured by low-throughput experiments in the past decades. Pathway resources such as KEGG (Kotera et al. 2012) or Reactome (Croft et al. 2011) and ontological tools such as GO (Gene Ontology Consortium 2006) provide a means to state for a large set of genes, pro- teins, or metabolites which processes are likely being affected. These tools remain central to most high-throughput studies. However, the ultimate understanding of a biological process comes only from a view of the actual molecular details underlying it. Specifically, the availability of multiple three-dimen- sional (3D) structures provides information down to the specific atoms involved in a process. Today, thanks to more than a decade of Structural Genomics driven advances in structure determination by X-ray, NMR, and electron microscopy, there are structural representatives for almost every globular domain, and the number of multi-protein complexes of known structures is also growing at an impressive rate. Concurrent advances in techniques to model protein structures by homology also means that increasingly accurate modeled structures are readily available for at least globular parts of most proteins of interest. There are also many tools for interrogating proteins structurally and increasingly these are addressing the needs of the high-throughput biologist. This chapter discusses recent advances in this broad area of Structural Systems Biology and Bioinformatics, and suggests future directions to meet new challenges of high-throughput biology. 2 A BRIEF HISTORY OF STRUCTURAL BIOINFORMATICS Structural Bioinformatics began with the first attempts to study and predict protein struc- tures (Blundell et al. 1987). While structure and sequences databases were small, the pri- mary focus was the grand challenge to predict protein 3D structures from primary sequences. Methods to predict protein secondary structure or 3D structure were approached by a variety of informatics-or physics-based methods, and had mixed success until the arrival of system- atic community wide assessment exercises (Critical Assessment of Structure Prediction, CASP (Moult et al. 2011)) where double-blind assessments of predictions (i.e. where the structures were unknown to both predictors and experimentalists during the predictions). These experi- ments identified the strengths and weaknesses of all approaches and ultimately have led to mature methods to predict secondary structure and tertiary structure either de novo or via homology modeling techniques. Today models for virtually all proteins that are modelable
- 23. 3 Structural analysis of interaction data 11 are now systematically available via online databases such as ModBase (Pieper et al. 2011) and Swissmodel (Kiefer et al. 2009). Structural bioinformatics now often focuses on methods that predict function of individual proteins of known structure, rather than methods that pre- dict structure per se. For instance, numerous methods have been developed to study protein surfaces to predict functional sites using a variety of geometrical or evolutionary criteria (e.g. Aloy et al. 2001; Capra et al. 2009; Casari et al. 1995; Landgraf et al. 2001; Wilkins et al. 2012; Yang et al. 2012). The initial genome sequencing projects produced the first large sets of genes and encoded proteins for which little information was available. Structural bioinformatics played a crucial role in identifying overall features of the genome in terms of domain distributions and com- binations (e.g. Apic et al. 2001; Gerstein and Levitt 1997), a process that was greatly aided by the availability of structure classification databases (Andreeva et al. 2008; Cuff et al. 2009; Holm and Rosenström 2010). These analyses ultimately matured and were incorporated into the protein databases used today, such as Pfam (Punta et al. 2012) and CDD (Marchler-Bauer et al. 2013) and are readily visible in primary databases such as Uniprot (Wu et al. 2006) or Refseq (Pruitt et al. 2005). 3 STRUCTURAL ANALYSIS OF INTERACTION DATA The arrival of various interaction datasets produced a new challenge for computational structural biologists. Suddenly thousands of new interactions and complexes became known with little or no structural information available. Modeling interactions is, of course, possible if one has a suitable template of known structure containing two or more interacting proteins in contact. However, early analyses of interaction data from a structural perspective high- lighted the relative paucity of these interaction templates (Aloy and Russell 2002). Indeed, while solving structures for single, small, globular proteins are now a relatively straightfor- ward process, solving experimental structures involving multiple proteins continues to be a challenge. Nevertheless, improved experimental techniques, and the increased focus on studying protein complexes in structural biology, means that there is now an exponential growth in the number of distinct interactions of known structure (Aloy and Russell 2004; Kim et al. 2006b; Tuncbag et al. 2008). There are currently several tools that allow biologists to study interactions in three-dimen- sions. Early tools such as InterPReTS (Aloy and Russell 2003) and MULTIPROSPECTOR (Lu et al. 2002) were designed to rapidly assess how well homologous sequences fit onto interact- ing proteins with 3D structures. Systematic analysis of thousands of interactions of known 3D structure showed that sequence similar proteins retain similar interactions, and a drop in sequence similarity increases a tendency to interact differently (Aloy and Russell 2004; Kim et al. 2006b; Tuncbag et al. 2008). Analyses also showed that structural interfaces (Figure 2.1) could be used to infer details about whether or not interactions could occur simul- taneously (Aloy and Russell 2006; Kim et al. 2006a) which helped the classification of protein interaction centers in terms of “party” or “date” hubs (Han et al. 2004). However, interroga- tion of interaction sources showed that the picture for many promiscuous proteins (in terms of interactions) is more complicated, with many having the ability to interact with multiple partners and multiple interfaces (e.g. Figure 2.2). This early work has since led to a number of databases that allow users to query interactions of known 3D structure, including 3DID (Stein
- 24. 12 2. STRUCTURAL SYSTEMS BIOLOGY: MODELING INTERACTIONS AND NETWORKS RAS RAS SOS1 RASSF5 RAFRBD RAS CDK6 CDK6 v-Cyclin P18-INK4C FIGURE 2.1 Structural interfaces can be used to assess whether interactions between proteins can occur simulta- neously. The top of the figure shows a schematic of a protein (hexagon) that can either bind multiple proteins at one interface or simultaneously via different interfaces and that this is not obvious when looking at interaction networks alone. The bottom left of the figure shows three structures of Ras or Ras-like proteins in complex with three structur- ally different proteins that all bind on the same interface; the bottom right shows how the CDK6 structure can accom- modate interactions with three proteins simultaneously. Interface 1: 17 interactors Interface 0: 14 interactors Interface 4: 3 interactors Interface 2: 7 interactors Interface 5: 6 interactors Interface 3: 7 interactors p115 FIGURE 2.2 An example of a highly promiscuous protein (p117) uncovered during a screen of interactions within Mycoplasma pneumoniae (Kühner et al. 2009) and how it can apparently interact with multiple partners on multiple interfaces as predicted by interface modeling techniques. Protein p117 is colored in gray with the interaction partners in other colors. The number of interactors given for each interface is taken from the TAP dataset generated in the same screen.
- 25. 5 Systems biology applications 13 et al. 2011), SCOPPI (Winter et al. 2006) and Interactome3D (Mosca et al. 2013). There have also been a number of applications of these tools to whole genomes to understand globally the structural repertoire of interactions and complexes present in an organism (Aloy et al. 2004; Kühner et al. 2009; Zhang et al. 2012) which has led to numerous insights into individ- ual complexes and the nature of protein-protein interactions in general. 4 OTHER INTERACTION TYPES Protein interactions come in many different flavors. Most of the above approaches work best when pairs of globular (i.e. folded) proteins or domains interact with one another. It has long been known that many interactions in biology do not occur in this way, but instead involve one globular protein or domain interacting with short peptide segments from other proteins. These peptide segments often show a particular pattern or motif that captures the features most responsible for binding to the globular partner. There are now several resources that capture these motifs systematically and allow users to search for motifs in query proteins (e.g. Dinkel et al. 2012). The fact that these motifs are more difficult to detect than globular segments using conventional sequence analysis tools (owing mostly to their short length) has led to various methods to identify new motif candidates (Davey et al. 2010; Neduva and Russell 2006) and most recently these approaches have been extended to methods to predict protein-peptide interactions using known 3D structures if available (Petsalaki et al. 2009). All of this work is complementary to earlier developments on protein-protein or protein- small-molecule docking. Whereas previous docking efforts were focused on individual pairs of proteins of interest, there are now a growing number of studies whereby hundreds or thou- sands of pairs of proteins are docked together in an attempt either to find a handful of likely biologically meaningful docked structures (Mosca et al. 2009) or to use docking as a means to predict protein-protein interactions (Wass et al. 2011). Other efforts have attempted to use docking to combine pairwise docking methods (i.e. that attempt to dock two proteins or domains together) model higher order complexes (Inbar et al. 2005; Lasker et al. 2009) that are known from protein complex discovery experiments (Gavin et al. 2006; Guruharsha et al. 2011). Protein-small-molecule docking is now applied in a systems-wide fashion. Specifically, virtual screening—whereby thousands of molecules can be docked simultaneously to one or often multiple proteins—is now commonplace and indeed a standard complementary approach to virtual screening (Lavecchia and Di Giovanni 2013). 5 SYSTEMS BIOLOGY APPLICATIONS Exciting applications of structural bioinformatics techniques to systems modelling are already emerging. Structures, for example, provide a means to provide critical missing parameters for metabolic modeling processes (Gabdoulline et al. 2007; Stein et al. 2007). On a large scale, struc- tures (experimental or modeled) can be used to identify missing substrates and products for metabolic reconstruction, which enables more accurate simulation and interpretation (Chang et al. 2013; Yus et al. 2009; Zhang et al. 2009). It is likely that these approaches will be applicable to more complex processes such as signaling or DNA repair in the future, but currently too little
- 26. 14 2. STRUCTURAL SYSTEMS BIOLOGY: MODELING INTERACTIONS AND NETWORKS structural information is available and there are additional challenges to be overcome, such as the ability to reliable estimate thermodynamic or kinetic parameters for protein-protein interac- tions. There are various hints that this will be possible, coming from several studies that attempt to predict interaction specificity across diverse sets of proteins such as (Kiel et al. 2008). 6 NEW DATASETS-SPECIFIC PROTEIN SITES With the advent of next generation sequencing thousands of new individual genomes of a species become available and these data are increasing at an explosive rate (Hanahan and Weinberg 2011; Xuan et al. 2012). While the previous goal was to understand the function of specific genomes or sets of proteins (i.e. a set of dysregulated genes or proteins), now one typically is presented with both a set of genes/proteins and multiple modifications within them. Therefore, these data can profit from computational predictions about the mechanistic consequences of alterations. Most tools for assessing DNA variations consider both protein sequence and structural information to some degree. For instance, tools like PolyPhen and MutationAssessor (Reva et al. 2011; Sunyaev et al. 2000) consider known or modeled struc- tures to assess whether a mutation or variant lies in the interior or at the surface of a protein which helps to suggest how deleterious the change is likely to be, and the latter considers additional contacts to small molecules or other proteins. General principles are also emerging, for example analysis of SNPs that lie within known or predicted 3D structures shows that they tend to be on protein surfaces and to lie at protein interaction interfaces (David et al. 2012). Other new datasets are also in need of the kind of mechanistic interpretation that struc tures can provide. Perhaps most significant among these are proteomics datasets related to the identification of post-translational modifications (PTMs) (Choudhary and Mann 2010; Pflieger et al. 2008). Here too the datasets consist of individual positions within hundreds or thousands of proteins that are often related to phenotypic differences or disease. Structural analyses of proteomic PTM datasets have found that these modifications too are enriched and protein-protein interfaces (van Noort et al. 2012) and that they show certain preferences according to type and that they tend to co-occur within interacting proteins (Minguez et al. 2012). 3D structures have also been suggested as a means to filter meaningful modification sites from possibly artifacts: it has been argued that sites known or predicted to be highly buried in a protein structure are less likely accessible to kinases and phosphatases and such sites likely need to be considered carefully in terms of their accuracy (Vandermarliere and Martens 2013). 7 CURRENT AND FUTURE NEEDS The unifying theme to both of these types of datasets is the need to first understand as much as possible about the mechanistic consequences of mutating or modifying a particular residue in a particular protein, and then, if possible, to identify from hundreds or thousands of data-points those that are most likely to have biological consequences. Thus, beyond the analysis of individual sites within large datasets, there is an increasing need to understand an entire set of genes, proteins, or their modifications in a kind of mechanistic context.
- 27. 7 Current and future needs 15 Q61R Q61R I36M I36M KRAS RASSF2 KRAS SOS1 FIGURE 2.3 View of KRAS mutations in terms of known or predicted interactions between functional elements. The top of the figure shows an interac- tion network of KRAS and a selection of interaction partners. The inset zooms in on interactions with KRAS and various Ras-binding domain proteins. Each protein is shown a series of domains (squares) and linear motifs (diamonds) connected N- to C-terminally. Boxes around regions of the protein denote regions of protein 3D structures that are either in contact with part of another protein in the network (darker or red lines) or with themselves (circular lines connecting individual proteins). Known interactions between linear motifs and domains are also shown as yellow/lighter lines. The location of two KRAS mutations at interaction interfaces are shown to the right of the figure (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this book.).
- 28. 16 2. STRUCTURAL SYSTEMS BIOLOGY: MODELING INTERACTIONS AND NETWORKS The combination of existing individual tools into a more systems-ready view of structural or mechanistic information appears to be a desirable development goal. For instance, consid- ering data on mutations in colorectal cancer (Kilpivaara and Aaltonen 2013) readily identifies sets of proteins of interest, such as KRAS (Lièvre et al. 2006), though mutations are also seen in many other cancers or developmental disorders. The STRING database (Franceschini et al. 2013) provides nine proteins that interact with KRAS (Figure 2.3). Like most eukaryotic pro- teins they are modular, consisting of several distinct modules, or domains with discrete func- tions and often with a discrete 3D structure. Considering predicted interactions via InterPReTS (Aloy and Russell 2002) and potential interactions between linear motifs (Dinkel et al. 2012) and protein domains (Punta et al. 2012) provides a set of potential interactions between these domains that provides various key insights about how KRAS interacts can interaction with its partners. For instance, structural analysis shows that it is unlikely that KRAS can interact with SOS1, RAF1, RALGDS, or RASSF2 at the same time as these interactions are predicted to occur that the same interface (Figure 2.1). The structures also suggest which of the known mutations within KRAS are likely to affect interactions (Figure 2.3 labeled) and how some of these interactions seem to contain mutations for cancer (Q61R) or NS2 (I36M). Analysis of individual KRAS modeled structures also helped to reveal how several key mutations affect nucleotide binding within the RAS domain (not shown). 8 CONCLUDING REMARKS Structural biology and structural bioinformatics have much to offer for systems-level studies. There is still a considerable gap between systems, assemblies or complexes that are understood in terms of their component molecules, but that lack most or all information about how the molecules come together at the atomic level or about the kinetic or thermo- dynamic parameters that are so important to model systems accurately. The ability to exploit and interpret known or predicted structural information quickly for these systems is of grow- ing importance as the datasets related to how these systems are modified either genetically or via PTMs grows. Tools and know how in structural bioinformatics thus provides a great boost to anybody wishing to understand molecular mechanism and how it can be perturbed by variation, modification, or the addition of other molecules. Acknowledgments This work was supported by the European Community’s Seventh Framework Programme FP7/2009 under the grant agreement no: 241955, SYSCILIA. References Aloy, P., and Russell, R. B. (2002). Interrogating protein interaction networks through structural biology. Proc. Nat. Acad. Sci. U.S.A. 99:5896–5901. Aloy, P., and Russell, R. B. (2003). InterPreTS: protein interaction prediction through tertiary structure. Bioinformatics 19:161–162. Aloy, P., and Russell, R. B. (2004). Ten thousand interactions for the molecular biologist. Nat. Biotechnol. 22:1317–1321.
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- 32. 21 © 2014 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/B978-0-12-405926-9.00003-4 Computational Systems Biology, Second Edition 3 Understanding Principles of the Dynamic Biochemical Networks of Life Through Systems Biology Hans V. Westerhoffa,b,c , Fei Hec,d , Ettore Murabitoc , Frédéric Crémazya , Matteo Barberisa a Department of Synthetic Systems Biology and Nuclear Organization, Swammerdam Institute for Life Sciences, University of Amsterdam, Amsterdam, The Netherlands, b Department of Molecular Cell Physiology, Faculty of Earth and Life Sciences, VU University Amsterdam, Amsterdam, The Netherlands, c Manchester Centre for Integrative Systems Biology (MCISB), Manchester, UK d Department of Automatic Control and systems Engineering, The University of Sheffield, Sheffield, UK C H A P T E R C O N T E N T S 1 Principles based on topology of the genome-wide metabolic network: limited numbers of possible flux patterns 22 2 Principles based on topology of the genome-wide metabolic network: toward personalized medicine 25 3 Industrially relevant applications of topology and objective-based modeling 26 4 Applications of topology and objective- based modeling to cancer research and drug discovery 27 5 Principles of control 30
- 33. 22 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS Abstract Systems Biology brings the potential to discover fundamental principles of Life that cannot be discovered by considering individual molecules. This chapter discusses a number of early, more recent, and upcoming dis- coveries of such network principles. These range from the balancing of fluxes through metabolic networks, the potential of those networks for truly individualized medicine, the time dependent control of fluxes and con- centrations in metabolism and signal transduction, the ways in which organisms appear to regulate metabolic processes vis-à-vis limitations therein, tradeoffs in robustness and fragility, and a relation between robustness and time dependences in the cell cycle. The robustness considerations will lead to the issue whether and how evolution has been able to put in place design principles of control engineering such as infinite robustness and perfect adaptation in the hierarchical biochemical networks of cell biology. 1 PRINCIPLES BASED ON TOPOLOGY OF THE GENOME-WIDE METABOLIC NETWORK: LIMITED NUMBERS OF POSSIBLE FLUX PATTERNS The genome-wide reconstructions of enzyme-mediated metabolic activities in various organisms have led to long lists of correspondences between genes, proteins, enzyme activi- ties, and to implied changes in the concentrations of metabolites (Herrgård et al. 2008; Thiele et al. 2013). If any reaction activity is represented by a reaction rate v, then the list of activities may be written as a long column (or vector) of v’s. For a reaction i, one may then write the change it effects in the number of Moles of any metabolite Xj by a stoichiometric number Nji that is defined by the reaction chemistry: Here the final term corresponds to the dilution due to growth at the specific growth rate μ. Doing this for all reactions and generalizing to vectors and matrix this leads to: Here v is a column of all the rates of all the reactions in the organism (i.e. one rate for every gene product at the level of enzyme or transporter) per unit intracellular volume. X is a col- umn of all the molecule numbers (in Moles) of the metabolites in and around the organism, and N the matrix of stoichiometric coefficients of that organism. N represents all single-step (3.1) dXj dt = Nji·vi − µ·Xj (3.2) dX dt = N·v − µ·X 6 Principles of regulation 32 7 Regulation versus control 33 8 Robustness and fragility and application to the cell cycle 35 9 Perfect adaptation and integral control in metabolism 38 References 42
- 34. 1 PRINCIPLES BASED ON TOPOLOGY OF THE GENOME-WIDE METABOLIC NETWORK 23 catalytic capabilities of the organism. In the consensus reconstruction of the human (Thiele et al. 2013), v is a list of 7440 reactions, and X of a list 5063 metabolites, 642 of which are extra- cellular. N is a 5063 by 7440 matrix of numbers like 1, 2, −1, with many zero’s. N is a genome-wide culmination of molecular biochemistry. For any molecule in an organ- ism, say molecule B, it shows from which molecules it can be made in a single step that is cata- lyzed by a protein encoded by the genome of the organism. It also shows into which other molecules the molecule can be converted in a single step. Although of great biochemical inter- est, this does not correspond to the solution of the biological question how an organism builds itself from components it takes from the environment, i.e. of how an organism recreates life from dead materials. For many components an organism cannot be built in a single step from the extracellular components. To address this issue, systems biology is needed, i.e. some way of reflecting how the indi- vidual reactions encoded by the genome integrate their actions. Because it is genome wide, i.e. contains (in principle) all reactions encoded by the genome, matrix N has the potential to do this. N may tell us that molecule A cannot be converted in a single step to molecule B, but may be converted into a molecule C, say by reaction number 5 (i.e. NA5 = −1 and NC5 = +1, while NB5 = 0), and that molecule C can be converted to molecule B by a reaction 9 (i.e. NA9 = 0, NB9 = 1, and NC9 = −1), so that indirectly by collaboration of enzymes 5 and 9, molecule A can be converted to molecule B: networking of enzyme molecules is needed, with metabolite C as communicator (Figure 3.1). If the enzymes work intracellularly and one would start with zero B and C but with a certain amount of A, one would see that the concentration of C would build up first and that only then the concentration of B should begin to increase. If A is kept constant by external supplies, C will increase with time until it becomes constant and the rates of reactions 5 and 9 have become the same. This is called the intracellular steady state. Because the extracellular compartment is much larger, an intracellular steady state will be A A C C B B 5 9 1 2 7 10 D D E E 3 4 F F 6 8 FIGURE 3.1 Example of a network described by matrix N, with molecule A converted to molecule B via equilib- rium reactions.
- 35. 24 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS achieved while the extracellular concentrations are still increasing or decreasing, very slowly with time. If one divides the metabolites into mi intracellular ones (Xi) and me extracellular ones (Xe), reorders the rows of matrix N such that its bottom rows make up the submatrix Nex containing extracellular metabolites, one finds for the upper submatrix of N, Nin: while: Most metabolites are not endpoints of a metabolic pathway, but intermediates with life times much shorter than the cell cycle time. We shall further focus on these cases and thereby be able to neglect the term containing the dilution due to growth. In cases where this does not apply, one may add the growth rate to the vector v and extend N accordingly. At this intracellular steady state, matrix N now puts a strong constraint on all the rates because the latter have to satisfy Equation. 3.3. Only the rate vectors that are in the Kernel of Nin, the subspace of all the possible rate vectors, are admissible. This limitation is enormous, i.e. from the 7444 dimensional space suggested by the length of the rate vector v, the reduc- tion is to a 7444-4421 = 3013 dimensional subspace. Clearly, the intracellular location of most enzymes and the consequent occurrence of steady state, it forces the enzymes to collaborate, to balance their fluxes, and to come to a concerted behavior that produces a steady state. Should a chemical reaction network be created at random, then it would often not relax to a steady state. Here we use a principle of Biology, i.e. that the living organisms we study are viable and hence not subject to metabolic explosions (Teusink et al. 1998), i.e. they exhibit stationary states, and the common stationary metabolic states is the steady state (Westerhoff Van Dam 1987). If life harbored a single linear pathway of 7442 enzymes and two transporters, then the number of intracellular metabolites would be 7443 and the space of possible reaction rates would have been reduced from dimension 7444 to dimension 1: it is the branching of path- ways that is at the basis of the remaining dimensionality of the possible rate distributions at steady state. In actual practice only a single (or a few) steady state is obtained with a single set of rates, although the steady-state conditions still permit an incredibly high number of steady states together filling the 3013 dimensional space. The genes are however expressed to a certain level, as defined by the environment plus the parameters of the intracellular networks, which begin to define the actual vector v, whereto the intracellular metabolite concentrations adjust so that the rates v change until the steady-state condition of Equation 3.3 is met, after which the system becomes constant in time, corresponding to steady state, which corresponds to a zero dimensional space. Evolution has selected the values of all the internal parameters such that a steady state can be obtained (see above) and possibly such that the actual rates are what is optimal for the organism if the extracellular conditions correspond to conditions that reigned during evolution. (3.3) 0 = dXi dt ss = Nin·v − µ·Xi (3.4) dXe dt ss = Nex·v
- 36. 2 PRINCIPLES BASED ON TOPOLOGY OF THE GENOME-WIDE METABOLIC NETWORK 25 If we measure the changes in time of the extracellular metabolites, and insert these into Equation 3.4, then this gives us an additional reduction of dimensionality by 642–2271. This is now not a boundary condition imposed by a fundamental principle, but an experimental observation that could help us to estimate the intracellular behavior of the network. However, we still cannot establish what the intracellular state is: the world of possible states is still 2271 dimensional for the human metabolic map. One approach is to determine intracellular fluxes experimentally by a procedure known as flux analysis, which often employs isotopically labeled growth. Here one may deduce from the growth rate and biomass composition a great many anabolic fluxes and use these to con- fine the possible fluxes (Sauer 2006). All these methodologies are empirical ways to establish what the actual flux distributions are. There are additional ways of limiting the space of possible fluxes. One is that of requiring that no single reaction runs in the direction that is uphill in terms of thermodynamics (Westerhoff Van Dam 1987). In principle the concentrations of intracellular metabolites are then needed, but assuming that these are within reasonable bounds (e.g. between 0.001 and 100 mM) certain directions of reaction can be excluded. Another way is to impose that no reaction rate can become higher than the Vmax of the enzyme that catalyzes the reaction, where the Vmax is determined in cell extracts (Mensonides et al. 2013; and see below). These two principles merely give bounds to values of reaction rates however; they do not reduce the dimensionality of the space of rates (we define reaction rates as net fluxes through processes not as unidirectional fluxes). A more fundamental principle is often used by what is called Flux Balance Analysis (FBA), which assumes that efficiency is maximal in terms of ATP yield, and yet another one assumes maximal biomass synthesis. We shall here discuss the former. For two parallel pathways that hydrolyze different amounts of ATP, this removes the pathways that hydrolyze most ATP. This principle has the advantages that it does not require experimental measurement if it is plainly assumed to apply and that it does reduce the dimensionality of the space of reaction rate distribution appreciably. However, this principle of optimal efficiency has been shown not to apply completely in a number of cases. Organisms such as baker’s yeast for instance do not grow at maximal efficiency when glucose is present in excess (Simeonidis et al. 2010). More in general organisms do not seem to be optimized for thermodynamic efficiency or yield (Westerhoff et al. 1983). On the other hand, the effect of reducing the world of solutions to Equation 3.3, may still be largely appropriate, and the approach may be useful as a first and limited approach in some cases (Reed and Palsson, 2004) and see below. 2 PRINCIPLES BASED ON TOPOLOGY OF THE GENOME-WIDE METABOLIC NETWORK: TOWARD PERSONALIZED MEDICINE If one is interested in whether the organism (through its matrix N) is actually capable of synthesizing a particular intracellular metabolite, say metabolite number 2031, one substi- tutes 1 for the zero at row 2031 of the zero vector at the left-hand side of Equation 3.3 and attempts to find solutions for the rate vector v. Often multiple solutions will be found. One may then ask whether metabolite number 2031 can be synthesized from a certain type of nutrition. To address this issue one should analyze the molecular composition of the nutri- tion, then require the rates of the transport (across the plasma membrane) reactions in v that
- 37. 26 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS correspond to substances that are not present in the nutrition to be nonnegative (positive being defined as outward transport), and again try to find a solution for the rate vector v that is consistent with these conditions. If such a rate vector is found then the map is consistent with producing the intracellular metabolite. Knowledge about the DNA sequence of an individual, enables one to understand where that individual may have inactive gene products on its metabolic map. Requiring in the above computations the corresponding reaction rates (elements of rate vector v) to be zero, one may again try to find a solution for the rate vector that delivers metabolite 2031. If this is impos- sible for the individual then it suffers from an inborn error of metabolism. Repeating this procedure for other nutrients, then enables one to examine whether the disease can be averted by using a special diet. By equating dXin/dt to the biomass composition in terms of all molecules in the living organism, and then solving the resulting equation for the rate vector v, one may ask whether the map is able to make its complete self, and thereby scout for all possible inborn errors of metabolism at the same time. Because of the large size of the matrix N, finding all possible solutions is computationally challenging, but finding one solution often suffices and is possible with modern algorithms. 3 INDUSTRIALLY RELEVANT APPLICATIONS OF TOPOLOGY AND OBJECTIVE-BASED MODELING If the goal of an FBA is to identify a pattern of fluxes fulfilling the steady-state condition imposed by Equation. 3.3 under the assumption that an objective function Z representing the biological process is optimal, the task is: where vL and vU are the lower and upper bound of the fluxes (defining the range of values that the different rates can have), and f is a set of coefficients defining the objective function Z in terms of a linear combination of the rates v. Depending on the specific information we want to retrieve through FBA, Z can also represent a non-biological criterion of optimality, as we shall see below. A promising applications of FBA is in industrial protein production. Proteins require com- plex systems for their synthesis that only living cells are equipped with. The complexity of these “cell factories” is far beyond that of man-made production systems and we are far from understanding their functioning in a comprehensive way. As a consequence protein produc- tion tends to be quite unpredictable. The complexity of these factories which derives from the intricate interconnectivity of its different components has to be taken into account at some level if one wants to make protein production predictable and hence be able to play with the “control knobs” of these factories to adjust the production process to our needs. The applica- tion of FBA, and more in general the adoption of the Systems Biology perspective, may help to make this process more predictable and design strategies to improve protein harvest. (3.5) maximize Z = f T · v subject to N · v = 0; vL ≤ v ≤ vU
- 38. 4 APPLICATIONS OF TOPOLOGY AND OBJECTIVE-BASED 27 Through FBA, for example, it is possible to predict the optimal pattern of internal fluxes rep- resenting the metabolic functioning of the cells cultured under specific conditions. This enables us to attempt to predict and compare the flux patterns of a control culture and a cul- ture expressing the recombinant protein. The superposition of these patterns would provide us with a set of reactions that are either (significantly) active in both scenarios or that turn on/ off when switching from one situation to the other. This set of reactions would host on the one hand the main metabolic processes common to both situations and on the other hand the main metabolic changes that cells undergo when expressing the protein. This would give us some insights on how cells redirect their metabolic trafficking in order to fulfill the new task of producing the recombinant protein. In the scenario illustrated above one would want the flux patterns predicted through FBA for the control and recombinant cultures to be as close as possible to the real functioning of the cells. To this end a good strategy consists of including in the computational representation of the system some experimental data, such as exchange fluxes and growth rate, retrieved in the two conditions. The objective function will be then defined as the negative mismatch between the predicted and the experimental value of the quantities that have been measured: where vi and mi are respectively the predicted and the experimental value of the measured quantity i. From a genetic engineering perspective a relevant question would be whether it is possible to increase the yield of the recombinant protein for a specific growth medium by diverting the internal flux toward more favorable metabolic routes. In this case one would compare the flux pattern obtained for the recombinant culture when Z is defined as in Equation 3.6 and the flux pattern obtained by setting Z = vr where vr is the rate of the pseudo-reaction introduced in the model to represent the recombinant protein production. Another relevant question concerns the growing medium composition. FBA could also be used to identifying the limiting nutrients and suggest alternative optimal feed design to fur- ther increase the protein production. 4 APPLICATIONS OF TOPOLOGY AND OBJECTIVE-BASED MODELING TO CANCER RESEARCH AND DRUG DISCOVERY Drugs are designed to affect one or more specific properties of the cells needing treatment. These properties usually represent what differentiates diseased cells from their normal coun- terparts, or a pathogenic organism from its host. The property one chooses to affect can vary depending on the specific clinical strategy pursued. Because neoplastic cells grow and repli- cate at a considerably faster rate than their normal counterparts, the rationale behind many of the possible choices in cancer treatment consists of halting the proliferative potential of the malignant tissue. Indeed, traditional clinical approaches such as chemotherapy and radio- therapy aim to kill cancer cells by disrupting their replication machinery. Similarly, in drug intervention at the metabolic level, the preliminary step consists of identifying a property (3.6) Z = − i |vi − mi|
- 39. 28 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS which characterizes the altered phenotype and which is therefore sensible to target. In this respect, constraint-based modeling approaches, and particularly FBA, can provide us with a way to identify these properties. If the system under study is known to optimize a certain biological requirement, then that requirement might be considered as the property one may want to target in order to disrupt the metabolic phenotype of the cell. However, the identification of the biological task that the objective function should represent is not always easy. For studies involving E. coli metabo- lism, the objective function Z is usually defined to represent the yield of biomass (Reed and Palsson 2004), assuming that bacteria aim to grow as fast as possible (although this assump- tion does not reflect a generally valid principle in microbiology (Schuster et al. 2008). By contrast, for human cells, things are not so straightforward. Since cancer cells grow at a much higher rate than their normal counterparts, it would seem reasonable to adopt the same approach as for E. coli by choosing the maximization of biomass production rate as the optimization criterion. Although this intuitive choice may seem sensible, the resulting FBA solution highlights a flux pattern which does not match with the observed characteristic of cancer metabolism (Warburg and Dickens 1931). Because of the high demand of ATP in the production of biomass, the flux pattern corresponding to the maximal yield shows the glucose uptake flux entirely entering the TCA cycle, with no lactate production. To retrieve a flux pattern highlighting the cancer metabolic features (a constitutive activation of the branch leading to lactate production and, possibly, the reduc- tion of the flux entering the TCA cycle), the FBA problem has then to be formulated differ- ently. A possible way to do so consists of replacing the maximal yield of biomass with a different criterion of optimality. In a recent work, Simeonidis et al. showed how an appropri- ate reformulation of FBA can be used to reproduce the Crabtree effect, an experimentally observed behavior whereby Saccharomyces. cerevisiae produces ethanol aerobically in the presence of high external glucose concentrations rather than producing biomass through the TCA cycle (Simeonidis et al. 2010) The authors hypothesized that (one of) the “driving forces” behind yeast metabolism is resource preservation (see also León et al. 2008). By mini- mizing the number of active reactions (and hence the number of enzymes) needed to pro- duce a required amount of biomass, the flux patterns obtained as solutions of the FBA problem showed the characteristic switch from respiration to fermentation that occurs when the concentration of glucose in the growing medium is increased above a certain threshold. Because of the commonalities in the metabolic features of fermenting yeast and cancerous cells (Diaz-Ruiz et al. 2009), a similar argument might be applied to reproduce the constitu- tive metabolic changes occurring in carcinogenesis. From an FBA perspective, higher con- centration of glucose in the growth medium and higher rate of glucose uptake due to over-expression of glycolytic enzymes are both implemented by increasing the upper limit of the glucose uptake flux. In both cases, the requirement of resource preservation would force the system to switch from respiration to fermentation/lactate production as soon as the glycolytic flux becomes high enough to provide the cell with the amount of ATP needed for the required production of biomass. A related issue that FBA could address is whether cancer cells are committed to optimize different biological functions concurrently. Indeed, the enhanced replication rate of neo- plastic cells, combined with a predilection for fermentation (which is not the most efficient way to produce ATP) would seem to support a multifunctional optimization hypothesis,
- 40. 4 APPLICATIONS OF TOPOLOGY AND OBJECTIVE-BASED 29 whereby different criteria of optimization have to be satisfied simultaneously. As initially hypothesized by Gatenby and Gawlinski (1996), the production and excretion of lactic acid constitutes a way for cancer cells to compete with their normal counterpart by creating a hostile environment for normal cells. However, the fact that sometimes the TCA cycle is nevertheless active (although to a smaller extent than its normal capacity) makes evident that competing through excretion of lactate is not the only task that cancer cells try to opti- mize. Using a specular argument, one could say that, despite the enhanced replication rate of cancer cells, the fact that the TCA cycle is somehow hampered shows that replicating most efficiently or at the highest possible rate is not the (only) objective that drives cancer cells, or, in other words, that there are multiple goals pushing the system toward a different metabolic flux pattern. The relevance of different possible optimization criteria in the func- tioning of the system and their relative weights could also help to elucidate why the pheno- typic traits of cancer metabolism are present to different extents in different types of cancer and in different cells in the same tumor. There are other points that an FBA approach might help to elucidate. Knowledge of the metabolic shift occurring in tumorigenesis predominantly involves central carbon metabo- lism. However, the shift may extend beyond central metabolism, and remarkable metabolic differences between normal and cancer cells may lie in pathways not yet studied within the context of cancer research. A further application of FBA could highlight particularly active metabolic pathways in cancer on a genome-scale level, and identify the regions where the flux pattern differs most between cancer and normal cells. Shlomi et al. (2008) have recently used an FBA approach to describe the tissue specificity of human metabolism, where tissue- specific gene and protein expression data were integrated with a genome-scale reconstruction of the human metabolic network. Different integer values were assigned to different gene- expression states, so to distinguish among highly (1), lowly (−1), and moderately (0) expressed genes. The objective function of the FBA problem was then set to account for the differences between the activity of each reaction in the predicted pattern of fluxes and the integer repre- sentation of the corresponding experimental gene-expression level. By minimizing such an objective function, the authors were able to retrieve stoichiometrically and topologically con- sistent flux patterns on a genome-scale level with the maximum number of reactions whose activity was in accordance with their expression state. This study may establish a FBA-based computational approach for the genome-wide study of normal and cancer human metabo- lism in a tissue-specific manner. Another interesting point FBA might address is the following. Given the selective pressure that biological systems undergo when functioning under mutual competition, it seems rea- sonable to assume that cancer cells fulfill their specific biological tasks in the most economical way. In other words, given the available external substrates and given a set of functionally important targets to accomplish, the cell would employ its resources most “effortlessly.” From a metabolic perspective, this would translate into the employment of a minimal number of active reactions, or, more generally, a minimal employment of resources. In E. coli, for exam- ple, experimental results have shown that fitness increases while unused catabolic functions decrease, this reduction being beneficial and therefore favored by selection (Cooper and Lenski 2000). In the context of FBA, this “principle of minimal effort” has been used in differ- ent forms to identify the pattern of fluxes that best portraits the system functioning with respect to specific criteria of optimality (León et al. 2008; Holzhütter 2004). It should be noted
- 41. 30 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS however that many cancer cells appear to secrete more metabolites into their surrounding medium than what may be consistent with minimal use of their resources (Jain et al. 2012). Combinations of optimality criteria with observed flux patterns as constraints for the FBA solutions might be a strategy. On the other hand, there exist different flux patterns that are equally optimal with respect to a certain criterion or set of criteria. Extension of FBA to find alternate optimal solutions (Lee et al. 2000) or alternate optimal patterns of fluxes (Murabito et al. 2009) have been devel- oped. In particular, an algorithm able to find all the minimal and equally optimal flux pat- terns of a metabolic network with respect to a given functional task has been proposed (Murabito et al. 2009). The superposition of all minimal optimal flux patterns allows us to identify those pathways or sets of reactions that must be active in order to optimally fulfill a given function, and other sets of reactions that can be alternatively active. The application of such an approach in the context of cancer research might help to identify and predict the nar- rowest region of human metabolism necessary to observe the carcinogenic metabolic shift. From the perspective of developing a kinetic model of cancer metabolism, these results might also provide modelers with a concise set of reactions that can be used as a backbone for a mechanistic representation of the system under study, as well as an idea about which path- ways and reactions can be reasonably neglected. 5 PRINCIPLES OF CONTROL In biochemical networks, rates of chemical conversions or transport reactions are not just determined by the properties of the enzyme or transporter that catalyzes them, but also by properties of other components of the network. Something similar applies to the concentra- tions of metabolites in the network. It therefore makes sense to define the control of a rate vi of any process in the network by the activity ei of that same process or of any other process ej in the network. The definition of the corresponding flux control coefficient reads as: This definition differs somewhat from the standard definition of the flux control coefficient (Burns et al. 1985), which is limited to the control of steady-state fluxes. Here we are more explicit about the fact that one may also define the flux control coefficient outside of steady state. This does require one to keep track of time, i.e. to be careful about defining the initial (t = 0) condition. The definition compares two effects that a given amount of agent pj, that modulates the rate of process vj specifically, may have on processes i and j (i may or may not equal j). The first is the effect agent pj has on the rate vi of process i when that process func- tions in the system. The second is the effect the same amount of the agent pj would have on process j when the process j would be outside the system but in the same conditions, with (3.7) Cej vi (t) def = ∂lnvi ∂lnej = ∂lnvi(t) ∂pi in the system ∂lnvj (t=0) ∂pj in a constant molecular environment
- 42. 5 Principles of control 31 those conditions frozen. For a network with n processes, Westerhoff (2008) has proven the general property or “law”: The right-hand side is the flux control coefficient of time defined by: It quantifies the extent to which the rate of process i varies with time. We first discuss the example of a signal-transduction cascade with all proteins in the inac- tive un-phosphorylated state, which is then confronted with a sudden activation of a receptor, the activity of which then decays slowly. The rate of phosphorylation of the target of this receptor (which we here assume to be a protein kinase) will jump from zero up to a rate that is almost constant initially, i.e. after that initial jump, the time-control coefficient of that rate will be virtually zero. As a consequence, the above law (Equation 3.8) predicts that all pro- cesses in the network together control the rate of phosphorylation of the target at a control coefficient of 1. However, since there is hardly any phosphorylated target in the beginning, none of the other processes can be active and only the first kinase (the active receptor) can control the rate of phosphorylation of its target. Consequently, that kinase will initially be in full control; a 10% activation of the kinase will produce a 10% higher degree of phosphoryla- tion of the target at any given (short) time t after receptor activation. Because it phosphorylates its target, the kinase will relatively quickly decrease in rate and this decrease will be quicker the more active the kinase is. Consequently, control by the kinase in the rate of phosphorylation of its target at a given moment in time will decrease fairly quickly to below 1 and the time control of the kinase reaction will become negative. As even more of the target gets phosphorylated, its phosphatase becomes active and gains in control. Paradoxically perhaps, this control on the rate of phosphorylation of this first tar- get is positive, as the phosphatase creates more substrate for the kinase reaction. As time proceeds, the control by the kinase will decrease further and that of the phosphatase will increase until the two add up to 1, as the time dependence control coefficient returns to zero, it steady-state value. In general both the kinase and the phosphatase control the rate of phos- phorylation of their substrate. For the concentration of any substance in the system, the time dependent control coeffi- cients sum to zero plus the time-control coefficient: This includes the classical summation law that the sum of all control coefficients with respect to any steady-state concentration equals zero. This law is general in the absence of metabolite channeling (Kholodenko and Westerhoff 1993). The sum must also equal zero when the variation of the concentrations with time exhibits a maximum or minimum. (3.8) n j=1 Cvi ej (t) = 1 + Cvi t (t) (3.9) Cvi t (t) def = ∂lnvi ∂lnt in the system (3.10) n j=1 CXk ej (t) = CXk t (t)
- 43. 32 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS Hornberg et al. (2005) have used this property to prove that in the MAP kinase cascade all the phosphatases (or strictly speaking all the negatively controlling processes) together are as important for the amplitude of the ERK phosphorylation as are all the kinases together. If instead one focuses on the time point where the ERK phosphorylation has decreased again to half its amplitude, then the time-control coefficient is negative, implying that the sum of the control by all the kinases and the control by all the phosphatases must be (equally) negative. Since the phosphatases exercise negative control and the kinases positive control, this implies that the phosphatases are more important for the concentration of Erk-PP at this time point than the kinases are. To the extent that the MAP kinase is important for transcrip- tion regulation, appreciating that transcription integrates the time dependence of Erk-PP, and accepting that the duration of Erk-PP signaling relative to its amplitude is important, Hornberg et al. (2005) concluded that the phosphatases are even more important for signal transduction than the kinases are. This conclusion was perhaps useful because much more attention had been paid to kinases that to phosphatases. Importantly also, the summation law states that all phosphatases together should exercise more control than all kinases together. The principle is not that the first phosphatase must exert more control than the first kinase and that these are the only two controlling enzymes. Indeed, in numerical simulations, con- trol was distributed over all kinases and phosphatases. The biologically important conclusion is that oncogenes and tumor suppressor genes should be sought among all genes encoding kinases and all genes encoding phosphatases or regulating their expression levels, explaining why there are so many of these genes and inducing us to infer that cancer is a systems biology disease (Hornberg et al. 2006). At the time point in which the ultimate signal (Erk-PP in the example of the MAP kinase cascade) has first increased from zero to half its amplitude, the control by time is positive, and the above summation law implies that the total control exercised by the kinases on the signal strength exceeds the total control by the phosphatases. Indeed, early on in signal transduction the kinases should be more important than the phosphatases for the concentration of the sig- nal molecule. Although the example is one of signal transduction, similar considerations apply to meta- bolic and gene-expression networks, and the above may serve to convey that, contrarily to what is often stated, control analysis and the fundamental principles that it brings, are not limited to steady state. 6 PRINCIPLES OF REGULATION The magnitude of the flux control coefficient of a step or of the enzyme catalyzing that step, corresponds to a potential, i.e. to the effect on the flux that an activation of that step or enzyme might have. That magnitude does not indicate whether that step is ever activated either by the network itself, in self-regulation, or by an external influence, e.g. by an engineer (Westerhoff et al. 2009). Regulation coefficients have been introduced to indicate how, when a process is actually regulated, the organism regulates it. The alternatives are regulation through metabolic inter- actions, through single transduction interactions leading to covalent modification of the enzyme, and through gene expression. The gene-expression regulation coefficient has been
- 44. 7 Regulation versus control 33 defined as the change in enzyme concentration divided by the change in flux through the enzyme, i.e. more precisely by: Here ei is the concentration of the enzyme catalyzing the process vi. The rate of an enzyme catalyzed reaction can often be written as the product of three factors, i.e. the enzyme concen- tration, the fraction φa of the enzyme that is in the covalent modification state that is active catalytically, and a factor υm comprising the rate’s dependence on the concentrations of the substrates, the products, and the metabolic modifiers that are not binding covalently or stably. The metabolic and signal-transduction regulation coefficients are defined, respectively by: and Regulation is also subject to a general principle or law: The sum of gene-expression, meta- bolic, and signal-transduction regulation of a metabolic rate is always the same and equal to 1 (Ter Kuile and Westerhoff 2001): 7 REGULATION VERSUS CONTROL As discussed above, regulation differs from control. Yet, it would seem that there might be connections between the two concepts. We shall limit the discussion to linear metabolic pathways. Such a pathway has a single steady-state flux, which is equal to the steady-state rates of all the reactions in the pathway. If the third step of the pathway were completely rate limiting and its expression level would be activated by 30% then the flux would also go up by 30% making its hierarchical regulation coefficient equal to 1. However, if its control on the flux were 0.2 only, then its activation by 30%, in the absence of hierarchical regulation of any of the other enzymes, would increase the flux by 6% only, so that its hierarchical regulation coefficients would equal 5. This suggests that there is some sort of reciprocity between regula- tion and control. When hierarchical regulation involves more enzymes of the pathway, this reciprocity becomes pathway wide, hence again a systems property. For a linear pathway of n enzymes the reciprocity is given by the law: (3.11) ρi g = dlnei dlnvi (3.12) ρi m = dlnϑm,i dlnvi (3.13) ρi s = dlnϕa,i dlnvi (3.14) ρi g + ρi m + ρi s ≡ 1 (3.15) n i=1 CJ i ·ρi h ≡ 1
- 45. 34 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS Here the hierarchical regulation coefficient ρi h comprises both gene-expression and signal- transduction regulation: The proof is as follows: Consider a regulation that results in a change in flux through the enzyme, dlnvi. The increase in that flux may be because gene expression is increased resulting in more enzyme ei, because the altered levels of metabolites (x) have altered the activity of the enzyme, or because signal transduction has led to activation of the enzyme (dlnϕa,i) by cova- lent modification: With the above definition (Equation 3.11) the change in enzyme concentration relates to the change in flux through the enzyme by: The effect of that change in activity of enzyme i on the steady-state flux through the path- way is given by: Here the C refers to the metabolic flux control coefficient, not the hierarchical one; the metabolic pathway is allowed to relax, the gene-expression and the signal-transduction regu- lation are supposed to be fixed by the external world (Westerhoff 2008; Westerhoff et al. 2009). Taking into account all changes in all enzymes, the change in steady-state flux is: And relating the change in enzyme to the change in rate of the enzyme, and then using that flux equals rate, one obtains: Division by dlnJ yields the law we wanted to prove. This law implies that if there is only a single rate-limiting step in the pathway and the pathway is being regulated, the hierarchical regulation coefficient of that enzyme is always 1. It turns out that the classical paradigm of metabolic control and regulation where there was a single rate-limiting step, and where it was not even considered to make a distinction between flux-limiting step and regulated step, corresponds to one and the same special and probably (3.16) ρi h def = ρi g + ρi s (3.17) dlnvi = dlnei + ∂lnϑm,i ∂lnx · dlnx + dlnϕa,i (3.18) dlnei = ρi g · dlnvi (3.19) (dlnJ)as a consequence of the change in activity of ei = CJ ei ·(dlnei + dlnϕa,i) (3.20) dlnJ = n i=1 CJ i ·(dlnei + dlnϕa,i) (3.21) dlnJ = n i=1 CJ i · (ρi g + ρi s) · dlnvi = n i=1 CJ i · (ρi g + ρi s) · dlnJ
- 46. 8 Robustness and fragility and application to the cell cycle 35 rare case. When flux control is distributed and only one pathway step is regulated hierarchi- cally, this needs not be the most rate-limiting step and the regulation coefficient equals the inverse of the control coefficient, i.e. there is much hierarchical regulation if the regulated step has little flux control. Let us consider the example of a three step linear metabolic pathway where the first and the third step have flux control coefficients of 1/3 and 2/3, respectively, and the second step therefore a flux control coefficient of zero. The cell may decide to regulate only the first step in the pathway. This makes the hierarchical regulation coefficient of that enzyme equal 3 (Equation (15)), i.e. the cell will have to increase the concentration of enzyme three times as much as the percentage increase in flux it wishes to obtain. The fluxes through enzymes 2 and 3 would increase due to metabolic regulation only, i.e. the increase in concentration of enzyme 1 would lead to an increase in the concentration of its product, which as substrate of enzyme 2 then would push more flux through enzyme 2. In this example, the metabolic regulation coefficients of enzymes 2 and 3 are 1, while their hierarchical regulation coefficients both equal zero. In the same example, the metabolic regulation of enzyme 1 must be negative, its metabolic regulation coefficient equaling −2 (Equations 3.14 and 3.16). This reflects a strong inhibition by its product or by the substrate of the third enzyme through allosteric feedback regulation. Rossell et al. (2006) have observed such, perhaps nonintuitive aspects of regula- tion experimentally. It could be more efficient for the cell to increase the concentration of the third enzyme and not to regulate the first enzyme hierarchically; then for a 10% increase in flux it would only have to increase the concentration of enzyme 3 by 15, rather than 30%. In the latter case, enzymes 1 and 2 would be regulated metabolically, again with metabolic regulation coeffi- cients of 1. The principles of metabolic regulation can be generalized to branched pathways, but then the meaning of some of the hierarchical regulation coefficients is less obvious. 8 ROBUSTNESS AND FRAGILITY AND APPLICATION TO THE CELL CYCLE To survive evolution, living systems may not only require optimal performance in terms of growth rate, yield, or efficiency, they may also need to be robust against perturbations. Since living systems depend fundamentally on nonequilibrium processes (Westerhoff Van Dam 1987; Westerhoff et al. 2009) an important issue is the robustness of an organism to the sustained perturbation of any one such process. Quinton-Tulloch et al. (2013) defined the robustness of a steady-state biological function vis-à-vis the sustained perturbation of any of its processes, as the percentage change in the activity of that process that would compromise the function by 1% only. Such a robustness is 1 for a process in isolation. Quinton-Tulloch and colleagues then calculated the robustness coefficients for fluxes in some 25 realistic models of biochemical networks. They found that virtually all robustness coefficients were much higher than the in vitro number of 1. Csete and Doyle (2002) had considered robustness with respect to periodic perturbations at various frequencies and found total robustness, in the sense of robustness integrated over all frequencies, to be conserved; making a network more robust at one frequency should
- 47. 36 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS always reduce its robustness at different frequencies. Quinton-Tulloch et al. (2013) examined whether steady-state robustness is conserved over all processes, i.e. whether the sum of the robustness over all perturbed molecular processes in the system should always be the same. They showed that such a conservation of total robustness is not found. The implication is that by increasing the activity of a process and thereby increasing the robustness of a network function with respect to perturbations in that process, one may increase the total robustness of the system. Defining fragility as the inverse of robustness, i.e. the fragility coefficient as the percentage reduction in function for a 1% reduction in the activity of a process in the system, Quinton- Tulloch et al. (2013) found that total fragility is conserved and should equal 1 if the fragility of a flux is considered. They proved this by identifying this fragility coefficient with the flux control coefficient. We here illustrate this principle for a model of an important regulatory aspect of the yeast cell, i.e. the cell cycle. The implementation of Metabolic Control Analysis (MCA) to metabolic pathways at steady state has been frequent, successful and is well-known. MCA has also been applied to mostly metabolic oscillations, either forced or autonomous, with the yeast glycoly- sis oscillations synchronized by acetaldehyde as significant examples (e.g. Richard et al. 1993; Kholodenko et al. 1997; Danø et al. 2001; Reijenga et al. 2001, 2002, 2005; du Preez et al. 2012a, 2012b). The cell cycle may however be a more important oscillation, which is rarely seen as a limit cycle however. Some initial control analysis has been done, revealing again distributed control, but there has been little induction toward general principles of cell cycle. We will here briefly discuss possible developments around unsuspected relationships between robust- ness, fragility and time dependence. Figure 3.2 shows a diagram underlying our dynamic model of a part of the cell cycle of S. cerevisiae, where activation of various mitotic kinase/cyclin (Cdk1/Clb) complexes occurs between DNA duplication (S phase) and cell division (M phase). A kinetic model describing Cdk1/Clb dynamics over time was implemented, where each kinase complex activates the next one in a linear cascade (Barberis et al. 2012). Their activation (and inactivation) occurs in a temporal fashion, and a design principle underlying the oscillatory behavior of Clb waves has been proposed (Barberis 2012). Cdk1-Clb5,6 + Sic1 Cdk1-Clb5,6-Sic1 Cdk1-Clb3,4-Sic1 Cdk1-Clb1,2-Sic1 Cdk1-Clb1,2 + Sic1 Cdk1-Clb3,4 + Sic1 Clb5,6 Clb1,2 Clb3,4 FIGURE 3.2 Signaling network describing Cdk1/Clb regulation from S to M phase of the cell cycle.
- 48. 8 Robustness and fragility and application to the cell cycle 37 Figure 3.3 shows that the three couples of Clb cyclins (Clb5,6, Clb3,4, and Clb1,2) undergo waves with amplitudes at different times. We shall first focus on the Clb5/6 couple and on the onset and the decay of the peak of their level. Figure 3.2 shows that Clb5/6 has a maximum at t = 23 and that at t = 8 it is hallway reaching that maximum and at t = 31.5 it is again half- way down. We computed the time-control coefficient Tc at those times, and this amounted to 0.87 and −4.57, respectively. We also computed the robustness R (defined as the inverse of the time-control coefficients) of the amplitude of Clb5/6 at the two halfway time points. We first computed the robustness of the Clb5/6 amplitude exercised by all processes in the network when perturbed simultaneously and equally in the same direction. The corresponding robust- nesses were 1.14849 and 0.21881 (see Table 3.1). Quinton-Tulloch et al. (2013) identified the inverse of the robustness with fragility, which in turn is equal to the control coefficient. As a consequence the above (Equation 3.10): can be reformulated as: For this case of equal perturbations of all processes amounts to: And the same for the other time point analyzed. The last two columns in Table 3.1 confirms this computationally. For the onset of the peak the time-control coefficient is positive. Hence the positive robust- nesses must be smaller (typically those with respect to kinases perturbations) than the robust- nesses with respect to the phosphatases (which are not considered explicitly in the system yet). For the decay of the peak, the inverse should be true. (3.10) n j=1 CXk ej (t) = CXk t (t) (3.22) n j=1 1 ReXk ej (t) = CXk t (t) (3.23) n j=1 1 ℜXk total for equal(t 1 2on ) = CXk t (t 1 2on ) 0 10 20 30 40 50 60 0 0.3 0.6 0.9 1.2 Time Clb3,4 Clb5,6 Clb1,2 [Clb] FIGURE 3.3 Computational time course of Clb cyclins couples over time.
- 49. 38 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS 9 PERFECT ADAPTATION AND INTEGRAL CONTROL IN METABOLISM Biochemical reaction networks can exhibit properties similar to those of control system structures in control engineering, but are they identical? The robustness of cellular adapta- tion to environmental conditions is often related to negative feedback control structures. For example, robust adaptations in a bacterial chemotaxis signaling network, in mammalian iron and calcium homeostasis, and in yeast osmoregulation have been interpreted as integral feed- back control systems (Yi et al. 2000; El-Samad et al. 2002; Ni et al. 2009; Muzzey et al. 2009). A recent study identified the three different types of control structures used in control engi- neering, i.e. proportional, integral, and derivative feedback control, in regulations of energy metabolism (Cloutier and Wellstead 2010). In addition, specific nonlinear dynamics in signal- ing networks, such as oscillation or bi-stability, can be induced by positive feedback loops. Feed-forward control structures are also observed in gene regulatory networks (Mangan and Alon 2003), as well as in the regulation of glycolytic intermediates (Bali and Thomas 2001). Regulation in living cells tends to occur at multiple levels simultaneously with a hierarchi- cal structure (Westerhoff 2008). In a metabolic network the regulation of a reaction rate can be TABLE 3.1 Calculation of time-control coefficient and robustness for Clb cyclins couples. Clb5,6 α(5,6) β(5,6) Max [5,6] Time Max [5,6]/2 t1/2 α(5,6) Max [5,6] Time Max [5,6]/2 t1/2 β(5,6) 1,41473 23 0,707365 8 0,076988 1,41473 23 0,789371 31,5 0,11453 Clb3,4 α(3,4) β(3,4) Max [3,4] Time Max [3,4]/2 t1/2 α(3,4) Max [3,4] Time Max [3,4]/2 t1/2 β(3,4) 0,959239 30 0,4796195 19,5 0,023046 0,959239 30 0,60479 37 0,05489 Clb1,2 α(1,2) β(1,2) Max [1,2] Time Max [1,2]/2 t1/2 α(1,2) Max [1,2] Time Max [1,2]/2 t1/2 β(1,2) 1,1148 34 0,5574 27 0,094539 1,1148 34 0,780522 41,5 0,049 Tcα Tcβ Rα Rβ 1/Rα 1/Rβ Tcα(5,6) Tcβ(5,6) Rα(5,6) Rβ(5,6) Rα(5,6) Rβ(5,6) 0,87071 4,57023 1,14849 0,21881 0,87071 4,57023 Tcα(3,4) Tcβ(3,4) Rα(3,4) Rβ(3,4) Rα(3,4) Rβ(3,4) 0,937 3,358332 1,06723 0,29777 0,937 3,35833 Tcα(1,2) Tcβ(1,2) Rα(1,2) Rβ(1,2) Rα(1,2) Rβ(1,2) 4,57937 2,605393 0,21837 0,38382 4,57937 2,60539
- 50. 9 Perfect adaptation and integral control in metabolism 39 achieved by the modulation of (i) enzyme activity (through a substrate or product effect, through a different metabolite competing with the substrate for its binding site or through an allosteric effect), i.e. metabolic regulation, of (ii) enzyme covalent modification status as end- effect of a signal transduction pathway, or of (iii) enzyme concentration via gene expression, i.e. gene-expression regulation. Such multiple-level regulations correspond to different con- trol loops in a control system. This may ensure the robustness versus perturbations at various frequencies. In engineering, an airplane wing has to be robust at high frequencies of varia- tions of air pressures, as well as with respect to low frequency perturbations. In order to achieve this combined robustness, different control loops have to be put in place simultane- ously, although a trade-off limits what one can do, in the sense that increased robustness at one frequency comes at reduced robustness at a different frequency (Csete and Doyle 2002). In systems biology, this can be illustrated through the end product feedback regulations (Goelzer et al. 2008). If the flux demand on the end product module increases rapidly, the concentration of the end product decreases rapidly. Often as a result of the allosteric effect of the penultimate metabolite directly on the first enzyme, the activity of that first enzyme increase quickly too. This metabolic control of enzyme activity is a fast actuator of the system. However, if there is a further increase in the flux demand, the first enzyme may “lose” its regulatory capacity since its activity may be approaching its maximum capacity (kcat). At this stage, the system has a second “adaptation” which is slow (because the cell has to produce enzyme) but leads to increase in the concentration of the first enzyme, which then decreases the direct stimulation of the catalytic activity of the first enzyme. The regulation of the first enzyme is then bi-functional in dynamic terms (Csete and Doyle 2002): The metabolic regula- tion rapidly buffers against high frequency perturbations but possibly with small amplitude or capability, while the gene-expression regulation is slow to adapt but may be able to reject very large constant perturbations (Ter Kuile and Westerhoff 2001). When interpreting metabolic and gene-expression regulation separately as specific control system structures, we identify the former more as a “proportional control” action (El-Samad et al. 2002; Yi et al. 2000) with limited range, and the latter more as an “integral control” action with potentially a wider range and acting more slowly. Mechanisms of integral control can lead to zero steady-state errors of the “controlled variable,” which is not possible with pro- portional control mechanisms. In the latter case, the perturbation of the controlled variable has to persist for the regulation as the homeostatic regulation is proportional to the perturba- tion of the controlled variable (the error function). The mechanism that operates in the former case is known as “perfect adaptation” in biology when the network becomes completely robust to the environmental perturbations: here the regulation is proportional to the time integral of the error function, which persists when the error function has returned to zero. The proportional control can often provide fast control response but the corresponding adapta- tion would be imperfect with nonzero steady state errors. The control engineering interpretations may be mapped onto Metabolic Control Analysis (MCA) and Hierarchical Control Analysis (HCA) (Westerhoff et al. 1990, 2009), respectively. The relatively fast metabolic regulation (proportional control) is related to the direct “elastici- ties” of MCA, while the slow gene-expression regulation (integral control) corresponds to the indirect “elasticities” of HCA. Let us consider the example illustrated in Figure 3.4, which is a two-step pathway with intermediate ATP at an ADP concentration, [ATP] = C-[ADP] and with the gene expression of
- 51. 40 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS the first enzyme (E = Es) being increased in proportion to the concentration of ADP, which is a gene-expression regulation. The moiety conservation sum C is the sum of the concentra- tions of ATP and ADP and constant here because the reactions only convert the one into the other. The two-step pathway (s and d) represent supply and demand parts of a metabolic pathway (Hofmeyr 1995), and metabolic regulation is assumed to be part of these processes. The dynamics of ADP and enzyme E can be described by simple kinetics: where the degradation of E is assumed to be a mixture of zero and first order processes. The closed-loop control system structure of the pathway can be represented in Figure 3.5. From the control system diagram, it can be noted that the ADP concentration is the con- trolled variable; enzyme concentration E is a control output (the manipulation variable) of the (3.24) d[ADP] dt = −ks·E·[ADP] + kd·(C − [ADP]) (3.25) dE dt = ka·[ADP] − kb·E − k0 FIGURE 3.4 Illustration of ATP energy metabolism in a two-step pathway with gene-expression regulation. FIGURE 3.5 Control system structure of ATP energy metabolism.
- 52. 9 Perfect adaptation and integral control in metabolism 41 gene-expression regulation control loop. When the degradation of enzyme is only zero order in terms of E (with kb = 0), the gene-expression regulation becomes an ideal integral control loop, and the metabolic network can exhibit robust perfect adaptation to the external or para- metric perturbations: Equation 3.25 set to zero then determines the steady level of ADP and Equation 3.24 set to zero the level of the enzyme E. This only happens when the cell popula- tion is in stationary phase, because in a dividing cell population, the enzyme level per cell would decay in a quasi first-order process. The zero order degradation rate k0 can be treated as a reference signal to the system. The metabolic regulation is included as a part of the ADP kinetic process. Such a control engineering insight is consistent with classical kinetic analysis and meta- bolic control analysis. By considering a small perturbation of kd from its steady-state value (δkd with δ denoting the small deviation), and reformulating the kinetics of dADP/dt and dE/dt, we have where the subscript ss denotes the steady state value. We recognize on the right-hand side first a proportional response term, then an integral response term, and then the perturbation term. The proportional response corresponds to the direct “elasticity” of the supply and demand reactions with respect to ADP, which is a metabolic and instantaneous regulation. The integral response is related to the protein synthesis and degradation and thus to the gene- expression regulation. If kb = 0, the second term corresponds to an ideal integral action. By further removing the time dependence of the change in ADP using the steady state condi- tions, the classical metabolic control coefficients, i.e. the control of the enzyme level by the demand reaction, and the flux control coefficient, can be obtained: Both the control of enzyme level and the control of demand flux by the perturbation are equal to 1 minus a hyperbolic function of kb. For an ideal integral control scenario with kb = 0 the enzyme concentration E perfectly tracks the activity of the pathway degrading ATP, and CE kd = 1. More importantly, the pathway flux perfectly tracks the perturbation in the demand flux and CJ kd = 1. The control of kd on ADP is zero (Using Equation 3.25 with zero change in enzyme and zero kb). This is the case of robust perfect adaptation. For other cases when kb ≠ 0, the adaptation of the pathway to the perturbation will not be perfect. Also the robustness coefficient as defined by Quinton-Tulloch et al. (2013) can be expressed (3.26) dδADP dt = −(ks · Ess + kd) · δADP − ks · ADPss · ∞ 0 (ka · δADP − kb · δE) · dt + (C − ADP) · δkd (3.27) CE kd = δ ln E δ ln kd = 1 − 1 1 + ks·([ADP]ss)2 kd·C ·ka kb CJ kd = δ ln J δ ln kd = 1 − [ADP]ss/C 1 + ks·([ADP]ss)2 kd·C ·ka kb (3.28) ℜADP kd = 1 ∂ ln[ADP]ss ∂ ln kd = kd · C + ks · ([ADP]ss)2 · ka kb (C − [ADP]ss) · kd
- 53. 42 3. UNDERSTANDING PRINCIPLES OF THE DYNAMIC BIOCHEMICAL NETWORKS Only when kb = 0, the pathway exhibits infinite robustness (ℜADP kd = ∞) to the external or parametric perturbation. This example shows the consistency of control engineering and clas- sical metabolic control analysis in understanding the adaptation of a metabolic pathway under both gene-expression and metabolic regulation. Acknowledgments This study was supported by the Netherlands Organization for Scientific Research NWO through the MOSES- SysMO grant, as well as by the BBSRC/EPSRC’s finding of the Manchester Centre for Integrative Systems Biology (BB/F003528/1, BB/C008219/1), BBSRC’s MOSES-SysMO project (BB/F003528/1), various other BBSRC projects (BB/G530225/1, BB/I004696/1, BB/I017186/1, BB/I00470X/1, BB/I004688/1, BB/J500422/1, BB/J003883/1, BB/ J0200601/1), and the EU-FP7 projects SYNPOL, EC-MOAN, UNICELLSYS, ITFoM, and BioSim. References Bali, M., and Thomas, S. R. (2001). A modelling study of feed-forward activation in human erythrocyte glycolysis. C. R. Acad. Sci. III 324:185–199. Barberis, M., Linke, C., Adrover, M. À., González-Novo, A., Lehrach, H., Krobitsch, S., Posas, F., and Klipp, E. (2012). Sic1 plays a role in timing and oscillatory behaviour of B-type cyclins. Biotechnol. Adv. 30:108–130. Barberis, M. (2012). Sic1 as a timer of Clb cyclin waves in the yeast cell cycle–design principle of not just an inhibitor. FEBS J. 279:3386–3410. Burns, J. A., Cornish-Bowden, A., Groen, A. K., Heinrich, R., Kacser, H., Porteous, J. W., Rapoport, S. M., Rapoport, T. A., Stucki, J. W., Tager, J. M., Wanders, R. J. A., and Westerhoff, H. V. (1985). Control analysis of metabolic sys- tems. Trends Biochem. Sci. 10:16. Cloutier, M., and Wellstead, P. (2010). The control systems structures of energy metabolism. J. R. Soc. Interface 7:651–665. Cooper, V. S., and Lenski, R. E. (2000). The population genetics of ecological specialization in evolving Escherichia coli populations. Nature 407:736–739. Csete, M. E., and Doyle, J. (2002). Reverse engineering of biological complexity. Science 295:1664–1669. Danø, S., Hynne, F., De Monte, S., d’Ovidio, F., Sørensen, P. G., and Westerhoff, H. W. (2001). Synchronization of glycolytic oscillations in a yeast cell population. Faraday Discuss. 120:261–276. Diaz-Ruiz, R., Uribe-Carvajal, S., Devin, A., and Rigoulet, M. (2009). Tumor cell energy metabolism and its common features with yeast metabolism. Biochim. Biophys. Acta 1796:252–265. du Preez, F. B., van Niekerk, D. D., Kooi, B., Rohwer, J. M., and Snoep, J. L. (2012a). From steady-state to synchronized yeast glycolytic oscillations I: model construction. FEBS J. 279:2810–2822. du Preez, F. B., van Niekerk, D. D., and Snoep, J. L. (2012b). From steady-state to synchronized yeast glycolytic oscil- lations II: model validation. FEBS J. 279:2823–2836. El-Samad, H., Goff, J. P., and Khammash, M. (2002). Calcium homeostasis and parturient hypocalcemia: an integral feedback perspective. J. Theor. Biol. 214:17–29. Gatenby, R. A., and Gawlinski, E. T. (1996). A reaction-diffusion model of cancer invasion. Cancer Res. 56:5745–5753. Goelzer, A., Briki, F. B., Marin-Verstraete, I., Noirot, P., Bessieres, P., Aymerich, S., and Fromion, V. (2008). Reconstruction and analysis of the genetic and metabolic regulatory networks of the central metabolism of Bacillus subtilis. BMC Syst. Biol. 2:20. Herrgård, M. J., Swainston, N., Dobson, P., Dunn, W. B., Arga, K. Y., Arvas, M., Blüthgen, N., Borger, S., Costenoble, E. R., Heinemann, M., Hucka, M., Li, P., Liebermeister, W., Mo, M. L., Oliveira, A. P., Petranovic, D., Pettifer, S., Simeonidis, E., Smallbone, K., Spasi, I., Weichart, D., Brent, R., Broomhead, D. S., Westerhoff, H. V., Kirdar, B., Penttilä, M., Klipp, E., Paton, N., Palsson, B. Ø., Sauer, U., Oliver, S. G., Mendes, P., Nielsen, J., and Kell, D. B. (2008). A consensus yeast metabolic network obtained from a community approach to systems biology. Nat. Biotechnol. 26:1155–1160. Hofmeyr, J.-H.S. (1995). Metabolic regulation: a control analytic perspective. J. Bioenerg. Biomembr. 27:479–490. Holzhütter, H. G. (2004). The principle of flux minimization and its application to estimate stationary fluxes in meta- bolic networks. Eur. J. Biochem. 271:2905–2922.
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- 56. 2nd BATT. M.I. 3rd BATT. M.I. 4th BATT. M.I. A company was raised from the 1st Battalion in South Africa before the war; it fought at Talana Hill (October the 20th, 1899), was in the Defence of Ladysmith, and later with Buller’s army until it arrived at Lydenburg in October, 1900. After this it was continually engaged in the Eastern Transvaal, until it joined the 25th Mounted Infantry in October, 1901 (see below). This Company lost twenty-five killed and thirty-three wounded during the war. A Company was raised from the 2nd Battalion upon its arrival in Natal, which was left outside Ladysmith, and, joining Buller’s army on the Tugela, took part in the campaign for the Relief of Ladysmith with Dundonald’s Mounted Troops. After the relief this Company joined Gough’s Mounted Infantry, and accompanied Buller’s army up to Lydenburg, being subsequently engaged in the Eastern Transvaal, Zululand, and the Orange River Colony until the end of the war. The wastage in personnel was such that only two officers and twenty-nine others of the original company then remained, but the fact that twenty per cent. of the original horses, received in October, 1899, were still doing duty, constituted a notable record in horse management. The 3rd Battalion contributed one section to “The Rifles’ Company” of the 1st M.I. (Vide 4th Battalion M.I.). A second section, formed in December, 1899, fought with Dundonald’s mounted troops in the Relief of Ladysmith, subsequently joining Gough’s M.I. at Blood River Poort, where it was severely handled and its commander, Mildmay, was killed. This section, in October, 1901, was united with a third section raised in 1900, and joined the 25th M.I. in October, 1901 (see below), when the strength was raised to a full company. The 4th Battalion contributed a section to “The Rifles’ Company,” under Captain Dewar, which, together with the section of the 3rd Battalion, and the two sections from the 3rd and 4th Battalions Rifle Brigade, formed one of the four companies composing the celebrated 1st M.I., organised and trained at Aldershot under Lieutenant-Colonel E. A. H. Alderson before the war. The “Rifles Company” was temporarily detached, and, landing at Port Elizabeth in November, 1899, joined the force under Major-General Sir William Gatacre, which was
- 57. 25th (THE KING’S ROYAL RIFLE CORPS) defeated at Stormberg on December the 12th, where it was mentioned for its gallant conduct in covering the retreat. The Company was then attached to French’s Cavalry Division, and was at the battle of Paardeburg, where Captain Dewar was killed, and was also present at the surrender of Cronje on the 27th of February, Majuba Day. It then rejoined the 1st M.I.; and took part in the battles of Poplar Grove and Driefontein, and the entry into Bloemfontein (10th of March). It was at the surprise of Broadwood’s Calvary Brigade at Sannah’s Post (31st of March), where it behaved with conspicuous gallantry, and it was at the relief of Wepener, and in the fighting near Thabanchu. The 1st M.I. were then allotted to Alderson’s Brigade with Hutton’s[78] Mounted Troops, and took part in Lord Roberts’ advance upon Pretoria on the 2nd May. The Company, therefore, was present in the actions of Brandfort, Vet River, Sand River, Kroonstadt, the Vaal River (27th of May), the battle of Doornkop, near Johannesburg (28th–29th of May), the actions at Kalkhoevel Defile, Six Mile Spruit (4th of June), and the entry into Pretoria (5th of June). It was similarly engaged at the battle of Diamond Hill (11th of June); in the fighting south-east of Pretoria and at the action of Rietvlei (July the 16th); in the advance to and operations round Middelburg; in the battle of Belfast (24th of August, 1900); and in the march east from Dalmanutha, including the assault of the almost impregnable position of Kaapsche Hoop during the night of the 12th–13th of September. From this time till the end of the war this Company was continually marching and fighting in the Orange River Colony and Cape Colony, pursuing De Wet, back again in the Transvaal, in countless forays and skirmishes, in the saddle night and day. When peace was declared it was at Vereeniging, whence it marched to Harrismith, and was absorbed into the Rifle Battalion of M.I. formed at that place. The 4th Battalion also sent out two complete companies from Cork early in 1901, which were employed in the Transvaal, and subsequently joined the 25th M.I. in October of that year (see below). On October the 18th, 1901, a complete Battalion of Mounted Infantry[79] was
- 58. MOUNTED INFANTRY BATTALION. formed from the Regiment—an unique distinction—and consisted of:— No. 1 Company 1st Battalion. No. 2 Company 4th Battalion. No. 3 Company 3rd Battalion. No. 4 Company 4th Battalion. The Battalion was concentrated at Middelburg in the Transvaal, and was placed under the command of Major C. L. E. Robertson- Eustace[80] until January, 1902, when he was succeeded by Major W. S. Kays.[81] The Battalion thus organised was composed of officers and riflemen who had been in the field from the beginning of the war, and were therefore tried and experienced soldiers. It joined Benson’s[82] column at Middelburg, a column of which it was said that no Dutchman dared sleep within thirty miles of its bivouac. The ceaseless activity and success of Benson eventually decided Louis Botha, the Boer Commander-in-Chief, to make a determined attempt to destroy his force. To achieve this purpose he collected nearly 2000 men, and by a skilful combination of his troops attacked the column while on the march near Bakenlaagte upon the 30th of October. By a rapid charge he overwhelmed the rear guard, captured two guns, killed Benson, and surrounded the column, but was eventually beaten off. The 25th M.I. fought with a stubborn courage, and by their sturdy gallantry kept the Boers at bay and gloriously upheld the traditions of the Regiment, losing in the action eleven men killed, five officers and forty-five men wounded. Thus—stoutly fought out on both sides by mounted troops of this especial type—ended a fight which has been described as unique in the annals of war.[83] The spirit of the Riflemen will best be understood from the lips of one of the wounded in this gallant fight, who remarked that “they were content if they had done their duty, and felt rewarded if their Regiment thought well of them.” The Mounted Infantry Battalion of the Regiment ended its short but brilliant career by taking part in all the great “drives” in the E. Transvaal and N.E. of the Orange Free State, and was finally at Greylingstad when peace was declared on the 1st June, 1902.
- 59. RIFLE DEPOT. Rifle Depot. The Depot, under the command of Colonel Horatio Mends, was at Gosport throughout the war. A narrative of the work of the Regiment at this strenuous period would not be complete without grateful reference to the splendid service of administration, training, and equipment, so devotedly performed by the Colonel Commandant, his Staff, and the Company officers generally of the Rifle Depot. The Adjutant was five times changed, but the Quarter-Master, Major Riley,[84] remained constant to his difficult duties throughout the whole of this trying ordeal. It is stated that 4470 recruits joined the Depot, were trained, and passed to the various Battalions, while many thousands of Reservists were mobilized, equipped, clothed, and drafted for duty. The work of discharge at the end of the war was not less severe, but there is no record of failure or of breakdown, and the success of the admirable system of administration was universally acknowledged.[85] The Rifle Depot was moved back to Winchester on the 29th of March, 1903, after nine years of exile at Gosport caused by the re- building of the Barracks which had been destroyed by fire.
- 60. PART IV.
- 61. A Retrospect. The preceding pages will have shown that the Regiment from its inception has possessed certain distinctive characteristics which are pre-eminently those required for making Light Infantry and Riflemen of the best type. Raised in 1755, the Regiment, inspired by the genius of Henry Bouquet, early displayed that strong individuality, that self-reliant courage, and that ready initiative coupled with steady discipline, which won from the intrepid Wolfe himself the proud motto of Celer et Audax. In 1797, under the experienced command of Baron de Rottenburg, the famous 5th Battalion (Rifles) was raised as a special type of Light Troops. Thus the 5th Battalion of the Regiment, the first Rifle Corps of the British Army, revived those special qualities of the Royal Americans which had rendered the Regiment so renowned in its earlier years, and were destined to win imperishable fame throughout the Peninsular War. After a long interval of peace the Regiment from 1836 to 1854 received a similar impetus at the hands of Molyneux and Dundas, and reaped a rich harvest of lasting honour and glory upon the Delhi Ridge by displaying the same supremely valuable characteristics which had distinguished it in America and in Spain. Again, from 1861–1873, under Hawley’s commanding influence and inspiring skill, the Regiment, through the 4th Battalion, opened up a more rapid and elastic system of drill and tactics, a more intelligent treatment of the soldier, and the betterment of his life in barracks, of which the good effects are felt to-day not only in the Regiment but in the Army at large. The qualities thus maintained for a century and a half, have borne in later years abundant fruit, of which the stubborn courage at the Ingogo fight, the calm discipline of the Warren Hastings, the eager valour of Talana Hill, and the impetuous assault up the slopes of the Twin Peaks are glorious examples.
- 62. To the same special qualities was due the inspiration which created the Mounted Infantry as a portion of the British Army, and it is to the officers and men of the 60th that the inception and success of that powerful arm is largely due. Let the Riflemen of to-day, who read the deeds of their gallant comrades of the past, remember that if they are to maintain the traditions and increase still more the reputation of the famous Corps to which they belong, it can only be by cultivating the same spirit of ready self-sacrifice and unsparing devotion to duty, and by developing the same prompt initiative, steady discipline, and unflinching courage, which have ever been the secret of the Regiment’s success. Let each Rifleman also recollect that a distinguished Past is rather a reproach than a glory unless maintained by an equally distinguished Present, and developed, if possible, by an even more distinguished future. MAP IV SOUTH AFRICA Illustrating the area of Operations referred to in Part III, Sections 7 and 10,
- 63. also upon Inset map, Part III, Section 8. Stanford’s Geogl . Estabt ., London. 1. Afterwards Brigadier-General Bouquet. Born 1719, died 1765. The victor of Bushey Run. A brilliant officer, of the highest capacity as a leader and administrator. It has been said that by his untimely death Great Britain lost a general whose presence might well have caused the American War of Independence to assume a different aspect. For biographical sketch vide Regimental Chronicle, 1910. 2. General James Abercromby, Colonel-in-Chief, 1757–1758. 3. Afterwards Lieut.-General Sir Frederick Haldimand. Born 1718, died 1791. Commander-in-Chief in North America, and Governor of Quebec—a distinguished soldier-statesman. 4. Afterwards Major-General John Bradstreet. Born 1710, died 1774; a successful leader of irregular troops. 5. Afterwards Major-General. Born 1723, died 1786; dangerously wounded in July, 1759, above Quebec; the victor of Savannah, 1779, and a distinguished soldier. 6. Afterwards Field Marshal Sir Jeffery Amherst, Baron Amherst, Colonel-in-Chief, 1758–1797. 7. The Grenadier Companies also of the 2nd and 3rd Battalions were included in the six companies composing the Louisberg Grenadiers, which occupied the place of honor in the front line. 8. General William Haviland was Colonel Commandant in 1761– 1762. 9. Lieut.-Colonel Marc Prevost, born 1736, died 1785, youngest brother of General Augustine Prevost—a brilliant and most promising officer, who succumbed to the effect of his wounds.
- 64. 10. Frederick, Duke of York, was the second son of George III, and brother of George IV and William IV. 11. Afterwards Lieutenant-General. Born 1760, died 1832. He commanded the 5th Battalion, 1797–1808. He afterwards served as Major-General commanding in Lower Canada, 1810–1815, during the American War, 1812–13. 12. Regulations for the Exercise of Riflemen and Light Infantry and Instructions for their conduct in the Field, with diagrams, published with a Memo, dated Horse Guards, August 1st, 1798. Copies of the editions 1808 and 1812 will be found in the Library, Royal United Service Institution, Whitehall. 13. Afterwards General Sir William Gabriel Davy, C.B., K.C.H., Colonel Commandant, 60th Rifles, 1842–1856. He succeeded Baron de Rottenburg in command of the 5th Battalion in 1808. 14. Formed in 1800, and now The Rifle Brigade. 15. The Battalion was especially mentioned in Wellesley’s despatch. 16. Formerly a Captain in the 60th. 17. Formerly Major in the 4th Battalion 60th. 18. Afterwards General the Earl of Hopetoun, G.C.B., Colonel- Commandant 6th Battalion 60th. 19. Afterwards Major-General Sir William Williams, K.C.B., K.T.S., died 1832. 20. Afterwards General Viscount Beresford, G.C.B., G.C.H., Colonel- in-Chief of the 60th Rifles, 1852–54. 21. Afterwards Field-Marshal Sir John Foster Fitzgerald, G.C.B. Born 1786, died 1877, aged 91. 22. Afterwards Colonel and C.B., died 1861.
- 65. 23. Afterwards Colonel and C.B., died 1848. 24. Afterwards Lieut.-General Sir James Holmes Schoedde, K.C.B., who received thirteen clasps with his war medal. Born 1786, died 1861. Major-Generals Sir Henry Clinton, Sir George Murray, and Sir James Kampt, Colonels Commandant of the Regiment, also served with distinction. 25. His Royal Highness’s sword and belts were presented to the officers of the 1st Battalion by H.M. King George IV, and are now in the Officers’ Mess. 26. The seventh son of George III and the Father of the late Field- Marshal H.R.H. George Duke of Cambridge, Colonel-in-Chief, 1869– 1904. 27. 3rd son of 2nd Earl of Sefton. Born 27th August, 1800; died 1841. 28. Afterwards General Viscount Melville, G.C.B., Colonel Commandant 1864–1875. 29. Afterwards Field-Marshal Viscount Gough, K.P., G.C.B., Colonel- in-Chief 1854–1869. 30. Afterwards Major-General Sir John Jones, K.C.B. 31. Colonel Dunbar Douglas Muter, who greatly distinguished himself, obtaining two brevets during the siege and subsequent operations. He was afterwards a Military Knight of Windsor; and died in 1909. 32. Governor-General’s despatch, London Gazette, May 18th, 1860, upon the departure of the Regiment from India. 33. Now the 2nd King Edward’s Own Gurkha Rifles (the Sirmoor Rifles). It is stated of this gallant Regiment that, when asked what reward they would like, they begged for and were granted the red facings of the 60th to be added to their Rifle uniform.
- 66. 34. Despatch, General Sir Archdale Wilson, 22nd September, 1857. 35. London Gazette, May 18th, 1860. 36. Afterwards Colonel and C.B. 37. Afterwards Lieut.-General Hawley, C.B., Colonel Commandant, 1890–98, vide Biographical Sketch, Regimental Chronicle, 1909. 38. Afterwards General Right Hon. Sir Redvers Buller, P.C., V.C., G.C.B., G.C.M.G., Colonel Commandant, 1895–1908. Born December 7th 1839, died June 2nd, 1908. His qualities as a distinguished soldier are well summed up by the inscription upon his Memorial Tomb recently erected in Winchester Cathedral, “A Great Leader—Beloved by his Men.” Vide Biographical Sketch, Regimental Chronicle, 1908, p. 157. 39. Now Field-Marshal Right Hon. F. W. Lord Grenfell, P.C., G.C.B., G.C.M.G., Colonel Commandant, 1898. Born April 29th, 1841. 40. H.R.H. George Duke of Cambridge died upon the 17th March, 1904, and was succeeded as Colonel-in-Chief by General H.R.H. the Prince of Wales, now His Majesty George V. 41. Afterwards Lieut.-General Feilden, C.M.G., died 1895. 42. Now Field-Marshal Viscount Wolseley, K.P., etc. 43. Now Field-Marshal Earl Roberts, K.G., V.C., etc., whose only son, Lieut. the Hon. Frederick Roberts, V.C., was killed at the battle of Colenso, December 15th, 1899, when an officer of the Regiment, and serving as A.D.C. to Sir Redvers Buller. 44. Now Colonel Sir Arthur Davidson, K.C.B., K.C.V.O., Equerry to H.M. Queen Alexandra. 45. Now Major-General Sir Wykeham Leigh-Pemberton, K.C.B., Colonel Commandant, 1906. Born 4th December, 1833.
- 67. 46. Afterwards Lieut.-Colonel Northey, mortally wounded at the Battle of Gingihlovo, Zulu War, April 2nd, 1879. 47. Now Major-General. 48. Now Major-General Sir Cromer Ashburnham, K.C.B., Colonel Commandant, 1907. Born 13th September, 1831. He succeeded Colonel Leigh-Pemberton, and commanded the 3rd Battalion throughout three campaigns, namely, Boer War, 1881; Egypt, 1882; Suakim, 1884, with conspicuous success, and was popularly known among his men as the “Lion of the Ingogo.” 49. Despatch, Mount Prospect, February 12th, 1881, para. 20. 50. Afterwards Colonel and C.B. 51. Afterwards General Right Hon. Sir Redvers Buller, vide p. 40 note. 52. Captain Hutton, now Lieut.-General Sir Edward Hutton, K.C.M.G., C.B. Colonel Commandant, 1908. Born December 6th, 1848. 53. Vide “Cool Courage,” an episode of the Egyptian War, 1882— Regimental Chronicle, 1908. 54. Now Major-General R. S. R. Fetherstonhaugh, C.B. 55. Afterwards Lieutenant-Colonel Berkeley Pigott, C.B., D.S.O., 21st Lancers. 56. W. Pitcairn Campbell, P. S. Marling, A. Miles, R. L. Bower, and two officers of The Rifle Brigade, namely, W. M. Sherston and Hon. H. Hardinge. 57. Afterwards General Sir Baker Russell, G.C.B., K.C.M.G., etc., a well-known Cavalry General and leader of men. Died November, 1911. 58. “Times” History of the War, Vol. II, p. 31.
- 68. 59. Afterwards C.B. 60. Now Lieut.-Colonel the Hon. Keith Turnour-Fetherstonhaugh, of Up Park, Petersfield. 61. Afterwards Colonel and C.B. 62. Now Brigadier-General and C.B. 63. Now Major-General and C.B. 64. Vide Regimental Chronicle, 1909, p. 60. 65. Special Army Order, March 13th, 1897. 66. Promoted Colonel for his conduct, and was selected for Staff employment as Chief Staff Officer in Egypt, where he was accidentally killed upon the 31st July, 1902. 67. Field-Marshal Viscount Wolseley. 68. Vide Official History of the War, Vol. I, pp. 131–136. 69. Now Major-General, C.B., and lately A.D.C. to the King. 70. Now Brigadier-General, C.B., C.M.G., M.V.O., D.S.O. 71. Vide Official History of the South African War, Vol. I, pp. 398– 9. 72. Now Brigadier-General and C.B. 73. Vide “Times” History of the South African War, Vol. III, p. 324. 74. Vide Official History of the South African War, Vol. I, pp. 476–484. 75. Now Colonel, C.B.
- 69. 76. Now Colonel, C.M.G., and A.D.C. to the King. 77. Two officers died on the voyage out. 78. Vide note p. 52. 79. For a more complete account, vide Regimental Chronicle, 1902, p. 94. 80. Afterwards D.S.O. This promising officer died suddenly at Cairo, October 4th, 1908. 81. Now Colonel. 82. Colonel G. E. Benson, R.A., a leader of much distinction and initiative. 83. Vide “Times” History of the War, Vol. V. 84. Major T. M. Riley. Died 28th February, 1908. Vide Regimental Chronicle, 1907, p. 115. 85. Vide Regimental Chronicle, 1903, pp. 202–207.
- 71. TRANSCRIBER’S NOTES 1. Silently corrected typographical errors. 2. Retained anachronistic and non-standard spellings as printed.
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