Noise in multiple sclerosis: unwanted and necessary

NEUROLOGICAL PROGRESS
Noise in multiple sclerosis: unwanted and necessary
Isabella Bordi1
, Vito A. G. Ricigliano2,3
, Renato Umeton2
, Giovanni Ristori2
, Francesca Grassi4
,
Andrea Crisanti1
, Alfonso Sutera1
& Marco Salvetti2
1
Department of Physics, Sapienza University of Rome, Rome, Italy
2
Neurology and Department of Neurosciences, Mental Health and Sensory Organs (NESMOS), Centre for Experimental Neurological Therapies
(CENTERS), Sapienza University of Rome, Rome, Italy
3
Neuroimmunology Unit, Fondazione Santa Lucia, (I.R.C.C.S.), Rome, Italy
4
Department of Physiology and Pharmacology, Sapienza University of Rome, Rome, Italy
Correspondence
Marco Salvetti, Neurology and Department of
Neurosciences, Mental Health and Sensory
Organs (NESMOS), Centre for Experimental
Neurological Therapies (CENTERS),
Sapienza University of Rome, Rome, Italy.
Tel: +39 0633775994;
Fax: +39 0633775900;
E-mail: marco.salvetti@uniroma1.it
Funding Information
This work was supported by Fondazione
Italiana Sclerosi Multipla (FISM).
Received: 3 April 2014; Revised: 12 May
2014; Accepted: 17 May 2014
Annals of Clinical and Translational
Neurology 2014; 1(7): 502–511
doi: 10.1002/acn3.72
Abstract
As our knowledge about the etiology of multiple sclerosis (MS) increases, deter-
ministic paradigms appear insufficient to describe the pathogenesis of the dis-
ease, and the impression is that stochastic phenomena (i.e. random events not
necessarily resulting in disease in all individuals) may contribute to the develop-
ment of MS. However, sources and mechanisms of stochastic behavior have not
been investigated and there is no proposed framework to incorporate nondeter-
ministic processes into disease biology. In this report, we will first describe
analogies between physics of nonlinear systems and cell biology, showing how
small-scale random perturbations can impact on large-scale phenomena, includ-
ing cell function. We will then review growing and solid evidence showing that
stochastic gene expression (or gene expression “noise”) can be a driver of phe-
notypic variation. Moreover, we will describe new methods that open unprece-
dented opportunities for the study of such phenomena in patients and the
impact of this information on our understanding of MS course and therapy.
Introduction
This place is a mystery Daniel, a sanctuary. Each book, each
one that you see, has a soul. The soul of who has written it
and the soul of those that have read it, experienced it, and
dreamed with it. Each time that a book changes hands, each
time that someone takes a look at its pages, his spirit grows
and becomes stronger.
La sombra del viento
Carlos Ruiz Zafon
Broadly speaking, infectious and mendelian diseases
originate from a perturbation which is traceable in most
cases. In other terms, the outcome (disease) is a function of
the initial condition (pathogen invasion or gene mutation).
This knowledge stems from decades of research, full of
old and recent successes, that have to some extent framed
our mind to think that, for each disease, initiating events
or a confluence of initiating events should be identifiable.
It is therefore not surprising that a similar attitude has
influenced also etiological research in multifactorial dis-
eases, including multiple sclerosis (MS). After decades of
studies on the heritable and nonheritable causes of MS, it
seems that something is perpetually missing.1
Large gen-
ome-wide association studies (GWAS) and prospective
surveys on environmental risk factors have unequivocally
identified elements associated with the disease. Nonethe-
less, these associations are neither sufficient nor necessary
for the development of the disease and for its prediction2
(including familial cases3–5
). The prevailing opinion is
that there is a big gap of knowledge that someday will be
filled, thanks to the identification of many common (or
few rare) variants of small (or large) effect, gene–gene, or
gene–environment interactions among others.6–10
This is
a strictly deterministic view: given a cause, the same effect
(MS, for instance) invariably results. Moreover, a given
effect always stems from the same set of causes. Thus, in
a largely reductionistic frame, the medical/scientific prob-
502 ª 2014 The Authors. Annals of Clinical and Translational Neurology published by Wiley Periodicals, Inc on behalf of American Neurological Association.
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and
distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

lem becomes finding the function that connects the right
set of initial conditions (yet unidentified, in some cases)
to the pathology.
However, the available information is already enor-
mous and offers various interpretative opportunities.11–15
Insofar as it is possible that eventually the key heritable
or nonheritable factor(s) will show up, it is somehow
peculiar that, in many years, we have been able to identify
many subtle variations while keeping on missing the raf-
ters we might have had in our eyes. Recently, similar con-
siderations prompted some reflection about the
inadequacy of transferring, as such, the deterministic
approach that applies for infectious and genetic diseases
to complex traits.2,15
So far, it is unclear which processes
may substitute for these paradigms, or flank them in
shaping a complete picture of disease etiology.
Here, in an attempt to take a further step, and suggest a
new framework to interpret events that may lead to the
disease, we will first discuss the limits of a strictly deter-
ministic view of the etiology of multifactorial diseases,
recalling that the behavior of complex physical systems
(including biological ones) can be significantly modified
by small random perturbations (or “noise”). We will then
review evidence suggesting that a major nondeterministic
component of phenotypic variation (which can include
the occurrence of diseases) is stochastic gene expression
(or gene expression “noise”), which, along with time, may
be a necessary component for the development of MS.
Finally, we will discuss how this information may impact
the studies on disease etiology, proposing a mechanistic
model in which noise, superimposed onto a system moving
on an energy landscape with many minima (multi-minima
landscape), well describes erratic oscillations between
relapses and remissions clinically observed in several indi-
vidual patients in the initial phases of MS. In particular, the
model integrates “noise” and time with the genetic and
environmental risk, in a process that can induce phenotypic
changes, including disease, also in the presence of heritable
and nonheritable factors that mistakenly appear too weak.
Instability of Complex Systems
In this study, we refer to nonlinear systems (where the
ratio between the output and the input is not constant)
that have multiple steady states, associated with energy
minima (multi-minima landscape). Energy barriers, corre-
sponding to energy maxima, separate the minima, so that,
in the absence of external energy inputs, the system settles
down in a minimum. Extremely different steady states
can be reached starting from relatively similar initial con-
ditions: two water drops falling few millimeters apart at a
watershed could end their course into different Oceans
(Fig. 1). In the absence of external energy inputs, this
disproportion in size between “causes” (small distance
between drops) and “effects” (different terminal Oceans)
may be fully predictable, although impressive. If energy to
overcome the barriers is available, transitions between
states are possible. To stay with our example, water can
be pumped upwards and allowed to flow on the other
side of the mountain. For physical systems, it is known
that small random forces (noise) can occasionally sum up
and provide this energy. In a system with more than one
steady state, noise can induce transitions among different
steady states (see Appendix). The theory of Earth’s cli-
mate is an example: climate changes that induce glacia-
tion cycles are negligible if compared to the temperature
variations that accompany the shift from a temperate cli-
mate to an ice-covered Earth. It is the cooperative effect
of small-scale stochastic perturbations and periodic for-
cing that amplifies the climate response.16–19
Obviously, the fact that the fate of nonlinear systems
can be influenced by small random perturbations results
into nondeterministic behavior: the state finally attained
depends on noise, in addition to the initial conditions.
In medical conditions, behaviors similar to those
observed for stochastic nonlinear systems manifest already
in diseases whose pathogenesis may be less “complex”
compared to MS. For instance, embolism that can be a
casual response to normally distributed liability traits such
as dyslipidemia or hypertension. Similarly, nonlinear
feed-forward processes are involved in distinguishing
between lethality and mild disease in influenza infection.20
If stochastic and/or nonlinear pathogenetic events play a
role in diseases with a relatively “simple” pathogenesis,
even more so they should be considered as inescapable
components of the mechanisms that lead to the
Figure 1. A nonlinear system with two energy minima (striped and
gray Oceans) separated by a barrier (energy maximum, mountain
peak). Minimal differences in the initial conditions (where the water
drops fall) will determine completely different outcomes (the Ocean
into which a water drop ends).
ª 2014 The Authors. Annals of Clinical and Translational Neurology published by Wiley Periodicals, Inc on behalf of American Neurological Association. 503
I. Bordi et al. Gene Expression Noise in Multiple Sclerosis

development of conditions such as MS. The attention to
such processes should increase as the evidence grows that
these diseases are indeed “complex”: their heritability
appears to be attributable to many common variants loci
of seemingly weak effect,10
with many additional suscepti-
bility alleles that remain to be identified in MS21
and non-
heritable risk factors that also appear to be common and
able to perturb the host with pleiotropic mechanisms.22,23
Gene Expression “Noise” is a
Nondeterministic Component of
Phenotypic Variation
If we accept that processes leading to multifactorial dis-
eases can have a stochastic component, the next question
to be asked is where does the noise of the system stem
from. Keeping in mind that what we perceive as noise is
the results of processes that act on a time scale much
shorter than the ones we are considering, noise permeates
biological phenomena. In processes such as multifactorial
diseases that involve genes, environment and their inter-
actions the most likely candidate source of noise resides
in gene expression.
Gene expression is the outcome of intrinsically stochas-
tic processes, for instance it depends on a Brownian ran-
dom walk of transcription factors through the cellular
volume before they find their promoters. As witnessed by
paradigmatic experiments, allowing enough time, even
genetically identical cells and organisms, grown in the
same environment, can become phenotypically differ-
ent.24,25
This happens because the expression of individual
genes takes place through discrete and random fluctua-
tions (gene expression “noise”) of the production of
mRNAs and proteins (Fig. 2).
Interestingly, noise also enforces the coordinated
expression of genes across large regulons,28
all this imply-
ing that any noise change may have profound conse-
quences. In fact, bursts in the expression of single genes,
due to intrinsic noise, can propagate to the expression of
downstream genes generating extensive and correlated
fluctuations (extrinsic noise).25
In mammalian cells, this
may lead to long-lasting and concerted noise in protein
levels that may, for example, cause the appearance of “out-
lier cells”29
that react differently to environmental signals
or drugs with respect to the bulk of the population.
The fact that the most basilar events that characterize
life (information storage in genes and retrieval through
gene expression) are intrinsically stochastic means that
living organisms can adapt to changing conditions much
better than any rigidly predetermined system could do.
Thus, noise plays an essential role in key cellular activities
and, at longer timescales, it may do so also at the evolu-
tionary level. Furthermore, noise may be viewed as a buf-
fer25
between the conflicting functions of genome (that
defines and constrains the system) and genes (that modify
and diversify it).30
Although these observations are not new,31
it took
some time before they ignited interest in stochastic gene
expression,32
perhaps because noise in gene expression is
instinctively perceived as a nuisance for a process that
ought to be tightly regulated. In MS, it took even longer
before the possibility of random events15
and finally
translational/transcriptional stochasticity33
were proposed
as a component of the etiology of disease, in spite of epi-
demiological evidence suggesting that unique, nonshared
environmental factors cannot be invoked to explain dis-
ease discordance in monozygotic twins.
If we acknowledge that gene expression noise can be a
source of clinically relevant phenotypic variation, we
should also start looking at the heritable risk in a more
dynamic way, that is, as a component that can fluctuate
over time (Fig. 3).
Time is the Other Ingredient
In experimental models of autoimmunity, there is
evidence of a multistep process where subtle alterations
resulting from quantitative trait loci variations
Figure 2. Effects of noise on gene expression and cell-to-cell variability. Individual E. coli expressing two identical promoters that control the
expression of two different fluorescent proteins, red and green. Scheme of the temporal variations of gene expression (noise) (A) and different
levels of the ratio of red to green intensity in the cell population at the end of the observation period (B). Adapted from refs. (26 and 27).
Gene Expression Noise in Multiple Sclerosis I. Bordi et al.

accumulate with time, resulting in large changes in the
susceptibility to autoimmunity when a threshold for the
occurrence of the disease is passed.34
In human autoim-
mune conditions, various studies indirectly suggest that
relatively long time intervals are a necessary factor in the
development of complex diseases. Immune response
defects, such as those linked to the PTPN22 variant
(which associates with many autoimmune diseases), pre-
cede the clinical onset of the disease itself (see ref. 35
for a review on the evidence of such mechanisms in
human autoimmune conditions).
As far as MS is concerned, persons with “radiologically
isolated syndromes” (i.e., incidental magnetic resonance
imaging findings suggestive of MS) develop the first
symptoms of the disease after 1–5 years in a 33% of the
cases,36
with a substantial proportion of subjects who
may experience the first symptoms much later or never in
a lifetime, reinforcing the idea that MS is a process start-
ing a long time before its clinical “onset.” And even after
a first clinical episode has occurred, a new relapse or a
radiological conversion into MS does not occur in a rela-
tively large proportion of patients even after a 20-year fol-
low-up.37
The relapsing/remitting course that patients
experience during the first years of the disease, suggests
that they actually spend time wandering between active
disease and a relatively healthy remission state.
But even more than clinical observations, epidemiologi-
cal data support the importance of time, suggesting that
it starts exerting its influence well before the subclinical
or clinical onset of the disease.38
After some debate, the
correlation between risk of the disease and place of resi-
dence in childhood seems to be confirmed,39
while the
role of longer “exposures,” perinatal, prenatal and
ancestral, needs further scrutiny.40
Finally, findings from
twin studies strongly suggest that a proportion of herita-
ble and nonheritable factors in MS are interactive rather
than independent, indirectly supporting the importance
of time to allow (presumably numerous and iterative)
interactions to take place.40
Noise and Time Can Amplify the
Effects of Weak Genetic and
Environmental Factors
So far, we have seen that gene expression noise can be a
source of phenotypic variation at the cellular level. Its
pervasive presence in biological processes, essential role in
regulation and phenotypic definition suggest that it may
have “macrosopic” effects, including the development of
pathologic states. Likewise, time is required for the
unfolding of pathogenetic events that lead to a disease,
and MS is no exception. The next step is to understand
how noise and time may combine and contribute to the
development of the disease.
Mechanistically, gene expression noise may contribute
to reaching a disease threshold through the gradual accu-
mulation of defects, by providing small random perturba-
tions that amplify the effects of heritable and
nonheritable predisposition or both. The multistep accre-
tion of subtle alterations can be intuitively appreciated
and is to some extent supported by data in animal mod-
els.34
However, the erratic manifestations of a disease
such as MS appear difficult to reconcile with this idea of
progressive accumulation of pathogenetic events.
A model that incorporates small random perturbations,
provided by gene expression noise, appears more
Figure 3. Dynamic effects of gene expression noise on the heritable risk. Let us consider two individuals, 1 and 2, with different heritable risk for
multiple sclerosis (MS). According to the canonical view of the pathogenesis of multifactorial diseases, given an identical environmental input, the
individual 1 will be at higher heritable risk than individual 2 (A). However, if we incorporate gene expression noise (bursty gene expression) in this
model, heritable risk cannot be viewed any more as a monolithic entity. Rather, it will fluctuate over time with gene expression bursts. At given
time points this may even revert the individual risk (B).

compatible with the relapsing-remitting course of the dis-
ease and with the pervasive and regulatory role of noise.
Supporting this hypothesis in MS is the observation that
the occurrence of relapses follows an exponentially decay-
ing distribution, implying that disease activity manifests
randomly in time. Hence, similar to models used for
instance for the Earth’s climate theory,17–19
MS can be
modeled as a nonlinear system with two steady states, dis-
eased and healthy (Appendix and Fig. 4).41
The system
will remain in either steady state even if exposed to small
random perturbations. However, these small stochastic
events can eventually force the system out of its steady
state and into the other one. Time is necessary to allow
the occurrence of these low-probability events.
Thus, a mechanistic model with random forcing
describes in a satisfactory manner, the disease course and
how small stochastic perturbations induced by (gene
expression) noise may interact with etiologic factors of
small effect-size (genetic and environmental), occasionally
reaching the disease threshold provided that enough
observation time is given (Fig. 4).
Consequences for Studies on Disease
Etiology
To verify this model, and to assess the proportion of phe-
notypic variance that can be attributed to gene expression
noise, the usual attempts to correlate average measure-
ments with the disease status should be complemented by
single-cell measurements and stochastic analyses, particu-
larly for genes with low transcription and high translation
rates (which may bring about large protein fluctuations).42
This approach is not frequent, and existing studies on cel-
lular heterogeneity (because of methodological limitations)
have quantified either few RNAs or proteins in relatively
large samples of cells or more gene products but on much
smaller numbers of cells. Furthermore, with few excep-
tions,43–49
data refer to model microbial systems.
The recent advent of single-cell genomics may now
open new opportunities to extend this kind of studies
also to patient populations and has already shown unex-
pected levels of heterogeneity between cells also for genes
that are very highly expressed at the population average.48
Figure 4. Schematic picture of a mechanistic stochastic model that describes disease risk and course. Health and disease are modeled as a
nonlinear system with steady states, health (H) and disease (D). The disease risk and course for the same subjects as in Figure 2 are considered. A
transition from health state (well H) to disease state (well D) is easier for subject 1 (green) than for subject 2 (red) as a result of his higher
heritable risk. For the same reason, reverting from the disease to the health state is more difficult for subject 1. However, the transitions remain
random as the underlying gene expression noise provides the required energy for switching from one well to the other.

Here, bimodality among highly expressed immune
response genes was detected, suggesting the suitability of
this kind of studies to reveal distinct cellular subtypes or
stochastic differences in the activation of regulatory cir-
cuits. Other very recent and potentially useful technologi-
cal approaches to go beyond average measurements
and explore noise and cell-to-cell variations include super-
resolution microscopy methods for live cell imaging, which
promise to display single molecule dynamics with second-
or even sub-second-scale time resolution.50
Besides these
new developments, also the complementary combination
of more established methods such as dynamic array chips
and single-molecule mRNA fluorescent in situ hybridiza-
tion has yielded important information, for example, about
variations in stochasticity in different phases of cellular
reprogramming.51
The same may be true for the use of new
approaches for the direct measurement of ongoing tran-
scription of nascent RNAs and other techniques.52,53
Other approaches may be less demanding in terms of
methodological innovation. This is the case of the large
and increasing number of studies on microRNAs, on epi-
genetic chromatin modifications and on more specific
mechanisms of regulation such as those linked to the
molecular chaperone Heat shock protein 9054
or to ultra-
sensitive response motifs.55
Any imperfection in these
mechanisms of global regulation, but also mutations in
genes with more specific functions52
may have conse-
quences on the robustness of transcriptional regulation,
affecting the buffering effect of microRNAs on fluctua-
tions in gene expression or through changes in the stabil-
ity and transition rates of promoter-activity states
brought about by chromatin modifications. The latter
may also lead to variations in the expression noise of
neighboring genes as “opening” of the chromatin sur-
rounding one gene is likely to affect other genes nearby,
leading to correlations in their expression.24,25,56
New
techniques to perturb histone modification patterns in a
locus-specific manner through the induction of site-spe-
cific heterochromatin domains in vivo promise to bring
new information about the connection between chroma-
tin state and gene transcription.57
As far as MS is concerned, the need for technological
advancements and data repositories (such as the recently
established genome-wide chromatin modifications maps58
)
that may clear studies on gene expression noise in patients
appears to be even stronger in light of results showing that
disease- and trait-associated variants are concentrated in
regulatory DNA.59–61
In this context, it is interesting that
transcription factors involved in chromatin remodeling
such as SP1 may be central to explain gender-based vari-
ability between persons with MS and controls.62
In addi-
tion, the presumptive role of vitamin D in the
pathogenesis of MS and various other diseases may be
ascribed to the vitamin D receptor preferential binding to
intronic and intergenic regions with regulatory role and
enhancer functions,63
again supporting possible conse-
quences on gene expression noise. Finally, an area of inter-
est for MS pathogenesis, the interplay between virus and
host, conceptually lends itself very well to the study of
gene expression noise. Viral reactivation from a “latent”
state can be stochastic, as recently shown for the reactiva-
tion of HIV reservoirs.64
Also for viruses such as Epstein-
Barr virus (EBV), which may contribute to MS etiology,
the study of gene expression noise and cell-to-cell variabil-
ity may be informative for the identification of pathoge-
netically relevant variations. Noncytopathic viruses have
established coregulated genomes and gene expression
programs with their hosts.65–67
These include the regula-
tion of higher order chromatin structure, “super-enhanc-
ers” or accelerators of transcription, all factors of potential
impact on gene expression noise. An example of potential
interest in MS is BRD4, a transcriptional coactivator that
co-occupies thousands of enhancers and a small set of
“super-enhancers”68
; this factor is an interactor of the
EBNA1 protein of EBV69
and co-regulates MYC which, in
turn, can accumulate in the promoter regions of active
genes causing transcriptional amplification.70,71
Further-
more, a low rate of transcription is a hallmark of virus
ability to establish a latency state. The reactivation rate of
latent to lytic cycle is also low, and intrinsically subjected
to stochastic bursts such as those driven by antigen stimu-
lation or receipt of a plasma cell differentiation signal,
once more suggesting that disease-associated differences
may be revealed by single-cell measurements and stochas-
tic analyses rather than bulk assays.
Other studies that encourage analyses at the single-cell
level in an immune-mediated disease such as MS are
those that describe how stochastic processes regulate the
physiology of the cytotoxic T cell (CTL) response to anti-
gens72
or the differentiation of T-cell subsets.73
As for
CTLs, time series of lymphocytes selectively activated to
cytotoxicity (that lacks a mature immunological synapse)
show that these cells have signaling patterns with lower
average calcium mobilization compared to fully activated
CTLs. However, when the time series are analyzed at the
single-cell level, the less mature elements have higher
spikes of calcium mobilization that comprise determinis-
tic (e.g., oscillations) and stochastic aspects. In the differ-
entiation of key T-cell subpopulations such as TH1 and
TH2 T cells, single cell variability is relevant in physiology
and may be altered in an autoimmune disease state: in
the early phase of T helper cell differentiation a “noisy”
cytokine expression is key in triggering a fully differenti-
ated state in the subpopulations but it is buffered by the
ubiquitous, high-level co-expression of antagonistic
transcription factors in individual cells. Finally, as far as

the T and B cell responses to antigens are concerned, sto-
chastic events such as the encounter of T and B cell epi-
topes contribute to the regulation or breakdown of
immunological tolerance.74,75
Conclusion
A stochastic (i.e., nondeterministic) component has sel-
dom been taken into account as a relevant actor in the
pathogenesis of a multifactorial disease like MS. For some
reason, our logical explorations tend to feel more com-
fortable in the presence of identifiable causes and effects.
In the case of a disease, this attitude is perhaps reinforced
by the fact that acknowledging a stochastic component in
the pathogenesis of a disease may be viewed as an obsta-
cle or, at best, useless in therapeutic terms.
On the contrary, particularly in the early phases of the
disease, noise itself may represent a target for etiologic
therapies, and might ultimately turn out to be less com-
plex to attack than genes or viruses. Encouraging preclini-
cal evidence – but also clinical data – about the
possibility of affecting the early course of MS with “mild”
interventions such as increase in vitamin D or other fat-
soluble vitamin levels22
or Bacille Calmette-Guerin (BCG)
vaccination,76,77
dietary sodium,78,79
and modulation of
the endocannabinoid system,80
among others, may reflect
the possibility of stabilizing noise and “deamplify” its
effects thanks to the pleiotropic, although “soft,” actions
of these interventions. If and when the integration of
genetic data with endophenotypes, magnetic resonance
imaging or other biomarkers will become useful for pre-
diction in a clinical circumstance,81
the importance of
such “soft” approaches will become even more evident.
We hope to have provided some conceptual and meth-
odological information that will encourage and help those
who will engage this new and promising field of research,
in MS and in other multifactorial diseases.
Acknowledgments
This study is dedicated to the memory of Alfonso Sutera.
His ideas shaped this work and his contribution to future
developments will be greatly missed. M. S. is supported
by Fondazione Italiana Sclerosi Multipla.
Conflict of Interest
None declared.
Appendix:
In the last years, there has been a growing interest in
understanding the role and impact of noise on many
aspects of biology and medicine82
. With “noise” one
generically means any small random perturbation acting
on a system. Due to its intrinsic “smallness,” it appears
obvious to expect that noise effect is “small” and, in the
presence of noise, the system behaves much as it would
do in its absence. In such cases, noise represents a nui-
sance, which usually one tries to filter out.
However, despite its smallness, noise may have dra-
matic effects, which can drive the systems far away from
its noiseless behavior. These situations are not so uncom-
mon. An example is climate changes. Here, the coopera-
tive effect of noise, arising from the internal dynamics of
the atmosphere and ocean, and the small periodic varia-
tion in solar energy over a period of about 100,000 years,
induced by the variation in the Earth’s eccentricity, pro-
vides an amplification of the climate response that leads
to the transition from a temperate climate to an ice-
covered Earth state and vice versa.17,18
The phenotypic differences between individual organ-
isms can often be ascribed to the underlying genetic and
environmental variations. However, it is known that
genetically identical organisms evolving in a homogeneous
environment may present phenotypic differences, indicat-
ing that the small perturbation of developmental pro-
cesses that stems from the gene expression noise may
generate macroscopic diversity. At a larger scale level, the
random fluctuations in the expression of individual genes
may then contribute to, or be responsible for, the transi-
tion between health and disease by exposing hidden
genetic and environmental risk. Following this idea,
recently Bordi et al.41
have shown that the transitions
between remissions and relapses in MS can be well
described by a simple stochastic model. The model can be
visualized by thinking of the motion of a particle in an
asymmetric double-well energy potential schematically
illustrated in figure. The position of the particle repre-
sents the patient state, while the two minima account for
the health (lower global minimum) and disease (higher
local minimum) states. In the absence of noise, for
(almost) all initial positions the particle will move down
to one of the two minima (uniquely determined by the
initial conditions), and there it will remain, with no tran-
sitions between states (remissions and relapses).
If noise is added, the particle will still move down to
one of the two minima and remain close to it for some
time. However, the stochastic perturbation due to noise
may eventually drive the particle over the hill separating
the minima and into the other minimum. In just the
same manner, the fate of a patient is no more uniquely
determined by the initial state and transitions between
remissions and relapses are now possible. It is intuitively
clear that as the transitions are driven by noise, they
occur randomly in time. It is also evident that for an

asymmetric double-well the time the particle spends close
to one minimum, i.e., the health/disease periods, is differ-
ent for the two minima. Such a stochastic model gives a
good description of the occurrence of remissions and
relapses in single patients affected by Multiple Sclerosis.
Glossary of terms used
Deterministic system: a system whose evolution is (at
least in principle) fully predictable from the knowledge of
its condition (state) at any given time.
Noise: random perturbation acting on a system.
Nonlinear systems: systems in which changes in the out-
put (or response) are not linearly related (i.e., directly
proportional) to changes in the input (or stimulus).
Stochastic: Random.
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