Could humans recognize odor by phonon assisted tunneling

arXiv:physics/0611205v1[physics.bio-ph]22Nov2006
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Could humans recognize odor by phonon assisted tunneling?
Jennifer C. Brookes,∗
Filio Hartoutsiou,†
A. P. Horsfield,‡
and A. M. Stoneham§
Department of Physics and Astronomy,
University College London, Gower Street,
London WC1E 6BT, United Kingdom
Abstract
Our sense of smell relies on sensitive, selective atomic-scale processes that are initiated when a
scent molecule meets specific receptors in the nose. However, the physical mechanisms of detec-
tion are not clear. While odorant shape and size are important, experiment indicates these are
insufficient. One novel proposal suggests inelastic electron tunneling from a donor to an accep-
tor mediated by the odorant actuates a receptor, and provides critical discrimination. We test
the physical viability of this mechanism using a simple but general model. Using values of key
parameters in line with those for other biomolecular systems, we find the proposed mechanism
is consistent both with the underlying physics and with observed features of smell, provided the
receptor has certain general properties. This mechanism suggests a distinct paradigm for selective
molecular interactions at receptors (the swipe card model): recognition and actuation involve size
and shape, but also exploit other processes.
∗
Electronic address: j.brookes@ucl.ac.uk
†
Electronic address: to˙milaraki@hotmail.com
‡
Electronic address: a.horsfield@ucl.ac.uk
§
Electronic address: a.stoneham@ucl.ac.uk
1

Our sense of smell affects our behavior profoundly. Discrimination between small
molecules, often in very low concentrations, allows us to make judgments about our immedi-
ate environment[1] and influence our perceptions. Even though odorants are key components
of many commercial products[2], the biomolecular processes of olfaction are inadequately un-
derstood: scent design is not straightforward. We know that odor detection involves several
types of receptor for a given odorant, and understand how a receptor signal is amplified and
processed[3, 4]. However, the initial selective atomic-scale processes as the scent molecule
meets its nasal receptors are not well understood. Odorant shape and size are certainly
important, but experiment shows these are insufficient. Here we assess the novel proposal
that a critical early step involves inelastic electron tunneling mediated by the odorant. We
test the physical viability of this mechanism[5] using electron transfer (ET) theory, with
values of key parameters in line with those for other biomolecular systems. The proposed
mechanism is viable (there are no physics-based objections and is consistent with known
features of olfaction) provided the receptor has certain general properties. This mechanism
has wider importance because it introduces a distinct paradigm for selective actuation of
receptors: whereas lock and key models[6] imply size, shape and non-bonding interactions
(the docking criteria) are all, in our swipe card model recognition and actuation involve
other processes in addition to docking. Thus it encompasses and goes beyond mechanisms
such as proton transfer, discussed by us previously[7].
All current theories agree that selective docking of odorants is important[2]. However,
odorants are small molecules (rarely more than a few tens of atoms[2]), and it is improba-
ble that docking criteria alone offer sufficient discrimination. For example, molecules with
almost identical shapes can smell very different: replacing carbon with its isosteres Si, Ge
and Sn invariably markedly alter odor character[8]. Something more is needed for olfaction,
leading to early suggestions that odorant vibration frequencies were critical [9, 10], though
without specific mechanisms. Both infrared and inelastic electron tunneling[11, 12] (IETS)
spectroscopies distinguish very precisely between different molecules through vibrational fre-
quencies and intensities, which makes the proposal appealing. The first specific mechanism
(based on IETS) was Turin’s[13] idea that there is odorant mediated inelastic tunneling of
an electron at the receptor: inelastic tunneling between receptor electronic states differing in
energy by ¯hω that occurs only when energy is conserved by emission of an odorant phonon of
the right energy, hence selectivity. Clearly, the vibration must also couple to the electronic
2

transition.
Experiment offers several tests of Turin’s idea. It explains why certain molecules with
very different shapes can smell similar (e.g. boranes and thiols), but also why some molecules
of essentially identical shape smell utterly different (e.g. 1,1-dimethylcyclohexane and its sila
counterpart) because of frequency or coupling changes. The question of whether humans
can distinguish between a molecule and its deuterated counterpart is still controversial.
There is evidence both for[13, 14] and against[15]. In animals, isotope discrimination is
well-documented[16]. Both left- and right-handed forms of enantiomers should have the
same vibrational spectrum. The odors of some enantiomer pairs are the same (type 1) while
others differ (type 2)[17]. Type 2 can be explained by docking criteria (different chiralities fit
different receptors), while type 1 is naturally explained by vibrational frequency. However,
docking and frequency together can account for both since chirality will affect the intensity
of response of receptors to the enantiomers (the helices that form the walls of the receptors
are chiral). Quantitative support for the theory comes from the successful correlation of odor
character with tunneling frequency spectrum[18] for a range of odorants. Indeed, vibrational
frequency has been found to correlate better with odor than structure [19]. Thus a molecule’s
vibrational spectrum appears closely linked to its odor. We now test whether the physical
processes underlying Turin’s proposed mechanism for detecting the frequency are credible.
First we focus on the odorant and perform a simple test of whether odor can be related
to vibrational frequency and to coupling to the odorant charges (as required by IETS).
We computed the vibrational spectra of H2S and four boranes (decaborane, m-, o- and p-
carborane). The boranes are structurally similar, but all quite distinct from H2S. However,
H2S and decaborane smell sulfuraceous, while the carboranes smell camphoraceous. Using
Gaussian 03[20] we computed vibrational frequencies and infrared (IR) couplings, defined
as |∂p/∂Qi|2
with p the dipole moment and Qi a displacement along normal mode i. The
sulfuraceous smell of H2S is associated with vibrations in the region of 2600 cm−1
[21]. In this
region decaborane has IR couplings that are one to two orders of magnitude greater than the
carboranes. Assuming that the IR couplings are a good estimate of the electron-oscillator
coupling in an olfactory receptor, this could explain sulfuraceous and less sulfuraceous odors.
Turning to the combined odorant and receptor system, we must determine whether ET
is possible on the relevant time scale, and if so whether the discriminating electron transfer
rate (with excitation of the critical odorant mode) is sufficiently large relative to rates
3

for non-discriminatory transfer channels (without excitation of the critical mode). This is
necessary because most IETS experiments observe inelastic tunneling with phonon emission
as a weak adjunct to the elastic component, detected only by complex post-processing of a
type unlikely in a nasal environment. Too little is currently known about the atomic and
electronic structure of real odorant receptors for full-scale calculations. Instead we make
general assumptions about the nature of the receptor, the odorant and their interaction.
These assumptions relate to a series of characteristic times corresponding to the required
physical processes (see Fig. 1).
Turin’s theory requires a source of electrons or holes to allow charge flow to take place.
The precise biological origin is not known, but may well consist of reducing (oxidizing)
species (X) in the cell fluid [2]. These molecules diffuse through the aqueous medium and
arrive with an average interval of τX. Using a standard approach for computing reactant
collision rates in solution from the diffusion equation and the Stokes-Einstein relation for the
diffusion coefficient[22] we get τX = 3η/2nXkBT where η is the viscosity of water (0.891 ×
10−3
kgm−1
s−1
), nX is the concentration of X, kB is Boltzmann’s constant and T is the
temperature. Note that this result is independent of the nature of X or the receptor. Since
nX will probably lie in the range 1 µM → 100 µM, we get a range of values for τX of
10 µs → 1 ms. The charge now has to cross from the molecule to the receptor molecule, a
process that can be described by Marcus theory [23, 24, 25], and characterized by a time
τI. In proteins times range from about 1 ms down to about 1 µs[26]. The injected charge
has to propagate through to the donor (D). The route is not known, but probably involves
hopping transport. Thus the journey time is likely be in the ms to µs range as for charge
injection. The next step is the inelastic tunneling from D to A (the acceptor), and it is this
charge movement that actuates the receptor. Now the charge must reach the mechanism
that releases the G-protein which in turn initiates the signal that is sent to the brain. Again,
we do not know the route taken but is likely to involve charge hopping. So the characteristic
time τR will probably be in the range ms to µs. Thus, overall charge injection and extraction
together are likely to occur on typical biological time scales of µs to ms.
For the mechanism to work there must be essentially no tunneling from D to A in the
absence of the odorant, either because the distance is too great or energy conservation
is problematic. The odorant must make inelastic transmission possible by a mechanism
coupling electron movement from D and A to vibrational excitation in the odorant. In
4

FIG. 1: The olfactory receptor is a G-protein coupled receptor with seven hydrophobic helices
that span the cell membrane. It responds to the arrival of a recognized odorant by releasing the
α-subunit of a neighboring G-protein, which in turn initiates a large influx of Ca ions into the cell,
a signal that can be communicated to the brain. This figure represents the model of the receptor we
use to describe its action. The electron (hole) source X is likely to be a reducing (oxidizing) agent
in the cell fluid. It arrives at a site on the outside of the receptor protein where it can exchange
charge after an average interval τX. Once in place, it exchanges a charge with a characteristic time
τI. The charge then travels to the donor D in one transmembrane helix of the protein over an
average time of τL, from where it then hops to the acceptor A (possibly in a different helix) with
either an average time τT0 for non-discriminating (“elastic”) tunneling or an average time τT1 for
discriminating (“inelastic”) tunneling. Only the inelastic contribution is sensitive to the odorant
(M) oscillator frequency ω0, and so needs to dominate the elastic contribution (τT0 ≫ τT1). The
electron then travels from A to trigger the release of the G-protein (G) over a time τR. Note that
the terms elastic and inelastic refer only to energy exchange with the odorant.
IETS there is a strong contribution to this coupling from the Coulomb interaction between
partial charges associated with oscillating atoms and a mobile electron[27, 28]. This same
mechanism allows us to account for observed features of olfaction including the detection of
oscillators buried inside a molecule (e.g. 2,6 di-t-butyl phenol [2]), and is compatible with
5

our swipe card model: the long-ranged interaction can couple the mobile electron to the
oscillator even with a loose fit.
The times characterising elastic (τT0) and inelastic (τT1) ET from D to A are central
to the success or failure of Turin’s mechanism. We treat D and A as single molecular or-
bitals with energies εD and εA, coupled to each other by a weak hopping integral t, but
not coupled to other electronic states. Since the hopping between D and A is slow on elec-
tronic time scales, the remaining electronic couplings must be very weak to prevent electron
leakage. However, D and A will be coupled to oscillators in the odorant, receptor protein
and the wider environment. The ET rate from D to A can be computed from standard
theory[23, 24, 25, 29, 30, 31] but with the odorant oscillator treated explicitly. We consider
one odorant oscillator of frequency ωo which couples with strength γD (γA) to D (A) . The
environment is treated as many oscillators with frequencies ωq and coupling strengths γqD
and γqA. The complete system is described by the Hamiltonian ˆH = ˆHD + ˆHA + ˆv, where
ˆHX = |X X| εX + ˆHosc + ˆHe−osc,X (X is D or A), ˆv = t (|D A| + |A D|) and |D (|A )
is an electronic state on D (A). ˆHosc = (â†
â+ 1
2
)¯hωo+ q(â†
qâq + 1
2
)¯hωq is the oscillator Hamil-
tonian for the odorant and environment, and ˆHe−osc,X = γX â + â†
+ q γqX âq + â†
q cou-
ples the electron to the oscillators. The eigenstates of ˆHosc are |nN , where n is the odorant
oscillator occupancy and N corresponds to a set of environment oscillator occupancies {nq}.
The eigenstates of ˆHX are |ΨXnN = exp(uX(â−â†
)+ q uqX(âq−â†
q))|XnN and have eigen-
values EXnN = εX +(n+ 1
2
−u2
X)¯hωo + q(nq + 1
2
−u2
qX)¯hωq. The states |XnN are products
of unperturbed electronic and oscillator basis states, uX = γX/¯hωo and uqX = γqX/¯hωq. The
times τT0 and τT1 follow from the standard golden rule result for the coupling of the system
with the electron on D and odorant oscillator in its ground state to that with the electron on
A and odorant oscillator in excited state |n : 1/τTn = (2π/¯h) NN′ PN | ΨD0N |ˆv|ΨAnN′ |2
where PN is the probability that the system starts in state |ΨD0N . After making stan-
dard approximations for an electron coupled to a bath of phonons[31, 32], and taking the
background fluctuations to be of low frequency, we get the Marcus-type expression
1
τTn
=
2π
¯h
t2 σn
√
4πkBTλ
exp −
(ǫn − λ)2
4kBTλ
(1)
where σn = exp(−S)Sn
/n!, S = (uD − uA)2
(a Huang-Rhys factor), ǫn = εD − εA − n¯hωo,
β = 1/kBT, λ = q Sq¯hωq (reorganisation energy), and Sq = (uqD − uqA)2
.
6

Quantity ¯hωo S λ |t|
Value 200 meV 0.01 30 meV 1 meV
TABLE I: Estimated values for the physical quantities needed to compute τT0 and τT1. See text
for explanation of their values.
We now estimate values for the parameters (Table I). The interesting range for ¯hωo in
olfaction is about 70 meV to 400 meV[18], so a typical value is 200 meV. To estimate the
Huang-Rhys factor S we introduce a physical mechanism for the electron-oscillator inter-
action based on the long-ranged electrostatic interaction between the electron and odorant
atomic partial charges. The definition S = (uD − uA)2
is equivalent to S = ∆F2
/2¯hMoω3
o
where ∆F is the change in force on the odorant oscillator as a result of the electronic
transition[33, 34]. We treat the oscillator as a dipole with charges ±qe and compute the
forces on the oscillator when the electron is on A and D (treated as pointlike), giving
S = 4q2 me
Mo
Ry
¯hωo
3 ˆRD · ˆp
(RD/a0)2
−
ˆRA · ˆp
(RA/a0)2
2
(2)
where ˆp is the direction of the dipole, RD is the vector from D to the dipole, RA is the vector
from A to the dipole, me is the electron mass, Ry the Rydberg and a0 the Bohr radius.
Setting q = 0.2 (a typical partial atomic charge in a polar molecule), me/Mo = 1/15000
(using a representative atomic mass for light elements), ¯hωo = 200 meV, ˆRD · ˆp = − ˆRA · ˆp = 1
and RD = RA = 6 a0 gives S ∼ 0.01.
We assume the odorant (M) contacts D and A but interacts with them only weakly with
hopping integral v. By considering the resulting admixtures of an M state with energy
εM with those of D and A we obtain an effective hopping integral between D and A (
t = v2
/(εM − εA)). If εM corresponds to a LUMO while εD and εA correspond to HOMOs
then the difference εM −εA can be as large as 10 eV. The hopping integrals can be estimated
for known molecular structures. Whilst the odorant structure is known, the donor and
acceptor structures interacting with it are unknown, and we have to make an educated
guess. If the bonds between M, and D and A are no stronger than hydrogen bonds, we can
put a rough upper bound on the associated hopping integrals of order 0.1 eV, and hence
obtain t ∼ 1 meV. Our final conclusions are not sensitive to this value.
Reorganisation energies are typically of order 1 eV, especially in hydrated systems, which
7

would result in the elastic channel being much faster than the inelastic. But much smaller
values have been found, and olfactory receptors are hydrophobic. Experiments on charge
separation in mutant reaction centers of the photosynthetic bacteria Rhodobacter capsulatus
show reorganisation energies at room temperature below 0.03 eV[35]. A generally low value
for odorant receptors would be a result of evolutionary optimization leading to almost no
reorganization during the transition. This requires that D and A are not too close to the
aqueous medium in the cell to prevent significant coupling to the polarization of the water;
thus we conjecture that D and A must lie well within the lipid bilayer region (see Fig. 1).
The reorganisation energy can also be reduced if electronic states on D and A are extended
in space[29], so residues with delocalized electrons may be candidates. (For example, the
conserved[36] tryptophan on helix 4 and 3 phenylalanines on helix 3. The surrounding highly
variable residues could modify their redox potentials, producing different receptors. ) We
take a value for the reorganisation energy of 0.03 eV for the table of values.
Substituting the values in Table I into Eq. 1 for the case of resonance (εD − εA = ¯hωo)
we get τT0 ∼ 87 ns and τT1 ∼ 1.3 ns, which satisfies the condition τT1 ≪ τT0, and shows that
the overall time for odor recognition is not limited by the discrimination process. Increasing
the reorganization energy to just 50 meV would make τT1 > τT0. Thus, provided the
reorganisation energy can be made not much bigger than kBT, we can obtain a large signal
to noise ratio. We note that the theory remains unaltered if a proton tunnel from D to A,
but the parameters t, εD and εA will be modified.
Our analysis indicates that Turin’s model is physically viable provided the receptor has
certain properties (notably, very low reorganization energy) within ranges known from other
biomolecular systems. Our model shows that the overall charge transfer rate is sufficient to
permit detection on the observed timescales, and the inelastic signal can be made sufficiently
large relative to the elastic signal for there to be an acceptable signal to noise ratio. Lack of
information on local receptor structure limits what can be verified. Our model illustrates a
more general idea of how molecules can actuate receptors selectively. Lock and key models
rely on docking for discrimination, and mechanical mechanisms for actuation. Selective
docking does have a role in our class of swipe card models, but the crucial discrimination
and non-mechanical actuation processes are different.
8

Acknowledgments
Many entertaining and instructive conversations with Luca Turin and helpful comments
from Rudolph Marcus are gratefully acknowledged. JB and AH are supported by the EPSRC
through the IRC in Nanotechnology.
[1] J. C. Leffingwell, Leffingwell Reports 5, 1 (2001).
[2] D. Rowe, ed., Chemistry and Technology of Flavours and Fragrances (Blackwells, 2005),
chap. 11.
[3] R. Axel, Angew. Chem. Int. Ed. 44, 6111 (2005).
[4] L. Buck, Angew. Chem. Int. Ed. 44, 6128 (2005).
[5] W. Bialek, Ann. Rev. Biophys. Biophys. Chem. 16, 455 (1987).
[6] R. B. Silverman, The Organic Chemistry of Enzyme-Catalyzed Reactions (Elsevier, 2002).
[7] D. Wallace, A. M. Stoneham, A. Testa, A. H. Harker, and M. M. D. Ramos, Molecular
Simulation 2, 385 (1993).
[8] D. Wrobel, U. Wannagat, and U. Harder, Chemical Monthly 113, 381 (1982).
[9] G. M. Dyson, Chem. Ind. 57, 647 (1938).
[10] R. H. Wright, The sense of smell (CRC press, Boca Raton, Florida, USA, 1982).
[11] J. Lambe and R. C. Jaklevic, Phys. Rev. 165, 821 (1968).
[12] C. J. Adkins and W. A. Phillips, J. Phys. C: Solid State Phys. 18, 1313 (1985).
[13] L. Turin, Chem. Senses 21, 773 (1996).
[14] L. J. W. Haffenden, V. A. Yaylayan, and J. Fortin, Food Chemistry 73, 67 (2001).
[15] A. Keller and L. B. Vosshall, Nature Neuroscience 7, 337 (2004).
[16] B. R. Havens and C. E. Meloan, Food Flavors: Generation, Analysis and Process Influence
37, 497 (1995).
[17] E. Brenna, C. Fuganti, and S. Serra, Tetrahedron: Asymmetry 14, 1 (2003).
[18] L. Turin, J. Theor. Biol. 216, 367 (2002).
[19] S.-y. Takane and J. B. O. Mitchella, Org. Biomol. Chem. 2, 3250 (2004).
[20] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman,
J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, et al., Gaussian 03, Revision
9

C.02, Gaussian, Inc., Wallingford, CT, 2004.
[21] D. R. Lide, ed., CRC Handbook of Chemistry and Physics (CRC Press, 2005), 86th ed.
[22] P. Atkins and J. de Paula, Atkins’ Physical Chemistry (OUP, 2002).
[23] R. A. Marcus, Annu. Rev. Phys. Chem. 15, 155 (1964).
[24] J. Ulstrup, Charge Transfer Processes in Condensed Media, vol. 10 of Lecture Notes in Chem-
istry (Springer-Verlag, 1979).
[25] D. S. Bendall, ed., ProteinElectronTransfer (Bios Scientiﬁc Publishers, 1996).
[26] H. B. Gray and J. R. Winkle, Annu Rev. Biochem. 65, 537 (1996).
[27] J. R. Kirtley, D. J. Scalapino, and P. K. Hansma, Phys. Rev. B 14, 3177 (1976).
[28] J. R. Kirtley and P. Soven, Phys. Rev. B 19, 1812 (1979).
[29] R. A. Marcus, J. Chem. Phys. 24, 966 (1956).
[30] R. A. Marcus, J. Chem. Phys. 43, 679 (1965).
[31] X. Song and R. A. Marcus, J. Chem. Phys. 99, 7768 (1993).
[32] C. P. Flynn and A. M. Stoneham, Phys. Rev. B 1, 3966 (1970).
[33] K. Huang and A. Rhys, Proc. Royal Soc. A204, 406 (1950).
[34] A. M. Stoneham, Theory of Defects in Solids (Oxford University Press, 2001).
[35] Y. Jia, T. J. DiMagno, C.-K. Chan, Z. Wang, M. Du, D. K. Hanson, M. Schiﬀer, J. R. Norris,
G. R. Fleming, and M. S. Popov, J. Phys. Chem. 97, 13180 (1993).
[36] T. Fuchs, G. Glusman, S. Horn-Saban, D. Lancet, and Y. Pilpel, Hum. Genet. 108, 1 (2001).
10

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