Identification of key factors that reduce the
variability of the single photon response
Giovanni Carusoa, Paolo Bisegnab, Daniele Andreuccic, Leonardo Lenocid, Vsevolod V. Gurevichd,
Heidi E. Hammd, and Emmanuele DiBenedettoe,1
aConstruction Technologies Institute, National Research Council, 00015 Rome, Italy;
00133 Rome, Italy;
Pharmacology, Vanderbilt University Medical Center, Nashville, TN 37232; and
bDepartment of Civil Engineering, University of Rome Tor Vergata,
cDepartment of Mathematical Methods and Models, University of Rome La Sapienza, 00161 Rome, Italy;
eDepartment of Mathematics, Vanderbilt University, Nashville, TN 37232
Edited* by Avner Friedman, The Ohio State University, Columbus, OH, and approved March 31, 2011 (received for review December 22, 2010)
Rod photoreceptors mediate vision in dim light. Their biological
function is to discriminate between distinct, very low levels of
illumination, i.e., they serve as reliable photon counters. This role
requires high reproducibility of the response to a particular number
of photons. Indeed, single photon responses demonstrate unex-
pected low variability, despite the stochastic nature of the indivi-
dual steps in the transduction cascade. We analyzed individual
system mechanisms to identify their contribution to variability
suppression. These include: (i) cooperativity of the regulation of
the second messengers; (ii) diffusion of cGMP and Ca2þin the
cytoplasm; and (iii) the effect of highly localized cGMP hydrolysis
by activated phosphodiesterase resulting in local saturation. We
find that (i) the nonlinear relationships between second messen-
gersandcurrent at theplasmamembrane,andthecGMPhydrolysis
saturation effects, play a major role in stabilizing the system;
(ii) the presence of a physical space where the second messengers
move by Brownian motion contributes to stabilization of the
photoresponse; and (iii) keeping Ca2þat its dark level has only a
minor effect on the variability of the system. The effects of diffu-
sion, nonlinearity, and saturation synergize in reducing variability,
supporting the notion that the observed high fidelity of the
photoresponse is the result of global system function of photo-
modeling ∣ rhodopsin ∣ deactivation ∣ phosphorylation
dom lifetime, by catalyzing GDP/GTP exchange on the G protein
α-subunit. Each T?molecule associates, one-to-one, with a cata-
lytic subunit of the effector, forming an active T?-E complex,
denoted by E?. Molecules of E?hydrolyze the second messenger,
cGMP. Reduction of the cGMP level induces its dissociation from
the cGMP-gated cation channels, causing channel closure and
suppression of the inward current. This current suppression is
the experimentally measured electrophysiological response,
which is usually normalized by the dark current jdark, yielding the
relative current suppression (1)
n vertebrate retinal rod photoreceptors, light-activated rhodop-
sin R?activates dozens of G proteins (T → T?) during its ran-
IðtÞ ¼ 1 − jtotðtÞ∕jdark:
The mechanism of R?deactivation contains several random
components, including the random number of phosphorylations
by rhodopsin kinase (RK), and the random sojourn time at each
phosphorylation level. These steps regulate the number of gen-
erated E?molecules and, hence, the response. Because of this
randomness the responses are expected to be inherently variable,
in the sense that any two rhodopsin photoisomerizations yield
different responses. The system would be stable if these responses
are statistically close. A measure of stability is the coefficient of
variation (CV), defined as the ratio of the standard deviation to
the mean, calculated over a large number of signaling events and
their corresponding responses. However, the measured single
photon response (SPR) is highly reproducible, i.e., the coefficient
of variation of the current response and its time integrals, is
relatively low, about one half of what would be theoretically
expected from this series of reactions in the test tube (2–4). For
example the CV of the peak current amplitudes in toad is re-
ported to be about 20% (5), and for a mouse, the CVof the area
integral (integral of the relative current suppression, over the
whole time course of the phenomenon), is about 36% (4). The
mechanisms that ensure such a low variability of the SPR are
not completely understood, and are the object of current experi-
mental and theoretical investigation (2–10).
We have recently shown in ref. 10 that the randomness of the
sojourn times of R?in each of its phosphorylation states is the
dominant contributor to the variability of the response. At the
same time, the number of R?phosphorylation sites has negligible
influence on variability suppression. We also showed that the
cascade in the cytoplasm of the rod outer segment (ROS) with
complex geometry greatly reduces variability (9).
Here we selectively examined the contribution of each of the
components of the transduction cascade and the cGMP replen-
ishing machinery to variability suppression. Designing experi-
ments that can selectively exclude these components is a major
challenge. Experimentally, only the photocurrent can be mea-
sured in intact rods at physiologically relevant light intensities,
and though biochemical steps can be measured, these studies
suffer from the necessity of isolating the mechanism in question,
often in homogenized tissue, and assays are not sensitive enough
to demonstrate changes at low light intensities. We accomplished
this dissection virtually, by means of the space resolved mathema-
tical model (9, 11), which is capable of tracking and selectively
including or excluding each component.
Our analysis shows that the positive cooperativity (Hill coeffi-
cient nH > 1) of the relationship between cGMP, Ca2þ, and
the photocurrent, the diffusion of the second messengers in the
cytoplasm, and the nonlinear relationship between cGMP hydro-
lysis and the number of activated effector molecules, are the main
variability suppressors of the single photon response. Moreover,
they act synergistically to yield low variability of the response.
The mathematical model introduced in refs. 10 and 12, populated by the
parameters in refs. 10 and 13, simulates several components of the SPR. These
include the stochastic effects of the activation/deactivation cascade (10), and
biophysical and electrophysiological processes taking place in the transduc-
tion part of the cascade. Among these are the effects of sophisticated
ROS geometry, the diffusion of the second messengers cGMP, and Ca2þin the
cytoplasm, and their role in generating the photocurrent with high coopera-
Author contributions: E.D. designed research; G.C. and L.L. performed research; G.C., P.B.,
and D.A. contributed new reagents/analytic tools; G.C., P.B., D.A., V.V.G., H.E.H., and E.D.
analyzed data; and E.D. wrote the paper.
The authors declare no conflict of interest.
*This Direct Submission article had a prearranged editor.
1To whom correspondence should be addressed. E-mail: firstname.lastname@example.org.
This article contains supporting information online at www.pnas.org/lookup/suppl/
7804–7807 ∣ PNAS ∣ May 10, 2011 ∣ vol. 108 ∣ no. 19www.pnas.org/cgi/doi/10.1073/pnas.1018960108
tivity. The model here is used as a tool to selectively include and or exclude
one or several of these components to gain insights from the behavior of a
virtually modified ROS. Below is a list of the processes and/or components
that were systematically included and/or excluded from the numerical simu-
i. The nonlinear relationships regulating the dynamics of the second mes-
sengers cGMP and Ca2þ, and ultimately current suppression. The nonli-
nearity arises from Hill’s type laws linking powers of ½Ca2þ? and [cGMP]
on the lateral boundary of the ROS to the current through the cGMP-
gated channels (9), and in the production ofcGMP by Ca2þregulated gua-
nylyl cyclase (GC), respectively. The presence of these nonlinear relations
is labeled by (N), whereas their exclusion is labeled by (n).
Ca2þfeedback in the cytoplasm is mediated by Ca2þregulation of GC
that regenerates cGMP (14). The SPR with clamped Ca2þexhibits a larger
amplitude and a delayed peak time, and is slower than WT SPR (3). The
presence of Ca2þfeedback islabeled by (F) andits absence (Ca2þclamped)
is labeled by (f).
iii. Diffusion of the cGMP and Ca2þin the highly compartmentalized cyto-
plasm of the ROS. This biophysical effect links the biochemical compo-
nents of the cascade (9), and is labeled by (D). Its absence, as in a
well-stirred system, is labeled by (d).
iv. Local cGMP hydrolysis by the T?-E?complex. This mechanism passes the
variability of the activated T?-E?along to the second messengers and
ultimately to current suppression. The cGMP drop is largely localized
in the interdiscal space adjacent to the activated disk, reducing the pos-
sibility of further cGMP hydrolysis and thus leading to a saturation effect.
For this reason this mechanism is labeled by (S) for “saturation.” If instead
in the hydrolysis term cGMP is kept at its dark value, this saturation effect
is not present and we label it by (s).
A mathematical description of each of these components is in SI Appendix.
Variability is monitored at two levels. The first is by the CV of the activated
effector E?(not experimentally accessible in intact rods), and the second is by
the CVof the photocurrent [the output of the system that can be experimen-
tally measured (2–4), downstream of the transduction process]. The first
bears the random elements of the deactivation cascade (10), and the second
is mitigated by the cytoplasm, the physical medium where the second mes-
sengers diffuse (9). The stochastic and biochemical aspects of R?deactivation
are described in (10). The technical aspect of the nonlinear couplings be-
tween second messengers and current and Ca2þfeedback are explained in
refs. 9, 11, and 12. Details of both are given in SI Appendix. The variability
of the activated effector E?is simulated by the CV of the functionals:
Here E?ðsÞ is the total number of molecules of E?in the activated disk at time
s, the first integral E?
process. The variability of the current suppression is measured and simulated
by the CV of the functionals (3, 4)
The first integral IintðtÞ is the total relative charge suppression up to time t,
and the second integral Iareais the total relative charge suppression over the
time course of the SPR. Random choices are made of the sojourn times of R?
in its phosphorylation states, according to their exponential distribution; the
ensuing deactivation is implemented according to the statistical scheme pre-
sented in (10) and the output E?, as a function of time, is fed into the spatio-
temporal model described in refs. 9 and 11 to compute the relative current
suppression IðtÞ and the values of the functionals in Eq. 3. This operation is
done on the full model in refs. 9 and 10, containing all features of diffusion
(D), Ca2þfeedback (F), nonlinear coupling of current to Ca2þand cGMP, local
cGMP hydrolysis by E?(S), and nonlinear regulation of cGMP synthesis by gua-
nylyl cyclase activating proteins (GCAPs) and Ca2þ(N), denoted by DFSN. This
procedure is then repeated with one or more of these components removed.
When one of these elements is mathematically removed from the model, it is
denoted by the same letter in lower case. For example, dFSN means that the
effects of diffusion have been eliminated from the model, making it globally
well-stirred, while the remaining features are kept operative. After 5,000
iterations of this process, for each of the indicated cases, the CVs of E?
and Iareafor both WT and serine triple mutant mouse (3-P mutant mouse),
that shows significantly slower recovery (15), are computed and shown in
intðtÞ is the total activity of E?up to time t, and the second
areais the total activity of E?over the entire time course of the
Tables 1 and 2. The CVs of E?
are computed as functions of time, and reported in Figs. 1 and 2. One can also
compute the CV of other functionals, such as the current I at its peak value
IðtpeakÞ. Tables for this functional, both for WT and mutant mice with differ-
ent numbers of rhodopsin phosphorylation sites removed, are presented in SI
Appendix, Tables S7–S10. The numerical values of the parameters involved
are determined as in refs. 10 and 13 and are reported in a parameter table
in SI Appendix, Table S1.
intðtÞ and IintðtÞ for both WTand 3P-mutant mouse
Results and Discussion
In the experimental literature, the variability of the SPR is mea-
sured only in terms of the relative current suppression IðsÞ, its
integral IintðtÞ, and the area integral Iarea, introduced in Eqs. 1
and 3, as these are the only experimentally accessible quantities
in intact rods (2–4, 16). Our CV(Iarea) of a virtual WT mouse re-
produces the experimental CV(Iarea) of a WT mouse: The DFSN
yields CV ¼ 37% (Table 1) vs. ≈36% reported in ref. 4. A more
detailed comparison between virtual and experimental data is in
ref. 10. However, often an explanation of variability suppression
is provided in terms of the variability of the activated complex
E?and the number of steps to R?deactivation (2, 4, 7, 16). The
underlying assumption is that the variability of E?and its func-
tional is essentially passed along one-to-one to that of the current
and its functional. However, careful consideration of rod struc-
ture and function clearly shows that this notion is unrealistic.
First, the activation of a single R?results in highly localized
cGMP hydrolysis in the small part of cytoplasm adjacent to
the activated disc. The hydrolysis results in an immediate drop
in local cGMP concentration, which affects local phosphodiester-
ase activity. Second, to affect the current, this drop in the cGMP
has to reach the outer membrane. Third, the relationship
between cGMP concentration near the channel and the current
is nonlinear. Fourth,Ca2þregulates cGMPsynthesis, and the sup-
pression of the current in the course of the SPR results in the
immediate reduction of Ca2þconcentration at the membrane,
next to closed channels. Fifth, this local drop in Ca2þspreads
to the GCAP-GC system by diffusion through the rod cytoplasm,
which has an intricate shape. Sixth, the effect of Ca2þconcentra-
tion on GC activity is nonlinear. Because all these events take
place within the time course of the SPR, the change of E?cannot
directly translate into current suppression. These nonlinear rela-
tions surface rather naturally from Hill’s type laws linking cGMP
and Ca2þto the photocurrent, the Ca2þfeedback, and the second
order reactions involved in the cGMP hydrolysis by E?.
In view of this frequent and improper identification of CV
stances one might expect such a one-to-one correspondence
these two CVs to be equal, two conditions must be simultaneously
met: hydrolysis of cGMP by E?occurs at constant rate, i.e.,
½cGMP? ¼ ½cGMP?dark, and the Hill’s relations linking the photo-
area) with CVðIareaÞ, it is natural to ask under what circum-
areaÞ and CVðIareaÞ. Our analysis shows that for
Table 1. CV of the functional Iareain WT mouse
FSN FSn FsNfSNfsN fSnFsnfsn
CV for models with (D) or without (d) diffusion plotted against
presence or absence of other stabilizing mechanisms, Ca2þfeedback
(F), saturation effects (S), and nonlinearity (N).
Table 2. CV of the functional Iareain serine triple mutant mouse
FSNFSn FsNfSN fsNfSn Fsnfsn
CV for models with (D) or without (d) diffusion plotted against
presence or absence of other stabilizing mechanisms, Ca2þfeedback
(F), saturations effects (S), and nonlinearity (N).
Caruso et al. PNAS
May 10, 2011
current current to ½cGMP? are linear. In short, if all sources of
nonlinearity are removed from the system. For well-stirred sys-
tems (dfsn), a rigorous mathematical proof of this fact is pre-
sented in SI Appendix.
In view of the unrealistic nature of such a linear rod outer seg-
ment, and given that, as shown in ref. 10, the number of steps to
R?deactivation does not act as a variability suppressor, one is led
to search for a stabilizing mechanism in other components of
the process. In ref. 9 we identified the diffusion of the second
messengers in the cytoplasm as a major variability suppressor;
here we separate the components of the transduction cascade
to identify further stabilizing mechanisms. The main results,
extracted from Tables 1 and 2 and Figs. 1 and 2 are as follows:
i. The cooperative, nonlinear relations between second messen-
gers and current, and their mutual nonlinear links through GC
(N), play a major role in stabilizing the system. That is, when
the (nonlinear) Hill’s type relations are replaced by their lin-
ear approximations (n), the resulting system exhibits a consid-
erably higher CV.
ii. By keeping ½cGMP? ¼ ½cGMP?darkin the hydrolysis of cGMP
by the T?-E?complex increases the CVof the relative photo-
current suppression. Thus, local hydrolysis of cGMP produ-
cing saturation effects acts as a variability suppressor.
iii. The presence of a physical space distributed system where the
second messengers move by Brownian motion (D), contri-
butes to stabilization of the photoresponse. That is, when
the space resolved model of refs. 9, 11, and 12 is replaced
by a lumped or well-stirred one, where the spatial component
and diffusion play no role (d), the CV of the photocurrent
functionals is considerably higher.
iv. There is a cooperative (although not additive) effect of the
three features: (D), (N), and (S). Indeed, each of them alone
(Dns), (dNs), or (dnS) has a moderate effect on the CVof the
photocurrent, whereas (D) with at least one of (S) and (N) or
both, significantly reduce variability, pointing to a system be-
v. Clamping Ca2þat its dark level (f), while changing the photo-
response (higher amplitude and slower recovery) has a minor
effect on the variability of the system. That is if ½Ca2þ? is kept
at its dark value ½Ca2þ?darkthroughout the process, the CVof
the relative photocurrent suppression, is essentially the same
as the CVof the relative current suppression, when Ca2þfeed-
back is permitted (F). This result is in agreement with the ex-
perimental data presented in refs. 2 and 3.
vi. These results continue to hold for mutant mice, where one or
more of the R?phosphorylation sites are mutated or made
inoperative (15, 17,18). Simulations are reported for a virtual
3-P mutant mouse, the mutant where three phosphorylation
sites have been mathematically removed, which is compared
to the experimental data shown in ref. 15. The simulated CVof
other virtual mutant mice is reported in SI Appendix.
We showed in ref. 10 that if the transduction functions of the
cytoplasm are in their WT state, the number of phosphorylation
sites does not act as a variability suppressor. On the one hand, this
result suggests that the response stabilizing mechanisms reside
elsewhere; on the other hand, it raises the question as to whether
genetically manipulated ROS, which have fewer sites for phos-
phorylation, exhibit stabilization mechanisms, downstream of
activation/deactivation, that could be different than in WT.
Therefore, we simulated the photoresponse of virtually mod-
ified mice expressing rhodopsin with 1–5 phopshorylation sites.
Table 2 and Fig. 2 report the simulations for the representative
case of 3-P mutant mouse, that shows significantly slower recov-
ery (15). Simulations for 4–5P virtual mutant mice are presented
in SI Appendix.
In all cases, although the numerical values of the CV func-
tionals are slightly different, the patterns are very similar. First
the largest CV is exhibited by the effector area integrals E?
CV, regardless of the presence or absence of diffusion, in WTand
transgenic mice. A comparison of Figs. 1 and 2 shows that asymp-
totically as t → ∞, the CVðIareaÞ is the same as that of the area
(DFsn), (dFsn), (Dfsn), and (dfsn), the CV of E?
along, asymptotically as t → ∞, to that of Iarea. This analysis iden-
tifies the nonlinearities arising from the Hill’s relations, and lo-
calized hydrolysis of cGMP by E?, as key players in the variability
suppression of IintðtÞ as t → ∞.
The removal of diffusion, keeping one or all, nonlinearities
active (dFSN), (dFsN), and (dFSn), yields CVðIareaÞ of the order
of 50%, regardless of Ca2þclamping, demonstrating only a mod-
erate CV suppression (Tables 1 and 2). Thus, diffusion is essential
for the nonlinearities to play their stabilizing role. However,
diffusion without both the nonlinearities generated by the Hill’s
laws and saturation effects (DFsn), (Dfsn) yields a CV of the
same order (about 55%). In the presence of diffusion, at least
area. The last two columns in Tables 1 and 2 show the same
areaof the activated complex E?. Thus for the models
some, or no stabilizing mechanisms. Plotted is the CV of the area integral
variability (brown dashed curves), and of the current suppression ∫t
functions of time, for the models that contain all the stabilizing mechanisms,
diffusion (D), Ca2þfeedback (F), saturation effects (S), and nonlinearity (N)
(DFSN, red), or remove them one at a time (DFSn, purple diamond; DFsN,
dashed red; DfSN, green circle; dFSN, blue triangle; or dfsn, light brown
Time course of variability suppression in a WT mouse containing all,
0E?ðsÞds of the activated complex E?on the rod disc surface, that has largest
0 0.51 1.5
the time course of variability suppression (serine triple mutant mouse). CV of
the area integral ∫t
curves), and of the current suppression ∫t
the models that contain all the stabilizing mechanisms, diffusion (D), Ca2þ
feedback (F), saturation effects (S), and nonlinearity (N) (DFSN red), or re-
move them one at a time (DFSn, purple diamond; DFsN, dashed red; DfSN,
green circle; dFSN, blue triangle; or dfsn, light brown square).
Effect of removing three phosphorylation sites on rhodopsin (3P) on
0E?ðsÞds of the activated complex E?(brown dashed
0IðsÞds as functions of time, for
www.pnas.org/cgi/doi/10.1073/pnas.1018960108Caruso et al.
one nonlinearity is needed to stabilize the system [models (DFSn) Download full-text
and (DFsN)]. Thus, it appears that the biophysical effects of
diffusion and the biochemical effects of the nonlinear second
order photocurrent generating reactions act cooperatively to sup-
press the variability of the single photon response. Neither factor
alone suffices to stabilize the system, suggesting that they play
To gain insight on the role of each, recall that the photocurrent
is stable if the system dampens the tail current generated by long
lasting activated rhodopsin (tail events), making these responses
statistically similar to those generated by R?of average lifetime.
After localized cGMP hydrolysis, most of the cGMP-gated
channels near the activation site, are closed. Therefore, ½cGMP?
and the current JcGit generates are close to their minimum values
(SI Appendix, Eq. S1), and the current suppression is maximum
(Eq. 1). Diffusion (D), nonlinearities (N), and saturation effects
(S), generate a concerted mechanism that keeps the channels
closed for a lag time Δt, during which further cGMP hydrolysis
due to a long lived R?is slowed, and cannot close additional chan-
nels locally, and generate more current suppression.
Diffusion forces the molecules to travel with finite speed, onto
or away from the sites where the biochemical machinery acts. For
example, after hydrolysis and the closing of the ionic channels,
molecules of cGMP produced by GC reach the lateral boundary
of the ROS by diffusion and with finite speed, where they bind
and reopen the channels. The Hill’s coefficient governing cGMP
binding to tetrameric cGMP-gated channels determines how
many cGMP are needed to reopen the closed channel (theoreti-
cally four because each monomer has one cGMP binding site).
This mechanism builds in a lag time for cGMP to accumulate
locally, to reopen the channel, and terminate photocurrent sup-
pression. Simultaneously, because [cGMP] remains close to its
minimum, hydrolysis events [saturation effects (S)] due to long
lasting R?are less effective, thereby extending this lag time. Thus,
in presence of diffusion (D), the nonlinearities (N), and the
saturation effects (S) act in cascade to stabilize the system. Each
of them alone (DFSn) or (DFsN) is capable of reducing the CV
to some extent (Tables 1 and 2), the maximum variability suppres-
sion occurs if they both are present.
In absence of diffusion (well-stirred ROS, i.e., zero spatial gra-
dients) molecules move, at least theoretically, with infinite speed,
thereby distributing the [cGMP] drop instantaneously and uni-
formly throughout the cytosol, and hence producing a very small
local cGMP reduction. Therefore, near the activation site, propor-
tionally fewer channels are closed, and the system is ready to re-
A similar argument can be produced for the saturation effects.
If in the process of hydrolysis, local [cGMP] is kept at its dark va-
lue, the activated effector E?constantly has substrate, and more
cGMP molecules are depleted per unit of time. As a consequence
the system keeps closing channels even in response to tail events,
thereby augmenting the variability of the current suppression.
The picture that emerges is that the observed high fidelity of
the photoresponse, (i.e., variability suppression) is not simply a
function of biochemical processes. Instead, it is a systemic func-
tion of biochemical, biophysical, and geometrical components.
Our analysis identifies local cGMP hydrolysis with subsequent
diffusion in rod cytoplasm with complex geometry and nonlinear-
ity of the regulation of cGMP-gated channels and GC by cGMP
and Ca2þ, respectively, as key factors in variability suppression,
ensuring high reproducibility of single photon response.
We would like to point out that our modeling of rods carrying
rhodopsin with a different number of phosphorylation sites
yielded an excellent approximation of experimental data (com-
pare refs. 10 and 15). Although it is impossible to mimic experi-
mentally the difference between the biologically relevant rod
cytoplasm of intricate shape and the well-stirred system without
local saturation and diffusion, it should be possible to construct
mutant cGMP-gated channels with linear responsiveness to
cGMP or GCAPs with more linear response to Ca2þ. However,
no such mutants currently exist, so the spatially resolved ROS
model remains the only available tool to probe the effects of non-
linear regulation of channels and cGMP hydrolysis.
In conclusion, we would like to note that the design of cGMP-
gated channels and Ca2þ-binding GC activating proteins em-
ployed by photoreceptors is not unique. Numerous regulatory
proteins, such as other cyclic nucleotide-gated channels, calmo-
dulin and related Ca2þ-binding proteins, protein kinase A, etc.,
have multiple binding sites for their ion/small molecule activa-
tors, which results in cooperative regulation. The complex geo-
metry of the cytoplasm distributed between stacks of detached
discs (vertebrate rods) or semidetached (vertebrate cones and in-
vertebrate photoreceptors) is a common feature of photoreceptor
cells preserved over hundreds of millions of years of evolution.
Interestingly, in neurons that are constantly integrating numerous
inputs, the signaling via excitatory and inhibitory synapses feeds
onto dendritic trees with extremely complex geometry, rather
than directly onto a well-stirred cell body. Thus, it appears that
nonlinearity of biochemical regulation and subsequent diffusion
of second messengers via the cytoplasm with sophisticated geo-
metry is a common theme in biological signaling.
ACKNOWLEDGMENTS. We thank Dr. Clint Makino for mouse electrophysiolo-
gical data. This work has been conducted in part using the resources of the
Advanced Computing Center for Research and Education at Vanderbilt
University. E.D. was supported by National Institutes of Health (NIH) Grant
1RO1GM068953 and National Science Foundation Grant DMS0652385;
H.E.H was supported by NIH Grants EY006062 and EY0102291; and V.V.G.
was supported by NIH Grants GM077561, GM081756, and EY011500.
1. Pugh ENJ, Lamb TD (2000) Phototransduction in vertebrate rods and cones: Molecular
mechanisms of amplification, recovery and light adaptation. Handbook of Biological
Physics, Molecular Mechanisms of Visual Transduction, eds DG Stavenga, WJ de Grip,
and ENJ Pugh (Elsevier Science, St. Louis), Vol 3, pp 183–255.
2. Rieke F, Baylor DA (1998) Origin of reproducibility in the responses of retinal rods to
single photons. Biophys J 75:1836–1857.
3. Whitlock GG, Lamb TD (1999) Variability in the time course of single photon responses
from toad rods: Termination of rhodopsin’s activity. Neuron 23:337–351.
4. Doan T, Mendez A, Detwiler P, Chen J, Rieke F (2006) Multiple phosphorylation sites
confer reproducibility of the rod’s single-photon responses. Science 313:530–533.
5. Baylor DA, Lamb TD, Yau KW (1979) Responses of retinal rods to single photons.
J Physiol 288:613–634.
6. Field GD, Rieke F (2002) Mechanisms regulating variability of the single photon
responses of mammalian rod photoreceptors. Neuron 35:733–747.
7. Doan T, Azevedo W, Hurley J, Rieke F (2009) Arrestin competition influences the
kinetics and variability of the single-photon responses of mammalian rod photorecep-
tors. J Neurosci 29:11879–11867.
8. Hamer RD, Nicholas SC, Tranchina D, Liebman PA, Lamb TD (2003) Multiple steps
of phosphorylation of activated rhodopsin can account for the reproducibility of
vertebrate rod single-photon responses. J Gen Physiol 122:419–444.
9. Bisegna P, et al. (2008) Diffusion of the second messengers in the cytoplasm acts as a
variability suppressor of the single photon response in vertebrate phototransduction.
Biophys J 94:3363–3383.
10. Caruso G, et al. (2010) Kinetics of rhodopsin deactivation and its role in regulating
recovery and reproducibility in rod photoresponse. PLoS Comput Biol 6:e1001031.
11. Caruso G, et al. (2006) Modeling the role of incisures in vertebrate phototransduction.
Biophys J 91:1192–1212.
12. Caruso G, et al. (2005) Mathematical and computational modeling of spatio-temporal
signaling in rod phototransduction. IEE Proc Syst Biol 152:119–137.
13. Shen L, et al. (2010) Dynamics of mouse rod phototransduction and its sensitivity to
variation of key parameters. IET Sys Biol 4:12–32.
14. Makino CL, et al. (2008) A role for GCAP2 in regulating the photoresponse. Guanylyl
cyclase activation and rod electrophysiology in GUCA1B knockout mice. J Biol Chem
15. Mendez A, et al. (2000) Rapid and reproducible deactivation of rhodopsin requires
multiple phosphorylation sites. Neuron 28:153–164.
16. Rieke F, Baylor DA (1998) Single photon detection by rod cells of the retina. Rev Mod
17. Burns ME, Mendez A, Chen J, Baylor DA (2002) Dynamics of cyclic GMP synthesis in
retinal rods. Neuron 36:81–91.
18. Xu J, et al. (1997) Prolonged photoresponses in transgenic mouse rods lacking arrestin.
Caruso et al.PNAS
May 10, 2011