 |
Cutting the Gordian Knot of the Rod Single-Photon Response (SPR) |
Ecological importance of reliable single-photon detection by rods
Most vertebrates can perform visually guided behaviors in light so dim that the rain of
photons onto the retina is extremely sparse -- so sparse that each rod being used in
identifying and responsding to features of the environment are absorbing only one
photon every 85 minutes1. Useful vision under such dim-light
conditions thus requires that each rod be able to reliably signal the absorption of
single photons of light. Such reliability of scotopic (night, rod-mediated) vision can
be argued to have contributed significantly to the very survival of many vertebrate species.
Evidence that rod SPRs are reliable and detected
That rods actually do this was first shown psychophysically in humans by Hecht, Schlaer
& Pirenne (1942)2 and Sakitt (1972)3, and then in single-cell recordings when Baylor,
Lamb & Yau (1979)4 recorded toad rod responses to dim flashes of light. They showed
that (1) a substantial subset of these were responses to the absorption of single photons,
and (2) that the variability of the response amplitude near the peak of the response
was low -- the standard deviation (σ) was ~1/5 of the mean (μ), i.e. a coefficient of
variation (CV=σ/μ) of 0.2. Subsequent studies5-8 confirmed this low amplitude
variability, and further showed that the whole SPR waveform had a high degree of stereotypy.
This Figure shows responses to 50 consecutive dim-flash (0.6 isomerizations per flash on average)
presentations in a toad rod8. SPRs (intermediate band of responses peaking at ~2sec) are readily distinguishable from
failures (no photon absorbed) and multiple photon absorptions. In our Theory section, we show that the CV of the area under the SPR (CVarea) is the preferred index of reponse variability (as opposed to the CV of SPR amplitude). The CVarea for the cell shown
was 0.36.
The problem
SPRs are electrical responses of rods to the activation of a
single molecule of rhodopsin (R*). Since all chemical reactions are inherently
stochastic, if R* inactivated in a single molecular step (and no other variability-reducing
mechanisms were available), R*'s active lifetime would be highly variable. In fact,
theory shows that the R* lifetime distribution would be exponential, with a CV of
1.0 (5x greater than the observed amplitude variability). If R* activity (the rate
of G-protein activation) were all-or-none, then the integrated activity (i.e.
the number of G-protein activations) would be proportional to R* lifetime, with the
same variability. If, further, the reactions downstream to R* were approximately
linear for dim-flashes, the area under the SPR would be ~proportional to the number
of G* produced (see Theory). Thus, if R* shut off in a
single step, the expected theoretical CVarea would be 1.0, about 3 times
the empirical value.
Hence, explaining the rod's high degree of reproducibility in terms of underlying
biochemical reactions in the phototransduction cascade has been an enduring
"Gordian Knot" in rod physiology.9
The solution
Using a detailed stochastic model of the phototransduction cascade and exhaustive
Monte-Carlo simulation methods, the present work explains SPR reproducibility in terms
of known biochemical mechanisms. We are able to show how multiple steps of R*
inactivation, each of which is stochastic, can dramatically reduce the overall
variability of the rod response to single photons. We present new theoretical
material that shows why the CV of SPR amplitude (or SPR duration) is not a valid
measure of the underlying variability in R* activity, and why the CV of the area
under the SPR is the correct measure.
The model also is able to reproduce the salient features of responses from rods that
have had specific inactivation reactions genetically "knocked out" (KO) or
transgenically altered. Our analyses of KO and transgenic data are able to rule out
several other major theories that have been proposed to explain SPR reproducibility.
(much of work presented here has been described in a different form in
Hamer et al., 2003)
How then might reproducibility be achieved?