Spero Nicholas

Multiple steps of phosphorylation of activated rhodopsin can account for the reproducibility of vertebrate rod Single-photon responses

Single-photon responses (SPRs) in vertebrate rods are considerably less variable than expected if isomerized rhodopsin (R*) inactivated in a single, memoryless step, and no other variability-reducing mechanisms were available. We present a new stochastic model, the core of which is the successive ratcheting down of R* activity, and a concomitant increase in the probability of quenching of R* by arrestin (Arr), with each phosphorylation of R* (Gibson, S.K., J.H. Parkes, and P.A. Liebman. 2000. Biochemistry. 39:5738–5749.). We evaluated the model by means of Monte-Carlo simulations of dim-flash responses, and compared the response statistics derived from them with those obtained from empirical dim-flash data (Whitlock, G.G., and T.D. Lamb. 1999. Neuron. 23:337–351.). The model accounts for four quantitative measures of SPR reproducibility. It also reproduces qualitative features of rod responses obtained with altered nucleotide levels, and thus contradicts the conclusion that such responses imply that phosphorylation cannot dominate R* inactivation (Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836–1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733–747.). Moreover, the model is able to reproduce the salient qualitative features of SPRs obtained from mouse rods that had been genetically modified with specific pathways of R* inactivation or Ca2+ feedback disabled. We present a theoretical analysis showing that the variability of the area under the SPR estimates the variability of integrated R* activity, and can provide a valid gauge of the number of R* inactivation steps. We show that there is a heretofore unappreciated tradeoff between variability of SPR amplitude and SPR duration that depends critically on the kinetics of inactivation of R* relative to the net kinetics of the downstream reactions in the cascade. Because of this dependence, neither the variability of SPR amplitude nor duration provides a reliable estimate of the underlying variability of integrated R* activity, and cannot be used to estimate the minimum number of R* inactivation steps. We conclude that multiple phosphorylation-dependent decrements in R* activity (with Arr-quench) can confer the observed reproducibility of rod SPRs; there is no compelling need to invoke a long series of non-phosphorylation dependent state changes in R* (as in Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836–1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733–747.). Our analyses, plus data and modeling of others (Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836–1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733–747.), also argue strongly against either feedback (including Ca2+-feedback) or depletion of any molecular species downstream to R* as the dominant cause of SPR reproducibility.

Toward a unified model of vertebrate rod phototransduction.

Recently, we introduced a phototransduction model that was able to account for the reproducibility of vertebrate rod single-photon responses (SPRs) (Hamer et al., 2003). The model was able to reproduce SPR statistics by means of stochastic activation and inactivation of rhodopsin (R*), transducin (G alpha ), and phosphodiesterase (PDE). The features needed to capture the SPR statistics were (1) multiple steps of R* inactivation by means of multiple phosphorylations (followed by arrestin capping) and (2) phosphorylation dependence of the affinity between R* and the three molecules competing to bind with R* (G alpha, arrestin, and rhodopsin kinase). The model was also able to account for several other rod response features in the dim-flash regime, including SPRs obtained from rods in which various elements of the cascade have been genetically disabled or disrupted. However, the model was not tested under high light-level conditions. We sought to evaluate the extent to which the multiple phosphorylation model could simultaneously account for single-photon response behavior, as well as responses to high light levels causing complete response saturation and/or significant light adaptation (LA). To date no single model, with one set of parameters, has been able to do this. Dim-flash responses and statistics were simulated using a hybrid stochastic/deterministic model and Monte-Carlo methods as in Hamer et al. (2003). A dark-adapted flash series, and stimulus paradigms from the literature eliciting various degrees of light adaptation (LA), were simulated using a full differential equation version of the model that included the addition of Ca2+-feedback onto rhodopsin kinase via recoverin. With this model, using a single set of parameters, we attempted to account for (1) SPR waveforms and statistics (as in Hamer et al., 2003); (2) a full dark-adapted flash-response series, from dim flash to saturating, bright flash levels, from a toad rod; (3) steady-state LA responses, including LA circulating current (as in Koutalos et al., 1995) and LA flash sensitivity measured in rods from four species; (4) step responses from newt rods ( Forti et al., 1989) over a large dynamic range; (5) dynamic LA responses, such as the step-flash paradigm of Fain et al. (1989), and the two-flash paradigm of Murnick and Lamb (1996); and (6) the salient response features from four knockout rod preparations. The model was able to meet this stringent test, accounting for almost all the salient qualitative, and many quantitative features, of the responses across this broad array of stimulus conditions, including SPR reproducibility. The model promises to be useful in testing hypotheses regarding both normal and abnormal photoreceptor function, and is a good starting point for development of a full-range model of cone phototransduction. Informative limitations of the model are also discussed.

Analysis of human vergence dynamics

Disparity vergence is commonly viewed as being controlled by at least two mechanisms, an open-loop vergence-specific burst mechanism analogous to the ballistic drive of saccades, and a closed-loop feedback mechanism controlled by the disparity error. We show that human vergence dynamics for disparity jumps of a large textured field have a typical time course consistent with predominant control by the open-loop vergence-specific burst mechanism, although various subgroups of the population show radically different vergence behaviors. Some individuals show markedly slow divergence responses, others slow convergence responses, others slow responses in both vergence directions, implying that the two vergence directions have separate control mechanisms. The faster time courses usually had time-symmetric velocity waveforms implying open-loop burst control, while the slow response waveforms were usually time-asymmetric implying closed-loop feedback control. A further type of behavior seen in a distinct subpopulation was a compound anomalous divergence response consisting of an initial convergence movement followed by a large corrective divergence movement with time courses implying closed-loop feedback control. This analysis of the variety of human vergence responses thus contributes substantially to the understanding of the oculomotor control mechanisms underlying the generation of vergence movements [corrected].

Deficits in the Activation of Human Oculomotor Nuclei in Chronic Traumatic Brain Injury

Binocular eye movements form a finely tuned system that requires accurate coordination of the oculomotor dynamics of the brainstem control nuclei when tracking the fine binocular disparities required for 3D vision. They are particularly susceptible to disruption by brain injury and other neural dysfunctions. Here, we report functional magnetic resonance imaging activation of the brainstem oculomotor control nuclei by binocular saccadic and vergence eye movements, and significant reductions in their response amplitudes in mild or diffuse traumatic brain injury (dTBI). Bilateral signals were recorded from a non-TBI control group (n = 11) in the oculomotor control system of the superior colliculi, the oculomotor nuclei, the abducens nuclei, and in the supra-oculomotor area (SOA), which mediate vergence eye movements. Signals from these nuclei were significantly reduced overall in a dTBI group (n = 12) and in particular for the SOA for vergence movements, which also showed significant decreases in velocity for both the convergence and divergence directions.

Consequences of Traumatic Brain Injury for Human Vergence Dynamics

Purpose: Traumatic brain injury involving loss of consciousness has focal effects in the human brainstem, suggesting that it may have particular consequences for eye movement control. This hypothesis was investigated by measurements of vergence eye movement parameters. Methods: Disparity vergence eye movements were measured for a population of 123 normally sighted individuals, 26 of whom had suffered diffuse traumatic brain injury (dTBI) in the past, while the remainder served as controls. Vergence tracking responses were measured to sinusoidal disparity modulation of a random-dot field. Disparity vergence step responses were characterized in terms of their dynamic parameters separately for the convergence and divergence directions. Results: The control group showed notable differences between convergence and divergence dynamics. The dTBI group showed significantly abnormal vergence behavior on many of the dynamic parameters. Conclusion: The results support the hypothesis that occult injury to the oculomotor control system is a common residual outcome of dTBI.

Analysis of Neural-BOLD Coupling Through Four Models of the Neural Metabolic Demand

The coupling of the neuronal energetics to the blood-oxygen-level-dependent (BOLD) response is still incompletely understood. To address this issue, we compared the fits of four plausible models of neurometabolic coupling dynamics to available data for simultaneous recordings of the local field potential and the local BOLD response recorded from monkey primary visual cortex over a wide range of stimulus durations. The four models of the metabolic demand driving the BOLD response were: direct coupling with the overall LFP; rectified coupling to the LFP; coupling with a slow adaptive component of the implied neural population response; and coupling with the non-adaptive intracellular input signal defined by the stimulus time course. Taking all stimulus durations into account, the results imply that the BOLD response is most closely coupled with metabolic demand derived from the intracellular input waveform, without significant influence from the adaptive transients and nonlinearities exhibited by the LFP waveform.

Perceptual coding for 3D reconstruction

A primary issue in 3D reconstruction is the realtime efficacy of different coding methods for the multiple decisions among competing 3D solutions. A common model framework making such coding decisions is the boundary limited drift-diffusion model, which has been developed in parallel in various branches of science from quantum physics to economics. A common property of all such models is the linear increase in variance of the diffusion processes over time, implying an inability to focus on the current information in the environment, and the inevitability of a forced random decision in the absence of any reliable evidence. We have developed an alternative, more plausible model framework for Bayesian information accumulation that solves both problems and provides an accurate account of many features of context effects in human 3D reconstruction performance.