Research A main goal of my work to understand the neural mechanisms underlying visual perception. My research combines theoretical analysis, mathematical modeling and computer simulation, with experimental studies. One goal is to account for how neurons in the visual system encode information, that is, how they transform visual stimuli into electrical signals. The idea is to explain this encoding in terms of the neural circuitry, properties of the neurotransmitter receptors, and the membrane biophysics of individual neurons. Ideally, one attempts to construct a mathematical model in which each term in the system of equations has a physiological correlate. A long-term goal is to be able to predict the responses of the various types of neurons in the visual system to arbitrary stimuli varying over time and space. I am currently studying topics at two levels in the visual system, retina and visual cortex. One of my projects is a study of synaptic transmission between photoreceptors and target neurons: horizontal and bipolar cells. The photoreceptor synapse is an unusual synapse in the central nervous system in that it is a tonic synapse between two cells that both encode information by slow, graded potentials. I am working in collaboration with experimentalists who are providing patch-clamp recording data of presynaptic voltage and postsynaptic conductance. We are working on developing a mathematical model for the transduction between these two signals that is based on known physiology and biophysics of the neurons and receptors. A central issue is the dependence of transmitter release on intracellular calcium. Evidence so far indicates a surprising, linear relationship between membrane calcium flux and the rate of release of synaptic transmitter. Classical synapses show a cooperative relationship. we are investigating the origin of this linear relationship by combining experiments with mathematical analysis. Once a good working model for synaptic transmission is developed, these results can be combined with my previous models of phototransduction in rods and cones to give a good model for information processing in the outer retina. Another ongoing project focuses on developing new methods for modeling huge neural networks that are intractable by standard techniques. The new methods employ the theory of the probability (population) density function, borrowed from the field of statistical mechanics. The factors which make conventional methods unwieldy or intractable---thousands of neurons and millions of synapses---are used to great advantage in these new methods. In the population density method, similar neurons are lumped together in a population, and one tracks the distribution of neurons over state space in each population. The state of a neuron is determined by the dynamic variables in the underlying single neuron model. The population firing rate is given by the flux of probability across a particular surface in state space. Neurons are coupled via stochastic synapses, and the rate of excitatory/inhibitory input events for a target neuron is determined by the rate of action potentials in each of the presynaptic populations and by the average number of synapses the postsynaptic neuron receives from each of these populations. Computation time in a simple model for orientation tuning in primary visual cortex can be sped up one hundred-fold using these techniques rather than conventional methods. My newest project is a study of the role of feedback from visual cortex to the lateral geniculate nucleus (dLGN) of the thalamus. Fernand Hayot, from Ohio State University, and I are developing models that account for the sensitivity of dLGN neurons to orientation discontinuities in visual stimuli. Teaching I teach both in the Department of Biology and the Department of Mathematics. Graduate Biology courses include:
Biosketch I received my Ph.D. in 1981 from the Rockefeller University, where I studied physical chemistry, membrane biophysics, neurophysiology, and mathematics. My dissertation was an analysis of information processing in the outer retina of the turtle. My postdoctoral research was a combined experimental and theoretical study of light adaptation -- a process by which the retina adjusts its sensitivity according to lighting conditions. In 1984, I joined the faculty of New York University with a joint appointment in the Courant Institute of Mathematical Sciences and the Department of Biology Areas of Research/Interest Biology and Mathematics Information processing in the retina Fellowships/Honors Whitehead Fellowship, New York University, 1986.
Publications
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