NYU/CNS : Faculty : Associates of CNS : Daniel Tranchina

My research combines experimental study with theoretical analysis, mathematical modeling, and computer simulation. A main goal is to understand the neural mechanisms underlying visual perception. One of my ongoing projects, in collaboration with Russ Hamer at the Smith-Kettlewell Eye Research Institute, is a study of vertebrate phototransduction. Two main issues are light adaptation in rods and cones, and the reproducibility of rod responses to single photons. The responses of rods and cones, under various states of adaptation, are recorded by the suction electrode technique. These data, in conjunction with other electrophysiological and biochemical data, provide a basis for developing a mathematical model that accounts for light adaptation and statistical properties of the singe-photon response in terms of the molecular mechanisms underlying phototransduction.

Another ongoing project focuses on new methods for modeling huge neural networks that are intractable by standard techniques. These methods are being used to model the physiology of primary visual cortex and the feedback from cortex to the lateral geniculate nucleus. The new methods employ the theory of the probability density function, borrowed from the field of statistical mechanics. The factors that make conventional methods unwieldy or intractable—thousands of neurons and millions of synapsesÑare 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 100-fold using these techniques rather than conventional methods.

E-mail: dant@cns.nyu.edu

Selected Publications

Tranchina, D. (1998) Commentary: the calculus of rod phototransduction. Journal of General Physiology 111: 3-6
Surkis, A., Peskin, C.S., Tranchina, D., and Leonard, C.S. (1998) Recovery of cable properties through active and passive modeling of subthreshold membrane responses from laterodorsal tegmental neurons. Journal of Neurophysiology 80: 2593-2607
Nykamp, D. and Tranchina, D. (2000) A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning. Journal of Computational Neuroscience 8: 19-50
Nykamp, D.Q. and Tranchina, D. (2000) Fast neural network simulations with population density methods. Neurocomputing 32-33: 487-492
Nykamp, D.Q. and Tranchina, D. (2001) A population density approach that facilitates large-scale modeling of neural networks: extension to slow inhibitory synapses. Neural Computation 13: 511-546
Witkovsky, P., Thoreson, W., and Tranchina, D. (2001) Transmission at the photoreceptor synapse. Progress in Brain Research 131: 145-159
Haskell, E., Nykamp, D.Q., and Tranchina, D. (2001) Population density methods for large-scale modeling of neural networks with realistic synaptic kinetics: cutting the dimension down to size. Network: Computation in Neural Systems 12: 141-174
Haskell, E., Nykamp, D.Q., and Tranchina, D. (2001) Population density methods for large-scale modeling of neural networks with realistic synaptic kinetics. Neurocomputing 38-40: 627-632
Hayot, F. and Tranchina, D. (2001) Modeling sensitivity of lateral geniculate neurons to orientation discontinuity and the role of feedback from visual cortex. Visual Neuroscience 18: 865-877
Tranchina, D. (2002) Mathematics in visual neuroscience: the retina. In An Introduction to Mathematical Modeling in Physiology, Cell Biology and Immunology, ed. J. Sneyd, Provide, RI: American Mathematical Society, in press