Simulation

Numerical simulation of a compartmental neuron model has its origins in the pioneering work of Hodgkin and Huxley. These simulations solve a set of simultaneous differential equations describing membrane potential, ion concentrations, and other parameters in the neuron from a set of initial conditions. Until recently most models used simplified geometries of neurons to decrease the computational requirements. As numerical methods have improved, a number of packages have become available that allow efficient solution of thousands of equations while shielding the end user from technical issues. There are literally hundreds of publications making use of the simulation environment NEURON. For large neurons in the hippocampus and neocortex, the past few years have led to a major rethinking of the role of the dendrites. We now know that the dendrites propagate action potentials, and that the conditions for propagation vary greatly and depend on prior synaptic activity, prior action potential activity, and input from neuromodulatory systems. These dependencies correlate well to the induction of long-term potentiation, a synaptic process thought to play a major role in learning and memory. However, these complex functions of the dendrites render the vast majority of biophysical models of pyramidal neurons as obsolete. Moreover, newer biophysical models that exist are incomplete because of a lack of knowledge about what happens in small branches of the dendrites. Thus, an important motivation for the present proposal is to rapidly enhance our understanding of the electrophysiology of small dendritic branches that are not amenable to study with conventional patch electrode techniques but are accessible with functional imaging.

Kinetic models of ion channels describing current through each channel as a function of time and membrane potential have been produced by fitting electrophysiological currents (using least squares methods) to either Markov models or to specific formalisms such as that of Hodkin & Huxley. Only recently has it been widely appreciated that the ion channels in the dendrites and axons have different properties than those in the cell body. Thus, although there are many single channel recordings of ion channels, only in the past few years and in only a limited number of laboratories have kinetic data from dendrites been acquired. The best-studied neurons in terms of available dendritic channel data are the CA1 pyramidal neurons in the hippocamous that we propose to study. We have electrophysiological data for the major channel types, and continued characterization of these ion channels is a large part of our ongoing funded research.