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NJIT Mathematical Biology Seminar

NJIT / Rutgers Biological Sciences Special Colloquium

Tuesday, March 18, 2008, 1:00pm
Life Science Center - Rm 103
Rutgers University (Newark)

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Understanding the relationship between maximal conductances and behavioral properties in a neuronal model

Adam Taylor

Volen Center for Complex Systems, Brandeis University

Neurons typically express many different types of voltage-gated channels. The density of these channels, their kinetics, and their spatial distribution determine how the neuron behaves, both endogenously and in response to external inputs. The ^Sbehavior^T of a neuron can be described in terms of many different quantities, such as the resting membrane potential, the input resistance, the amount of postinhibitory rebound following a hyperpolarizing current injection, and the duration of plateau potentials evoked by a depolarizing current pulse. Understanding the mapping from channel kinetics and densities to these behavioral quantities is a recurring problem in cellular biophysics, and one that must be solved for each different type of neuron one encounters.

We faced this problem in the process of building a simplified model of the LP cell in the pyloric network of the crab Cancer borealis. The model contains two compartments, one for the soma+neurites and one for the axon. We generated a large number of models (~600,000) by choosing each model parameter (maximal conductances, etc.) at random from a realistic biological range. We then simulated the response of each model to a synaptic input designed to mimic the rhythmic synaptic inhibition the LP cell receives during the ongoing pyloric rhythm. Several aspects of the model^Rs response to this input were quantified, including the phase of burst onset, the phase of burst offset, the frequency of spiking during the burst, and the slow-wave amplitude. We then selected admissible LP models by keeping only those models that had realistic values for all of these quantities. This yielded a population of ~1500 admissible LP models. For this population, we were able to fit the individual mappings from parameters to behavioral quantities with either quadratic or cubic functions. The coefficients of these fits lend insight into which parameters are the main determinants of a given neuronal behavior, and in what relative amounts. Furthermore, they implicitly specify ways in which parameters can be varied while leaving a single behavior, or a combination of them, constant.

This is a joint work with Eve Marder