A strategy for mapping biophysical to abstract neuronal network models applied to primary visual cortex.

Anton V Chizhov,Lyle J Graham,Andrea Barreiro

doi:10.1371/journal.pcbi.1009007

Abstract

A fundamental challenge for the theoretical study of neuronal networks is to make the link between complex biophysical models based directly on experimental data, to progressively simpler mathematical models that allow the derivation of general operating principles. We present a strategy that successively maps a relatively detailed biophysical population model, comprising conductance-based Hodgkin-Huxley type neuron models with connectivity rules derived from anatomical data, to various representations with fewer parameters, finishing with a firing rate network model that permits analysis. We apply this methodology to primary visual cortex of higher mammals, focusing on the functional property of stimulus orientation selectivity of receptive fields of individual neurons. The mapping produces compact expressions for the parameters of the abstract model that clearly identify the impact of specific electrophysiological and anatomical parameters on the analytical results, in particular as manifested by specific functional signatures of visual cortex, including input-output sharpening, conductance invariance, virtual rotation and the tilt after effect. Importantly, qualitative differences between model behaviours point out consequences of various simplifications. The strategy may be applied to other neuronal systems with appropriate modifications.

Highlights

Theoretical modelling of a neural system can be accomplished with different degrees of biological detail and, different degrees of mathematical abstraction
Our work provides a navigation of the complex parameter space of neural network models faithful to biology, as well as highlighting how simplifications made for mathematical convenience can fundamentally change their behaviour
In this paper we address the challenge of parameter reduction and quantitative mapping from original biophysical quantities to simplified model parameters, using the orientation hyper-column, or pinwheel, architecture in the visual cortex of higher mammals as a model system

Summary

Introduction

Theoretical modelling of a neural system can be accomplished with different degrees of biological detail and, different degrees of mathematical abstraction. Because detail does not necessarily yield understanding, a more abstract description with fewer parameters and fewer degrees of freedom offers the possibility of better insight It follows that mapping between different categories of models is necessary to relate analytical results obtained from more abstract models, to simulations from detailed models which can hardly be analyzed in their parameter space. This sort of back and forth process can facilitate understanding about how specific model assumptions may be linked to detailed model behaviour. Extensions of population models have taken into account different connection profiles [4] or delays [5], both excitatory and inhibitory neuronal populations [3], or more elaborate rate models [6]

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Discussion

Conclusion