An Algorithmic Method for Reducing Conductance-based Neuron Models

Abstract

Although conductance-based neural models provide a realistic depiction of neuronal activity, their complexity often limits effective implementation and analysis. Neuronal model reduction methods provide a means to reduce model complexity while retaining the original model's realism and relevance. Such methods, however, typically include ad hoc components that require that the modeler already be intimately familiar with the dynamics of the original model. We present an automated, algorithmic method for reducing conductance-based neuron models using the method of equivalent potentials (Kelper et al., Biol Cybern 66(5):381-387, 1992) Our results demonstrate that this algorithm is able to reduce the complexity of the original model with minimal performance loss, and requires minimal prior knowledge of the model's dynamics. Furthermore, by utilizing a cost function based on the contribution of each state variable to the total conductance of the model, the performance of the algorithm can be significantly improved.

Functional consequences of model complexity in rhythmic systems: I. Systematic reduction of a bursting neuron model

“…These two reductions, the elimination of h K1 and I CaF , were discovered through direct examination of the model's parameter space. To supplement this method, we employed the method of equivalent potentials to reveal similarities among the state variables [15,21,22]. The equivalent potential of a state variable is the value of the membrane potential at which the state variable's steady-state value would be equal to its current value.…”

Decoding complex biological networks - tracing essential and modulatory parameters in complex and simplified models of the cell cycle

“…By reformulating the model , the original model is approximated to another hopefully more transparent modeling formalism, with a structure that better captures the key qualities of the original system. Examples of model reduction [17] include lumping of variables [10,11], separation of timescales [14] (or, for example, the classical Michaelis-Menten equation describing enzyme kinetics), sensitivity analysis based methods, and methods based on identifiability analysis [13]. Examples of transformation of modeling formalism include boolean approximations [4,12], hybrid stochastic approximations [18], or the simplified model used throughout this study, a delayed piecewise linear approximation [15] of an ordinary differential model.…”