A parallel nonlinear-linear neuronal model

Traditionally the electrical properties of neuronal membranes were modeled using a parallel combination of nonlinear and linear compartments representing the active and passive properties, respectively. In this study, the linear compartment was characterized by the first order Volterra kernel of the system, and the nonlinear compartment was represented by a static nonlinearity characterized by its current-voltage (I-V) relationship. The parallel nonlinear-linear (PNL) model was investigated using a system identification strategy based on the Volterra-Wiener approach to estimate the first order Volterra kernel of the system, and a network theoretic approach to estimate the I-V relationships of the two parallel compartments. The PNL model demonstrated the presence of an effective resistance that accounts for the loading effects of the higher order Volterra kernels on the linear compartment.