Response Characteristics of a Low-Dimensional Model Neuron

Abstract

It is shown that a low-dimensional model neuron with a response time constant smaller than the membrane time constant closely reproduces the activity and excitability behavior of a detailed conductance-based model of Hodgkin-Huxley type. The fast response of the activity variable also makes it possible to reduce the model to a one-dimensional model, in particular for typical conditions. As an example, the reduction to a single-variable model from a multivariable conductance-based model of a neocortical pyramidal cell with somatic input is demonstrated. The conditions for avoiding a spurious damped oscillatory response to a constant input are derived, and it is shown that a limit-cycle response cannot occur. The capability of the low-dimensional model to approximate higher-dimensional models accurately makes it useful for describing complex dynamics of nets of interconnected neurons. The simplicity of the model facilitates analytic studies, elucidations of neurocomputational mechanisms, and applications to large-scale systems.

Neuromodulatory Control of Neocortical Microcircuits with Activity-Dependent Short-Term Synaptic Depression

“…The model neurons are of a low-dimensional type incorporating firing-rate adaptation [24,25]. Two of the principal neuron types in the brain are selected as prototypes of the model neurons: the regularly spiking pyramidal cell and the fastspiking interneuron [30,31].…”

“…The normalized firing rate of a neuron is determined from the total input current, and for pyramidal cells also from the intracellular calcium concentration, by means of generalized activation functions [24,25] defined in Eqs. (8) and (9) …”

“…The development of the intracellular calcium concentration is described by Eq. (5), in which q e (c e jk (t)) relates the inflow of calcium to the normalized activity and can be fitted by the expression q e (c e jk (t)) = a e /(b e + c e jk (t)) [24,25]. The calcium concentration is measured on an arbitrary scale which is fixed by selecting b e = 1.0.…”

“…The model neurons employed are of a low-dimensional type also accounting for neuronal adaptation, i.e. the coupling between neuronal activity and excitability, and neuromodulation thereof [24][25][26][27][28][29]. The functional aspects considered refer to the observed resolution of multiple objects in working memory as well as the binding of different features for the perception of an object [28,29].…”

Control of Neural Information Transmission by Synaptic Dynamics

“…The post-synaptic membrane potential response to pre-synaptic action potentials is determined by eqns (6)}(9), which describe a low-dimensional model neuron (Cartling, 1995b(Cartling, , 1996a(Cartling, , b, 1997 derived from a detailed multicompartment conductance-based model (Ekeberg et al, 1991;FranseH n & Lansner, 1998). The parameters of the latter model are determined from experimental data of a regularly spiking neocortical pyramidal cell, and the model is composed of six compartments corresponding to the soma, axon initial segment, basal dendrite and three sections of the apical dendrite.…”