Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
The computational brain
Reduction of conductance-based models with slow synapses to neural nets
Neural Computation
Shunting inhibition does not have a divisive effect on firing rates
Neural Computation
Linearization of F-1 curves by adaptation
Neural Computation
Dynamics of the firing probability of noisy integrate-and-fire neurons
Neural Computation
Minimal Models of Adapted Neuronal Response to In Vivo–lLike Input Currents
Neural Computation
Stationary Bumps in Networks of Spiking Neurons
Neural Computation
Patterns of Synchrony in Neural Networks with Spike Adaptation
Neural Computation
LFP spectral peaks in V1 cortex: network resonance and cortico-cortical feedback
Journal of Computational Neuroscience
A systematic method for configuring vlsi networks of spiking neurons
Neural Computation
Dynamic state and parameter estimation applied to neuromorphic systems
Neural Computation
Spike suppression in a local cortical circuit induced by transcranial magnetic stimulation
Journal of Computational Neuroscience
Encoding binary neural codes in networks of threshold-linear neurons
Neural Computation
Conductance-based refractory density model of primary visual cortex
Journal of Computational Neuroscience
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Population rate models provide powerful tools for investigating the principles that underlie the cooperative function of large neuronal systems. However, biophysical interpretations of these models have been ambiguous. Hence, their applicability to real neuronal systems and their experimental validation have been severely limited. In this work, we show that conductance-based models of large cortical neuronal networks can be described by simplified rate models, provided that the network state does not possess a high degree of synchrony. We first derive a precise mapping between the parameters of the rate equations and those of the conductance-based network models for time-independent inputs. This mapping is based on the assumption that the effect of increasing the cell's input conductance on its f-I curve is mainly subtractive. This assumption is confirmed by a single compartment Hodgkin-Huxley type model with a transient potassium A-current. This approach is applied to the study of a network model of a hypercolumn in primary visual cortex. We also explore extensions of the rate model to the dynamic domain by studying the firing-rate response of our conductance-based neuron to time-dependent noisy inputs. We show that the dynamics of this response can be approximated by a time-dependent second-order differential equation. This phenomenological single-cell rate model is used to calculate the response of a conductance-based network to time-dependent inputs.