Effects of synaptic conductance on the voltage distribution and firing rate of spiking neurons

Abstract

A neuron in an active cortical circuit is subject to a fluctuating synaptic drive mediated by conductance changes. It was recently demonstrated that synaptic conductance effects in vivo significantly alter the integrative properties of neurons. These effects are missed in models that approximate the synaptic drive as a fluctuating current. Here the membrane-potential distribution and firing rate are derived for the integrate-and-fire neuron with delta correlated conductance-based synaptic input using the Fokker-Planck formalism. A number of different input scenarios are examined, including balanced drive and fluctuation changes at constant conductance, the latter of which corresponds to shifts in synchrony in the presynaptic population. This minimal model captures many experimentally observed conductance-related effects such as reduced membrane-potential fluctuations in response to increasing synaptic noise. The solvability of the model allows for a direct comparison with current-based approaches, providing a basis for assessing the validity of existing approximation schemes that have dealt with conductance change. In particular, a commonly used heuristic approach, whereby the passive membrane time constant is replaced by a drive-dependent effective time constant, is examined. It is demonstrated that this approximation is valid in the same limit that the underlying diffusion approximation holds, both for delta correlated as well as filtered synaptic drive.

Short-Term Synaptic Plasticity Orchestrates the Response of Pyramidal Cells and Interneurons to Population Bursts

“…A more pertinent effect of conductance, relevant to an extension of this study to include effects of inhibition, is the hidden shunting inhibition. This is not directly visible in the voltage traces, due to the method of injecting hyperpolarising current to bring the average rest voltage to near the inhibitory reversal potential, but has an indirect effect on the excitation through a control of the neuronal gain (Chance et al, 2002;Burkitt et al, 2003;Fellous et al, 2003;Richardson, 2004). Such effects can sculpt the voltage response to excitatory bursts and will further contribute to changes in the peak and median shifts seen experimentally.…”

“…(1) will be assumed to hold for the input across a large population of N f input fibres. This is an approximation because conductance effects will vary the gain of the neuronal response (Chance et al, 2002;Burkitt et al, 2003;Fellous et al, 2003;Richardson, 2004). However, given the spatially extended and compartmentalised nature of neurons, to include conductance would complicate the analysis in a way that could not be constrained experimentally (without any qualitative change in the results).…”

Predicting spike times of a detailed conductance-based neuron model driven by stochastic spike arrival

“…In order to make the EPSPs and IPSPs input dependent, we parameterize + and À using the linearized theory of a conductance-driven integrate-and-fire model [5,29,31]; see Section 2 for details.…”

“…Hence, the purpose of this paper is to propose extensions of our previous work which address the latter problem. Using recent theoretical results [29,31], we propose a generalization of the spike response model so as to make model parameters input dependent. This improved version of the SRM is shown to be very efficient and robust at predicting the spike train of a detailed Hodgkin-Huxley-type neuron model.…”

“…Thus, the extended spike response model SRM c that we derive in this paper is directly related to the subthreshold dynamics of a conductance-driven integrate-and-fire neuron model (CIF) [5,29,31].…”