The role of negative conductances in neuronal subthreshold properties and synaptic integration

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The role of negative conductances in neuronal subthreshold properties and synaptic integration Cesar C. Ceballos 1,2 & Antonio C. Roque 2 & Ricardo M. Leão 1

Received: 25 May 2017 / Accepted: 27 July 2017 # International Union for Pure and Applied Biophysics (IUPAB) and Springer-Verlag GmbH Germany 2017

Abstract Based on passive cable theory, an increase in membrane conductance produces a decrease in the membrane time constant and input resistance. Unlike the classical leak currents, voltage-dependent currents have a nonlinear behavior which can create regions of negative conductance, despite the increase in membrane conductance (permeability). This negative conductance opposes the effects of the passive membrane conductance on the membrane input resistance and time constant, increasing their values and thereby substantially affecting the amplitude and time course of postsynaptic potentials at the voltage range of the negative conductance. This paradoxical effect has been described for three types of voltage-dependent inward currents: persistent sodium currents, L- and T-type calcium currents and ligand-gated glutamatergic N-methyl-D-aspartate currents. In this review, we describe the impact of the creation of a negative conductance region by these currents on neuronal membrane properties and synaptic integration. We also discuss recent contributions of the quasi-active cable approximation, an extension of the passive cable theory that includes voltage-dependent currents, and its effects on neuronal subthreshold properties.

This article is part of a Special Issue on ‘Latin America’ edited by Pietro Ciancaglini and Rosangela Itri * Antonio C. Roque [email protected] * Ricardo M. Leão [email protected] 1

Department of Physiology, School of Medicine of Ribeirão Preto, University of São Paulo, Ribeirão Preto, Brazil

2

Department of Physics, School of Philosophy, Sciences and Letters, University of São Paulo, Ribeirão Preto, Brazil

Keywords Passive cable theory . Voltage-dependent inward currents . Neuronal membrane . Synaptic integration . Neuronal subthreshold properties

What is a negative slope conductance? Ion channels are considered to be biological conductors in the neuronal membrane. By definition, the conductance of a single channel is positive following the linear Ohm’s law. According to the passive cable model of the biological membrane, the opening of the channels increases ionic permeability and decreases membrane resistance (Rm) and the time constant (τm). Each neuronal type has a distinct membrane resistance which affects its excitability, integrative and temporal properties. Potassium background leak channels are considered to be the classical determinants of Rm (Enyedi and Czirják 2010). For example, in a heterogeneous neuronal population, membrane input resistance, action potential latency and threshold are inversely correlated with the expression of potassium leak currents (Dagostin et al. 2015). It is also well known that volatile anesthetics decrease membrane excitability by open