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Biophysics of ComputationInformation Processing in Single Neurons$
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Christof Koch

Print publication date: 1998

Print ISBN-13: 9780195104912

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195104912.001.0001

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Input Resistance, Time Constants, and Spike Initiation

Input Resistance, Time Constants, and Spike Initiation

(p.381) 17 Input Resistance, Time Constants, and Spike Initiation
Biophysics of Computation

Christof Koch

Oxford University Press

This chapter represents somewhat of a tephnical interlude. Having introduced the reader to both simplified and more complex compartmental single neuron models, we need to revisit terrain with which we are already somewhat familiar. In the following pages we reevaluate two important concepts we defined in the first few chapters: the somatic input resistance and the neuronal time constant. For passive systems, both are simple enough variables: Rin is the change in somatic membrane potential in response to a small sustained current injection divided by the amplitude of the current injection, while τm is the slowest time constant associated with the exponential charging or discharging of the neuronal membrane in response to a current pulse or step. However, because neurons express nonstationary and nonlinear membrane conductances, the measurement and interpretation of these two variables in active structures is not as straightforward as before. Having obtained a more sophisticated understanding of these issues, we will turn toward the question of the existence of a current, voltage, or charge threshold at which a biophysical faithful model of a cell triggers action potentials. We conclude with recent work that suggests how concepts from the subthreshold domain, like the input resistance or the average membrane potential, could be extended to the case in which the cell is discharging a stream of action potentials. This chapter is mainly for the cognoscendi or for those of us that need to make sense of experimental data by comparing therp to theoretical models that usually fail to reflect reality adequately. In Sec. 3.4, we defined Kii (f) for passive cable structures as the voltage change at location i in response to a sinusoidal current injection of frequency f at the same location. Its dc component is also referred to as input resistance or Rin. Three difficulties render this definition of input resistance problematic in real cells: (1) most membranes, in particular at the soma, show voltage-dependent nonlinearities, (2) the associated ionic membrane conductances are time dependent and (3) instrumental aspects, such as the effect of the impedance of the recording electrode on Rin, add uncertainty to the measuring process.

Keywords:   Action potentials, Charge threshold, Dynamic input conductance, Equilibrium points, Frequency-current curves, Input conductance, Membrane capacitance, Repetitive spiking, Slope conductance

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