TY - JOUR

T1 - Frequency-dependent responses of neuronal models to oscillatory inputs in current versus voltage clamp

AU - Rotstein, Horacio G.

AU - Nadim, Farzan

N1 - Funding Information:
This work was partially supported by the National Science Foundation Grants DMS-1313861 and DMS-1608077 and National Institutes of Health Grants MH060605 and NS083319.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - Action potential generation in neurons depends on a membrane potential threshold and therefore on how subthreshold inputs influence this voltage. In oscillatory networks, for example, many neuron types have been shown to produce membrane potential (Vm) resonance: a maximum subthreshold response to oscillatory inputs at a nonzero frequency. Resonance is usually measured by recording Vm in response to a sinusoidal current (Iapp), applied at different frequencies (f), an experimental setting known as current clamp (I-clamp). Several recent studies, however, use the voltage clamp (V-clamp) method to control Vm with a sinusoidal input at different frequencies [Vapp(f) ] and measure the total membrane current (Im). The two methods obey systems of differential equations of different dimensionality, and while I-clamp provides a measure of electrical impedance [Z(f) = Vm(f) / Iapp(f) ], V-clamp measures admittance [Y(f) = Im(f) / Vapp(f) ]. We analyze the relationship between these two measurement techniques. We show that, despite different dimensionality, in linear systems the two measures are equivalent: Z= Y- 1. However, nonlinear model neurons produce different values for Z and Y- 1. In particular, nonlinearities in the voltage equation produce a much larger difference between these two quantities than those in equations of recovery variables that describe activation and inactivation kinetics. Neurons are inherently nonlinear, and notably, with ionic currents that amplify resonance, the voltage clamp technique severely underestimates the current clamp response. We demonstrate this difference experimentally using the PD neurons in the crab stomatogastric ganglion. These findings are instructive for researchers who explore cellular mechanisms of neuronal oscillations.

AB - Action potential generation in neurons depends on a membrane potential threshold and therefore on how subthreshold inputs influence this voltage. In oscillatory networks, for example, many neuron types have been shown to produce membrane potential (Vm) resonance: a maximum subthreshold response to oscillatory inputs at a nonzero frequency. Resonance is usually measured by recording Vm in response to a sinusoidal current (Iapp), applied at different frequencies (f), an experimental setting known as current clamp (I-clamp). Several recent studies, however, use the voltage clamp (V-clamp) method to control Vm with a sinusoidal input at different frequencies [Vapp(f) ] and measure the total membrane current (Im). The two methods obey systems of differential equations of different dimensionality, and while I-clamp provides a measure of electrical impedance [Z(f) = Vm(f) / Iapp(f) ], V-clamp measures admittance [Y(f) = Im(f) / Vapp(f) ]. We analyze the relationship between these two measurement techniques. We show that, despite different dimensionality, in linear systems the two measures are equivalent: Z= Y- 1. However, nonlinear model neurons produce different values for Z and Y- 1. In particular, nonlinearities in the voltage equation produce a much larger difference between these two quantities than those in equations of recovery variables that describe activation and inactivation kinetics. Neurons are inherently nonlinear, and notably, with ionic currents that amplify resonance, the voltage clamp technique severely underestimates the current clamp response. We demonstrate this difference experimentally using the PD neurons in the crab stomatogastric ganglion. These findings are instructive for researchers who explore cellular mechanisms of neuronal oscillations.

KW - Impedance profile

KW - Neural oscillations

KW - Resonance

KW - Sub-threshold resonance

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U2 - 10.1007/s00422-019-00802-z

DO - 10.1007/s00422-019-00802-z

M3 - Article

C2 - 31286211

AN - SCOPUS:85069622359

VL - 113

SP - 373

EP - 395

JO - Biological Cybernetics

JF - Biological Cybernetics

SN - 0340-1200

IS - 4

ER -