A Negative Slope Conductance of the Persistent Sodium Current Prolongs Subthreshold Depolarizations

Abstract

Neuronal subthreshold voltage-dependent currents determine membrane properties such as the input resistance (R) and the membrane time constant (τ) in the subthreshold range. In contrast with classical cable theory predictions, the persistent sodium current (I), a non-inactivating mode of the voltage-dependent sodium current, paradoxically increases R and τ when activated. Furthermore, this current amplifies and prolongs synaptic currents in the subthreshold range. Here, using a computational neuronal model, we showed that the creation of a region of negative slope conductance by I activation is responsible for these effects and the ability of the negative slope conductance to amplify and prolong R and τ relies on the fast activation of I. Using dynamic clamp in hippocampal CA1 pyramidal neurons in brain slices, we showed that the effects of I on R and τ can be recovered by applying an artificial I after blocking endogenous I with tetrodotoxin. Furthermore, we showed that injection of a pure negative conductance is enough to reproduce the effects of I on R and τ and is also able to prolong artificial excitatory post synaptic currents. Since both the negative slope conductance and the almost instantaneous activation are critical for producing these effects, the I is an ideal current for boosting the amplitude and duration of excitatory post synaptic currents near the action potential threshold.

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

“…Making a parallel between the parameter μ obtained using quasi-active cable approximation and the mathematical description of the slope conductance obtained by differentiating the current equation as in Koch (1998), one can say that the parameter μ and the derivative conductance are equivalent (Moore et al 1995). Recently, Ceballos et al (2017) were able to measure experimentally the derivative conductance of the I NaP , suggesting that it is possible to test these theories experimentally.…”

“…This approach allowed classifying I NaP as a regenerative current, which produces a positive feedback and amplifies membrane potential changes, boosting and broadening excitatory postsynaptic potentials (EPSPs). The effectiveness of I NaP in modulating the shape of EPSPs is determined by the activation time constant: the faster the activation time constant, the stronger its effect on EPSP amplitude (Ceballos et al 2017). These effects are controlled by a single dimensionless parameter μ.…”

“…The effect of a slowly gated active current on the EPSP shape is caused by its contribution to the chord conductance, since τ act is typically too slow for its dynamics (characterized by the parameter μ) to significantly affect the shape of a single EPSP. In contrast, a very fast current (τ act < <τ m ) varies continuously in steady state with the voltage and will therefore effectively act via its negative slope conductance (Ceballos et al 2017;Remme and Rinzel 2011). A disadvantage of the linear approximation is that it is only valid for small voltage changes; the larger the voltage changes, the more the linearized system will deviate from the nonlinear system.…”

“…These authors injected artificial linear negative and positive conductance using a dynamic clamp in entorhinal stellate cells and observed that negative conductance increased R m while a positive conductance decreased R m , suggesting that is the negative slope conductance-and not the positive chord conductance-that determines R in and τ m (Ceballos et al 2017). In a case like this, slope conductances (positive and negative) from each current (linear and voltage-dependent) are simply added up algebraically, and it is this sum that determines R m and τ m following a simple mathematical rule: R m = 1/ΣG and τ m = R m C m , (where C m is membrane capacitance) (Buchanan et al 1992;Moore et al 1994;Yoshii et al 1988).…”

“…In order to increase R m and τ m , a critical feature for a current with a negative slope conductance is a fast activation (Ceballos et al 2017;Manuel et al 2007;Remme and Rinzel 2011). But how fast?…”