The influence of the chloride currents on action potential firing and volume regulation of excitable cells studied by a kinetic model

Abstract

In excitable cells, the generation of an action potential (AP) is associated with transient changes of the intra- and extracellular concentrations of small ions such as Na⁺, K⁺ and Cl⁻. If these changes cannot be fully reversed between successive APs cumulative changes of trans-membrane ion gradients will occur, impinging on the cell volume and the duration, amplitude and frequency of APs. Previous computational studies focused on effects associated with excitation-induced changes of potassium and sodium. Here we present a model based study on the influence of chloride on the fidelity of AP firing and cellular volume regulation during excitation. Our simulations show that depending on the magnitude of the basal chloride permeability two complementary types of responsiveness and volume variability exist: (i) At high chloride permeability (typical for muscle cells), large excitatory stimuli are required to elicit APs; repetitive stimuli of equal strength result in almost identical spike train patterns (Markovian behavior), however, long excitation may lead to after discharges due to an outward directed current of intracellular chloride ions which accumulate during excitation; cell volume changes are large. (ii) At low chloride permeability (e.g., neurons), small excitatory stimuli are sufficient to elicit APs, repetitive stimuli of equal strength produce spike trains with progressively changing amplitude, frequency and duration (short-term memory effects or non-Markovian behavior); cell volume changes are small. We hypothesize that variation of the basal chloride permeability could be an important mechanism of neuronal cells to adapt their responsiveness to external stimuli during learning and memory processes.

Introduction

Action potentials (APs) represent elevations of the membrane potential from a typical resting value of about −70 mV to a peak value of about +40 mV within a few milliseconds, followed by an equally fast decline back to the resting value. During an AP, voltage-gated membrane channels for small ions such as Na⁺ and K⁺ open and close in a timely well-coordinated fashion to enable transient extra currents of these ions along their concentration gradients: Sodium ions enter the cell and potassium ions flow into the extracellular space. Changes of the membrane potential feed back not only to voltage-gated ion channels but also to the electro-diffusion of ions through passive channels, in particular chloride channels, which in most excitable cells possess a high resting conductivity. Shifts in the trans-membrane distribution of ${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$ and ${\mathrm{Cl}}^{-}$ occurring during an AP have to be reset by active ion transport. If this resetting has not been completed before a new AP is elicited, the perturbation of small-ion gradients across the membrane may successively progress during a series of APs (spike train).

Progressive changes of trans-membrane ion gradients during excitation may induce volume changes (Andrew and MacVicar, 1994, Ballanyi et al., 1990, Hill, 1950). In the brain, swelling of neurons can be critical as it further reduces the small interstitial space and hence raises the external potassium concentration. This causes a shift of the membrane potential toward the firing threshold and thus increases excitability, which at the extreme can ignite seizures, spreading depression (SD) or hypoxic SD-like depolarization (Andrew, 1991, Kager et al., 2007).

For the regulation of the cell volume chloride is very prominent (Jentsch, 1996), as membrane currents of this negative and diffusible small ion may rapidly compensate additional anion currents. The basal chloride permeability is also an important determinant of the firing threshold. In many excitable cells as well as in the non-dendritic parts of the neuron, the cellular chloride concentration is mainly controlled by passive chloride currents implying that the reversal potential of chloride is very close to the cell's resting membrane potential. Thus, initial depolarization by excitatory cation currents causes a counteracting inward directed chloride current. As a consequence, in order to reach a depolarization that is sufficient to open voltage-gated sodium channels, increasing chloride permeabilities entail higher excitatory currents. An important exception from this general behavior is the postsynaptic membrane of GABAergic neurons. Here, active transport of chloride is indispensable for the corresponding membrane region to either hyperpolarize (inhibitory synapse) or depolarize (excitatory synapse) upon neurotransmitter-gated opening of chloride channels (Coull et al., 2003, Kahle et al., 2008, Woo et al., 2002, Zhu et al., 2008).

In this work we present a detailed computational study on the impact of chloride currents on the volume regulation and firing pattern of excitable cells. The mathematical model used to simulate temporal changes in the intra- and extracellular concentrations of Na⁺, K⁺ and Cl^‐ couples changes of ion concentrations to trans-membrane ion currents mediated by active ion pumps, non-gated and voltage-gated ion channels and membrane permeabilities. The simulations correctly recapitulate observed volume changes of active neuronal cells and the hyper-excitability of muscle cells underlying the neuromuscular disease myotonia congenita. The simulations also predict a number of novel and hitherto experimentally unstudied effects that a variable passive chloride permeability may have on the frequency, shape and duration of spike trains. Based on our theoretical findings we hypothesize that variations of the chloride permeability may represent a hitherto underestimated mechanism to tailor neuron responsiveness to specific profiles of excitatory stimuli.