A Biophysical Model for Cytotoxic Cell Swelling

Abstract

We present a dynamic biophysical model to explain neuronal swelling underlying cytotoxic edema in conditions of low energy supply, as observed in cerebral ischemia. Our model contains Hodgkin-Huxley-type ion currents, a recently discovered voltage-gated chloride flux through the ion exchanger SLC26A11, active KCC2-mediated chloride extrusion, and ATP-dependent pumps. The model predicts changes in ion gradients and cell swelling during ischemia of various severity or channel blockage with realistic timescales. We theoretically substantiate experimental observations of chloride influx generating cytotoxic edema, while sodium entry alone does not. We show a tipping point of Na ϩ /K ϩ -ATPase functioning, where below cell volume rapidly increases as a function of the remaining pump activity, and a Gibbs-Donnan-like equilibrium state is reached. This precludes a return to physiological conditions even when pump strength returns to baseline. However, when voltage-gated sodium channels are temporarily blocked, cell volume and membrane potential normalize, yielding a potential therapeutic strategy.

Biophysical models reveal the relative importance of transporter proteins and impermeant anions in chloride homeostasis

“…Consistent with previous results ( Xiao et al, 2002 ; Dierkes et al, 2006 ; Dijkstra et al, 2016 ), ‘turning off’ the activity of the Na + /K + -ATPase in our model led to a progressive collapse of transmembrane ion gradients, progressive membrane depolarization and continuous and unstable cell swelling. Such effects could be reversed by reactivation of the pump ( Figure 1C ).…”

“…Previous theoretical models, which account for the dynamics of Cl - ions, have been useful in determining how changes to the driving force for Cl - are critical for controlling the effect of synaptic inhibition in the brain ( Qian and Sejnowski, 1990 ; Staley and Proctor, 1999 ; Doyon et al, 2011 ; Jedlicka et al, 2011 ; Lewin et al, 2012 ; Mohapatra et al, 2016 ). Whilst these models have included the Na + /K + -ATPase, the interacting dynamics of several ion species, CCCs ( Doyon et al, 2011 ; Krishnan and Bazhenov, 2011 ), electrodiffusion ( Qian and Sejnowski, 1989 ) and impermeant anions and volume regulation ( Dijkstra et al, 2016 ), none have combined all these mechanisms to explore how their combination determines the local driving force for Cl - . Our theoretical approach is based on the pump-leak formulation ( Tosteson and Hoffman, 1960 ).…”

Enhancing neuronal chloride extrusion rescues α2/α3 GABAA-mediated analgesia in neuropathic pain

“…The equilibrium value of E Cl . As described in Dijkstra et al 153 , the flux of Cl − through the KCC2 cotransporter is given by J Cl ¼ U KCC2 Á ðE Cl À E K Þ. The strength of the KCC2 cotransporter is denoted by U KCC2 and is in units of mol•s −1 •V −1 while the Cl − flux has units of mol Á s À1 .…”

Chloride Dysregulation, Seizures, and Cerebral Edema: A Relationship with Therapeutic Potential

“…During cytotoxic edema, net cytoplasmic Na + influx will depolarize the membrane and trigger Cl − influx through voltage gated Cl − channels or transporters such as SLC26A11 to maintain electroneutrality [130,131]. Cell swelling under these circumstances indicates a corresponding water influx, although the pathway for water entry is currently unclear.…”