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Title: The Role of Cell Volume in the Dynamics of Seizure, Spreading Depression, and Anoxic Depolarization}
Article:
Abstract:
Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little of how cell volume affects neuronal dynamics. We here performed the first detailed study of the effects of cell volume on neuronal dynamics. By incorporating cell swelling together with dynamic ion concentrations and oxygen supply into Hodgkin-Huxley type spiking dynamics, we demonstrate the spontaneous transition between epileptic seizure and spreading depression states as the cell swells and contracts in response to changes in osmotic pressure. Our use of volume as an order parameter further revealed a dynamical definition for the experimentally described physiological ceiling that separates seizure from spreading depression, as well as predicted a second ceiling that demarcates spreading depression from anoxic depolarization. Our model highlights the neuroprotective role of glial K buffering against seizures and spreading depression, and provides novel insights into anoxic depolarization and the relevant cell swelling during ischemia. We argue that the dynamics of seizures, spreading depression, and anoxic depolarization lie along a continuum of the repertoire of the neuron membrane that can be understood only when the dynamic ion concentrations, oxygen homeostasis, and cell swelling in response to osmotic pressure are taken into consideration. Our results demonstrate the feasibility of a unified framework for a wide range of neuronal behaviors that may be of substantial importance in the understanding of and potentially developing universal intervention strategies for these pathological states.
Introduction:
Cells swell during a wide variety of pathologies, including trauma, ischemia, hypoxia, seizures, and spreading depression[1–3]. Changes in osmolality can change the susceptibility to epileptiform activity[4–6], and affect the amplitude of intra- and extracellularly recorded electrical signals[7]. Cells also change their volume during normal activity, and the change in cell size during individual action potentials has been estimated[8, 9]. Despite this ubiquity of observed phenomena, the effect of cell swelling on single cell behavior is incompletely understood. It is now accepted that the dynamic microenvironment within the extracellular space( ECS), modified by ionic fluxes from neurons, glia, and blood vessels, plays a critical role in neuronal behavior[1]. In particular, pathological states involving excessive neuronal depolarization such as epileptic seizure( SZ), spreading depression( SD), and anoxic depolarization( AD) during ischemia are characterized by major rearrangements of various ions across the cell membrane and neuronal microenvironment[1, 10–16]. In each of these three conditions, collapse of transmembrane ionic gradients requires enhanced oxygen and glucose consumption required by active transport systems to reestablish the gradients[17, 18]. For the purpose of this paper, we define SZ, SD, and AD respectively as the ion concentrations-induced high-frequency bursts not usually seen in the normal condition of the same cell[1, 19], the nearly complete depolarization of the cell’s membrane potential that recovers spontaneously on the scale of seconds[13, 19], and the nearly complete depolarization of the cell’s membrane potential triggered by oxygen( O2) and glucose deprivation( OGD) that may or may not recover depending on the cell type after O2 and glucose is restored[1, 20, 21]. During the pathological states mentioned above, the massive rearrangement of ions across plasma membrane drives water molecules from the extra- to intracellular space leading cell swelling. For example, pyramidal neurons in slices from cortical layer V swell by as much as 60% during AD caused by 20 minutes OGD[20]. Although lacking functional aquaporins, neurons swell significantly in response to OGD and extracellular K+ elevations[22]. Although still debated, the K+/Cl− and Na+/K+/2Cl− cotransporters are suspected to mediate the entry of water molecules into neurons[23, 24]. Astrocytes on the other hand, express aquaporins[25]. The clearance of excessive K+ due to high neuronal activity by astrocytes leads to osmotic gradients resulting in water influx through aquaporins and astrocytic dilation[26–28]. This paper focusses on the role of neuronal swelling in response to osmolality changes in cell behavior without considering the specifics of pathways involved in the water influx. Despite the fact that SD was first observed by Leão as the silencing of spontaneous electrical activity during experiments on epileptic SZs, the two phenomena have long been considered separate physiological events[1]. They are characterized by different patterns of neuronal activities[29–31], characteristic ionic changes[13–16, 19], and known interactions with oxygen[17, 32]. By expanding the Hodgkin-Huxley type framework to incorporate conservation of particles and charge, and accounting for the energy required to restore ionic gradients, we recently uncovered a unified mechanism for SZ and SD[33]. Specifically, we showed that a wide-range of neuronal behaviors can be accounted for as a function of the cell’s extracellular potassium concentration and oxygen supply. More recently, Hübel and Dahlem performed a detailed bifurcation analysis of different time-scales arising from the consideration of dynamic ion concentrations in conjunction with Hodgkin-Huxley type framework[34]. Extensive work has been done on the role of ion pumps, channels, and transporters in stroke[35]. Recently, Andrew and colleagues showed that neuronal populations in lower brain regions such as the hypothalamus are resistant while those in higher brain regions such as neocortex are more susceptible to ischemic injury[20]. They further showed that the thalamus-hypothalamus interface represents a discrete boundary where neurons in thalamus are more vulnerable than hypothalamus to ischemia, generating stronger AD in response to OGD, and do not recover as readily after restoring normal O2 and glucose supply[21]. The authors postulated that the variability of ATP-dependent Na+ − K+ pumps in these regions could lead to the contrasting neuronal response in OGD conditions. In this paper, we explore the effect of cell swelling on neuronal behavior by demonstrating the ability of cell volume to act as a bifurcation parameter. We seek a better understanding of how human brain cells respond to osmotic pressure-induced swelling in states such as SZ, SD, and AD, and universal intervention strategies for controlling these conditions. Here, we show that spontaneous transition between SZ and SD can be seen in a model neuron if volumetric changes in response to intense neuronal activity and ionic fluxes are taken into account. Without any adjustments, our model behaves in similar fashion as in vitro experiments under OGD. We further show that the variability in the geometry and microenvironment of neurons could play a significant part in their differential response in OGD conditions observed in in vitro experiments in different brain regions. Based on our results, we conclude that combining ion concentration dynamics during spiking with the sizes of intra- and extracellular spaces supports a unified framework for epileptic SZ, SD, and AD.
Discussion:
This is, to our knowledge, the first detailed study of the effects of cell volume on neuronal dynamics. We employed a recently discovered unification framework, where extending the Hodgkin-Huxley equations for mammalian neurons with energy balance and conservative principles demonstrated that a broad variety of neuronal states lie along a continuum of the repertoire of the neuronal membrane[33]. Using a variety of model simplifications, we were able to perform detailed bifurcation analyses that explained the full model effects as a function of volume itself as an order parameter. We can now better understand and unify a range of effects and factors that are critical in the transitions to the pathological states of SZ, SD, and AD. Our study of the role of volume as an order parameter revealed a dynamical definition for the experimentally described physiological ceiling that separates seizure from SD activity[42]. Furthermore, we have delineated and predict a second ceiling, one that demarcates SD from AD. Our observations unveil a new way of investigating neuronal behavior where different states need not be treated separately but rather as a dynamical continuum of the neuronal membrane potential, ion concentrations, metabolic energy, and volume. Previous experiments support our observations about the volume as an order parameter regulating the neuronal excitability. Exposure of brain cells to hyposmolality and the resultant shrinkage of extracellular space at clinically relevant levels promotes epilepiform activity in hippocampus and neocortex[53–55] and clinically[5]. Hyperosmolality( dehydration), on the other hand inhibits epilepiform activity. Mannitol, which reverses the hyposmolar state, abolishes synchronous neuronal bursting in the dentate gyrus and CA1 area of the hippocampus[4]. Furthermore, hyposmolality increases the amplitude of evoked field potentials and excitatory postsynaptic potentials recorded intracellularly in rat neocortical slices[7]. Conversely, mannitol-induced hyperosmolality reverses these features[7]. Similarly, decreasing the extracellular osmotic pressure converted non-bursting neurons to bursting neurons and decreased the stimulus requirements for evoking burst firing in native bursters, while increasing extracellular osmotic pressure suppressed burst firing[56]. Glial reactivity and scarring is a prominent feature of a broad variety of brain pathologies[57], and is prominent in epilepsy[58]. We found that when glial K+ buffering is impaired, the cells can swell enough to cause transition from SZ to SD. Previous observations by Foley et al.[59] support this mechanism. The excitability of neurohypophysial neurons due to accumulating K+ in the extracellular space decreased significantly by increasing the size of interstitial space[59]. The decrease in action potential amplitude( showing the cell’s transition towards a depolarized state( SSS2)) in control cells in response to a train of 40 stimuli at 25Hz, diminished when a hypertonic solution containing 100mM sucrose was added to the normal ringer solution perfusate[59]. The membrane-impermeable sucrose increases extracellular osmotic pressure causing neurons to shrink. A similar protocol could be used to test the predictions of our model. Our hypothesis is that adding hypertonic solution to the tissue going though SD would transition the cell to SZ and possibly to the resting state. Taking glial swelling into account would make the shrinkage of interstitial space more dramatic, further supporting our claim that the reduction in extracellular space can be strong enough to cause the cell to transition from SZ to SD. Our results also highlight the importance of glial K+ buffering strength in pathological states and shows that the cell is less likely to go into SZ and SD and the transition between the two when glia are functioning efficiently. The different time-scales in our model provide a parsimonious explanation for the transition between SZ and SD states in Fig 1A. As mentioned above, there are four different time-scales in our model: fast( variables V, n, and h; Eq( 1)), intermediate([K]o,[Na]i; Eqs( 3, 7), slow([O2],[Cl]i; Eqs( 5, 10)), and infra-slow( Vol; Eq( 14)). Strictly speaking, the ultra-fast m-gate( m) if modeled with the rate equation instead of the steady state approximation can be considered as a fifth time-scale. We believe that this could underlie the dramatic increase in the amplitude of[K]o oscillations—reminiscent of canard explosion—which is a feature of a slow-fast system such as ours[60]. Testing this claim using geometric singular perturbation theory is beyond the scope of this study and will be the subject of future research. In addition to the spontaneous transition between SZ and SD, our model closely reproduces AD, the hyperpolarization after O2 is restored, and the cell swelling in AD. The close resemblance of our results to the experimental data makes our model a good candidate for future studies to understand hypoxia and ischemia and ways to protect against metabolic insults. As pointed out above, Brisson et al.[20, 21] emphasized the importance of variable pump rates in the stronger AD observed in the upper brain regions as compared to the lower brain regions in response to OGD. Our study shows that the cell volume and microenvironment play an important role in the strength of AD( Fig 7A). Our preliminary phase space analysis for the cell’s failure in the higher brain regions to recover from AD reveals that the cell volume affects[K]o and[Na]i in such a way that they lead to lower pump activity and consequently the cell’s failure to recover from AD after O2 and glucose is restored. A complete phase space analysis of the recovery failure from AD is beyond the scope of this paper and the subject of our future research. This current model is a simplified picture of a very complex reality. Although Na+ − K+-ATPase consumes 91% of total available O2[61], other pathways such as Ca2+-ATPase and synaptic communication expend significant amounts of metabolic energy which is not taken into account in the current model. Similarly, the clearance of excessive K+ accompanied by Cl− uptake and Na+ expulsion by astrocytes in face of high neuronal activity would lead to significant dilation of astrocytes[26–28] during the pathological states discussed in this paper, which is missing from our model. Also missing from the model is the dynamic intra- and extracellular Ca2+ concentrations, which are suspected to play a crucial role in neuronal excitotoxicity( see for example, chapter 4 of[1]). Osmotic pressure also affects the re-depolarizing component of spike after-depolarization and apparent membrane time-constant that are attributed to changes in the persistent Na+ current[56]. These factors are important for developing a more comprehensive understanding of the pathological states discussed in this paper, and is the subject of future research. To conclude, our finding further explored a unified mechanism that accounts for SZ, SD, and AD. The detailed biophysical models that take neuronal microenvironment such as ion concentrations, glia, blood vessels, metabolic energy requirements, and volume homeostasis into account will provide a better understanding of these conditions and may lead to unified therapies for SZ, SD, and possibly ischemic stroke-like injury prevention.
Massive rearrangement of ions across the plasma membrane and changes in cellular volume are common features of states such as seizures , spreading depression , and ischemia . In this paper , we focus on how volume itself influences neuronal activity . We build a unified computational framework for a wide range of neuronal behaviors by exploiting their previously unexplored common features . By combining the dynamic ion concentrations and volume , conservation of charge , and the energy requirements of the cell within a Hodgkin-Huxley type framework , we demonstrate the feasibility of a comprehensive framework encompassing a wide range of neuronal behaviors . We show the spontaneous transition of a neuron between seizure and spreading depression when the cell swells and contracts in response to varying osmotic pressure as a result of the rearrangement of different ions . Our model closely reproduces anoxic depolarization and relevant neuronal swelling during ischemia and reveals a dynamical definition for the experimentally described physiological ceilings that demarcate seizure from spreading depression and spreading depression from anoxic depolarization . This study opens up a new way of studying neuronal behavior where different states need not be treated separately but rather as a dynamical continuum of the neuronal membrane potential and its microenvironment .