Abstracts

Rationale: In the mature adult brain, GABA_A neurotransmission is primarily inhibitory. However, an abnormal down-regulation of chloride (Cl) transporters may cause a build-up of Cl ions within excitatory neurons, increasing the reversal potential of GABA_A and making GABA_A synapses excitatory. We have developed a novel compartmental framework to explain how this depolarizing effect of GABA_A may lead to a seizure.


Methods:

We introduce compartmental frameworks from epidemiology to model the interaction between an excitatory and an inhibitory neuronal population. Neurons exist either in a bursting (infected) state or a quiescent (susceptible) state, and the propagation of action potentials is considered an epidemic spreading through the neuronal population. The resulting framework captures the proportion of excitatory and inhibitory neurons active at any given time. Steady-state solutions of the framework portray various states associated with epilepsy: a seizure is marked by an attractor in which all excitatory neurons are bursting, while an attractor with a constant non-zero proportion of neurons bursting represents normal activity.




Our framework captures three types of interactions: recruitment, decay, and sustenance. Bursting excitatory neurons interact with quiescent excitatory and inhibitory neurons and recruit them into bursting. Busting neurons return to quiescence proportional to their current number. High interconnectivity among excitatory neurons facilitates sustained bursting through positive feedback, whose strength is quantified by sustenance1.

To model the depolarising effect of GABA_A, we consider two subdivisions within the excitatory population: neurons with no Cl accumulation where GABA_A is inhibitory and neurons with high Cl accumulation where GABA_A is excitatory. If GABA_A is inhibitory, it prevents the recruitment of excitatory neurons into bursting and promotes their decay to quiescence. If GABA_A is excitatory, it aids the recruitment into bursting and prevents the decay to quiescence. A schematic describing the framework setup is shown in Fig. 1.





[1] Kamaraj, AK, Szuromi MP, et al. Using compartmental models to understand excitation-inhibition imbalance in epilepsy. bioRxiv 2023.11.03.565450.








Results: Our results show that when a significant proportion of postsynaptic excitatory neurons accumulate Cl, the model exhibits bistability, with normal brain activity and seizure being coexisting attractors (see Fig. 2). Under such conditions, an increase in neuronal activity could cause the brain to transition from normal activity to a seizure. The brain returns to normal activity when the accumulated Cl ions are dissipated.


Conclusions: We present a simple framework that considers the propagation of action potentials as an epidemic spreading through the neuronal population to study excitation–inhibition imbalance in epilepsy. We show that the depolarizing effect of GABA_A neurotransmission may lead to bistability in the brain, wherein an increase in neuronal activity could trigger a seizure.


Funding: No funding was received for this work.