Migraine mutation of a Na+ channel induces a switch in excitability type and energetically expensive spikes in an experimentally-constrained model of fast-spiking neurons

Familial hemiplegic migraine type 3 (FHM-3) is a type of migraine with aura, caused by gain-of-function mutations of NaV1.1 [1,2]. This voltage-gated channel is mainly expressed in fast-spiking inhibitory neurons as their dominant Na+ channel. Cortical spreading depolarization, a wave of hyperexcitability followed by silencing of firing, is the proposed mechanism for the generation of migraine attacks. The exact pathways driving this wave are unclear, although extracellular K+ build-up is thought to be involved in both its onset [3] and propagation. Recent direct recordings from axons of fast-spiking PV+ neurons by the Jonas lab suggest that the metabolic cost per spike in those neurons is surprisingly low [4]. This efficiency stems from rapid Na+ inactivation combined with delayed activation of specific K+ channels, minimizing ion current overlap. Is this complementary tuning preserved in the pathological case of FHM-3? Hu et al. used axonal voltage-clamp data to derive a conductance-based model that captures the energy efficiency of fast-spiking PV+ neurons [4]. Here, we investigate the effects of a FHM-3 mutation in this model. Based on experimental data, we implement the mutation as a shift of the voltage dependence of Na+ inactivation and increase of persistent Na+ current [5]. We find that the mutation substantially increases the metabolic cost of each spike. Incomplete inactivation of Na+ channels leads to greater overlap between the Na+ and K+ currents (Fig 1A,D), resulting in ion concentration changes that do not contribute to the voltage signal. In agreement with previous findings [6], both ion fluxes are increased at each spike. A faster dissipation of the gradients places more strain on active pumping by the Na+/K+-ATPase, consistent with an accumulation of extracellular K+ in case of failure. Interestingly, the mutation also modifies the model’s dynamical type. In the wild type, the neuron exhibits class 2 excitability, with onset of spiking mediated by a Hopf bifurcation and a discontinuous f-I curve (Fig 1B,C). Incorporating the mutation distorts the bifurcation diagram, yielding a more exotic onset bifurcation, the big homoclinic (Fig 1E,F), with potential consequences for network dynamics. We use numerical continuation with respect to a mutation strength parameter to explore how altered Na+ inactivation organizes the transition in type. We study its consequences on the dynamics and discuss their relevance in the pathological context.