  Familial hemiplegic migraine (FHM) is a rare subtype of migraine with aura. A
mutation causing FHM type 3 (FHM3) has been identified in SCN1A encoding the
Nav1.1 Na$^+$ channel. This genetic defect affects the inactivation gate. While
the Na$^+$ tail currents following voltage steps are consistent with both
hyperexcitability and hypoexcitability, in this computational study, we
investigate functional consequences beyond these isolated events. Our extended
Hodgkin-Huxley framework establishes a connection between genotype and cellular
phenotype, i.e., the pathophysiological dynamics that spans over multiple time
scales and is relevant to migraine with aura. In particular, we investigate the
dynamical repertoire from normal spiking (milliseconds) to spreading depression
and anoxic depolarization (tens of seconds) and show that FHM3 mutations render
gray matter tissue more vulnerable to spreading depression despite opposing
effects associated with action potential generation. We conclude that the
classification in terms of hypoexcitability vs. hyperexcitability is too simple
a scheme. Our mathematical analysis provides further basic insight into also
previously discussed criticisms against this scheme based on psychophysical and
clinical data.
