  Real neurons connect to each other non-randomly. How the connectivity of
networks of conductance-based neuron models like the classical Hodgkin-Huxley
model, or the Morris-Lecar model, impacts synchronizability remains unknown.
One powerful tool to resolve the synchronizability of these networks is the
Master Stability Function (MSF). Here, we apply and extend the MSF approach to
networks of Morris-Lecar neurons with conductance-based coupling to determine
under which parameters and graphs synchronous solutions are stable. We consider
connectivity graphs with a constant row-sum, where the MSF approach can be
readily extended to conductance-based synapses rather than the more
well-studied diffusive connectivity case, which primarily applies to gap
junction connectivity. In this formulation, the synchronous solution is a
single, self-coupled or 'autaptic' neuron. We find that the primary determining
parameter for the stability of the synchronous solution is, unsurprisingly, the
reversal potential, as it largely dictates the excitatory/inhibitory potential
of a synaptic connection. However, the change between "excitatory" and
"inhibitory'' synapses is rapid, with only a few millivolts separating
stability and instability of the synchronous state for most graphs. We also
find that for specific coupling strengths (as measured by the global synaptic
conductance), islands of synchronizability in the MSF can emerge for inhibitory
connectivity. We verified the stability of these islands by direct simulation
of pairs of neurons coupled with eigenvalues in the matching spectrum. These
results were robust for different transitions to spiking (Hodgkin Class I vs
Class II), which displayed very similar synchronizability characteristics.
