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Changes in brain states, as found in many neurological diseases such asepilepsy, are often described as bifurcations in mesoscopic neural models.Nearly all of these models rely on a mathematically convenient, butbiophysically inaccurate, description of the synaptic input to neurons calledcurrent-based synapses. We develop a novel analytical framework to analyze theeffects of a more biophysically realistic description, known asconductance-based synapses. These are implemented in a mesoscopic neural modeland compared to the standard approximation via a single parameter homotopicmapping. A bifurcation analysis using the homotopy parameter demonstrates thatif a more realistic synaptic coupling mechanism is used in this class ofmodels, then a bifurcation or transition to an abnormal brain state does notoccur in the same parameter space. We show that the more realistic coupling hasadditional mathematical parameters that require a fundamentally differentbiophysical mechanism to undergo a state transition. These results demonstratethe importance of incorporating more realistic synapses in mesoscopic neuralmodels and challenge the accuracy of previous models, especially thosedescribing brain state transitions such as epilepsy.

A homotopic mapping between current-based and conductance-based synapses in a mesoscopic neural model of epilepsy