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

TL;DR

This paper introduces a homotopic mapping to compare current-based and conductance-based synapses in neural models of epilepsy, revealing that realistic synapses alter bifurcation behavior and challenge previous model assumptions.

Contribution

It develops a novel analytical framework and demonstrates that realistic conductance-based synapses significantly change the bifurcation structure in neural models.

Findings

Conductance-based synapses require different parameters for state transitions.

Bifurcation behavior differs between current-based and conductance-based models.

Realistic synapses challenge previous assumptions in epilepsy modeling.

Abstract

Changes in brain states, as found in many neurological diseases such as epilepsy, are often described as bifurcations in mesoscopic neural models. Nearly all of these models rely on a mathematically convenient, but biophysically inaccurate, description of the synaptic input to neurons called current-based synapses. We develop a novel analytical framework to analyze the effects of a more biophysically realistic description, known as conductance-based synapses. These are implemented in a mesoscopic neural model and compared to the standard approximation via a single parameter homotopic mapping. A bifurcation analysis using the homotopy parameter demonstrates that if a more realistic synaptic coupling mechanism is used in this class of models, then a bifurcation or transition to an abnormal brain state does not occur in the same parameter space. We show that the more realistic coupling has additional mathematical parameters that require a fundamentally different biophysical mechanism to undergo a state transition. These results demonstrate the importance of incorporating more realistic synapses in mesoscopic neural models and challenge the accuracy of previous models, especially those describing brain state transitions such as epilepsy.