Mechanism-Based Mathematical Model for Gating of Ionotropic Glutamate Receptors.

We present a mathematical model for ionotropic glutamate receptors (iGluR's) that is built on mechanistic understanding and yields a number of thermodynamic and kinetic properties of channel gating. iGluR's are ligand-gated ion channels responsible for the vast majority of fast excitatory neurotransmission in the central nervous system. The effects of agonist-induced closure of the ligand-binding domain (LBD) are transmitted to the transmembrane channel (TMC) via interdomain linkers. Our model demonstrates that, relative to full agonists, partial agonists may reduce either the degree of LBD closure or the curvature of the LBD free energy basin, leading to less stabilization of the channel open state and hence lower channel open probability. A rigorous relation is derived between the channel closed-to-open free energy difference and the tension within the linker. Finally, by treating LBD closure and TMC opening as diffusive motions, we obtain gating trajectories that resemble stochastic current traces from single-channel recordings and calculate the rate constants for transitions between the channel open and closed states. Our model can be implemented by molecular dynamics simulations to realistically depict iGluR gating and may guide functional experiments in gaining deeper insight into this essential family of channel proteins.