Shriver

Lauren Shriver

Recently, much interest has accumulated with regards to metabotropic glutamate receptors (mGluRs) as potential targets for the pharmacological treatment of numerous neurobiological disorders. Despite the fact that there is still much unknown about the underlying structure and mechanism of mGluRs, one well-known feature is that they exist as homodimers. While this feature introduces additional complexity in regards to modeling the pharmokinetics of mGluRs, implementation of models that correspond to receptor monomers with graph theory have a promising outcome for modeling these complexities in a compact and consistent way. Specifically, graph theory can be used in order to expand a four-state Markov chain cycle, known as the ternary complex model (TCM), into a model that corresponds to allosteric interactions between homodimer receptors and ligand and modulator molecules. In terms of graph theory, the Markov chain that is depicted in the original TCM can be viewed as a simple, cyclic graph with four nodes (states) and four edges (transitions between states). Taking the reduced Cartesian graph product of two of these Markov-chains results in a graph comprised of seven linearly independent, four-state cycles. This method for receptor modeling allows one to easily and systematically derive expressions for the dissociation constants that correspond with transitions between states under steady state conditions.