Synaptic transmission requires that the binding of the transmitter to the receptor to occur under rapidly changing transmitter levels, and this binding interaction is unlikely to be at equilibrium. We have sought to numerically solve for binding kinetics using ordinary differential equations and simultaneous difference equations for use in stochastic conditions. The reaction scheme of GABA interacting with the ligand-gated ion-channel demonstrates numerical stiffness. Implicit methods (Backward Euler, ode23s) performed orders of magnitude better than explicit methods (Forward Euler, ode23, RK4, ode45) in terms of step size required for stability, number of steps and cpu time. Interestingly, upon solving the system of 8 ordinary differential equations for the GABA reaction scheme we observed the existence of low dimensional invariant manifolds that may have important consequences for information processing in synapses. We also describe a mathematical approach that models complex receptor interactions in which the timing and amplitude of transmitter release are noisy. Exact solutions for simple bimolecular interactions that include stoichiometric interactions and receptor transitions can be used to model complex reaction schemes. We used the difference method to investigate the information processing capabilities of GABAA receptors and to predict how pharmacological agents may modify these properties. Initial simulations using a model for heterosynaptic regulation shows that signal to noise ratios can be decreased in the presence of background presynaptic activity both in the presence and absence of chlorpromazine. These types of simulations provide a platform for investigating the effect of psycho-active drugs on complex responses of transmitter-receptor interactions in noisy cellular environments such as the synapse. Understanding this process of transmitter-receptor interactions may be useful in the development of more specific and highly targeted modes of action.
Keywords: gaba reaction scheme, stiffness, desensitization, stoichiometric interactions, psycho-active drugs
Rights & PermissionsPrintExport