Fig. 6.

Correlation between changes in binding and physiological parameters in receptor models. Binding constants K_D and deactivation time constants tau_deact were examined in a conventional single-ligand model (Kessler et al., 1996, 2008) (A) and in a 2-ligand model similar to that used by Sekiguchi et al. (2002) (B). Simplified schemes of the models are shown at the top, with R indicating closed receptor states, O indicating open states, and D indicating desensitized states. The number after these letters indicates the number of agonists bound. Lines indicate transitions between states assumed to be significant. These transitions are governed by forward and reverse rate constants shown next to the line (left to right = above the line; right to left = below; downward = right side; upward = left side). Rate constants involving agonist association are expressed in μMol⁻¹ · s⁻¹ and must be multiplied with the glutamate concentration in μM. All other rate constants are in s⁻¹. To calculate binding, receptor-state distributions after adding ligand were calculated iteratively until a stable steady-state was reached; binding at 12 agonist concentrations was then used to determine the dissociation constant K_D. In parallel, responses to 1-ms pulses of agonist were computed and fitted with exponential decay functions to obtain the deactivation time constant tau_deact. These calculations were then repeated after introducing progressively larger changes in certain rate constants to assess the impact on K_D and tau_deact. Two sets of changes in rate constants were examined in particular: 1) a reduction in the channel closing rate k_close, and 2) a reduction in the agonist dissociation rate constant k_dissoc combined with a reduction in the desensitization rate constant k_desens. The factor by which each rate constant was reduced is indicated in the figure next to the symbol. In B, if two numbers are shown then the upper one indicates the slowing in all the rates of dissociation, and the lower one indicates the slowing in all the rates of desensitization. The impact on binding and physiology is shown as the factor by which the deactivation time constant (tau_deact) is increased (x-axis) and the factor by which the K_D constant is decreased (i.e., the factor by which binding affinity is increased; y-axis). The changes produced in the 2-ligand model are illustrated further in C, where “a” indicates responses of and binding to the unmodified receptor and “b” and “c” represent receptors in which dissociation and desensitization rate constants are assumed to be slowed 10/100 times (b) or 20/400 times (c). The traces on the left show responses to a 1-ms pulse of glutamate, and those at the middle show responses to a 100-ms pulse of glutamate. Binding is shown in Scatchard format where “bound” indicates the number of agonists bound per 100 receptors and the K_D is given by −1/slope of the regression line.