The dynamic properties of the inositol (1,4,5)-trisphosphate (IP3) receptor are crucial for the control of intracellular Ca 2؉ , including the generation of Ca 2؉ oscillations and waves. However, many models of this receptor do not agree with recent experimental data on the dynamic responses of the receptor. We construct a model of the IP 3 receptor and fit the model to dynamic and steady-state experimental data from type-2 IP 3 receptors. Our results indicate that, (i) Ca 2؉ binds to the receptor using saturating, not mass-action, kinetics; (ii) Ca 2؉ decreases the rate of IP 3 binding while simultaneously increasing the steady-state sensitivity of the receptor to IP 3; (iii) the rate of Ca 2؉ -induced receptor activation increases with Ca 2؉ and is faster than Ca 2؉ -induced receptor inactivation; and (iv) IP3 receptors are sequentially activated and inactivated by Ca 2؉ even when IP3 is bound. Our results emphasize that measurement of steady-state properties alone is insufficient to characterize the functional properties of the receptor. O scillations and waves in the concentration of free intracellular calcium (Ca 2ϩ ) are seen in many cell types and are known to be an important intra-and intercellular signaling system. It is thus of interest to determine the mechanisms underlying such complex dynamic behavior. One of the most important of these mechanisms is the inositol trisphosphate receptor (IPR), which also functions as a Ca 2ϩ channel. There is now a great deal of experimental evidence that in many cell types, oscillations and waves of Ca 2ϩ are mediated in major part by the release through the IPR of Ca 2ϩ from the endoplasmic reticulum, and that it is the modulation of the IPR by Ca Consider, for example, the reaction scheme shown in Fig. 1. If we assume that à and Ā are in instantaneous equilibrium, we have cà ϭ L 1 Ā , where L 1 ϭ l Ϫ1 ͞l 1 , and c denotes [Ca 2ϩ ]. Hence, letting A ϭ Ā ϩ à , we have dA͞dt ϭ (k Ϫ1 ϩ l Ϫ2 )I Ϫ (c)A, where (c) ϭ c(k 1 L 1 ϩl 2 )͞cϩL 1 . Thus, this scheme is a simple way in which saturating binding kinetics can be incorporated into a model. It is similar to the Michaelis-Menten model of an enzyme-catalyzed reaction, in which a saturating reaction rate is obtained by assuming the existence of an intermediate complex. In this introductory model, the state Ā plays a role similar to that of the enzyme complex. By assuming that the original state à (analogous to the substrate) is in fast equilibrium with state Ā , we attain saturating kinetics of the Michaelis-Menten type.
An IPR ModelA diagram of the IPR model is given in Fig. 2. Although it appears to contain a multiplicity of states, there are specific reasons for each one. The background structure is simple. Fig. 3.States R , Ō , Ā , and RЈ are used to give Ca 2ϩ -dependent transitions that have saturable kinetics, as in the simple example of Fig. 1. These states will ultimately disappear, leaving behind only functions of c. Note that the inactivated states I 1 and I 2 both have Ca 2ϩ bound to the same site...