Comparison of models for IP3 receptor kinetics using stochastic simulations

Abstract

Inositol 1,4,5-trisphosphate receptor (IP3R) is a ubiquitous intracellular calcium (Ca(2+)) channel which has a major role in controlling Ca(2+) levels in neurons. A variety of computational models have been developed to describe the kinetic function of IP3R under different conditions. In the field of computational neuroscience, it is of great interest to apply the existing models of IP3R when modeling local Ca(2+) transients in dendrites or overall Ca(2+) dynamics in large neuronal models. The goal of this study was to evaluate existing IP3R models, based on electrophysiological data. This was done in order to be able to suggest suitable models for neuronal modeling. Altogether four models (Othmer and Tang, 1993; Dawson et al., 2003; Fraiman and Dawson, 2004; Doi et al., 2005) were selected for a more detailed comparison. The selection was based on the computational efficiency of the models and the type of experimental data that was used in developing the model. The kinetics of all four models were simulated by stochastic means, using the simulation software STEPS, which implements the Gillespie stochastic simulation algorithm. The results show major differences in the statistical properties of model functionality. Of the four compared models, the one by Fraiman and Dawson (2004) proved most satisfactory in producing the specific features of experimental findings reported in literature. To our knowledge, the present study is the first detailed evaluation of IP3R models using stochastic simulation methods, thus providing an important setting for constructing a new, realistic model of IP3R channel kinetics for compartmental modeling of neuronal functions. We conclude that the kinetics of IP3R with different concentrations of Ca(2+) and IP3 should be more carefully addressed when new models for IP3R are developed.

Figure 1. Schematic representation of the states and transitions of the IP₃R models.

(A) Othmer and Tang (forward direction of a reaction is to the right) (B) Doi et al. (forward direction of a reaction is to the right or up), (C) Fraiman and Dawson (forward direction of a reaction is to the right or down) (D) Dawson et al. (forward direction of a reaction is the to the direction of binding a ligand or in the plain state transitions from left to the right).

Figure 2. Open probability of IP₃R as a function of (A) cytosolic Ca²⁺ concentration (IP₃  = 10 M) and (B) cytosolic IP₃ concentration (Ca²⁺  = 0.25 M).

Green: Othmer and Tang , Blue: Dawson et al. , Red: Fraiman and Dawson , Magenta: Doi et al. .

Figure 3. Open probability of IP₃R as a function of cytosolic Ca²⁺ concentration in different IP₃ concentrations.

(A) Othmer and Tang (B) Dawson et al. (C) Fraiman and Dawson (D) Doi et al. .

Figure 4. Distribution of IP₃R open and closed times for all the selected models obtained in simulation conditions Sim 1 (A–F) and Sim 2 (G–L).

(A) Open time distributions of all the models in conditions Sim 1, (B) Enlarged from A, (C) Enlarged from B, (D) Closed time distributions of all the models conditions Sim 1, (E) Enlarged from D, (F) Enlarged from E, (G) Open time distributions of all the models conditions Sim 2, (H) Enlarged from G, (I) Enlarged from H, (J) Closed time distributions of all the models conditions Sim 2, (K) Enlarged from J, (L) Enlarged from K. Experimental data is from . In simulation conditions Sim 1 [Ca²⁺]  = 0.2 M, [IP₃]  =  2 M and Sim 2 [Ca²⁺]  = 0.2 M, [IP₃]  = 10 M (as shown in Table 6).

Figure 5. Distributions of IP₃R open and closed times for all the selected models obtained in simulation conditions Sim 3 (A–F) and Sim 4 (G–L).

(A) Open time distributions of all the models in conditions Sim 3, (B) Enlarged from A, (C) Enlarged from B, (D) Closed time distributions of all the models in conditions Sim 3, (E) Enlarged from D, (F) Enlarged from E, (G) Open time distributions of all the models conditions Sim 4, (H) Enlarged from G, (I) Enlarged from H, (J) Closed time distributions of all the models conditions Sim 4, (K) Enlarged from J, (L) Enlarged from K. Experimental data is from . In simulation conditions Sim 3 [Ca²⁺] = 0.1 M, [IP₃] = 2 M and Sim 4 [Ca²⁺]  =  0.1 M, [IP₃]  = 10 M (as shown in Table 6).

Figure 6. Distribution of IP₃R open and closed times for all the selected models obtained in simulation conditions Sim 5 (A–F) and Sim 6 (G–L).

(A) Open time distributions of all the models conditions Sim 5, (B) Enlarged from A, (C) Enlarged from B, (D) Closed time distributions of all the models conditions Sim 5, (E) Enlarged from D, (F) Enlarged from E, (G) Open time distributions of all the models conditions Sim 6, (H) Enlarged from G, (I) Enlarged from H, (J) Closed time distributions of all the models conditions Sim 6, (K) Enlarged from J, (L) Enlarged from K. Experimental data is from . In simulation conditions Sim 5 [Ca²⁺]  = 0.01 M, [IP₃]  = 2 M and Sim 6 [Ca²⁺]  = 0.01 M, [IP₃]  = 10 M (as shown in Table 6).