A Kinetic Model for Type I and II IP3R Accounting for Mode Changes

Abstract

Based upon an extensive single-channel data set, a Markov model for types I and II inositol trisphosphate receptors (IP(3)R) is developed. The model aims to represent accurately the kinetics of both receptor types of IP(3)R depending on the concentrations of inositol trisphosphate (IP(3)), adenosine trisphosphate (ATP), and intracellular calcium (Ca(2+)). In particular, the model takes into account that for some combinations of ligands the IP(3)R switches between extended periods of inactivity alternating with intervals of bursting activity (mode changes). In a first step, the inactive and active modes are modeled separately. It is found that, within modes, both receptor types are ligand-independent. In a second step, the submodels are connected by transition rates. Ligand-dependent regulation of the channel activity is achieved by modulating these transitions between active and inactive modes. As a result, a compact representation of the IP(3)R is obtained that accurately captures stochastic single-channel dynamics including mode changes in a model with six states and 10 rate constants, only two of which are ligand-dependent.

Statistical analysis of modal gating in ion channels

“…The probability distribution P(p, j, J | Y) approximated by the RJMCMC sampler answers several questions at once. Most of these questions cannot be answered confidently or cannot be answered at all by the heuristic algorithm described by Ionescu et al [45] or approaches based upon moving averages like in Siekmann et al [52]. Interestingly, for 1000 nM Ca 2+ , type I IP 3 R shows some evidence for a third mode at probabilities between 20 and 30% which has also been observed by Ionescu et al [45], who reported a mode of intermediate activity for their type I IP 3 R dataset (figure 1a).…”

“…By contrast, changes of ligand concentrations have little influence on the modulation of the short-term kinetics of openings and closings. This idea has been realized in a model by Siekmann et al [52], who represented modal gating of the IP 3 R by two ligand-independent models that were connected by ligand-dependent transition rates.…”

“…For our dataset from the IP 3 R, we classified currents below half of the average open currentĪ O as closed and currents above this threshold as open. We have found this approach for dealing with noise to be sufficient when we developed a Markov model for the same dataset [11,52]. In the application considered here, occasional misclassification of events should be even less important because the modes depend on the frequency of observed open and closed events rather than their exact sequence.…”

Mode switching of Inositol 1,4,5-trisphosphate receptor channel shapes the Spatiotemporal scales of Ca2+ signals

“…Neither is ours the first instance where a model representing the modal behavior of InsP 3 R is used for simulating puffs. Siekmann et al developed a six-state model incorporating the modal behavior of the channel [33] that was shown to reproduce the statistics of puffs [34] and whole-cell oscillations [35]. Simplifying the six states to a two-state model by getting rid of the intra-modal structure and using the two versions of the model, Siekmann et al [36] demonstrated that the fundamental process governing the generation of Ca 2+ puffs and oscillations is primarily controlled by the inter-modal structure, not the intra-modal structure.…”

Mitochondrial calcium handling within the interstitial cells of Cajal

“…See Appendix A for details of the boundary flux and reaction terms depicting calcium transporters and buffering. Briefly, we deploy a model of the MCU based on observations (40), include the LetM1 as characterized (37), and utilize a recent IP 3R model (64 Table 2 for a model geometry region and corresponding biological domain summary; each boundary flux term is also given in Table 3.…”