Continuous-time Markov models have been considered the best representation for the stochastic dynamics of ion channels for more than thirty years. For most single-channel data sets, several open and closed states are required for accurately representing the dynamics. However, each data point only shows if the channel is open or closed but not in which state it is. Consequently, some model structures are inherently overparameterized and therefore, in principle, unsuitable for representing any data--those models are called "nonidentifiable". As of this writing, it seems to be poorly understood which continuous-time Markov models are identifiable and which are not, therefore the unconscious use of a nonidentifiable model is a considerable concern. To address this problem, an improved variant of a recently published Markov-chain Monte Carlo method is presented. The algorithm is tested using test data as well as experimental data. We demonstrate that, opposed to a widely used maximum-likelihood estimator, it gives clear warning signs when a nonidentifiable model is used for fitting. Furthermore, for test data that was generated from a nonidentifiable model, the Markov-chain Monte Carlo results recover much more information from the data than maximum-likelihood estimation.

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.

Ion channels are characterized by inherently stochastic behavior which can be represented by continuous-time Markov models (CTMM). Although methods for collecting data from single ion channels are available, translating a time series of open and closed channels to a CTMM remains a challenge. Bayesian statistics combined with Markov chain Monte Carlo (MCMC) sampling provide means for estimating the rate constants of a CTMM directly from single channel data. In this article, different approaches for the MCMC sampling of Markov models are combined. This method, new to our knowledge, detects overparameterizations and gives more accurate results than existing MCMC methods. It shows similar performance as QuB-MIL, which indicates that it also compares well with maximum likelihood estimators. Data collected from an inositol trisphosphate receptor is used to demonstrate how the best model for a given data set can be found in practice.

Spatio-temporal dynamics of intracellular calcium, [Ca2+]i, regulate the contractile function of cardiac muscle cells. Measuring [Ca2+]i flux is central to the study of mechanisms that underlie both normal cardiac function and calcium-dependent etiologies in heart disease. However, current imaging techniques are limited in the spatial resolution to which changes in [Ca2+]i can be detected. Using spatial point process statistics techniques we developed a novel method to simulate the spatial distribution of RyR clusters, which act as the major mediators of contractile Ca2+ release, upon a physiologically-realistic cellular landscape composed of tightly-packed mitochondria and myofibrils. We applied this method to computationally combine confocal-scale (~ 200 nm) data of RyR clusters with 3D electron microscopy data (~ 30 nm) of myofibrils and mitochondria, both collected from adult rat left ventricular myocytes. Using this hybrid-scale spatial model, we simulated reaction-diffusion of [Ca2+]i during the rising phase of the transient (first 30 ms after initiation). At 30 ms, the average peak of the simulated [Ca2+]i transient and of the simulated fluorescence intensity signal, F/F0, reached values similar to that found in the literature ([Ca2+]i ≈1 μM; F/F0≈5.5). However, our model predicted the variation in [Ca2+]i to be between 0.3 and 12.7 μM (~3 to 100 fold from resting value of 0.1 μM) and the corresponding F/F0 signal ranging from 3 to 9.5. We demonstrate in this study that: (i) heterogeneities in the [Ca2+]i transient are due not only to heterogeneous distribution and clustering of mitochondria; (ii) but also to heterogeneous local densities of RyR clusters. Further, we show that: (iii) these structure-induced heterogeneities in [Ca2+]i can appear in line scan data. Finally, using our unique method for generating RyR cluster distributions, we demonstrate the robustness in the [Ca2+]i transient to differences in RyR cluster distributions measured between rat and human cardiomyocytes.

Ion channels regulate the concentrations of ions within cells. By stochastically opening and closing its pore, they enable or prevent ions from crossing the cell membrane. However, rather than opening with a constant probability, many ion channels switch between several different levels of activity even if the experimental conditions are unchanged. This phenomenon is known as modal gating: instead of directly adapting its activity, the channel seems to mix sojourns in active and inactive modes in order to exhibit intermediate open probabilities. Evidence is accumulating that modal gating rather than modulation of opening and closing at a faster time scale is the primary regulatory mechanism of ion channels. However, currently, no method is available for reliably calculating sojourns in different modes. In order to address this challenge, we develop a statistical framework for segmenting singlechannel datasets into segments that are characteristic for particular modes. The algorithm finds the number of mode changes, detects their locations and infers the open probabilities of the modes. We apply our approach to data from the inositoltrisphosphate receptor. Based upon these results, we propose that mode changes originate from alternative conformational states of the channel protein that determine a certain level of channel activity.