Population of human ventricular cell models calibrated with in vivo measurements unravels ionic mechanisms of cardiac alternans

Cardiac alternansis an important risk factor in cardiac physiology, and is related to the initiation of many pathophysiological conditions. However, the mechanisms underlying the generation of alternans remain unclear. In this study, we used a population of computational human ventricle models based onthe O’Hara model [1] to explore the effect of 11 key factors experimentally reported to be related to alternans. In vivo experimental datasets coming from patients undergoing cardiac surgery were used in the calibration of our in silico population of models. The calibrated models in the population were divided into two groups (Normal and Alternans) depending on alternans occurrence. Our results showed that there were significant differences in the following 5 ionic currents between the two groups: fast sodium current, sodium calcium exchanger current, sodium potassium pump current, sarcoplasmic reticulum (SR) calcium release flux and SR calcium reuptake flux. Further analysis indicated that fast sodium current and SR calcium uptake were the two most significant currents that contributed to voltage and calcium alternans generation, respectively

Markov chain models of instantaneously coupled intracellular calcium channels

Localized calcium elevations known as calcium puffs or sparks are cellular signals arising from cooperative activity of clusters of inositol 1,4,5-trisphosphate receptors (IP3Rs) or ryanodine receptors (RyRs) located at calcium release sites on the endoplasmic or sarcoplasmic reticulum membrane. When Markov chain models of these intracellular calcium-regulated calcium channels are coupled via a mathematical representation of the calcium microdomain, simulated calcium release sites may exhibit the phenomenon of stochastic calcium excitability where the IP3Rs or RyRs open and close in a concerted fashion. Although the biophysical theory relating the kinetics of single channels to the collective phenomena of puffs and sparks is only beginning to be developed, Markov chain models of coupled intracellular channels give insight into the dynamics of calcium puffs and sparks.;Interestingly, under some conditions simulated puffs and sparks can be observed even when the single channel model used does not include slow calcium inactivation or any long-lived closed state. In this case termination of the localized calcium elevation occurs when all of the intracellular channels at a release site simultaneously close through a process called stochastic attrition. This dissertation investigates the statistical properties of stochastic attrition viewed as an absorption time on a terminating Markov chain that represents a calcium release site composed of two-state channels that are activated by calcium. Assuming that the local calcium concentration experienced by a channel depends only on the number of open channels at the calcium release site, the probability distribution function for the time until stochastic attrition occurs is derived and an analytical formula for the expectation of this random variable is presented. Also explored is how the contribution of stochastic attrition to the termination of calcium puffs and sparks depends on the number of channels at a release site, the source amplitude of the channels, the background calcium concentration, channel kinetics, and the cooperativity of calcium binding.;This dissertation also studies whether single channel models with calcium inactivation are less sensitive to the details of release site ultrastructure than models that lack a slow calcium-inactivation process. Release site dynamics obtained from simulated calcium release sites composed of instantaneously coupled calcium-regulated calcium channels whose random spatial locations were chosen from a uniform distribution on a disc of specified radius are compared to simulations with channels arranged on hexagonal lattices. Analysis of puff/spark statistics confirms that puffs and sparks are less sensitive to the spatial organization of release sites when the single channel model includes a slow inactivation process. The validity of several different mean-field reductions that do not explicitly account for the details of release site ultrastructure is also investigated.;Calcium release site models are stochastic automata networks that involve many functional transitions, that is, the transition probabilities of each channel depend on the local calcium concentration and thus the state of the other channels. A Kronecker structured representation for calcium release site models is presented and benchmark stationary distribution calculations using both exact and approximate iterative numerical solution techniques that leverage this structure are performed. When it is possible to obtain an exact solution, response measures such as the number of channels in a particular state converge more quickly using the iterative numerical methods than occupation measures calculated via Monte Carlo simulation. When an exact solution is not feasible, iterative approximate methods based on the Power method may be used, with performance similar to Monte Carlo estimates

Reduction of Calcium Release Site Models via Fast/Slow Analysis and Iterative Aggregation/Disaggregation

Mathematical models of calcium release sites derived from Markov chain models of intracellular calcium channels exhibit collective gating reminiscent of the experimentally observed phenomenon of calcium puffs and sparks. Such models often take the form of stochastic automata networks in which the transition probabilities of each channel depend on the local calcium concentration and thus the state of the other channels. In order to overcome the state-space explosion that occurs in such compositionally defined calcium release site models, we have implemented several automated procedures for model reduction using fast/slow analysis. After categorizing rate constants in the single channel model as either fast or slow, groups of states in the expanded release site model that are connected by fast transitions are lumped, and transition rates between reduced states are chosen consistent with the conditional probability distribution among states within each group. For small problems these conditional probability distributions can be numerically calculated from the full model without approximation. For large problems the conditional probability distributions can be approximated without the construction of the full model by assuming rapid mixing of states connected by fast transitions. Alternatively, iterative aggregation/disaggregation may be employed to obtain reduced calcium release site models in a memory-efficient fashion. Benchmarking of several different iterative aggregation/disaggregation-based fast/slow reduction schemes establishes the effectiveness of automated calcium release site reduction utilizing the Koury–McAllister–Stewart method. Mathematical modeling has played an important role in understanding the relationship between single channel gating of intracellular calcium (Ca2+) channels and the stochastic dynamics of Ca2+ release events known as Ca2+ puffs and sparks. Ca2+ release site models are defined by the composition of single channel models whose transition probabilities depend on the local calcium concentration and thus the state of the other channels. Because the large state space of such models impedes computational analysis of the dynamics of Ca2+ release sites, we implement and validate the application of several automated model reduction techniques that leverage separation of time scales, a common feature of single channel models of inositol 1,4,5-trisphosphate receptors (IP3Rs) and ryanodine receptors (RyRs). The authors show for the first time that memory-efficient iterative aggregation/disaggregation (IAD)-based numerical schemes are effective for fast/slow reduction in compositionally defined Ca2+ release site models

Mean Field Strategies Induce Unrealistic Non-Linearities in Calcium Puffs

Mean field models are often useful approximations to biological systems, but sometimes, they can yield misleading results. In this work, we compare mean field approaches with stochastic models of intracellular calcium release. In particular, we concentrate on calcium signals generated by the concerted opening of several clustered channels (calcium puffs). To this end we simulate calcium puffs numerically and then try to reproduce features of the resulting calcium distribution using mean field models were all the channels open and close simultaneously. We show that an unrealistic non-linear relationship between the current and the number of open channels is needed to reproduce the simulated puffs. Furthermore, a single channel current which is five times smaller than the one of the stochastic simulations is also needed. Our study sheds light on the importance of the stochastic kinetics of the calcium release channel activity to estimate the release fluxes

Role of the Calcium Plateau in the Neuronal Injury and Behavioral Morbidities Following Organophosphate Intoxication

Organophosphate (OP) chemicals include nerve agents and pesticides, and there is a growing concern of OP based chemical attacks against civilians. Current antidotes are essential in limiting immediate mortality associated with OP exposure. However, further research is needed to identify molecular mechanisms underlying long-term neurological deficits following survival of OP toxicity in order to develop effective therapeutics. We have developed rat survival models of OP induced status epilepticus (SE) that mimic chronic mortality and morbidity following OP intoxication. We have observed significant elevations in hippocampal calcium levels after OP SE that persisted for weeks following initial survival. Drugs inhibiting intracellular calcium-induced calcium release such as dantrolene, levetiracetam, and carisbamate lowered OP-SE mediated protracted calcium elevations. Given the critical role of calcium signaling in modulating behavior and cell-death mechanisms, drugs targeted at preventing the development of the calcium plateau could enhance neuroprotection, help reduce morbidity and improve outcome following survival of OP SE

Translating intracellular calcium signaling into models

The rich experimental data on intracellular calcium has put theoreticians in an ideal position to derive models of intracellular calcium signaling. Over the last 25 years, a large number of modeling frameworks have been suggested. Here, I will review some of the milestones of intracellular calcium modeling with a special emphasis on calcium-induced calcium release (CICR) through inositol-1,4,5-trisphosphate and ryanodine receptors. I will highlight key features of CICR and how they are represented in models as well as the challenges that theoreticians face when translating our current understanding of calcium signals into equations. The selected examples demonstrate that a successful model provides mechanistic insights into the molecular machinery of the Ca2+ signaling toolbox and determines the contribution of local Ca2+ release to global Ca2+ patterns, which at the moment cannot be resolved experimentally

Sparks and waves in a stochastic fire-diffuse-fire model of Ca2+

Calcium ions are an important second messenger in living cells. Indeed calcium signals in the form of waves have been the subject of much recent experimental interest. It is now well established that these waves are composed of elementary stochastic release events (calcium puffs) from spatially localized calcium stores. Here we develop a computationally inexpensive model of calcium release based upon a stochastic generalization of the Fire-Diffuse-Fire (FDF) threshold model. Our model retains the discrete nature of calcium stores, but also incorporates a notion of release probability via the introduction of threshold noise. Numerical simulations of the model illustrate that stochastic calcium release leads to the spontaneous production of calcium sparks that may merge to form saltatory waves. In the parameter regime where deterministic waves exist it is possible to identify a critical level of noise defining a non-equilibrium phase-transition between propagating and abortive structures. A statistical analysis shows that this transition is the same as for models in the directed percolation universality class. Moreover, in the regime where no initial structure can survive deterministically, threshold noise is shown to generate a form of array enhanced coherence resonance whereby all calcium stores release periodically and simultaneously

Role of the JP45-Calsequestrin Complex on Calcium Entry in Slow Twitch Skeletal Muscles

We exploited a variety of mouse models to assess the roles of JP45-CASQ1 (CASQ, calsequestrin) and JP45-CASQ2 on calcium entry in slow twitch muscles. In flexor digitorum brevis (FDB) fibers isolated from JP45-CASQ1-CASQ2 triple KO mice, calcium transients induced by tetanic stimulation rely on calcium entry via La3+- and nifedipine-sensitive calcium channels. The comparison of excitation-coupled calcium entry (ECCE) between FDB fibers from WT, JP45KO, CASQ1KO, CASQ2KO, JP45-CASQ1 double KO, JP45-CASQ2 double KO, and JP45-CASQ1-CASQ2 triple KO shows that ECCE enhancement requires ablation of both CASQs and JP45. Calcium entry activated by ablation of both JP45-CASQ1 and JP45-CASQ2 complexes supports tetanic force development in slow twitch soleus muscles. In addition, we show that CASQs interact with JP45 at Ca2+ concentrations similar to those present in the lumen of the sarcoplasmic reticulum at rest, whereas Ca2+ concentrations similar to those present in the SR lumen after depolarization-induced calcium release cause the dissociation of JP45 from CASQs. Our results show that the complex JP45-CASQs is a negative regulator of ECCE and that tetanic force development in slow twitch muscles is supported by the dynamic interaction between JP45 and CASQs