M. Saleet Jafri

Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load.

We construct a detailed mathematical model for Ca2+ regulation in the ventricular myocyte that includes novel descriptions of subcellular mechanisms based on recent experimental findings: 1) the Keizer-Levine model for the ryanodine receptor (RyR), which displays adaptation at elevated Ca2+; 2) a model for the L-type Ca2+ channel that inactivates by mode switching; and 3) a restricted subspace into which the RyRs and L-type Ca2+ channels empty and interact via Ca2+. We add membrane currents from the Luo-Rudy Phase II ventricular cell model to our description of Ca2+ handling to formulate a new model for ventricular action potentials and Ca2+ regulation. The model can simulate Ca2+ transients during an action potential similar to those seen experimentally. The subspace [Ca2+] rises more rapidly and reaches a higher level (10-30 microM) than the bulk myoplasmic Ca2+ (peak [Ca2+]i approximately 1 microM). Termination of sarcoplasmic reticulum (SR) Ca2+ release is predominately due to emptying of the SR, but is influenced by RyR adaptation. Because force generation is roughly proportional to peak myoplasmic Ca2+, we use [Ca2+]i in the model to explore the effects of pacing rate on force generation. The model reproduces transitions seen in force generation due to changes in pacing that cannot be simulated by previous models. Simulation of such complex phenomena requires an interplay of both RyR adaptation and the degree of SR Ca2+ loading. This model, therefore, shows improved behavior over existing models that lack detailed descriptions of subcellular Ca2+ regulatory mechanisms.

Stimulated Emission Depletion Live-Cell Super-Resolution Imaging Shows Proliferative Remodeling of T-Tubule Membrane Structures After Myocardial Infarction

Rationale: Transverse tubules (TTs) couple electric surface signals to remote intracellular Ca2+ release units (CRUs). Diffraction-limited imaging studies have proposed loss of TT components as disease mechanism in heart failure (HF). Objectives: Objectives were to develop quantitative super-resolution strategies for live-cell imaging of TT membranes in intact cardiomyocytes and to show that TT structures are progressively remodeled during HF development, causing early CRU dysfunction. Methods and Results: Using stimulated emission depletion (STED) microscopy, we characterized individual TTs with nanometric resolution as direct readout of local membrane morphology 4 and 8 weeks after myocardial infarction (4pMI and 8pMI). Both individual and network TT properties were investigated by quantitative image analysis. The mean area of TT cross sections increased progressively from 4pMI to 8pMI. Unexpectedly, intact TT networks showed differential changes. Longitudinal and oblique TTs were significantly increased at 4pMI, whereas transversal components appeared decreased. Expression of TT-associated proteins junctophilin-2 and caveolin-3 was significantly changed, correlating with network component remodeling. Computational modeling of spatial changes in HF through heterogeneous TT reorganization and RyR2 orphaning (5000 of 20 000 CRUs) uncovered a local mechanism of delayed subcellular Ca2+ release and action potential prolongation. Conclusions: This study introduces STED nanoscopy for live mapping of TT membrane structures. During early HF development, the local TT morphology and associated proteins were significantly altered, leading to differential network remodeling and Ca2+ release dyssynchrony. Our data suggest that TT remodeling during HF development involves proliferative membrane changes, early excitation-contraction uncoupling, and network fracturing.

STED Live Cell Super-Resolution Imaging Shows Proliferative Remodeling of T-Tubule Membrane Structures After Myocardial Infarction

Rationale: Transverse tubules (TTs) couple electric surface signals to remote intracellular Ca2+ release units (CRUs). Diffraction-limited imaging studies have proposed loss of TT components as disease mechanism in heart failure (HF). Objectives: Objectives were to develop quantitative super-resolution strategies for live-cell imaging of TT membranes in intact cardiomyocytes and to show that TT structures are progressively remodeled during HF development, causing early CRU dysfunction. Methods and Results: Using stimulated emission depletion (STED) microscopy, we characterized individual TTs with nanometric resolution as direct readout of local membrane morphology 4 and 8 weeks after myocardial infarction (4pMI and 8pMI). Both individual and network TT properties were investigated by quantitative image analysis. The mean area of TT cross sections increased progressively from 4pMI to 8pMI. Unexpectedly, intact TT networks showed differential changes. Longitudinal and oblique TTs were significantly increased at 4pMI, whereas transversal components appeared decreased. Expression of TT-associated proteins junctophilin-2 and caveolin-3 was significantly changed, correlating with network component remodeling. Computational modeling of spatial changes in HF through heterogeneous TT reorganization and RyR2 orphaning (5000 of 20 000 CRUs) uncovered a local mechanism of delayed subcellular Ca2+ release and action potential prolongation. Conclusions: This study introduces STED nanoscopy for live mapping of TT membrane structures. During early HF development, the local TT morphology and associated proteins were significantly altered, leading to differential network remodeling and Ca2+ release dyssynchrony. Our data suggest that TT remodeling during HF development involves proliferative membrane changes, early excitation-contraction uncoupling, and network fracturing.

Modeling Gain and Gradedness of Ca2+ Release in the Functional Unit of the Cardiac Diadic Space

A model of the functional release unit (FRU) in rat cardiac muscle consisting of one dihydropyridine receptor (DHPR) and eight ryanodine receptor (RyR) channels, and the volume surrounding them, is formulated. It is assumed that no spatial [Ca2+] gradients exist in this volume, and that each FRU acts independently. The model is amenable to systematic parameter studies in which FRU dynamics are simulated at the channel level using Monte Carlo methods with Ca2+ concentrations simulated by numerical integration of a coupled system of differential equations. Using stochastic methods, Ca(2+)-induced Ca2+ release (CICR) shows both high gain and graded Ca2+ release that is robust when parameters are varied. For a single DHPR opening, the resulting RyR Ca2+ release flux is insensitive to the DHPR open duration, and is determined principally by local sarcoplasmic reticulum (SR) Ca2+ load, consistent with experimental data on Ca2+ sparks. In addition, single RyR openings are effective in triggering Ca2+ release from adjacent RyRs only when open duration is long and SR Ca2+ load is high. This indicates relatively low coupling between RyRs, and suggests a mechanism that limits the regenerative spread of RyR openings. The results also suggest that adaptation plays an important modulatory role in shaping Ca2+ release duration and magnitude, but is not solely responsible for terminating Ca2+ release. Results obtained with the stochastic model suggest that high gain and gradedness can occur by the recruitment of independent FRUs without requiring spatial [Ca2+] gradients within a functional unit or cross-coupling between adjacent functional units.

Cardiac sodium channel Markov model with temperature dependence and recovery from inactivation.

A Markov model of the cardiac sodium channel is presented. The model is similar to the CA1 hippocampal neuron sodium channel model developed by Kuo and Bean (1994. Neuron. 12:819-829) with the following modifications: 1) an additional open state is added; 2) open-inactivated transitions are made voltage-dependent; and 3) channel rate constants are exponential functions of enthalpy, entropy, and voltage and have explicit temperature dependence. Model parameters are determined using a simulated annealing algorithm to minimize the error between model responses and various experimental data sets. The model reproduces a wide range of experimental data including ionic currents, gating currents, tail currents, steady-state inactivation, recovery from inactivation, and open time distributions over a temperature range of 10 degrees C to 25 degrees C. The model also predicts measures of single channel activity such as first latency, probability of a null sweep, and probability of reopening.

Models of cardiac excitation–contraction coupling in ventricular myocytes

Mathematical and computational modeling of cardiac excitation-contraction coupling has produced considerable insights into how the heart muscle contracts. With the increase in biophysical and physiological data available, the modeling has become more sophisticated with investigations spanning in scale from molecular components to whole cells. These modeling efforts have provided insight into cardiac excitation-contraction coupling that advanced and complemented experimental studies. One goal is to extend these detailed cellular models to model the whole heart. While this has been done with mechanical and electrophysiological models, the complexity and fast time course of calcium dynamics have made inclusion of detailed calcium dynamics in whole heart models impractical. Novel methods such as the probability density approach and moment closure technique which increase computational efficiency might make this tractable.

Superresolution Modeling of Calcium Release in the Heart

Stable calcium-induced calcium release (CICR) is critical for maintaining normal cellular contraction during cardiac excitation-contraction coupling. The fundamental element of CICR in the heart is the calcium (Ca2+) spark, which arises from a cluster of ryanodine receptors (RyR). Opening of these RyR clusters is triggered to produce a local, regenerative release of Ca2+ from the sarcoplasmic reticulum (SR). The Ca2+ leak out of the SR is an important process for cellular Ca2+ management, and it is critically influenced by spark fidelity, i.e., the probability that a spontaneous RyR opening triggers a Ca2+ spark. Here, we present a detailed, three-dimensional model of a cardiac Ca2+ release unit that incorporates diffusion, intracellular buffering systems, and stochastically gated ion channels. The model exhibits realistic Ca2+ sparks and robust Ca2+ spark termination across a wide range of geometries and conditions. Furthermore, the model captures the details of Ca2+ spark and nonspark-based SR Ca2+ leak, and it produces normal excitation-contraction coupling gain. We show that SR luminal Ca2+-dependent regulation of the RyR is not critical for spark termination, but it can explain the exponential rise in the SR Ca2+ leak-load relationship demonstrated in previous experimental work. Perturbations to subspace dimensions, which have been observed in experimental models of disease, strongly alter Ca2+ spark dynamics. In addition, we find that the structure of RyR clusters also influences Ca2+ release properties due to variations in inter-RyR coupling via local subspace Ca2+ concentration ([Ca2+]ss). These results are illustrated for RyR clusters based on super-resolution stimulated emission depletion microscopy. Finally, we present a believed-novel approach by which the spark fidelity of a RyR cluster can be predicted from structural information of the cluster using the maximum eigenvalue of its adjacency matrix. These results provide critical insights into CICR dynamics in heart, under normal and pathological conditions.

NFAT and NFκB Activation in T Lymphocytes: A Model of Differential Activation of Gene Expression

Mathematical models for the regulation of the Ca2+-dependent transcription factors NFAT and NFκB that are involved in the activation of the immune and inflammatory responses in T lymphocytes have been developed. These pathways are important targets for drugs, which act as powerful immunosuppressants by suppressing activation of NFAT and NFκB in T cells. The models simulate activation and deactivation over physiological concentrations of Ca2+, diacyl glycerol (DAG), and PKCθ using single and periodic step increases. The model suggests the following: (1) the activation NFAT does not occur at low frequencies as NFAT requires calcineurin activated by Ca2+ to remain dephosphorylated and in the nucleus; (2) NFκB is activated at lower Ca2+ oscillation frequencies than NFAT as IκB is degraded in response to elevations in Ca2+ allowing free NFκB to translocate into the nucleus; and (3) the degradation of IκB is essential for efficient translocation of NFκB to the nucleus. Through sensitivity analysis, the model also suggests that the largest controlling factor for NFAT activation is the dissociation/reassociation rate of the NFAT:calcineurin complex and the translocation rate of the complex into the nucleus and for NFκB is the degradation/resynthesis rate of IκB and the import rate of IκB into the nucleus.

Mitochondrial Calcium Signaling and Energy Metabolism

Abstract: A computational model of energy metabolism in the mammalian ventricular myocyte is developed to study the effect of cytosolic calcium (Ca2+) transients on adenosine triphosphate (ATP) production. The model couples the Jafri‐Dudycha model for tricarboxylic acid cycle regulation to a modified version of the Magnus‐Keizer model for the mitochondria. The fluxes associated with Ca2+ uptake and efflux (i.e., the Ca2+ uniporter and Na+‐Ca2+ exchanger) and the F1F0‐ATPase were modified to better model heart mitochondria. Simulations were performed at steady state and with Ca2+ transients at various pacing frequencies generated by the Rice‐Jafri‐Winslow model for the guinea pig ventricular myocyte. The effects of the Ca2+ transients for mitochondria both adjacent to the dyadic space and in the bulk myoplasm were studied. The model shows that Ca2+ activation of both the tricarboxylic acid cycle and the F1F0‐ATPase are necessary to produce increases in ATP production. The model also shows that in mitochondria located near the subspace, the large Ca2+ transients can depolarize the mitochondrial membrane potential sufficiently to cause a transient decline in ATP production. However, this transient is of short duration, minimizing its impact on overall ATP production.

Moment Closure for Local Control Models of Calcium-Induced Calcium Release in Cardiac Myocytes

In prior work, we introduced a probability density approach to modeling local control of Ca2+-induced Ca2+ release in cardiac myocytes, where we derived coupled advection-reaction equations for the time-dependent bivariate probability density of subsarcolemmal subspace and junctional sarcoplasmic reticulum (SR) [Ca2+] conditioned on Ca2+ release unit (CaRU) state. When coupled to ordinary differential equations (ODEs) for the bulk myoplasmic and network SR [Ca2+], a realistic but minimal model of cardiac excitation-contraction coupling was produced that avoids the computationally demanding task of resolving spatial aspects of global Ca2+ signaling, while accurately representing heterogeneous local Ca2+ signals in a population of diadic subspaces and junctional SR depletion domains. Here we introduce a computationally efficient method for simulating such whole cell models when the dynamics of subspace [Ca2+] are much faster than those of junctional SR [Ca2+]. The method begins with the derivation of a system of ODEs describing the time-evolution of the moments of the univariate probability density functions for junctional SR [Ca2+] jointly distributed with CaRU state. This open system of ODEs is then closed using an algebraic relationship that expresses the third moment of junctional SR [Ca2+] in terms of the first and second moments. In simulated voltage-clamp protocols using 12-state CaRUs that respond to the dynamics of both subspace and junctional SR [Ca2+], this moment-closure approach to simulating local control of excitation-contraction coupling produces high-gain Ca2+ release that is graded with changes in membrane potential, a phenomenon not exhibited by common pool models. Benchmark simulations indicate that the moment-closure approach is nearly 10,000-times more computationally efficient than corresponding Monte Carlo simulations while leading to nearly identical results. We conclude by applying the moment-closure approach to study the restitution of Ca2+-induced Ca2+ release during simulated two-pulse voltage-clamp protocols.