Johan Hake

Modelling cardiac calcium sparks in a three‐dimensional reconstruction of a calcium release unit

•  We have developed a detailed computational model of a cardiac Ca2+ spark based on a three dimensional reconstruction of electron tomograms. •  Our model predicts near total junctional Ca2+ depletion after the spark, while regional Ca2+ reserve is preserved. The local Ca2+ gradient inferred by these findings reconciles previous model predictions with experimental measurements. •  Differences in local distribution of calsequestrin have a profound impact on spark termination time, as reported by Fluo5, solely based on its Ca2+ buffering capacity. •  The SERCA pump can prolong spark release time by pumping Ca2+ back into the junctional SR during the spark.

DOLFIN: a C++/Python finite element library

DOLFIN is a C++/Python library that functions as the main user interface of FEniCS. In this 4806 chapter, we review the functionality of DOLFIN. We also discuss the implementation of some key 4807 features of DOLFIN in detail.

Control of Ca2+ Release by Action Potential Configuration in Normal and Failing Murine Cardiomyocytes

Cardiomyocytes from failing hearts exhibit spatially nonuniform or dyssynchronous sarcoplasmic reticulum (SR) Ca(2+) release. We investigated the contribution of action potential (AP) prolongation in mice with congestive heart failure (CHF) after myocardial infarction. AP recordings from CHF and control myocytes were included in a computational model of the dyad, which predicted more dyssynchronous ryanodine receptor opening during stimulation with the CHF AP. This prediction was confirmed in cardiomyocyte experiments, when cells were alternately stimulated by control and CHF AP voltage-clamp waveforms. However, when a train of like APs was used as the voltage stimulus, the control and CHF AP produced a similar Ca(2+) release pattern. In this steady-state condition, greater integrated Ca(2+) entry during the CHF AP lead to increased SR Ca(2+) content. A resulting increase in ryanodine receptor sensitivity synchronized SR Ca(2+) release in the mathematical model, thus offsetting the desynchronizing effects of reduced driving force for Ca(2+) entry. A modest nondyssynchronous prolongation of Ca(2+) release was nevertheless observed during the steady-state CHF AP, which contributed to increased time-to-peak measurements for Ca(2+) transients in failing cells. Thus, dyssynchronous Ca(2+) release in failing mouse myocytes does not result from electrical remodeling, but rather other alterations such as T-tubule reorganization.

Slow Ca2 + sparks de-synchronize Ca2 + release in failing cardiomyocytes: Evidence for altered configuration of Ca2 + release units?

In heart failure, cardiomyocytes exhibit slowing of the rising phase of the Ca(2+) transient which contributes to the impaired contractility observed in this condition. We investigated whether alterations in ryanodine receptor function promote slowing of Ca(2+) release in a murine model of congestive heart failure (CHF). Myocardial infarction was induced by left coronary artery ligation. When chronic CHF had developed (10 weeks post-infarction), cardiomyocytes were isolated from viable regions of the septum. Septal myocytes from SHAM-operated mice served as controls. Ca(2+) transients rose markedly slower in CHF than SHAM myocytes with longer time to peak (CHF=152 ± 12% of SHAM, P<0.05). The rise time of Ca(2+) sparks was also increased in CHF (SHAM=9.6 ± 0.6 ms, CHF=13.2 ± 0.7 ms, P<0.05), due to a sub-population of sparks (≈20%) with markedly slowed kinetics. Regions of the cell associated with these slow spontaneous sparks also exhibited slowed Ca(2+) release during the action potential. Thus, greater variability in spark kinetics in CHF promoted less uniform Ca(2+) release across the cell. Dyssynchronous Ca(2+) transients in CHF additionally resulted from T-tubule disorganization, as indicated by fast Fourier transforms, but slow sparks were not associated with orphaned ryanodine receptors. Rather, mathematical modeling suggested that slow sparks could result from an altered composition of Ca(2+) release units, including a reduction in ryanodine receptor density and/or distribution of ryanodine receptors into sub-clusters. In conclusion, our findings indicate that slowed, dyssynchronous Ca(2+) transients in CHF result from alterations in Ca(2+) sparks, consistent with rearrangement of ryanodine receptors within Ca(2+) release units.

Stochastic Binding of Ca2+ Ions in the Dyadic Cleft; Continuous versus Random Walk Description of Diffusion

Ca2+ signaling in the dyadic cleft in ventricular myocytes is fundamentally discrete and stochastic. We study the stochastic binding of single Ca2+ ions to receptors in the cleft using two different models of diffusion: a stochastic and discrete Random Walk (RW) model, and a deterministic continuous model. We investigate whether the latter model, together with a stochastic receptor model, can reproduce binding events registered in fully stochastic RW simulations. By evaluating the continuous model goodness-of-fit for a large range of parameters, we present evidence that it can. Further, we show that the large fluctuations in binding rate observed at the level of single time-steps are integrated and smoothed at the larger timescale of binding events, which explains the continuous model goodness-of-fit. With these results we demonstrate that the stochasticity and discreteness of the Ca2+ signaling in the dyadic cleft, determined by single binding events, can be described using a deterministic model of Ca2+ diffusion together with a stochastic model of the binding events, for a specific range of physiological relevant parameters. Time-consuming RW simulations can thus be avoided. We also present a new analytical model of bimolecular binding probabilities, which we use in the RW simulations and the statistical analysis.

Nonequilibrium reactivation of Na+ current drives early afterdepolarizations in mouse ventricle.

Background—Early afterdepolarizations (EADs) are triggers of cardiac arrhythmia driven by L-type Ca2+ current (ICaL) reactivation or sarcoplasmic reticulum Ca2+ release and Na+/Ca2+ exchange. In large mammals the positive action potential plateau promotes ICaL reactivation, and the current paradigm holds that cardiac EAD dynamics are dominated by interaction between ICaL and the repolarizing K+ currents. However, EADs are also frequent in the rapidly repolarizing mouse action potential, which should not readily permit ICaL reactivation. This suggests that murine EADs exhibit unique dynamics, which are key for interpreting arrhythmia mechanisms in this ubiquitous model organism. We investigated these dynamics in myocytes from arrhythmia-susceptible calcium calmodulin-dependent protein kinase II delta C (CaMKII&dgr;C)-overexpressing mice (Tg), and via computational simulations. Methods and Results—In Tg myocytes, &bgr;-adrenergic challenge slowed late repolarization, potentiated sarcoplasmic reticulum Ca2+ release, and initiated EADs below the ICaL activation range (–47±0.7 mV). These EADs were abolished by caffeine and tetrodotoxin (but not ranolazine), suggesting that sarcoplasmic reticulum Ca2+ release and Na+ current (INa), but not late INa, are required for EAD initiation. Simulations suggest that potentiated sarcoplasmic reticulum Ca2+ release and Na+/Ca2+ exchange shape late action potential repolarization to favor nonequilibrium reactivation of INa and thereby drive the EAD upstroke. Action potential clamp experiments suggest that lidocaine eliminates virtually all inward current elicited by EADs, and that this effect occurs at concentrations (40–60 &mgr;mol/L) for which lidocaine remains specific for inactivated Na+ channels. This strongly suggests that previously inactive channels are recruited during the EAD upstroke, and that nonequilibrium INa dynamics underlie murine EADs. Conclusions—Nonequilibrium reactivation of INa drives murine EADs.

Modeling Effects of L-Type Ca2+ Current and Na+-Ca2+ Exchanger on Ca2+ Trigger Flux in Rabbit Myocytes with Realistic T-Tubule Geometries

The transverse tubular system of rabbit ventricular myocytes consists of cell membrane invaginations (t-tubules) that are essential for efficient cardiac excitation-contraction coupling. In this study, we investigate how t-tubule micro-anatomy, L-type Ca2+ channel (LCC) clustering, and allosteric activation of Na+/Ca2+ exchanger by L-type Ca2+ current affects intracellular Ca2+ dynamics. Our model includes a realistic 3D geometry of a single t-tubule and its surrounding half-sarcomeres for rabbit ventricular myocytes. The effects of spatially distributed membrane ion-transporters (LCC, Na+/Ca2+ exchanger, sarcolemmal Ca2+ pump, and sarcolemmal Ca2+ leak), and stationary and mobile Ca2+ buffers (troponin C, ATP, calmodulin, and Fluo-3) are also considered. We used a coupled reaction-diffusion system to describe the spatio-temporal concentration profiles of free and buffered intracellular Ca2+. We obtained parameters from voltage-clamp protocols of L-type Ca2+ current and line-scan recordings of Ca2+ concentration profiles in rabbit cells, in which the sarcoplasmic reticulum is disabled. Our model results agree with experimental measurements of global Ca2+ transient in myocytes loaded with 50 μM Fluo-3. We found that local Ca2+ concentrations within the cytosol and sub-sarcolemma, as well as the local trigger fluxes of Ca2+ crossing the cell membrane, are sensitive to details of t-tubule micro-structure and membrane Ca2+ flux distribution. The model additionally predicts that local Ca2+ trigger fluxes are at least threefold to eightfold higher than the whole-cell Ca2+ trigger flux. We found also that the activation of allosteric Ca2+-binding sites on the Na+/Ca2+ exchanger could provide a mechanism for regulating global and local Ca2+ trigger fluxes in vivo. Our studies indicate that improved structural and functional models could improve our understanding of the contributions of L-type and Na+/Ca2+ exchanger fluxes to intracellular Ca2+ dynamics.

Molecular and Subcellular-Scale Modeling of Nucleotide Diffusion in the Cardiac Myofilament Lattice

Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions.

Computational modeling of subcellular transport and signaling.

Numerous signaling processes in the cell are controlled in microdomains that are defined by cellular structures ranging from nm to μm in size. Recent improvements in microscopy enable the resolution and reconstruction of these micro domains, while new computational methods provide the means to elucidate their functional roles. Collectively these tools allow for a biophysical understanding of the cellular environment and its pathological progression in disease. Here we review recent advancements in microscopy, and subcellular modeling on the basis of reconstructed geometries, with a special focus on signaling microdomains that are important for the excitation contraction coupling in cardiac myocytes.

uPy: A Ubiquitous CG Python API with Biological-Modeling Applications

The uPy Python extension module provides a uniform abstraction of the APIs of several 3D computer graphics programs (called hosts), including Blender, Maya, Cinema 4D, and DejaVu. A plug-in written with uPy can run in all uPy-supported hosts. Using uPy, researchers have created complex plug-ins for molecular and cellular modeling and visualization. uPy can simplify programming for many types of projects (not solely science applications) intended for multihost distribution. Its available at http://upy.scripps.edu. The first featured Web extra is a video that shows interactive analysis of a calcium dynamics simulation. YouTube URL: http://youtu.be/wvs-nWE6ypo. The second featured Web extra is a video that shows rotation of the HIV virus. YouTube URL: http://youtu.be/vEOybMaRoKc.