Modeling Calcium Cycling in the Heart: Progress, Pitfalls, and Challenges

Figures

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  Figure 1. Ca cycling/signaling in cardiac myocytes. (A) Schematic diagram showing Ca cycling and signaling and its coupling with voltage, including the major components: (1) ionic currents and their regulation by Ca/calmodulin (CaM) and Ca/calmodulin-dependent protein kinase II (CaMKII); (2) SR Ca release and uptake and their regulation by CaMKII and protein kinase A and C (PKA and PKC); (3) mitochondrial Ca cycling; (4) Ca and myofilament interaction; and (5) Ca-dependent signaling pathways. DS stands for dyadic space and ROS for reactive oxygen species. For a detailed explanation of each component in the diagram, see Ref. [22]. (B) RyR clusters measured from a ventricular myocyte, adapted from Ref. [9].

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  Figure 2. RyR models and Ca cycling dynamics. (A) A two-state model. The rate constant from C to O (kCO) as a function cytosolic Ca without or with luminal SR Ca regulation. (B) A four-state model with cytosolic Ca-dependent inactivation developed by Stern et al. [29,38]. (C) A four-state model with calsequestrin-dependent inactivation developed by Restrepo et al. [40]. (D) Left: SR Ca during a spark and after caffeine. Right: SR Ca nadir distribution measured during sparks. Data from Zima et al. [36]. (E) Bistable switch for spark firing and termination. Red arrow marks the SR Ca threshold for spark firing and cyan arrow marks the SR Ca threshold for spark termination. Gray marks the bistable region in which the high state and low state are stable and the middle one (dashed) is unstable. (F) Upper: Time-space plots of Ca from a computer simulation of a 3D cell with the RyR model in C. Lower: Time-space plots of Ca from a computer simulation of the same 3D cell with the RyR model without the CSQN-dependent inactivation, equivalent to the two-state model in A. Simulations were done under voltage clamped at −80 mV using the 3D cell model by Song et al. [59]. (G). Time-space plots of Ca from…

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  Figure 3. Single CRU and CRU network models. (A) CRU model with realistic structure, adapted with permission from Ref. [63], copyright 2012, John Wiley and Sons. Upper: Structure. Lower: A Ca snapshot during a Ca spark. (B) A detailed CRU model, adapted with permission from Ref. [32], copyright 2013, Elsevier. Left: Model structure. Right: Snapshots of Ca at different time points in the dyadic space. (C) A CRU network model to represent the whole cell [57,66]. Left: A 3D network consisting of 100 × 20 × 10 CRUs, representing a whole cell. Right: Structure of a CRU. Colored cubes mark different spaces and arrows indicate different fluxes.

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  Figure 4. Spatiotemporal Ca cycling dynamics in a 3D CRU network model [57]. (A) Snapshots of Ca concentration in the cytoplasmic space for different Ca loading achieved by altering extracellular [Ca]o. From left to right, [Ca]o = 3 mM, 9 mM, 10 mM, and 16 mM. (B) Averaged whole-cell Ca concentration for the corresponding loading conditions. (C) Number of clusters versus spark cluster size. Symbols are data from simulations and lines are reference lines. The line in the left most panel is exponential, but those in other panels are linear, indicating power-law distribution. Power-law clustering indicates that a critical phenomenon [70,71] occurs during the transition from individual sparks to waves. Adapted with permission from Ref. [57], copyright 2012, Elsevier.

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  Figure 5. Computer simulation of a 100 × 100-cell 2D tissue using a 3D spatial cell model showing spontaneous Ca release and DAD following a paced beat. (A). Voltage (left) and whole-cell Ca transient (right) from a line of 100 cells in the tissue. The action potential was elicited by a stimulus applied at t = 0. (B). Ca snapshots (recorded on the surfaces of the 3D cells) in the 100 × 100-cell tissue taken from three time points as marked. (C). A zoom-in view of Ca snapshots from a small area (20 × 20 cells) for the three time points. (D). A zoom-in view of Ca snapshots from an even smaller area (3 × 3 cells) showing stochastic Ca wave dynamics inside the cells. Plotted is a 3D surface view of Ca on the surface of the 9 cells. The 3D cell model consist of 100 × 20 × 10 CRUs and the cell model is the same as in Song et al. [59]. The tissue model contains 2 × 1010 RyRs (four-state model in Figure 2C) and 2 × 109 LCCs, both are simulated with stochastic Markovian transitions. The time step for the simulation is Δt=0.01.