Models of Myocyte Excitation- Contraction Coupling

Calcium-Induced Calcium Release

Human Cardiac Force-Frequency Relation Mulieri et al, Circulation, 1992

Frequency-dependent changes in force (filled symbols), Ca transients (gray), and RCCs (open) in human atrial (A) and ventricular muscles (B) Maier L S et al. Am J Physiol Heart Circ Physiol 2000;279:H952-H958 ©2000 by American Physiological Society

Early Model of Cardiac Excitation-Contraction Coupling Wong AYK, J Theor Biol 1981;90:37-61 Wong AYK, Fabiato A, Bassingthwaighte JBB, Bull Math Biol 1992;54:95-116

Key Model Components Wong AYK, J Theor Biol 1981;90:37-61 Wong AYK, Fabiato A, Bassingthwaighte JBB, Bull Math Biol 1992;54: Slow inward current (L-type Ca current) Borrowed from earlier ionic model of Beeler and Reuter (1977) Calcium concentration and release from the junctional SR (CSR) Calcium uptake by the network SR (LSR) via SR Ca ATPase and Ca transfer from LSR to CSR Ca uptake and release by the mitochondria (now considered minor for EC coupling) Calcium extrusion by Na-Ca exchanger or sarcolemmal Ca pump Myofilament activation and contraction (from Huxley ‘57)

Slow Inward Current

Junctional SR Calcium Concentration and Release

Longitudinal SR Calcium Concentration and Uptake

Cytoplasmic (SP) Calcium Concentration

Results: Voltage Clamp

Effects of Stimulation Frequency Force (and Ca) frequency “staircase” Increasing frequency increases Ca influx per time and decreases diastolic interval available for efflux This increases SR Ca load and thus release

Post Extra-Systolic Potentiation A premature extra stimulus results in a much smaller beat but the following contraction is actually stronger than the steady- state beat The extrasystolic stimulus occurs before CSR has fully reloaded. It therefore releases less Ca and is left with more for the next beat This also explains the biphasic “staircase” phenomenon in the force- frequency experiment

Post-Rest Potentiation: Strength-Interval Relation Strength-interval relation reflects a balance of the foregoing effects

Luo and Rudy, Circ Res 1994 Ionic currents and [Ca 2+ ] i handling

Puglisi and Bers, AJP Cell Physiol 2001 Shannon et al., Biophys J 2004 E-C coupling and Ca 2+ subspaces LabHEART

Common Pool Models of CICR Stern MD, Biophys J 1992;63: “Common Pool” models with realistic representations of Ca-induced Ca release all give rise to “all-or- none” regenerative Ca release But myocytes display “graded release”

Graded Ca Release Stern MD, Biophys J 1992;63: Myocytes display “graded” Ca release with increased Ca current here caused by increased duration of voltage clamp depolarizations from -60 mV to 0 mV

Local Control Model Stern MD, Biophys J 1992;63:

Ventricular myocyte (VM) Atrial myocyte (AM) Bootman et al., Journal of Cell Science 2006 AM VM Differences in the sub-cellular structure might be a reason cardiac muscle cells to display different Ca 2+ patterns in response to depolarization

Blatter et al., J Physiology 2003 Spatio-temporal pattern of action potential induced [Ca 2+ ] i transients recorded with confocal microscopy

Reaction-Diffusion Equations [Ca 2+ ] i free Ca 2+ ; [B m ] mobile buffer; [B s ] stationary buffer; J Ca flux Ca 2+ fluxes; D Ca, D CaBm diffusion constants for free Ca 2+ and Ca 2+ bound to mobile buffers; k i kinetic rate constants

Pharmacologically blocked sarcoplasmic reticulum 100 μM Fluo-3 Lu et al., IEEE EMB D Ca 2+ distributions and spatial profiles in transverse cell direction at Ca 2+ peak. Membrane Ca 2+ fluxes distributed heterogeneously (A) or uniformly (B) along the t-tubule membrane. Membrane Ca 2+ fluxes distributed homogeneously along the whole cell surface (C).

Ca 2+ concentration (  M) Pharmacologically blocked sarcoplasmic reticulum 0 μM Fluo-3 Calcium concentration changes and 3-D Ca 2+ distribution at Ca 2+ peak with Ca 2+ flux pathways heterogeneously distributed along the t-tubule and surface membrane. Distance to surface membrane (μm) time (ms) Lu et al., IEEE EMB 2009 Ca 2+ concentration (μM)

Visualization of single t-tubule (a,b) through mouth into cavity and (c, d) from lateral in rabbit ventricular cells. The surface is shown with (a, c) filled triangles and (c, d) edges only. Sachse et al., PSB 2008 Lu et al., IEEE EMB 2009 GEOMETRY Visualization of t-tubule network in mouse ventricular myocytes Yu et al., J Structural Biol 2008

Realistic Model Construction and Mesh

Reconstruction of Dyadic Cleft