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Krishna A, Sun L, Valderrábano M, Palade PT, Clark JW. Modeling CICR in rat ventricular myocytes: voltage clamp studies. Theor Biol Med Model 2010; 7:43. [PMID: 21062495 PMCID: PMC3245510 DOI: 10.1186/1742-4682-7-43] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2010] [Accepted: 11/10/2010] [Indexed: 01/08/2023] Open
Abstract
Background The past thirty-five years have seen an intense search for the molecular mechanisms underlying calcium-induced calcium-release (CICR) in cardiac myocytes, with voltage clamp (VC) studies being the leading tool employed. Several VC protocols including lowering of extracellular calcium to affect Ca2+ loading of the sarcoplasmic reticulum (SR), and administration of blockers caffeine and thapsigargin have been utilized to probe the phenomena surrounding SR Ca2+ release. Here, we develop a deterministic mathematical model of a rat ventricular myocyte under VC conditions, to better understand mechanisms underlying the response of an isolated cell to calcium perturbation. Motivation for the study was to pinpoint key control variables influencing CICR and examine the role of CICR in the context of a physiological control system regulating cytosolic Ca2+ concentration ([Ca2+]myo). Methods The cell model consists of an electrical-equivalent model for the cell membrane and a fluid-compartment model describing the flux of ionic species between the extracellular and several intracellular compartments (cell cytosol, SR and the dyadic coupling unit (DCU), in which resides the mechanistic basis of CICR). The DCU is described as a controller-actuator mechanism, internally stabilized by negative feedback control of the unit's two diametrically-opposed Ca2+ channels (trigger-channel and release-channel). It releases Ca2+ flux into the cyto-plasm and is in turn enclosed within a negative feedback loop involving the SERCA pump, regulating[Ca2+]myo. Results Our model reproduces measured VC data published by several laboratories, and generates graded Ca2+ release at high Ca2+ gain in a homeostatically-controlled environment where [Ca2+]myo is precisely regulated. We elucidate the importance of the DCU elements in this process, particularly the role of the ryanodine receptor in controlling SR Ca2+ release, its activation by trigger Ca2+, and its refractory characteristics mediated by the luminal SR Ca2+ sensor. Proper functioning of the DCU, sodium-calcium exchangers and SERCA pump are important in achieving negative feedback control and hence Ca2+ homeostasis. Conclusions We examine the role of the above Ca2+ regulating mechanisms in handling various types of induced disturbances in Ca2+ levels by quantifying cellular Ca2+ balance. Our model provides biophysically-based explanations of phenomena associated with CICR generating useful and testable hypotheses.
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Affiliation(s)
- Abhilash Krishna
- Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005, USA.
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52
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Cheng Y, Yu Z, Hoshijima M, Holst MJ, McCulloch AD, McCammon JA, Michailova AP. Numerical analysis of Ca2+ signaling in rat ventricular myocytes with realistic transverse-axial tubular geometry and inhibited sarcoplasmic reticulum. PLoS Comput Biol 2010; 6:e1000972. [PMID: 21060856 PMCID: PMC2965743 DOI: 10.1371/journal.pcbi.1000972] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2009] [Accepted: 09/23/2010] [Indexed: 12/21/2022] Open
Abstract
The t-tubules of mammalian ventricular myocytes are invaginations of the cell membrane that occur at each Z-line. These invaginations branch within the cell to form a complex network that allows rapid propagation of the electrical signal, and hence synchronous rise of intracellular calcium (Ca2+). To investigate how the t-tubule microanatomy and the distribution of membrane Ca2+ flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca2+ signaling, buffering and diffusion in rat ventricular myocytes. The transverse-axial t-tubule geometry was derived from light microscopy structural data. To solve the nonlinear reaction-diffusion system we extended SMOL software tool (http://mccammon.ucsd.edu/smol/). The analysis suggests that the quantitative understanding of the Ca2+ signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca2+ flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca2+ buffers, including the Ca2+ indicator dye. In agreement with experiment, in the presence of fluorescence dye and inhibited sarcoplasmic reticulum, the lack of detectible differences in the depolarization-evoked Ca2+ transients was found when the Ca2+ flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca2+ signals are predicted. Even at modest elevation of Ca2+, reached during Ca2+ influx, large and steep Ca2+ gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca2+ flux density along the cell membrane support initiation and propagation of Ca2+ waves in rat myocytes. In cardiac muscle cells, calcium (Ca2+) is best known for its role in contraction activation. A remarkable amount of quantitative data on cardiac cell structure, ion-transporting protein distributions and intracellular Ca2+ dynamics has been accumulated. Various alterations in the protein distributions or cell ultra-structure are now recognized to be the primary mechanisms of cardiac dysfunction in a diverse range of common pathologies including cardiac arrhythmias and hypertrophy. Using a 3-D computational model, incorporating more realistic transverse-axial t-tubule geometry and considering geometric irregularities and inhomogeneities in the distribution of ion-transporting proteins, we analyze several important spatial and temporal features of Ca2+ signaling in rat ventricular myocytes. This study demonstrates that the computational models could serve as powerful tools for prediction and analyses of how the Ca2+ dynamics and cardiac excitation-contraction coupling are regulated under normal conditions or certain pathologies. The use of computational and mathematical approaches will help also to better understand aspects of cell functions that are not currently amenable to experimental investigation.
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Affiliation(s)
- Yuhui Cheng
- Department of Bioengineering, University of California San Diego, La Jolla, California, United States of America
| | - Zeyun Yu
- Department of Computer Science, University of Wisconsin, Milwaukee, Wisconsin, United States of America
| | - Masahiko Hoshijima
- Department of Medicine, University of California San Diego, La Jolla, California, United States of America
| | - Michael J. Holst
- Department of Mathematics, University of California San Diego, La Jolla, California, United States of America
| | - Andrew D. McCulloch
- Department of Bioengineering, University of California San Diego, La Jolla, California, United States of America
| | - J. Andrew McCammon
- Department of Chemistry and Biochemistry, Department of Pharmacology, University of California San Diego, La Jolla, California, United States of America
- Howard Hughes Medical Institute, University of California San Diego, La Jolla, California, United States of America
| | - Anushka P. Michailova
- Department of Bioengineering, University of California San Diego, La Jolla, California, United States of America
- * E-mail:
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53
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Huertas MA, Smith GD, Györke S. Ca2+ alternans in a cardiac myocyte model that uses moment equations to represent heterogeneous junctional SR Ca2+. Biophys J 2010; 99:377-87. [PMID: 20643055 DOI: 10.1016/j.bpj.2010.04.032] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2009] [Revised: 04/08/2010] [Accepted: 04/12/2010] [Indexed: 11/29/2022] Open
Abstract
Multiscale whole-cell models that accurately represent local control of Ca2+-induced Ca2+ release in cardiac myocytes can reproduce high-gain Ca2+ release that is graded with changes in membrane potential. Using a recently introduced formalism that represents heterogeneous local Ca2+ using moment equations, we present a model of cardiac myocyte Ca2+ cycling that exhibits alternating sarcoplasmic reticulum (SR) Ca2+ release when periodically stimulated by depolarizing voltage pulses. The model predicts that the distribution of junctional SR [Ca2+] across a large population of Ca2+ release units is distinct on alternating cycles. Load-release and release-uptake functions computed from this model give insight into how Ca2+ fluxes and stimulation frequency combine to determine the presence or absence of Ca2+ alternans. Our results show that the conditions for the onset of Ca2+ alternans cannot be explained solely by the steepness of the load-release function, but that changes in the release-uptake process also play an important role. We analyze the effect of the junctional SR refilling time constant on Ca2+ alternans and conclude that physiologically realistic models of defective Ca2+ cycling must represent the dynamics of heterogeneous junctional SR [Ca2+] without assuming rapid equilibration of junctional and network SR [Ca2+].
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Affiliation(s)
- Marco A Huertas
- Department of Applied Science, College of William and Mary, Williamsburg, Virginia, USA.
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54
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Winslow RL, Cortassa S, O'Rourke B, Hashambhoy YL, Rice JJ, Greenstein JL. Integrative modeling of the cardiac ventricular myocyte. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2010; 3:392-413. [PMID: 20865780 DOI: 10.1002/wsbm.122] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
Cardiac electrophysiology is a discipline with a rich 50-year history of experimental research coupled with integrative modeling which has enabled us to achieve a quantitative understanding of the relationships between molecular function and the integrated behavior of the cardiac myocyte in health and disease. In this paper, we review the development of integrative computational models of the cardiac myocyte. We begin with a historical overview of key cardiac cell models that helped shape the field. We then narrow our focus to models of the cardiac ventricular myocyte and describe these models in the context of their subcellular functional systems including dynamic models of voltage-gated ion channels, mitochondrial energy production, ATP-dependent and electrogenic membrane transporters, intracellular Ca dynamics, mechanical contraction, and regulatory signal transduction pathways. We describe key advances and limitations of the models as well as point to new directions for future modeling research. WIREs Syst Biol Med 2011 3 392-413 DOI: 10.1002/wsbm.122
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Affiliation(s)
- Raimond L Winslow
- Institute of Computational Medicine and Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD, USA.
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55
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Hartman JM, Sobie EA, Smith GD. Spontaneous Ca2+ sparks and Ca2+ homeostasis in a minimal model of permeabilized ventricular myocytes. Am J Physiol Heart Circ Physiol 2010; 299:H1996-2008. [PMID: 20852058 DOI: 10.1152/ajpheart.00293.2010] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Many issues remain unresolved concerning how local, subcellular Ca(2+) signals interact with bulk cellular concentrations to maintain homeostasis in health and disease. To aid in the interpretation of data obtained in quiescent ventricular myocytes, we present here a minimal whole cell model that accounts for both localized (subcellular) and global (cellular) aspects of Ca(2+) signaling. Using a minimal formulation of the distribution of local [Ca(2+)] associated with a large number of Ca(2+)-release sites, the model simulates both random spontaneous Ca(2+) sparks and the changes in myoplasmic and sarcoplasmic reticulum (SR) [Ca(2+)] that result from the balance between stochastic release and reuptake into the SR. Ca(2+)-release sites are composed of clusters of two-state ryanodine receptors (RyRs) that exhibit activation by local cytosolic [Ca(2+)] but no inactivation or regulation by luminal Ca(2+). Decreasing RyR open probability in the model causes a decrease in aggregate release flux and an increase in SR [Ca(2+)], regardless of whether RyR inhibition is mediated by a decrease in RyR open dwell time or an increase in RyR closed dwell time. The same balance of stochastic release and reuptake can be achieved, however, by either high-frequency/short-duration or low-frequency/long-duration Ca(2+) sparks. The results are well correlated with recent experimental observations using pharmacological RyR inhibitors and clarify those aspects of the release-reuptake balance that are inherent to the coupling between local and global Ca(2+) signals and those aspects that depend on molecular-level details. The model of Ca(2+) sparks and homeostasis presented here can be a useful tool for understanding changes in cardiac Ca(2+ )release resulting from drugs, mutations, or acquired diseases.
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Affiliation(s)
- Jana M Hartman
- Department of Applied Science, The College of William and Mary, Williamsburg, Virginia 23187, USA
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56
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Abramson D, Bernabeu MO, Bethwaite B, Burrage K, Corrias A, Enticott C, Garic S, Gavaghan D, Peachey T, Pitt-Francis J, Pueyo E, Rodriguez B, Sher A, Tan J. High-throughput cardiac science on the Grid. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2010; 368:3907-3923. [PMID: 20643684 DOI: 10.1098/rsta.2010.0170] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
Cardiac electrophysiology is a mature discipline, with the first model of a cardiac cell action potential having been developed in 1962. Current models range from single ion channels, through very complex models of individual cardiac cells, to geometrically and anatomically detailed models of the electrical activity in whole ventricles. A critical issue for model developers is how to choose parameters that allow the model to faithfully reproduce observed physiological effects without over-fitting. In this paper, we discuss the use of a parametric modelling toolkit, called Nimrod, that makes it possible both to explore model behaviour as parameters are changed and also to tune parameters by optimizing model output. Importantly, Nimrod leverages computers on the Grid, accelerating experiments by using available high-performance platforms. We illustrate the use of Nimrod with two case studies, one at the cardiac tissue level and one at the cellular level.
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Affiliation(s)
- David Abramson
- Faculty of Information Technology, Monash University, Caulfield East, Melbourne, Victoria 3145, Australia.
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57
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Tania N, Keener JP. Calsequestrin mediates changes in spontaneous calcium release profiles. J Theor Biol 2010; 265:359-76. [PMID: 20648970 DOI: 10.1016/j.jtbi.2010.05.028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
Calsequestrin (CSQ) is the primary calcium buffer within the sarcoplasmic reticulum (SR) of cardiac cells. It has also been identified as a regulator of Ryanodine receptor (RyR) calcium release channels by serving as a SR luminal sensor. When calsequestrin is free and unbound to calcium, it can bind to RyR and desensitize the channel from cytoplasmic calcium activation. In this paper, we study the role of CSQ as a buffer and RyR luminal sensor using a mechanistic model of RyR-CSQ interaction. By using various asymptotic approximations and mean first exit time calculation, we derive a minimal model of a calcium release unit which includes CSQ dependence. Using this model, we then analyze the effect of changing CSQ expression on the calcium release profile and the rate of spontaneous calcium release. We show that because of its buffering capability, increasing CSQ increases the spark duration and size. However, because of luminal sensing effects, increasing CSQ depresses the basal spark rate and increases the critical SR level for calcium release termination. Finally, we show that with increased bulk cytoplasmic calcium concentration, the CRU model exhibits deterministic oscillations.
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Affiliation(s)
- Nessy Tania
- Department of Mathematics, University of Utah, 155 S. 1400 E. Room 233, Salt Lake City, UT 84112, USA.
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58
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Li L, Niederer SA, Idigo W, Zhang YH, Swietach P, Casadei B, Smith NP. A mathematical model of the murine ventricular myocyte: a data-driven biophysically based approach applied to mice overexpressing the canine NCX isoform. Am J Physiol Heart Circ Physiol 2010; 299:H1045-63. [PMID: 20656884 DOI: 10.1152/ajpheart.00219.2010] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Mathematical modeling of Ca(2+) dynamics in the heart has the potential to provide an integrated understanding of Ca(2+)-handling mechanisms. However, many previous published models used heterogeneous experimental data sources from a variety of animals and temperatures to characterize model parameters and motivate model equations. This methodology limits the direct comparison of these models with any particular experimental data set. To directly address this issue, in this study, we present a biophysically based model of Ca(2+) dynamics directly fitted to experimental data collected in left ventricular myocytes isolated from the C57BL/6 mouse, the most commonly used genetic background for genetically modified mice in studies of heart diseases. This Ca(2+) dynamics model was then integrated into an existing mouse cardiac electrophysiology model, which was reparameterized using experimental data recorded at consistent and physiological temperatures. The model was validated against the experimentally observed frequency response of Ca(2+) dynamics, action potential shape, dependence of action potential duration on cycle length, and electrical restitution. Using this framework, the implications of cardiac Na(+)/Ca(2+) exchanger (NCX) overexpression in transgenic mice were investigated. These simulations showed that heterozygous overexpression of the canine cardiac NCX increases intracellular Ca(2+) concentration transient magnitude and sarcoplasmic reticulum Ca(2+) loading, in agreement with experimental observations, whereas acute overexpression of the murine cardiac NCX results in a significant loss of Ca(2+) from the cell and, hence, depressed sarcoplasmic reticulum Ca(2+) load and intracellular Ca(2+) concentration transient magnitude. From this analysis, we conclude that these differences are primarily due to the presence of allosteric regulation in the canine cardiac NCX, which has not been observed experimentally in the wild-type mouse heart.
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Affiliation(s)
- L Li
- Computing Laboratory, University of Oxford and John Radcliffe Hospital, Oxford, United Kingdom
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59
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Williams GSB, Smith GD, Sobie EA, Jafri MS. Models of cardiac excitation-contraction coupling in ventricular myocytes. Math Biosci 2010; 226:1-15. [PMID: 20346962 PMCID: PMC5499386 DOI: 10.1016/j.mbs.2010.03.005] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2009] [Revised: 03/09/2010] [Accepted: 03/12/2010] [Indexed: 01/27/2023]
Abstract
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.
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Affiliation(s)
- George S B Williams
- The Department of Bionformatics and Computational Biology, George Mason University, VA, USA.
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60
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Fink M, Niederer SA, Cherry EM, Fenton FH, Koivumäki JT, Seemann G, Thul R, Zhang H, Sachse FB, Beard D, Crampin EJ, Smith NP. Cardiac cell modelling: observations from the heart of the cardiac physiome project. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2010; 104:2-21. [PMID: 20303361 DOI: 10.1016/j.pbiomolbio.2010.03.002] [Citation(s) in RCA: 108] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2009] [Revised: 12/06/2009] [Accepted: 03/04/2010] [Indexed: 10/19/2022]
Abstract
In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.
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Affiliation(s)
- Martin Fink
- Department of Physiology, Anatomy and Genetics, University of Oxford, OX1 3JP, United Kingdom
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61
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Swietach P, Spitzer KW, Vaughan-Jones RD. Modeling calcium waves in cardiac myocytes: importance of calcium diffusion. FRONT BIOSCI-LANDMRK 2010; 15:661-80. [PMID: 20036839 PMCID: PMC2825568 DOI: 10.2741/3639] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Under certain conditions, cardiac myocytes engage in a mode of calcium signaling in which calcium release from the sarcoplasmic reticulum (SR) to myoplasm occurs in self-propagating succession along the length of the cell. This event is called a calcium wave and is fundamentally a diffusion-reaction phenomenon. We present a simple, continuum mathematical model that simulates calcium waves. The framework features calcium diffusion within the SR and myoplasm, and dual modulation of ryanodine receptor (RyR) release channels by myoplasmic and SR calcium. The model is used to illustrate the effect of varying RyR permeability, sarco/endoplasmic reticulum Ca2+ ATPase (SERCA) activity and calcium ion mobility in myoplasm and SR on wave velocity. The model successfully reproduces calcium waves using experimentally-derived variables. It also supports the proposal for wave propagation driven by the diffusive spread of myoplasmic calcium, and highlights the importance of SR calcium load on wave propagation.
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Affiliation(s)
- Pawel Swietach
- Burdon Sanderson Cardiac Science Centre, Department of Physiology, Anatomy and Genetics, Oxford OX1 3PT, UK
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62
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Lu S, Michailova A, Saucerman J, Cheng Y, Yu Z, Kaiser T, Li W, Bank R, Holst M, McCammon J, Hayashi T, Hoshijima M, Arzberger P, McCulloch A. Multiscale modeling in rodent ventricular myocytes. ACTA ACUST UNITED AC 2009; 28:46-57. [PMID: 19349251 DOI: 10.1109/memb.2009.931787] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
There is a growing body of experimental evidence suggesting that the Ca(2+) signaling in ventricular myocytes is characterized by a high gradient near the cell membrane and a more uniform Ca(2+) distribution in the cell interior [1]--[7]. An important reason for this phenomenon might be that in these cells the t-tubular system forms a network of extracellular space, extending deep into the cell interior. This allows the electrical signal, that propagates rapidly along the cell membrane, to reach the vicinity of the sarcoplasmic reticulum (SR), where intracellular Ca(2+) required for myofilament activation is stored [1], [8]--[11]. Early studies of cardiac muscle showed that the t-tubules are found at intervals of about 2 lm along the longitudinal cell axis in close proximity to the Z-disks of the sarcomeres [12]. Subsequent studies have demonstrated that the t-tubular system has also longitudinal extensions [9]--[11], [13].
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Affiliation(s)
- Shaoying Lu
- Department of Bioengineering, University of California San Diego, La Jolla, 92093-0412, USA.
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63
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Maleckar MM, Greenstein JL, Giles WR, Trayanova NA. K+ current changes account for the rate dependence of the action potential in the human atrial myocyte. Am J Physiol Heart Circ Physiol 2009; 297:H1398-410. [PMID: 19633207 DOI: 10.1152/ajpheart.00411.2009] [Citation(s) in RCA: 95] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Ongoing investigation of the electrophysiology and pathophysiology of the human atria requires an accurate representation of the membrane dynamics of the human atrial myocyte. However, existing models of the human atrial myocyte action potential do not accurately reproduce experimental observations with respect to the kinetics of key repolarizing currents or rate dependence of the action potential and fail to properly enforce charge conservation, an essential characteristic in any model of the cardiac membrane. In addition, recent advances in experimental methods have resulted in new data regarding the kinetics of repolarizing currents in the human atria. The goal of this study was to develop a new model of the human atrial action potential, based on the Nygren et al. model of the human atrial myocyte and newly available experimental data, that ensures an accurate representation of repolarization processes and reproduction of action potential rate dependence and enforces charge conservation. Specifically, the transient outward K(+) current (I(t)) and ultrarapid rectifier K(+) current (I(Kur)) were newly formulated. The inwardly recitifying K(+) current (I(K1)) was also reanalyzed and implemented appropriately. Simulations of the human atrial myocyte action potential with this new model demonstrated that early repolarization is dependent on the relative conductances of I(t) and I(Kur), whereas densities of both I(Kur) and I(K1) underlie later repolarization. In addition, this model reproduces experimental measurements of rate dependence of I(t), I(Kur), and action potential duration. This new model constitutes an improved representation of excitability and repolarization reserve in the human atrial myocyte and, therefore, provides a useful computational tool for future studies involving the human atrium in both health and disease.
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Affiliation(s)
- Mary M Maleckar
- Department of Biomedical Engineering and Institute for Computational Medicine, Johns Hopkins University, Baltimore,Maryland, USA.
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64
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Stochastic simulation of calcium microdomains in the vicinity of an L-type calcium channel. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2009; 39:1079-88. [PMID: 19568739 DOI: 10.1007/s00249-009-0504-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2009] [Revised: 05/29/2009] [Accepted: 06/08/2009] [Indexed: 02/07/2023]
Abstract
We study numerically the local dynamics of the intracellular calcium concentration in the vicinity of a voltage- and calcium-dependent plasma membrane L-type calcium channel. To account for the low number of Ca(2+) ions and buffer molecules present in sub-femtoliter volumes, we use an exact stochastic simulation algorithm including diffusion. We present a novel, unified simulation method that implements reaction-diffusion events of Ca(2+) ions and buffer molecules, stochastic ion channel gating and channel conductance as a multivariate Markov process. For fixed-voltage dynamics, e.g. under voltage-clamp conditions, it is shown that voltage-sensitive channel-gating steps can be incorporated exactly. We compare multi- and single-voxel geometries and show that the single-voxel approach leads to almost identical first- and second-order moments, at much lower computation time. Numerical examples illustrate the variability in local Ca(2+) fluctuations as induced by bursts of channel openings in response to membrane depolarisations. Finally, by introducing calmodulin as a link, it is shown how this variability is passed on to downstream signalling pathways. The method may prove useful to study calcium microdomains and calcium-regulated processes triggered by membrane depolarisations as evoked by, e.g., viral channel-forming proteins during virus-host cell interactions.
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65
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Fink M, Noble D. Markov models for ion channels: versatility versus identifiability and speed. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2009; 367:2161-2179. [PMID: 19414451 DOI: 10.1098/rsta.2008.0301] [Citation(s) in RCA: 77] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Markov models (MMs) represent a generalization of Hodgkin-Huxley models. They provide a versatile structure for modelling single channel data, gating currents, state-dependent drug interaction data, exchanger and pump dynamics, etc. This paper uses examples from cardiac electrophysiology to discuss aspects related to parameter estimation. (i) Parameter unidentifiability (found in 9 out of 13 of the considered models) results in an inability to determine the correct layout of a model, contradicting the idea that model structure and parameters provide insights into underlying molecular processes. (ii) The information content of experimental voltage step clamp data is discussed, and a short but sufficient protocol for parameter estimation is presented. (iii) MMs have been associated with high computational cost (owing to their large number of state variables), presenting an obstacle for multicellular whole organ simulations as well as parameter estimation. It is shown that the stiffness of models increases computation time more than the number of states. (iv) Algorithms and software programs are provided for steady-state analysis, analytical solutions for voltage steps and numerical derivation of parameter identifiability. The results provide a new standard for ion channel modelling to further the automation of model development, the validation process and the predictive power of these models.
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Affiliation(s)
- Martin Fink
- Department of Physiology, Anatomy and Genetics, University of Oxford, Parks Road, Oxford OX1 3PT, UK.
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66
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Lee J, Niederer S, Nordsletten D, Le Grice I, Smaill B, Kay D, Smith N. Coupling contraction, excitation, ventricular and coronary blood flow across scale and physics in the heart. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2009; 367:2311-2331. [PMID: 19414457 DOI: 10.1098/rsta.2008.0311] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
In this study, we review the development and application of multi-physics and multi-scale coupling in the construction of whole-heart physiological models. Through an examination of recent computational modelling developments, we analyse the significance of coupling mechanisms for the increased understanding of cardiac function in the areas of excitation-contraction, coronary blood flow and ventricular fluid mechanical coupling. Within these physiological domains, we demonstrate and discuss the importance of model parametrization, imaging-based model anatomy and computational implementation.
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Affiliation(s)
- Jack Lee
- Oxford University Computing Laboratory, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK
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67
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Niederer SA, Smith NP. The role of the Frank-Starling law in the transduction of cellular work to whole organ pump function: a computational modeling analysis. PLoS Comput Biol 2009; 5:e1000371. [PMID: 19390615 PMCID: PMC2668184 DOI: 10.1371/journal.pcbi.1000371] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2008] [Accepted: 03/20/2009] [Indexed: 12/01/2022] Open
Abstract
We have developed a multi-scale biophysical electromechanics model of the rat left ventricle at room temperature. This model has been applied to investigate the relative roles of cellular scale length dependent regulators of tension generation on the transduction of work from the cell to whole organ pump function. Specifically, the role of the length dependent Ca(2+) sensitivity of tension (Ca(50)), filament overlap tension dependence, velocity dependence of tension, and tension dependent binding of Ca(2+) to Troponin C on metrics of efficient transduction of work and stress and strain homogeneity were predicted by performing simulations in the absence of each of these feedback mechanisms. The length dependent Ca(50) and the filament overlap, which make up the Frank-Starling Law, were found to be the two dominant regulators of the efficient transduction of work. Analyzing the fiber velocity field in the absence of the Frank-Starling mechanisms showed that the decreased efficiency in the transduction of work in the absence of filament overlap effects was caused by increased post systolic shortening, whereas the decreased efficiency in the absence of length dependent Ca(50) was caused by an inversion in the regional distribution of strain.
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68
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Niederer SA, Ter Keurs HEDJ, Smith NP. Modelling and measuring electromechanical coupling in the rat heart. Exp Physiol 2009; 94:529-40. [PMID: 19218357 DOI: 10.1113/expphysiol.2008.045880] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Tension-dependent binding of Ca(2+) to troponin C in the cardiac myocyte has been shown to play an important role in the regulation of Ca(2+) and the activation of tension development. The significance of this regulatory mechanism is quantified experimentally by the quantity of Ca(2+) released following a rapid change in the muscle length. Using a computational, coupled, electromechanics cell model, we have confirmed that the tension dependence of Ca(2+) binding to troponin C, rather than cross-bridge kinetics or the rate of Ca(2+) uptake by the sarcoplasmic reticulum, determines the quantity of Ca(2+) released following a length step. This cell model has been successfully applied in a continuum model of the papillary muscle to analyse experimental data, suggesting the tension-dependent binding of Ca(2+) to troponin C as the likely pathway through which the effects of localized impaired tension generation alter the Ca(2+) transient. These experimental results are qualitatively reproduced using a three-dimensional coupled electromechanics model. Furthermore, the model predicts that changes in the Ca(2+) transient in the viable myocardium surrounding the impaired region are amplified in the absence of tension-dependent binding of Ca(2+) to troponin C.
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Affiliation(s)
- S A Niederer
- University Computing Laboratory, University of Oxford, Oxford, UK
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69
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Li P, Wei W, Cai X, Soeller C, Cannell MB, Holden AV. Evolution of Intracellular Ca2 + Waves from about 10,000 RyR Clusters: Towards Solving a Computationally Daunting Task. FUNCTIONAL IMAGING AND MODELING OF THE HEART 2009. [DOI: 10.1007/978-3-642-01932-6_2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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70
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Hunter PJ, Viceconti M. The VPH-Physiome Project: Standards and Tools for Multiscale Modeling in Clinical Applications. IEEE Rev Biomed Eng 2009. [DOI: 10.1109/rbme.2009.2036204] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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71
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Early afterdepolarisations and ventricular arrhythmias in cardiac tissue: a computational study. Med Biol Eng Comput 2008; 47:291-300. [PMID: 18850126 DOI: 10.1007/s11517-008-0405-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2008] [Accepted: 09/03/2008] [Indexed: 10/21/2022]
Abstract
Afterdepolarisations are associated with arrhythmias in the heart, but are difficult to study experimentally. In this study we used a simplified computational model of 1D and 2D cardiac ventricular tissue, where we could control the size of the region generating afterdepolarisations, as well as the properties of the afterdepolarisation waveform. Provided the size of the afterdepolarisation region was greater than around 1 mm, propagating extrasystoles were produced in both 1D and 2D. The number of extrasystoles produced depended on the amplitude, period, and duration of the oscillatory EAD waveform. In 2D, re-entry was also initiated for specific combinations of EAD amplitude, period, and duration, with the afterdepolarisation region acting as a common pathway. The main finding from this modelling study is therefore that afterdepolarisations can act as potent sources of propagating extrasystoles, as well as a source of re-entrant activation.
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72
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Campbell SG, Flaim SN, Leem CH, McCulloch AD. Mechanisms of transmurally varying myocyte electromechanics in an integrated computational model. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2008; 366:3361-80. [PMID: 18593662 PMCID: PMC2556206 DOI: 10.1098/rsta.2008.0088] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The mechanical properties of myocardium vary across the transmural aspect of the left ventricular wall. Some of these functional heterogeneities may be related to differences in excitation-contraction coupling characteristics that have been observed in cells isolated from the epicardial, mid-myocardial and endocardial regions of the left ventricle of many species, including canine. Integrative models of coupled myocyte electromechanics are reviewed and used here to investigate sources of heterogeneous electromechanical behaviour in these cells. The simulations (i) illustrate a previously unrecognized role of the transient outward potassium current in mechanical function and (ii) suggest that there may also exist additional heterogeneities affecting crossbridge cycling rates in cells from different transmural regions.
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Affiliation(s)
- Stuart G. Campbell
- Department of Bioengineering, University of California, San Diego9500 Gilman Drive no. 0412, La Jolla, CA 92093, USA
| | - Sarah N. Flaim
- Computing Laboratory, University of OxfordWolfson Building, Parks Road, Oxford OX1 3QD, UK
| | - Chae H. Leem
- Department of Physiology, University of Ulsan College of Medicine388-1 Poongnap-Dong Songpa-Ku, Seoul 138-736, South Korea
| | - Andrew D. McCulloch
- Department of Bioengineering, University of California, San Diego9500 Gilman Drive no. 0412, La Jolla, CA 92093, USA
- Author for correspondence ()
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73
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Plank G, Zhou L, Greenstein JL, Cortassa S, Winslow RL, O'Rourke B, Trayanova NA. From mitochondrial ion channels to arrhythmias in the heart: computational techniques to bridge the spatio-temporal scales. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2008; 366:3381-409. [PMID: 18603526 PMCID: PMC2778066 DOI: 10.1098/rsta.2008.0112] [Citation(s) in RCA: 97] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Computer simulations of electrical behaviour in the whole ventricles have become commonplace during the last few years. The goals of this article are (i) to review the techniques that are currently employed to model cardiac electrical activity in the heart, discussing the strengths and weaknesses of the various approaches, and (ii) to implement a novel modelling approach, based on physiological reasoning, that lifts some of the restrictions imposed by current state-of-the-art ionic models. To illustrate the latter approach, the present study uses a recently developed ionic model of the ventricular myocyte that incorporates an excitation-contraction coupling and mitochondrial energetics model. A paradigm to bridge the vastly disparate spatial and temporal scales, from subcellular processes to the entire organ, and from sub-microseconds to minutes, is presented. Achieving sufficient computational efficiency is the key to success in the quest to develop multiscale realistic models that are expected to lead to better understanding of the mechanisms of arrhythmia induction following failure at the organelle level, and ultimately to the development of novel therapeutic applications.
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Affiliation(s)
- Gernot Plank
- Institute of Biophysics, Medical University Graz8010 Graz, Austria
- Institute for Computational Medicine, Johns Hopkins UniversityBaltimore, MD 21218, USA
| | - Lufang Zhou
- Institute of Molecular Cardiobiology, Johns Hopkins School of MedicineBaltimore, MD 21205, USA
- Department of Biomedical Engineering, Johns Hopkins UniversityBaltimore, MD 21205, USA
| | - Joseph L Greenstein
- Institute for Computational Medicine, Johns Hopkins UniversityBaltimore, MD 21218, USA
- Department of Biomedical Engineering, Johns Hopkins UniversityBaltimore, MD 21205, USA
| | - Sonia Cortassa
- Institute of Molecular Cardiobiology, Johns Hopkins School of MedicineBaltimore, MD 21205, USA
- Department of Biomedical Engineering, Johns Hopkins UniversityBaltimore, MD 21205, USA
| | - Raimond L Winslow
- Institute for Computational Medicine, Johns Hopkins UniversityBaltimore, MD 21218, USA
- Department of Biomedical Engineering, Johns Hopkins UniversityBaltimore, MD 21205, USA
| | - Brian O'Rourke
- Institute of Molecular Cardiobiology, Johns Hopkins School of MedicineBaltimore, MD 21205, USA
| | - Natalia A Trayanova
- Institute for Computational Medicine, Johns Hopkins UniversityBaltimore, MD 21218, USA
- Department of Biomedical Engineering, Johns Hopkins UniversityBaltimore, MD 21205, USA
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74
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Abstract
The sarcoplasmic reticulum (SR) in ventricular myocytes contains releasable Ca(2+) for activating cellular contraction. Recent measurements of intra-SR (luminal) Ca(2+) suggest a high diffusive Ca(2+)-mobility constant (D(CaSR)). This could help spatially to unify SR Ca(2+)-content ([Ca(2+)](SRT)) and standardize Ca(2+)-release throughout the cell. But measurements of localized depletions of luminal Ca(2+) (Ca(2+)-blinks), associated with local Ca(2+)-release (Ca(2+)-sparks), suggest D(CaSR) may actually be low. Here we describe a novel method for measuring D(CaSR). Using a cytoplasmic Ca(2+)-fluorophore, we estimate regional [Ca(2+)](SRT) from localized, caffeine-induced SR Ca(2+)-release. Caffeine microperfusion of one end of a guinea pig or rat myocyte diffusively empties the whole SR at a rate indicating D(CaSR) is 8-9 microm(2)/s, up to tenfold lower than previous estimates. Ignoring background SR Ca(2+)-leakage in our measurement protocol produces an artifactually high D(CaSR) (>40 microm(2)/s), which may also explain the previous high values. Diffusion-reaction modeling suggests that a low D(CaSR) would be sufficient to support local SR Ca(2+)-signaling within sarcomeres during excitation-contraction coupling. Low D(CaSR) also implies that [Ca(2+)](SRT) may readily become spatially nonuniform, particularly under pathological conditions of spatially nonuniform Ca(2+)-release. Local control of luminal Ca(2+), imposed by low D(CaSR), may complement the well-established local control of SR Ca(2+)-release by Ca(2+)-channel/ryanodine receptor couplons.
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Terkildsen JR, Niederer S, Crampin EJ, Hunter P, Smith NP. Using Physiome standards to couple cellular functions for rat cardiac excitation-contraction. Exp Physiol 2008; 93:919-29. [PMID: 18344258 DOI: 10.1113/expphysiol.2007.041871] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Scientific endeavour is reliant upon the extension and reuse of previous knowledge. The formalization of this process for computational modelling is facilitated by the use of accepted standards with which to describe and simulate models, ensuring consistency between the models and thus reducing the development and propagation of errors. CellML 1.1, an XML-based programming language, has been designed as a modelling standard which, by virtue of its import and grouping functions, facilitates model combination and reuse. Using CellML 1.1, we demonstrate the process of formalized model reuse by combining three separate models of rat cardiomyocyte function (an electrophysiology model, a model of cellular calcium dynamics and a mechanics model) which together make up the Pandit-Hinch-Niederer et al. cell model. Not only is this integrative model of rat electromechanics a useful tool for cardiac modelling but it is also an ideal framework with which to demonstrate both the power of model reuse and the challenges associated with this process. We highlight and classify a number of these issues associated with combining models and provide some suggested solutions.
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76
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Stochastic binding of Ca2+ ions in the dyadic cleft; continuous versus random walk description of diffusion. Biophys J 2008; 94:4184-201. [PMID: 18263662 PMCID: PMC2480677 DOI: 10.1529/biophysj.106.103523] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Ca(2+) signaling in the dyadic cleft in ventricular myocytes is fundamentally discrete and stochastic. We study the stochastic binding of single Ca(2+) 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 Ca(2+) signaling in the dyadic cleft, determined by single binding events, can be described using a deterministic model of Ca(2+) 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.
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77
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Findlay I, Suzuki S, Murakami S, Kurachi Y. Physiological modulation of voltage-dependent inactivation in the cardiac muscle L-type calcium channel: A modelling study. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2008; 96:482-98. [PMID: 17822746 DOI: 10.1016/j.pbiomolbio.2007.07.002] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Abstract
The inactivation of the L-type Ca2+ current is composed of voltage-dependent and calcium-dependent mechanisms. The relative contribution of these processes is still under dispute and the idea that the voltage-dependent inactivation could be subject to further modulation by other physiological processes had been ignored. This study sought to model physiological modulation of inactivation of the current in cardiac ventricular myocytes, based upon the recent detailed experimental data that separated total and voltage-dependent inactivation (VDI) by replacing extracellular Ca2+ with Mg2+ and monitoring L-type Ca2+ channel behaviour by outward K+ current flowing through the channel in the absence of inward current flow. Calcium-dependent inactivation (CDI) was based upon Ca2+ influx and formulated from data that was recorded during beta-adrenergic stimulation of the myocytes. Ca2+ influx and its competition with non-selective monovalent cation permeation were also incorporated into channel permeation in the model. The constructed model could closely reproduce the experimental Ba2+ and Ca2+ current results under basal condition where no beta-stimulation was added after a slight reduction of the development of fast voltage-dependent inactivation with depolarization. The model also predicted that under beta-adrenergic stimulation voltage-dependent inactivation is lost and calcium-dependent inactivation largely compensates it. The developed model thus will be useful to estimate the respective roles of VDI and CDI of L-type Ca2+ channels in various physiological and pathological conditions of the heart which would otherwise be difficult to show experimentally.
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Affiliation(s)
- Ian Findlay
- CNRS UMR 6542, Faculté des Sciences, Université François-Rabelais de Tours, France
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78
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The role of the Na+/Ca2+ exchangers in Ca2+ dynamics in ventricular myocytes. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2008; 96:377-98. [DOI: 10.1016/j.pbiomolbio.2007.07.018] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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79
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Maurya MR, Subramaniam S. A kinetic model for calcium dynamics in RAW 264.7 cells: 1. Mechanisms, parameters, and subpopulational variability. Biophys J 2007; 93:709-28. [PMID: 17483174 PMCID: PMC1913151 DOI: 10.1529/biophysj.106.097469] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Calcium (Ca(2+)) is an important second messenger and has been the subject of numerous experimental measurements and mechanistic studies in intracellular signaling. Calcium profile can also serve as a useful cellular phenotype. Kinetic models of calcium dynamics provide quantitative insights into the calcium signaling networks. We report here the development of a complex kinetic model for calcium dynamics in RAW 264.7 cells stimulated by the C5a ligand. The model is developed using the vast number of measurements of in vivo calcium dynamics carried out in the Alliance for Cellular Signaling (AfCS) Laboratories. Ligand binding, phospholipase C-beta (PLC-beta) activation, inositol 1,4,5-trisphosphate (IP(3)) receptor (IP(3)R) dynamics, and calcium exchange with mitochondria and extracellular matrix have all been incorporated into the model. The experimental data include data from both native and knockdown cell lines. Subpopulational variability in measurements is addressed by allowing nonkinetic parameters to vary across datasets. The model predicts temporal response of Ca(2+) concentration for various doses of C5a under different initial conditions. The optimized parameters for IP(3)R dynamics are in agreement with the legacy data. Further, the half-maximal effect concentration of C5a and the predicted dose response are comparable to those seen in AfCS measurements. Sensitivity analysis shows that the model is robust to parametric perturbations.
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Affiliation(s)
- Mano Ram Maurya
- Department of Bioengineering, University of California, San Diego, California 92093-0412, USA
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80
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Winslow RL, Tanskanen A, Chen M, Greenstein JL. Multiscale modeling of calcium signaling in the cardiac dyad. Ann N Y Acad Sci 2007; 1080:362-75. [PMID: 17132795 DOI: 10.1196/annals.1380.027] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Calcium (Ca(2+))-induced Ca(2+)-release (CICR) takes place in spatially restricted microdomains known as dyads. The length scale over which CICR occurs is on the order of nanometers and relevant time scales range from micro- to milliseconds. Quantitative understanding of CICR therefore requires development of models that are applicable over a range of spatio-temporal scales. We will present several new approaches for multiscale modeling of CICR. First, we present a model of dyad Ca(2+) dynamics in which the Fokker-Planck equation (FPE) is solved for the probability P(x, t) that a Ca(2+) ion is located at dyad position x at time t. Using this model, we demonstrate that (a) Ca(2+) signaling in the dyad is mediated by approximately tens of Ca(2+) ions; (b) these signaling events are noisy due to the small number of ions involved; and (c) the geometry of the RyR (ryanodine receptors) protein may function to restrict the diffusion of and to "funnel" Ca(2+) ions to activation-binding sites on the RyR, thus increasing RyR open probability and excitation-contraction (EC) coupling gain. Simplification of this model to one in which the dyadic space is represented using a single compartment yields the stochastic local-control model of CICR developed previously. We have shown that this model captures fundamental properties of CICR, such as graded release and voltage-dependent gain, may be integrated within a model of the myocyte and may be simulated in reasonable times using a combination of efficient numerical methods and parallel computing, but remains too complex for general use in cell simulations. To address this problem, we show how separation of time scales may be used to formulate a model in which nearby L-type Ca(2+) channels (LCCs) and RyRs gate as a coupled system that may be described using low-dimensional systems of ordinary differential equations, thus reducing computational complexity while capturing fundamentally important properties of CICR. The simplified model may be solved many orders of magnitude faster than can either of the more detailed models, thus enabling incorporation into tissue-level simulations.
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Affiliation(s)
- Raimond L Winslow
- Institute for Computational Medicine and Center for Cardiovascular Bioinformatics & Modeling, The Johns Hopkins University School of Medicine and Whiting School of Engineering, Baltimore, MD 21218, USA.
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81
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Niederer SA, Smith NP. A mathematical model of the slow force response to stretch in rat ventricular myocytes. Biophys J 2007; 92:4030-44. [PMID: 17369410 PMCID: PMC1868992 DOI: 10.1529/biophysj.106.095463] [Citation(s) in RCA: 84] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We developed a model of the rat ventricular myocyte at room temperature to predict the relative effects of different mechanisms on the cause of the slow increase in force in response to a step change in muscle length. We performed simulations in the presence of stretch-dependent increases in flux through the Na(+)-H(+) exchanger (NHE) and Cl(-)-HCO(3)(-) exchanger (AE), stretch-activated channels (SAC), and the stretch-dependent nitric oxide (NO) induced increased open probability of the ryanodine receptors to estimate the capacity of each mechanism to produce the slow force response (SFR). Inclusion of stretch-dependent NHE & AE, SACs, and stretch-dependent NO effects caused an increase in tension following 15 min of stretch of 0.87%, 32%, and 0%, respectively. Comparing [Ca(2+)](i) dynamics before and after stretch in the presence of combinations of the three stretch-dependent elements, which produced significant SFR values (>20%), showed that the inclusion of stretch-dependent NO effects produced [Ca(2+)](i) transients, which were not consistent with experimental results. Further simulations showed that in the presence of SACs and the absence of stretch-dependent NHE & AE inhibition of NHE attenuated the SFR, such that reduced SFR in the presence of NHE blockers does not indicate a stretch dependence of NHE. Rather, a functioning NHE is responsible for a portion of the SFR. Based on our simulations we estimate that in rat cardiac myocytes at room temperature SACs play a significant role in producing the SFR, potentially in the presence of stretch-dependent NHE & AE and that NO effects, if any, must involve more mechanisms than just increasing the open probability of ryanodine receptors.
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Affiliation(s)
- Steven A Niederer
- Bioengineering Institute, University of Auckland, Auckland, New Zealand
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82
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Sher AA, Hinch R, Noble PJ, Gavaghan DJ, Noble D. Functional Significance of Na+/Ca2+ Exchangers Co-localization with Ryanodine Receptors. Ann N Y Acad Sci 2007; 1099:215-20. [PMID: 17446461 DOI: 10.1196/annals.1387.047] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Co-localization of Na+/Ca2+ exchangers (NCX) with ryanodine receptors (RyRs) is debated. We incorporate local NCX current in a biophysically detailed model of L-type Ca2+ channels (LCCs) and RyRs and study the effect of NCX on the regulation of Ca2+-induced Ca2+ release and the shape of the action potential. In canine ventricular cells, under pathological conditions, e.g., impaired LCCs, local NCXs become an enhancer of sarcoplasmic reticulum release. Under such conditions incorporation of local NCXs is critical to accurately capture mechanisms of excitation-contraction coupling.
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Affiliation(s)
- Anna A Sher
- Computational Biology Group, University of Oxford Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, Oxford, UK
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83
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Huertas MA, Smith GD. The dynamics of luminal depletion and the stochastic gating of Ca2+-activated Ca2+ channels and release sites. J Theor Biol 2007; 246:332-54. [PMID: 17286986 DOI: 10.1016/j.jtbi.2007.01.003] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2006] [Revised: 12/08/2006] [Accepted: 01/03/2007] [Indexed: 10/23/2022]
Abstract
Single channel models of intracellular calcium (Ca(2+)) channels such as the 1,4,5-trisphosphate receptor and ryanodine receptor often assume that Ca(2+)-dependent transitions are mediated by constant background cytosolic [Ca(2+)]. This assumption neglects the fact that Ca(2+) released by open channels may influence subsequent gating through the processes of Ca(2+)-activation or inactivation. Similarly, the influence of the dynamics of luminal depletion on the stochastic gating of intracellular Ca(2+) channels is often neglected, in spite of the fact that the sarco/endoplasmic reticulum [Ca(2+)] near the luminal face of intracellular Ca(2+) channels influences the driving force for Ca(2+), the rate of Ca(2+) release, and the magnitude and time course of the consequent increase in cytosolic domain [Ca(2+)]. Here we analyze how the steady-state open probability of several minimal Ca(2+)-regulated Ca(2+) channel models depends on the conductance of the channel and the time constants for the relaxation of elevated cytosolic [Ca(2+)] and depleted luminal [Ca(2+)] to the bulk [Ca(2+)] of both compartments. Our approach includes Monte Carlo simulation as well as numerical solution of a system of advection-reaction equations for the multivariate probability density of elevated cytosolic [Ca(2+)] and depleted luminal [Ca(2+)] conditioned on each state of the stochastically gating channel. Both methods are subsequently used to study the role of luminal depletion in the dynamics of Ca(2+) puff/spark termination in release sites composed of Ca(2+) channels that are activated, but not inactivated, by cytosolic Ca(2+). The probability density approach shows that such minimal Ca(2+) release site models may exhibit puff/spark-like dynamics in either of two distinct parameter regimes. In one case, puffs/spark termination is due to the process of stochastic attrition and facilitated by rapid Ca(2+) domain collapse [cf. DeRemigio, H., Smith, G., 2005. The dynamics of stochastic attrition viewed as an absorption time on a terminating Markov chain. Cell Calcium 38, 73-86]. In the second case, puff/spark termination is promoted by the local depletion of luminal Ca(2+).
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Affiliation(s)
- Marco A Huertas
- Department of Applied Science, College of William and Mary, Williamsburg, VA 23187, USA
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84
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Faber GM, Silva J, Livshitz L, Rudy Y. Kinetic properties of the cardiac L-type Ca2+ channel and its role in myocyte electrophysiology: a theoretical investigation. Biophys J 2006; 92:1522-43. [PMID: 17158566 PMCID: PMC1796810 DOI: 10.1529/biophysj.106.088807] [Citation(s) in RCA: 100] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
The L-type Ca(2+) channel (Ca(V)1.2) plays an important role in action potential (AP) generation, morphology, and duration (APD) and is the primary source of triggering Ca(2+) for the initiation of Ca(2+)-induced Ca(2+)-release in cardiac myocytes. In this article we present: 1), a detailed kinetic model of Ca(V)1.2, which is incorporated into a model of the ventricular mycoyte where it interacts with a kinetic model of the ryanodine receptor in a restricted subcellular space; 2), evaluation of the contribution of voltage-dependent inactivation (VDI) and Ca(2+)-dependent inactivation (CDI) to total inactivation of Ca(V)1.2; and 3), description of dynamic Ca(V)1.2 and ryanodine receptor channel-state occupancy during the AP. Results are: 1), the Ca(V)1.2 model reproduces experimental single-channel and macroscopic-current data; 2), the model reproduces rate dependence of APD, [Na(+)](i), and the Ca(2+)-transient (CaT), and restitution of APD and CaT during premature stimuli; 3), CDI of Ca(V)1.2 is sensitive to Ca(2+) that enters the subspace through the channel and from SR release. The relative contributions of these Ca(2+) sources to total CDI during the AP vary with time after depolarization, switching from early SR dominance to late Ca(V)1.2 dominance. 4), The relative contribution of CDI to total inactivation of Ca(V)1.2 is greater at negative potentials, when VDI is weak; and 5), loss of VDI due to the Ca(V)1.2 mutation G406R (linked to the Timothy syndrome) results in APD prolongation and increased CaT.
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Affiliation(s)
- Gregory M Faber
- Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio, USA
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85
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Valent I, Zahradníková A, Pavelková J, Zahradník I. Spatial and temporal Ca2+, Mg2+, and ATP2- dynamics in cardiac dyads during calcium release. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2006; 1768:155-66. [PMID: 17034755 DOI: 10.1016/j.bbamem.2006.08.020] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2006] [Revised: 08/10/2006] [Accepted: 08/17/2006] [Indexed: 11/16/2022]
Abstract
We have constructed a three-dimensional reaction-diffusion model of the mammalian cardiac calcium release unit. We analyzed effects of diffusion coefficients, single channel current amplitude, density of RyR channels, and reaction kinetics of ATP(2-) with Ca(2+) and Mg(2+) ions on spatiotemporal concentration profiles of Ca(2+), Mg(2+), and ATP(2-) in the dyadic cleft during Ca(2+) release. The model revealed that Ca(2+) concentration gradients persist near RyRs in the steady state. Even with low number of open RyRs, peak [Ca(2+)] in the dyadic space reached values similar to estimates of luminal [Ca(2+)] in approximately 1 ms, suggesting that during calcium release the Ca(2+) gradient moves from the cisternal membrane towards the boundary of the dyadic space with the cytosol. The released Ca(2+) bound to ATP(2-), and thus substantially decreased ATP(2-) concentration in the dyadic space. The released Ca(2+) could also replace Mg(2+) in its complex with ATP(2-) during first milliseconds of release if dissociation of MgATP was fast. The results suggest that concentration changes of Ca(2+), Mg(2+), and ATP(2-) might be large and fast enough to reduce dyadic RyR activity. Thus, under physiological conditions, termination of calcium release may be facilitated by the synergic effect of the construction and chemistry of mammalian cardiac dyads.
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Affiliation(s)
- Ivan Valent
- Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Bratislava, Slovakia
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86
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Flaim SN, Giles WR, McCulloch AD. Contributions of sustained INa and IKv43 to transmural heterogeneity of early repolarization and arrhythmogenesis in canine left ventricular myocytes. Am J Physiol Heart Circ Physiol 2006; 291:H2617-29. [PMID: 16829642 DOI: 10.1152/ajpheart.00350.2006] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
The roles of sustained components of I(Na) and I(Kv43) in shaping the action potentials (AP) of myocytes isolated from the canine left ventricle (LV) have not been studied in detail. Here we investigate the hypothesis that these two currents can contribute substantially to heterogeneity of early repolarization and arrhythmic risk. Quantitative data from voltage-clamp and expression profiling experiments were used to complete meaningful modifications to an existing "local control" model of canine midmyocardial myocyte excitation-contraction coupling for epicardial and endocardial cells. We include 1) heterogeneous I(Kv43), I(Ks), and I(SERCA) density; 2) modulation of I(Kv43) by Kv channel interacting protein type 2 (KChIP2) channel subunits; 3) a possible Ca(2+)-dependent open-state inactivation of I(Kv43); and 4) a sustained component of the inward Na(+) current, I(NaL). The resulting simulations illustrate ways in which KChIP2- and Ca(2+)-dependent control of I(Kv43) can result in a sustained outward current that can neutralize I(NaL) in a rate- and myocyte subtype-dependent manner. Both these currents appear to play significant roles in modulating AP duration and rate dependence in midmyocardial myocytes. Furthermore, an increased ratio of I(Kv43) to I(NaL) is capable of protecting epicardial myocytes from the early afterdepolarizations resulting from the SCN5A-I1768V mutation-induced increase in I(NaL). Experimentally observed transmural differences in Ca(2+) handling, including greater sarcoplasmic reticulum Ca(2+) content and faster Ca(2+) transient decay rates on the epicardium, were recapitulated in our simulations. By design, these models allow upward integration into organ models or may be used as a basis for further investigations into cellular heterogeneities.
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Affiliation(s)
- Sarah N Flaim
- University of California, San Diego, La Jolla, CA 92093-0412, USA
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87
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Jones PP, Bazzazi H, Kargacin GJ, Colyer J. Inhibition of cAMP-dependent protein kinase under conditions occurring in the cardiac dyad during a Ca2+ transient. Biophys J 2006; 91:433-43. [PMID: 16632511 PMCID: PMC1483070 DOI: 10.1529/biophysj.106.083931] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The space between the t-tubule invagination and the sarcoplasmic reticulum (SR) membrane, the dyad, in ventricular myocytes has been predicted to experience very high [Ca2+] for short periods of time during a Ca2+ transient. The dyadic space accommodates many protein kinases responsible for the regulation of Ca2+ handling proteins of the cell. We show in vitro that cAMP-dependent protein kinase (PKA) is inhibited by high [Ca2+] through a shift in the ratio of CaATP/MgATP toward CaATP. We further generate a three-dimensional mathematical model of Ca2+ and ATP diffusion within dyad. We use this model to predict the extent to which PKA would be inhibited by an increased CaATP/MgATP ratio during a Ca2+ transient in the dyad in vivo. Our results suggest that under normal physiological conditions a myocyte paced at 1 Hz would experience up to 55% inhibition of PKA within the cardiac dyad, with inhibition averaging 5% throughout the transient, an effect which becomes more pronounced as the myocyte contractile frequency increases (at 7 Hz, PKA inhibition averages 28% across the dyad throughout the duration of a Ca2+ transient).
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Affiliation(s)
- Peter P Jones
- Institute of Membrane and Systems Biology, University of Leeds, Leeds LS2 9JT, United Kingdom.
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88
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Hopenfeld B. A mathematical analysis of the action potential plateau duration of a human ventricular myocyte. J Theor Biol 2005; 240:311-22. [PMID: 16303142 DOI: 10.1016/j.jtbi.2005.09.021] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2005] [Revised: 07/13/2005] [Accepted: 09/21/2005] [Indexed: 11/24/2022]
Abstract
The plateau phase of a human ventricular myocyte is analysed. The plateau duration is a function of the time required for a myocyte's transmembrane voltage to decrease by a certain voltage, DeltaV. The timing of the plateau is shown to be controlled by two slowly changing gate variables, the inactivation gate that controls the inward/depolarizing L-type calcium current and the inactivation gate that controls the outward/repolarizing slow rectifier potassium current. The amount of current controlled by these variables is a function of the net conductivity of the corresponding sodium and potassium channels. An equation is derived that relates action potential duration to these net conductivities and the time dependence of the slowly moving variables. This equation is used to estimate plateau duration for a given value of DeltaV. The initial conditions of the slowly moving inactivation variables are shown to affect plateau duration. These initial conditions depend on the amount of time that has elapsed between a previous repolarization and a current depolarization (diastolic interval). The analysis thus helps to quantify the characteristics of action potential duration restitution.
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Affiliation(s)
- B Hopenfeld
- National Institutes of Health, National Heart, Lung and Blood Institute, 10 Center Dr., MSC 1061, Bethesda, MD 20892-1061, USA.
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89
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Greenstein JL, Hinch R, Winslow RL. Mechanisms of excitation-contraction coupling in an integrative model of the cardiac ventricular myocyte. Biophys J 2005; 90:77-91. [PMID: 16214852 PMCID: PMC1367039 DOI: 10.1529/biophysj.105.065169] [Citation(s) in RCA: 112] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
It is now well established that characteristic properties of excitation-contraction (EC) coupling in cardiac myocytes, such as high gain and graded Ca(2+) release, arise from the interactions that occur between L-type Ca(2+) channels (LCCs) and nearby ryanodine-sensitive Ca(2+) release channels (RyRs) in localized microdomains. Descriptions of Ca(2+)-induced Ca(2+) release (CICR) that account for these local mechanisms are lacking from many previous models of the cardiac action potential, and those that do include local control of CICR are able to reconstruct properties of EC coupling, but require computationally demanding stochastic simulations of approximately 10(5) individual ion channels. In this study, we generalize a recently developed analytical approach for deriving simplified mechanistic models of CICR to formulate an integrative model of the canine cardiac myocyte which is computationally efficient. The resulting model faithfully reproduces experimentally measured properties of EC coupling and whole cell phenomena. The model is used to study the role of local redundancy in L-type Ca(2+) channel gating and the role of dyad configuration on EC coupling. Simulations suggest that the characteristic steep rise in EC coupling gain observed at hyperpolarized potentials is a result of increased functional coupling between LCCs and RyRs. We also demonstrate mechanisms by which alterations in the early repolarization phase of the action potential, resulting from reduction of the transient outward potassium current, alters properties of EC coupling.
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Affiliation(s)
- Joseph L Greenstein
- The Center for Cardiovascular Bioinformatics and Modeling and The Whitaker Biomedical Engineering Institute, The Johns Hopkins University Whiting School of Engineering and School of Medicine, Baltimore, Maryland, USA.
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