The functional role of cardiac T-tubules explored in a model of rat ventricular myocytes

Optogenetic confirmation of transverse-tubular membrane excitability in intact cardiac myocytes

T-tubules (TT) form a complex network of sarcolemmal membrane invaginations, essential for well-co-ordinated excitation-contraction coupling (ECC) and thus homogeneous mechanical activation of cardiomyocytes. ECC is initiated by rapid depolarization of the sarcolemmal membrane. Whether TT membrane depolarization is active (local generation of action potentials; AP) or passive (following depolarization of the outer cell surface sarcolemma; SS) has not been experimentally validated in cardiomyocytes. Based on the assessment of ion flux pathways needed for AP generation, we hypothesize that TT are excitable. We therefore explored TT excitability experimentally, using an all-optical approach to stimulate and record trans-membrane potential changes in TT that were structurally disconnected, and hence electrically insulated, from the SS membrane by transient osmotic shock. Our results establish that cardiomyocyte TT can generate AP. These AP show electrical features that differ substantially from those observed in SS, consistent with differences in the density of ion channels and transporters in the two different membrane domains. We propose that TT-generated AP represent a safety mechanism for TT AP propagation and ECC, which may be particularly relevant in pathophysiological settings where morpho-functional changes reduce the electrical connectivity between SS and TT membranes. KEY POINTS: Cardiomyocytes are characterized by a complex network of membrane invaginations (the T-tubular system) that propagate action potentials to the core of the cell, causing uniform excitation-contraction coupling across the cell. In the present study, we investigated whether the T-tubular system is able to generate action potentials autonomously, rather than following depolarization of the outer cell surface sarcolemma. For this purpose, we developed a fully optical platform to probe and manipulate the electrical dynamics of subcellular membrane domains. Our findings demonstrate that T-tubules are intrinsically excitable, revealing distinct characteristics of self-generated T-tubular action potentials. This active electrical capability would protect cells from voltage drops potentially occurring within the T-tubular network.

Mechanisms of spontaneous Ca2+ release-mediated arrhythmia in a novel 3D human atrial myocyte model: II. Ca2+ -handling protein variation

Disruption of the transverse-axial tubule system (TATS) in diseases such as heart failure and atrial fibrillation occurs in combination with changes in the expression and distribution of key Ca2+ -handling proteins. Together this ultrastructural and ionic remodelling is associated with aberrant Ca2+ cycling and electrophysiological instabilities that underlie arrhythmic activity. However, due to the concurrent changes in TATs and Ca2+ -handling protein expression and localization that occur in disease it is difficult to distinguish their individual contributions to the arrhythmogenic state. To investigate this, we applied our novel 3D human atrial myocyte model with spatially detailed Ca2+ diffusion and TATS to investigate the isolated and interactive effects of changes in expression and localization of key Ca2+ -handling proteins and variable TATS density on Ca2+ -handling abnormality driven membrane instabilities. We show that modulating the expression and distribution of the sodium-calcium exchanger, ryanodine receptors and the sarcoplasmic reticulum (SR) Ca2+ buffer calsequestrin have varying pro- and anti-arrhythmic effects depending on the balance of opposing influences on SR Ca2+ leak-load and Ca2+ -voltage relationships. Interestingly, the impact of protein remodelling on Ca2+ -driven proarrhythmic behaviour varied dramatically depending on TATS density, with intermediately tubulated cells being more severely affected compared to detubulated and densely tubulated myocytes. This work provides novel mechanistic insight into the distinct and interactive consequences of TATS and Ca2+ -handling protein remodelling that underlies dysfunctional Ca2+ cycling and electrophysiological instability in disease. KEY POINTS: In our companion paper we developed a 3D human atrial myocyte model, coupling electrophysiology and Ca2+ handling with subcellular spatial details governed by the transverse-axial tubule system (TATS). Here we utilize this model to mechanistically examine the impact of TATS loss and changes in the expression and distribution of key Ca2+ -handling proteins known to be remodelled in disease on Ca2+ homeostasis and electrophysiological stability. We demonstrate that varying the expression and localization of these proteins has variable pro- and anti-arrhythmic effects with outcomes displaying dependence on TATS density. Whereas detubulated myocytes typically appear unaffected and densely tubulated cells seem protected, the arrhythmogenic effects of Ca2+ handling protein remodelling are profound in intermediately tubulated cells. Our work shows the interaction between TATS and Ca2+ -handling protein remodelling that underlies the Ca2+ -driven proarrhythmic behaviour observed in atrial fibrillation and may help to predict the effects of antiarrhythmic strategies at varying stages of ultrastructural remodelling.

Models of the cardiac L-type calcium current: A quantitative review

The L-type calcium current (I CaL ) plays a critical role in cardiac electrophysiology, and models ofI CaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelingI CaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalianI CaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model ofI CaL . This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.

Fraction of the T-Tubular Membrane as an Important Parameter in Cardiac Cellular Electrophysiology: A New Way of Estimation

The transverse-axial tubular system (t-tubules) plays an essential role in excitation-contraction coupling in cardiomyocytes. Its remodelling is associated with various cardiac diseases. Numerous attempts were made to analyse characteristics essential for proper understanding of the t-tubules and their impact on cardiac cell function in health and disease. The currently available methodical approaches related to the fraction of the t-tubular membrane area produce diverse data. The widely used detubulation techniques cause irreversible cell impairment, thus, distinct cell samples have to be used for estimation of t-tubular parameters in untreated and detubulated cells. Our proposed alternative method is reversible and allows repetitive estimation of the fraction of t-tubular membrane (f t) in cardiomyocytes using short-term perfusion of the measured cell with a low-conductive isotonic sucrose solution. It results in a substantial increase in the electrical resistance of t-tubular lumen, thus, electrically separating the surface and t-tubular membranes. Using the whole-cell patch-clamp measurement and the new approach in enzymatically isolated rat atrial and ventricular myocytes, a set of data was measured and evaluated. The analysis of the electrical equivalent circuit resulted in the establishment of criteria for excluding measurements in which perfusion with a low conductivity solution did not affect the entire cell surface. As expected, the final average f t in ventricular myocytes (0.337 ± 0.017) was significantly higher than that in atrial myocytes (0.144 ± 0.015). The parameter f t could be estimated repetitively in a particular cell (0.345 ± 0.021 and 0.347 ± 0.023 in ventricular myocytes during the first and second sucrose perfusion, respectively). The new method is fast, simple, and leaves the measured cell intact. It can be applied in the course of experiments for which it is useful to estimate both the surface and t-tubular capacitance/area in a particular cell.

Cardiac Arrhythmias as Manifestations of Nanopathies: An Emerging View

A nanodomain is a collection of proteins localized within a specialized, nanoscale structural environment, which can serve as the functional unit of macroscopic physiologic processes. We are beginning to recognize the key roles of cardiomyocyte nanodomains in essential processes of cardiac physiology such as electrical impulse propagation and excitation–contraction coupling (ECC). There is growing appreciation of nanodomain dysfunction, i.e., nanopathy, as a mechanistic driver of life-threatening arrhythmias in a variety of pathologies. Here, we offer an overview of current research on the role of nanodomains in cardiac physiology with particular emphasis on: (1) sodium channel-rich nanodomains within the intercalated disk that participate in cell-to-cell electrical coupling and (2) dyadic nanodomains located along transverse tubules that participate in ECC. The beat to beat function of cardiomyocytes involves three phases: the action potential, the calcium transient, and mechanical contraction/relaxation. In all these phases, cell-wide function results from the aggregation of the stochastic function of individual proteins. While it has long been known that proteins that exist in close proximity influence each other’s function, it is increasingly appreciated that there exist nanoscale structures that act as functional units of cardiac biophysical phenomena. Termed nanodomains, these structures are collections of proteins, localized within specialized nanoscale structural environments. The nano-environments enable the generation of localized electrical and/or chemical gradients, thereby conferring unique functional properties to these units. Thus, the function of a nanodomain is determined by its protein constituents as well as their local structural environment, adding an additional layer of complexity to cardiac biology and biophysics. However, with the emergence of experimental techniques that allow direct investigation of structure and function at the nanoscale, our understanding of cardiac physiology and pathophysiology at these scales is rapidly advancing. Here, we will discuss the structure and functions of multiple cardiomyocyte nanodomains, and novel strategies that target them for the treatment of cardiac arrhythmias.

Quantitative assessment of passive electrical properties of the cardiac T-tubular system by FRAP microscopy

Well-coordinated activation of all cardiomyocytes must occur on every heartbeat. At the cell level, a complex network of sarcolemmal invaginations, called the transverse-axial tubular system (TATS), propagates membrane potential changes to the cell core, ensuring synchronous and uniform excitation-contraction coupling. Although myocardial conduction of excitation has been widely described, the electrical properties of the TATS remain mostly unknown. Here, we exploit the formal analogy between diffusion and electrical conductivity to link the latter with the diffusional properties of TATS. Fluorescence recovery after photobleaching (FRAP) microscopy is used to probe the diffusion properties of TATS in isolated rat cardiomyocytes: A fluorescent dextran inside TATS lumen is photobleached, and signal recovery by diffusion of unbleached dextran from the extracellular space is monitored. We designed a mathematical model to correlate the time constant of fluorescence recovery with the apparent diffusion coefficient of the fluorescent molecules. Then, apparent diffusion is linked to electrical conductivity and used to evaluate the efficiency of the passive spread of membrane depolarization along TATS. The method is first validated in cells where most TATS elements are acutely detached by osmotic shock and then applied to probe TATS electrical conductivity in failing heart cells. We find that acute and pathological tubular remodeling significantly affect TATS electrical conductivity. This may explain the occurrence of defects in action potential propagation at the level of single T-tubules, recently observed in diseased cardiomyocytes.

Cardiac T-Tubule Microanatomy and Function

Unique to striated muscle cells, transverse tubules (t-tubules) are membrane organelles that consist of sarcolemma penetrating into the myocyte interior, forming a highly branched and interconnected network. Mature t-tubule networks are found in mammalian ventricular cardiomyocytes, with the transverse components of t-tubules occurring near sarcomeric z-discs. Cardiac t-tubules contain membrane microdomains enriched with ion channels and signaling molecules. The microdomains serve as key signaling hubs in regulation of cardiomyocyte function. Dyad microdomains formed at the junctional contact between t-tubule membrane and neighboring sarcoplasmic reticulum are critical in calcium signaling and excitation-contraction coupling necessary for beat-to-beat heart contraction. In this review, we provide an overview of the current knowledge in gross morphology and structure, membrane and protein composition, and function of the cardiac t-tubule network. We also review in detail current knowledge on the formation of functional membrane subdomains within t-tubules, with a particular focus on the cardiac dyad microdomain. Lastly, we discuss the dynamic nature of t-tubules including membrane turnover, trafficking of transmembrane proteins, and the life cycles of membrane subdomains such as the cardiac BIN1-microdomain, as well as t-tubule remodeling and alteration in diseased hearts. Understanding cardiac t-tubule biology in normal and failing hearts is providing novel diagnostic and therapeutic opportunities to better treat patients with failing hearts.

Myokit: A simple interface to cardiac cellular electrophysiology

Myokit is a new powerful and versatile software tool for modeling and simulation of cardiac cellular electrophysiology. Myokit consists of an easy-to-read modeling language, a graphical user interface, single and multi-cell simulation engines and a library of advanced analysis tools accessible through a Python interface. Models can be loaded from Myokit's native file format or imported from CellML. Model export is provided to C, MATLAB, CellML, CUDA and OpenCL. Patch-clamp data can be imported and used to estimate model parameters. In this paper, we review existing tools to simulate the cardiac cellular action potential to find that current tools do not cater specifically to model development and that there is a gap between easy-to-use but limited software and powerful tools that require strong programming skills from their users. We then describe Myokit's capabilities, focusing on its model description language, simulation engines and import/export facilities in detail. Using three examples, we show how Myokit can be used for clinically relevant investigations, multi-model testing and parameter estimation in Markov models, all with minimal programming effort from the user. This way, Myokit bridges a gap between performance, versatility and user-friendliness.

BIN1 regulates dynamic t-tubule membrane

Cardiac transverse tubules (t-tubules) are specific membrane organelles critical in calcium signaling and excitation-contraction coupling required for beat-to-beat heart contraction. T-tubules are highly branched and form an interconnected network that penetrates the myocyte interior to form junctions with the sarcoplasmic reticulum. T-tubules are selectively enriched with specific ion channels and proteins crucial in calcium transient development necessary in excitation-contraction coupling, thus t-tubules are a key component of cardiac myocyte function. In this review, we focus primarily on two proteins concentrated within the t-tubular network, the L-type calcium channel (LTCC) and associated membrane anchor protein, bridging integrator 1 (BIN1). Here, we provide an overview of current knowledge in t-tubule morphology, composition, microdomains, as well as the dynamics of the t-tubule network. Secondly, we highlight multiple aspects of BIN1-dependent t-tubule function, which includes forward trafficking of LTCCs to t-tubules, LTCC clustering at t-tubule surface, microdomain organization and regulation at t-tubule membrane, and the formation of a slow diffusion barrier within t-tubules. Lastly, we describe progress in characterizing how acquired human heart failure can be attributed to abnormal BIN1 transcription and associated t-tubule remodeling. Understanding BIN1-regulated cardiac t-tubule biology in human heart failure management has the dual benefit of promoting progress in both biomarker development and therapeutic target identification. This article is part of a Special Issue entitled: Cardiomyocyte Biology: Integration of Developmental and Environmental Cues in the Heart edited by Marcus Schaub and Hughes Abriel.

Cellular cardiac electrophysiology modeling with Chaste and CellML

Chaste is an open-source C++ library for computational biology that has well-developed cardiac electrophysiology tissue simulation support. In this paper, we introduce the features available for performing cardiac electrophysiology action potential simulations using a wide range of models from the Physiome repository. The mathematics of the models are described in CellML, with units for all quantities. The primary idea is that the model is defined in one place (the CellML file), and all model code is auto-generated at compile or run time; it never has to be manually edited. We use ontological annotation to identify model variables describing certain biological quantities (membrane voltage, capacitance, etc.) to allow us to import any relevant CellML models into the Chaste framework in consistent units and to interact with them via consistent interfaces. This approach provides a great deal of flexibility for analysing different models of the same system. Chaste provides a wide choice of numerical methods for solving the ordinary differential equations that describe the models. Fixed-timestep explicit and implicit solvers are provided, as discussed in previous work. Here we introduce the Rush–Larsen and Generalized Rush–Larsen integration techniques, made available via symbolic manipulation of the model equations, which are automatically rearranged into the forms required by these approaches. We have also integrated the CVODE solvers, a ‘gold standard’ for stiff systems, and we have developed support for symbolic computation of the Jacobian matrix, yielding further increases in the performance and accuracy of CVODE. We discuss some of the technical details of this work and compare the performance of the available numerical methods. Finally, we discuss how this is generalized in our functional curation framework, which uses a domain-specific language for defining complex experiments as a basis for comparison of model behavior.

Cardiac BIN1 folds T-tubule membrane, controlling ion flux and limiting arrhythmia

Cardiomyocyte T tubules are important for regulating ion flux. Bridging integrator 1 (BIN1) is a T-tubule protein associated with calcium channel trafficking that is downregulated in failing hearts. Here we find that cardiac T tubules normally contain dense protective inner membrane folds that are formed by a cardiac isoform of BIN1. In mice with cardiac Bin1 deletion, T-tubule folding is decreased, which does not change overall cardiomyocyte morphology but leads to free diffusion of local extracellular calcium and potassium ions, prolonging action-potential duration and increasing susceptibility to ventricular arrhythmias. We also found that T-tubule inner folds are rescued by expression of the BIN1 isoform BIN1+13+17, which promotes N-WASP-dependent actin polymerization to stabilize the T-tubule membrane at cardiac Z discs. BIN1+13+17 recruits actin to fold the T-tubule membrane, creating a 'fuzzy space' that protectively restricts ion flux. When the amount of the BIN1+13+17 isoform is decreased, as occurs in acquired cardiomyopathy, T-tubule morphology is altered, and arrhythmia can result.

Effect of ion concentration changes in the limited extracellular spaces on sarcolemmal ion transport and Ca2+ turnover in a model of human ventricular cardiomyocyte

We have developed a computer model of human cardiac ventricular myocyte (CVM), including t-tubular and cleft spaces with the aim of evaluating the impact of accumulation-depletion of ions in restricted extracellular spaces on transmembrane ion transport and ionic homeostasis in human CVM. The model was based on available data from human CVMs. Under steady state, the effect of ion concentration changes in extracellular spaces on [Ca²⁺]_i-transient was explored as a function of critical fractions of ion transporters in t-tubular membrane (not documented for human CVM). Depletion of Ca²⁺ and accumulation of K⁺ occurring in extracellular spaces slightly affected the transmembrane Ca²⁺ flux, but not the action potential duration (APD₉₀). The [Ca²⁺]_i-transient was reduced (by 2%–9%), depending on the stimulation frequency, the rate of ion exchange between t-tubules and clefts and fractions of ion-transfer proteins in the t-tubular membrane. Under non-steady state, the responses of the model to changes of stimulation frequency were analyzed. A sudden increase of frequency (1–2.5 Hz) caused a temporal decrease of [Ca²⁺] in both extracellular spaces, a reduction of [Ca²⁺]_i-transient (by 15%) and APD₉₀ (by 13 ms). The results reveal different effects of activity-related ion concentration changes in human cardiac t-tubules (steady-state effects) and intercellular clefts (transient effects) in the modulation of membrane ion transport and Ca²⁺ turnover.

How the Hodgkin-Huxley equations inspired the Cardiac Physiome Project

Early modelling of cardiac cells (1960-1980) was based on extensions of the Hodgkin-Huxley nerve axon equations with additional channels incorporated, but after 1980 it became clear that processes other than ion channel gating were also critical in generating electrical activity. This article reviews the development of models representing almost all cell types in the heart, many different species, and the software tools that have been created to facilitate the cardiac Physiome Project.

Role of t-tubules in the control of trans-sarcolemmal ion flux and intracellular Ca2+ in a model of the rat cardiac ventricular myocyte

The t-tubules of mammalian ventricular myocytes are invaginations of the surface membrane that form a complex network within the cell, with restricted diffusion to the bulk extracellular space. The trans-sarcolemmal flux of many ions, including Ca(2+), occurs predominantly across the t-tubule membrane and thus into and out of this restricted diffusion space. It seems possible, therefore, that ion concentration changes may occur in the t-tubule lumen, which would alter ion flux across the t-tubule membrane. We have used a computer model of the ventricular myocyte, incorporating a t-tubule compartment and experimentally determined values for diffusion between the t-tubule lumen and bulk extracellular space, and ion fluxes across the t-tubule membrane, to investigate this possibility. The results show that influx and efflux of different ion species across the t-tubule membrane are similar, but not equal. Changes of ion concentration can therefore occur close to the t-tubular membrane, thereby altering trans-sarcolemmal ion flux and thus cell function, although such changes are reduced by diffusion to the bulk extracellular space. Slowing diffusion results in larger changes in luminal ion concentrations. These results provide a deeper understanding of the role of the t-tubules in normal cell function, and are a basis for understanding the changes that occur in heart failure as a result of changes in t-tubule structure and ion fluxes.

Modeling CICR in rat ventricular myocytes: voltage clamp studies

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.

Uniform action potential repolarization within the sarcolemma of in situ ventricular cardiomyocytes

Previous studies have speculated, based on indirect evidence, that the action potential at the transverse (t)-tubules is longer than at the surface membrane in mammalian ventricular cardiomyocytes. To date, no technique has enabled recording of electrical activity selectively at the t-tubules to directly examine this hypothesis. We used confocal line-scan imaging in conjunction with the fast response voltage-sensitive dyes ANNINE-6 and ANNINE-6plus to resolve action potential-related changes in fractional dye fluorescence (DeltaF/F) at the t-tubule and surface membranes of in situ mouse ventricular cardiomyocytes. Peak DeltaF/F during action potential phase 0 depolarization averaged -21% for both dyes. The shape and time course of optical action potentials measured with the water-soluble ANNINE-6plus were indistinguishable from those of action potentials recorded with intracellular microelectrodes in the absence of the dye. In contrast, optical action potentials measured with the water-insoluble ANNINE-6 were significantly prolonged compared to the electrical recordings obtained from dye-free hearts, suggesting electrophysiological effects of ANNINE-6 and/or its solvents. With either dye, the kinetics of action potential-dependent changes in DeltaF/F during repolarization were found to be similar at the t-tubular and surface membranes. This study provides what to our knowledge are the first direct measurements of t-tubule electrical activity in ventricular cardiomyocytes, which support the concept that action potential duration is uniform throughout the sarcolemma of individual cells.

The role of mammalian cardiac t-tubules in excitation-contraction coupling: experimental and computational approaches

The sarcolemmal membrane of mammalian cardiac ventricular myocytes is characterized by the presence of invaginations called transverse tubules (t-tubules). Transverse tubules occur at the Z-line as transverse elements with longitudinal extensions. While the existence of t-tubules has been known for some time, recent experimental studies have suggested that their structure and function are more complex than previously believed. There are, however, aspects of t-tubule function that are not currently amenable to experimental investigation, but can be investigated using computational and mathematical approaches. Such studies have helped elucidate further the possible role of t-tubules in cell function. This review summarizes recent experimental and complementary computational studies which highlight the important role of t-tubules in cardiac excitation-contraction coupling.

Resurgence of cardiac t-tubule research

The transverse tubules of mammalian cardiac ventricular myocytes are invaginations of the surface membrane. Recent data have revealed that their structure and function are more complex than previously believed. Here, we review current knowledge about their role in cardiac function, focusing on Ca2+ signaling and changes observed in pathological conditions.

Acidosis in models of cardiac ventricular myocytes

The effects of acidosis on cardiac electrophysiology and excitation-contraction coupling have been studied extensively. Acidosis decreases the strength of contraction and leads to altered calcium transients as a net result of complex interactions between protons and a variety of intracellular processes. The relative contributions of each of the changes under acidosis are difficult to establish experimentally, however, and significant uncertainties remain about the key mechanisms of impaired cardiac function. In this paper, we review the experimental findings concerning the effects of acidosis on the action potential and calcium handling in the cardiac ventricular myocyte, and we present a modelling study that establishes the contribution of the different effects to altered Ca2+ transients during acidosis. These interactions are incorporated into a dynamical model of pH regulation in the myocyte to simulate respiratory acidosis in the heart.

Mathematical models in physiology

Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over 58000 entries in PubMed, with more than 34000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5-6 years, compared to only about one-third in the preceding 5-6 decades. The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function-the Physiome. The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experimental data-based model development in biological research from sub-cellular events to whole organ simulations.

Modulatory effect of calmodulin-dependent kinase II (CaMKII) on sarcoplasmic reticulum Ca2+ handling and interval-force relations: a modelling study

We hypothesize that slow inactivation of Ca2+/calmodulin-dependent kinase II (CaMKII) and its modulatory effect on sarcoplasmic reticulum (SR) Ca2+ handling are important for various interval-force (I-F) relations, in particular for the beat interval dependency in transient alternans during the decay of post-extrasystolic potentiation. We have developed a mathematical model of a single cardiomyocyte to integrate various I-F relations, including alternans, by incorporating a conceptual CaMKII kinetics model into the SR Ca2+ handling model. Our model integrates I-F relations, such as the beat interval-dependent twitch force duration, restitution and potentiation, positive staircase phenomenon and alternans. We found that CaMKII affects more or less all I-F relations, and it is a key factor for integration of the various I-F relations in our model. Alternans arises, in the model, out of a steep relation between SR Ca2+ load and release, owing to SR load-dependent changes in the releasability of Ca2+ via the ryanodine receptor. Beat interval-dependent CaMKII activity, owing to its kinetic properties and amplifying effect on SR Ca2+ load dependency of Ca2+ release, replicated the beat interval dependency of alternans, as observed experimentally. Additionally, our model enabled reproduction of the effects of various interventions on alternans, such as the slowing or accelerating of Ca2+ release and/or uptake. We conclude that a slow time-dependent factor, represented in the model by CaMKII, is important for the integration of I-F relations, including alternans, and that our model offers a useful tool for further analysis of the roles of integrative Ca2+ handling in myocardial I-F relations.