Modelling the heart: insights, failures and progress

Evaluating the predictive accuracy of ion-channel models using data from multiple experimental designs

Mathematical models are increasingly being relied upon to provide quantitatively accurate predictions of cardiac electrophysiology. Many such models concern the behaviour of particular subcellular components (namely, ion channels) which, together, allow the propagation of electrical signals through heart-muscle tissue; that is, the firing of action potentials. In particular, IKr, a voltage-sensitive potassium ion-channel current, is of interest owing to the central pore of its primary protein having a propensity to blockage by various small molecules. We use newly collected data obtained from an ensemble of voltage-clamp experiment designs (protocols) to validate the predictive accuracy of various dynamical models of IKr. To do this, we fit models to each protocol individually and quantify the error in the resultant model predictions for other protocols. This allows the comparison of predictive accuracy for IKr models under a diverse collection of previously unexplored dynamics. Our results highlight heterogeneity between parameter estimates obtained from different cells, suggesting the presence of latent effects not yet accounted for in our models. This heterogeneity has a significant effect on our parameter estimates and suggests routes for model improvement.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 1)'.

Analysis of Intestinal Movements with Spatiotemporal Maps: Beyond Anatomy and Physiology

Over 150 years ago, methods for quantitative analysis of gastrointestinal motor patterns first appeared. Graphic representations of physiological variables were recorded with the kymograph after the mid-1800s. Changes in force or length of intestinal muscles could be quantified, however most recordings were limited to a single point along the digestive tract.In parallel, photography and cinematography with X-Rays visualised changes in intestinal shape, but were hard to quantify. More recently, the ability to record physiological events at many sites along the gut in combination with computer processing allowed construction of spatiotemporal maps. These included diameter maps (DMaps), constructed from video recordings of intestinal movements and pressure maps (PMaps), constructed using data from high-resolution manometry catheters. Combining different kinds of spatiotemporal maps revealed additional details about gut wall status, including compliance, which relates forces to changes in length. Plotting compliance values along the intestine enabled combined DPMaps to be constructed, which can distinguish active contractions and relaxations from passive changes. From combinations of spatiotemporal maps, it is possible to deduce the role of enteric circuits and pacemaker cells in the generation of complex motor patterns. Development and application of spatiotemporal methods to normal and abnormal motor patterns in animals and humans is ongoing, with further technical improvements arising from their combination with impedance manometry, magnetic resonance imaging, electrophysiology, and ultrasonography.

Evolution of mathematical models of cardiomyocyte electrophysiology

Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane ion fluxes in normal and pathological states. We also present the use of these models in the study of various arrhythmogenesis mechanisms, particularly the integration of experimental pharmacology data into advanced humanized models for in silico proarrhythmogenic risk prediction as an essential component of the Comprehensive in vitro Proarrhythmia Assay (CiPA) drug safety paradigm.

Improvement of the Cardiac Oscillator Based Model for the Simulation of Bundle Branch Blocks

In this paper, we propose an improvement of the cardiac conduction system based on three modified Van der Pol oscillators. Each oscillator represents one of the components of the heart conduction system: Sino-Atrial node (SA), Atrio-Ventricular node (AV) and His–Purkinje system (HP). However, while SA and AV nodes can be modelled through a single oscillator, the modelling of HP by using a single oscillator is a rough simplification of the cardiac behaviour. In fact, the HP bundle is composed of Right (RB) and Left Bundle (LB) branches that serve, respectively, the right and left ventricles. In order to describe the behaviour of each bundle branch, we build a phenomenological model based on four oscillators: SA, AV, RB and LB. For the characterization of the atrial and ventricular muscles, we used the modified FitzHugh–Nagumo (FHN) equations. The numerical simulation of the model has been implemented in Simulink. The simulation results show that the new model is able to reproduce the heart dynamics generating, besides the physiological signal, also the pathological rhythm in case of Right Bundle Branch Block (RBBB) and Left Bundle Branch Block (LBBB). In particular, our model is able to describe the communication interruption of the conduction system, when one of the HP bundle branches is damaged.

The control of cardiac ventricular excitability by autonomic pathways

Central to the genesis of ventricular cardiac arrhythmia are variations in determinants of excitability. These involve individual ionic channels and transporters in cardiac myocytes but also tissue factors such as variable conduction of the excitation wave, fibrosis and source-sink mismatch. It is also known that in certain diseases and particularly the channelopathies critical events occur with specific stressors. For example, in hereditary long QT syndrome due to mutations in KCNQ1 arrhythmic episodes are provoked by exercise and in particular swimming. Thus not only is the static substrate important but also how this is modified by dynamic signalling events associated with common physiological responses. In this review, we examine the regulation of ventricular excitability by signalling pathways from a cellular and tissue perspective in an effort to identify key processes, effectors and potential therapeutic approaches. We specifically focus on the autonomic nervous system and related signalling pathways.

Electrochemical Na+ and Ca2+ gradients drive coupled-clock regulation of automaticity of isolated rabbit sinoatrial nodal pacemaker cells

Coupling of an intracellular Ca(2+) clock to surface membrane ion channels, i.e., a "membrane clock, " via coupling of electrochemical Na(+) and Ca(2+) gradients (ENa and ECa, respectively) has been theorized to regulate sinoatrial nodal cell (SANC) normal automaticity. To test this hypothesis, we measured responses of [Na(+)]i, [Ca(2+)]i, membrane potential, action potential cycle length (APCL), and rhythm in rabbit SANCs to Na(+)/K(+) pump inhibition by the digitalis glycoside, digoxigenin (DG, 10-20 μmol/l). Initial small but significant increases in [Na(+)]i and [Ca(2+)]i and reductions in ENa and ECa in response to DG led to a small reduction in maximum diastolic potential (MDP), significantly enhanced local diastolic Ca(2+) releases (LCRs), and reduced the average APCL. As [Na(+)]i and [Ca(2+)]i continued to increase at longer times following DG exposure, further significant reductions in MDP, ENa, and ECa occurred; LCRs became significantly reduced, and APCL became progressively and significantly prolonged. This was accompanied by increased APCL variability. We also employed a coupled-clock numerical model to simulate changes in ENa and ECa simultaneously with ion currents not measured experimentally. Numerical modeling predicted that, as the ENa and ECa monotonically reduced over time in response to DG, ion currents (ICaL, ICaT, If, IKr, and IbNa) monotonically decreased. In parallel with the biphasic APCL, diastolic INCX manifested biphasic changes; initial INCX increase attributable to enhanced LCR ensemble Ca(2+) signal was followed by INCX reduction as ENCX (ENCX = 3ENa - 2ECa) decreased. Thus SANC automaticity is tightly regulated by ENa, ECa, and ENCX via a complex interplay of numerous key clock components that regulate SANC clock coupling.

Anti-oxidative cellular protection effect of fasting-induced autophagy as a mechanism for hormesis

The aim of this investigation was to test the hypothesis that fasting-induced augmented lysosomal autophagic turnover of cellular proteins and organelles will reduce potentially harmful lipofuscin (age-pigment) formation in cells by more effectively removing oxidatively damaged proteins. An animal model (marine snail--common periwinkle, Littorina littorea) was used to experimentally test this hypothesis. Snails were deprived of algal food for 7 days to induce an augmented autophagic response in their hepatopancreatic digestive cells (hepatocyte analogues). This treatment resulted in a 25% reduction in the cellular content of lipofuscin in the digestive cells of the fasting animals in comparison with snails fed ad libitum on green alga (Ulva lactuca). Similar findings have previously been observed in the digestive cells of marine mussels subjected to copper-induced oxidative stress. Additional measurements showed that fasting significantly increased cellular health based on lysosomal membrane stability, and reduced lipid peroxidation and lysosomal/cellular triglyceride. These findings support the hypothesis that fasting-induced augmented autophagic turnover of cellular proteins has an anti-oxidative cytoprotective effect by more effectively removing damaged proteins, resulting in a reduction in the formation of potentially harmful proteinaceous aggregates such as lipofuscin. The inference from this study is that autophagy is important in mediating hormesis. An increase was demonstrated in physiological complexity with fasting, using graph theory in a directed cell physiology network (digraph) model to integrate the various biomarkers. This was commensurate with increased health status, and supportive of the hormesis hypothesis. The potential role of enhanced autophagic lysosomal removal of damaged proteins in the evolutionary acquisition of stress tolerance in intertidal molluscs is discussed and parallels are drawn with the growing evidence for the involvement of autophagy in hormesis and anti-ageing processes.

Systems biology approaches for studying the pathogenesis of non-alcoholic fatty liver disease

Non-alcoholic fatty liver disease (NAFLD) is a progressive disease of increasing public health concern. In western populations the disease has an estimated prevalence of 20%-40%, rising to 70%-90% in obese and type II diabetic individuals. Simplistically, NAFLD is the macroscopic accumulation of lipid in the liver, and is viewed as the hepatic manifestation of the metabolic syndrome. However, the molecular mechanisms mediating both the initial development of steatosis and its progression through non-alcoholic steatohepatitis to debilitating and potentially fatal fibrosis and cirrhosis are only partially understood. Despite increased research in this field, the development of non-invasive clinical diagnostic tools and the discovery of novel therapeutic targets has been frustratingly slow. We note that, to date, NAFLD research has been dominated by in vivo experiments in animal models and human clinical studies. Systems biology tools and novel computational simulation techniques allow the study of large-scale metabolic networks and the impact of their dysregulation on health. Here we review current systems biology tools and discuss the benefits to their application to the study of NAFLD. We propose that a systems approach utilising novel in silico modelling and simulation techniques is key to a more comprehensive, better targeted NAFLD research strategy. Such an approach will accelerate the progress of research and vital translation into clinic.

Using systems biology approaches to understand cardiac inflammation and extracellular matrix remodeling in the setting of myocardial infarction

Inflammation and extracellular matrix (ECM) remodeling are important components regulating the response of the left ventricle to myocardial infarction (MI). Significant cellular- and molecular-level contributors can be identified by analyzing data acquired through high-throughput genomic and proteomic technologies that provide expression levels for thousands of genes and proteins. Large-scale data provide both temporal and spatial information that need to be analyzed and interpreted using systems biology approaches in order to integrate this information into dynamic models that predict and explain mechanisms of cardiac healing post-MI. In this review, we summarize the systems biology approaches needed to computationally simulate post-MI remodeling, including data acquisition, data analysis for biomarker classification and identification, data integration to build dynamic models, and data interpretation for biological functions. An example for applying a systems biology approach to ECM remodeling is presented as a reference illustration.

Mathematical modeling of physiological systems: an essential tool for discovery

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?"

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNP04 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity θ and the wavelength λ of a plane wave; we show that PD leads to a periodic, spatial modulation of θ and a temporally periodic modulation of λ; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNP04 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNP04 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.

Modern perspectives on numerical modeling of cardiac pacemaker cell

Cardiac pacemaking is a complex phenomenon that is still not completely understood. Together with experimental studies, numerical modeling has been traditionally used to acquire mechanistic insights in this research area. This review summarizes the present state of numerical modeling of the cardiac pacemaker, including approaches to resolve present paradoxes and controversies. Specifically we discuss the requirement for realistic modeling to consider symmetrical importance of both intracellular and cell membrane processes (within a recent "coupled-clock" theory). Promising future developments of the complex pacemaker system models include the introduction of local calcium control, mitochondria function, and biochemical regulation of protein phosphorylation and cAMP production. Modern numerical and theoretical methods such as multi-parameter sensitivity analyses within extended populations of models and bifurcation analyses are also important for the definition of the most realistic parameters that describe a robust, yet simultaneously flexible operation of the coupled-clock pacemaker cell system. The systems approach to exploring cardiac pacemaker function will guide development of new therapies such as biological pacemakers for treating insufficient cardiac pacemaker function that becomes especially prevalent with advancing age.

Complex activity patterns in arterial wall: results from a model of calcium dynamics

Using a dynamical model of smooth muscle cells in an arterial wall, defined as a system of coupled five-dimensional nonlinear oscillators, on a grid with cylindrical symmetry, we compare the admissible activity patterns with those known from the heart tissue. We postulate on numerical basis the possibility to induce a stable spiral wave in the arterial wall. Such a spiral wave can inhibit the propagation of the axial calcium wave and effectively stop the vasomotion. We also discuss the dynamics of the circumferential calcium wave in comparison to rotors in venous ostia that are a common source of supraventricular ectopy. We show that the velocity and in consequence the frequency range of the circumferential calcium wave is by orders of magnitude too small compared to that of the rotors. The mechanism of the rotor is not likely to involve the calcium-related dynamics of the smooth muscle cells. The calcium-related dynamics which is voltage-independent and hard to be reset seems to actually protect the blood vessels against the electric activity of the atria. We also discuss the microreentry phenomenon, which was found in numerical experiments in the studied model.

Extended physics as a theoretical framework for systems biology?

In this essay we examine whether a theoretical and conceptual framework for systems biology could be built from the Bailly and Longo (2008, 2009) proposal. These authors aim to understand life as a coherent critical structure, and propose to develop an extended physical approach of evolution, as a diffusion of biomass in a space of complexity. Their attempt leads to a simple mathematical reconstruction of Gould's assumption (1989) concerning the bacterial world as a "left wall of least complexity" that we will examine. Extended physical systems are characterized by their constructive properties. Time is acting and new properties emerge by their history that can open the list of their initial properties. This conceptual and theoretical framework is nothing more than a philosophical assumption, but as such it provides a new and exciting approach concerning the evolution of life, and the transition between physics and biology.

Systems biology: an approach

In just over a decade, Systems Biology has moved from being an idea, or rather a disparate set of ideas, to a mainstream feature of research and funding priorities. Institutes, departments, and centers of various flavors of Systems Biology have sprung up all over the world. An Internet search now produces more than 2 million hits. Of the 2,800 entries in PubMed with "Systems Biology" in either the title or the abstract, only two papers were published before 2000, and >90% were published in the past five years. In this article, we interpret Systems Biology as an approach rather than as a field or a destination of research. We illustrate that this approach is productive for the exploration of systems behavior, or "phenotypes," at all levels of structural and functional complexity, explicitly including the supracellular domain, and suggest how this may be related conceptually to genomes and biochemical networks. We discuss the role of models in Systems Biology and conclude with a consideration of their utility in biomedical research and development.

Simulation of the QRS complex using papillary muscle positions as the site of early activation in human subjects

BACKGROUND

Simulation of the electrical activation of the heart and its comparison with real in vivo activation is a promising method in testing potential determinants of excitation. Simulation of the electrical activity of the human heart is now emerging as a step forward for understanding and predicting electrophysiologic patterns in humans. Initial points of excitation and the manner in which the activation spreads from these points are important variables determining QRS complex characteristics. It has been suggested that in humans, the initial excitation of the left ventricle is a primary determinant of QRS complex characteristics, and that excitation begins at the papillary muscles and septum, where the fascicles of the left bundle branch insert. The aim of this study is to test the hypothesis that QRS duration and direction of QRS axis in the frontal plane have excellent agreement between real QRS and simulated QRS using papillary muscle position to indicate the border of the origin of early ventricular activation.

METHODS

Fourteen healthy adult volunteers were included in the study. Magnetic resonance imaging data were obtained to assess the papillary muscle positions. Twelve-lead electrocardiographic (ECG) recordings were used to obtain real ECG data for assessment of QRS duration and QRS axis in each subject. Simulation software developed by ECG-TECH Corp (Huntington, NY) was used to simulate the ECG of each subject to determine simulated QRS duration and QRS frontal plane axis. QRS duration and QRS axis data were compared between simulated and real ECG and agreement between these variables was calculated.

RESULTS

Seventy-nine percent of subjects had a difference of the QRS duration between real and simulated ECG of less than 10 milliseconds. The calculated strength of agreement between simulated and real QRS duration was 71% and considered as "good" (kappa statistics). In 70% of subjects, the difference in the QRS axis was less than 10 degrees . The calculated strength of agreement between simulated and real QRS axis was 80% and considered as "excellent" (kappa statistics).

CONCLUSIONS

The results of this study suggest that the sites of the initiation of electrical activity in the left ventricle, as assessed by the positions of papillary muscles, may be considered as primary determinants of the QRS duration and QRS axis in humans. This knowledge may help in predicting normal QRS characteristic on a patient-specific basis. In this study, simulation of the QRS complex was based on papillary muscles from human hearts.

Mathematical modeling of mechanically modulated rhythm disturbances in homogeneous and heterogeneous myocardium with attenuated activity of na+ -k+ pump

A mathematical model of the cardiomyocyte electromechanical function is used to study contribution of mechanical factors to rhythm disturbances in the case of the cardiomyocyte calcium overload. Particular attention is paid to the overload caused by diminished activity of the sodium-potassium pump. It is shown in the framework of the model, where mechano-calcium feedback is accounted for that myocardium mechanics may significantly enhance arrhythmogenicity of the calcium overload. Specifically, a role of cross-bridge attachment/detachment processes, a role of mechanical conditions of myocardium contractions (length, load), and a role of myocardium viscosity in the case of simulated calcium overload have been revealed. Underlying mechanisms are analyzed. Several approaches are designed in the model and compared to each other for recovery of the valid myocardium electrical and mechanical performance in the case of the partially suppressed sodium-potassium pump.

Genetic mutations and arrhythmia: simulation from DNA to electrocardiogram

In the past two decades, mutations in cardiac ion channels have been shown to underlie a number of rare inherited cardiac arrhythmias. Defects in cardiac Na(+) channels can disrupt channel gating and cause electrical abnormalities that increase susceptibility to cardiac arrhythmia. Dozens of mutations have been identified in the gene SCN5A, which encodes the alpha subunit of the cardiac Na(+) channel, and have been causally linked to a wide spectrum of cardiac arrhythmic disorders. An important step in understanding genetically based arrhythmias is to clarify the relationship between molecular defects and the disruption of the delicate balance of dynamic interactions at the cell, tissue, and organ levels. Here, we provide an overview of cardiac Na(+) channel mutations that are associated with inherited arrhythmia syndromes. We also address pros and cons of current methodologies used to understand how specific genetic defects disrupt channel-gating kinetics and underlie cardiac arrhythmia. Finally, we discuss effects of mutations on predictability and efficacy of treatment with Na(+) channel-blocking drugs.

Claude Bernard, the first systems biologist, and the future of physiology

The first systems analysis of the functioning of an organism was Claude Bernard's concept of the constancy of the internal environment (le milieu intérieur), since it implied the existence of control processes to achieve this. He can be regarded, therefore, as the first systems biologist. The new vogue for systems biology today is an important development, since it is time to complement reductionist molecular biology by integrative approaches. Claude Bernard foresaw that this would require the application of mathematics to biology. This aspect of Claude Bernard's work has been neglected by physiologists, which is why we are not as ready to contribute to the development of systems biology as we should be. In this paper, I outline some general principles that could form the basis of systems biology as a truly multilevel approach from a physiologist's standpoint. We need the insights obtained from higher-level analysis in order to succeed even at the lower levels. The reason is that higher levels in biological systems impose boundary conditions on the lower levels. Without understanding those conditions and their effects, we will be seriously restricted in understanding the logic of living systems. The principles outlined are illustrated with examples from various aspects of physiology and biochemistry. Applying and developing these principles should form a major part of the future of physiology.

Scale relativity theory and integrative systems biology: 1. Founding principles and scale laws

In these two companion papers, we provide an overview and a brief history of the multiple roots, current developments and recent advances of integrative systems biology and identify multiscale integration as its grand challenge. Then we introduce the fundamental principles and the successive steps that have been followed in the construction of the scale relativity theory, and discuss how scale laws of increasing complexity can be used to model and understand the behaviour of complex biological systems. In scale relativity theory, the geometry of space is considered to be continuous but non-differentiable, therefore fractal (i.e., explicitly scale-dependent). One writes the equations of motion in such a space as geodesics equations, under the constraint of the principle of relativity of all scales in nature. To this purpose, covariant derivatives are constructed that implement the various effects of the non-differentiable and fractal geometry. In this first review paper, the scale laws that describe the new dependence on resolutions of physical quantities are obtained as solutions of differential equations acting in the scale space. This leads to several possible levels of description for these laws, from the simplest scale invariant laws to generalized laws with variable fractal dimensions. Initial applications of these laws to the study of species evolution, embryogenesis and cell confinement are discussed.

Scale relativity theory and integrative systems biology: 2. Macroscopic quantum-type mechanics

In these two companion papers, we provide an overview and a brief history of the multiple roots, current developments and recent advances of integrative systems biology and identify multiscale integration as its grand challenge. Then we introduce the fundamental principles and the successive steps that have been followed in the construction of the scale relativity theory, which aims at describing the effects of a non-differentiable and fractal (i.e., explicitly scale dependent) geometry of space-time. The first paper of this series was devoted, in this new framework, to the construction from first principles of scale laws of increasing complexity, and to the discussion of some tentative applications of these laws to biological systems. In this second review and perspective paper, we describe the effects induced by the internal fractal structures of trajectories on motion in standard space. Their main consequence is the transformation of classical dynamics into a generalized, quantum-like self-organized dynamics. A Schrödinger-type equation is derived as an integral of the geodesic equation in a fractal space. We then indicate how gauge fields can be constructed from a geometric re-interpretation of gauge transformations as scale transformations in fractal space-time. Finally, we introduce a new tentative development of the theory, in which quantum laws would hold also in scale space, introducing complexergy as a measure of organizational complexity. Initial possible applications of this extended framework to the processes of morphogenesis and the emergence of prokaryotic and eukaryotic cellular structures are discussed. Having founded elements of the evolutionary, developmental, biochemical and cellular theories on the first principles of scale relativity theory, we introduce proposals for the construction of an integrative theory of life and for the design and implementation of novel macroscopic quantum-type experiments and devices, and discuss their potential applications for the analysis, engineering and management of physical and biological systems and properties, and the consequences for the organization of transdisciplinary research and the scientific curriculum in the context of the SYSTEMOSCOPE Consortium research and development agenda.

From the Hodgkin-Huxley axon to the virtual heart

Experimentally based models of the heart have been developed since 1960, starting with the discovery and modelling of potassium channels. The early models were based on extensions of the Hodgkin-Huxley nerve impulse equations. The first models including calcium balance and signalling were made in the 1980s and have now reached a high degree of physiological detail. During the 1990s these cell models have been incorporated into anatomically detailed tissue and organ models to create the first virtual organ, the Virtual Heart. With over 40 years of interaction between simulation and experiment, the models are now sufficiently refined to begin to be of use in drug development.

Alternans and the influence of ionic channel modifications: Cardiac three-dimensional simulations and one-dimensional numerical bifurcation analysis

Cardiac propagation is investigated by simulations using a realistic three-dimensional (3D) geometry including muscle fiber orientation of the ventricles of a rabbit heart and the modified Beeler-Reuter ionic model. Electrical excitation is introduced by a periodic pacing of the lower septum. Depending on the pacing frequency, qualitatively different dynamics are observed, namely, normal heart beat, T-wave alternans, and 2:1 conduction block at small, intermediate, and large pacing frequencies, respectively. In a second step, we performed a numerical stability and bifurcation analysis of a pulse propagating in a one-dimensional (1D) ring of cardiac tissue. The precise onset of the alternans instability is obtained from computer-assisted linear stability analysis of the pulse and computation of the associated spectrum. The critical frequency at the onset of alternans and the profiles of the membrane potential agree well with the ones obtained in the 3D simulations. Next, we computed changes in the wave profiles and in the onset of alternans for the Beeler-Reuter model with modifications of the sodium, calcium, and potassium channels, respectively. For this purpose, we employ the method of numerical bifurcation and stability analysis. While blocking of calcium channels has a stabilizing effect, blocked sodium or potassium channels lead to the occurrence of alternans at lower pacing frequencies. The findings regarding channel blocking are verified within three-dimensional simulations. Altogether, we have found T-wave alternans and conduction block in 3D simulations of a realistic rabbit heart geometry. The onset of alternans has been analyzed by numerical bifurcation and stability analysis of 1D wave trains. By comparing the results of the two approaches, we find that alternans is not strongly influenced by ingredients such as 3D geometry and propagation anisotropy, but depends mostly on the frequency of pacing (frequency of subsequent action potentials). In addition, we have introduced numerical bifurcation and stability analysis as a tool into heart modeling and demonstrated its efficiency in scanning a large set of parameters in the case of models with reduced conductivity. Bifurcation analysis also provides an accurate test for analytical theories of alternans as is demonstrated for the case of the restitution hypothesis.

Systems biology--an engineering perspective

The interdisciplinary field of systems biology has evolved rapidly over the last years. Different disciplines have aided the development of both its experimental and theoretical branches. One field, which has played a significant role is engineering science and, in particular chemical engineering. Here, we review and illustrate some of these contributions, ranging from modeling approaches to model analysis with a special focus on technique which have not yet been substantially exploited but can be potentially useful in the analysis of biochemical systems.

The helical ventricular myocardial band of Torrent-Guasp

We live in an era of substantial progress in understanding myocardial structure and function at genetic, molecular, and microscopic levels. Yet, ventricular myocardium has proven remarkably resistant to macroscopic analyses of functional anatomy. Pronounced and practically indefinite global and local structural anisotropy of its fibers and other ventricular wall constituents produces electrical and mechanical properties that are nonlinear, anisotropic, time varying, and spatially inhomogeneous. The helical ventricular myocardial band of Torrent-Guasp is a revolutionary new concept in understanding global, 3-dimensional, functional architecture of the ventricular myocardium. This concept defines the principal, cumulative vectors, integrating the tissue architecture (ie, form) and net forces developed (ie, function) within the ventricular mass. The primary purpose of this review is to emphasize the importance of this concept, in the light of collaborative efforts to establish an integrative approach, defining ventricular form and function by linking across multiple scales of biological organization, as explained in the ongoing Physiome project. Because one of the most important scientific missions in this century is integration of basic research with clinical medicine, we believe that this knowledge is not of merely academic importance, but is also the essential prerequisite in clinical evaluation and treatment of different heart diseases.

Do nanoparticles present ecotoxicological risks for the health of the aquatic environment?

Nanotechnology is a major innovative scientific and economic growth area, which may present a variety of hazards for environmental and human health. The surface properties and very small size of nanoparticles and nanotubes provide surfaces that may bind and transport toxic chemical pollutants, as well as possibly being toxic in their own right by generating reactive radicals. There is a wealth of evidence for the harmful effects of nanoscale combustion-derived particulates (ultrafines), which when inhaled can cause a number of pulmonary pathologies in mammals and humans. However, release of manufactured nanoparticles into the aquatic environment is largely an unknown. This review addresses the possible hazards associated with nanomaterials and harmful effects that may result from exposure of aquatic animals to nanoparticles. Possible nanoparticle association with naturally occurring colloids and particles is considered together with how this could affect their bioavailability and uptake into cells and organisms. Uptake by endocytotic routes are identified as probable major mechanisms of entry into cells; potentially leading to various types of toxic cell injury. The higher level consequences for damage to animal health, ecological risk and possible food chain risks for humans are also considered based on known behaviours and toxicities for inhaled and ingested nanoparticles in the terrestrial environment. It is concluded that a precautionary approach is required with individual evaluation of new nanomaterials for risk to the health of the environment. Although current toxicity testing protocols should be generally applicable to identify harmful effects associated with nanoparticles, research into new methods is required to address the special properties of nanomaterials.

The emergence of a general theory of the initiation and strength of the heartbeat

Sarcoplasmic reticulum (SR) Ca(2+) cycling, that is, the Ca(2+) clock, entrained by externally delivered action potentials has been a major focus in ventricular myocyte research for the past 5 decades. In contrast, the focus of pacemaker cell research has largely been limited to membrane-delimited pacemaker mechanisms (membrane clock) driven by ion channels, as the immediate cause for excitation. Recent robust experimental evidence, based on confocal cell imaging, and supported by numerical modeling suggests a novel concept: the normal rhythmic heart beat is governed by the tight integration of both intracellular Ca(2+) and membrane clocks. In pacemaker cells the intracellular Ca(2+) clock is manifested by spontaneous, rhythmic submembrane local Ca(2+) releases from SR, which are tightly controlled by a high degree of basal and reserve PKA-dependent protein phosphorylation. The Ca(2+) releases rhythmically activate Na(+)/Ca(2+) exchange inward currents that ignite action potentials, whose shape and ion fluxes are tuned by the membrane clock which, in turn, sustains operation of the intracellular Ca(2+) clock. The idea that spontaneous SR Ca(2+) releases initiate and regulate normal automaticity provides the key that reunites pacemaker and ventricular cell research, thus evolving a general theory of the initiation and strength of the heartbeat.

Environmental prognostics: an integrated model supporting lysosomal stress responses as predictive biomarkers of animal health status

The potential prognostic use of lysosomal reactions to environmental pollutants is explored in relation to predicting animal health in marine mussels, based on diagnostic biomarker data. Cellular lysosomes are already known to accumulate many metals and organic xenobiotics and the lysosomal accumulation of the carcinogenic polycyclic aromatic hydrocarbon 3-methylcholanthrene (3-MC) is demonstrated here in the hepatopancreatic digestive cells and ovarian oocytes of the blue mussel. Lysosomal membrane integrity or stability appears to be a generic indicator of cellular well-being in eukaryotes; and in bivalve molluscs it is correlated with total oxygen and nitrogen radical scavenging capacity (TOSC), protein synthesis, scope for growth and larval viability; and inversely correlated with DNA damage (micronuclei), as well as lysosomal swelling (volume density), lipidosis and lipofuscinosis, which are all characteristic of failed or incomplete autophagy. Integration of multiple biomarker data is achieved using multivariate statistics and then mapped onto "health status space" by using lysosomal membrane stability as a measure of cellular well-being. This is viewed as a crucial step towards the derivation of explanatory frameworks for prediction of pollutant impact on animal health; and has facilitated the development of a conceptual mechanistic model linking lysosomal damage and autophagic dysfunction with injury to cells, tissues and the whole animal. This model has also complemented the creation and use of a cell-based bioenergetic computational model of molluscan hepatopancreatic cells that simulates lysosomal and cellular reactions to pollutants. More speculatively, the use of coupled empirical measurements of biomarker reactions and modelling is proposed as a practical approach to the development of an operational toolbox for predicting the health of the environment.

Laplace-Dirichlet energy field specification for deformable models. an FEM approach to active contour fitting

The construction of large scale computer models for complex biological systems requires the fitting of curves or surfaces to anatomical data sets. Algorithms recently developed to perform this task are based on the displacement of an initial model contour. There are several problems associated with this approach. Here we present improvements which eliminate the (i) sensitivity to the initial model position and shape; (ii) existence of local minima or maxima in the field used to displace the model; and (iii) presence of multiple solutions in the rules governing model displacement. Key elements of our algorithm are first that both the energy field used to displace the model and the model displacement itself are governed by partial differential equations. Secondly, we approximate the model with a polygonal contour which facilitates accurate displacement. Tests performed against cases that are known to be problematic show that our algorithm can fit complex data sets entirely automatically.

Bridging proteomics and systems biology: What are the roads to be traveled?

The comprehensive study of proteomes has become an important part of attempts to uncover the systemic properties of biological systems. Proteomics provides data of a quality which increasingly fulfills strict requirements of systems biology for quantitative and qualitative information. Notably, proteomics can generate rich datasets that describe dynamic changes of proteomes. On the other hand, large-scale modeling requires the development of mathematic tools that are adequate for the processing of largely uncertain biological data. In this review, recent developments that pave the way for the integration of proteomics into systems biology are discussed. These developments include the standardization of data acquisition and presentation, the increased comprehensiveness of proteomics studies in description of functional status, localization and dynamics of proteins, and advanced modeling approaches.

Towards a Grid infrastructure to support integrative approaches to biological research

This paper discusses the scientific rationale behind the e-Science project, Integrative Biology, which is developing mathematical modelling tools, HPC-enabled simulations and an underpinning Grid infrastructure to provide an integrative approach to the modelling of complex biological systems. The project is focusing on two key applications to validate the approach: the modelling of heart disease and cancer, which together are responsible for over 60% of deaths in the United Kingdom. This paper provides an overview of the project, describes the initial prototype architecture and discusses the long-term scientific aims.

QT prolongation through hERG K(+) channel blockade: current knowledge and strategies for the early prediction during drug development

Prolongation of the QT interval of the electrocardiogram is a typical effect of Class III antiarrhythmic drugs, achieved through blockade of potassium channels. In the past decade, evidence has accrued that several classes of drugs used for non-cardiovascular indications may prolong the QT interval with the same mechanism (namely, human ether-a-go-go-related gene (hERG) K(+) channel blockade). The great interest in QT prolongation is because of several reasons. First, drug-induced QT prolongation increases the likelihood of a polymorphous ventricular arrhythmia (namely, torsades de pointes, TdP), which may cause syncope and degenerate into ventricular fibrillation and sudden death. Second, the fact that several classes of drugs, such as antihistamines, fluoroquinolones, macrolides, and neuroleptics may cause the long QT syndrome (LQTS) raises the question whether this is a class effect (e.g., shared by all agents of a given pharmacological class) or a specific effect of single agents within a class. There is now consensus that, in most cases, only a few agents within a therapeutic class share the ability to significantly affect hERG K(+) channels. These compounds should be identified as early as possible during drug development. Third, QT prolongation and interaction with hERG K(+) channels have become surrogate markers of cardiotoxicity and have received increasing regulatory attention. This review briefly outlines the mechanisms leading to QT prolongation and the different strategies that can be followed to predict this unwanted effect. In particular, it will focus on the approaches recently proposed for the in silico screening of new compounds.

Computational physiology and the Physiome Project

Bioengineering analyses of physiological systems use the computational solution of physical conservation laws on anatomically detailed geometric models to understand the physiological function of intact organs in terms of the properties and behaviour of the cells and tissues within the organ. By linking behaviour in a quantitative, mathematically defined sense across multiple scales of biological organization--from proteins to cells, tissues, organs and organ systems--these methods have the potential to link patient-specific knowledge at the two ends of these spatial scales. A genetic profile linked to cardiac ion channel mutations, for example, can be interpreted in relation to body surface ECG measurements via a mathematical model of the heart and torso, which includes the spatial distribution of cardiac ion channels throughout the myocardium and the individual kinetics for each of the approximately 50 types of ion channel, exchanger or pump known to be present in the heart. Similarly, linking molecular defects such as mutations of chloride ion channels in lung epithelial cells to the integrated function of the intact lung requires models that include the detailed anatomy of the lungs, the physics of air flow, blood flow and gas exchange, together with the large deformation mechanics of breathing. Organizing this large body of knowledge into a coherent framework for modelling requires the development of ontologies, markup languages for encoding models, and web-accessible distributed databases. In this article we review the state of the field at all the relevant levels, and the tools that are being developed to tackle such complexity. Integrative physiology is central to the interpretation of genomic and proteomic data, and is becoming a highly quantitative, computer-intensive discipline.

Towards computational models of cells for environmental toxicology

This paper outlines an approach to the development of computational models of cells for marine environmental toxicology. Exposure of cells to pollutants can lead to lysosomal damage and dysfunction, augmented autophagy, cellular dysfunction and atrophy and ultimately tissue pathology and organ damage. The application of carbon and nitrogen based models of intra cellular vesicular traffic for simulating the autophagic and lysosomal response of the hepatopancreatic digestive cells of marine molluscs is described. Two numerical models of the vesicular transport of carbon and nitrogen in the cell are presented. These demonstrate the importance of endocytotic uptake as a driver of lysosomal dynamics and the need to recognize and model it as a discrete process. Conceptual and mathematical models of the toxic impact of polycyclic aromatic hydrocarbons on the digestive gland are presented. The role of experimental research and the need to integrate it with modelling is highlighted.

Editorial: Computational modelling of cell & tissue processes & function

Computational modelling of whole biological systems from cells to organs is gaining momentum in cell biology and disease studies. This pathway is essential for the derivation of explanatory frameworks that will facilitate the development of a predictive capacity for estimating outcomes or risk associated with particular disease processes and therapeutic or stressful treatments. This article introduces a series of invited papers covering a hierarchy of issues and modelling problems, ranging from crucial conceptual considerations of the validity of cellular modelling through to multi-scale modelling up to organ level. The challenges and approaches in cellular modelling are described, including the potential of 'in silico ' modelling applications for receptor-ligand interactions in cell signalling, simulated organ dysfunction (i.e., heart), human and environmental toxicity and the progress of the IUPS Physiome Project. A major challenge now facing biologists is how to translate the wealth of reductionist detail about cells and tissues into a real understanding of how these systems function and are perturbed in disease processes. In biomedicine, simulation models of biological systems now contain sufficient detail, not only to reconstruct normal functions, but also, to reconstruct major disease states. More widely, simulation modelling will aid the targeting of current 'knowledge gaps' and how to fill them; and also provide a research tool for selecting critical factors from multiple simulated experiments for real experimental design. The envisaged longer-term end- product is the creation of simulation models for predicting drug interactions and harmful side-effects; and their use in therapeutic and environmental health risk management. Finally, we take a speculative look at possible future scenarios in cellular modelling, where it is envisioned that integrative biology will move from being largely qualitative and instead become a highly quantitative, computer-intensive discipline.

An integrated biomarker-based strategy for ecotoxicological evaluation of risk in environmental management

Environmental impacts by both natural events and man-made interventions are a fact of life; and developing the capacity to minimise these impacts and their harmful consequences for biological resources, ecosystems and human health is a daunting task for environmental legislators and regulators. A major challenge in impact and risk assessment, as part of integrated environmental management (IEM), is to link harmful effects of pollution (including toxic chemicals) in individual sentinel animals to their ecological consequences. This obstacle has resulted in a knowledge-gap for those seeking to develop effective policies for sustainable use of resources and environmental protection. Part of the solution to this problem may lie with the use of diagnostic clinical-type laboratory-based ecotoxicological tests or biomarkers, utilising sentinel animals as integrators of pollution, coupled with direct immunochemical tests for contaminants. These rapid and cost-effective ecotoxicological tools can provide information on the health status of individuals and populations based on relatively small samples of individuals. In the context of ecosystem status or health of the environment, biomarkers are also being used to link processes of molecular and cellular damage through to higher levels (i.e., prognostic capability), where they can result in pathology with reduced physiological performance and reproductive success. Complex issues are involved in evaluating environmental risk, such as the effects of the physico-chemical environment on the speciation and uptake of pollutant chemicals and inherent inter-individual and inter-species differences in vulnerability to toxicity; and the toxicity of complex mixtures. Effectively linking the impact of pollutants through the various hierarchical levels of biological organisation to ecosystem and human health requires a pragmatic integrated approach based on existing information that either links or correlates processes of pollutant uptake, detoxication and pathology with each other and higher level effects. It is further proposed here that this process will be facilitated by pursuing a holistic or whole systems approach with the development of computational simulation models of cells, organs and animals in tandem with empirical data (i.e., the middle-out approach). In conclusion, an effective integrated environmental management strategy to secure resource sustainability requires an integrated capability for risk assessment and prediction. Furthermore, if such a strategy is to influence and help in the formulation of environmental policy decisions, then it is crucial to demonstrate scientific robustness of predictions concerning the long-term consequences of pollution to politicians, industrialists and environmental managers; and also increase stakeholder awareness of environmental problems.

Modeling the Heart

Models of the heart have been developed since 1960, starting with the discovery and modeling of potassium channels. The first models of calcium balance were made in the 1980s and have now reached a high degree of physiological detail. During the 1990s, these cell models were incorporated into anatomically detailed tissue and organ models.

The research career of Richard B. Stein (1940–)

This report reviews the research and mentoring career of Richard B. Stein (1940–). In 1962, he completed a B.S. degree in physics at the Massachusetts Institute of Technology, USA, and thereafter an M.A. (1964), Ph.D. (1966), and postdoctoral training (1966–68) at the University of Oxford, UK. He subsequently assumed a faculty position at the University of Alberta (Canada), where he is currently an active researcher and mentor. To this point in 2004, Stein has trained and collaborated closely with over 160 scientists, largely neuroscientists and biomedical engineers, from 27 countries. He and his former trainees and collaborators have made important contributions on topics that span the cellular-to-behavioral spectrum of movement and rehabilitation–prosthetics neuroscience. His mentors, trainees, and collaborators include scientists whose countries of origin are: Australia, 2; Austria, 1; Belgium, 1; Bulgaria, 1; Canada, 64; China, 6; Denmark, 1; Germany, 1; Great Britain, 16; Hong Kong, 4; India, 5; Iraq, 2; Italy, 2; Japan, 10; Kenya, 1; New Zealand, 4; Pakistan, 1; Palestine, 1; Poland, 1; Romania, 1; South Africa, 1; Sri Lanka, 1; The Netherlands, 1; Turkey, 1; Uruguay, 1; USA, 21; and Yugoslavia, 6. In all instances, Stein's research collaborations and mentoring have advanced the careers of his trainees and junior collaborators, a well-deserved and important compliment to a stellar movement neuroscientist.Key words: movement neuroscience, rehabilitation neuroscience, prosthetics.

Mechanistic systems models of cell signaling networks: a case study of myocyte adrenergic regulation

Signal transduction networks coordinate a wide variety of cellular functions, including gene expression, metabolism, and cell fate processes. Understanding biological networks quantitatively is a major challenge to post-genomic biology, and mechanistic systems models will be crucial for this task. Here, we review approaches towards developing mechanistic systems models of established cell signaling networks. The ability of mechanistic system models to generate testable biological hypotheses and experimental strategies is discussed. As a case study of model development and analysis, we examined the functional roles of phospholamban, the L-type calcium channel, the ryanodine receptor, and troponin I phosphorylation upon beta-adrenergic stimulation in the rat ventricular myocyte. Model analysis revealed that while protein kinase A-mediated phosphorylation of the ryanodine receptor greatly increases its calcium sensitivity, calcium autoregulation may adapt quickly by negating potential increases in contractility. Systematic combinations of in silico perturbations supported the conclusion that phospholamban phosphoregulation is the primary mechanism for increased sarcoplasmic reticulum load and calcium relaxation rate during beta-adrenergic stimulation, while both phospholamban and the L-type calcium channel contribute to increased systolic calcium. Combined with detailed experimental studies, mechanistic systems models will be valuable for developing a quantitative understanding of cell signaling networks.

In silico multicellular systems biology and minimal genomes

The in vivo and in silico understanding of genomes and networks in cellular and multicellular systems is essential for drug discovery for multicellular diseases. In silico methodologies, when integrated with in vivo engineering methods, lay the groundwork for understanding multicellular organisms and their genomes. The quest to construct a minimal cell can be followed by designed, minimal multicellular organisms. In silico multicellular systems biology will be essential in the design and construction of minimal genomes for minimal multicellular organisms. Advanced methodologies come to light that can aid drug discovery. These novel approaches include multicellular pharmacodynamics and networked multicellular pharmacodynamics.

Modeling beta-adrenergic control of cardiac myocyte contractility in silico

The beta-adrenergic signaling pathway regulates cardiac myocyte contractility through a combination of feedforward and feedback mechanisms. We used systems analysis to investigate how the components and topology of this signaling network permit neurohormonal control of excitation-contraction coupling in the rat ventricular myocyte. A kinetic model integrating beta-adrenergic signaling with excitation-contraction coupling was formulated, and each subsystem was validated with independent biochemical and physiological measurements. Model analysis was used to investigate quantitatively the effects of specific molecular perturbations. 3-Fold overexpression of adenylyl cyclase in the model allowed an 85% higher rate of cyclic AMP synthesis than an equivalent overexpression of beta 1-adrenergic receptor, and manipulating the affinity of Gs alpha for adenylyl cyclase was a more potent regulator of cyclic AMP production. The model predicted that less than 40% of adenylyl cyclase molecules may be stimulated under maximal receptor activation, and an experimental protocol is suggested for validating this prediction. The model also predicted that the endogenous heat-stable protein kinase inhibitor may enhance basal cyclic AMP buffering by 68% and increasing the apparent Hill coefficient of protein kinase A activation from 1.0 to 2.0. Finally, phosphorylation of the L-type calcium channel and phospholamban were found sufficient to predict the dominant changes in myocyte contractility, including a 2.6x increase in systolic calcium (inotropy) and a 28% decrease in calcium half-relaxation time (lusitropy). By performing systems analysis, the consequences of molecular perturbations in the beta-adrenergic signaling network may be understood within the context of integrative cellular physiology.

Will genomics revolutionise pharmaceutical R&D?

The successful identification of drug targets requires an understanding of the high-level functional interactions between the key components of cells, organs and systems, and how these interactions change in disease states. This information does not reside in the genome, or in the individual proteins that genes code for, it is to be found at a higher level. Genomics will succeed in revolutionising pharmaceutical research and development only if these interactions are also understood by determining the logic of healthy and diseased states. The rapid growth in biological databases, models of cells, tissues and organs, and in computing power has made it possible to explore functionality all the way from the level of genes to whole organs and systems. Combined with genomic and proteomic data, in silico simulation technology is set to transform all stages of drug discovery and development. The major obstacle to achieving this will be obtaining the relevant experimental data at levels higher than genomics and proteomics.