From the Hodgkin-Huxley axon to the virtual heart

Modeling signaling pathways in biology with MaBoSS: From one single cell to a dynamic population of heterogeneous interacting cells

As a result of the development of experimental technologies and the accumulation of data, biological and molecular processes can be described as complex networks of signaling pathways. These networks are often directed and signed, where nodes represent entities (genes/proteins) and arrows interactions. They are translated into mathematical models by adding a dynamic layer onto them. Such mathematical models help to understand and interpret non-intuitive experimental observations and to anticipate the response to external interventions such as drug effects on phenotypes. Several frameworks for modeling signaling pathways exist. The choice of the appropriate framework is often driven by the experimental context. In this review, we present MaBoSS, a tool based on Boolean modeling using a continuous time approach, which predicts time-dependent probabilities of entities in different biological contexts. MaBoSS was initially built to model the intracellular signaling in non-interacting homogeneous cell populations. MaBoSS was then adapted to model heterogeneous cell populations (EnsembleMaBoSS) by considering families of models rather than a unique model. To account for more complex questions, MaBoSS was extended to simulate dynamical interacting populations (UPMaBoSS), with a precise spatial distribution (PhysiBoSS). To illustrate all these levels of description, we show how each of these tools can be used with a running example of a simple model of cell fate decisions. Finally, we present practical applications to cancer biology and studies of the immune response.

Oxidative Stress Evaluation in Ischemia Reperfusion Models: Characteristics, Limits and Perspectives

Ischemia reperfusion injury is a complex process consisting of a seemingly chaotic but actually organized and compartmentalized shutdown of cell function, of which oxidative stress is a key component. Studying oxidative stress, which results in an imbalance between reactive oxygen species (ROS) production and antioxidant defense activity, is a multi-faceted issue, particularly considering the double function of ROS, assuming roles as physiological intracellular signals and as mediators of cellular component damage. Herein, we propose a comprehensive overview of the tools available to explore oxidative stress, particularly in the study of ischemia reperfusion. Applying chemistry as well as biology, we present the different models currently developed to study oxidative stress, spanning the vitro and the silico, discussing the advantages and the drawbacks of each set-up, including the issues relating to the use of in vitro hypoxia as a surrogate for ischemia. Having identified the limitations of historical models, we shall study new paradigms, including the use of stem cell-derived organoids, as a bridge between the in vitro and the in vivo comprising 3D intercellular interactions in vivo and versatile pathway investigations in vitro. We shall conclude this review by distancing ourselves from "wet" biology and reviewing the in silico, computer-based, mathematical modeling, and numerical simulation options: (a) molecular modeling with quantum chemistry and molecular dynamic algorithms, which facilitates the study of molecule-to-molecule interactions, and the integration of a compound in a dynamic environment (the plasma membrane...); (b) integrative systemic models, which can include many facets of complex mechanisms such as oxidative stress or ischemia reperfusion and help to formulate integrated predictions and to enhance understanding of dynamic interaction between pathways.

Modeling and Analysis of Cardiac Hybrid Cellular Automata via GPU-Accelerated Monte Carlo Simulation

The heart consists of a complex network of billions of cells. Under physiological conditions, cardiac cells propagate electrical signals in space, generating the heartbeat in a synchronous and coordinated manner. When such a synchronization fails, life-threatening events can arise. The inherent complexity of the underlying nonlinear dynamics and the large number of biological components involved make the modeling and the analysis of electrophysiological properties in cardiac tissue still an open challenge. We consider here a Hybrid Cellular Automata (HCA) approach modeling the cardiac cell-cell membrane resistance with a free variable. We show that the modeling approach can reproduce important and complex spatiotemporal properties paving the ground for promising future applications. We show how GPU-based technology can considerably accelerate the simulation and the analysis. Furthermore, we study the cardiac behavior within a unidimensional domain considering inhomogeneous resistance and we perform a Monte Carlo analysis to evaluate our approach.

From digital hype to analogue reality: Universal simulation beyond the quantum and exascale eras

Many believe that the future of innovation lies in simulation. However, as computers are becoming ever more powerful, so does the hyperbole used to discuss their potential in modelling across a vast range of domains, from subatomic physics to chemistry, climate science, epidemiology, economics and cosmology. As we are about to enter the era of quantum and exascale computing, machine learning and artificial intelligence have entered the field in a significant way. In this article we give a brief history of simulation, discuss how machine learning can be more powerful if underpinned by deeper mechanistic understanding, outline the potential of exascale and quantum computing, highlight the limits of digital computing - classical and quantum - and distinguish rhetoric from reality in assessing the future of modelling and simulation, when we believe analogue computing will play an increasingly important role.

Periodic propagating waves coordinate RhoGTPase network dynamics at the leading and trailing edges during cell migration

Migrating cells need to coordinate distinct leading and trailing edge dynamics but the underlying mechanisms are unclear. Here, we combine experiments and mathematical modeling to elaborate the minimal autonomous biochemical machinery necessary and sufficient for this dynamic coordination and cell movement. RhoA activates Rac1 via DIA and inhibits Rac1 via ROCK, while Rac1 inhibits RhoA through PAK. Our data suggest that in motile, polarized cells, RhoA–ROCK interactions prevail at the rear, whereas RhoA-DIA interactions dominate at the front where Rac1/Rho oscillations drive protrusions and retractions. At the rear, high RhoA and low Rac1 activities are maintained until a wave of oscillatory GTPase activities from the cell front reaches the rear, inducing transient GTPase oscillations and RhoA activity spikes. After the rear retracts, the initial GTPase pattern resumes. Our findings show how periodic, propagating GTPase waves coordinate distinct GTPase patterns at the leading and trailing edge dynamics in moving cells.

Mathematical model of the ventricular action potential and effects of isoproterenol-induced cardiac hypertrophy in rats

Mathematical action potential (AP) modeling is a well-established but still-developing area of research to better understand physiological and pathological processes. In particular, changes in AP mechanisms in the isoproterenol (ISO) -induced hypertrophic heart model are incompletely understood. Here we present a mathematical model of the rat AP based on recordings from rat ventricular myocytes. In our model, for the first time, all channel kinetics are defined with a single type of function that is simple and easy to apply. The model AP and channels dynamics are consistent with the APs recorded from rats for both Control (absence of ISO) and ISO-treated cases. Our mathematical model helps us to understand the reason for the prolongation in AP duration after ISO application while ISO treatment helps us to validate our mathematical model. We reveal that the smaller density and the slower gating kinetics of the transient K⁺ current help explain the prolonged AP duration after ISO treatment and the increasing amplitude of the rapid and the slow inward rectifier currents also contribute to this prolongation alongside the flux in Ca²⁺ currents. ISO induced an increase in the density of the Na⁺ current that can explain the faster upstroke. We believe that AP dynamics from rat ventricular myocytes can be reproduced very well with this mathematical model and that it provides a powerful tool for improved insights into the underlying dynamics of clinically important AP properties such as ISO application.

Model based estimation of QT intervals in non-invasive fetal ECG signals

The end timing of T waves in fetal electrocardiogram (fECG) is important for the evaluation of ST and QT intervals which are vital markers to assess cardiac repolarization patterns. Monitoring malignant fetal arrhythmias in utero is fundamental to care in congenital heart anomalies preventing perinatal death. Currently, reliable detection of end of T waves is possible only by using fetal scalp ECG (fsECG) and fetal magnetocardiography (fMCG). fMCG is expensive and less accessible and fsECG is an invasive technique available only during intrapartum period. Another safer and affordable alternative is the non-invasive fECG (nfECG) which can provide similar assessment provided by fsECG and fMECG but with less accuracy (not beat by beat). Detection of T waves using nfECG is challenging because of their low amplitudes and high noise. In this study, a novel model-based method that estimates the end of T waves in nfECG signals is proposed. The repolarization phase has been modeled as the discharging phase of a capacitor. To test the model, fECG signals were collected from 58 pregnant women (age: (34 ± 6) years old) bearing normal and abnormal fetuses with gestational age (GA) 20-41 weeks. QT and QTc intervals have been calculated to test the level of agreement between the model-based and reference values (fsECG and Doppler Ultrasound (DUS) signals) in normal subjects. The results of the test showed high agreement between model-based and reference values (difference < 5%), which implies that the proposed model could be an alternative method to detect the end of T waves in nfECG signals.

Systems Biology, Systems Medicine, Systems Pharmacology: The What and The Why

Systems biology is today such a widespread discipline that it becomes difficult to propose a clear definition of what it really is. For some, it remains restricted to the genomic field. For many, it designates the integrated approach or the corpus of computational methods employed to handle the vast amount of biological or medical data and investigate the complexity of the living. Although defining systems biology might be difficult, on the other hand its purpose is clear: systems biology, with its emerging subfields systems medicine and systems pharmacology, clearly aims at making sense of complex observations/experimental and clinical datasets to improve our understanding of diseases and their treatments without putting aside the context in which they appear and develop. In this short review, we aim to specifically focus on these new subfields with the new theoretical tools and approaches that were developed in the context of cancer. Systems pharmacology and medicine now give hope for major improvements in cancer therapy, making personalized medicine closer to reality. As we will see, the current challenge is to be able to improve the clinical practice according to the paradigm shift of systems sciences.

The Role of Time in the Quest for Understanding Psychological Mechanisms

The lead-lag structure of multivariate time-ordered observations and the possibility to disentangle between-person (BP) from within-person (WP) sources of variance are major assets of longitudinal (panel) data. Hence, psychologists are making increasing use of such data, often with the intent to delineate the dynamic properties of psychological mechanisms, understood as a sequence of causal effects that govern psychological functioning. However, even with longitudinal data, psychological mechanisms are not easily identified. In this article, we show how an adequate representation of time may enhance the tenability of causal interpretations in the context of multivariate longitudinal data analysis. We anchor our considerations with an example that illustrates some of the main problems and questions faced by applied researchers and practitioners. We distinguish between static versus dynamic and discrete versus continuous time modeling approaches and discuss their advantages and disadvantages. We place particular emphasis on different ways of addressing BP differences and stress their dual role as potential confounds versus valuable sources of information for improving estimation and aiding causal inference. We conclude by outlining an approach that offers the potential of better integration of information on BP differences and WP changes in the search for causal mechanisms along with a discussion of current problems and limitations.

Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves

The goal of this review article is to assess how relevant is the concept of dissipative structure for understanding the dynamical bases of non-equilibrium self-organization in biological systems, and to see where it has been applied in the five decades since it was initially proposed by Ilya Prigogine. Dissipative structures can be classified into four types, which will be considered, in turn, and illustrated by biological examples: (i) multistability, in the form of bistability and tristability, which involve the coexistence of two or three stable steady states, or in the form of birhythmicity, which involves the coexistence between two stable rhythms; (ii) temporal dissipative structures in the form of sustained oscillations, illustrated by biological rhythms; (iii) spatial dissipative structures, known as Turing patterns; and (iv) spatio-temporal structures in the form of propagating waves. Rhythms occur with widely different periods at all levels of biological organization, from neural, cardiac and metabolic oscillations to circadian clocks and the cell cycle; they play key roles in physiology and in many disorders. New rhythms are being uncovered while artificial ones are produced by synthetic biology. Rhythms provide the richest source of examples of dissipative structures in biological systems. Bistability has been observed experimentally, but has primarily been investigated in theoretical models in an increasingly wide range of biological contexts, from the genetic to the cell and animal population levels, both in physiological conditions and in disease. Bistable transitions have been implicated in the progression between the different phases of the cell cycle and, more generally, in the process of cell fate specification in the developing embryo. Turing patterns are exemplified by the formation of some periodic structures in the course of development and by skin stripe patterns in animals. Spatio-temporal patterns in the form of propagating waves are observed within cells as well as in intercellular communication. This review illustrates how dissipative structures of all sorts abound in biological systems.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Humans Vary, So Cardiac Models Should Account for That Too!

The utilization of mathematical modeling and simulation in drug development encompasses multiple mathematical techniques and the location of a drug candidate in the development pipeline. Historically speaking they have been used to analyze experimental data (i.e., Hill equation) and clarify the involved physical and chemical processes (i.e., Fick laws and drug molecule diffusion). In recent years the advanced utilization of mathematical modeling has been an important part of the regulatory review process. Physiologically based pharmacokinetic (PBPK) models identify the need to conduct specific clinical studies, suggest specific study designs and propose appropriate labeling language. Their application allows the evaluation of the influence of intrinsic (e.g., age, gender, genetics, disease) and extrinsic [e.g., dosing schedule, drug-drug interactions (DDIs)] factors, alone or in combinations, on drug exposure and therefore provides accurate population assessment. A similar pathway has been taken for the assessment of drug safety with cardiac safety being one the most advanced examples. Mechanistic mathematical model-informed safety evaluation, with a focus on drug potential for causing arrhythmias, is now discussed as an element of the Comprehensive in vitro Proarrhythmia Assay. One of the pillars of this paradigm is the use of an in silico model of the adult human ventricular cardiomyocyte to integrate in vitro measured data. Existing examples (in vitro—in vivo extrapolation with the use of PBPK models) suggest that deterministic, epidemiological and clinical data based variability models can be merged with the mechanistic models describing human physiology. There are other methods available, based on the stochastic approach and on population of models generated by randomly assigning specific parameter values (ionic current conductance and kinetic) and further pruning. Both approaches are briefly characterized in this manuscript, in parallel with the drug-specific variability.

Dissipative structures and biological rhythms

Sustained oscillations abound in biological systems. They occur at all levels of biological organization over a wide range of periods, from a fraction of a second to years, and with a variety of underlying mechanisms. They control major physiological functions, and their dysfunction is associated with a variety of physiological disorders. The goal of this review is (i) to give an overview of the main rhythms observed at the cellular and supracellular levels, (ii) to briefly describe how the study of biological rhythms unfolded in the course of time, in parallel with studies on chemical oscillations, (iii) to present the major roles of biological rhythms in the control of physiological functions, and (iv) the pathologies associated with the alteration, disappearance, or spurious occurrence of biological rhythms. Two tables present the main examples of cellular and supracellular rhythms ordered according to their period, and their role in physiology and pathophysiology. Among the rhythms discussed are neural and cardiac rhythms, metabolic oscillations such as those occurring in glycolysis in yeast, intracellular Ca⁺⁺ oscillations, cyclic AMP oscillations in Dictyostelium amoebae, the segmentation clock that controls somitogenesis, pulsatile hormone secretion, circadian rhythms which occur in all eukaryotes and some bacteria with a period close to 24 h, the oscillatory dynamics of the enzymatic network driving the cell cycle, and oscillations in transcription factors such as NF-ΚB and tumor suppressors such as p53. Ilya Prigogine's concept of dissipative structures applies to temporal oscillations and allows us to unify within a common framework the various rhythms observed at different levels of biological organization, regardless of their period and underlying mechanism.

Computational modeling of inhibition of voltage-gated Ca channels: identification of different effects on uterine and cardiac action potentials

The uterus and heart share the important physiological feature whereby contractile activation of the muscle tissue is regulated by the generation of periodic, spontaneous electrical action potentials (APs). Preterm birth arising from premature uterine contractions is a major complication of pregnancy and there remains a need to pursue avenues of research that facilitate the use of drugs, tocolytics, to limit these inappropriate contractions without deleterious actions on cardiac electrical excitation. A novel approach is to make use of mathematical models of uterine and cardiac APs, which incorporate many ionic currents contributing to the AP forms, and test the cell-specific responses to interventions. We have used three such models-of uterine smooth muscle cells (USMC), cardiac sinoatrial node cells (SAN), and ventricular cells-to investigate the relative effects of reducing two important voltage-gated Ca currents-the L-type (ICaL) and T-type (ICaT) Ca currents. Reduction of ICaL (10%) alone, or ICaT (40%) alone, blunted USMC APs with little effect on ventricular APs and only mild effects on SAN activity. Larger reductions in either current further attenuated the USMC APs but with also greater effects on SAN APs. Encouragingly, a combination of ICaL and ICaT reduction did blunt USMC APs as intended with little detriment to APs of either cardiac cell type. Subsequent overlapping maps of ICaL and ICaT inhibition profiles from each model revealed a range of combined reductions of ICaL and ICaT over which an appreciable diminution of USMC APs could be achieved with no deleterious action on cardiac SAN or ventricular APs. This novel approach illustrates the potential for computational biology to inform us of possible uterine and cardiac cell-specific mechanisms. Incorporating such computational approaches in future studies directed at designing new, or repurposing existing, tocolytics will be beneficial for establishing a desired uterine specificity of action.

Necessity of noise in physiology and medicine

Noise is omnipresent in biomedical systems and signals. Conventional views assume that its presence is detrimental to systems' performance and accuracy. Hence, various analytic approaches and instrumentation have been designed to remove noise. On the contrary, recent contributions have shown that noise can play a beneficial role in biomedical systems. The results of this literature review indicate that noise is an essential part of biomedical systems and often plays a fundamental role in the performance of these systems. Furthermore, in preliminary work, noise has demonstrated therapeutic potential to alleviate the effects of various diseases. Further research into the role of noise and its applications in medicine is likely to lead to novel approaches to the treatment of diseases and prevention of disability.

Characterization and modeling of the peripheral cardiac conduction system

The development of biophysical models of the heart has the potential to get insights in the patho-physiology of the heart, which requires to accurately modeling anatomy and function. The electrical activation sequence of the ventricles depends strongly on the cardiac conduction system (CCS). Its morphology and function cannot be observed in vivo, and therefore data available come from histological studies. We present a review on data available of the peripheral CCS including new experiments. In order to build a realistic model of the CCS we designed a procedure to extract morphological characteristics of the CCS from stained calf tissue samples. A CCS model personalized with our measurements has been built using L-systems. The effect of key unknown parameters of the model in the electrical activation of the left ventricle has been analyzed. The CCS models generated share the main characteristics of observed stained Purkinje networks. The timing of the simulated electrical activation sequences were in the physiological range for CCS models that included enough density of PMJs. These results show that this approach is a potential methodology for collecting knowledge-domain data and build improved CCS models of the heart automatically.

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.

A theory of biological relativity: no privileged level of causation

Must higher level biological processes always be derivable from lower level data and mechanisms, as assumed by the idea that an organism is completely defined by its genome? Or are higher level properties necessarily also causes of lower level behaviour, involving actions and interactions both ways? This article uses modelling of the heart, and its experimental basis, to show that downward causation is necessary and that this form of causation can be represented as the influences of initial and boundary conditions on the solutions of the differential equations used to represent the lower level processes. These insights are then generalized. A priori, there is no privileged level of causation. The relations between this form of 'biological relativity' and forms of relativity in physics are discussed. Biological relativity can be seen as an extension of the relativity principle by avoiding the assumption that there is a privileged scale at which biological functions are determined.

Transmural and apicobasal gradients in repolarization contribute to T-wave genesis in human surface ECG

The cellular basis of the T-wave morphology of surface ECG remains controversial in clinical cardiology. We examined the effect of action potential duration (APD) distribution on T-wave morphology using a realistic model of the human ventricle and torso. We developed a finite-element model of the ventricle consisting of ∼26 million elements, including the conduction system, each implemented with the ion current model of cardiomyocytes. This model was embedded in a torso model with distinct organ structures to obtain the standard ECG leads. The APD distribution was changed in the transmural direction by locating the M cells in either the endocardial or epicardial region. We also introduced apicobasal gradients by modifying the ion channel parameters. Both the transmural gradient (with M cells on the endocardial side) and the apicobasal gradient produced positive T waves, although a very large gradient was required for the apicobasal gradient. By contrast, T waves obtained with the transmural gradient were highly symmetric and, therefore, did not represent the true physiological state. Only combination of the transmural and the moderate apicobasal gradients produced physiological T waves in surface ECG. Positive T waves in surface ECG mainly originated from the transmural distribution of APD with M cells on the endocardial side, although the apicobasal gradient was also required to attain the physiological waveform.

Multiscale modeling for biologists

Biomedical research frequently involves performing experiments and developing hypotheses that link different scales of biological systems such as, for instance, the scales of intracellular molecular interactions to the scale of cellular behavior and beyond to the behavior of cell populations. Computational modeling efforts that aim at exploring such multiscale systems quantitatively with the help of simulations have to incorporate several different simulation techniques because of the different time and space scales involved. Here, we provide a nontechnical overview of how different scales of experimental research can be combined with the appropriate computational modeling techniques. We also show that current modeling software permits building and simulating multiscale models without having to become involved with the underlying technical details of computational modeling.

Differential and integral views of genetics in computational systems biology

This article uses an integrative systems biological view of the relationship between genotypes and phenotypes to clarify some conceptual problems in biological debates about causality. The differential (gene-centric) view is incomplete in a sense analogous to using differentiation without integration in mathematics. Differences in genotype are frequently not reflected in significant differences in phenotype as they are buffered by networks of molecular interactions capable of substituting an alternative pathway to achieve a given phenotype characteristic when one pathway is removed. Those networks integrate the influences of many genes on each phenotype so that the effect of a modification in DNA depends on the context in which it occurs. Mathematical modelling of these interactions can help to understand the mechanisms of buffering and the contextual-dependence of phenotypic outcome, and so to represent correctly and quantitatively the relations between genomes and phenotypes. By incorporating all the causal factors in generating a phenotype, this approach also highlights the role of non-DNA forms of inheritance, and of the interactions at multiple levels.

Environmental causes of cancer: endocrine disruptors as carcinogens

Environmental endocrine disrupting chemicals (EDCs), including pesticides and industrial chemicals, have been and are released into the environment producing deleterious effects on wildlife and humans. The effects observed in animal models after exposure during organogenesis correlate positively with an increased incidence of malformations of the male genital tract and of neoplasms and with the decreased sperm quality observed in European and US populations. Exposure to EDCs generates additional effects, such as alterations in male and female reproduction and changes in neuroendocrinology, behavior, metabolism and obesity, prostate cancer and thyroid and cardiovascular endocrinology. This Review highlights the carcinogenic properties of EDCs, with a special focus on bisphenol A. However, humans and wildlife are exposed to a mixture of EDCs that act contextually. To explain this mindboggling complexity will require the design of novel experimental approaches that integrate the effects of different doses of structurally different chemicals that act at different ages on different target tissues. The key to this complex problem lies in the adoption of mathematical modeling and computer simulations afforded by system biology approaches. Regardless, the data already amassed highlight the need for a public policy to reduce exposure to EDCs.

The use of computer models in pharmaceutical safety evaluation

With the ever increasing volume of data available to scientists in drug discovery and development, the opportunity to leverage an increasing amount of these data in the assessment of drug safety is clear. The challenge in an environment of increasing data volume is in the structuring and the analysis of these data, such that decisions can be made without excluding information or overstating their meaning. Informatics and modelling play a crucial role in addressing this challenge in two basic ways: a) the data are structured and analysed in a transparent and objective way; and b) new experiments are designed with the model as part of the design process, much like modern experimental physics. Enhancing the use and impact of informatics and modelling on drug discovery is not simply a matter of increasing processor speed and memory capacity. The transformation of raw data to usable, and useful, information is a scientific, technical and, perhaps most importantly, cultural challenge within drug discovery. This review will highlight some of the history, current approaches and promising future directions in this rapidly expanding area.

Effects of the purkinje system and cardiac geometry on biventricular pacing: a model study

Heart failure leads to gross cardiac structural changes. While cardiac resynchronization therapy (CRT) is a recognized treatment for restoring synchronous activation, it is not clear how changes in cardiac shape and size affect the electrical pacing therapy. This study used a human heart computer model which incorporated anatomical structures such as myofiber orientation and a Purkinje system (PS) to study how pacing affected failing hearts. The PS was modeled as a tree structure that reproduced its retrograde activation feature. In addition to a normal geometry, two cardiomyopathies were modeled: dilatation and hypertrophy. A biventricular pacing protocol was tested in the context of atrio-ventricular block. The contribution of the PS was examined by removing it, as well as by increasing endocardial conductivity. Results showed that retrograde conduction into the PS was a determining factor for achieving intraventricular synchrony. Omission of the PS led to an overestimate of the degree of electrical dyssynchrony while assessing CRT. The activation patterns for the three geometries showed local changes in the order of activation of the lateral wall in response to the same pacing strategy. These factors should be carefully considered when determining lead placement and optimizing device parameters in clinical practice.

Interpreting endocrine disruption from an integrative biology perspective

The ability of reductionism to advance our understanding of complex biological phenomena is limited. The ecological developmental biology (eco-devo) movement rejects the notion that development is merely the unfolding of a genetic program. Fetal exposure to environmental endocrine disruptors may contribute to the increased incidence of male genital tract malformations, decreased sperm quality, several neoplasms, and altered body weight. Here we discuss problems hindering the study of endocrine disruption (reductionist stance, technically driven research biases, and study of single end points, chemicals and exposure periods). We propose the study of both upward and downward causation and a Systems Biology approach to develop quantitative mathematical models for use in computer simulations that would generate testable predictions. This integrative approach will allow the simultaneous consideration of organismal (systemic) effects and effects on various organ systems. It will promote the identification of similar and unique effects of different endocrine disruptors, and their inter-relationships.

The virtual cell--a candidate co-ordinator for 'middle-out' modelling of biological systems

Understanding the functioning of biological systems depends on tackling complexity spanning spatial scales from genome to organ to whole organism. The basic unit of life, the cell, acts to co-ordinate information received across these scales and processes the myriad of signals to produce an integrated cellular response. Cells interact with and respond to other cells through direct or indirect contact, resulting in emergent structure and function of tissues and organs. Systems biology has traditionally used either a 'top-down' or 'bottom-up' approach. However, neither approach takes account of heterogeneity or 'noise', which is an inherent feature of cellular behaviour and may have significant impact on system level behaviour. We review existing approaches to modelling that use cellular automata or agent-based methodologies, where individual cells are represented as equivalent virtual entities governed by simple rules. These paradigms allow a direct one-to-one mapping between real and virtual cells that can be exploited in terms of acquiring parameters from experimental systems, or for model validation. Such models are inherently extensible and can be integrated with other modelling modalities (e.g. partial or ordinary differential equations) to model multi-scale phenomena. Alternatively, hierarchical agent models may be used to explore the functions of biological systems across temporal and spatial scales. This review examines individual-based models and the application of the paradigm to explore multi-scale phenomena in biology. In so doing, it demonstrates how cellular-based models have begun to play an important role in the development of 'middle-out' models, but with considerable potential for future development.

Computational cardiac atlases: from patient to population and back

Integrative models of cardiac physiology are important for understanding disease and planning intervention. Multimodal cardiovascular imaging plays an important role in defining the computational domain, the boundary/initial conditions, and tissue function and properties. Computational models can then be personalized through information derived from in vivo and, when possible, non-invasive images. Efforts are now established to provide Web-accessible structural and functional atlases of the normal and pathological heart for clinical, research and educational purposes. Efficient and robust statistical representations of cardiac morphology and morphodynamics can thereby be obtained, enabling quantitative analysis of images based on such representations. Statistical models of shape and appearance can be built automatically from large populations of image datasets by minimizing manual intervention and data collection. These methods facilitate statistical analysis of regional heart shape and wall motion characteristics across population groups, via the application of parametric mathematical modelling tools. These parametric modelling tools and associated ontological schema also facilitate data fusion between different imaging protocols and modalities as well as other data sources. Statistical priors can also be used to support cardiac image analysis with applications to advanced quantification and subject-specific simulations of computational physiology.

Modeling K(ATP) channel gating and its regulation

ATP-sensitive potassium (K(ATP)) channels couple cell metabolism to plasmalemmal potassium fluxes in a variety of cell types. The activity of these channels is primarily determined by intracellular adenosine nucleotides, which have both inhibitory and stimulatory effects. The role of K(ATP) channels has been studied most extensively in pancreatic beta-cells, where they link glucose metabolism to insulin secretion. Many mutations in K(ATP) channel subunits (Kir6.2, SUR1) have been identified that cause either neonatal diabetes or congenital hyperinsulinism. Thus, a mechanistic understanding of K(ATP) channel behavior is necessary for modeling beta-cell electrical activity and insulin release in both health and disease. Here, we review recent advances in the K(ATP) channel structure and function. We focus on the molecular mechanisms of K(ATP) channel gating by adenosine nucleotides, phospholipids and sulphonylureas and consider the advantages and limitations of various mathematical models of macroscopic and single-channel K(ATP) currents. Finally, we outline future directions for the development of more realistic models of K(ATP) channel gating.

Late sodium current in failing heart: friend or foe?

Most cardiac Na+ channels open transiently upon membrane depolarization and then are quickly inactivated. However, some channels remain active, carrying the so-called persistent or late Na+ current (INaL) throughout the action potential (AP) plateau. Experimental data and the results of numerical modeling accumulated over the past decade show the emerging importance of this late current component for the function of both normal and failing myocardium. INaL is produced by special gating modes of the cardiac-specific Na+ channel isoform. Heart failure (HF) slows channel gating and increases INaL, but HF-specific Na+ channel isoform underlying these changes has not been found. Na+ channels represent a multi-protein complex and its activity is determined not only by the pore-forming alpha subunit but also by its auxiliary beta subunits, cytoskeleton, calmodulin, regulatory kinases and phosphatases, and trafficking proteins. Disruption of the integrity of this protein complex may lead to alterations of INaL in pathological conditions. Increased INaL and the corresponding Na+ flux in failing myocardium contribute to abnormal repolarization and an increased cell Ca2+ load. Interventions designed to correct INaL rescue normal repolarization and improve Ca2+ handling and contractility of the failing cardiomyocytes. This review considers (1) quantitative integration of INaL into the established electrophysiological and Ca2+ regulatory mechanisms in normal and failing cardiomyocytes and (2) a new therapeutic strategy utilizing a selective inhibition of INaL to target both arrhythmias and impaired contractility in HF.