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There is an inherent tension in Quantitative Systems Pharmacology (QSP) between the need to incorporate mathematical descriptions of complex physiology and drug targets with the necessity of developing robust, predictive and well-constrained models. In addition to this, there is no "gold standard" for model development and assessment in QSP. Moreover, there can be confusion over terminology such as model and parameter identifiability; complex and simple models; virtual populations; and other concepts, which leads to potential miscommunication and misapplication of methodologies within modeling communities, both the QSP community and related disciplines. This perspective article highlights the pros and cons of using simple (often identifiable) vs. complex (more physiologically detailed but often non-identifiable) models, as well as aspects of parameter identifiability, sensitivity and inference methodologies for model development and analysis. The paper distills the central themes of the issue of identifiability and optimal model size and discusses open challenges., (© 2022. The Author(s).)

On the tenth anniversary of two key International Conference on Harmonisation (ICH) guidelines relating to cardiac proarrhythmic safety, an initiative aims to consider the implementation of a new paradigm that combines in vitro and in silico technologies to improve risk assessment. The Comprehensive In Vitro Proarrhythmia Assay (CiPA) initiative (co-sponsored by the Cardiac Safety Research Consortium, Health and Environmental Sciences Institute, Safety Pharmacology Society and FDA) is a bold and welcome step in using computational tools for regulatory decision making. This review compares and contrasts the state-of-the-art tools from empirical to mechanistic models of cardiac electrophysiology, and how they can and should be used in combination with experimental tests for compound decision making., (Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Experimental results in epigenetics and related fields of biological research show that the Modern Synthesis (neo-Darwinist) theory of evolution requires either extension or replacement. This article examines the conceptual framework of neo-Darwinism, including the concepts of 'gene', 'selfish', 'code', 'program', 'blueprint', 'book of life', 'replicator' and 'vehicle'. This form of representation is a barrier to extending or replacing existing theory as it confuses conceptual and empirical matters. These need to be clearly distinguished. In the case of the central concept of 'gene', the definition has moved all the way from describing a necessary cause (defined in terms of the inheritable phenotype itself) to an empirically testable hypothesis (in terms of causation by DNA sequences). Neo-Darwinism also privileges 'genes' in causation, whereas in multi-way networks of interactions there can be no privileged cause. An alternative conceptual framework is proposed that avoids these problems, and which is more favourable to an integrated systems view of evolution., (© 2015. Published by The Company of Biologists Ltd.)

The history of the constitution perspective in medical care dates back thousands of years and extends from the East to the West. Among the various forms of constitutional medicine, Sasang constitutional medicine (SCM) is a holistic, tailored medical approach that is based on a well-structured theoretical system that includes physiopathological disciplines. Scientific evidence has demonstrated that SCM typology has a constitution-specific basis in anthropometrics, physiological characteristics, disease vulnerability, and genetic origins. Furthermore, the recent rise of systems biology, which requires whole body modeling, uses a state-of-the-art approach in interpreting the holistic spirit of Oriental medicine. This article aims to provide an overview of the recent achievements in SCM research and to discuss how the concept of balance in SCM may contribute to the development of large scale modeling in systems biology., (Copyright © 2014. Published by Elsevier Ltd.)

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.

The use of mathematical models to study cardiac electrophysiology has a long history, and numerous cellular scale models are now available, covering a range of species and cell types. Their use to study emergent properties in tissue is also widespread, typically using the monodomain or bidomain equations coupled to one or more cell models. Despite the relative maturity of this field, little has been written looking in detail at the interface between the cellular and tissue-level models. Mathematically this is relatively straightforward and well-defined. There are however many details and potential inconsistencies that need to be addressed, in order to ensure correct operation of a cellular model within a tissue simulation. This paper will describe these issues and how to address them. Simply having models available in a common format such as CellML is still of limited utility, with significant manual effort being required to integrate these models within a tissue simulation. We will thus also discuss the facilities available for automating this in a consistent fashion within Chaste, our robust and high-performance cardiac electrophysiology simulator. It will be seen that a common theme arising is the need to go beyond a representation of the model mathematics in a standard language, to include additional semantic information required in determining the model's interface, and hence to enhance interoperability. Such information can be added as metadata, but agreement is needed on the terms to use, including development of appropriate ontologies, if reliable automated use of CellML models is to become common., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Cardiovascular disease, and the cardiovascular side effects of drugs, are essentially multifactorial problems involving interactions between many proteins, dependent on highly organized cell, tissue and organ structures. This is one reason why the side effects of drugs are often unanticipated. It is impossible to unravel such problems without using a systems approach, i.e. focussing on processes, not just molecular components. This inevitably involves modelling as the interactions require quantitative analysis. Modelling is a tool of analysis aimed at understanding, first, and predicting, eventually. We illustrate these principles using modelling of the heart. Models of the cardiac myocyte have benefited from several decades of interaction between experimentation and simulation. They are now sufficiently detailed to have been of use in the development of new drug compounds like ranolazine and ivabradine. With the help of cardiac modelling, we have also been able to unravel the mechanisms underlying the beneficial effect of sodium calcium exchange block for long QT syndrome (LQTS) 2 and LQTS3 patients. Detailed models of the interaction between ion channels and blocking agents provide the basis for modelling drug action from basic principles and predict changes in the inhomogeneous tissue of the heart. We demonstrate that mathematical models are beneficial for unravelling the complex interactions of pharmacodynamics in the heart. Embedding these detailed biophysical cellular scale models into anatomically correct models of the ventricle geometry will enable reconstructions of Torsades de Pointes arrhythmias and of fibrillation, providing a mechanism for linking detailed cellular scale experimental data to clinical applications.

Markov models (MMs) represent a generalization of Hodgkin-Huxley models. They provide a versatile structure for modelling single channel data, gating currents, state-dependent drug interaction data, exchanger and pump dynamics, etc. This paper uses examples from cardiac electrophysiology to discuss aspects related to parameter estimation. (i) Parameter unidentifiability (found in 9 out of 13 of the considered models) results in an inability to determine the correct layout of a model, contradicting the idea that model structure and parameters provide insights into underlying molecular processes. (ii) The information content of experimental voltage step clamp data is discussed, and a short but sufficient protocol for parameter estimation is presented. (iii) MMs have been associated with high computational cost (owing to their large number of state variables), presenting an obstacle for multicellular whole organ simulations as well as parameter estimation. It is shown that the stiffness of models increases computation time more than the number of states. (iv) Algorithms and software programs are provided for steady-state analysis, analytical solutions for voltage steps and numerical derivation of parameter identifiability. The results provide a new standard for ion channel modelling to further the automation of model development, the validation process and the predictive power of these models.

Early development of ionic models for cardiac myocytes, from the pioneering modification of the Hodgkin-Huxley giant squid axon model by Noble to the iconic DiFrancesco-Noble model integrating voltage-gated ionic currents, ion pumps and exchangers, Ca(2+) sequestration and Ca(2+)-induced Ca(2+) release, provided a general description for a mammalian Purkinje fibre (PF) and the framework for modern cardiac models. In the past two decades, development has focused on tissue-specific models with an emphasis on the sino-atrial (SA) node, atria and ventricles, while the PFs have largely been neglected. However, achieving the ultimate goal of creating a virtual human heart will require detailed models of all distinctive regions of the cardiac conduction system, including the PFs, which play an important role in conducting cardiac excitation and ensuring the synchronized timing and sequencing of ventricular contraction. In this paper, we present details of our newly developed model for the human PF cell including validation against experimental data. Ionic mechanisms underlying the heterogeneity between the PF and ventricular action potentials in humans and other species are analysed. The newly developed PF cell model adds a new member to the family of human cardiac cell models developed previously for the SA node, atrial and ventricular cells, which can be incorporated into an anatomical model of the human heart with details of its electrophysiological heterogeneity and anatomical complexity.

Myocardial ischemia is one of the main causes of sudden cardiac death, with 80% of victims suffering from coronary heart disease. In acute myocardial ischemia, the obstruction of coronary flow leads to the interruption of oxygen flow, glucose, and washout in the affected tissue. Cellular metabolism is impaired and severe electrophysiological changes in ionic currents and concentrations ensue, which favor the development of lethal cardiac arrhythmias such as ventricular fibrillation. Due to the burden imposed by ischemia in our societies, a large body of research has attempted to unravel the mechanisms of initiation, sustenance, and termination of cardiac arrhythmias in acute ischemia, but the rapidity and complexity of ischemia-induced changes as well as the limitations in current experimental techniques have hampered evaluation of ischemia-induced alterations in cardiac electrical activity and understanding of the underlying mechanisms. Over the last decade, computer simulations have demonstrated the ability to provide insight, with high spatiotemporal resolution, into ischemic abnormalities in cardiac electrophysiological behavior from the ionic channel to the whole organ. This article aims to review and summarize the results of these studies and to emphasize the role of computer simulations in improving the understanding of ischemia-related arrhythmias and how to efficiently terminate them.

Airway myocytes are the primary effectors of airway reactivity which modulates airway resistance and hence ventilation. Stimulation of airway myocytes results in an increase in the cytosolic Ca(2+) concentration ([Ca(2+)](i)) and the subsequent activation of the contractile apparatus. Many contractile agonists, including acetylcholine, induce [Ca(2+)](i) increase via Ca(2+) release from the sarcoplasmic reticulum through InsP(3) receptors. Several models have been developed to explain the characteristics of InsP(3)-induced [Ca(2+)](i) responses, in particular Ca(2+) oscillations. The article reviews the modelling of the major structures implicated in intracellular Ca(2+) handling, i.e., InsP(3) receptors, SERCAs, mitochondria and Ca(2+)-binding cytosolic proteins. We developed theoretical models specifically dedicated to the airway myocyte which include the major mechanisms responsible for intracellular Ca(2+) handling identified in these cells. These biocomputations pointed out the importance of the relative proportion of InsP(3) receptor isoforms and the respective role of the different mechanisms responsible for cytosolic Ca(2+) clearance in the pattern of [Ca(2+)](i) variations. We have developed a theoretical model of membrane conductances that predicts the variations in membrane potential and extracellular Ca(2+) influx. Stimulation of this model by simulated increase in [Ca(2+)](i) predicts membrane depolarisation, but not great enough to trigger a significant opening of voltage-dependant Ca(2+) channels. This may explain why airway contraction induced by cholinergic stimulation does not greatly depend on extracellular calcium. The development of such models of airway myocytes is important for the understanding of the cellular mechanisms of airway reactivity and their possible modulation by pharmacological agents.

In airway myocytes signal transduction via cytosolic calcium plays an important role. In relation with experimental results we review models of basic molecular and cellular mechanisms involved in the signal transduction from the myocyte stimulation to the activation of the contractile apparatus. We concentrate on mechanisms for encoding of input signals into Ca2+ signals and the mechanisms for their decoding. The mechanisms are arranged into a general scheme of cellular signaling, the so-called bow-tie architecture of signaling, in which calcium plays the role of a common media for cellular signals and links the encoding and decoding part. The encoding of calcium signals in airway myocytes is better known and is presented in more detail. In particular, we focus on three recent models taking into account the intracellular calcium handling and ion fluxes through the plasma membrane. The model of membrane conductances was originally proposed for predicting membrane depolarization and voltage-dependent Ca2+ influx triggered by initial cytosolic Ca2+ increase as observed on cholinergic stimulation. Cellular models of intracellular Ca2+ handling were developed to investigate the role of a mixed population of InsP3 receptor isoforms and the cellular environment in the occurrence of Ca2+ oscillations, and the respective role of the sarcoplasmic reticulum, mitochondria, and cytosolic Ca2+-binding proteins in cytosolic Ca2+ clearance. Modeling the mechanisms responsible for the decoding of calcium signals is developed in a lesser extent; however, the most recent theoretical studies are briefly presented in relation with the known experimental results.

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.

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.

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.

The Physiome Project of the International Union of Physiological Sciences (IUPS) is attempting to provide a comprehensive framework for modelling the human body using computational methods which can incorporate the biochemistry, biophysics and anatomy of cells, tissues and organs. A major goal of the project is to use computational modelling to analyse integrative biological function in terms of underlying structure and molecular mechanisms. To support that goal the project is establishing web-accessible physiological databases dealing with model-related data, including bibliographic information, at the cell, tissue, organ and organ system levels. Here we discuss the background and goals of the project, the problems of modelling across multiple spatial and temporal scales, and the development of model ontologies and markup languages at all levels of biological function.

Introduction: The ionic basis underlying the negative chronotropic effect of acetylcholine (ACh) on sinoatrial (SA) node cells is unresolved and controversial. In the present study, mathematical modeling was used to address this issue., Methods and Results: The known concentration-dependent effects of ACh on iK,ACh, iCa,L, and i(f) were introduced into models of rabbit central and peripheral SA node cells. In the central and peripheral models, 9 x 10(-8) and 14 x 10(-8) M ACh, respectively, caused a 50% decrease in pacemaking rate, whereas in rabbit SA node to approximately 7.4 x 10(-8) M ACh caused such a decrease. In the models, iK,ACh was primarily responsible for the decrease and actions of ACh on iCa,L or i(f) alone caused a negligible effect. Although the inhibition of i(f) did not directly contribute to the chronotropic effect, it was indirectly important, because it minimized the opposition by i(f ) to the decrease of rate caused by activation of iK,ACh. The central model was more sensitive to ACh than the peripheral model., Conclusion: The chronotropic effect of ACh is principally the result of activation of iK,ACh, and inhibition of iCa,L plays little or no role. Inhibition of i(f) and possible inhibition of ib,Na play an important facilitative role by reducing the ability of i(f) and ib,Na to curtail the chronotropic effect caused by activation of iK,ACh.