Multiscale modeling of cardiac cellular energetics

Analysis of Pattern Formation by Colored Petri Nets With Quantitative Regulation of Gene Expression Level

Modeling and simulation are becoming indispensable tools for studying multicellular events such as pattern formation during embryonic development. In this paper, we propose a new approach for analyzing multicellular biological phenomena by combining colored hybrid Petri nets (ColHPNs) with newly devised biological experiments that can control level of a gene quantitatively. With this approach, we analyzed patterning of the boundary cells in the Drosophila large intestine, where one-cell-wide domain of boundary cells differentiate through Delta-Notch signaling. Biological experiments regulating the level of Delta resulted in six distinct patterns of boundary cells correlating with the level of Delta. All these patterns were successfully reproduced by simulation based on ColHPN modeling only by changing the parameter related to the level of Delta. By monitoring the concentration of the active form of Notch in each cell during simulation, it was revealed that these distinct modes of patterning correlate with the fluctuation range of active Notch. Combination of simulation and quantitative manipulation of a gene activity described here is a reliable and powerful approach for analyzing and understanding the patterning process regulated by Notch signaling. This approach can be easily adapted to address other similar pattern formation issues in the systems biology area.

Multiscale modelling in immunology: a review

One of the greatest challenges in biomedicine is to get a unified view of observations made from the molecular up to the organism scale. Towards this goal, multiscale models have been highly instrumental in contexts such as the cardiovascular field, angiogenesis, neurosciences and tumour biology. More recently, such models are becoming an increasingly important resource to address immunological questions as well. Systematic mining of the literature in multiscale modelling led us to identify three main fields of immunological applications: host-virus interactions, inflammatory diseases and their treatment and development of multiscale simulation platforms for immunological research and for educational purposes. Here, we review the current developments in these directions, which illustrate that multiscale models can consistently integrate immunological data generated at several scales, and can be used to describe and optimize therapeutic treatments of complex immune diseases.

Systems approaches in integrative cardiac biology: illustrations from cardiac heterocellular signalling studies

Understanding the complexity of cardiac physiology requires system-level studies of multiple cardiac cell types. Frequently, however, the end result of published research lacks the detail of the collaborative and integrative experimental design process, and the underlying conceptual framework. We review the recent progress in systems modelling and omics analysis of the heterocellular heart environment through complementary forward and inverse approaches, illustrating these conceptual and experimental frameworks with case studies from our own research program. The forward approach begins by collecting curated information from the niche cardiac biology literature, and connecting the dots to form mechanistic network models that generate testable system-level predictions. The inverse approach starts from the vast pool of public omics data in recent cardiac biological research, and applies bioinformatics analysis to produce novel candidates for further investigation. We also discuss the possibility of combining these two approaches into a hybrid framework, together with the benefits and challenges. These interdisciplinary research frameworks illustrate the interplay between computational models, omics analysis, and wet lab experiments, which holds the key to making real progress in improving human cardiac wellbeing.

Modeling biology spanning different scales: an open challenge

It is coming nowadays more clear that in order to obtain a unified description of the different mechanisms governing the behavior and causality relations among the various parts of a living system, the development of comprehensive computational and mathematical models at different space and time scales is required. This is one of the most formidable challenges of modern biology characterized by the availability of huge amount of high throughput measurements. In this paper we draw attention to the importance of multiscale modeling in the framework of studies of biological systems in general and of the immune system in particular.

JSim, an open-source modeling system for data analysis

JSim is a simulation system for developing models, designing experiments, and evaluating hypotheses on physiological and pharmacological systems through the testing of model solutions against data. It is designed for interactive, iterative manipulation of the model code, handling of multiple data sets and parameter sets, and for making comparisons among different models running simultaneously or separately. Interactive use is supported by a large collection of graphical user interfaces for model writing and compilation diagnostics, defining input functions, model runs, selection of algorithms solving ordinary and partial differential equations, run-time multidimensional graphics, parameter optimization (8 methods), sensitivity analysis, and Monte Carlo simulation for defining confidence ranges. JSim uses Mathematical Modeling Language (MML) a declarative syntax specifying algebraic and differential equations. Imperative constructs written in other languages (MATLAB, FORTRAN, C++, etc.) are accessed through procedure calls. MML syntax is simple, basically defining the parameters and variables, then writing the equations in a straightforward, easily read and understood mathematical form. This makes JSim good for teaching modeling as well as for model analysis for research.   For high throughput applications, JSim can be run as a batch job.  JSim can automatically translate models from the repositories for Systems Biology Markup Language (SBML) and CellML models. Stochastic modeling is supported. MML supports assigning physical units to constants and variables and automates checking dimensional balance as the first step in verification testing. Automatic unit scaling follows, e.g. seconds to minutes, if needed. The JSim Project File sets a standard for reproducible modeling analysis: it includes in one file everything for analyzing a set of experiments: the data, the models, the data fitting, and evaluation of parameter confidence ranges. JSim is open source; it and about 400 human readable open source physiological/biophysical models are available at http://www.physiome.org/jsim/.

Graphical approach to model reduction for nonlinear biochemical networks

Model reduction is a central challenge to the development and analysis of multiscale physiology models. Advances in model reduction are needed not only for computational feasibility but also for obtaining conceptual insights from complex systems. Here, we introduce an intuitive graphical approach to model reduction based on phase plane analysis. Timescale separation is identified by the degree of hysteresis observed in phase-loops, which guides a “concentration-clamp” procedure for estimating explicit algebraic relationships between species equilibrating on fast timescales. The primary advantages of this approach over Jacobian-based timescale decomposition are that: 1) it incorporates nonlinear system dynamics, and 2) it can be easily visualized, even directly from experimental data. We tested this graphical model reduction approach using a 25-variable model of cardiac β₁-adrenergic signaling, obtaining 6- and 4-variable reduced models that retain good predictive capabilities even in response to new perturbations. These 6 signaling species appear to be optimal “kinetic biomarkers” of the overall β₁-adrenergic pathway. The 6-variable reduced model is well suited for integration into multiscale models of heart function, and more generally, this graphical model reduction approach is readily applicable to a variety of other complex biological systems.

Multi-scale modeling in biology: how to bridge the gaps between scales?

Human physiological functions are regulated across many orders of magnitude in space and time. Integrating the information and dynamics from one scale to another is critical for the understanding of human physiology and the treatment of diseases. Multi-scale modeling, as a computational approach, has been widely adopted by researchers in computational and systems biology. A key unsolved issue is how to represent appropriately the dynamical behaviors of a high-dimensional model of a lower scale by a low-dimensional model of a higher scale, so that it can be used to investigate complex dynamical behaviors at even higher scales of integration. In the article, we first review the widely-used different modeling methodologies and their applications at different scales. We then discuss the gaps between different modeling methodologies and between scales, and discuss potential methods for bridging the gaps between scales.

CytoSolve: A Scalable Computational Method for Dynamic Integration of Multiple Molecular Pathway Models

A grand challenge of computational systems biology is to create a molecular pathway model of the whole cell. Current approaches involve merging smaller molecular pathway models’ source codes to create a large monolithic model (computer program) that runs on a single computer. Such a larger model is difficult, if not impossible, to maintain given ongoing updates to the source codes of the smaller models. This paper describes a new system called CytoSolve that dynamically integrates computations of smaller models that can run in parallel across different machines without the need to merge the source codes of the individual models. This approach is demonstrated on the classic Epidermal Growth Factor Receptor (EGFR) model of Kholodenko. The EGFR model is split into four smaller models and each smaller model is distributed on a different machine. Results from four smaller models are dynamically integrated to generate identical results to the monolithic EGFR model running on a single machine. The overhead for parallel and dynamic computation is approximately twice that of a monolithic model running on a single machine. The CytoSolve approach provides a scalable method since smaller models may reside on any computer worldwide, where the source code of each model can be independently maintained and updated.

Multiscale models of angiogenesis

Vascular disease, cancer, stroke, neurodegeneration, diabetes, inflammation, asthma, obesity, arthritis--the list of conditions that involve angiogenesis reads like main chapters in a book on pathology. Angiogenesis, the growth of capillaries from preexisting vessels, also occurs in normal physiology, in response to exercise or in the process of wound healing.Why and when is angiogenesis prevalent? What controls the process? How can we intelligently control it? These are the key questions driving researchers in fields as diverse as cell biology, oncology, cardiology, neurology, biomathematics, systems biology, and biomedical engineering. As bioengineers, we approach angiogenesis as a complex, interconnected system of events occurring in sequence and in parallel, on multiple levels, triggered by a main stimulus, e.g., hypoxia.

Multi-scale computational modelling in biology and physiology

Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of biology. One of the main aims of systems biology is to couple these together to produce integrated models across multiple spatial scales and physical processes. In this review, we formulate a definition of multi-scale in terms of levels of biological organisation and describe the types of model that are found at each level. Key issues that arise in trying to formulate and solve multi-scale and multi-physics models are considered and examples of how these issues have been addressed are given for two of the more mature fields in computational biology: the molecular dynamics of ion channels and cardiac modelling. As even more complex models are developed over the coming few years, it will be necessary to develop new methods to model them (in particular in coupling across the interface between stochastic and deterministic processes) and new techniques will be required to compute their solutions efficiently on massively parallel computers. We outline how we envisage these developments occurring.

The challenge of cardiac modeling--interaction and integration

The goal of clinical cardiology is to obtain an integrated picture of the interacting parameters of muscle and vessel mechanics, blood circulation and myocardial perfusion, oxygen consumption and energy metabolism, and electrical activation and heart rate, thus relating to the true physiological and pathophysiological characteristics of the heart. Scientific insight into the cardiac physiology and performance is achieved by utilizing life sciences, for example, molecular biology, genetics and related intra- and intercellular phenomena, as well as the exact sciences, for example, mathematics, computer science, and related imaging and visualization techniques. The tools to achieve these goals are based on the intimate interactions between engineering science and medicine and the developments of modern, medically oriented technology. Most significant is the beneficiary effect of the globalization of science, the Internet, and the unprecedented international interaction and scientific cooperation in facing difficult multidisciplined challenges. This meeting aims to explore some important interactions in the cardiac system and relate to the integration of spatial and temporal interacting system parameters, so as to gain better insight into the structure and function of the cardiac system, thus leading to better therapeutic modalities.

Toward a multiscale model of antigen presentation in immunity

A functioning immune system and the process of antigen presentation in particular encompass events that occur at multiple length and time scales. Despite a wealth of information in the biological literature regarding each of these scales, no single representation synthesizing this information into a model of the overall immune response as it depends on antigen presentation is available. In this article, we outline an approach for integrating information over relevant biological and temporal scales to generate such a representation for major histocompatibility complex class II-mediated antigen presentation. In addition, we begin to address how such models can be used to answer questions about mechanisms of infection and new strategies for treatment and vaccines.

Integration of calcium with the signaling network in cardiac myocytes

Calcium has evolved as global intracellular messenger for signal transduction in the millisecond time range by reversibly binding to calcium-sensing proteins. In the cardiomyocyte, ion pumps, ion exchangers and channels keep the cytoplasmic calcium level at rest around approximately 100 nM which is more than 10,000-fold lower than outside the cell. Intracellularly, calcium is mainly stored in the sarcoplasmic reticulum, which comprises the bulk of calcium available for the heartbeat. Regulation of cardiac function including contractility and energy production relies on a three-tiered control system, (i) immediate and fast feedback in response to mechanical load on a beat-to-beat basis (Frank-Starling relation), (ii) more sustained regulation involving transmitters and hormones as primary messengers, and (iii) long-term adaptation by changes in the gene expression profile. Calcium signaling over largely different time scales requires its integration with the protein kinase signaling network which is governed by G-protein-coupled receptors, growth factor and cytokine receptors at the surface membrane. Short-term regulation is dominated by the beta-adrenergic system, while long-term regulation with phenotypic remodeling depends on sustained signaling by growth factors, cytokines and calcium. Mechanisms and new developments in intracellular calcium handling and its interrelation with the MAPK signaling pathways are discussed in detail.