E-CELL: software environment for whole-cell simulation

Computational Systems Biology in Cancer: Modeling Methods and Applications

In recent years it has become clear that carcinogenesis is a complex process, both at the molecular and cellular levels. Understanding the origins, growth and spread of cancer, therefore requires an integrated or system-wide approach. Computational systems biology is an emerging sub-discipline in systems biology that utilizes the wealth of data from genomic, proteomic and metabolomic studies to build computer simulations of intra and intercellular processes. Several useful descriptive and predictive models of the origin, growth and spread of cancers have been developed in an effort to better understand the disease and potential therapeutic approaches. In this review we describe and assess the practical and theoretical underpinnings of commonly-used modeling approaches, including ordinary and partial differential equations, petri nets, cellular automata, agent based models and hybrid systems. A number of computer-based formalisms have been implemented to improve the accessibility of the various approaches to researchers whose primary interest lies outside of model development. We discuss several of these and describe how they have led to novel insights into tumor genesis, growth, apoptosis, vascularization and therapy.

A blueprint for human whole-cell modeling

Whole-cell dynamical models of human cells are a central goal of systems biology. Such models could help researchers understand cell biology and help physicians treat disease. Despite significant challenges, we believe that human whole-cell models are rapidly becoming feasible. To develop a plan for achieving human whole-cell models, we analyzed the existing models of individual cellular pathways, surveyed the biomodeling community, and reflected on our experience developing whole-cell models of bacteria. Based on these analyses, we propose a plan for a project, termed the Human Whole-Cell Modeling Project, to achieve human whole-cell models. The foundations of the plan include technology development, standards development, and interdisciplinary collaboration.

Mathematical modelling of microbes: metabolism, gene expression and growth

The growth of microorganisms involves the conversion of nutrients in the environment into biomass, mostly proteins and other macromolecules. This conversion is accomplished by networks of biochemical reactions cutting across cellular functions, such as metabolism, gene expression, transport and signalling. Mathematical modelling is a powerful tool for gaining an understanding of the functioning of this large and complex system and the role played by individual constituents and mechanisms. This requires models of microbial growth that provide an integrated view of the reaction networks and bridge the scale from individual reactions to the growth of a population. In this review, we derive a general framework for the kinetic modelling of microbial growth from basic hypotheses about the underlying reaction systems. Moreover, we show that several families of approximate models presented in the literature, notably flux balance models and coarse-grained whole-cell models, can be derived with the help of additional simplifying hypotheses. This perspective clearly brings out how apparently quite different modelling approaches are related on a deeper level, and suggests directions for further research.

Quantitative computational models of molecular self-assembly in systems biology

Molecular self-assembly is the dominant form of chemical reaction in living systems, yet efforts at systems biology modeling are only beginning to appreciate the need for and challenges to accurate quantitative modeling of self-assembly. Self-assembly reactions are essential to nearly every important process in cell and molecular biology and handling them is thus a necessary step in building comprehensive models of complex cellular systems. They present exceptional challenges, however, to standard methods for simulating complex systems. While the general systems biology world is just beginning to deal with these challenges, there is an extensive literature dealing with them for more specialized self-assembly modeling. This review will examine the challenges of self-assembly modeling, nascent efforts to deal with these challenges in the systems modeling community, and some of the solutions offered in prior work on self-assembly specifically. The review concludes with some consideration of the likely role of self-assembly in the future of complex biological system models more generally.

Master equations and the theory of stochastic path integrals

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Excluded volume effects in on- and off-lattice reaction-diffusion models

Mathematical models are important tools to study the excluded volume effects on reaction-diffusion systems, which are known to play an important role inside living cells. Detailed microscopic simulations with off-lattice Brownian dynamics become computationally expensive in crowded environments. In this study, the authors therefore investigate to which extent on-lattice approximations, the so-called cellular automata models, can be used to simulate reactions and diffusion in the presence of crowding molecules. They show that the diffusion is most severely slowed down in the off-lattice model, since randomly distributed obstacles effectively exclude more volume than those ordered on an artificial grid. Crowded reaction rates can be both increased and decreased by the grid structure and it proves important to model the molecules with realistic sizes when excluded volume is taken into account. The grid artefacts increase with increasing crowder density and they conclude that the computationally more efficient on-lattice simulations are accurate approximations only for low crowder densities.

Systems Biology of Metabolism

Metabolism is highly complex and involves thousands of different connected reactions; it is therefore necessary to use mathematical models for holistic studies. The use of mathematical models in biology is referred to as systems biology. In this review, the principles of systems biology are described, and two different types of mathematical models used for studying metabolism are discussed: kinetic models and genome-scale metabolic models. The use of different omics technologies, including transcriptomics, proteomics, metabolomics, and fluxomics, for studying metabolism is presented. Finally, the application of systems biology for analyzing global regulatory structures, engineering the metabolism of cell factories, and analyzing human diseases is discussed.

Parallelization and High-Performance Computing Enables Automated Statistical Inference of Multi-scale Models

Mechanistic understanding of multi-scale biological processes, such as cell proliferation in a changing biological tissue, is readily facilitated by computational models. While tools exist to construct and simulate multi-scale models, the statistical inference of the unknown model parameters remains an open problem. Here, we present and benchmark a parallel approximate Bayesian computation sequential Monte Carlo (pABC SMC) algorithm, tailored for high-performance computing clusters. pABC SMC is fully automated and returns reliable parameter estimates and confidence intervals. By running the pABC SMC algorithm for ∼10⁶ hr, we parameterize multi-scale models that accurately describe quantitative growth curves and histological data obtained in vivo from individual tumor spheroid growth in media droplets. The models capture the hybrid deterministic-stochastic behaviors of 10⁵-10⁶ of cells growing in a 3D dynamically changing nutrient environment. The pABC SMC algorithm reliably converges to a consistent set of parameters. Our study demonstrates a proof of principle for robust, data-driven modeling of multi-scale biological systems and the feasibility of multi-scale model parameterization through statistical inference.

Simulation of diffusion using a modular cell dynamic simulation system

A variety of mathematical models is used to describe and simulate the multitude of natural processes examined in life sciences. In this paper we present a scalable and adjustable foundation for the simulation of natural systems. Based on neighborhood relations in graphs and the complex interactions in cellular automata, the model uses recurrence relations to simulate changes on a mesoscopic scale. This implicit definition allows for the manipulation of every aspect of the model even during simulation. The definition of value rules ω facilitates the accumulation of change during time steps. Those changes may result from different physical, chemical or biological phenomena. Value rules can be combined into modules, which in turn can be used to create baseline models. Exemplarily, a value rule for the diffusion of chemical substances was designed and its applicability is demonstrated. Finally, the stability and accuracy of the solutions is analyzed.

Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist

We present StochSS: Stochastic Simulation as a Service, an integrated development environment for modeling and simulation of both deterministic and discrete stochastic biochemical systems in up to three dimensions. An easy to use graphical user interface enables researchers to quickly develop and simulate a biological model on a desktop or laptop, which can then be expanded to incorporate increasing levels of complexity. StochSS features state-of-the-art simulation engines. As the demand for computational power increases, StochSS can seamlessly scale computing resources in the cloud. In addition, StochSS can be deployed as a multi-user software environment where collaborators share computational resources and exchange models via a public model repository. We demonstrate the capabilities and ease of use of StochSS with an example of model development and simulation at increasing levels of complexity.

Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist

We present StochSS: Stochastic Simulation as a Service, an integrated development environment for modeling and simulation of both deterministic and discrete stochastic biochemical systems in up to three dimensions. An easy to use graphical user interface enables researchers to quickly develop and simulate a biological model on a desktop or laptop, which can then be expanded to incorporate increasing levels of complexity. StochSS features state-of-the-art simulation engines. As the demand for computational power increases, StochSS can seamlessly scale computing resources in the cloud. In addition, StochSS can be deployed as a multi-user software environment where collaborators share computational resources and exchange models via a public model repository. We demonstrate the capabilities and ease of use of StochSS with an example of model development and simulation at increasing levels of complexity.

Multi-omics integration accurately predicts cellular state in unexplored conditions for Escherichia coli

A significant obstacle in training predictive cell models is the lack of integrated data sources. We develop semi-supervised normalization pipelines and perform experimental characterization (growth, transcriptional, proteome) to create Ecomics, a consistent, quality-controlled multi-omics compendium for Escherichia coli with cohesive meta-data information. We then use this resource to train a multi-scale model that integrates four omics layers to predict genome-wide concentrations and growth dynamics. The genetic and environmental ontology reconstructed from the omics data is substantially different and complementary to the genetic and chemical ontologies. The integration of different layers confers an incremental increase in the prediction performance, as does the information about the known gene regulatory and protein-protein interactions. The predictive performance of the model ranges from 0.54 to 0.87 for the various omics layers, which far exceeds various baselines. This work provides an integrative framework of omics-driven predictive modelling that is broadly applicable to guide biological discovery.

Multi-omics data integration is a great challenge. Here, the authors compile a database of E. coli proteomics, transcriptomics, metabolomics and fluxomics data to train models of recurrent neural network and constrained regression, enabling prediction of bacterial responses to perturbations.

A novel proposal of a simplified bacterial gene set and the neo-construction of a general minimized metabolic network

A minimal gene set (MGS) is critical for the assembly of a minimal artificial cell. We have developed a proposal of simplifying bacterial gene set to approximate a bacterial MGS by the following procedure. First, we base our simplified bacterial gene set (SBGS) on experimentally determined essential genes to ensure that the genes included in the SBGS are critical. Second, we introduced a half-retaining strategy to extract persistent essential genes to ensure stability. Third, we constructed a viable metabolic network to supplement SBGS. The proposed SBGS includes 327 genes and required 431 reactions. This report describes an SBGS that preserves both self-replication and self-maintenance systems. In the minimized metabolic network, we identified five novel hub metabolites and confirmed 20 known hubs. Highly essential genes were found to distribute the connecting metabolites into more reactions. Based on our SBGS, we expanded the pool of targets for designing broad-spectrum antibacterial drugs to reduce pathogen resistance. We also suggested a rough semi-de novo strategy to synthesize an artificial cell, with potential applications in industry.

Perspective: On the importance of hydrodynamic interactions in the subcellular dynamics of macromolecules

An outstanding challenge in computational biophysics is the simulation of a living cell at molecular detail. Over the past several years, using Stokesian dynamics, progress has been made in simulating coarse grained molecular models of the cytoplasm. Since macromolecules comprise 20%-40% of the volume of a cell, one would expect that steric interactions dominate macromolecular diffusion. However, the reduction in cellular diffusion rates relative to infinite dilution is due, roughly equally, to steric and hydrodynamic interactions, HI, with nonspecific attractive interactions likely playing rather a minor role. HI not only serve to slow down long time diffusion rates but also cause a considerable reduction in the magnitude of the short time diffusion coefficient relative to that at infinite dilution. More importantly, the long range contribution of the Rotne-Prager-Yamakawa diffusion tensor results in temporal and spatial correlations that persist up to microseconds and for intermolecular distances on the order of protein radii. While HI slow down the bimolecular association rate in the early stages of lipid bilayer formation, they accelerate the rate of large scale assembly of lipid aggregates. This is suggestive of an important role for HI in the self-assembly kinetics of large macromolecular complexes such as tubulin. Since HI are important, questions as to whether continuum models of HI are adequate as well as improved simulation methodologies that will make simulations of more complex cellular processes practical need to be addressed. Nevertheless, the stage is set for the molecular simulations of ever more complex subcellular processes.

Modeling Intercellular Communication as a Survival Strategy of Cancer Cells: An In Silico Approach on a Flexible Bioinformatics Framework

Intercellular communication is very important for cell development and allows a group of cells to survive as a population. Cancer cells have a similar behavior, presenting the same mechanisms and characteristics of tissue formation. In this article, we model and simulate the formation of different communication channels that allow an interaction between two cells. This is a first step in order to simulate in the future processes that occur in healthy tissue when normal cells surround a cancer cell and to interrupt the communication, thus preventing the spread of malignancy into these cells. The purpose of this study is to propose key molecules, which can be targeted to allow us to break the communication between cancer cells and surrounding normal cells. The simulation is carried out using a flexible bioinformatics platform that we developed, which is itself based on the metaphor chemistry-based model.

Translation of Genotype to Phenotype by a Hierarchy of Cell Subsystems

Accurately translating genotype to phenotype requires accounting for the functional impact of genetic variation at many biological scales. Here we present a strategy for genotype-phenotype reasoning based on existing knowledge of cellular subsystems. These subsystems and their hierarchical organization are defined by the Gene Ontology or a complementary ontology inferred directly from previously published datasets. Guided by the ontology's hierarchical structure, we organize genotype data into an "ontotype," that is, a hierarchy of perturbations representing the effects of genetic variation at multiple cellular scales. The ontotype is then interpreted using logical rules generated by machine learning to predict phenotype. This approach substantially outperforms previous, non-hierarchical methods for translating yeast genotype to cell growth phenotype, and it accurately predicts the growth outcomes of two new screens of 2,503 double gene knockouts impacting DNA repair or nuclear lumen. Ontotypes also generalize to larger knockout combinations, setting the stage for interpreting the complex genetics of disease.

Reaction rates for a generalized reaction-diffusion master equation

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.

Kinetic modeling of cell metabolism for microbial production

Kinetic models of cellular metabolism are important tools for the rational design of metabolic engineering strategies and to explain properties of complex biological systems. The recent developments in high-throughput experimental data are leading to new computational approaches for building kinetic models of metabolism. Herein, we briefly survey the available databases, standards and software tools that can be applied for kinetic models of metabolism. In addition, we give an overview about recently developed ordinary differential equations (ODE)-based kinetic models of metabolism and some of the main applications of such models are illustrated in guiding metabolic engineering design. Finally, we review the kinetic modeling approaches of large-scale networks that are emerging, discussing their main advantages, challenges and limitations.

Automated Learning of Subcellular Variation among Punctate Protein Patterns and a Generative Model of Their Relation to Microtubules

Characterizing the spatial distribution of proteins directly from microscopy images is a difficult problem with numerous applications in cell biology (e.g. identifying motor-related proteins) and clinical research (e.g. identification of cancer biomarkers). Here we describe the design of a system that provides automated analysis of punctate protein patterns in microscope images, including quantification of their relationships to microtubules. We constructed the system using confocal immunofluorescence microscopy images from the Human Protein Atlas project for 11 punctate proteins in three cultured cell lines. These proteins have previously been characterized as being primarily located in punctate structures, but their images had all been annotated by visual examination as being simply "vesicular". We were able to show that these patterns could be distinguished from each other with high accuracy, and we were able to assign to one of these subclasses hundreds of proteins whose subcellular localization had not previously been well defined. In addition to providing these novel annotations, we built a generative approach to modeling of punctate distributions that captures the essential characteristics of the distinct patterns. Such models are expected to be valuable for representing and summarizing each pattern and for constructing systems biology simulations of cell behaviors.

Examining and elucidation of human weight cycle model adopting e-cell simulation system

Cellular rhythms regulate various physiological functions in circadian oscillatory mechanisms. Weight cycling or 'yo-yo' dieting is an evitable process in human, because of subsequent loss and regain of body weight due to irregular diet. Human weight cycle (HWC) is the major factor for causing global epidemic diseases in human beings. Understanding the HWC process would provide potent additional knowledge to prevent obesity. However till date, there is no study dealing with examine the HWC model using virtual cell simulation based on system biological approach. Therefore, the present study was designed to develop a computational HWC model, which was simulated using E-cell system v3.0. The developed model has the cyclic feedback reactions of three significant variables (the consecutive cycles of weight loss in continuous food intake (Q) and regain of body weight (P) at highest threshold point of cognitive restraint (R)) which are obtained by mathematical modelling. The dynamic plot results supported that the PQR variables depicted sustained oscillation with reversible modification due to protein diet. By contrast, the virtual model simulation would provide extensive information on HWC, which might provide knowledge to develop HWC linked with obesity pathway. The presents study concludes that optimization of body weight is essential to prevent the obesity based diseases.

Large Scale Tissue Morphogenesis Simulation on Heterogenous Systems Based on a Flexible Biomechanical Cell Model

The complexity of biological tissue morphogenesis makes in silico simulations of such system very interesting in order to gain a better understanding of the underlying mechanisms ruling the development of multicellular tissues. This complexity is mainly due to two elements: firstly, biological tissues comprise a large amount of cells; secondly, these cells exhibit complex interactions and behaviors. To address these two issues, we propose two tools: the first one is a virtual cell model that comprise two main elements: firstly, a mechanical structure (membrane, cytoskeleton, and cortex) and secondly, the main behaviors exhibited by biological cells, i.e., mitosis, growth, differentiation, molecule consumption, and production as well as the consideration of the physical constraints issued from the environment. An artificial chemistry is also included in the model. This virtual cell model is coupled to an agent-based formalism. The second tool is a simulator that relies on the OpenCL framework. It allows efficient parallel simulations on heterogenous devices such as micro-processors or graphics processors. We present two case studies validating the implementation of our model in our simulator: cellular proliferation controlled by cell signalling and limb growth in a virtual organism.

Complex systems in metabolic engineering

Metabolic engineers manipulate intricate biological networks to build efficient biological machines. The inherent complexity of this task, derived from the extensive and often unknown interconnectivity between and within these networks, often prevents researchers from achieving desired performance. Other fields have developed methods to tackle the issue of complexity for their unique subset of engineering problems, but to date, there has not been extensive and comprehensive examination of how metabolic engineers use existing tools to ameliorate this effect on their own research projects. In this review, we examine how complexity affects engineering at the protein, pathway, and genome levels within an organism, and the tools for handling these issues to achieve high-performing strain designs. Quantitative complexity metrics and their applications to metabolic engineering versus traditional engineering fields are also discussed. We conclude by predicting how metabolic engineering practices may advance in light of an explicit consideration of design complexity.

The principles of whole-cell modeling

Whole-cell models which comprehensively predict how phenotypes emerge from genotype promise to enable rational bioengineering and precision medicine. Here, we outline the key principles of whole-cell modeling which have emerged from our work developing bacterial whole-cell models: single-cellularity; functional, genetic, molecular, and temporal completeness; biophysical realism including temporal dynamics and stochastic variation; species-specificity; and model integration and reproducibility. We also outline the whole-cell model construction process, highlighting existing resources. Numerous challenges remain to achieving fully complete models including developing new experimental tools to more completely characterize cells and developing a strong theoretical understanding of hybrid mathematics. Solving these challenges requires collaboration among computational and experimental biologists, biophysicists, biochemists, applied mathematicians, computer scientists, and software engineers.

Particle Simulation of Oxidation Induced Band 3 Clustering in Human Erythrocytes

Oxidative stress mediated clustering of membrane protein band 3 plays an essential role in the clearance of damaged and aged red blood cells (RBCs) from the circulation. While a number of previous experimental studies have observed changes in band 3 distribution after oxidative treatment, the details of how these clusters are formed and how their properties change under different conditions have remained poorly understood. To address these issues, a framework that enables the simultaneous monitoring of the temporal and spatial changes following oxidation is needed. In this study, we established a novel simulation strategy that incorporates deterministic and stochastic reactions with particle reaction-diffusion processes, to model band 3 cluster formation at single molecule resolution. By integrating a kinetic model of RBC antioxidant metabolism with a model of band 3 diffusion, we developed a model that reproduces the time-dependent changes of glutathione and clustered band 3 levels, as well as band 3 distribution during oxidative treatment, observed in prior studies. We predicted that cluster formation is largely dependent on fast reverse reaction rates, strong affinity between clustering molecules, and irreversible hemichrome binding. We further predicted that under repeated oxidative perturbations, clusters tended to progressively grow and shift towards an irreversible state. Application of our model to simulate oxidation in RBCs with cytoskeletal deficiency also suggested that oxidation leads to more enhanced clustering compared to healthy RBCs. Taken together, our model enables the prediction of band 3 spatio-temporal profiles under various situations, thus providing valuable insights to potentially aid understanding mechanisms for removing senescent and premature RBCs.

In order to maintain a steady internal environment, our bodies must be able to specifically recognize old and damaged red blood cells (RBCs), and remove them from the circulation in a timely manner. Clusters of membrane protein band 3, which form in response to elevated oxidative damage, serve as essential molecular markers that initiate this cell removal process. However, little is known about the details of how these clusters are formed and how their properties change under different conditions. To understand these mechanisms in detail, we developed a computational model that enables the prediction of the time course profiles of metabolic intermediates, as well as the visualization of the resulting band 3 distribution during oxidative treatment. Our model predictions were in good agreement with previous published experimental data, and provided predictive insights on the key factors of cluster formation. Furthermore, simulation experiments of the effects of multiple oxidative pulses and cytoskeletal defect using the model also suggested that clustering is enhanced under such conditions. Analyses using our model can provide hypotheses and suggest experiments to aid the understanding of the physiology of anemia-associated RBC disorders, and optimization of quality control of RBCs in stored blood.

Data-driven integration of genome-scale regulatory and metabolic network models

Microbes are diverse and extremely versatile organisms that play vital roles in all ecological niches. Understanding and harnessing microbial systems will be key to the sustainability of our planet. One approach to improving our knowledge of microbial processes is through data-driven and mechanism-informed computational modeling. Individual models of biological networks (such as metabolism, transcription, and signaling) have played pivotal roles in driving microbial research through the years. These networks, however, are highly interconnected and function in concert-a fact that has led to the development of a variety of approaches aimed at simulating the integrated functions of two or more network types. Though the task of integrating these different models is fraught with new challenges, the large amounts of high-throughput data sets being generated, and algorithms being developed, means that the time is at hand for concerted efforts to build integrated regulatory-metabolic networks in a data-driven fashion. In this perspective, we review current approaches for constructing integrated regulatory-metabolic models and outline new strategies for future development of these network models for any microbial system.

Plant synthetic biology

Plant synthetic biology is an emerging field that combines engineering principles with plant biology toward the design and production of new devices. This emerging field should play an important role in future agriculture for traditional crop improvement, but also in enabling novel bioproduction in plants. In this review we discuss the design cycles of synthetic biology as well as key engineering principles, genetic parts, and computational tools that can be utilized in plant synthetic biology. Some pioneering examples are offered as a demonstration of how synthetic biology can be used to modify plants for specific purposes. These include synthetic sensors, synthetic metabolic pathways, and synthetic genomes. We also speculate about the future of synthetic biology of plants.

Complete atomistic model of a bacterial cytoplasm for integrating physics, biochemistry, and systems biology

A model for the cytoplasm of Mycoplasma genitalium is presented that integrates data from a variety of sources into a physically and biochemically consistent model. Based on gene annotations, core genes expected to be present in the cytoplasm were determined and a metabolic reaction network was reconstructed. The set of cytoplasmic genes and metabolites from the predicted reactions were assembled into a comprehensive atomistic model consisting of proteins with predicted structures, RNA, protein/RNA complexes, metabolites, ions, and solvent. The resulting model bridges between atomistic and cellular scales, between physical and biochemical aspects, and between structural and systems views of cellular systems and is meant as a starting point for a variety of simulation studies.

Reaction rates for mesoscopic reaction-diffusion kinetics

The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer

Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is growing and they have been the target of several recent modeling efforts. Signal transduction pathways (STPs) constitute a class of biochemical networks that receive, process, and respond to stimuli from the environment, as well as stimuli that are internal to the organism. An STP consists of a chain of intracellular signaling processes that ultimately result in generating different cellular responses. This primer presents the methodologies used for the modeling and simulation of biochemical networks, illustrated for STPs. These methodologies range from qualitative to quantitative, and include structural as well as dynamic analysis techniques. We describe the different methodologies, outline their underlying assumptions, and provide an assessment of their advantages and disadvantages. Moreover, publicly and/or commercially available implementations of these methodologies are listed as appropriate. In particular, this primer aims to provide a clear introduction and comprehensive coverage of biochemical modeling and simulation methodologies for the non-expert, with specific focus on relevant literature of STPs.

In silico models for dynamic connected cell cultures mimicking hepatocyte-endothelial cell-adipocyte interaction circle

The biochemistry of a system made up of three kinds of cell is virtually impossible to work out without the use of in silico models. Here, we deal with homeostatic balance phenomena from a metabolic point of view and we present a new computational model merging three single-cell models, already available from our research group: the first model reproduced the metabolic behaviour of a hepatocyte, the second one represented an endothelial cell, and the third one described an adipocyte. Multiple interconnections were created among these three models in order to mimic the main physiological interactions that are known for the examined cell phenotypes. The ultimate aim was to recreate the accomplishment of the homeostatic balance as it was observed for an in vitro connected three-culture system concerning glucose and lipid metabolism in the presence of the medium flow. The whole model was based on a modular approach and on a set of nonlinear differential equations implemented in Simulink, applying Michaelis-Menten kinetic laws and some energy balance considerations to the studied metabolic pathways. Our in silico model was then validated against experimental datasets coming from literature about the cited in vitro model. The agreement between simulated and experimental results was good and the behaviour of the connected culture system was reproduced through an adequate parameter evaluation. The developed model may help other researchers to investigate further about integrated metabolism and the regulation mechanisms underlying the physiological homeostasis.

Plant systems biology: insights, advances and challenges

Plants dwelling at the base of biological food chain are of fundamental significance in providing solutions to some of the most daunting ecological and environmental problems faced by our planet. The reductionist views of molecular biology provide only a partial understanding to the phenotypic knowledge of plants. Systems biology offers a comprehensive view of plant systems, by employing a holistic approach integrating the molecular data at various hierarchical levels. In this review, we discuss the basics of systems biology including the various 'omics' approaches and their integration, the modeling aspects and the tools needed for the plant systems research. A particular emphasis is given to the recent analytical advances, updated published examples of plant systems biology studies and the future trends.

An integrative, multi-scale, genome-wide model reveals the phenotypic landscape of Escherichia coli

Given the vast behavioral repertoire and biological complexity of even the simplest organisms, accurately predicting phenotypes in novel environments and unveiling their biological organization is a challenging endeavor. Here, we present an integrative modeling methodology that unifies under a common framework the various biological processes and their interactions across multiple layers. We trained this methodology on an extensive normalized compendium for the gram-negative bacterium Escherichia coli, which incorporates gene expression data for genetic and environmental perturbations, transcriptional regulation, signal transduction, and metabolic pathways, as well as growth measurements. Comparison with measured growth and high-throughput data demonstrates the enhanced ability of the integrative model to predict phenotypic outcomes in various environmental and genetic conditions, even in cases where their underlying functions are under-represented in the training set. This work paves the way toward integrative techniques that extract knowledge from a variety of biological data to achieve more than the sum of their parts in the context of prediction, analysis, and redesign of biological systems.

Systems biology in inflammatory bowel diseases: ready for prime time

PURPOSE OF REVIEW

Ulcerative colitis and Crohn's disease are the two predominant types of inflammatory bowel disease (IBD), affecting over 1.4 million individuals in the United States. IBD results from complex interactions between pathogenic components, including genetic and epigenetic factors, the immune response, and the microbiome, through an unknown sequence of events. The purpose of this review is to describe a systems biology approach to IBD as a novel and exciting methodology aiming at developing novel IBD therapeutics based on the integration of molecular and cellular 'omics' data.

RECENT FINDINGS

Recent evidence suggested the presence of genetic, epigenetic, transcriptomic, proteomic, and metabolomic alterations in IBD patients. Furthermore, several studies have shown that different cell types including fibroblasts, epithelial, immune, and endothelial cells together with the intestinal microbiota are involved in IBD pathogenesis. Novel computational methodologies have been developed aiming to integrate high-throughput molecular data.

SUMMARY

A systems biology approach could potentially identify the central regulators (hubs) in the IBD interactome and improve our understanding of the molecular mechanisms involved in IBD pathogenesis. The future IBD therapeutics should be developed on the basis of targeting the central hubs in the IBD network.

CANDO and the infinite drug discovery frontier

The Computational Analysis of Novel Drug Opportunities (CANDO) platform (http://protinfo.org/cando) uses similarity of compound-proteome interaction signatures to infer homology of compound/drug behavior. We constructed interaction signatures for 3733 human ingestible compounds covering 48,278 protein structures mapping to 2030 indications based on basic science methodologies to predict and analyze protein structure, function, and interactions developed by us and others. Our signature comparison and ranking approach yielded benchmarking accuracies of 12-25% for 1439 indications with at least two approved compounds. We prospectively validated 49/82 'high value' predictions from nine studies covering seven indications, with comparable or better activity to existing drugs, which serve as novel repurposed therapeutics. Our approach may be generalized to compounds beyond those approved by the FDA, and can also consider mutations in protein structures to enable personalization. Our platform provides a holistic multiscale modeling framework of complex atomic, molecular, and physiological systems with broader applications in medicine and engineering.

Kinetic modeling of plant metabolism and its predictive power: peppermint essential oil biosynthesis as an example

The integration of mathematical modeling with analytical experimentation in an iterative fashion is a powerful approach to advance our understanding of the architecture and regulation of metabolic networks. Ultimately, such knowledge is highly valuable to support efforts aimed at modulating flux through target pathways by molecular breeding and/or metabolic engineering. In this article we describe a kinetic mathematical model of peppermint essential oil biosynthesis, a pathway that has been studied extensively for more than two decades. Modeling assumptions and approximations are described in detail. We provide step-by-step instructions on how to run simulations of dynamic changes in pathway metabolites concentrations.

Exploring emergent properties in cellular homeostasis using OnGuard to model K+ and other ion transport in guard cells

It is widely recognized that the nature and characteristics of transport across eukaryotic membranes are so complex as to defy intuitive understanding. In these circumstances, quantitative mathematical modeling is an essential tool, both to integrate detailed knowledge of individual transporters and to extract the properties emergent from their interactions. As the first, fully integrated and quantitative modeling environment for the study of ion transport dynamics in a plant cell, OnGuard offers a unique tool for exploring homeostatic properties emerging from the interactions of ion transport, both at the plasma membrane and tonoplast in the guard cell. OnGuard has already yielded detail sufficient to guide phenotypic and mutational studies, and it represents a key step toward 'reverse engineering' of stomatal guard cell physiology, based on rational design and testing in simulation, to improve water use efficiency and carbon assimilation. Its construction from the HoTSig libraries enables translation of the software to other cell types, including growing root hairs and pollen. The problems inherent to transport are nonetheless challenging, and are compounded for those unfamiliar with conceptual 'mindset' of the modeler. Here we set out guidelines for the use of OnGuard and outline a standardized approach that will enable users to advance quickly to its application both in the classroom and laboratory. We also highlight the uncanny and emergent property of OnGuard models to reproduce the 'communication' evident between the plasma membrane and tonoplast of the guard cell.

Simulations of living cell origins using a cellular automata model

Understanding the generalized mechanisms of cell self-assembly is fundamental for applications in various fields, such as mass producing molecular machines in nanotechnology. Thus, the details of real cellular reaction networks and the necessary conditions for self-organized cells must be elucidated. We constructed a 2-dimensional cellular automata model to investigate the emergence of biological cell formation, which incorporated a looped membrane and a membrane-bound information system (akin to a genetic code and gene expression system). In particular, with an artificial reaction system coupled with a thermal system, the simultaneous formation of a looped membrane and an inner reaction process resulted in a more stable structure. These double structures inspired the primitive biological cell formation process from chemical evolution stage. With a model to simulate cellular self-organization in a 2-dimensional cellular automata model, 3 phenomena could be realized: (1) an inner reaction system developed as an information carrier precursor (akin to DNA); (2) a cell border emerged (akin to a cell membrane); and (3) these cell structures could divide into 2. This double-structured cell was considered to be a primary biological cell. The outer loop evolved toward a lipid bilayer membrane, and inner polymeric particles evolved toward precursor information carriers (evolved toward DNA). This model did not completely clarify all the necessary and sufficient conditions for biological cell self-organization. Further, our virtual cells remained unstable and fragile. However, the "garbage bag model" of Dyson proposed that the first living cells were deficient; thus, it would be reasonable that the earliest cells were more unstable and fragile than the simplest current unicellular organisms.

Meeting report from the fourth meeting of the Computational Modeling in Biology Network (COMBINE)

The Computational Modeling in Biology Network (COMBINE) is an initiative to coordinate the development of community standards and formats in computational systems biology and related fields. This report summarizes the topics and activities of the fourth edition of the annual COMBINE meeting, held in Paris during September 16-20 2013, and attended by a total of 96 people. This edition pioneered a first day devoted to modeling approaches in biology, which attracted a broad audience of scientists thanks to a panel of renowned speakers. During subsequent days, discussions were held on many subjects including the introduction of new features in the various COMBINE standards, new software tools that use the standards, and outreach efforts. Significant emphasis went into work on extensions of the SBML format, and also into community-building. This year’s edition once again demonstrated that the COMBINE community is thriving, and still manages to help coordinate activities between different standards in computational systems biology.

The future of whole-cell modeling

Integrated whole-cell modeling is poised to make a dramatic impact on molecular and systems biology, bioengineering, and medicine--once certain obstacles are overcome. From our group's experience building a whole-cell model of Mycoplasma genitalium, we identified several significant challenges to building models of more complex cells. Here we review and discuss these challenges in seven areas: first, experimental interrogation; second, data curation; third, model building and integration; fourth, accelerated computation; fifth, analysis and visualization; sixth, model validation; and seventh, collaboration and community development. Surmounting these challenges will require the cooperation of an interdisciplinary group of researchers to create increasingly sophisticated whole-cell models and make data, models, and simulations more accessible to the wider community.

Accelerated discovery via a whole-cell model

To test the promise of whole-cell modeling to facilitate scientific inquiry, we compared growth rates simulated in a whole-cell model with experimental measurements for all viable single-gene disruption Mycoplasma genitalium strains. Discrepancies between simulations and experiments led to predictions about kinetic parameters of specific enzymes that we subsequently validated. These findings represent, to our knowledge, the first application of whole-cell modeling to accelerate biological discovery.

A software architecture for multi-cellular system simulations on graphics processing units

The first aim of simulation in virtual environment is to help biologists to have a better understanding of the simulated system. The cost of such simulation is significantly reduced compared to that of in vivo simulation. However, the inherent complexity of biological system makes it hard to simulate these systems on non-parallel architectures: models might be made of sub-models and take several scales into account; the number of simulated entities may be quite large. Today, graphics cards are used for general purpose computing which has been made easier thanks to frameworks like CUDA or OpenCL. Parallelization of models may however not be easy: parallel computer programing skills are often required; several hardware architectures may be used to execute models. In this paper, we present the software architecture we built in order to implement various models able to simulate multi-cellular system. This architecture is modular and it implements data structures adapted for graphics processing units architectures. It allows efficient simulation of biological mechanisms.