The Beta Workbench: a computational tool to study the dynamics of biological systems

Tools for time-course simulation in systems biology: a brief overview

Dynamic modeling of biological systems is essential for understanding all properties of a given organism as it allows us to look not only at the static picture of an organism but also at its behavior under various conditions. With the increasing amount of experimental data, the number of tools that enable dynamic analysis also grows. However, various tools are based on different approaches, use different types of data and offer different functions for analyses; so it can be difficult to choose the most suitable tool for a selected type of model. Here, we bring a brief overview containing descriptions of 50 tools for the reconstruction of biological models, their time-course simulation and dynamic analysis. We examined each tool using test data and divided them based on the qualitative and quantitative nature of the mathematical apparatus they use.

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.

Computational Modeling, Formal Analysis, and Tools for Systems Biology

As the amount of biological data in the public domain grows, so does the range of modeling and analysis techniques employed in systems biology. In recent years, a number of theoretical computer science developments have enabled modeling methodology to keep pace. The growing interest in systems biology in executable models and their analysis has necessitated the borrowing of terms and methods from computer science, such as formal analysis, model checking, static analysis, and runtime verification. Here, we discuss the most important and exciting computational methods and tools currently available to systems biologists. We believe that a deeper understanding of the concepts and theory highlighted in this review will produce better software practice, improved investigation of complex biological processes, and even new ideas and better feedback into computer science.

Modeling for (physical) biologists: an introduction to the rule-based approach

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particular site or domain of a protein. In other words, a rule defines a transformation and the properties that reactants must possess to participate in the transformation. A rule also provides a rate law. A rule-based approach to modeling enables consideration of mechanistic details at the level of functional sites of biomolecules and provides a facile and visual means for constructing computational models, which can be analyzed to study how system-level behaviors emerge from component interactions.

Modeling cellular compartmentation in one-carbon metabolism

Folate-mediated one-carbon metabolism (FOCM) is associated with risk for numerous pathological states including birth defects, cancers, and chronic diseases. Although the enzymes that constitute the biological pathways have been well described and their interdependency through the shared use of folate cofactors appreciated, the biological mechanisms underlying disease etiologies remain elusive. The FOCM network is highly sensitive to nutritional status of several B-vitamins and numerous penetrant gene variants that alter network outputs, but current computational approaches do not fully capture the dynamics and stochastic noise of the system. Combining the stochastic approach with a rule-based representation will help model the intrinsic noise displayed by FOCM, address the limited flexibility of standard simulation methods for coarse-graining the FOCM-associated biochemical processes, and manage the combinatorial complexity emerging from reactions within FOCM that would otherwise be intractable.

State of the art in silico tools for the study of signaling pathways in cancer

In the last several years, researchers have exhibited an intense interest in the evolutionarily conserved signaling pathways that have crucial roles during embryonic development. Interestingly, the malfunctioning of these signaling pathways leads to several human diseases, including cancer. The chemical and biophysical events that occur during cellular signaling, as well as the number of interactions within a signaling pathway, make these systems complex to study. In silico resources are tools used to aid the understanding of cellular signaling pathways. Systems approaches have provided a deeper knowledge of diverse biochemical processes, including individual metabolic pathways, signaling networks and genome-scale metabolic networks. In the future, these tools will be enormously valuable, if they continue to be developed in parallel with growing biological knowledge. In this study, an overview of the bioinformatics resources that are currently available for the analysis of biological networks is provided.

Transcriptional regulation is a major controller of cell cycle transition dynamics

DNA replication, mitosis and mitotic exit are critical transitions of the cell cycle which normally occur only once per cycle. A universal control mechanism was proposed for the regulation of mitotic entry in which Cdk helps its own activation through two positive feedback loops. Recent discoveries in various organisms showed the importance of positive feedbacks in other transitions as well. Here we investigate if a universal control system with transcriptional regulation(s) and post-translational positive feedback(s) can be proposed for the regulation of all cell cycle transitions. Through computational modeling, we analyze the transition dynamics in all possible combinations of transcriptional and post-translational regulations. We find that some combinations lead to ‘sloppy’ transitions, while others give very precise control. The periodic transcriptional regulation through the activator or the inhibitor leads to radically different dynamics. Experimental evidence shows that in cell cycle transitions of organisms investigated for cell cycle dependent periodic transcription, only the inhibitor OR the activator is under cyclic control and never both of them. Based on these observations, we propose two transcriptional control modes of cell cycle regulation that either STOP or let the cycle GO in case of a transcriptional failure. We discuss the biological relevance of such differences.

BLENX MODELS OF α-SYNUCLEIN AND PARKIN KINETICS IN NEUROPATHOLOGY OF PARKINSON'S DISEASE

In this paper two stochastic kinetic models of a faulty ubiquitin–proteasome are presented. In the first model, mutant variants of the α-synuclein, induced by environmental stress factors, inhibit the ubiquitin–proteasome pathway that is in charge to start the degradation of misfolded proteins. In the second model mutant variants of parkin proteins are not able to transfer the ubiquitin molecules on the faulty proteins, so that they are not targeted and recognized as toxic products. The models are specified in BlenX and simulated with Beta Workbench (Beta WB) simulator. BlenX is a new programming language that has been recently designed by the CoSBi team of researchers to describe components and interactions among components of a biochemical system. It implements a process calculus in which the communication and synchronization between computational processes abstract the biochemical interaction and reactions between molecules, proteins and functional complexes. The aim of this study is twofold: (i) to move the current focus on the structural studies of the components of the protein ubiquitination and degradation to the dynamics of such components in a typical systems biology perspective; (ii) to provide first stochastic models in a new language suitable to systemic approach to the modelling of biochemical kinetics. This tool makes it possible for biologists and medical researchers a high-level modeling of molecular mechanisms underlying the pathogenesis of the disease. Consequently, the suitable abstraction provided by the language makes possible the elucidation of important and still elusive aspects of the involved biochemical interactions. The agreement of the simulations of our models with the available qualitative experimental observations and previous theoretical studies supports the confidence in the model validity.

A unique transformation from ordinary differential equations to reaction networks

Many models in Systems Biology are described as a system of Ordinary Differential Equations, which allows for transient, steady-state or bifurcation analysis when kinetic information is available. Complementary structure-related qualitative analysis techniques have become increasingly popular in recent years, like qualitative model checking or pathway analysis (elementary modes, invariants, flux balance analysis, graph-based analyses, chemical organization theory, etc.). They do not rely on kinetic information but require a well-defined structure as stochastic analysis techniques equally do. In this article, we look into the structure inference problem for a model described by a system of Ordinary Differential Equations and provide conditions for the uniqueness of its solution. We describe a method to extract a structured reaction network model, represented as a bipartite multigraph, for example, a continuous Petri net (CPN), from a system of Ordinary Differential Equations (ODEs). A CPN uniquely defines an ODE, and each ODE can be transformed into a CPN. However, it is not obvious under which conditions the transformation of an ODE into a CPN is unique, that is, when a given ODE defines exactly one CPN. We provide biochemically relevant sufficient conditions under which the derived structure is unique and counterexamples showing the necessity of each condition. Our method is implemented and available; we illustrate it on some signal transduction models from the BioModels database. A prototype implementation of the method is made available to modellers at http://contraintes.inria.fr/~soliman/ode2pn.html, and the data mentioned in the “Results” section at http://contraintes.inria.fr/~soliman/ode2pn_data/. Our results yield a new recommendation for the import/export feature of tools supporting the SBML exchange format.

Snazer: the simulations and networks analyzer

BACKGROUND

Networks are widely recognized as key determinants of structure and function in systems that span the biological, physical, and social sciences. They are static pictures of the interactions among the components of complex systems. Often, much effort is required to identify networks as part of particular patterns as well as to visualize and interpret them.From a pure dynamical perspective, simulation represents a relevant way-out. Many simulator tools capitalized on the "noisy" behavior of some systems and used formal models to represent cellular activities as temporal trajectories. Statistical methods have been applied to a fairly large number of replicated trajectories in order to infer knowledge.A tool which both graphically manipulates reactive models and deals with sets of simulation time-course data by aggregation, interpretation and statistical analysis is missing and could add value to simulators.

RESULTS

We designed and implemented Snazer, the simulations and networks analyzer. Its goal is to aid the processes of visualizing and manipulating reactive models, as well as to share and interpret time-course data produced by stochastic simulators or by any other means.

CONCLUSIONS

Snazer is a solid prototype that integrates biological network and simulation time-course data analysis techniques.

Computational modeling of the EGFR network elucidates control mechanisms regulating signal dynamics

Background

The epidermal growth factor receptor (EGFR) signaling pathway plays a key role in regulation of cellular growth and development. While highly studied, it is still not fully understood how the signal is orchestrated. One of the reasons for the complexity of this pathway is the extensive network of inter-connected components involved in the signaling. In the aim of identifying critical mechanisms controlling signal transduction we have performed extensive analysis of an executable model of the EGFR pathway using the stochastic pi-calculus as a modeling language.

Results

Our analysis, done through simulation of various perturbations, suggests that the EGFR pathway contains regions of functional redundancy in the upstream parts; in the event of low EGF stimulus or partial system failure, this redundancy helps to maintain functional robustness. Downstream parts, like the parts controlling Ras and ERK, have fewer redundancies, and more than 50% inhibition of specific reactions in those parts greatly attenuates signal response. In addition, we suggest an abstract model that captures the main control mechanisms in the pathway. Simulation of this abstract model suggests that without redundancies in the upstream modules, signal transduction through the entire pathway could be attenuated. In terms of specific control mechanisms, we have identified positive feedback loops whose role is to prolong the active state of key components (e.g., MEK-PP, Ras-GTP), and negative feedback loops that help promote signal adaptation and stabilization.

Conclusions

The insights gained from simulating this executable model facilitate the formulation of specific hypotheses regarding the control mechanisms of the EGFR signaling, and further substantiate the benefit to construct abstract executable models of large complex biological networks.

Elucidation of functional consequences of signalling pathway interactions

BACKGROUND

A great deal of data has accumulated on signalling pathways. These large datasets are thought to contain much implicit information on their molecular structure, interaction and activity information, which provides a picture of intricate molecular networks believed to underlie biological functions. While tremendous advances have been made in trying to understand these systems, how information is transmitted within them is still poorly understood. This ever growing amount of data demands we adopt powerful computational techniques that will play a pivotal role in the conversion of mined data to knowledge, and in elucidating the topological and functional properties of protein - protein interactions.

RESULTS

A computational framework is presented which allows for the description of embedded networks, and identification of common shared components thought to assist in the transmission of information within the systems studied. By employing the graph theories of network biology - such as degree distribution, clustering coefficient, vertex betweenness and shortest path measures - topological features of protein-protein interactions for published datasets of the p53, nuclear factor kappa B (NF-kappaB) and G1/S phase of the cell cycle systems were ascertained. Highly ranked nodes which in some cases were identified as connecting proteins most likely responsible for propagation of transduction signals across the networks were determined. The functional consequences of these nodes in the context of their network environment were also determined. These findings highlight the usefulness of the framework in identifying possible combination or links as targets for therapeutic responses; and put forward the idea of using retrieved knowledge on the shared components in constructing better organised and structured models of signalling networks.

CONCLUSION

It is hoped that through the data mined reconstructed signal transduction networks, well developed models of the published data can be built which in the end would guide the prediction of new targets based on the pathway's environment for further analysis. Source code is available upon request.

Biological pathways as communicating computer systems

Time and cost are the enemies of cell biology. The number of experiments required to rigorously dissect and comprehend a pathway of even modest complexity is daunting. Methods are needed to formulate biological pathways in a machine-analysable fashion, which would automate the process of considering all possible experiments in a complex pathway and identify those that command attention. In this Essay, we describe a method that is based on the exploitation of computational tools that were originally developed to analyse reactive communicating computer systems such as mobile phones and web browsers. In this approach, the biological process is articulated as an executable computer program that can be interrogated using methods that were developed to analyse complex software systems. Using case studies of the FGF, MAPK and Delta/Notch pathways, we show that the application of this technology can yield interesting insights into the behaviour of signalling pathways, which have subsequently been corroborated by experimental data.

Calibration of dynamic models of biological systems with KInfer

Methods for parameter estimation that are robust to experimental uncertainties and to stochastic and biological noise and that require a minimum of a priori input knowledge are of key importance in computational systems biology. The new method presented in this paper aims to ensure an inference model that deduces the rate constants of a system of biochemical reactions from experimentally measured time courses of reactants. This new method was applied to some challenging parameter estimation problems of nonlinear dynamic biological systems and was tested both on synthetic and real data. The synthetic case studies are the 12-state model of the SERCA pump and a model of a genetic network containing feedback loops of interaction between regulator and effector genes. The real case studies consist of a model of the reaction between the inhibitor kappaB kinase enzyme and its substrate in the signal transduction pathway of NF-kappaB, and a stiff model of the fermentation pathway of Lactococcus lactis.

Narrative-based computational modelling of the Gp130/JAK/STAT signalling pathway

BACKGROUND

Appropriately formulated quantitative computational models can support researchers in understanding the dynamic behaviour of biological pathways and support hypothesis formulation and selection by "in silico" experimentation. An obstacle to widespread adoption of this approach is the requirement to formulate a biological pathway as machine executable computer code. We have recently proposed a novel, biologically intuitive, narrative-style modelling language for biologists to formulate the pathway which is then automatically translated into an executable format and is, thus, usable for analysis via existing simulation techniques.

RESULTS

Here we use a high-level narrative language in designing a computational model of the gp130/JAK/STAT signalling pathway and show that the model reproduces the dynamic behaviour of the pathway derived by biological observation. We then "experiment" on the model by simulation and sensitivity analysis to define those parameters which dominate the dynamic behaviour of the pathway. The model predicts that nuclear compartmentalisation and phosphorylation status of STAT are key determinants of the pathway and that alternative mechanisms of signal attenuation exert their influence on different timescales.

CONCLUSION

The described narrative model of the gp130/JAK/STAT pathway represents an interesting case study showing how, by using this approach, researchers can model biological systems without explicitly dealing with formal notations and mathematical expressions (typically used for biochemical modelling), nevertheless being able to obtain simulation and analysis results. We present the model and the sensitivity analysis results we have obtained, that allow us to identify the parameters which are most sensitive to perturbations. The results, which are shown to be in agreement with existing mathematical models of the gp130/JAK/STAT pathway, serve us as a form of validation of the model and of the approach itself.

Computational systems biology of the cell cycle

One of the early success stories of computational systems biology was the work done on cell-cycle regulation. The earliest mathematical descriptions of cell-cycle control evolved into very complex, detailed computational models that describe the regulation of cell division in many different cell types. On the way these models predicted several dynamical properties and unknown components of the system that were later experimentally verified/identified. Still, research on this field is far from over. We need to understand how the core cell-cycle machinery is controlled by internal and external signals, also in yeast cells and in the more complex regulatory networks of higher eukaryotes. Furthermore, there are many computational challenges what we face as new types of data appear thanks to continuing advances in experimental techniques. We have to deal with cell-to-cell variations, revealed by single cell measurements, as well as the tremendous amount of data flowing from high throughput machines. We need new computational concepts and tools to handle these data and develop more detailed, more precise models of cell-cycle regulation in various organisms. Here we review past and present of computational modeling of cell-cycle regulation, and discuss possible future directions of the field.