COPASI--a COmplex PAthway SImulator

Rule-based modeling of biochemical systems with BioNetGen

Rule-based modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate site-specific details about protein-protein interactions into a model for the dynamics of a signal-transduction system, but the method has other applications as well, such as following the fates of individual carbon atoms in metabolic reactions. The consequences of protein-protein interactions are difficult to specify and track with a conventional modeling approach because of the large number of protein phosphoforms and protein complexes that these interactions potentially generate. Here, we focus on how a rule-based model is specified in the BioNetGen language (BNGL) and how a model specification is analyzed using the BioNetGen software tool. We also discuss new developments in rule-based modeling that should enable the construction and analyses of comprehensive models for signal transduction pathways and similarly large-scale models for other biochemical systems.

Enzyme kinetics and computational modeling for systems biology

Enzyme kinetics is a century-old area of biochemical research which is regaining popularity due to its use in systems biology. Computational models of biochemical networks depend on rate laws and kinetic parameter values that describe the behavior of enzymes in the cellular milieu. While there is a considerable body of enzyme kinetic data available from the past several decades, a large number of enzymes of specific organisms were never assayed or were assayed in conditions that are irrelevant to those models. The result is that systems biology projects are having to carry out large numbers of enzyme kinetic assays. This chapter reviews the main methodologies of enzyme kinetic data analysis and proposes using computational modeling software for that purpose. It applies the biochemical network modeling software COPASI to data from enzyme assays of yeast triosephosphate isomerase (EC 5.3.1.1).

A consensus yeast metabolic network reconstruction obtained from a community approach to systems biology

Genomic data allow the large-scale manual or semi-automated assembly of metabolic network reconstructions, which provide highly curated organism-specific knowledge bases. Although several genome-scale network reconstructions describe Saccharomyces cerevisiae metabolism, they differ in scope and content, and use different terminologies to describe the same chemical entities. This makes comparisons between them difficult and underscores the desirability of a consolidated metabolic network that collects and formalizes the 'community knowledge' of yeast metabolism. We describe how we have produced a consensus metabolic network reconstruction for S. cerevisiae. In drafting it, we placed special emphasis on referencing molecules to persistent databases or using database-independent forms, such as SMILES or InChI strings, as this permits their chemical structure to be represented unambiguously and in a manner that permits automated reasoning. The reconstruction is readily available via a publicly accessible database and in the Systems Biology Markup Language (http://www.comp-sys-bio.org/yeastnet). It can be maintained as a resource that serves as a common denominator for studying the systems biology of yeast. Similar strategies should benefit communities studying genome-scale metabolic networks of other organisms.

Global kinetic explorer: a new computer program for dynamic simulation and fitting of kinetic data

We describe a new dynamic kinetic simulation program that allows multiple data sets to be fit simultaneously to a single model based on numerical integration of the rate equations describing the reaction mechanism. Unlike other programs that allow fitting based on numerical integration of rate equations, in the dynamic simulation rate constants, output factors, and starting concentrations of reactants can be scrolled while observing the change in the shape of the simulated reaction curves. Fast dynamic simulation facilitates the exploration of initial parameters that serve as the starting point for nonlinear regression in fitting data and facilitates exploration of the relationships between individual constants and observable reactions. The exploration of parameter space by dynamic simulation provides a powerful tool for learning kinetics and for evaluating the extent to which parameters are constrained by the data. This feature is critical to avoid overly complex models that are not supported by the data.

Modelling the dynamics of signalling pathways

In the present chapter we discuss methodologies for the modelling, calibration and validation of cellular signalling pathway dynamics. The discussion begins with the typical range of techniques for modelling that might be employed to go from the chemical kinetics to a mathematical model of biochemical pathways. In particular, we consider the decision-making processes involved in selecting the right mechanism and level of detail of representation of the biochemical interactions. These include the choice between (i) deterministic and stochastic chemical kinetics representations, (ii) discrete and continuous time models and (iii) representing continuous and discrete state processes. We then discuss the task of calibrating the models using information available in web-based databases. For situations in which the data are not available from existing sources we discuss model calibration based upon measured data and system identification methods. Such methods, together with mathematical modelling databases and computational tools, are often available in standard packages. We therefore make explicit mention of a range of popular and useful sites. As an example of the whole modelling and calibration process, we discuss a study of the cross-talk between the IL-1 (interleukin-1)-stimulated NF-kappaB (nuclear factor kappaB) pathway and the TGF-beta (transforming growth factor beta)-stimulated Smad2 pathway.

Modelling phagosomal lipid networks that regulate actin assembly

Background

When purified phagosomes are incubated in the presence of actin under appropriate conditions, microfilaments start growing from the membrane in a process that is affected by ATP and the lipid composition of the membrane. Isolated phagosomes are metabolically active organelles that contain enzymes and metabolites necessary for lipid interconversion. Hence, addition of ATP, lipids, and actin to the system alter the steady-state composition of the phagosomal membrane at the same time that the actin nucleation is initiated. Our aim was to model all these processes in parallel.

Results

We compiled detailed experimental data on the effects of different lipids and ATP on actin nucleation and we investigated experimentally lipid interconversion and ATP metabolism in phagosomes by using suitable radioactive compounds.

In a first step, a complex lipid network interconnected by chemical reactions catalyzed by known enzymes was modelled in COPASI (Complex Pathway Simulator). However, several lines of experimental evidence indicated that only the phosphatidylinositol branch of the network was active, an observation that dramatically reduced the number of parameters in the model. The results also indicated that a lipid network-independent ATP-consuming activity should be included in the model. When this activity was introduced, the set of differential equations satisfactorily reproduced the experimental data. On the other hand, a molecular mechanism connecting membrane lipids, ATP, and the actin nucleation process is still missing. We therefore adopted a phenomenological (black-box) approach to represent the empirical observations. We proposed that lipids and ATP influence the dynamic interconversion between active and inactive actin nucleation sites. With this simple model, all the experimental data were satisfactorily fitted with a single positive parameter per lipid and ATP.

Conclusion

By establishing an active 'dialogue' between an initial complex model and experimental observations, we could narrow the set of differential equations and parameters required to characterize the time-dependent changes of metabolites influencing actin nucleation on phagosomes. For this, the global model was dissected into three sub-models: ATP consumption, lipid interconversion, and nucleation of actin on phagosomal membranes. This scheme allowed us to describe this complex system with a relatively small set of differential equations and kinetic parameters that satisfactorily reproduced the experimental data.

Biocatalytical production of (5S)-hydroxy-2-hexanone

Biocatalytical approaches have been investigated in order to improve accessibility of the bifunctional chiral building block (5S)-hydroxy-2-hexanone ((S)-2). As a result, a new synthetic route starting from 2,5-hexanedione (1) was developed for (S)-2, which is produced with high enantioselectivity (ee >99%). Since (S)-2 can be reduced further to furnish (2S,5S)-hexanediol ((2S,5S)-3), chemoselectivity is a major issue. Among the tested biocatalysts the whole-cell system S. cerevisiae L13 surpasses the bacterial dehydrogenase ADH-T in terms of chemoselectivity. The use of whole-cells of S. cerevisiae L13 affords (S)-2 from prochiral 1 with 85% yield, which is 21% more than the value obtained with ADH-T. This is due to the different reaction rates of monoreduction (1-->2) and consecutive reduction (2-->3) of the respective biocatalysts. In order to optimise the performance of the whole-cell-bioreduction 1 2 with S. cerevisiae, the system was studied in detail, revealing interactions between cell-physiology and xenobiotic substrate and by-products, respectively. This study compares the whole-cell biocatalytic route with the enzymatic route to enantiopure (S)-2 and investigates factors determining performance and outcome of the bioreductions.

Elementary mode analysis: a useful metabolic pathway analysis tool for characterizing cellular metabolism

Elementary mode analysis is a useful metabolic pathway analysis tool to identify the structure of a metabolic network that links the cellular phenotype to the corresponding genotype. The analysis can decompose the intricate metabolic network comprised of highly interconnected reactions into uniquely organized pathways. These pathways consisting of a minimal set of enzymes that can support steady state operation of cellular metabolism represent independent cellular physiological states. Such pathway definition provides a rigorous basis to systematically characterize cellular phenotypes, metabolic network regulation, robustness, and fragility that facilitate understanding of cell physiology and implementation of metabolic engineering strategies. This mini-review aims to overview the development and application of elementary mode analysis as a metabolic pathway analysis tool in studying cell physiology and as a basis of metabolic engineering.

A new strategy for assessing sensitivities in biochemical models

An integral part of any systems biology approach is the modelling and simulation of the respective system under investigation. However, the values of many parameters of the system have often not been determined or are not identifiable due to technical experimental difficulties or other constraints. Sensitivity analysis is often employed to quantify the importance of each of the model's parameters in the behaviour of the system. This approach can also be useful in identifying those parts of the system that are most sensitive with the potential of becoming drug targets. A problem of the commonly used methods of sensitivity analysis is that they constitute local methods meaning that they depend directly on the exact parameter space, which in turn is not known exactly. One way to circumvent this problem is to carry out sensitivity analysis over a wide range of values for all parameters, but this is handicapped by expensive computations when the systems are high dimensional. Another approach is to employ global sensitivity analysis, which in this context is mostly based on random sampling methods. In this paper we present an efficient approach that involves using numerical optimizing methods that search a wide region of parameter space for a given model to determine the maximum and minimum values of its metabolic control coefficients. A relevant example for drug development is presented to demonstrate the strategy using the software COPASI.

Web-based applications for building, managing and analysing kinetic models of biological systems

Mathematical modelling and computational analysis play an essential role in improving our capability to elucidate the functions and characteristics of complex biological systems such as metabolic, regulatory and cell signalling pathways. The modelling and concomitant simulation render it possible to predict the cellular behaviour of systems under various genetically and/or environmentally perturbed conditions. This motivates systems biologists/bioengineers/bioinformaticians to develop new tools and applications, allowing non-experts to easily conduct such modelling and analysis. However, among a multitude of systems biology tools developed to date, only a handful of projects have adopted a web-based approach to kinetic modelling. In this report, we evaluate the capabilities and characteristics of current web-based tools in systems biology and identify desirable features, limitations and bottlenecks for further improvements in terms of usability and functionality. A short discussion on software architecture issues involved in web-based applications and the approaches taken by existing tools is included for those interested in developing their own simulation applications.

FERN - a Java framework for stochastic simulation and evaluation of reaction networks

Background

Stochastic simulation can be used to illustrate the development of biological systems over time and the stochastic nature of these processes. Currently available programs for stochastic simulation, however, are limited in that they either a) do not provide the most efficient simulation algorithms and are difficult to extend, b) cannot be easily integrated into other applications or c) do not allow to monitor and intervene during the simulation process in an easy and intuitive way. Thus, in order to use stochastic simulation in innovative high-level modeling and analysis approaches more flexible tools are necessary.

Results

In this article, we present FERN (Framework for Evaluation of Reaction Networks), a Java framework for the efficient simulation of chemical reaction networks. FERN is subdivided into three layers for network representation, simulation and visualization of the simulation results each of which can be easily extended. It provides efficient and accurate state-of-the-art stochastic simulation algorithms for well-mixed chemical systems and a powerful observer system, which makes it possible to track and control the simulation progress on every level. To illustrate how FERN can be easily integrated into other systems biology applications, plugins to Cytoscape and CellDesigner are included. These plugins make it possible to run simulations and to observe the simulation progress in a reaction network in real-time from within the Cytoscape or CellDesigner environment.

Conclusion

FERN addresses shortcomings of currently available stochastic simulation programs in several ways. First, it provides a broad range of efficient and accurate algorithms both for exact and approximate stochastic simulation and a simple interface for extending to new algorithms. FERN's implementations are considerably faster than the C implementations of gillespie2 or the Java implementations of ISBJava. Second, it can be used in a straightforward way both as a stand-alone program and within new systems biology applications. Finally, complex scenarios requiring intervention during the simulation progress can be modelled easily with FERN.

Computational modelling of genome-wide [corrected] transcription assembly networks using a fluidics analogy

Understanding how a myriad of transcription regulators work to modulate mRNA output at thousands of genes remains a fundamental challenge in molecular biology. Here we develop a computational tool to aid in assessing the plausibility of gene regulatory models derived from genome-wide expression profiling of cells mutant for transcription regulators. mRNA output is modelled as fluid flow in a pipe lattice, with assembly of the transcription machinery represented by the effect of valves. Transcriptional regulators are represented as external pressure heads that determine flow rate. Modelling mutations in regulatory proteins is achieved by adjusting valves' on/off settings. The topology of the lattice is designed by the experimentalist to resemble the expected interconnection between the modelled agents and their influence on mRNA expression. Users can compare multiple lattice configurations so as to find the one that minimizes the error with experimental data. This computational model provides a means to test the plausibility of transcription regulation models derived from large genomic data sets.

Rapidly exploring structural and dynamic properties of signaling networks using PathwayOracle

BACKGROUND

In systems biology the experimentalist is presented with a selection of software for analyzing dynamic properties of signaling networks. These tools either assume that the network is in steady-state or require highly parameterized models of the network of interest. For biologists interested in assessing how signal propagates through a network under specific conditions, the first class of methods does not provide sufficiently detailed results and the second class requires models which may not be easily and accurately constructed. A tool that is able to characterize the dynamics of a signaling network using an unparameterized model of the network would allow biologists to quickly obtain insights into a signaling network's behavior.

RESULTS

We introduce PathwayOracle, an integrated suite of software tools for computationally inferring and analyzing structural and dynamic properties of a signaling network. The feature which differentiates PathwayOracle from other tools is a method that can predict the response of a signaling network to various experimental conditions and stimuli using only the connectivity of the signaling network. Thus signaling models are relatively easy to build. The method allows for tracking signal flow in a network and comparison of signal flows under different experimental conditions. In addition, PathwayOracle includes tools for the enumeration and visualization of coherent and incoherent signaling paths between proteins, and for experimental analysis - loading and superimposing experimental data, such as microarray intensities, on the network model.

CONCLUSION

PathwayOracle provides an integrated environment in which both structural and dynamic analysis of a signaling network can be quickly conducted and visualized along side experimental results. By using the signaling network connectivity, analyses and predictions can be performed quickly using relatively easily constructed signaling network models. The application has been developed in Python and is designed to be easily extensible by groups interested in adding new or extending existing features. PathwayOracle is freely available for download and use.

SBML-SAT: a systems biology markup language (SBML) based sensitivity analysis tool

Background

It has long been recognized that sensitivity analysis plays a key role in modeling and analyzing cellular and biochemical processes. Systems biology markup language (SBML) has become a well-known platform for coding and sharing mathematical models of such processes. However, current SBML compatible software tools are limited in their ability to perform global sensitivity analyses of these models.

Results

This work introduces a freely downloadable, software package, SBML-SAT, which implements algorithms for simulation, steady state analysis, robustness analysis and local and global sensitivity analysis for SBML models. This software tool extends current capabilities through its execution of global sensitivity analyses using multi-parametric sensitivity analysis, partial rank correlation coefficient, SOBOL's method, and weighted average of local sensitivity analyses in addition to its ability to handle systems with discontinuous events and intuitive graphical user interface.

Conclusion

SBML-SAT provides the community of systems biologists a new tool for the analysis of their SBML models of biochemical and cellular processes.

Genetic design: rising above the sequence

Genetic engineering has developed around technologies enabling the targeted in vitro recombination of DNA molecules found in living organisms. As a result, the development of new DNA molecules has been primarily focused on cloning strategies that allow their assembly from existing DNA fragments. As chemical gene synthesis matures, the design of synthetic DNA molecules becomes the bottleneck of many biotechnology projects. It becomes urgent to develop representations of synthetic genetic systems more abstract than their DNA sequence. Abstraction makes it possible to reuse simple components to build complex systems or to break down a complex engineering problem into manageable tasks. Specialized computer languages or a general purpose XCell Description Language are promising avenues to build abstraction hierarchies for synthetic biology.

An allosteric model of calmodulin explains differential activation of PP2B and CaMKII

Calmodulin plays a vital role in mediating bidirectional synaptic plasticity by activating either calcium/calmodulin-dependent protein kinase II (CaMKII) or protein phosphatase 2B (PP2B) at different calcium concentrations. We propose an allosteric model for calmodulin activation, in which binding to calcium facilitates the transition between a low-affinity [tense (T)] and a high-affinity [relaxed (R)] state. The four calcium-binding sites are assumed to be nonidentical. The model is consistent with previously reported experimental data for calcium binding to calmodulin. It also accounts for known properties of calmodulin that have been difficult to model so far, including the activity of nonsaturated forms of calmodulin (we predict the existence of open conformations in the absence of calcium), an increase in calcium affinity once calmodulin is bound to a target, and the differential activation of CaMKII and PP2B depending on calcium concentration.

Membrane identity and GTPase cascades regulated by toggle and cut-out switches

Key cellular functions and developmental processes rely on cascades of GTPases. GTPases of the Rab family provide a molecular ID code to the generation, maintenance and transport of intracellular compartments. Here, we addressed the molecular design principles of endocytosis by focusing on the conversion of early endosomes into late endosomes, which entails replacement of Rab5 by Rab7. We modelled this process as a cascade of functional modules of interacting Rab GTPases. We demonstrate that intermodule interactions share similarities with the toggle switch described for the cell cycle. However, Rab5-to-Rab7 conversion is rather based on a newly characterized ‘cut-out switch' analogous to an electrical safety-breaker. Both designs require cooperativity of auto-activation loops when coupled to a large pool of cytoplasmic proteins. Live cell imaging and endosome tracking provide experimental support to the cut-out switch in cargo progression and conversion of endosome identity along the degradative pathway. We propose that, by reconciling module performance with progression of activity, the cut-out switch design could underlie the integration of modules in regulatory cascades from a broad range of biological processes.

Dynamical modeling and multi-experiment fitting with PottersWheel

Motivation: Modelers in Systems Biology need a flexible framework that allows them to easily create new dynamic models, investigate their properties and fit several experimental datasets simultaneously. Multi-experiment-fitting is a powerful approach to estimate parameter values, to check the validity of a given model, and to discriminate competing model hypotheses. It requires high-performance integration of ordinary differential equations and robust optimization.

Results: We here present the comprehensive modeling framework Potters-Wheel (PW) including novel functionalities to satisfy these requirements with strong emphasis on the inverse problem, i.e. data-based modeling of partially observed and noisy systems like signal transduction pathways and metabolic networks. PW is designed as a MATLAB toolbox and includes numerous user interfaces. Deterministic and stochastic optimization routines are combined by fitting in logarithmic parameter space allowing for robust parameter calibration. Model investigation includes statistical tests for model-data-compliance, model discrimination, identifiability analysis and calculation of Hessian- and Monte-Carlo-based parameter confidence limits. A rich application programming interface is available for customization within own MATLAB code. Within an extensive performance analysis, we identified and significantly improved an integrator–optimizer pair which decreases the fitting duration for a realistic benchmark model by a factor over 3000 compared to MATLAB with optimization toolbox.

Availability: PottersWheel is freely available for academic usage at http://www.PottersWheel.de/. The website contains a detailed documentation and introductory videos. The program has been intensively used since 2005 on Windows, Linux and Macintosh computers and does not require special MATLAB toolboxes.

Contact:maiwald@fdm.uni-freiburg.de

Supplementary information:Supplementary data are available at Bioinformatics online.

Comparing simulation results of SBML capable simulators

MOTIVATION

Simulations are an essential tool when analyzing biochemical networks. Researchers and developers seeking to refine simulation tools or develop new ones would benefit greatly from being able to compare their simulation results.

SUMMARY

We present an approach to compare simulation results between several SBML capable simulators and provide a website for the community to share simulation results.

AVAILABILITY

The website with simulation results and additional material can be found under: http://sys-bio.org/sbwWiki/compare. The software used to generate the simulation results is available on the website for download.

A structured approach for the engineering of biochemical network models, illustrated for signalling pathways

Quantitative models of biochemical networks (signal transduction cascades, metabolic pathways, gene regulatory circuits) are a central component of modern systems biology. Building and managing these complex models is a major challenge that can benefit from the application of formal methods adopted from theoretical computing science. Here we provide a general introduction to the field of formal modelling, which emphasizes the intuitive biochemical basis of the modelling process, but is also accessible for an audience with a background in computing science and/or model engineering. We show how signal transduction cascades can be modelled in a modular fashion, using both a qualitative approach--qualitative Petri nets, and quantitative approaches--continuous Petri nets and ordinary differential equations (ODEs). We review the major elementary building blocks of a cellular signalling model, discuss which critical design decisions have to be made during model building, and present a number of novel computational tools that can help to explore alternative modular models in an easy and intuitive manner. These tools, which are based on Petri net theory, offer convenient ways of composing hierarchical ODE models, and permit a qualitative analysis of their behaviour. We illustrate the central concepts using signal transduction as our main example. The ultimate aim is to introduce a general approach that provides the foundations for a structured formal engineering of large-scale models of biochemical networks.

A system for generating transcription regulatory networks with combinatorial control of transcription

We have developed a new software system, REgulatory Network generator with COmbinatorial control (RENCO), for automatic generation of differential equations describing pre-transcriptional combinatorics in artificial regulatory networks. RENCO has the following benefits: (a) it explicitly models protein-protein interactions among transcription factors, (b) it captures combinatorial control of transcription factors on target genes and (c) it produces output in Systems Biology Markup Language (SBML) format, which allows these equations to be directly imported into existing simulators. Explicit modeling of the protein interactions allows RENCO to incorporate greater mechanistic detail of the transcription machinery compared to existing models and can provide a better assessment of algorithms for regulatory network inference.

AVAILABILITY

RENCO is a C++ command line program, available at http://sourceforge.net/projects/renco/

Simulated de novo assembly of golgi compartments by selective cargo capture during vesicle budding and targeted vesicle fusion

The Golgi apparatus is comprised of stacked cisternal membranes forming subcompartments specialized for posttranslational processing of newly synthesized secretory cargo. Recent experimental evidence indicates that the Golgi apparatus can undergo de novo biogenesis from the endoplasmic reticulum, but the mechanism by which the membranes self assemble into compartmentalized structures remains unknown. We developed a discrete-event computer simulation model to test whether two fundamental mechanisms-vesicle-coat-mediated selective concentration of soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins during vesicle formation, and SNARE-mediated selective fusion of vesicles-suffice to generate and maintain compartments. Simulations verified that this minimal model is adequate for homeostasis of preestablished compartments, even in response to small perturbations, and for de novo formation of stable compartments. The model led to a novel prediction that Golgi size is in part dependent on target SNARE expression level. This prediction was supported by a demonstration that exogenous expression of the Golgi target SNARE syntaxin-5 alters Golgi size in living cells.

SYCAMORE--a systems biology computational analysis and modeling research environment

SYCAMORE is a browser-based application that facilitates construction, simulation and analysis of kinetic models in systems biology. Thus, it allows e.g. database supported modelling, basic model checking and the estimation of unknown kinetic parameters based on protein structures. In addition, it offers some guidance in order to allow non-expert users to perform basic computational modelling tasks.

AVAILABILITY

SYCAMORE is freely available for academic use at http://sycamore.eml.org. Commercial users may acquire a license.

CONTACT

ursula.kummer@bioquant.uni-heidelberg.de.

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

We introduce the Beta Workbench (BWB), a scalable tool built on top of the newly defined BlenX language to model, simulate and analyse biological systems. We show the features and the incremental modelling process supported by the BWB on a running example based on the mitogen-activated kinase pathway. Finally, we provide a comparison with related approaches and some hints for future extensions.

SBMLsqueezer: a CellDesigner plug-in to generate kinetic rate equations for biochemical networks

Background

The development of complex biochemical models has been facilitated through the standardization of machine-readable representations like SBML (Systems Biology Markup Language). This effort is accompanied by the ongoing development of the human-readable diagrammatic representation SBGN (Systems Biology Graphical Notation). The graphical SBML editor CellDesigner allows direct translation of SBGN into SBML, and vice versa. For the assignment of kinetic rate laws, however, this process is not straightforward, as it often requires manual assembly and specific knowledge of kinetic equations.

Results

SBMLsqueezer facilitates exactly this modeling step via automated equation generation, overcoming the highly error-prone and cumbersome process of manually assigning kinetic equations. For each reaction the kinetic equation is derived from the stoichiometry, the participating species (e.g., proteins, mRNA or simple molecules) as well as the regulatory relations (activation, inhibition or other modulations) of the SBGN diagram. Such information allows distinctions between, for example, translation, phosphorylation or state transitions. The types of kinetics considered are numerous, for instance generalized mass-action, Hill, convenience and several Michaelis-Menten-based kinetics, each including activation and inhibition. These kinetics allow SBMLsqueezer to cover metabolic, gene regulatory, signal transduction and mixed networks. Whenever multiple kinetics are applicable to one reaction, parameter settings allow for user-defined specifications. After invoking SBMLsqueezer, the kinetic formulas are generated and assigned to the model, which can then be simulated in CellDesigner or with external ODE solvers. Furthermore, the equations can be exported to SBML, LaTeX or plain text format.

Conclusion

SBMLsqueezer considers the annotation of all participating reactants, products and regulators when generating rate laws for reactions. Thus, for each reaction, only applicable kinetic formulas are considered. This modeling scheme creates kinetics in accordance with the diagrammatic representation. In contrast most previously published tools have relied on the stoichiometry and generic modulators of a reaction, thus ignoring and potentially conflicting with the information expressed through the process diagram. Additional material and the source code can be found at the project homepage (URL found in the Availability and requirements section).

Mathematical modeling identifies Smad nucleocytoplasmic shuttling as a dynamic signal-interpreting system

TGF-beta-induced Smad signal transduction from the membrane into the nucleus is not linear and unidirectional, but rather a dynamic network that couples Smad phosphorylation and dephosphorylation through continuous nucleocytoplasmic shuttling of Smads. To understand the quantitative behavior of this network, we have developed a tightly constrained computational model, exploiting the interplay between mathematical modeling and experimental strategies. The model simultaneously reproduces four distinct datasets with excellent accuracy and provides mechanistic insights into how the network operates. We use the model to make predictions about the outcome of fluorescence recovery after photobleaching experiments and the behavior of a functionally impaired Smad2 mutant, which we then verify experimentally. Successful model performance strongly supports the hypothesis of a dynamic maintenance of Smad nuclear accumulation during active signaling. The presented work establishes Smad nucleocytoplasmic shuttling as a dynamic network that flexibly transmits quantitative features of the extracellular TGF-beta signal, such as its duration and intensity, into the nucleus.

Synthesis of dihydropyridines and pyridines from imines and alkynes via C-H activation

A convenient one-pot C-H alkenylation/electrocyclization/aromatization sequence has been developed for the synthesis of highly substituted pyridine derivatives from alkynes and alpha,beta-unsaturated N-benzyl aldimines and ketimines that proceeds through dihydropyridine intermediates. A new class of ligands for C-H activation was developed, providing broader scope for the alkenylation step than could be achieved with previously reported ligands. Substantial information was obtained about the mechanism of the reaction. This included the isolation of a C-H activated complex and its structure determination by X-ray analysis; in addition, kinetic simulations using the Copasi software were employed to determine rate constants for this transformation, implicating facile C-H oxidative addition and slow reductive elimination steps.

From DNA nanotechnology to synthetic biology

Attempts to construct artificial systems from biological molecules such as DNA and RNA by self-assembly are compatible with the recent development of synthetic biology. Genetic mechanisms can be used to produce or control artificial structures made from DNA and RNA, and these structures can in turn be used as artificial gene regulatory elements, in vitro as well as in vivo. Artificial biochemical circuits can be incorporated into cell-like reaction compartments, which opens up the possibility to operate them permanently out of equilibrium. In small systems, stochastic effects become noticeable and will have to be accounted for in the design of future systems.

Modelling dynamic processes in yeast

Yeast molecular and cell biology has accumulated large amounts of qualitative and quantitative data of diverse cellular processes. The results are often summarized as verbal or graphical descriptions. Moreover, a series of mathematical models has been developed that should help to interpret such data, to integrate them into a coherent picture and to allow for an understanding of the underlying processes. Dynamic modelling of regulatory processes in yeast focuses on central carbon metabolism, on a number of selected signalling pathways and on cell cycle regulation. These models can explain questions of general relevance, such as whether the dynamics of a network can be understood from the combination of in vitro kinetics of its individual reactions. They help to elucidate complicated dynamic features, such as glycolytic oscillations, effects of feedback regulation or the optimal regulation of gene expression. The availability of comprehensive qualitative information, such as protein interactions or pathway composition, and sets of quantitative data make yeast a perfect model organism. Therefore, yeast-related data are often used to develop and examine computational approaches and modelling methods.

Insights into Zn2+homeostasis in neurons from experimental and modeling studies

To understand the mechanisms of neuronal Zn2+homeostasis better, experimental data obtained from cultured cortical neurons were used to inform a series of increasingly complex computational models. Total metals (inductively coupled plasma-mass spectrometry), resting metallothionein,65Zn2+uptake and release, and intracellular free Zn2+levels using ZnAF-2F were determined before and after neurons were exposed to increased Zn2+, either with or without the addition of a Zn2+ionophore (pyrithione) or metal chelators [EDTA, clioquinol (CQ), and N, N, N′, N′-tetrakis(2-pyridylmethyl)ethylenediamine]. Three models were tested for the ability to match intracellular free Zn2+transients and total Zn2+content observed under these conditions. Only a model that incorporated a muffler with high affinity for Zn2+, trafficking Zn2+to intracellular storage sites, was able to reproduce the experimental results, both qualitatively and quantitatively. This “muffler model” estimated the resting intracellular free Zn2+concentration to be 1.07 nM. If metallothionein were to function as the exclusive cytosolic Zn2+muffler, the muffler model predicts that the cellular concentration required to match experimental data is greater than the measured resting concentration of metallothionein. Thus Zn2+buffering in resting cultured neurons requires additional high-affinity cytosolic metal binding moieties. Added CQ, as low as 1 μM, was shown to selectively increase Zn2+influx. Simulations reproduced these data by modeling CQ as an ionophore. We conclude that maintenance of neuronal Zn2+homeostasis, when challenged with Zn2+loads, relies heavily on the function of a high-affinity muffler, the characteristics of which can be effectively studied with computational models.

Modelling and simulation of biological processes in BlenX

We introduce a scalable framework built upon the BlenX language and inspired by the Beta-binders process calculus to model, simulate and analyse biological systems. We show the features of the Beta Workbench framework on a running example based on the mitogen-activated kinase pathway. We also discuss an incremental modelling process that allows us to scale up from pathway to network modelling and analysis. We finally provide a comparison with related approaches and some hints for future extensions of the framework.

The SBML discrete stochastic models test suite

MOTIVATION

Stochastic simulation is a very important tool for mathematical modelling. However, it is difficult to check the correctness of a stochastic simulator, since any two realizations from a single model will typically be different.

RESULTS

We have developed a test suite of stochastic models that have been solved either analytically or using numerical methods. This allows the accuracy of stochastic simulators to be tested against known results. The test suite is already being used by a number of stochastic simulator developers.

AVAILABILITY

The latest version of the test suite can be obtained from http://www.calibayes.ncl.ac.uk/Resources/dsmts/ and is licensed under GNU Lesser General Public License.

On the killing of mycobacteria by macrophages

Both pathogenic and non-pathogenic mycobacteria are internalized into macrophage phagosomes. Whereas the non-pathogenic types are invariably killed by all macrophages, the pathogens generally survive and grow. Here, we addressed the survival, production of nitrogen intermediates (RNI) and intracellular trafficking of the non-pathogenic Mycobacterium smegmatis, the pathogen-like, BCG and the pathogenic M. bovis in different mouse, human and bovine macrophages. The bacteriocidal effects of RNI were restricted for all bacterial species to the early stages of infection. EM analysis showed clearly that all the mycobacteria remained within phagosomes even at late times of infection. The fraction of BCG and M. bovis found in mature phagolysosomes rarely exceeded 10% of total, irrespective of whether bacteria were growing, latent or being killed, with little correlation between the extent of phagosome maturation and the degree of killing. Theoretical modelling of our data identified two different potential sets of explanations that are consistent with our results. The model we favour is one in which a small but significant fraction of BCG is killed in an early phagosome, then maturation of a small fraction of phagosomes with both live and killed bacteria, followed by extremely rapid killing and digestion of the bacteria in phago-lysosomes.

Synthetic microarray data generation with RANGE and NEMO

MOTIVATION

For testing and sensitivity analysis purposes, it is beneficial to have known transcription networks of sufficient size and variability during development of microarray data and network deconvolution algorithms. Description of such networks in a simple language translatable to Systems Biology Markup Language would allow generation of model data for the networks.

RESULTS

Described herein is software (RANGE: RAndom Network GEnerator) to generate large random transcription networks in the NEMO (NEtwork MOtif) language. NEMO is recognized by a grammar for transcription network motifs using lex and yacc to output Systems Biology Markup Language models for either specified or randomized gene input functions. These models of known networks may be input to a biochemical simulator, allowing the generation of synthetic microarray data.

AVAILABILITY

http://range.sourceforge.net

MetaCrop: a detailed database of crop plant metabolism

MetaCrop is a manually curated repository of high quality information concerning the metabolism of crop plants. This includes pathway diagrams, reactions, locations, transport processes, reaction kinetics, taxonomy and literature. MetaCrop provides detailed information on six major crop plants with high agronomical importance and initial information about several other plants. The web interface supports an easy exploration of the information from overview pathways to single reactions and therefore helps users to understand the metabolism of crop plants. It also allows model creation and automatic data export for detailed models of metabolic pathways therefore supporting systems biology approaches. The MetaCrop database is accessible at http://metacrop.ipk-gatersleben.de.