Model building and model checking for biochemical processes

A central claim of computational systems biology is that, by drawing on mathematical approaches developed in the context of dynamic systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis, and reasoning tools for working biologists to decipher existing data, devise new experiments, and ultimately to understand functional properties of genomes, proteomes, cells, organs, and organisms. In this article, a novel computational tool is described that achieves many of the goals of this new discipline. The novelty of this system involves an automaton-based semantics of the temporal evolution of complex biochemical reactions starting from the representation given as a set of differential equations. The related tools also provide ability to qualitatively reason about the systems using a propositional temporal logic that can express an ordered sequence of events succinctly and unambiguously. The implementation of mathematical and computational models in the Simpathica and XSSYS systems is described briefly. Several example applications of these systems to cellular and biochemical processes are presented: the two most prominent are Leibler et al.'s repressilator (an artificial synthesized oscillatory network), and Curto-Voit-Sorribas-Cascante's purine metabolism reaction model.     

Accelerated maximum likelihood parameter estimation for stochastic biochemical systems

ABSTRACT: BACKGROUND: A prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems; methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs). MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence. RESULTS: We have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM2): an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM) algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM2 substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods. CONCLUSIONS: This work provides a novel, accelerated version of a likelihood-based parameter estimation method that can be readily applied to stochastic biochemical systems. In addition, our results suggest opportunities for added efficiency improvements that will further enhance our ability to mechanistically simulate biological processes.     

COPASI--a COmplex PAthway SImulator

MOTIVATION: Simulation and modeling is becoming a standard approach to understand complex biochemical processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these methods. RESULTS: Here, we present COPASI, a platform-independent and user-friendly biochemical simulator that offers several unique features. We discuss numerical issues with these features; in particular, the criteria to switch between stochastic and deterministic simulation methods, hybrid deterministic-stochastic methods, and the importance of random number generator numerical resolution in stochastic simulation. AVAILABILITY: The complete software is available in binary (executable) for MS Windows, OS X, Linux (Intel) and Sun Solaris (SPARC), as well as the full source code under an open source license from http://www.copasi.org.     

Carbon sequestration in Synechococcus Sp.: from molecular machines to hierarchical modeling

The U.S. Department of Energy recently announced the first five grants for the Genomes to Life (GTL) Program. The goal of this program is to "achieve the most far-reaching of all biological goals: a fundamental, comprehensive, and systematic understanding of life." While more information about the program can be found at the GTL website (www.doegenomestolife.org), this paper provides an overview of one of the five GTL projects funded, "Carbon Sequestration in Synechococcus Sp.: From Molecular Machines to Hierarchical Modeling." This project is a combined experimental and computational effort emphasizing developing, prototyping, and applying new computational tools and methods to elucidate the biochemical mechanisms of the carbon sequestration of Synechococcus Sp., an abundant marine cyanobacteria known to play an important role in the global carbon cycle. Understanding, predicting, and perhaps manipulating carbon fixation in the oceans has long been a major focus of biological oceanography and has more recently been of interest to a broader audience of scientists and policy makers. It is clear that the oceanic sinks and sources of CO(2) are important terms in the global environmental response to anthropogenic atmospheric inputs of CO(2) and that oceanic microorganisms play a key role in this response. However, the relationship between this global phenomenon and the biochemical mechanisms of carbon fixation in these microorganisms is poorly understood. The project includes five subprojects: an experimental investigation, three computational biology efforts, and a fifth which deals with addressing computational infrastructure challenges of relevance to this project and the Genomes to Life program as a whole. Our experimental effort is designed to provide biology and data to drive the computational efforts and includes significant investment in developing new experimental methods for uncovering protein partners, characterizing protein complexes, identifying new binding domains. We will also develop and apply new data measurement and statistical methods for analyzing microarray experiments. Our computational efforts include coupling molecular simulation methods with knowledge discovery from diverse biological data sets for high-throughput discovery and characterization of protein-protein complexes and developing a set of novel capabilities for inference of regulatory pathways in microbial genomes across multiple sources of information through the integration of computational and experimental technologies. These capabilities will be applied to Synechococcus regulatory pathways to characterize their interaction map and identify component proteins in these pathways. We will also investigate methods for combining experimental and computational results with visualization and natural language tools to accelerate discovery of regulatory pathways. Furthermore, given that the ultimate goal of this effort is to develop a systems-level of understanding of how the Synechococcus genome affects carbon fixation at the global scale, we will develop and apply a set of tools for capturing the carbon fixation behavior of complex of Synechococcus at different levels of resolution. Finally, because the explosion of data being produced by high-throughput experiments requires data analysis and models which are more computationally complex, more heterogeneous, and require coupling to ever increasing amounts of experimentally obtained data in varying formats, we have also established a companion computational infrastructure to support this effort as well as the Genomes to Life program as a whole.     

Farm animal genome databases

The requirements for bioinformatics resources to support genome research in farm animals is reviewed.The resources developed to meet these needs are described. Resource databases and associated tools have been developed to handle experimental data. Several of these systems serve the needs of multinational collaborations. Genome databases have been established to provide contemporary summaries of the status of genome maps in a range of farm and domestic animals along with experimental details and citations. New resources and tools will be required to address the informatics needs of emerging technologies such as microarrays. However, continued investment is also required to maintain the currency and utility of the current systems, especially the genome databases.     

ChemChains: a platform for simulation and analysis of biochemical networks aimed to laboratory scientists

Background  

New mathematical models of complex biological structures and computer simulation software allow modelers to simulate and analyze biochemical systems in silico and form mathematical predictions. Due to this potential predictive ability, the use of these models and software has the possibility to compliment laboratory investigations and help refine, or even develop, new hypotheses. However, the existing mathematical modeling techniques and simulation tools are often difficult to use by laboratory biologists without training in high-level mathematics, limiting their use to trained modelers.     

Modular modeling of cellular systems with ProMoT/Diva

MOTIVATION: Need for software to setup and analyze complex mathematical models for cellular systems in a modular way, that also integrates the experimental environment of the cells. RESULTS: A computer framework is described which allows the building of modularly structured models using an abstract, modular and general modeling methodology. With this methodology, reusable modeling entities are introduced which lead to the development of a modeling library within the modeling tool ProMot. The simulation environment Diva is used for numerical analysis and parameter identification of the models. The simulation environment provides a number of tools and algorithms to simulate and analyze complex biochemical networks. The described tools are the first steps towards an integrated computer-based modeling, simulation and visualization environment Availability: Available on request to the authors. The software itself is free for scientific purposes but requires commercial libraries. SUPPLEMENTARY INFORMATION: http://www.mpi-magdeburg.mpg.de/projects/promot     

Resources, standards and tools for systems biology.

Modelling and simulation techniques are valuable tools for the understanding of complex biological systems. The design of a computer model necessarily has many diverse inputs, such as information on the model topology, reaction kinetics and experimental data, derived either from the literature, databases or direct experimental investigation. In this review, we describe different data resources, standards and modelling and simulation tools that are relevant to integrative systems biology.     

Software for systems biology: from tools to integrated platforms

Understanding complex biological systems requires extensive support from software tools. Such tools are needed at each step of a systems biology computational workflow, which typically consists of data handling, network inference, deep curation, dynamical simulation and model analysis. In addition, there are now efforts to develop integrated software platforms, so that tools that are used at different stages of the workflow and by different researchers can easily be used together. This Review describes the types of software tools that are required at different stages of systems biology research and the current options that are available for systems biology researchers. We also discuss the challenges and prospects for modelling the effects of genetic changes on physiology and the concept of an integrated platform.     

Transition from stochastic to deterministic behavior in calcium oscillations

Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism.     

Systems chemical biology

The increasing availability of data related to genes, proteins and their modulation by small molecules has provided a vast amount of biological information leading to the emergence of systems biology and the broad use of simulation tools for data analysis. However, there is a critical need to develop cheminformatics tools that can integrate chemical knowledge with these biological databases and simulation approaches, with the goal of creating systems chemical biology.     

Experimental determination and computational interpretation of biophysical properties of lipid bilayers enriched by cholesteryl hemisuccinate

Cholesteryl hemisuccinate (CHS) is one of the cholesterol-mimicking detergents not observed in nature. It is, however, widely used in protein crystallography, in biochemical studies of proteins, and in pharmacology. Here, we performed an extensive experimental and theoretical study on the behavior of CHS in lipid membranes rich in unsaturated phospholipids. We found that the deprotonated form of CHS (that is the predominant form under physiological conditions) does not mimic cholesterol very well. The protonated form of CHS does better in this regard, but also its ability to mimic the physical effects of cholesterol on lipid membranes is limited. Overall, although ordering and condensing effects characteristic to cholesterol are present in systems containing any form of CHS, their strength is appreciably weaker compared to cholesterol. Based on the considerable amount of experimental and atomistic simulation data, we conclude that these differences originate from the fact that the ester group of CHS does not anchor it in an optimal position at the water–membrane interface. The implications of these findings for considerations of protein–cholesterol interactions are briefly discussed.     

Advances to Bayesian network inference for generating causal networks from observational biological data

MOTIVATION: Network inference algorithms are powerful computational tools for identifying putative causal interactions among variables from observational data. Bayesian network inference algorithms hold particular promise in that they can capture linear, non-linear, combinatorial, stochastic and other types of relationships among variables across multiple levels of biological organization. However, challenges remain when applying these algorithms to limited quantities of experimental data collected from biological systems. Here, we use a simulation approach to make advances in our dynamic Bayesian network (DBN) inference algorithm, especially in the context of limited quantities of biological data. RESULTS: We test a range of scoring metrics and search heuristics to find an effective algorithm configuration for evaluating our methodological advances. We also identify sampling intervals and levels of data discretization that allow the best recovery of the simulated networks. We develop a novel influence score for DBNs that attempts to estimate both the sign (activation or repression) and relative magnitude of interactions among variables. When faced with limited quantities of observational data, combining our influence score with moderate data interpolation reduces a significant portion of false positive interactions in the recovered networks. Together, our advances allow DBN inference algorithms to be more effective in recovering biological networks from experimentally collected data. AVAILABILITY: Source code and simulated data are available upon request. SUPPLEMENTARY INFORMATION: http://www.jarvislab.net/Bioinformatics/BNAdvances/     

Representations of molecular pathways: an evaluation of SBML, PSI MI and BioPAX

MOTIVATION: Analysis and simulation of pathway data is of high importance in bioinformatics. Standards for representation of information about pathways are necessary for integration and analysis of data from various sources. Recently, a number of representation formats for pathway data, SBML, PSI MI and BioPAX, have been proposed. RESULTS: In this paper we compare these formats and evaluate them with respect to their underlying models, information content and possibilities for easy creation of tools. The evaluation shows that the main structure of the formats is similar. However, SBML is tuned towards simulation models of molecular pathways while PSI MI is more suitable for representing details about particular interactions and experiments. BioPAX is the most general and expressive of the formats. These differences are apparent in allowed information and the structure for representation of interactions. We discuss the impact of these differences both with respect to information content in existing databases and computational properties for import and analysis of data.     

A new dynamical layout algorithm for complex biochemical reaction networks

Background  

To study complex biochemical reaction networks in living cells researchers more and more rely on databases and computational methods. In order to facilitate computational approaches, visualisation techniques are highly important. Biochemical reaction networks, e.g. metabolic pathways are often depicted as graphs and these graphs should be drawn dynamically to provide flexibility in the context of different data. Conventional layout algorithms are not sufficient for every kind of pathway in biochemical research. This is mainly due to certain conventions to which biochemists/biologists are used to and which are not in accordance to conventional layout algorithms. A number of approaches has been developed to improve this situation. Some of these are used in the context of biochemical databases and make more or less use of the information in these databases to aid the layout process. However, visualisation becomes also more and more important in modelling and simulation tools which mostly do not offer additional connections to databases. Therefore, layout algorithms used in these tools have to work independently of any databases. In addition, all of the existing algorithms face some limitations with respect to the number of edge crossings when it comes to larger biochemical systems due to the interconnectivity of these. Last but not least, in some cases, biochemical conventions are not met properly.     

Integrated web visualizations for protein-protein interaction databases

Background

Understanding living systems is crucial for curing diseases. To achieve this task we have to understand biological networks based on protein-protein interactions. Bioinformatics has come up with a great amount of databases and tools that support analysts in exploring protein-protein interactions on an integrated level for knowledge discovery. They provide predictions and correlations, indicate possibilities for future experimental research and fill the gaps to complete the picture of biochemical processes. There are numerous and huge databases of protein-protein interactions used to gain insights into answering some of the many questions of systems biology. Many computational resources integrate interaction data with additional information on molecular background. However, the vast number of diverse Bioinformatics resources poses an obstacle to the goal of understanding. We present a survey of databases that enable the visual analysis of protein networks.

Results

We selected M =10 out of N =53 resources supporting visualization, and we tested against the following set of criteria: interoperability, data integration, quantity of possible interactions, data visualization quality and data coverage. The study reveals differences in usability, visualization features and quality as well as the quantity of interactions. StringDB is the recommended first choice. CPDB presents a comprehensive dataset and IntAct lets the user change the network layout. A comprehensive comparison table is available via web. The supplementary table can be accessed on http://tinyurl.com/PPI-DB-Comparison-2015.

Conclusions

Only some web resources featuring graph visualization can be successfully applied to interactive visual analysis of protein-protein interaction. Study results underline the necessity for further enhancements of visualization integration in biochemical analysis tools. Identified challenges are data comprehensiveness, confidence, interactive feature and visualization maturing.     

Bifurcations in Turing systems of the second kind may explain blastula cleavage plane orientation

Spontaneous pattern formation (emergence of Turing structures) may take place in biological systems as primary and secondary bifurcations to nonlinear parabolic partial differential equations describing biochemical reaction-diffusion systems. Bipolarity in mitosis and cleavage planes in cytokinesis may be related to this formation of prepatterns. Cleavage planes in early blastulas have an apparently well controlled spatial relationship to the polarity known as the animal-vegetal (A-V) axis: the mitotic spindles form perpendicular to this axis in the first two division stages, with cleavage planes going strictly through the A-V poles. The third-stage spindles are parallel to the A-V axis, and cleavage is roughly in the equatorial plane, thus separating the A-V poles. The reason for these phenomena are poorly understood with current mitosis/cytokinesis models based on intrinsic spindle properties. It is shown here by numerical simulation that a simple modification to the usual Turing equations yields selection rules which lead directly to these orientations of the prepatterns, without any further ad hoc assumptions. These results strongly support the prepattern model for mitosis and cytokinesis and the viewpoint that prepatterns play a fundamental role in nature.