8,118 research outputs found

    BioSimulator.jl: Stochastic simulation in Julia

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    Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in generating time-evolution trajectories for these systems because they can adequately capture the influence of random fluctuations and quantify rare events. We present a simple and flexible package, BioSimulator.jl, for implementing the Gillespie algorithm, τ\tau-leaping, and related stochastic simulation algorithms. The objective of this work is to provide scientists across domains with fast, user-friendly simulation tools. We used the high-performance programming language Julia because of its emphasis on scientific computing. Our software package implements a suite of stochastic simulation algorithms based on Markov chain theory. We provide the ability to (a) diagram Petri Nets describing interactions, (b) plot average trajectories and attached standard deviations of each participating species over time, and (c) generate frequency distributions of each species at a specified time. BioSimulator.jl's interface allows users to build models programmatically within Julia. A model is then passed to the simulate routine to generate simulation data. The built-in tools allow one to visualize results and compute summary statistics. Our examples highlight the broad applicability of our software to systems of varying complexity from ecology, systems biology, chemistry, and genetics. The user-friendly nature of BioSimulator.jl encourages the use of stochastic simulation, minimizes tedious programming efforts, and reduces errors during model specification.Comment: 27 pages, 5 figures, 3 table

    On functional module detection in metabolic networks

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    Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models

    Modeling and evolving biochemical networks: insights into communication and computation from the biological domain

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    This paper is concerned with the modeling and evolving of Cell Signaling Networks (CSNs) in silico. CSNs are complex biochemical networks responsible for the coordination of cellular activities. We examine the possibility to computationally evolve and simulate Artificial Cell Signaling Networks (ACSNs) by means of Evolutionary Computation techniques. From a practical point of view, realizing and evolving ACSNs may provide novel computational paradigms for a variety of application areas. For example, understanding some inherent properties of CSNs such as crosstalk may be of interest: A potential benefit of engineering crosstalking systems is that it allows the modification of a specific process according to the state of other processes in the system. This is clearly necessary in order to achieve complex control tasks. This work may also contribute to the biological understanding of the origins and evolution of real CSNs. An introduction to CSNs is first provided, in which we describe the potential applications of modeling and evolving these biochemical networks in silico. We then review the different classes of techniques to model CSNs, this is followed by a presentation of two alternative approaches employed to evolve CSNs within the ESIGNET project. Results obtained with these methods are summarized and discussed

    Data-driven modelling of biological multi-scale processes

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    Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

    The Reachability Problem for Petri Nets is Not Elementary

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    Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. Decidability was proved by Mayr in his seminal STOC 1981 work, and the currently best published upper bound is non-primitive recursive Ackermannian of Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound, i.e. that the reachability problem needs a tower of exponentials of time and space. Until this work, the best lower bound has been exponential space, due to Lipton in 1976. The new lower bound is a major breakthrough for several reasons. Firstly, it shows that the reachability problem is much harder than the coverability (i.e., state reachability) problem, which is also ubiquitous but has been known to be complete for exponential space since the late 1970s. Secondly, it implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi and other areas, that are known to admit reductions from the Petri nets reachability problem, are also not elementary. Thirdly, it makes obsolete the currently best lower bounds for the reachability problems for two key extensions of Petri nets: with branching and with a pushdown stack.Comment: Final version of STOC'1

    In-silico-Systemanalyse von Biopathways

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    Chen M. In silico systems analysis of biopathways. Bielefeld (Germany): Bielefeld University; 2004.In the past decade with the advent of high-throughput technologies, biology has migrated from a descriptive science to a predictive one. A vast amount of information on the metabolism have been produced; a number of specific genetic/metabolic databases and computational systems have been developed, which makes it possible for biologists to perform in silico analysis of metabolism. With experimental data from laboratory, biologists wish to systematically conduct their analysis with an easy-to-use computational system. One major task is to implement molecular information systems that will allow to integrate different molecular database systems, and to design analysis tools (e.g. simulators of complex metabolic reactions). Three key problems are involved: 1) Modeling and simulation of biological processes; 2) Reconstruction of metabolic pathways, leading to predictions about the integrated function of the network; and 3) Comparison of metabolism, providing an important way to reveal the functional relationship between a set of metabolic pathways. This dissertation addresses these problems of in silico systems analysis of biopathways. We developed a software system to integrate the access to different databases, and exploited the Petri net methodology to model and simulate metabolic networks in cells. It develops a computer modeling and simulation technique based on Petri net methodology; investigates metabolic networks at a system level; proposes a markup language for biological data interchange among diverse biological simulators and Petri net tools; establishes a web-based information retrieval system for metabolic pathway prediction; presents an algorithm for metabolic pathway alignment; recommends a nomenclature of cellular signal transduction; and attempts to standardize the representation of biological pathways. Hybrid Petri net methodology is exploited to model metabolic networks. Kinetic modeling strategy and Petri net modeling algorithm are applied to perform the processes of elements functioning and model analysis. The proposed methodology can be used for all other metabolic networks or the virtual cell metabolism. Moreover, perspectives of Petri net modeling and simulation of metabolic networks are outlined. A proposal for the Biology Petri Net Markup Language (BioPNML) is presented. The concepts and terminology of the interchange format, as well as its syntax (which is based on XML) are introduced. BioPNML is designed to provide a starting point for the development of a standard interchange format for Bioinformatics and Petri nets. The language makes it possible to exchange biology Petri net diagrams between all supported hardware platforms and versions. It is also designed to associate Petri net models and other known metabolic simulators. A web-based metabolic information retrieval system, PathAligner, is developed in order to predict metabolic pathways from rudimentary elements of pathways. It extracts metabolic information from biological databases via the Internet, and builds metabolic pathways with data sources of genes, sequences, enzymes, metabolites, etc. The system also provides a navigation platform to investigate metabolic related information, and transforms the output data into XML files for further modeling and simulation of the reconstructed pathway. An alignment algorithm to compare the similarity between metabolic pathways is presented. A new definition of the metabolic pathway is proposed. The pathway defined as a linear event sequence is practical for our alignment algorithm. The algorithm is based on strip scoring the similarity of 4-hierarchical EC numbers involved in the pathways. The algorithm described has been implemented and is in current use in the context of the PathAligner system. Furthermore, new methods for the classification and nomenclature of cellular signal transductions are recommended. For each type of characterized signal transduction, a unique ST number is provided. The Signal Transduction Classification Database (STCDB), based on the proposed classification and nomenclature, has been established. By merging the ST numbers with EC numbers, alignments of biopathways are possible. Finally, a detailed model of urea cycle that includes gene regulatory networks, metabolic pathways and signal transduction is demonstrated by using our approaches. A system biological interpretation of the observed behavior of the urea cycle and its related transcriptomics information is proposed to provide new insights for metabolic engineering and medical care

    Hybrid modeling and optimization of biological processes

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    Proß S. Hybrid modeling and optimization of biological processes. Bielefeld: Bielefeld University; 2013
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