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Identifying parameter regions for multistationarity.

ABSTRACT: Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria. The procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity.

SUBMITTER: Conradi C

PROVIDER: S-EPMC5626113 | biostudies-literature | 2017 Oct

REPOSITORIES: biostudies-literature

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Identifying parameter regions for multistationarity.

Conradi Carsten C Feliu Elisenda E Mincheva Maya M Wiuf Carsten C

PLoS computational biology 20171003 10

Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure to partition the parameter space of a parameterized ...[more]

PMID: 28972969

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Project description:BACKGROUND:DNA methylation is an epigenetic modification that is studied at a single-base resolution with bisulfite treatment followed by high-throughput sequencing. After alignment of the sequence reads to a reference genome, methylation counts are analyzed to determine genomic regions that are differentially methylated between two or more biological conditions. Even though a variety of software packages is available for different aspects of the bioinformatics analysis, they often produce results that are biased or require excessive computational requirements. RESULTS:DMRfinder is a novel computational pipeline that identifies differentially methylated regions efficiently. Following alignment, DMRfinder extracts methylation counts and performs a modified single-linkage clustering of methylation sites into genomic regions. It then compares methylation levels using beta-binomial hierarchical modeling and Wald tests. Among its innovative attributes are the analyses of novel methylation sites and methylation linkage, as well as the simultaneous statistical analysis of multiple sample groups. To demonstrate its efficiency, DMRfinder is benchmarked against other computational approaches using a large published dataset. Contrasting two replicates of the same sample yielded minimal genomic regions with DMRfinder, whereas two alternative software packages reported a substantial number of false positives. Further analyses of biological samples revealed fundamental differences between DMRfinder and another software package, despite the fact that they utilize the same underlying statistical basis. For each step, DMRfinder completed the analysis in a fraction of the time required by other software. CONCLUSIONS:Among the computational approaches for identifying differentially methylated regions from high-throughput bisulfite sequencing datasets, DMRfinder is the first that integrates all the post-alignment steps in a single package. Compared to other software, DMRfinder is extremely efficient and unbiased in this process. DMRfinder is free and open-source software, available on GitHub ( github.com/jsh58/DMRfinder ); it is written in Python and R, and is supported on Linux.

Dataset Information

Identifying parameter regions for multistationarity.

Publications

Identifying parameter regions for multistationarity.

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