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Hierarchical optimization for the efficient parametrization of ODE models.

ABSTRACT: Motivation:Mathematical models are nowadays important tools for analyzing dynamics of cellular processes. The unknown model parameters are usually estimated from experimental data. These data often only provide information about the relative changes between conditions, hence, the observables contain scaling parameters. The unknown scaling parameters and corresponding noise parameters have to be inferred along with the dynamic parameters. The nuisance parameters often increase the dimensionality of the estimation problem substantially and cause convergence problems. Results:In this manuscript, we propose a hierarchical optimization approach for estimating the parameters for ordinary differential equation (ODE) models from relative data. Our approach restructures the optimization problem into an inner and outer subproblem. These subproblems possess lower dimensions than the original optimization problem, and the inner problem can be solved analytically. We evaluated accuracy, robustness and computational efficiency of the hierarchical approach by studying three signaling pathways. The proposed approach achieved better convergence than the standard approach and required a lower computation time. As the hierarchical optimization approach is widely applicable, it provides a powerful alternative to established approaches. Availability and implementation:The code is included in the MATLAB toolbox PESTO which is available at http://github.com/ICB-DCM/PESTO. Supplementary information:Supplementary data are available at Bioinformatics online.

SUBMITTER: Loos C

PROVIDER: S-EPMC6289139 | biostudies-literature | 2018 Dec

REPOSITORIES: biostudies-literature

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Hierarchical optimization for the efficient parametrization of ODE models.

Loos Carolin C Krause Sabrina S Hasenauer Jan J

Bioinformatics (Oxford, England) 20181201 24

<h4>Motivation</h4>Mathematical models are nowadays important tools for analyzing dynamics of cellular processes. The unknown model parameters are usually estimated from experimental data. These data often only provide information about the relative changes between conditions, hence, the observables contain scaling parameters. The unknown scaling parameters and corresponding noise parameters have to be inferred along with the dynamic parameters. The nuisance parameters often increase the dimensi ...[more]

PMID: 30010716

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Project description:Network representations of biological systems are widespread and reconstructing unknown networks from data is a focal problem for computational biologists. For example, the series of biochemical reactions in a metabolic pathway can be represented as a network, with nodes corresponding to metabolites and edges linking reactants to products. In a different context, regulatory relationships among genes are commonly represented as directed networks with edges pointing from influential genes to their targets. Reconstructing such networks from data is a challenging problem receiving much attention in the literature. There is a particular need for approaches tailored to time-series data and not reliant on direct intervention experiments, as the former are often more readily available. In this paper, we introduce an approach to reconstructing directed networks based on dynamic systems models. Our approach generalizes commonly used ODE models based on linear or nonlinear dynamics by extending the functional class for the functions involved from parametric to nonparametric models. Concomitantly we limit the complexity by imposing an additive structure on the estimated slope functions. Thus the submodel associated with each node is a sum of univariate functions. These univariate component functions form the basis for a novel coupling metric that we define in order to quantify the strength of proposed relationships and hence rank potential edges. We show the utility of the method by reconstructing networks using simulated data from computational models for the glycolytic pathway of Lactocaccus Lactis and a gene network regulating the pluripotency of mouse embryonic stem cells. For purposes of comparison, we also assess reconstruction performance using gene networks from the DREAM challenges. We compare our method to those that similarly rely on dynamic systems models and use the results to attempt to disentangle the distinct roles of linearity, sparsity, and derivative estimation.

Dataset Information

Hierarchical optimization for the efficient parametrization of ODE models.

Publications

Hierarchical optimization for the efficient parametrization of ODE models.

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