Detailed dynamical systems models used in life sciences may include dozens or even hundreds of state variables. Models of large dimension are not only harder from the numerical perspective (e.g., for parameter estimation or simulation), but it is also becoming challenging to derive mechanistic insights from such models. Exact model reduction is a way to address this issue by finding a self-consistent lower-dimensional projection of the corresponding dynamical system. A recent algorithm CLUE allows one to construct an exact linear reduction of the smallest possible dimension such that the fixed variables of interest are preserved. However, CLUE is restricted to systems with polynomial dynamics. Since rational dynamics occurs frequently in the life sciences (e.g., Michaelis-Menten or Hill kinetics), it is desirable to extend CLUE to the models with rational dynamics. In this paper, we present an extension of CLUE to the case of rational dynamics and demonstrate its applicability on examples from literature. Our implementation is available in version 1.5 of CLUE (https://github.com/pogudingleb/CLUE).
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CLUE: exact maximal reduction of kinetic models by constrained lumping of differential equations
Abstract Motivation Detailed mechanistic models of biological processes can pose significant challenges for analysis and parameter estimations due to the large number of equations used to track the dynamics of all distinct configurations in which each involved biochemical species can be found. Model reduction can help tame such complexity by providing a lower-dimensional model in which each macro-variable can be directly related to the original variables. Results We present CLUE, an algorithm for exact model reduction of systems of polynomial differential equations by constrained linear lumping. It computes the smallest dimensional reduction as a linear mapping of the state space such that the reduced model preserves the dynamics of user-specified linear combinations of the original variables. Even though CLUE works with non-linear differential equations, it is based on linear algebra tools, which makes it applicable to high-dimensional models. Using case studies from the literature, we show how CLUE can substantially lower model dimensionality and help extract biologically intelligible insights from the reduction. Availabilityand implementation An implementation of the algorithm and relevant resources to replicate the experiments herein reported are freely available for download at https://github.com/pogudingleb/CLUE. Supplementary information Supplementary data are available at Bioinformatics online.
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- NSF-PAR ID:
- 10251738
- Editor(s):
- Valencia, Alfonso
- Date Published:
- Journal Name:
- Bioinformatics
- ISSN:
- 1367-4803
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Background In systems biology, the dynamics of biological networks are often modeled with ordinary differential equations (ODEs) that encode interacting components in the systems, resulting in highly complex models. In contrast, the amount of experimentally available data is almost always limited, and insufficient to constrain the parameters. In this situation, parameter estimation is a very challenging problem. To address this challenge, two intuitive approaches are to perform experimental design to generate more data, and to perform model reduction to simplify the model. Experimental design and model reduction have been traditionally viewed as two distinct areas, and an extensive literature and excellent reviews exist on each of the two areas. Intriguingly, however, the intrinsic connections between the two areas have not been recognized.
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/bioinformatics/btab010
