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Symmetry structures in dynamic models of biochemical systems.

ABSTRACT: Understanding the complex interactions of biochemical processes underlying human disease represents the holy grail of systems biology. When processes are modelled in ordinary differential equation (ODE) fashion, the most common tool for their analysis is linear stability analysis where the long-term behaviour of the model is determined by linearizing the system around its steady states. However, this asymptotic behaviour is often insufficient for completely determining the structure of the underlying system. A complementary technique for analysing a system of ODEs is to consider the set of symmetries of its solutions. Symmetries provide a powerful concept for the development of mechanistic models by describing structures corresponding to the underlying dynamics of biological systems. To demonstrate their capability, we consider symmetries of the nonlinear Hill model describing enzymatic reaction kinetics and derive a class of symmetry transformations for each order of the model. We consider a minimal example consisting of the application of symmetry-based methods to a model selection problem, where we are able to demonstrate superior performance compared to ordinary residual-based model selection. Moreover, we demonstrate that symmetries reveal the intrinsic properties of a system of interest based on a single time series. Finally, we show and propose that symmetry-based methodology should be considered as the first step in a systematic model building and in the case when multiple time series are available it should complement the commonly used statistical methodologies.

SUBMITTER: Ohlsson F

PROVIDER: S-EPMC7423443 | biostudies-literature | 2020 Jul

REPOSITORIES: biostudies-literature

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Symmetry structures in dynamic models of biochemical systems.

Ohlsson Fredrik F Borgqvist Johannes J Cvijovic Marija M

Journal of the Royal Society, Interface 20200722 168

Understanding the complex interactions of biochemical processes underlying human disease represents the holy grail of systems biology. When processes are modelled in ordinary differential equation (ODE) fashion, the most common tool for their analysis is linear stability analysis where the long-term behaviour of the model is determined by linearizing the system around its steady states. However, this asymptotic behaviour is often insufficient for completely determining the structure of the under ...[more]

PMID: 32693742

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Project description:BackgroundModels of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model.ResultsIn this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in baker's yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved.ConclusionsWe introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to nonlinear models.

Project description:BackgroundMathematical modeling and in silico analysis are widely acknowledged as complementary tools to biological laboratory methods, to achieve a thorough understanding of emergent behaviors of cellular processes in both physiological and perturbed conditions. Though, the simulation of large-scale models-consisting in hundreds or thousands of reactions and molecular species-can rapidly overtake the capabilities of Central Processing Units (CPUs). The purpose of this work is to exploit alternative high-performance computing solutions, such as Graphics Processing Units (GPUs), to allow the investigation of these models at reduced computational costs.ResultsLASSIE is a "black-box" GPU-accelerated deterministic simulator, specifically designed for large-scale models and not requiring any expertise in mathematical modeling, simulation algorithms or GPU programming. Given a reaction-based model of a cellular process, LASSIE automatically generates the corresponding system of Ordinary Differential Equations (ODEs), assuming mass-action kinetics. The numerical solution of the ODEs is obtained by automatically switching between the Runge-Kutta-Fehlberg method in the absence of stiffness, and the Backward Differentiation Formulae of first order in presence of stiffness. The computational performance of LASSIE are assessed using a set of randomly generated synthetic reaction-based models of increasing size, ranging from 64 to 8192 reactions and species, and compared to a CPU-implementation of the LSODA numerical integration algorithm.ConclusionsLASSIE adopts a novel fine-grained parallelization strategy to distribute on the GPU cores all the calculations required to solve the system of ODEs. By virtue of this implementation, LASSIE achieves up to 92× speed-up with respect to LSODA, therefore reducing the running time from approximately 1 month down to 8 h to simulate models consisting in, for instance, four thousands of reactions and species. Notably, thanks to its smaller memory footprint, LASSIE is able to perform fast simulations of even larger models, whereby the tested CPU-implementation of LSODA failed to reach termination. LASSIE is therefore expected to make an important breakthrough in Systems Biology applications, for the execution of faster and in-depth computational analyses of large-scale models of complex biological systems.

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Symmetry structures in dynamic models of biochemical systems.

Publications

Symmetry structures in dynamic models of biochemical systems.

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