Abstract
Many biological processes are described with coupled non-linear systems of ordinary differential equations that contain a plethora of parameters. The goal is to understand these systems and to predict the effect of different influences. This asks for a dynamical systems approach where numerical continuation methods and bifurcation analysis are used to detect the solutions and their stability as a function of the parameters. We developed PyNCT – Python Numerical Continuation Toolbox – an open source Python package that implements numerical continuation methods and can perform bifurcation analysis based on sparse linear algebra. The software gives the user the choice of different solvers (direct and iterative) and allows the use of preconditioners to reduce the number of iterations and guarantee the convergence when working with complex non-linear models.
In this paper we demonstrate the usefulness of the toolbox with a class of models pertaining to auxin transport between cells in plant organs.We show how easy it is to compute the steady state solutions for different parameter values, to calculate how they depend on each other and to map parts of the solution landscape.
An interactive model development and discovery cycle is key in bio-systems research. It allows one to investigate and compare different model parameter settings and even different models and gauge the model’s usefulness. Our toolbox allows for such quick experimentation and has a low entry barrier for non-technical users.
Although PyNCT was developed particularly for the study of transport models in biology, its implementation is generic and extensible, and can be used in many other dynamical system applications.
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Acknowledgements
DD acknowledges financial support from the Department of Mathematics and Computer Science of the University of Antwerp. This work is part of the Geconcerteerde Onderzoeksactie (G.O.A.) research grant “A System Biology Approach of Leaf Morphogenesis” granted by the research council of the University of Antwerp. We acknowledge Giovanni Samaey for sharing basic version of a continuation code.
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Draelants, D., Kłosiewicz, P., Broeckhove, J., Vanroose, W. (2015). Solving General Auxin Transport Models with a Numerical Continuation Toolbox in Python: PyNCT. In: Abate, A., Šafránek, D. (eds) Hybrid Systems Biology. HSB 2015. Lecture Notes in Computer Science(), vol 9271. Springer, Cham. https://doi.org/10.1007/978-3-319-26916-0_12
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