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Open Access Research article

Stochastic and deterministic multiscale models for systems biology: an auxin-transport case study

Jamie Twycross1, Leah R Band1, Malcolm J Bennett1, John R King12 and Natalio Krasnogor13*

Author Affiliations

1 Centre for Plant Integrative Biology, School of Biosciences, Sutton Bonington Campus, University of Nottingham, Nottingham, LE12 5RD, UK

2 School of Mathematical Sciences, University Park, University of Nottingham, Nottingham, NG7 2RD, UK

3 Automatic Scheduling and Planning Group, School of Computer Science, Jubilee Campus, University of Nottingham, Nottingham, NG8 1BB, UK

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BMC Systems Biology 2010, 4:34  doi:10.1186/1752-0509-4-34

Published: 26 March 2010



Stochastic and asymptotic methods are powerful tools in developing multiscale systems biology models; however, little has been done in this context to compare the efficacy of these methods. The majority of current systems biology modelling research, including that of auxin transport, uses numerical simulations to study the behaviour of large systems of deterministic ordinary differential equations, with little consideration of alternative modelling frameworks.


In this case study, we solve an auxin-transport model using analytical methods, deterministic numerical simulations and stochastic numerical simulations. Although the three approaches in general predict the same behaviour, the approaches provide different information that we use to gain distinct insights into the modelled biological system. We show in particular that the analytical approach readily provides straightforward mathematical expressions for the concentrations and transport speeds, while the stochastic simulations naturally provide information on the variability of the system.


Our study provides a constructive comparison which highlights the advantages and disadvantages of each of the considered modelling approaches. This will prove helpful to researchers when weighing up which modelling approach to select. In addition, the paper goes some way to bridging the gap between these approaches, which in the future we hope will lead to integrative hybrid models.