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

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.Biological systems are naturally multiscale and to understand their behaviour fully we must understand the interaction of a number of processes that may occur on diverse temporal and spatial scales. To gain insight into such multiprocess and multiscale systems, there is a range of modelling frameworks that could potentially be employed. Different modelling approaches serve to highlight certain aspects of a biological system, and which modelling approach is most appropriate depends on the biological questions that are being addressed, as well as on the available data that could be used to calibrate or validate a given model. In this paper, we present several modelling approaches and show how these can be used to gain understanding of a realistic multiscale systems biology problem. We compare the different modelling approaches to each other and discuss their applicability.To compare the modelling approaches, we focus on a particular case study: the transport of the hormone auxin through a file of plant cells.