Cell-Based Models in Plant Developmental Biology: Insights into Hybrid Approaches

Computer models are nowadays part of the biologist's toolbox for studying biological dynamics and processes. Tissue development and functioning results from extremely complicated dynamics, that usual analysis does not come very far in terms of understanding the processes underlying those dynamics. In this context, mathematical and numerical models can help to disentangle complex interactions and to analyze non-intuitive dynamics that drives tissue development and functioning. Since these are multi-scale processes, both in time and space, there is the need to develop an appropriate modeling approach. The most promising one is hybrid modeling, that is a synthesis of the differential equation based reaction-diffusion approach at molecular and chemical continuous scales, and the Individual-Based modeling approach for simulating the mechanical and behavioral interactions of the cell ensemble constituting the tissue. Such an approach has been often used in developmental biology, both for plants and animals. In this paper, a brief history of hybrid modeling approaches and tools will be reviewed, and a simple example of its application to a current problem in plant developmental biology (the appearance of vascular patterning during plant growth) will be illustrated, showing the intuitiveness and the strength of such an approach.