Modelling language for biology with applications
Understanding the links between biological processes at multiple scales, from molecular regulation to populations and evolution along with their interactions with the environment, is a major challenge in understanding life. Apart from understanding this is also becoming important in attempts to engineer traits, for example in crops, starting from genetics or from genomes and at different environmental conditions (genotype x environment → trait). As systems become more complex relying on intuition alone is not enough and formal modelling becomes necessary for integrating data across different processes and allowing us to test hypotheses. The more complex the systems become, however, the harder the modelling process becomes and the harder the models become to read and write. In particular intuitive formalisms like Chemical Reaction Networks are not powerful enough to express ideas at higher levels, for example dynamic environments, dynamic state spaces, and abstraction relations between different parts of the model. Other formalisms are more powerful (for example general purpose programming languages) but they lack the readability of more domain specific approaches. The first contribution of this thesis is a modelling language with stochastic semantics, Chromar, that extends the visually intuitive formalisms of reactions, in which simple objects, called agents, are extended with attributes. Dynamics are given as stochastic rules that can operate on the level of agents (removing/adding) or at the level of attributes (updating their values). Chromar further allows the seamless integration of time and state functions with the normal set of expressions – crucial in multi-scale plant models for describing the changing environment and abstractions between scales. This leads to models that are both formal enough for simulations and easy to read and write. The second contribution of this thesis is a whole-life-cycle multi-model of the growth and reproduction of Arabidopsis Thaliana, FM-life, expressed in a declarative way in Chromar. It combines phenology models from ecology to time developmental processes and physical development, which allows to scale to the population and address ecological questions at different genotype x environment scenarios. This is a step in the path for mechanistic links between genotype x environment and higher-level crop traits. Finally, I show a way of using optimal control techniques to engineer traits of plants by controlling their growth environmental conditions. In particular we explore (i) a direct problem where the control is temperature – assuming homogeneous growth conditions and (ii) indirect problem where the control is the position of the plants – assuming inhomogeneous growth conditions.