Section: Application Domains

Models of growth

In systems and synthetic biology (engineered systems) one would like study the environment of a given cellular process (such as signaling pathways mentioned earlier) and the ways in which that process interacts with different resources provided by the host. To do this, we have built coarse-grained models of cellular physiology which summarize fundamental processes (transcription, translation, transport, metabolism). such models describe global growth in mechanistic way and allow one to plug the model of one's process of interest into a simplified and yet realistic and reactive model of the process interaction with its immediate environment. A first ODE-based deterministic version of this model [30] explaining the famous bacterial growth laws and how the allocation of resources to different genomic sectors depends on the growth conditions- was published in 2015 and has already received nearly 150 citations. The model also allows one to bridge between population genetic models which describe cells in terms of abstract features and fitness and intra-cellular models. For instance, we find that fastest growing strategies are not evolutionary stable in competitive experiments. We also find that vastly different energy storage strategies exist[16]. In a recent article[17] in Nature Communications we build a stochastic version of the above model. We predict the empirical size and doubling time distributions as a function of growth conditions. To be able to fit the parameters of the model to available single-cell data (note that the fitting constraints are far tighter than in the deterministic case), we introduce new techniques for the approximation of reaction-division systems which generalize continuous approximations of Langevin type commonly used for pure reaction systems. We also use cross-correlations to visualize causality and modes in noise propagation in the model (in a way reminiscent to abstract computational traces mentioned earlier). In other work, we show how to connect our new class of models to more traditional ones stemming from “flux balance analysis” by introducing an allocation vector which allows one to assign a formal growth rate to a class of reaction systems [25].