From qualitative data to quantitative models: analysis of the phage shock protein stress response in Escherichia coli

We develop a model of the Psp response system, and illustrate how such models can be constructed and analyzed in light of available sparse and qualitative information in order to generate novel biological hypotheses about their dynamical behaviour. We analyze this model using tools from Petri-net theory and study its dynamical range that is consistent with currently available knowledge by conditioning model parameters on the available data in an approximate Bayesian computation (ABC) framework. Within this ABC approach we analyze stochastic and deterministic dynamics. This analysis allows us to identify different types of behaviour and these mechanistic insights can in turn be used to design new, more detailed and time-resolved experiments.We have developed the first mechanistic model of the Psp response in E. coli. This model allows us to predict the possible qualitative stochastic and deterministic dynamic behaviours of key molecular players in the stress response. Our inferential approach can be applied to stress response and signalling systems more generally: in the ABC framework we can condition mathematical models on qualitative data in order to delimit e.g. parameter ranges or the qualitative system dynamics in light of available end-point or qualitative information.Bacteria have evolved diverse mechanisms for sensing and adapting to adverse conditions in their environment [1,2]. These stress response mechanisms have been extensively studied for decades due to their biomedical importance (e.g. development of antibiotic therapies). With the advent of molecular biology technologies it is now possible to study biochemical and molecular mechanisms underlying stress response signalling. However, due to the complexity of these pathways, the development of theoretical models is important in order to comprehend better the underlying biological mechanisms. Models can be especially useful when a system under study involves a large number of components and is too comple