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

Tina Toni,Maxime Huvet,Michael Ph Stumpf,Goran Jovanovic,Martin Buck

doi:10.1186/1752-0509-5-69

Abstract

BackgroundBacteria have evolved a rich set of mechanisms for sensing and adapting to adverse conditions in their environment. These are crucial for their survival, which requires them to react to extracellular stresses such as heat shock, ethanol treatment or phage infection. Here we focus on studying the phage shock protein (Psp) stress response in Escherichia coli induced by a phage infection or other damage to the bacterial membrane. This system has not yet been theoretically modelled or analysed in silico.ResultsWe 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.ConclusionsWe 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.

Highlights

Bacteria have evolved a rich set of mechanisms for sensing and adapting to adverse conditions in their environment
We need to decide which of the molecular species and numerous pieces of biological information have to be included in the phage shock protein (Psp) model to capture the basic stress response dynamics
Our study was motivated by the following general questions: Can knowledge about quantitative stress response dynamics be inferred from available qualitative data? And can we thereby generate hypotheses which can be tested experimentally? We have approached these problems in an inference-based manner

Summary

Introduction

Bacteria have evolved a rich set of mechanisms for sensing and adapting to adverse conditions in their environment These are crucial for their survival, which requires them to react to extracellular stresses such as heat shock, ethanol treatment or phage infection. We focus on studying the phage shock protein (Psp) stress response in Escherichia coli induced by a phage infection or other damage to the bacterial membrane. This system has not yet been theoretically modelled or analysed in silico. 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). We lack models that would allow for more detailed quantitative, computational or mathematical analysis of this system

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