Stochastic Mechanisms of Information Flow in Phosphate Economy of Escherichia coli

Abstract

In previous work, we have presented a computational model and experimental results that quantify the dynamic mechanisms of auto-regulation in E. coli in response to varying external phosphate levels. In a cycle of deterministic ODE simulations and experimental verification, our model predicts and explores phenotypes with various modifications at the genetic level that can optimise inorganic phosphate intake. Here, we extend our analysis with extensive stochastic simulations at a single-cell level so that noise due to small numbers of certain molecules, e.g., genetic material, can be better observed. For the simulations, we resort to a conservative extension of Gillespie’s stochastic simulation algorithm that can be used to quantify the information flow in the biochemical system. Besides the common time series analysis, we present a dynamic visualisation of the time evolution of the model mechanisms in the form of a video, which is of independent interest. We argue that our stochastic analysis of information flow provides insights for designing more stable synthetic applications that are not affected by noise.

Appendix

The CRN in [1] that models the auto-regulation mechanism of E. coli in response to varying external phosphate concentrations. The time unit of the reactions is in seconds. The fold-change fc factor in reactions r01 and r03 model the variations in external $P_i$ concentration. The $\texttt {fc} = 1.0$ value corresponds to the starvation condition and a lower $\texttt {fc}$ value corresponds to a higher external $P_i$ concentration. The binding factor bf in reactions r16, r18 and unbinding factor uf in reactions r17, r19 are scalar factors. They represent the affinity of the active transcription factor to the promoter region. In the control model, the default values of $\texttt {bf} = 1.0$ and $\texttt {uf} = 1.0$ are used.