Abstract
The chemotaxis pathway of the bacterium Rhodobacter sphaeroides shares many similarities with that of Escherichia coli. It exhibits robust adaptation and has several homologues of the latter's chemotaxis proteins. Recent theoretical results have correctly predicted that the E. coli output behaviour is unchanged under scaling of its ligand input signal; this property is known as fold-change detection (FCD). In the light of recent experimental results suggesting that R. sphaeroides may also show FCD, we present theoretical assumptions on the R. sphaeroides chemosensory dynamics that can be shown to yield FCD behaviour. Furthermore, it is shown that these assumptions make FCD a property of this system that is robust to structural and parametric variations in the chemotaxis pathway, in agreement with experimental results. We construct and examine models of the full chemotaxis pathway that satisfy these assumptions and reproduce experimental time-series data from earlier studies. We then propose experiments in which models satisfying our theoretical assumptions predict robust FCD behaviour where earlier models do not. In this way, we illustrate how transient dynamic phenotypes such as FCD can be used for the purposes of discriminating between models that reproduce the same experimental time-series data.
Highlights
Dynamic models of biological mechanisms are meaningful if they can explain experimental data, can make a priori predictions of biological behaviour, and are liable to invalidation through testing. several competing models of a given mechanism can often be made to reproduce experimental data through parameter tuning, in many cases, it is possible to discriminate between such models by comparing the experimentally observed output response and the simulated response to judiciously designed perturbations
In the light of this preliminary evidence for fold-change detection (FCD), here we model the dynamics of the two R. sphaeroides receptor clusters using the Monod–Wyman– Changeux (MWC) allosteric model [11] that has been used to model the receptor activity in E. coli in earlier studies [4,12,13]
To allow for a wide range of possible interactions between the cytoplasmic cluster on the one hand and, on the other hand, the externally sensed ligands L and the phosphorylated chemotaxis proteins, collectively represented by a signal u, we let signal L be the output of a dynamical system given in assumption A.1 in the appendix
Summary
Dynamic models of biological mechanisms are meaningful if they can explain experimental data, can make a priori predictions of biological behaviour, and are liable to invalidation through testing. Besides detecting internalized ligand concentrations, it may sense internal signals, such as signals reporting the cell’s metabolic state This bacterium has multiple homologues of the E. coli chemotaxis proteins, which play roles similar to those found in the latter, the exact structure of their connectivity with the two sensory clusters and the flagellum is not known with certainty. We present a theorem that shows that if this is an accurate model of the receptor dynamics, the receptor activities will exhibit FCD This observed behaviour is robust to the connectivity between the chemotaxis proteins, the receptors and the flagellum. It is robust to parametric variations, in line with the observed evidence for FCD in bacteria grown in different conditions To illustrate these points, we construct two models of the integrated R. sphaeroides chemotaxis pathway based on our receptor dynamics assumptions, with each model featuring a different internal connectivity. Transient dynamic phenotypes can be used to discriminate between models that explain experimental data well
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