A free-energy-based stochastic simulation of the Tar receptor complex.

We recently developed a stochastic-based program that allows individual molecules in a cell signalling pathway to be simulated. This program has now been used to model the Tar complex, a multimeric signalling complex employed by coliform bacteria. This complex acts as a solid-state computational cassette, integrating and disseminating information on the presence of attractants and repellents in the environment of the bacterium. In our model, the Tar complex exists in one of two conformations which differ in the rate at which they generate labile phosphate groups and hence signal to the flagellar motor. Individual inputs to the complex (aspartate binding, methylation at different sites, binding of CheB, CheR and CheY) are represented as binary flags, and each combination of flags confers a different free energy to the two conformations. Binding and catalysis by the complex are performed stochastically according to the complete set of known reactions allowing the swimming performance of the bacterium to be predicted. The assumption of two conformational states together with the use of free energy values allows us to bring together seemingly unrelated experimental parameters. Because of thermodynamic constraints, we find that the binding affinity for aspartate is linked to changes in phosphorylation activity. We estimate the pattern of Tar methylation and effective affinity constant of receptors over a range of aspartate levels. We also obtain evidence that both the methylating and demethylating enzymes must operate exclusively on one or other of the two conformations, and that sites of methylation of the complex are occupied in sequential order rather than independently. Detailed analysis of the response to aspartate reveals several quantitative discrepancies between simulated and experimental data which indicate areas for future research.

Predicting temporal fluctuations in an intracellular signalling pathway.

We used a newly developed stochastic-based program to predict the fluctuations in numbers of molecules in a chemotactic signalling pathway of coliform bacteria. Specifically, we examined temporal changes in molecules of CheYp, a cytoplasmic protein known to influence the direction of rotation of the flagellar motor. Signalling molecules in the vicinity of a flagellar motor were represented as individual software objects interacting according to probabilities derived from experimentally-observed concentrations rate constants. The simulated CheYp molecules were found to undergo random fluctuations in number about an average corresponding to the deterministically calculated concentration. Both the relative amplitude of the fluctuations, as a proportion of the total number of molecules, and their average duration, increased as the simulated volume was reduced. In a simulation corresponding to 10% of the volume of a bacterium, the average duration of fluctuations was found to be 80.7 ms, which is much shorter than the observed alternations between clockwise and counter clockwise rotations of tethered bacteria (typically 2.6 s). Our results are therefore not in agreement with a simple threshold-crossing model for motor switching. However, it is possible to filter the CheYp fluctuations to produce temporal distributions closer to the observed swimming behaviour and we discuss the possible implications for the control of motor rotation.

Receptor clustering as a cellular mechanism to control sensitivity.

Chemotactic bacteria such as Escherichia coli can detect and respond to extremely low concentrations of attractants, concentrations of less than 5 nM in the case of aspartate. They also sense gradients of attractants extending over five orders of magnitude in concentration (up to 1 mM aspartate). Here we consider the possibility that this combination of sensitivity and range of response depends on the clustering of chemotactic receptors on the surface of the bacterium. We examine what will happen if ligand binding changes the activity of a receptor, propagating this change in activity to neighbouring receptors in a cluster. Calculations based on these assumptions show that sensitivity to extracellular ligands increases with the extent of spread of activity through an array of receptors, but that the range of concentrations over which the array works is severely diminished. However, a combination of low threshold of response and wide dynamic range can be attained if the cell has both clusters and single receptors on its surface, particularly if the extent of activity spread can adapt to external conditions. A mechanism of this kind can account quantitatively for the sensitivity and response range of E. coli to aspartate.

Origins of individual swimming behavior in bacteria.

Cells in a cloned population of coliform bacteria exhibit a wide range of swimming behaviors--a form of non-genetic individuality. We used computer models to examine the proposition that these variations are due to differences in the number of chemotaxis signaling molecules from one cell to the next. Simulations were run in which the concentrations of seven gene products in the chemotaxis pathway were changed either deterministically or stochastically, with the changes derived from independent normal distributions. Computer models with two adaptation mechanisms were compared with experimental results from observations on individuals drawn from genetically identical populations. The range of swimming behavior predicted for cells with a standard deviation of protein copy number per cell of 10% of the mean was found to match closely the experimental range of the wild-type population. We also make predictions for the swimming behaviors of mutant strains lacking the adaptational mechanism that can be tested experimentally.