Theoretical insights into bacterial chemotaxis

A schematic comparison of the intracellular signaling pathways and related components (receptor clusters and flagellar motors) in: (a) E. coli, (b) B. subtilis, and (c) R. sphaeroides chemotactic bacteria. Each cell may detect an external attractant or repellent gradient by ligand molecules binding to a receptor cluster (red boxes). These then signal via the intracellular biochemical cascades using a histidine kinase, CheA, regulating the CheBs which control the adaptation pathways, and CheYs which control the flagellar motor switching (smaller blue boxes on the cell membrane). CheZ is a phosphatase which dephosphorylates phosphorylated CheY. The complexity of each pathway varies considerably. Although E. coli and B. subtilis each contain one CheY (the role of CheV is not fully understood in B. subtilis) and multiple flagella, R. sphaeroides requires a minimum of three CheYs, of a total of six, for chemotaxis. It also comprises cytoplasmic‐based receptor clusters which probably sense intracellular metabolites. The B. subtilis cascade is also augmented by two further proteins CheC and CheD. CheC is involved in a second adaptation pathway by binding with CheY‐P and CheD.2 CheD further acts as a phosphatase for CheY‐P.3 In each bacterium CheR is the methyltransferase which works with CheB to control adaptation.

A summary of the main components of bacterial chemotactic species which have been modeled on the single cell and population scale. For an understanding of how individual‐based processes (e.g., intracellular signaling cascades) affect the overall population scale behavior links between the two scales are required.

(a) The components of an E. coli bacterial motor. (b) The concept of conformational spread. In the upper figure none of the 32 proteins in the C‐ring of the bacteria are activated. Over time, some of the proteins may become activated (gray‐colored circles) through stochastic fluctuations or signaling. The theorized connectivity amongst the proteins leads to a spread of this activity (middle figure) which can either increase (lower figure) or decrease, back to the original state (upper figure).

Upper: Trimers of receptor dimers cluster as viewed from above (after Ref 48). The homodimers (indicated by circles of the same color) interact with other dimers to form a cluster of heterotrimers of homodimers. Lower: The statistical mechanically derived inequality49 describes the theoretical maximum cluster size N of trimers of dimers as a function of the ligand diffusion rate D, the average receptor size a, the average diffusion ligand time τ, the ligand concentration L, and the receptor–ligand binding affinities and (note the superscripts do not denote a mathematical power). Fitting of such relationships to experimental data has allowed predictions to be made as to how cluster size varies amongst receptor types and under different experimental conditions.

In a uniform environment Escherichia coli alternates between runs, where all the flagella rotate counter‐clockwise as a bundle, and tumbles, where some switch to clockwise rotation and the bundle falls apart. When going up an attractant gradient the period between switching increases, when going down a gradient it decreases.