Box 1. Model for receptor signaling

Box 1 Chemoreceptors cluster at multiple scales ranging from receptor dimers, to trimers of dimers, to large polar and lateral clusters. Signaling properties are believed to arise from groups of several trimers of dimers forming signaling teams. Within a signaling team, receptors are assumed to be coupled strongly enough that the receptors are either all in the on state or all in the off state (A). In the on state, the receptor-associated kinase CheA is assumed to be active, autophosphorylating itself and transferring the phospho-group to the response regulators CheY and CheB. In the off state, CheA is inactive and unable to autophosphorylate (B). Importantly, the two-state property of the receptor dimers and signaling teams leads to two characteristic regimens of activity as described below. Single two-state receptor: We assume that an individual chemoreceptor (homodimer) has two states, on or off (Asakura and Honda, 1984). Attractant binding favors the off state, in which the receptor-bound kinase CheA is inactive, whereas modification of the receptor favors the on state, in which CheA is active. At equilibrium, the probability that the receptor dimer is on is

where all energies are expressed in units of the thermal energy k_BT. The receptor dimer free-energy difference between on and off states is given by

where ligand binding in the on (off) state with dissociation constant K_D^on (K_D^off) is included. For attractant binding K_D^off<K_D^on, and for repellent binding, K_D^off>K_D^on. The modification state of the receptor dimer enters only through the offset energy (m). The probability of the on state is considered to be the receptor activity. Two regimens of activity are apparent. (C) A schematic energy-level diagram as a function of attractant (ligand) concentration [L] for a fully demethylated (unmodified) receptor dimer (left, regimen I) and a fully modified receptor dimer (right, regimen II) is shown (Keymer et al, 2006). The receptor dimer can either be on or off. For clarity in the figure, only the off state can bind attractant (red disc), with ligand dissociation constant K_D^off. Methyl groups or glutamines (diamonds) lower the free energy of the on state. In regimen I, the on-state free energy is above the off-state free energy (>0) in the absence of attractant, leading to a low activity; the crossing of the lowest levels occurs at [L]=K_D^off (black dot). In regimen II, the on-state free energy is below the off-state free energy (<0) in the absence of a ligand, leading to a high activity; the crossing of the lowest levels occurs at an increased ligand concentration [L]=K_D^offexp(||) (black dot). In both regimens I and II, the crossing of the lowest levels corresponds to the inhibition constant K_i (ligand concentration at half-maximal activity), obtainable from dose–response curves. Receptor signaling team: Within the allosteric Monod–Wyman–Changeux (MWC) model (Monod et al, 1965), two-state receptor dimers form signaling teams with all receptors in a team either on or off together (Sourjik and Berg, 2004; Mello and Tu, 2005; Keymer et al, 2006). Assuming for simplicity a single receptor type, such as Tar, the equilibrium probability that a signaling team of N receptor dimers will be on is

Importantly, signaling-team formation enhances the difference between the two regimens (Keymer et al, 2006). In regimen I, where >0 (e.g. for Tar{EEEE}), receptor dimers have an even lower activity, exp(-N), and an inhibition constant K_iK_D^off/N, indicating an N times higher sensitivity than that of a single receptor dimer. In regimen II, where <0 (e.g. for Tar{QQQQ}), receptor dimers are even more fully active, and turn off at attractant concentration K_iK_D^offexp(||) with enhanced cooperativity, specifically with a Hill coefficient n_HN. The strong effect of signaling-team size on the sensitivity of demethylated (unmodified) receptors and on the Hill coefficient of more highly modified receptors allows us to deduce signaling-team size from signaling dose–response curves (Supplementary Table I; Keymer et al, 2006; Endres et al, 2007).