Dynamics of Cooperativity in Chemical Sensing among Cell-Surface Receptors

Cooperative interactions among sensory receptors provide a general mechanism to increase the sensitivity of signal transduction. In particular, bacterial chemotaxis receptors interact cooperatively to produce an ultrasensitive response to chemoeffector concentrations. However, cooperativity between receptors in large macromolecular complexes is necessarily based on local interactions and consequently is fundamentally connected to slowing of receptor-conformational dynamics, which increases intrinsic noise. Therefore, it is not clear whether or under what conditions cooperativity actually increases the precision of the concentration measurement. We explicitly calculate the signal-to-noise ratio (SNR) for sensing a concentration change using a simple, Ising-type model of receptor-receptor interactions, generalized via scaling arguments, and find that the optimal SNR is always achieved by independent receptors.

Figure 1

(a) Schematic diagram of cooperatively interacting receptors. Receptors interconvert between active and inactive states and preferentially bind ligand in the inactive state. The interaction energy $J$ between neighbors favors receptors in the same activity state. (b) The normalized static response $R(\infty )/n$ for closed chains (rings) of various lengths $n$ (for open chains, see 4). (c) Response $R$, (d) noise ${\sigma }^2$, and (e) SNR as functions of coupling strength $J$ for a closed chain of $n=10$ receptors for various averaging times ${\tau }_{\mathrm{av}}$. In (e), the SNR is normalized by the averaging time.

Figure 2

Ratio of the SNR for independent receptors to the SNR for cooperative receptors as a function of the correlation length $\xi$ for a 1D ring and a 2D square lattice of $n=100$ receptors with periodic boundary conditions, as well as mean field theory (MFT). Averaging times are $\alpha {\tau }_{\mathrm{av}}=100$ (solid curve) and $\alpha {\tau }_{\mathrm{av}}=\infty$ (dashed curve), with power law plots for comparison (dotted lines).