Energy Dissipation and Noise Correlations in Biochemical Sensing

To measure chemical concentrations, cells need to extract information from stochastic receptor signals via signaling networks which are also inherently stochastic. Here, we study how the accuracy of sensing depends on the correlations between these extrinsic and intrinsic sources of noise. We find that the sensing precision of signaling networks that are not driven out of equilibrium is fundamentally limited by the fluctuation-dissipation theorem, which generates a tradeoff between the removal of extrinsic and intrinsic noise. As a result, the sensing precision of equilibrium systems is limited by the number of receptors; the downstream network can never improve sensing. To lift the tradeoff, energy dissipation is essential. This allows the receptor to transduce the signal as a catalyst and enables time integration of the receptor state. To beat the sensing limit of equilibrium systems, a canonical nonequilibrium signaling network based on the push-pull motif needs to dissipate at least $1k_{\text{B}}T$ per receptor.

Figure 1

Different sensing strategies. (a) In equilibrium systems, the energy of ligand binding is used to change the state of the readout. Here, ligand binding drives readout unbinding: it lowers the system’s free energy, overcoming the rise in free energy due to readout unbinding. (b) In nonequilibrium systems, like the Goldbeter-Koshland push-pull motif, fuel turnover drives chemical modification of the readout, and the receptor catalyzes the modification when ligand bound.

Figure 2

The different resource requirements for equilibrium and nonequilibrium sensing lead to a tradeoff between these two modes. The tradeoff is illustrated for a network that combines both modes: $RL+x\rightleftharpoons RLx$, $RLx\rightleftharpoons RL+x^{*}$, $x^{*}\rightleftharpoons x$. The blue dots show the sensing error for different parameter values [22]. The solid red lines show, respectively, the predictions of Eqs. (2) and (9), while the dashed red line shows the minimum sensing error obtained from the numerical optimization. When the energy per receptor $w/R_T$ is less than a few $k_{B}T$, the optimized system employs the equilibrium strategy, with bound $4/R_T$, while if it is higher, it uses the nonequilibrium strategy, achieving the bound $4/w$.