Abstract
Recent experiments have uncovered a fundamental information scale for cellular signaling networks: the correlation between input and output concentrations of molecules in a signaling pathway corresponds to at most 1-3 bits of mutual information. Our understanding of the physical constraints and evolutionary pressures that determine this scale remains incomplete. By focusing on a basic element of signaling pathways, the kinase-phosphatase enzymatic push-pull loop, we highlight the pivotal role played by energy resources available for signaling and their expenditure: the chemical potential energy of ATP hydrolysis, and the rate of ATP consumption. Scanning a broad range of reaction parameters based on enzymatic databases, we find that ATP chemical potentials in modern organisms are just above the threshold necessary to achieve empirical mutual information values. We also derive an analytical relation for the minimum ATP consumption required to maintain a certain signal fidelity across a range of input frequencies, where we quantify fidelity either through instantaneous or time-delayed mutual information. Attempting to increase signal fidelity beyond a few bits lowers the bandwidth, the maximum characteristic signal frequency that the network can handle at a given energy cost. The observed information scale thus represents a balancing act between fidelity and the ability to process fast-changing environmental signals. Our analytical relation defines a performance limit for kinase-phosphatase networks, and we find evidence that a component of the yeast osmotic shock pathway may be close to the optimality line. By quantifying the evolutionary pressures that operate on these networks, we argue that this is not a coincidence: natural selection on energy expenditures is capable of pushing signaling systems toward optimality, particularly in unicellular organisms. Our theoretical framework is directly verifiable using existing experimental techniques, and predicts that more examples of such optimality should exist in nature.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
The theory in the manuscript has been extended to include both time-delayed and instantaneous mutual information. In particular, there is now a general analytical bound that covers both scenarios.
