The price of a bit: energetic costs and the evolution of cellular signaling

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. 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.

Cellular signaling beyond the Wiener-Kolmogorov limit

“…A recent example of the versatility of the WK theory is the study of kinase-phosphatase signaling networks in Ref. 15. A simple analytical WK bound, derived from a linearized = 1 network, explains a previously unknown optimal relationship between signal fidelity, bandwidth, and minimum ATP consumption.…”

“…Other processes in development and regulation depend on suppressing noise through homeostatic mechanisms like negative feedback [11][12][13][14] . Either scenario, whether maintaining a certain signal fidelity or suppressing fluctuations, can be quite expensive in terms of metabolic resources 3,15 , and hence potentially an area where optimization is relevant.…”

“…Once the identification is made, the payoff is substantial: one can use the WK solution for the optimal noise filter function to derive closed form analytical bounds on measures of signal fidelity (like mutual information) or noise suppression (like Fano factors). These bounds depend on the network's reaction rate parameters, allowing us to determine a minimum energetic price associated with a certain level of performance 15 . Finally, the theory specifies the conditions under which optimality can be realized in a particular network.…”

“…Discussions of signaling performance limits are often framed in terms of information theory concepts like channel capacity 16,17 , and complemented by direct experimental estimates [18][19][20][21][22][23][24][25] . In recent years, another tool has emerged for understanding constraints on biological signal propagation: optimal noise filter theory 15,[26][27][28][29][30] , drawing on the classic work of Wiener and Kolmogorov (WK) in engineered communications systems [31][32][33] . The theory maps the behavior of a biological network onto three basic components: a signal time series, noise corrupting the signal, and a filter mechanism to remove the noise.…”

Physical bioenergetics: Energy fluxes, budgets, and constraints in cells

“…Alternatively, since the energy fluxes through all cellular processes sum up to the global energy flux of the cell, energic cost of a specific cellular process can be quantified by the fraction of the global energy flux associated with that process. Cellular energetic costs include biosynthesis (72), signaling (23,24,73,74), maintaining chemical gradients (75), error correction (8,9), motility (75), gene regulation (76,77), and building of cellular structures, such as the cytoskeleton (22). Fig.…”