Trade-Offs in Delayed Information Transmission in Biochemical Networks

Abstract

In order to transmit biochemical signals, biological regulatory systems dissipate energy with concomitant entropy production. Additionally, signaling often takes place in challenging environmental conditions. In a simple model regulatory circuit given by an input and a delayed output, we explore the trade-offs between information transmission and the system's energetic efficiency. We determine the maximally informative network, given a fixed amount of entropy production and delayed response, exploring both the case with and without feedback. We find that feedback allows the circuit to overcome energy constraints and transmit close to the maximum available information even in the dissipationless limit. Negative feedback loops, characteristic of shock responses, are optimal at high dissipation. Close to equilibrium positive feedback loops, known for their stability, become more informative. Asking how the signaling network should be constructed to best function in the worst possible environment, rather than an optimally tuned one or in steady state, we discover that at large dissipation the same universal motif is optimal in all of these conditions.

What we learn from the learning rate

“…Knowing the fundamental thermodynamic limits on sensor operation is also relevant to the engineering of synthetic sensors. Drawing on the connections between information and thermodynamics, several groups have considered the intrinsic costs associated with sensing and adaption (sensors that adapt revert to zero after lengthy exposure to a constant input) [12,13,[22][23][24][25][26][27][28][29][30][31]. For example, Govern and ten Wolde showed that molecular readout molecules of cell-surface receptors must consume free energy to form long-lived memories of receptor states [26,27], a process equivalent to thermodynamic measurement of the kind performed by Maxwell's demon [13].…”

Statistics of optimal information flow in ensembles of regulatory motifs

“…During the past decade many studies have addressed this issue within an information theoretic framework in different contexts [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The general idea behind this line of work is that optimal effectiveness of a regulatory module is achieved when the mutual information between input and output nodes is maximized.…”

Out-of-equilibrium statistical dynamics of spatial pattern generating cellular automata

“…But such general frameworks are lacking for understanding the dynamics of an important class of systems -networks of cells such as tissues and biofilms in which multiple cells, without any morphogen gradients, collectively generate spatial patterns by regulating each other's genes with diffusing chemicals and genetic circuits 9 . Indeed, it is unclear if and how principles such as information-optimization 12 and metrics such as thermodynamic potentials, despite their utility in other contexts [13][14][15][16][17][18][19] , apply to spatiotemporal gene regulations by hundreds of cells. Moreover, we usually do not know which metrics suitably describe these systems.…”

“…Until now, we have analysed deterministic cellular automata. But real cells are noisytheir gene expressions are stochastic 1,[8][9][10][12][13][14][15][16]18,19 . We can treat such biological noise by having the secretion rate and the threshold K to fluctuate over time for each cell.…”

“…Previous studies have provided deep insights into how efficiently genetic networks in a cell can process information to generate accurate input-output relationships in which the input usually is a steady state gradient of signal that a cell detects and the output is the cell's steady state gene expression [12][13][14][15][16][17][18][19] . For example, researchers have quantified the amount of information encoded in gene expressions of fly embryos 19 and mouse cells 15 .…”