title: The cost of sensitive response and accurate adaptation in networks with an incoherent type-1 feed-forward loop.
abstract: The incoherent type-1 feed-forward loop (I1-FFL) is ubiquitous in biological regulatory circuits. Although much is known about the functions of the I1-FFL motif, the energy cost incurred in the network and how it affects the performance of the network have not been investigated. Here, we study a generic I1-FFL enzymatic reaction network modelled after the GEF-GAP-Ras pathway responsible for chemosensory adaptation in eukaryotic cells. Our analysis shows that the I1-FFL network always operates out of equilibrium. Continuous energy dissipation is necessary to drive an internal phosphorylation-dephosphorylation cycle that is crucial in achieving strong short-time response and accurate long-time adaptation. In particular, we show quantitatively that the energy dissipated in the I1-FFL network is used (i) to increase the system's initial response to the input signals; (ii) to enhance the adaptation accuracy at steady state; and (iii) to expand the range of such accurate adaptation. Moreover, we find that the energy dissipation rate, the catalytic speed and the maximum adaptation accuracy in the I1-FFL network satisfy the same energy-speed-accuracy relationship as in the negative-feedback-loop (NFL) networks. Because the I1-FFL and NFL are the only two basic network motifs that enable accurate adaptation, our results suggest that a universal cost-performance trade-off principle may underlie all cellular adaptation processes independent of the detailed biochemical circuit architecture.
authors.affiliation: Department of Physics, George Washington University, 725 21st Street NW, Washington, DC 20052, USA.
authors.forename: Ganhui
authors.initials: G
authors.lastname: Lan
authors.forename: Yuhai
authors.initials: Y
authors.lastname: Tu
mesh_terms: D000220:Adaptation, Biological; D025461:Feedback, Physiological; D020690:GTPase-Activating Proteins / Q000737:chemistry*; D020662:Guanine Nucleotide Exchange Factors / Q000737:chemistry*; D007700:Kinetics; D008954:Models, Biological; D018631:ras Proteins / Q000737:chemistry*
chemical_list: D020690:GTPase-Activating Proteins; D020662:Guanine Nucleotide Exchange Factors; D018631:ras Proteins
keywords: adaptation accuracy; energy dissipation; incoherent type-1 feed-forward loop; non-equilibrium system; sensitivity