title: Cumulative signal transmission in nonlinear reaction-diffusion networks.
abstract: Quantifying signal transmission in biochemical systems is key to uncover the mechanisms that cells use to control their responses to environmental stimuli. In this work we use the time-integral of chemical species as a measure of a network's ability to cumulatively transmit signals encoded in spatiotemporal concentrations. We identify a class of nonlinear reaction-diffusion networks in which the time-integrals of some species can be computed analytically. The derived time-integrals do not require knowledge of the solution of the reaction-diffusion equation, and we provide a simple graphical test to check if a given network belongs to the proposed class. The formulae for the time-integrals reveal how the kinetic parameters shape signal transmission in a network under spatiotemporal stimuli. We use these to show that a canonical complex-formation mechanism behaves as a spatial low-pass filter, the bandwidth of which is inversely proportional to the diffusion length of the ligand.
authors.affiliation: Centre for Synthetic Biology and Innovation, Department of Bioengineering, Imperial College London, London, United Kingdom. d.oyarzun@imperial.ac.uk
authors.forename: Diego A
authors.initials: DA
authors.lastname: Oyarzún
authors.forename: Fernando
authors.initials: F
authors.lastname: López-Caamal
authors.forename: Míriam R
authors.initials: MR
authors.lastname: García
authors.forename: Richard H
authors.initials: RH
authors.lastname: Middleton
authors.forename: Andrea Y
authors.initials: AY
authors.lastname: Weiße
mesh_terms: D004777:Environment; D007700:Kinetics; D008024:Ligands; D008954:Models, Biological; D015398:Signal Transduction / Q000502:physiology*; D013997:Time Factors
chemical_list: D008024:Ligands