title: Global entrainment of transcriptional systems to periodic inputs.
abstract: This paper addresses the problem of providing mathematical conditions that allow one to ensure that biological networks, such as transcriptional systems, can be globally entrained to external periodic inputs. Despite appearing obvious at first, this is by no means a generic property of nonlinear dynamical systems. Through the use of contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all their solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific cases of models of transcriptional systems as well as constructs of interest in synthetic biology. A self-contained exposition of all needed results is given in the paper.
authors.affiliation: Department of Systems and Computer Engineering, University of Naples Federico II, Naples, Italy.
authors.forename: Giovanni
authors.initials: G
authors.lastname: Russo
authors.forename: Mario
authors.initials: M
authors.lastname: di Bernardo
authors.forename: Eduardo D
authors.initials: ED
authors.lastname: Sontag
mesh_terms: D000465:Algorithms; D053263:Gene Regulatory Networks; D053858:Metabolic Networks and Pathways; D008954:Models, Biological; D017711:Nonlinear Dynamics; D015398:Signal Transduction; D049490:Systems Biology / Q000379:methods*; D013598:Systems Theory; D014158:Transcription, Genetic