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.
|Translated title of the contribution||Global entrainment of transcriptional systems to periodic inputs|
|Number of pages||26|
|Journal||PLoS Computational Biology|
|Publication status||Published - Apr 2010|
- Bristol BioDesign Institute
- SYNTHETIC BIOLOGY