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.
Global entrainment of transcriptional systems to periodic inputs / G., Russo; DI BERNARDO, Mario; E. D., Sontag. - In: PLOS COMPUTATIONAL BIOLOGY. - ISSN 1553-7358. - ELETTRONICO. - 6:4(2010), pp. 1-26. [10.1371/journal.pcbi.1000739]
Global entrainment of transcriptional systems to periodic inputs
DI BERNARDO, MARIO;
2010
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.File | Dimensione | Formato | |
---|---|---|---|
PLoS Computational Biology 2010 Russo-1.pdf
non disponibili
Tipologia:
Documento in Post-print
Licenza:
Accesso privato/ristretto
Dimensione
1.68 MB
Formato
Adobe PDF
|
1.68 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.