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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
Published on: December 7, 2021
Global entrainment of transcriptional systems to periodic inputs
Giovanni Russo1, Mario di Bernardo, Eduardo D Sontag
1Department of Systems and Computer Engineering, University of Naples Federico II, Naples, Italy.
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.
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Transcription
Transcription is the process of synthesizing RNA from a DNA sequence by RNA polymerase. It is the first step in producing a protein from a gene sequence. Additionally, many other proteins and regulatory sequences are involved in the proper synthesis of messenger RNA (mRNA). Regulation of transcription is responsible for the differentiation of all the different types of cells and often for the proper cellular response to environmental signals.
Transcription Can Produce Different Kinds...

