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On the Role of Delays in Biological Systems : Analysis and Design


Gomez, Marcella Mary (2015) On the Role of Delays in Biological Systems : Analysis and Design. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9JH3J4W.


This work quantifies the nature of delays in genetic regulatory networks and their effect on system dynamics. It is known that a time lag can emerge from a sequence of biochemical reactions. Applying this modeling framework to the protein production processes, delay distributions are derived in a stochastic (probability density function) and deterministic setting (impulse function), whilst being shown to be equivalent under different assumptions. The dependence of the distribution properties on rate constants, gene length, and time-varying temperatures is investigated. Overall, the distribution of the delay in the context of protein production processes is shown to be highly dependent on the size of the genes and mRNA strands as well as the reaction rates. Results suggest longer genes have delay distributions with a smaller relative variance, and hence, less uncertainty in the completion times, however, they lead to larger delays. On the other hand large uncertainties may actually play a positive role, as broader distributions can lead to larger stability regions when this formalization of the protein production delays is incorporated into a feedback system.

Furthermore, evidence suggests that delays may play a role as an explicit design into existing controlling mechanisms. Accordingly, the reccurring dual-feedback motif is also investigated with delays incorporated into the feedback channels. The dual-delayed feedback is shown to have stabilizing effects through a control theoretic approach. Lastly, a distributed delay based controller design method is proposed as a potential design tool. In a preliminary study, the dual-delayed feedback system re-emerges as an effective controller design.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Delays, Biological Systems, Controls, Systems biology
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Murray, Richard M.
Thesis Committee:
  • Burdick, Joel Wakeman (chair)
  • Murray, Richard M.
  • Beck, James L.
  • Balas, Mark J.
Defense Date:24 July 2014
Non-Caltech Author Email:marcellagomez951 (AT)
Funding AgencyGrant Number
Record Number:CaltechTHESIS:08282014-165029252
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8648
Deposited By: Marcella Gomez
Deposited On:29 Aug 2014 18:36
Last Modified:04 Oct 2019 00:06

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