SURF 2013: Role of Delays in Biological Processes

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2013 SURF project description

  • Mentor: Richard Murray
  • Co-mentor: Marcella Gomez

Project Description: With the development of technology in synthetic biology there is an increased need for a standard methodology in designing synthetic genetic regulatory networks (GRNs). It seems only natural to extend results in control theory for design and analysis. Due to the large scale and intricacy of GRNs, it also makes sense to make use of the network structure to extract as much information possible of the potential dynamics.

There are many inherent delays in biological systems. More specifically, in GRNs, there are delays that arise in the time it takes for transcription and translation in the production of proteins. Previous work includes analysis of systems with multiple feedback delays and stochastic delays. The student would apply control theory tools to analyzing such systems.

One area that has not been explored much is how the structure of a network plays into the dynamics of the system. The structure of a GRN refers to the interconnection of the network based on activation or inhibition of protein production by other proteins (or absence of such a relationship). Furthermore, how does the choice of placement of delays in the network affect the dynamics? A potential project may be to do a case study with various network topologies and investigate stability bounds for different placements of delays. A more advanced project may consist of selecting non-delayed networks with known permissible behavior based on theorems such as the Feinberg Deficiency Theorems and investigating delay based bifurcations, events where phase portraits change drastically, perhaps leading to unpredicted behavior. A project can be purely computational, theoretical or both.


  • Must have taken at minimum an introductory course in control theory.
  • Background in biology is not required.
  • Preferably know how to use MATLAB.


  1. G. Orosz, J. Moehlis, and R. M. Murray. 
Controlling biological networks by time-delayed signals. 
Philosophical Transactions of the Royal Society A, 368(1911):439-454, 2010.
  2. Feinberg, Martin. Chemical reaction network structure and the stability of complex isothermal reactors--I. The deficiency zero and deficiency one theorems. Chemical Engineering Science, 42(10): 2229-2268, 1987.