Research Initiation Award: Studying the Dynamics of Network Systems by Using Ordinary Differential Equations and Boolean Frameworks

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Research Initiation Awards provide support for junior and mid-career faculty at Historically Black Colleges and Universities who are building new research programs or redirecting and rebuilding existing research programs. It is expected that the award helps to further the faculty member's research capability and effectiveness, improves research and teaching at the home institution, and involves undergraduate students in research experiences. The award to Texas Southern University has potential broader impacts in a number of areas. The goal of the project is to better understand the relationships between the structures of network systems and their dynamics. Undergraduate students will gain research experiences and the research will be integrated in a number of undergraduate courses.The research goal of this proposed study is to decipher the relationships between the architecture of network systems and their dynamics in the context of biological network systems, gene regulatory networks and neuronal networks in particular. Based on two popular modeling frameworks, Boolean networks and coupled ordinary differential equations (ODEs), this proposed study will use both numerical and analytical methods to address the following questions: What are the necessary conditions on the principle parameters in an ODE system so that a network will achieve certain target dynamics? In the context of gene regulatory networks, what are the general bifurcations with a given network architecture? What are the possible effects of missing interactions on the dynamics of networks? The potential results will facilitate the modeling and analysis of mathematical models in biology. The study will also address a problem rising from the binocular rivalry phenomenon: Can mechanisms accounting for the dynamics of bistable perceptual rivalry be extended to multi-stable perceptual rivalry? Potential results will add to knowledge on the functions of our brain.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.