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

研究启动奖为传统黑人学院和大学的初级和中期职业教师提供支持，他们正在建立新的研究项目或重新指导和重建现有的研究项目。期望该奖项有助于提高教师的研究能力和效率，改善所在机构的研究和教学，并使本科生参与研究经验。授予德克萨斯南方大学的奖项可能在许多领域产生更广泛的影响。该项目的目标是更好地理解网络系统的结构和它们的动态之间的关系。本科生将获得研究经验，研究将被整合到一些本科课程中。本研究的研究目标是在生物网络系统、基因调控网络和神经网络的背景下，破译网络系统的结构及其动力学之间的关系。基于两种流行的建模框架，布尔网络和耦合常微分方程（ODE），本研究将使用数值和解析方法来解决以下问题：ODE系统的主要参数是什么，使网络达到一定的目标动力学？在基因调控网络的背景下，给定网络结构的一般分支是什么？缺少相互作用对网络动态的可能影响是什么？潜在的结果将有助于生物学数学模型的建模和分析。该研究还将解决双目竞争现象引起的一个问题：双稳态知觉竞争的动力学机制是否可以扩展到多稳态知觉竞争？潜在的结果将增加我们对大脑功能的了解。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.