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

研究启动奖为历史悠久的黑人学院和大学的初级和职业生涯中期教师提供支持，这些教师正在建立新的研究计划或重新定向和重建现有的研究计划。预计该奖项有助于进一步提高教师的研究能力和有效性，改善所在机构的研究和教学，并让本科生参与研究经验。授予德克萨斯南方大学的奖项可能会在许多领域产生更广泛的影响。该项目的目标是更好地了解网络系统的结构及其动力学之间的关系。本科生将获得研究经验，并将研究整合到一些本科课程中。本研究的目的是在生物网络系统，特别是基因调控网络和神经元网络的背景下，破译网络系统的体系结构和它们的动力学之间的关系。基于布尔网络和耦合常微分方程组这两个流行的建模框架，本研究将使用数值和解析方法来解决以下问题：一个常微分方程组系统中的主要参数需要满足哪些条件才能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叉是什么？缺失交互对网络动态的可能影响是什么？这些潜在的结果将有助于生物学中数学模型的建模和分析。这项研究还将解决由双眼竞争现象引起的一个问题：解释双稳态知觉竞争动态的机制是否可以扩展到多稳定的知觉竞争？潜在的结果将增加关于我们大脑功能的知识。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.