Intellectual Merit. This research analyzed mathematical models for bimolecular activities, in particular, reaction networks endowed with mass-action kinetics. These dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly parametrized (due to noisy measurement data and a small number of data points and repetitions). Therefore, it is often difficult to establish the existence of (positive) steady states or to determine whether more complicated phenomena such as multistationarity exist. Addressing this challenge, the investigator achieved the following results: (1) resolved a special case of the Global Attractor Conjecture, a problem which has been open since the 1970s, in joint work with Manoj Gopalkrishnan and Ezra Miller, (2) classified small multistationary reaction networks and contributed to the understanding of multistationarity more generally, in joint work with Badal Joshi, and (3) analyzed equilibria of post-translational modification systems, which are important signal motifs in biology, in joint work with Carsten Conradi, Mercedes Pérez Millán, and Alicia Dickenstein. Broader Impacts. This research provided new insights about the dynamical behavior of medically relevant biochemical reaction networks. Also, the investigator took leadership roles in conferences and seminars related to the award. Additionally, the investigator served as a mentor as part of the Women and Mathematics Mentoring Program of Durham County, directed an undergraduate student research project as part of the Duke Program for Research for Undergraduates in the math department, and gave five lectures in the University of Chicago REU (Research Experience for Undergraduates).
