Bryan Hernandez is an assistant professor at the Institute of Mathematics, University of the Philippines Diliman. He currently serves as an associate editor for the journal Mathematics in Medical and Life Sciences and is a board member of the Philippine Society for Mathematical Biology (PSMB). In recognition of his academic achievements, he was the sole recipient of the Mathematical Society of the Philippines’ 2021 Outstanding PhD Graduate Award and one of the recipients of the 2024 Distinguished Alumni Award from the Institute of Mathematical Sciences and Physics at the University of the Philippines Los Baños. He specializes in the theory and methods for chemical reaction networks, applying his expertise to computational biology and biochemistry. His earlier research includes the development of a multistationarity algorithm for power-law systems, a critical tool for identifying multiple positive steady states and analyzing the long-term behaviors of complex biological and chemical systems. He also focuses on network decomposition and transformation techniques, employing a divide-and-conquer strategy to simplify computations. This approach makes smaller networks more manageable and facilitates the computation of analytic forms of positive steady states. His contributions have led to the creation of computational packages that are helpful for applied mathematicians and scientists. These tools have been utilized both locally and internationally to analyze various biochemical models. Notable applications include comparing insulin signaling pathways in healthy cells versus those with type 2 diabetes, investigating the structural and kinetic properties of Wnt signaling, examining the regulation of cholesterol concentration in the human retina, and modeling the Earth’s carbon cycle.

The study of complex biochemical reaction networks poses significant challenges due to their intricate structures and dynamic behaviors. To address these complexities, we utilize network decomposition techniques in analyzing the structural and dynamical properties of biochemical models.

We observe the ubiquity among biochemical reaction networks that can be decomposed into (stoichiometrically) independent subnetworks. This decomposition is characterized by the ability to directly sum their stoichiometric matrices, resulting in the stoichiometric matrix of the entire network. Furthermore, we find that these independent subnetworks can often be refined into incidence-independent components, preserving the same property through direct summation of incidence matrices. We characterize this phenomenon and explore the conditions under which the two types of decomposition coincide. Additionally, we also identify relationships between the two types of decompositions and their linkage classes, which correspond to the connected components of the network. These relationships allow a deeper level of understanding of the algebraic architecture of reaction networks.

We will also present the computational methods that we developed to derive these independent decompositions and discuss their application in calculating steady states, thus facilitating investigations into long-term behaviors of biochemical systems. Our methods have been effectively applied to a variety of biochemical models, including the insulin signaling pathway, the Wnt signaling pathway, the regulatory mechanism of cholesterol in the human retina, and models of the Earth's carbon cycle. Through these applications, we demonstrate the importance of our approach in elucidating the complexities of biochemical networks.