Presentation Information
[PT05-01]Unveiling the Complex Biological Systems: New Horizons in Solution Landscapes
*Lei Zhang1 (1. Beijing International Center for Mathematical Research, Center for Quantitative Biology, Center for Machine Learning Research (China))
Keywords:
Mathematics
Biological systems are often characterized by nonlinear interactions, feedback loops, and the ability to adapt and evolve, making them challenging to study and model. Energy landscape has been widely applied to many biological systems. A long standing problem in computational physics is how to search for the entire family tree of possible stationary states on the energy landscape without unwanted random guesses? Here we introduce a novel concept “Solution Landscape”, which is a pathway map consisting of all stationary points and their connections. We develop a generic and efficient saddle dynamics method to construct the solution landscape, which not only identifies all possible minima, but also advances our understanding of how a complex system moves on the energy landscape. As illustrations, we apply the solution landscape approach to study two problems: One is construction of the solution landscapes of gene regulatory networks in cell fate decisions, and the other one is to construct the solution landscape of reaction-diffusion systems, which reveals a nonlinear mechanism for pattern formation beyond Turing instability.