CAREER: Reaction-Diffusion Kinetics with Tensor Networks

Northwestern University, Evanston IL

Investigators

Abstract

With support from the Chemical Theory, Models, and Computational Methods Program in the Division of Chemistry Todd Gingrich of Northwestern University will develop and assess algorithms for simulating reaction-diffusion kinetics. Many self-assembly and signal transduction processes in both biological and synthetic systems are implemented through the reaction and diffusion of molecules. For example, proteins collude together in signaling cascades to detect stimuli and transduce that detection into a desired response. While there has been great progress both in understanding natural systems and in engineering synthetic ones, chemical reaction networks (CRNs) continue to pose a challenge, particularly when accounting for random fluctuations characteristic to the molecular scale. Currently, repeated noisy simulations can be combined to assess how fast-timescale events (individual reactions and diffusive steps) build together to generate slow-timescale responses. Dr. Gingrich and his research group will utilize a mathematical construction called a tensor network (TN) to pursue computational approaches that yield novel methods to analyze CRNs without the need for many repeated simulations. The work will result in disseminated computer code, which will also form the basis for two educational web-based simulation modules about fluctuations in chemical kinetics. Connecting microscopic interactions with emergent macroscopic phenomena is a central challenge of statistical mechanics. In chemical kinetics, this challenge manifests in the nonequilibrium spatio-temporal patterns which emerge from a balance between chemical reactions and diffusion. Subtle changes in the kinetic interactions between species in CRNs can sensitively impact the patterns that emerge, e.g., oscillatory chemical clocks, Turing patterns, and cellular signal transduction. The Gingrich team will develop, characterize, optimize, and ultimately apply a new computational method to study the sensitivity of patterns to the microscopic kinetic model. The research program will combine analytical techniques known as the Doi-Peliti (DP) framework with mature computational methods for TN many-body problems to offer an alternative perspective to kinetics problems which are routinely attacked through Monte Carlo sampling alone. An accompanying educational plan will use web simulations to teach aspects of stochastic kinetics, with one module targeting undergraduates and another targeting graduate students. 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.