Data-driven Markov modeling of nonequilibrium processes

• Applicant: Professor Dr. Gerhard Stock
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 431945604

Project P5 "Data-driven Markov modeling of nonequilibrium processes" by Stock and Thoss is concerned with the extension of the theory and the numerical implementation of Markov state models (MSM) to treat non-Markovian and nonequilibrium data. To model non-Markovian data by a generalized master equation, we will employ the quasi-MSM ansatz and also consider time-convolutionless formulations. We will study various approximations to evaluate the associated memory kernel matrix and time-dependent rate matrix, respectively, considering in particular the case of noisy input data. To model the nonequilibrium response of photoswitchable proteins, we will construct a network of weakly interacting MSMs representing contact clusters, which mediate a multi-step structural reorganization process consisting of cooperative conformational transitions within a cluster and of the communication between clusters. Moreover, we will develop an advanced dynamical clustering scheme to construct metastable states, which lumps microstates according to their transition probability distribution, invokes geometrical information, and is suited for nonequilibrium data. The project is closely linked to projects P1 and P2 of the Research Unit, which deal with quantum and classical generalized master equations based on model Hamiltonians. Moreover, we will analyze molecular dynamics trajectories describing ligand binding and allosteric communication from project P7, and provide our expertise to construct nonequilibrium master equations of energy transport in project P11.

• DFG Programme: Research Units
• Subproject of: FOR 5099: Reducing complexity of nonequilibrium systems
• Co-Investigator: Professor Dr. Michael Thoss