**Transition path theory**

Transition path theory (TPT) is developed to allow a complete statistical characterization of the ensemble of transition pathways between an initial and a target state. Under assumption of ergodicity, TPT singles out any two subsets in the state-space and analyzes the statistical properties of the associated reactive trajectories, i.e., those trajectories by which the random walker transits from one subset to another. TPT gives properties such as the probability distribution of the reactive trajectories, their probability current and flux, and their rate of occurrence and the dominant reaction pathways.

TPT has been developed from time-continuous as well as time-discrete processes in continuous as well as discrete state space. Particularly TPT for Markov jump processes in discrete state spaces offers a powerful tool since it even allows to compute a ranking of all transition pathways in the order of their contribution to the overall transition rate. We have successfully applied TPT to several examples including protein folding processes, ligand docking, and network analysis. Our aim is the further development of TPT, e.g., for non-reversible processes.

The project is funded through MATHEON project A19 and the Berlin Mathematical School (BMS).

**Selected Publications**

- Noe, F. and Schuette, Ch. and Vanden-Eijnden, E. and Reich, L. and Weikl, T. (2009) Constructing the Full Ensemble of Folding Pathways from Short Off-Equilibrium Simulations. Proc. Natl. Acad. Sci. USA, 106 (45). pp. 19011-19016.

- Metzner, Ph. and Schütte, Ch. and Vanden-Eijnden, E. (2009) Transition Path Theory for Markov Jump Processes. Mult. Mod. Sim., 7 (3). pp. 1192-1219.

- Metzner, Ph. and Schütte, Ch. and Vanden-Eijnden, E. (2006) Illustration of Transition Path Theory on a Collection of

Simple Examples. J. Chem. Phys., 125 (8). 084110.

Head:

Christof Schütte

**Project researchers**

Marco Sarich, Frank Noe, Natasa Djurdjevac, Jan-Hendrik Prinz, Christof Schuette