Luca Donati & Marco Reidelbach, Freie Universität Berlin: **Mini Project Presentation**

Luca Donati:** Transition rate matrix in molecular kinetics by Square Root Approximation**

We have studied a method to construct the transition rate matrix of a molecular system. The method considers a Voronoi discretization of the conformational space and exploits the Gauss theorem, to write the instantaneous rate between adjacent cells in terms of the Boltzmann weight of the intersecting surface. This quantity can be approximated by the geometric average of the Boltzmann weights of the cells. By Perron cluster analysis we can also identify the metastable sets and obtain the rates between conformations. This rate matrix is associated to the transition probability matrix between metastable states and can be used to estimate the implied timescales. The method can be used to study the effect of small perturbations in the potential energy function. We present results for 2d diffusion process and Alanine dipeptide.

The study was carried out in a miniproject of two months at ZIB under the supervision of PD Dr. Marcus Weber. It has been particularly useful to deepen theoretical aspects of molecular dynamics and also to learn new mathematical methods. The project also improved the collaboration between the project B05 and A05 inside the CRC1114.

Marco Reidelbach: **Proton Transfer in Cytochrome c Oxidase - Calculation and Prediction of Transition Networks**

In Cytochrome c Oxidase protons are transferred from the complex surface towards the interior via two distinct channels. How the proton transfer occurs inside the channels, however, is unclear. The Transition Network Approach allows the identification of such proton transfer pathways without introducing any bias. Thereby, a pathway displaying several experimental characteristics was identified. To circumvent numerous Transition Network re-calculations, e.g. for different redox-states, Transition Network predictions via Committor Probabilities, Mean First Passage Times and Minimum Spanning Trees were tested in a Mini-Project with Marcus Weber. Using Minimum Spanning Tree sensitivities proved to be efficient.