16-22 February 2020

Prof Theodora Ioannidou

Home Institution
Aristotle University of Thessaloniki, Thessaloniki, EL

Host Contact
Prof Antti Niemi

Host Institution
Nordita, AlbaNova Univ. Center Nordita Roslagstullsbacken 23 SE-106 91 ( Stockholm)

Aim of the mission
To visit Prof Niemi at Stockholm to work on issues related to protein folding by studying the dynamics of the discrete nonlinear Schroedinger equation. We expect to finalise one paper and initialise the writing of another two. We have already manage to construct the algebra of discrete chains and introduce an integrable version of the discrete nonlinear Schroedinger equation (dNLS). We have to check and confirm our results and finalise the paper. That way we have introduced a bi-Hamiltonian formulation for the dNLSE. Next we want to solve the corresponding semi-discrete Hamilton equations and connect/derive the formulation of existing protein folding.

Summary of the results
During the visit, we tried to continue and complete a part of our on-going research project, that relates to protein dynamics. The visit helped us to address the remaining issues on Poisson brackets that we have to resolve, in our goal to describe protein dynamics using the framework of discrete nonlinear Schroedinger equation.
During the visit we planned and initiate numerical simulations, where we apply our theoretical formalism to describe dynamics of simple chain-like objects. We also make some preliminary studies and develop work plan, how we simulate dynamics of actual protein chains using the techniques we are developing.
The model that underlies our approach, is based on the discrete nonlinear Schroedinger equation, which we have shown is a computationally most effective way to describe protein structures.
Thus, we have a good hope that in our approach, we can model actual protein dynamics in different scenarios, in an effective coarse grained picture.
The description and study of the discrete non-linear Schoedinger equation using the bi-Hamiltonian form is our aim. Two different variables are obtained: the link and the vertex variables. The correct form of the Poisson brackets of the vertex variables is identified. We continue to work among the lines of this project since it is a rather modern and unexploded field.