Status
Completed

Period
17-24 September 2021

Applicant
Prof. Theodora Ioannidou

Home Institution
Aristotele University of Thessaloniki, Greece

Host Contact
Prof. Antti Niemi

Host Institution
Nordita Institute, Stockholm, Sweden

Aim of the mission
Since the beginning of the grant EUTOPIA we have been collaborating with Prof Niemi in studying and modeling the dynamics of protein folding usins the Frenet- Serret Frame and its relation with the Non-linear Schroedinger Equation. That way we have been able to construct a set of global variables (so-called link variables) that could nicely describe the dynamics of our proteins. So far the Hamiltonian and the algebra has been defined in terms of the local variables(so-called vertex variables). Our main achievement is to use the connection between the vertex and link variables and to derive a new algebra that will lead to new research paths both in applied mathematics and in mathematical biology.

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.

Dissemination
One published paper: SU(2) Lie-Poisson algebra and its descendants