Annual Report 2003


In cooperation with the scientists from the Technical University of Kosice, the Slovak Republic, and the Laboratory of Computational and Statistical Physics of Academia Sinica, Taiwan, research in the mathematical modelling of proteins folding was continued:

  • In the calculation of thermodynamic properties and three-dimensional structures of macromolecules, such as proteins, it is important to have a good algorithm for computing solvent-accessible surface area and volume of macromolecules. A new analytical method have been proposed for this purpose. This allows one to consider only integrals over the circular trajectories on the plane. The algorithm is suitable for parallelization. Testing on several small proteins has shown a high accuracy of the algorithm and a good performance [21].
  • A FORTRAN code PBSOLVE was created for a numerical solution of a linear Poisson-Boltzman equation. Finite different discretization and successive over relaxation iterations on the sequence of grids were used to obtain the approximate electrostatic potential on the grid. A parallel version of the PBSOLVE has also been constructed. The performance of the program and the efficiency of parallelization have been tested on the small peptide Met-Enkephalin [22].

In cooperation with the Technical University of Aachen, Germany, the original involutive algorithms designed at LIT for constructing involutive bases were implemented in the form of Maple packages "Involutive" and "Janet" [23]. These packages are destined for computing Janet bases for polynomial systems and for systems of partial differential equations, respectively.

By using the above-mentioned program complex [18] and in cooperation with the Nuclear Physics Institute, the Czech Republic, a new type of exact solvability of the Schr oedinger equation in a large spatial dimension and for central polynomial potential was found. This is because the solvability of Schr oedinger equation under the conditions indicated is reduced to solvability of the overdetermined system of nonlinear algebraic equations (Magyari equations) [24].

© Laboratory of Information Technologies, JINR, Dubna, 2004