1. INFSO-RI-508833 Enabling Grids for E-sciencE www.eu-egee.org Application of GRID resource for modeling of charge transfer in DNA Nadezhda S. Fialko, Victor D. Lakhno, Alexandr Yu. Zaytsev Institute of Mathematical Problems of Biology RAS EGEE User Forum CERN, 01-03.03.2006

2. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, 01-03.03.2006 2 Charge transfer in DNA Processes of electron and hole transfer along DNA helix are of intense interest for researchers, since: Transcription and reparation of DNA happen under charge transfer; The migration of radicals through DNA plays a crucial role in the processes of mutagenesis and carcinogenesis; Understanding the mechanism of charge transfer may be of great utility for using DNA as a molecular wire in nanotechnology.

3. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, 01-03.03.2006 3 Model of charge transfer in DNA DNA is very complicated molecule. We use the assumptions: Base pair corresponds to site (oscillator) Charge can be transferred along one strand of DNA helix Hamiltonian of the quantum-classical system H = H Pot + H Kin + H Q + H Int H Int is the linear function of the site displacements u n and the probability of charge localization at this site

4. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, 01-03.03.2006 4 Motion equations b n is the amplitude of the probability of a hole occurrence at the n-th site, u n is the displacement of the n-th site from its equilibrium position u 0,  ′ is the constant of relating of a hole occurrence with the site displacement The classical motion equations are modified in such a way as to add the friction term, and a random force A(t) with special statistical characteristics, so the site motion is described by Langevine equation T is temperature of surrounding environment (prescribed)

5. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, 01-03.03.2006 5 Hole mobility A sequential algorithm is used for dynamics calculating of one realization. Initial values of site velocities and displacements are preset randomly from requirement of equilibrium distribution at a given temperature. In calculating individual realizations, at each step a random number with specified characteristics is generated for the Langevine term. The coefficients b n (t) thus found are used to calculate the root-mean- square displacement Mobility of a hole can be calculated by Kubo formula where a is the distance between neighboring sites ( a  3.4 Å),    means averaging over an assembly of realizations.

6. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, 01-03.03.2006 6 Distributed computing This formulation of the problem permits trivial paralleling “one processor – one realization”. Accuracy of averaging value is proportional to 1/  N (N is the number of realizations) When modeling charge transfer in DNA at finite temperature, calculations should be carried out for a great many realizations so that to find average values of physical parameters.

7. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, 01-03.03.2006 7 GRID application, 1 part For adaptation to GRID resource, original program was divided into 2 parts. The first program calculates one realization. Using special script many copies of the program run with the same parameters and random initial data. Finally the files of results are compressed and transmitted to a predefined SE.

8. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, 01-03.03.2006 8 GRID application, 2 part After calculating enough number of realizations, the second program runs. It must calculate average values. A special script is sent to be calculated on WN. This WN takes from SE files with results of realizations in series of 10 items, for every series the averaging program runs. At the same time if for some reason output file of one realization is absent or defective, it is ignored, and the next output file is taken. To files obtained the same program of averaging applies again.

9. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, 01-03.03.2006 9 Some results We estimated values of hole mobility  at different prescribed temperature with various parameters close to DNA’ parameter values. The temperature dependence  ( T ) was approximated by power function  = C  T  For each set of parameters power dependence found was negative,  < 0, i.e. the mobility value increases with lowering of temperature.

10. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, 01-03.03.2006 10 Application of GRID resource Using GRID resource with this method, we made calculations of hole mobility  at different temperature from 10 to 300 K for (GG) and (GC) polynucleotide sequences Each  was obtained with averaging by 100 calculated realizations. One realization takes ~ 3 hours (P4 – 3000 MHz). Compressed output files take ~ 45 MB. So, for one value obtained we need 300 hours of computer time and 4.5 GB storage. Such tasks can hardly be solved without the EGEE resources and facilities