Enabling Grids for Escienc E Application of GRID

Enabling Grids for E-scienc. E 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. 2006 www. eu-egee. org INFSO-RI-508833

Charge transfer in DNA Enabling Grids for E-scienc. E 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. INFSO-RI-508833 EGEE User Forum, CERN, 01 -03. 2006 2

Model of charge transfer in DNA Enabling Grids for E-scienc. E 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 = HPot + HKin+ HQ + HInt • HInt is the linear function of the site displacements un and the probability of charge localization at this site INFSO-RI-508833 EGEE User Forum, CERN, 01 -03. 2006 3

Motion equations Enabling Grids for E-scienc. E bn is the amplitude of the probability of a hole occurrence at the n-th site, un 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) INFSO-RI-508833 EGEE User Forum, CERN, 01 -03. 2006 4

Hole mobility Enabling Grids for E-scienc. E 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 bn(t) thus found are used to calculate the root-meansquare 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. INFSO-RI-508833 EGEE User Forum, CERN, 01 -03. 2006 5

Distributed computing Enabling Grids for E-scienc. E 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. 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) INFSO-RI-508833 EGEE User Forum, CERN, 01 -03. 2006 6

GRID application, 1 part Enabling Grids for E-scienc. E 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. INFSO-RI-508833 EGEE User Forum, CERN, 01 -03. 2006 7

GRID application, 2 part Enabling Grids for E-scienc. E 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. INFSO-RI-508833 EGEE User Forum, CERN, 01 -03. 2006 8

Some results Enabling Grids for E-scienc. E 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. INFSO-RI-508833 EGEE User Forum, CERN, 01 -03. 2006 9

Application of GRID resource Enabling Grids for E-scienc. E 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 (P 4 – 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 INFSO-RI-508833 EGEE User Forum, CERN, 01 -03. 2006 10