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Diffusion-controlled reactions modeling in Geant4-DNA. (English) Zbl 1352.92054

Summary: Context. Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing all the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method. This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k-d tree data structure for quickly locating, for a given molecule, its closest reactants. The performance advantage is presented in terms of complexity, and the accuracy of the new algorithm is demonstrated by simulating radiation chemistry in the context of the Geant4-DNA project. Application. The time-dependent radiolytic yields of the main chemical species formed after irradiation are computed for incident protons at different energies (from 50 MeV to 500 keV). Both the time-evolution and energy dependency of the yields are discussed. The evolution, at one microsecond, of the yields of hydroxyls and solvated electrons with respect to the linear energy transfer is compared to theoretical and experimental data. According to our results, at high linear energy transfer, modeling radiation chemistry in the trading compartment representation might be adopted.

MSC:

92C40 Biochemistry, molecular biology
92E20 Classical flows, reactions, etc. in chemistry
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
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[1] Hirayama, R.; Ito, A.; Tomita, M., Contributions of direct and indirect actions in cell killing by high-LET radiations, Radiat. Res., 171, 2, 212-218 (2009)
[2] LaVerne, J. A.; Pimblott, S. M., Scavenger and time dependences of radicals and molecular products in the electron radiolysis of water: examination of experiments and models, J. Phys. Chem., 95, 8, 3196-3206 (1991)
[3] Kreipl, M. S.; Friedland, W.; Paretzke, H. G., Time- and space-resolved Monte Carlo study of water radiolysis for photon, electron and ion irradiation, Radiat. Environ. Biophys., 48, 1, 11-20 (2009)
[4] Kreipl, M. S.; Friedland, W.; Paretzke, H. G., Interaction of ion tracks in spatial and temporal proximity, Radiat. Environ. Biophys., 48, 4, 349-359 (2009)
[5] Friedland, W.; Jacob, P.; Kundrát, P., Mechanistic simulation of radiation damage to DNA and its repair: on the track towards systems radiation biology modelling, Radiat. Prot. Dosim., 143, 2-4, 542-548 (2011)
[6] Karr, J. R., A whole-cell computational model predicts phenotype from genotype, Cell, 150, 2, 389-401 (2012)
[7] Ohno, H.; Naito, Y.; Nakajima, H.; Tomita, M., Construction of a biological tissue model based on a single-cell model: a computer simulation of metabolic heterogeneity in the liver lobule, Artif. Life, 14, 1, 3-28 (2008)
[8] Ishii, N.; Robert, M.; Nakayama, Y.; Kanai, A.; Tomita, M., Toward large-scale modeling of the microbial cell for computer simulation, J. Biotechnol., 113, 1, 281-294 (2004)
[9] Sandersius, S.; Weijer, C.; Newman, T., Emergent cell and tissue dynamics from subcellular modeling of active biomechanical processes, Phys. Biol., 8, 4, 045007 (2011)
[10] Tomita, M., Whole-cell simulation: a grand challenge of the 21st century, Trends Biotechnol., 19, 6, 205-210 (2001)
[11] Andrews, S. S.; Bray, D., Stochastic simulation of chemical reactions with spatial resolution and single molecule detail, Phys. Biol., 1, 3, 137 (2004)
[12] Kerr, R. A., Fast Monte Carlo simulation methods for biological reaction-diffusion systems in solution and on surfaces, SIAM J. Sci. Comput., 30, 6, 3126-3149 (2008) · Zbl 1178.65004
[14] Moraru, I. I., Virtual cell modelling and simulation software environment, IET Syst. Biol., 2, 5, 352-362 (2008)
[15] Tomita, M., E-cell: software environment for whole-cell simulation, Bioinformatics, 15, 1, 72-84 (1999)
[16] van Zon, J. S.; Ten Wolde, P. R., Green’s-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space, J. Chem. Phys., 123, 23, 234910 (2005)
[17] Takahashi, K.; Tănase-Nicola, S.; Ten Wolde, P. R., Spatio-temporal correlations can drastically change the response of a MAPK pathway, Proc. Natl. Acad. Sci., 107, 6, 2473-2478 (2010)
[18] Arjunan, S. N.V., A guide to modeling reaction-diffusion of molecules with the E-Cell system, (E-Cell System (2013), Springer), 43-62
[19] Andrews, S. S., Accurate particle-based simulation of adsorption, desorption and partial transmission, Phys. Biol., 6, 4, 046015 (2009)
[20] Gladkov, D. V.; Alberts, S.; D’Souza, R. M.; Andrews, S., Accelerating the Smoldyn spatial stochastic biochemical reaction network simulator using GPUs, (Proceedings of the 19th High Performance Computing Symposia (2011), Society for Computer Simulation International), 151-158
[21] Dematte, L., Smoldyn on graphics processing units: massively parallel Brownian dynamics simulations, IEEE/ACM Trans. Comput. Biol. Bioinform., 9, 3, 655-667 (2012)
[22] Takahashi, K.; Kaizu, K.; Hu, B.; Tomita, M., A multi-algorithm, multi-timescale method for cell simulation, Bioinformatics, 20, 4, 538-546 (2004)
[23] Morelli, M. J.; Ten Wolde, P. R., Reaction brownian dynamics and the effect of spatial fluctuations on the gain of a push-pull network, J. Chem. Phys., 129, 5, 538-546 (2008)
[24] Štěpán, V.; Davídková, M., Impact of oxygen concentration on yields of DNA damages caused by ionizing radiation, J. Phys. Conf. Ser., 101, 012015 (2008), IOP Publishing
[25] Štěpán, V., Development, testing and application of theoretical models for prediction of damage to biomolecules (DNA and proteins) by ionizing radiation of different qualities (2012), Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Ph.D. thesis
[26] Štěpán, V.; Davídková, M., RADAMOL tool: role of radiation quality and charge transfer in damage distribution along DNA oligomer, Eur. Phys. J. D (2014)
[27] Friedland, W.; Dingfelder, M.; Kundrát, P.; Jacob, P., Track structures, DNA targets and radiation effects in the biophysical Monte Carlo simulation code PARTRAC, Mutat. Res., 711, 1, 28-40 (2011)
[28] Incerti, S.; Champion, C.; Tran, H.; Karamitros, M.; Bernal, M.; Francis, Z.; Ivanchenko, V.; Mantero, A., Energy deposition in small-scale targets of liquid water using the very low energy electromagnetic physics processes of the Geant4 toolkit, Nucl. Instrum. Methods Phys. Res., Sect. B, Beam Interact. Mater. Atoms, 306, 158-164 (2013)
[29] Karamitros, M.; Mantero, A.; Incerti, S.; Baldacchino, G.; Barberet, P.; Bernal, M.; Capra, R.; Champion, C.; El Bitar, Z.; Francis, Z., Modeling radiation chemistry in the Geant4 Toolkit, Progr. Nucl. Sci. Technol., 2, 503-508 (2011)
[30] Nikjoo, H.; Uehara, S.; Emfietzoglou, D.; Cucinotta, F., Track-structure codes in radiation research, Radiat. Meas., 41, 9-10, 1052-1074 (2006)
[31] Incerti, S.; Ivanchenko, A.; Karamitros, M.; Mantero, A.; Moretto, P.; Tran, H. N.; Mascialino, B.; Champion, C.; Ivanchenko, V. N.; Bernal, M. A.; Francis, Z.; Villagrasa, C.; Baldacchino, G.; Gueye, P.; Capra, R.; Nieminen, P.; Zacharatou, C., Comparison of GEANT4 very low energy cross section models with experimental data in water, Med. Phys., 37, 9, 4692-4708 (2010)
[32] Hamm, R.; Turner, J.; Stabin, M., Monte Carlo simulation of diffusion and reaction in water radiolysis — a study of reactant ‘jump through’ and jump distances, Radiat. Environ. Biophys., 36, 4, 229-234 (1998)
[33] de Berg, M.; Cheong, O.; van Kreveld, M., Computational Geometry: Algorithms and Applications (2008), Springer · Zbl 1140.68069
[34] Car, R.; Parrinello, M., Unified approach for molecular dynamics and density-functional theory, Phys. Rev. Lett., 55, 22, 2471-2474 (1985)
[35] Runge, E.; Gross, E., Density-functional theory for time-dependent systems, Phys. Rev. Lett., 52, 12, 997-1000 (1984)
[36] Li, X.; Moss, C. L.; Liang, W.; Feng, Y., Car-Parrinello density matrix search with a first principles fictitious electron mass method for electronic wave function optimization, J. Chem. Phys., 130, 23, 234115 (2009)
[37] Liang, W.; Chapman, C. T.; Li, X., Efficient first-principles electronic dynamics, J. Chem. Phys., 134, 18, 184102 (2011)
[38] Bowler, D. R.; Miyazaki, T., \(O(N)\) methods in electronic structure calculations, Rep. Prog. Phys., 75, 3, 036503 (2012), Physical Society (Great Britain)
[39] Vellela, M.; Qian, H., A quasistationary analysis of a stochastic chemical reaction: Keizer’s paradox, Bull. Math. Biol., 69, 5, 1727-1746 (2007) · Zbl 1298.92129
[40] Klann, M.; Ganguly, A.; Koeppl, H., Hybrid spatial Gillespie and particle tracking simulation, Bioinformatics, 28, 18, i549-i555 (2012), Oxford, England
[41] Michalik, V.; Begusova, M., Computer-aided stochastic modeling of the radiolysis of liquid water, Radiat. Res., 149, 3, 224-236 (1998)
[42] Friedman, J. H.; Bentley, J. L.; Finkel, R. A., An algorithm for finding best matches in logarithmic expected time, ACM Trans. Math. Softw., 3, 3, 209-226 (1977) · Zbl 0364.68037
[43] Musser, D. R., Introspective sorting and selection algorithms, Softw. Pract. Exp., 27, 8, 983-993 (1997)
[44] Meagher, D. J., Octree encoding: a new technique for the representation, manipulation and display of arbitrary 3-d objects by computer (1980), Electrical and Systems Engineering Department Rensseiaer Polytechnic Institute Image Processing Laboratory
[45] Risken, H., The Fokker-Planck Equation: Methods of Solutions and Applications, Springer Series in Synergetics (1996), Springer · Zbl 0866.60071
[46] Hilhorst, H. J., Physique statistique, Une sélection de sujets, Lecture Notes in Statistical Physics (2010), Université de Paris-Sud, visited in July 2012
[47] Schulten, K., Non-Equilibrium Statistical Mechanics, Lecture Notes (1999), University of Illinois, visited in July 2012
[48] Berg, H. C., Random Walks in Biology (1993), Princeton University Press
[49] Plante, I., A Monte-Carlo step-by-step simulation code of the non-homogeneous chemistry of the radiolysis of water and aqueous solutions. Part I: theoretical framework and implementation, Radiat. Environ. Biophys., 50, 3, 389-403 (2011)
[50] Green, N. J.B.; Pilling, M. J.; Pimblott, S. M.; Clifford, P., Stochastic modeling of fast kinetics in a radiation track, J. Phys. Chem., 94, 1, 251-258 (1990)
[51] Ermak, D. L.; McCammon, J. A., Brownian dynamics with hydrodynamic interactions, J. Chem. Phys., 69, 4, 1352-1360 (2008)
[52] Park, S.; Agmon, N., Theory and simulation of diffusion-controlled Michaelis-Menten kinetics for a static enzyme in solution, J. Phys. Chem. B, 112, 19, 5977-5987 (2008)
[53] Djamai, D.; Oudira, H.; Saifi, A., Application d’un modèle hybride à l’étude des dommages radio-induits par un faisceau d’électrons sur la molécule d’adn dans son environnement, Radioprotection, 43, 3, 357-387 (2008)
[54] Clifford, P.; Green, N. J.B.; Pilling, M. J., Stochastic models of scavenging in radiation-induced spurs, J. Phys. Chem., 89, 6, 925-930 (1985)
[55] Clifford, P.; Green, N. J.B., Stochastic models of diffusion-controlled ionic reactions in radiation-induced spurs. 1. High-permittivity solvents, J. Phys. Chem., 91, 16, 4417-4422 (1987)
[56] Appleby, A.; Schwarz, H., Radical and molecular yields in water irradiated by gamma-rays and heavy ions, J. Phys. Chem., 73, 6, 1937-1941 (1969)
[57] Naleway, C. A.; Sauer, M. C.; Jonah, C. D.; Schmidt, K. H., Theoretical analysis of the LET dependence of transient yields observed in pulse radiolysis with ion beams, Radiat. Res., 77, 1, 47-61 (1979)
[58] Burns, W. G.; Sims, H. E., Effect of radiation type in water radiolysis, J. Chem. Soc. Faraday Trans. 1, 77, 11, 2803-2813 (1981)
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