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Modeling the Effect of Ion-Induced Shock Waves and DNA Breakage

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Modeling the Effect of Ion-Induced Shock Waves and DNA Breakage Modeling the effect of ion-induced shock waves and DNA breakage with the reactive CHARMM force field Ida Friis,1 Alexey V. Verkhovtsev,2, ∗ Ilia A. Solov’yov,3, ∗ and Andrey V. Solov’yov2, ∗ 1Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark 2MBN Research Center, Altenh¨oferallee 3, 60438 Frankfurt am Main, Germany 3Department of Physics, Carl von Ossietzky Universit¨at Oldenburg, Carl-von-Ossietzky-Str. 9-11, 26129 Oldenburg, Germany Ion-induced DNA damage is an important effect underlying ion beam cancer therapy. This paper introduces the methodology of modeling DNA damage induced by a shock wave caused by a projectile ion. Specifically it is demonstrated how single- and double strand breaks in a DNA molecule could be described by the reactive CHARMM (rCHARMM) force field implemented in the program MBN Explorer. The entire work flow of performing the shock wave simulations, including obtaining the crucial simulation parameters, is described in seven steps. Two exemplary analyses are provided for a case study simulation serving to: (i) quantify the shock wave propagation, and (ii) describe the dynamics of formation of DNA breaks. The paper concludes by discussing the computational cost of the simulations and revealing the possible maximal computational time for different simulation setups. I. INTRODUCTION changes of their topology and molecular composition [9, 11, 12]. It takes into account additional parameters Classical molecular dynamics (MD) enables studying of the system, such as bond dissociation energy, bond of structure and dynamics of biological systems and inor- order and the valence of atoms. The functional form ganic materials, nowadays constituting of up to 106 108 of interatomic interactions is also adjusted to account atoms, on the nanosecond time scale [1]. In biological− for the finite dissociation energy of the chemical bonds systems, which are in focus of this work, the interac- [9]. The rCHARMM force field is particularly applicable tion between constituent atoms in such systems is com- for simulating irradiation- and collision-induced damage monly described through empirical molecular mechanics phenomena where breaking of chemical bonds plays an force fields, for example, CHARMM [2, 3] or AMBER [4], essential role. It was used previously to study thermal which are governed by the type of individual atoms and splitting of water [9], ion-induced water radiochemistry by the network of chemical bonds between them. Being [13], collision-induced fusion and fragmentation of C60 based on harmonic potentials, such force fields are well fullerenes [14], irradiation-induced fragmentation of an suited for modeling non-reactive conformational changes organometallic compound W(CO)6 [15] as well as the in (bio)molecular systems, but cannot be used to sim- formation and growth of metal nanostructures in the ulate processes of breaking and formation of chemical process of focused electron beam induced deposition bonds which involve changes in atom connectivity. Re- [12]. active force fields can overcome this limitation and enable This paper reports the first application of rCHARMM simulation of chemical reactions in large systems which for modelling chemical transformations in complex bio- cannot be simulated by ab initio methods. Well-known logical systems. The number of systems and phenomena examples of reactive force fields are ReaxFF [5, 6] and that can be studied using this approach is very large and reactive empirical bond-order (REBO) potentials [7, 8]. cannot be described in one paper. Therefore we focus In both approaches, the interatomic potential describes here on an exemplar case study and apply rCHARMM reactive events through a bond-order formalism where to simulate an important effect arising when an ion pro- jectile propagates through a biological medium, namely arXiv:2107.03736v1 [physics.bio-ph] 8 Jul 2021 bond order is empirically calculated from interatomic dis- tances. thermomechanical damage of a DNA molecule by an ion- Recently, the so-called reactive CHARMM induced shock wave. Understanding radiation effects pro- (rCHARMM) force field [9] was introduced and duced by charged projectiles traversing biological media implemented in the MBN Explorer software pack- is of utmost importance for radiotherapy with ion beams age [10]. Being an important extension of the standard [16, 17] and space radiation protection [18]. Since mod- CHARMM force field [2, 3], rCHARMM permits classical eling of chemical transformations in DNA (and other MD simulations of a large variety of molecular systems complex biomolecular systems) involves many different experiencing chemical transformations whilst monitoring technical and computational aspects, we present a de- tailed methodology for modeling such effects by means of rCHARMM. The formation of ion-induced shock waves on the ∗ On leave from Ioffe Institute, Polytekhnicheskaya 26, 194021 St. nanometer scale was predicted theoretically [19] and Petersburg, Russia studied computationally in a series of subsequent works 2 [13, 20–23]. Ions traversing a biological medium can de- caused by the propagation of different ions through vari- posit large amounts of energy per unit path length and ous media. It is also demonstrated how other important most of this energy is used to ionize water molecules observables, such as the number of molecular fragments and eject low-energy (below 50 eV) secondary electrons created by the shock wave impact on the speed of shock [24]. Most of these electrons transfer their energy to elec- wave propagation in the medium, can be derived from the tronic excitations of the medium in less than a nanome- simulations. This analysis is important for understanding ter on a femtosecond time scale [25]. This time is much the radiation damage with ions on a quantitative level, shorter than the typical time for energy dissipation via focusing on particular physical, chemical, and biological the electron-phonon coupling mechanism, which occurs effects that bring about lethal damage to cells exposed on a few picosecond timescale [25]. As a result, the to ion beams [24, 33, 34]. The methodology described medium in a nanometer-size cylinder around the ion in the present paper can be applied in further computa- track is strongly heated thus providing conditions for a tional studies considering irradiation of DNA with differ- “strong cylindrical explosion”. This creates a discontinu- ent ions and different orientations between the ion’s path ity in the initial conditions for pressure that starts prop- and the DNA molecule. agating in the radial direction away from the ion path. This propagation also features discontinuities in density and collective flow velocity and is referred to as a shock wave [26, 27]. II. METHODOLOGY Two possible effects of ion-induced shock waves in the radiation damage scenario have been suggested [20]. The first is related to direct DNA damage (such as the cre- Computational modeling of an ion-induced shock wave ation of DNA strand breaks) by thermomechanical stress hitting DNA in an aqueous environment is a multi- [20, 21, 28–30]. The other effect is the significant role step process. The simulations rely in particular on the of shock waves in transporting reactive species (such as rCHARMM force field [9, 12], and in this section, details hydroxyl radicals and solvated electrons) due to radial are provided for every step that is required to successfully collective flows initiated by them [13, 25]. perform simulations. Earlier MD studies [20, 21, 28] of possible bond break- age in DNA by ion-induced shock waves were done using the standard CHARMM force field. In these non-reactive simulations, the potential energy stored in a certain DNA A. Construction of the system (step 1) bond was monitored in time as its length varies around its equilibrium distance [20, 21]. When the potential en- The study of a shock wave damaging DNA can be ergy of the bond exceeded a given threshold (which is performed on different systems, but it is most natu- about 3 to 6 eV for covalent bonds in the DNA backbone ral here to consider a generic piece of DNA in a wa- [31]), the bond was considered as broken. ter box. Thus, the system is made from three joined A deeper understanding of the shock wave induced DNA molecules (PDB-ID 309D [35]) with the sequence DNA damage requires a more systematic approach im- (CGACGATCGT) which corresponds to the sequence plying the use of reactive force fields. Such considera- (GCTGCTAGCA) in the complementary strand. For the tion involves the following aspects. First, a stable DNA sake of simplicity, the DNA molecule is placed in a pure structure should be constructed. Second, the force field water box representing the biological medium. The box describing the rupture of covalent bonds in the DNA (or extends 17 nm from the DNA to the edge of the water at least in a specific part of it, e.g. in the backbone) box in the x- and y-directions, as illustrated in Fig. 1A. must be developed. Finally, the process of shock wave The dimensions of the water box are chosen here con- formation and propagation through a molecular medium sistently with previous studies [21], where it was shown should be simulated. Details of the whole computational that a size of 17 nm is sufficient to simulate propaga- protocol and interlinks between its constituent parts are tion of a shock wave generated by a carbon or iron ion presented and discussed in this paper. The methodol- on the timescale of approximately 10 ps. To neutralize ogy reported here represents an alternative approach to the system, one sodium ion is placed for every phosphate other methods (such as ReaxFF [6, 30, 32]) enabling sim- group in the DNA to ensure a charge neutrality of the ulations of bond breakage and formation within the MD entire system. The total system size is 1,010,994 atoms framework.
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