DNA Damage Induced by Low-Energy Electrons: A Theoretical Approach

This is mainly due to the high activation energy barrier associated with electron transfer from the π∗orbital of the base to the σ∗ orbital of the N-C glycosidic bond. Comparison of the salient features of the two dissociation events, i.e., 3′C–O single strand breakage and glycosidic cleavage of the N–C bond in the 3′-dCMPH molecule are also given.

Fig. 3.1(a) and DFT-B3LYP method [6] after the formation of metastable compound anion are shown in Region 1

Ionizing radiations and it’s role in DNA damage

In particular, the ionization and excitation of biomolecules occurs within femtoseconds after the deposition of high-energy quanta [ 16 , 17 ]. The biological phase of radiation damage usually occurs within seconds of the chemical phase.

Fig. 1.1 Schematic representation of various stages of DNA damage induced by ionizing radiations

An insight into electron-driven processes in general

Apparently, the events that take place at the physical and chemical stages have a great influence on the final biological effects that develop after the deposition of primary quanta. All these discussions lead us to understand the role of ionizing radiation and also the importance of secondary species (e.g. LEEs and OH•) in inducing DNA damage, since more than 80% of the energy in primary quanta are carried by LEEs after the primary ionization events.

Dissociative electron attachment

Furthermore, the DEA process is significantly affected in those molecules where the metastable state formed redistributes excess energy by a process known as intramolecular vibrational energy redistribution (IVR) [24]. Additionally, experimental findings were reported in the literature discussing the high probability of generation of LEEs surrounding living tissues through interatomic Coulombic decay (ICD) [ 26 ].

Electron molecule scattering theory: A quantum approach

Feshbach and Shape resonance

Let's briefly consider, due to the electronic configuration of a generic TNI, what these devices are. If a resonant state is produced without causing any variation in the electronic configuration of the target molecule, then a "one".

Fig. 1.2 M, M ∗ are the neutral species at their ground and excited state respectively

Overview of the resonance scattering process

A particle initially trapped in a barrier can tunnel through depending on its kinetic energy. A situation arises where the combined action of both attractive and repulsive regions prevents re-emission of the particle (also called self-detachment) at least for the time required for TNI to be experimentally detected.

Recent findings in LEE induced DNA damage

Factors affecting the DEA in DNA fragments

Investigations of DNA damage to various DNA fragments in both the gas phase and aqueous phase suggest that solvation has a profound impact on LEE-regulated DNA damage. Another important factor to address when investigating the DEA reaction on DNA fragments is the role of DNA-binding proteins in electron-induced DNA damage [ 52 ].

Our objective

Energy can be effectively transferred to and from the electronic degrees of freedom of the target molecule during electronic collisions. These energies are determined on the ground state geometries of isolated neutral and anionic molecules.

Challenges of theoretical modeling

Information about these energies will be very useful in developing suitable theoretical models for the discussion of electron transfer occurring in DNA. Once the LCP-TDWP approach is implemented to deduce the molecular mechanism of various DNA damages, our goal is to find out the role of LEEs in chemically modified DNA fragments that can act as potential radiosensitizers used in the treatment of cancer is used.

Applications of electron induced processes

5.2 (b) and may indicate quantum tunneling of the 5′ C–O bond from the χ10 state to the dissociative region. Graph of the transfer coefficient (T) of the C–O bond from the anionic vibrational states (i)χi=0−19 for HF and (ii)χi=0−17 for the MP2 part of 5′-dCMPH.

Theoretical Method

An outline of wavepacket approach
LCP-TDWP approach
Modeling of 3 ′ –dCMPH molecule
Electronic structure calculation

In general, the initial wave packet corresponds to the core wave function of the neutral system in a given vibrational state. As we can see from eq. 2.4), one can control the decay pattern and hence the nuclear motion of the wave function by controlling α and δ1.

Fig. 2.1 Fragment excised from DNA molecule representing base-sugar-phosphate group (taken from Ref

Results and Discussions

A careful analysis of the time evolution plots leads to the following observations: (a) the amplitude of the wave function decreases significantly with time, (b) the wave function moves slowly towards the right turning point in the classical region, (c) there is no reflection of the wave function from the right turning point, and (d) near 18 fs the probability amplitude spreads over to the classical region. Single occupied molecular orbitals (SOMOs) of the anionic species (Fig. 2.4) show that the electron migration from cytosine to phosphate radical is evident as it lies in the π∗orbital of the cytosine base at the equilibrium bond length (1.45 Å) [Fig.

Fig. 2.2 (a) Potential energy curves for neutral [E A (R)] and the real part [E A − (R)] of the local complex potential [W A − (R)] for A=3 ′ –dCMPH, (b) the width function [Γ A − (R)], and (c) ground state vibrational eigenfunctions for neutral [φ 0 (R)]

Concluding Remarks

This implies a pronounced glycosidic tunneling of the N–C bond in the eigenvibrational states of the 3'-dCMPH molecule above an energy of 2 eV. This therefore means a pronounced tunneling of the 5′C–O bond in the eigenvibrational states of the 5′-dCMPH molecule above an energy of 1.5 eV. Plot of the transfer coefficient (T) of the N–C bond from the anionic vibrational states (i)χi=0−19 for HF and (ii)χi=0−17 for the MP2 part of 3′-dCMPH.

Computational Method

Electronic structure calculations
Quantum dynamical calculations
Tunneling

Details on the modeling of the 3′-dCMPH system can be found in methods section 2.2.3 of Chapter 2. Thus, to calculate the transfer coefficient T, we will look for any of the following functional forms [9, 10]. In this study, m is the reduced C–O bond mass and Ei is the energy of the bound vibrational state (i) of the PE [EA−(R)] anion curve.

Results and Discussions

LEE and χ i=0−5 (R) vibrational states with energy below 1 eV [S N 2
LEE and χ i=6−9 (R) vibrational states with energy above 1 eV [SSB

We also see that the wave function is slowly moving towards the right turning point of the PE anion curve. The bound vibrational states in region 1 of the MP2 anionic PE curve are labeled as χi=0−9 from lower to higher energy levels. The effect of the extended lifetime of the metastable anion is also evident from the autocorrelation function, χ6 (R) | ψ6 (R, t) ⟩ [top panel of Fig. 1b].

Fig. 3.1 (a) MP2/6-31+G(d) calculations based potential energy curves for the neutral [E A (R)] (green solid line) and the anionic [E A − (R)] (red solid line) 3 ′ -dCMPH molecules.

Concluding Remarks

70 Glycosidic bond cleavage in 2'-deoxycytidine-3'-monophosphate where K=8mU0/¯h2a2 with "m" being the reduced mass of the N-C bond. The transmission coefficient values for the N–C bond tunnel from each of the bonded vibrational levels are tabulated in table 4.2. However, since the barrier in EA−(R) is not symmetric, it is therefore difficult to find the value of width parameter (a) which is the full width at half maximum (FWHM) of the anionic PE curve.

Computational Method

In this regard, we considered the molecule 2'-deoxycytidine-3'-monophosphate, 3'-dCMPH for short (Figure 4.1), which consists of a cytosine base, a ribose sugar, and a phosphate group balanced by a proton in the negative center. However, as mentioned earlier, we did not consider these changes in this bottom-up analysis. In Chapters 2 and 3 [1–3], we separately discussed the dissociation of the 3′ C–O bond induced by LEE as a 1-D process.

Fig. 4.1 The pyrimidine nucleotide 2 ′ -deoxycytidine-3 ′ -monophosphate (3 ′ -dCMPH) excised from DNA double helix, neutralized by adding hydrogens at the radical centers and a proton at the phosphate negative center with the N–C bond cleavage marked with

Results and Discussions

PE curves, Width functions, and Eigen functions
Singly occupied molecular orbitals (SOMOs)
Tunneling
Wave-packet propagation, Life time, and Cross section
Comparison with 3 ′ C–O bond dissociation

The qualitative description of the electron transfer process begins at the cytosine base center where electron attachment occurs. Essentially the same pattern follows in both ab initio methods (Please see Fig. A4 of Appendix A). The lifetime of the decay state is found to be longer for SSB than that for N-C bond scission.

Fig. 4.2 Potential energy curves for the neutral [E A (R)] (green solid line) and the anionic [E A − (R)] (red solid line) 3 ′ -dCMPH molecule computed at the (a) HF/6-31+G(d) and (b) MP2/6-31+G(d) accuracy levels

Concluding Remarks

The other major pathway (60%) leading to 5′C–O bond fragmentation is the initial localization of LEE to the phosphate center of the nucleotide [10]. Modeling of the SPS molecule and the possible fragmentation schemes are discussed in the methods section. The features of the time-evolved states follow the same pattern as that of 3′C–O bond dissociation.

Computational Method

Geometry optimization and Potential energy scan
Quantum dynamical calculations

Before explaining the details of the time-dependent quantum mechanical aspects, let us briefly discuss the modeled gas-phase system 2'-deoxycytidine-5'-monophosphate, 5'-dCMPH for short (Fig. 5.1) for induced SSB from the LEE considered in the present investigation. The local complex potential (LCP) formalism for describing the dynamics of the nuclei of a metastable anion is briefly explained below. The first term is the PEs of the anion [EA-(R)] which is obtained using the program suite G09 [12] as discussed in section 5.2.1 and the other unknown quantity ΓA-(R) is calculated as an exponential function [ please see Eq.

Fig. 5.1 The Base-Sugar-Phosphate unit of 2 ′ -deoxycytidine-5 ′ -monophosphate (5 ′ -dCMPH) neutralized by adding hydrogens at the radical center and a proton at the phosphate negative center

Results and Discussions

Optimized geometries and PE curves
Width functions and Vibrational eigen functions
SSB from the ground vibrational level [φ 0 (R)]
SSB due to the C–O bond tunneling

We then calculated the vibrational eigenfunctions of the neutral [φi(R)] and anionic [χi(R)] systems to obtain the dynamics of LEE-induced single-strand breaks in the 5′-dCMPH moiety. We used a modeled hyperbolic cosine barrier of the following form [19] to obtain the value as:. The wave packet motion of the initial state ψ10(R, t=0) = φ10 (R) was calculated using the Lanczos scheme [16] and some of them are shown in Figure 2.

Concluding Remarks

It is difficult to predict the nature of the orbital [π∗orσ∗] at the equilibrium SPS geometry. A4 "S-shaped" transmission coefficient (T) tunneling curve of the N–C bond from the vibrational modes χi=0−19 (HF, green solid line with black circles), andχi=0−17 (MP2, blue solid line with red circles) of the restricted anionic PE curves in fig. B4 "S-shaped" transmission coefficient (T) tunneling curve of the C–O bond from the vibrational modes χi=0−19 (HF, green solid line with black circles), andχi=0−17 (MP2, blue solid line with red circles) of the restricted anionic PE curves in fig.

Computational Method

If these centers are not neutralized, they can obscure the electron bond leading to the wrong electronic state of the system. An electron is attached to the lowest unoccupied molecular orbital (LUMO) of the neutral system to obtain the anionic molecule. The optimized structures were further used for quantum mechanical calculation of adiabatic potential energy (PE) curves for neutral [EA(R)] and anionic [EA−(R)] systems (A = SPS molecules) using G09.

Fig. 6.1 Schematic representation of low energy electron (LEE) induced single strand break (SSB) in a modeled sugar-phosphate-sugar (SPS) fragment excised from DNA double helix.

Results and Discussions

Tunneling
Molecular orbital analysis
Time-dependent analysis

Singly occupied molecular orbitals (SOMOs) generated at different 3' and 5' C–O bond distances, showing electron transfer leading to C–O bond breakage in the central sugar and phosphate, are given in the figure. On the other hand, since the anionic PE curve near the equilibrium C–O bond distance shows characteristics of the bound state for the π∗ orbital (and also metastable behavior), we believe that the electron resides in the π∗orbital of the phosphate group and not in the σ∗orbital. We can also see that the wave packet is slowly moving towards the right turning point of the PE curve.

Fig. 6.2 Potential Energy curves generated for neutral (green line) and anionic (red line) moieties for the 3 ′ and 5 ′ C–O bonds dissociation are shown in (a) and (b) respectively

Concluding Remarks

Plots of wave packet propagation from time t = 0–22 fs for the ground state wave function φ0 (R) of the target 3′-dCMPH molecule in the HF method under the action of anionic Hamiltonian. A5Plots of wave packet propagation from time t = 0–22 fs for the ground state wave functionφ0(R) of the target 3′-dCMPH molecule in the HF method under the influence of anionic Hamiltonian. Plots of wave packet propagation from time t = 0–22 fs for the ground state wave function φ0 (R) of the target 5′-dCMPH molecule in the HF method under the action of anionic Hamiltonian.