High-Resolution Electron Energy Loss Spectroscopy: Absolute Cross Section Measurements for Low Energy Electron Scattering from Biomolecules

Abstract

Low-energy electron (LEE) scattering by molecules is a topic of importance in many areas, such as astrochemistry, plasma science, nanolithography, fast-laser photochemistry and the radiobiological sciences. In the latter field, the passage of high-energy particles or photons in biological matter produces copious amounts of LEEs. These latter are highly reactive and interact within biological media via inelastic collisions that ionize and excite vibrationally and electronically biomolecules. They can additionally attach temporarily to biomolecules to form transient anion states that modulate and enhance excitation and dissociation cross sections (CSs). Since LEEs are one of the most abundant immediate species formed following irradiation, it is necessary to comprehend and model their interactions within biological media. Radiobiological models often rely on Monte Carlo (MC) simulations that can describe event-by-event modifications of the biological medium, predict the number of secondary species created and calculate the deposited energy after the passage of ionizing radiation. These MC and track-structure calculations require a large number of parameters and values that are related to interaction probabilities, including CSs for LEEs scattering from biomolecules. Preferably, these CSs should be obtained in the condensed phase, for such calculations to produce data closer to cellular conditions. In this chapter, we explain the use of high-resolution electron energy loss spectroscopy (HREELS), as a powerful experimental technique to study and measure absolute CSs for LEEs scattering from condensed molecules. We review absolute CSs from the literature, which were derived from this technique with biologically relevant molecules, including those of the basic DNA constituents.

1 Introduction

1.1 General

The passage of high-energy particles or photons in biological matter produces copious numbers of secondary species along their tracks. It is well established that high-energy ionizing radiation (HEIR) deposits most of its energy in biological media via the secondary electrons it generates (Inokuti 1983; Pimblott et al. 1996; Boudaı̈ffa et al. 2000; Pimblott and LaVerne 2007; Mucke et al. 2010; Duque et al. 2015). About 40,000 electrons per MeV of deposited energy (Pimblott and LaVerne 2007) are produced by single and multiple ionizations of biomolecules. Due to their abundance and their high reactivity, secondary electrons are considered as one of the most important species in radiobiology (Pimblott and LaVerne 2007; Mucke et al. 2010). The vast majority of these electrons have energies of less than 30 eV (Pimblott et al. 1996), the most probable energy being 9–10 eV (Pimblott and LaVerne 2007). These low-energy electrons (LEEs) interact with biological media by inelastic processes to vibrationally or electronically excite or ionize biomolecules. Subsequently, LEEs either recombine with ions or are thermalized by multiple processes such as intermolecular trapping, solvation, dissociative electron attachment (DEA) or resonance stabilisation. Ion-electron recombination and LEE inelastic scattering can create highly-reactive species including excited molecules, cations, anions and radicals. These species can damage cell components, change the biochemistry of the cell and create DNA damage. If DNA lesions are not repaired, they can lead to mutagenesis and lethality (Chiari et al. 2014). Moreover, it has been shown that LEEs even of sub-ionization energies can induce cluster DNA damage (Boudaı̈ffa et al. 2000; Huels et al. 2003; Chen et al. 2016; Shao et al. 2017) and thus have the capacity to induce cell death.

The primary objective of radiobiology is a complete understanding of the biological effects of HEIR. Since LEEs are one of the most abundant immediate species formed following irradiation, it is necessary to comprehend and model their interactions within biological media. Radiobiological models often rely on Monte Carlo (MC) simulations that can describe event-by-event modifications of the biological medium, predict the number of secondary species created and calculate the deposited energy after the passage of HEIR (Muñoz et al. 2008; Alloni et al. 2012; Liljequist et al. 2012; Sanz et al. 2012). These MC and track-structure calculations require a large number of parameters and values that are related to interaction probabilities, including cross sections (CSs). Because of the abundance and strong interactions of LEEs, MC simulations should incorporate as many CSs for their interactions with biological matter as possible (i.e., vibrational and electronic excitations, ionization, elastic scattering, DEA, etc.), to most accurately represent the biological effects of HEIR. Since biological media typically exist in a condensed phase, such CSs should be preferably measured in this phase.

In this chapter, we explain the use of high-resolution electron energy loss spectroscopy (HREELS), as a powerful experimental technique to study and measure absolute CSs for LEEs scattering from condensed molecules. We provide data on absolute CSs from the literature, which were derived from HREELS experiments with biologically relevant molecules, including those of the basic DNA constituents (Fig. 1.1). Even though this chapter is focused on CSs for dose calculations, particularly in localized radiotherapy, these values for LEEs induced processes are relevant to many other fields in which HEIR, and hence LEEs, play important roles. These include astrochemistry (Kaiser 2002; Holtom et al. 2005; Lafosse et al. 2006; Bennett and Kaiser 2007; Esmaili et al. 2017, 2018), planetary science (Lu and Sanche 2001; Samara et al. 2015), high-energy electron and extreme UV photon nanolithography (Wu et al. 2010), dosimetry for irradiation in space (Sridharan et al. 2015), plasma science (Lozano et al. 2017), biomedical imaging (Brix et al. 2005; Einstein et al. 2007; Eisenberg et al. 2011; Fazel et al. 2016) and radioprotection (Siragusa et al. 2017).

Fig. 1.1

(Adapted from Lemelin et al. (2017), with the permission of AIP Publishing.)

Chemical structure of a short DNA strand including its four bases

1.2 Radiotherapy Modalities and Low-Energy Electrons

The most important parameter to predict in any radiotherapy treatment is the energy deposited by HEIR per unit mass (i.e., absorbed dose (J/kg or Gy)). This parameter is crucial to maximise the damaging effects of HEIR to cancer cells, while minimizing them for healthy cells (Gaze 1996; Connell and Hellman 2009). Conventional radiotherapy modalities (e.g., external irradiation) deposit doses in macroscopic volumes (i.e., at organ and tissue level (>mm³)). Radiobiological models presently used for these conventional treatments accurately predict the macroscopic doses (i.e., macro-dosimetry) to be administrated to patients. In conventional radiotherapy modalities, healthy cells are inevitably exposed to HEIR, thus increasing the risk of their death or of later secondary cancer development (Hall and Wuu 2003). It is thus crucial to protect healthy cells from HEIR. Moreover, macro-dosimetric methods usually take into account only the primary particles (high-energy photons and particles) and their interactions with molecules of the biological media, particularly the water molecules (Meesungnoen et al. 2002; Emfietzoglou et al. 2005; Plante and Cucinotta 2009; Francis et al. 2011). Hence, while they can calculate the macroscopic dose, they do not consider the damage produced at the cellular and molecular levels by LEEs and other reactive species.

New radiotherapy modalities are being developed to selectively deliver a toxic dose exclusively to cancer cells, while preserving healthy cells (Gaze 1996; Seiwert et al. 2007; Reilly 2008; Connell and Hellman 2009; Chattopadhyay et al. 2010; Zalustky 2013; Sanche 2015; Hayes 2017; Rezaee et al. 2017). These new modalities focus on delivering localized nanoscopic or molecular doses using the reactivity of LEEs and/or other secondary species (Rezaee et al. 2017). Targeted radionuclide therapy (TRT) (Chattopadhyay et al. 2010; Hayes 2017) and concomitant chemoradiation therapy (CRT) (Seiwert et al. 2007) are two examples of these new improved modalities. The former uses radio-labeled molecules that localize preferentially in cancer cells and release, for example, Auger electrons (Zalustky 2013). Since the energy distribution of Auger electrons lies at low energy, they have short range (~10–12 nm) and generate a large quantity of secondary LEEs in the vicinity of the cancer cell. These LEEs thus have the capacity to deposit most of their energy at the DNA level. Furthermore, the density of LEEs can be increased by combining targeted radionuclides with gold nanoparticles (GNPs) or by embedding radionuclides in gold nanocages (Sanche 2015). In these cases, the longer-range particles or photons emitted by the radionuclide strongly interact with the heavy metal, generating large quantities of LEEs. The incorporation of GNPs in TRT is an active field of research (Reilly 2008; Chattopadhyay et al. 2010; Hainfeld et al. 2010; Rezaee et al. 2017; Ghandi et al. 2018) and considerable efforts are being made to improve this new modality. Multiple studies (Hainfeld et al. 2004, 2008, 2010; Hyun Cho et al. 2005; Kong et al. 2008; Rahman et al. 2009; Lechtman et al. 2011; Chattopadhyay et al. 2013) have demonstrated dose and damage enhancements by GNPs in biological tissues, marking them promising tools for future radiotherapeutic treatments.

In cancer therapy, clinical protocols often combine chemotherapy, surgery and radiotherapy. CRT is the combination of chemotherapeutic agents (CAs) and radiotherapy, an approach that often enhances tumor treatment (Seiwert et al. 2007) since, when used in concomitance with HEIR, CAs can often radiosensitize cancer cells. It has been shown that CRT may rely, at least in part, on an increase in damage inflicted to the genome of the cancer cells due to the binding of the CA to DNA.

Conventional methods of estimating radiation doses for macroscopic volumes are obviously not suitable for predicting the subcellular radiobiological effectiveness of these new modalities. TRT and CRT require the details of energy deposition at the nanoscopic level to predict damages and radiobiological risks associated with locally delivered doses. Since these rely on the damages induced by secondary particles such as LEEs, TRT and CRT require new dosimetric models that can predict and calculate doses and damages at subcellular levels. Therefore, it is imperative to develop and improve nanodosimetric models for the continued development of these promising targeted radiotherapy modalities.

1.3 Monte Carlo Simulations and Nanodosimetry

MC simulations can predict damage to a biological medium and the deposited dose at nanoscopic scales, produced by primaries and secondary species, including LEEs (Rogers 2006; Nikjoo et al. 2016). Thus, TRT and CRT can benefit from the detailed description that MC simulations provide. However, for accuracy, MC codes must incorporate a panoply of CSs values for LEE interactions with the biological medium. MC simulations in water have received the most attention (Meesungnoen et al. 2002; Emfietzoglou et al. 2005; Plante and Cucinotta 2009; Francis et al. 2011) and CSs for LEEs interactions with water are incorporated in MC codes, such as Geant4-DNA simulation toolkit (Kyriakou et al. 2017), PENELOPE (Kyriakou et al. 2017) and TOPAS-nBio (McNamara et al. 2017). The general conclusion from these studies is that in MC simulations, LEEs interactions with water and biological medium play a crucial role in describing the chemical and biophysical stages of radiation damage in cells.

Many parameters are user-defined in MC simulations, particularly in modelling radiation damage to DNA (Pater et al. 2014). For each relevant biomolecule present in cells and their nuclei, (e.g., water, DNA fundamentals units, amino acids, etc.), the various parameters needed for MC simulations include CSs for: total ionization, total excitation, total elastic scattering, partial ionization, electronic and vibrational excitation and phonon scattering of all particles involved in the energy deposition process. More specifically, MC simulations require such integral and differential CSs for all the relevant interaction mechanisms involving the fundamental units of DNA. Presently, there is a lack of information on these CSs for material relevant to radiation biology. There exist various experimental techniques to probe LEE-induced processes in biomolecules, including DNA, and measure corresponding CSs; these include X-ray photoelectron spectroscopy (XPS) (Klyachko et al. 1999), electron stimulated desorption (ESD) (Hervé Du Penhoat et al. 2001), electron transmission spectroscopy (ETS) (Burrow et al. 2008), coupled with chemical analysis of degradation products.

The next section focuses on HREELS, one of the most powerful tools to generate CSs for LEE-scattering from biomolecules. We will explain from basic principles, how this is possible and provide the most complete set of absolute CSs for condensed DNA constituents available.

2 Absolute Cross Sections Measurements with HREELS

2.1 Condensed Phase Scattering

At sufficiently high energy, the electron’s wavelength is usually much smaller than the distance between biomolecules in cells. Accordingly, above about 100 eV, electrons interactions may begin to be approximated by collisions with individual targets for fairly disordered materials. Below this energy, the wavelength of a LEE may be comparable to intermolecular and interatomic distances, hence permitting simultaneous interactions with multiple targets (Bauer 1994). In fact, various quantum phenomena appear at low energies, such as diffraction of the electron’s wave by the molecules of the solid (Zheng et al. 2006) and effects from the band structure of the molecular solid (Nagesha and Sanche 1998). Also, in condensed media, many excitation modes can be affected and new modes such as intermolecular vibrations or phonons are observed (Michaud et al. 2003). To take into account these latter processes and quantum phenomena, as well as to study biomolecules as close as possible to their biological environment, CSs should be preferably measured in condensed phase. This chapter focuses on the generation of absolute LEE-scattering CSs from off-specular HREELS data.

2.2 HREEL Spectroscopy

HREEL spectroscopy has been widely applied to many areas of surface and interface related research, e.g., to characterize substrates and adsorbates on surfaces. Multiple review articles exist on this technique (Ibach and Mills 1982; Bass and Sanche 1998; Lafosse and Azria 2011; Conrad and Kordesch 2017). As shown in this section, HREELS can also produce electron-scattering CSs for both gas and condensed phase molecules. For the latter, the majority of studies have focused on DNA constituents, such as the molecular moieties of its backbone (i.e., deoxyribose and phosphate group) and the bases (i.e., adenine, cytosine, thymine and guanine), as well as self-assembled monolayers (SAM) of DNA (Vilar et al. 2008).

Figure 1.2 represents a schematic diagram of a typical HREEL spectrometer for condensed-phase measurements. It consists of two hemispherical electrostatic deflectors; a monochromator and an analyzer (Michaud and Sanche 1984a). The monochromator produces monoenergetic electrons with energy ranging from 0 to 100 eV. In some HREELS systems, the monochromator and the analyzer can be rotated around the target. In this manner, it is possible to study the angular dependence of the electron scattering process with the condensed biomolecules. All the components are housed in an ultra-high vacuum chamber (UHV) where biomolecular films may be prepared by cryogenic condensation, as thin molecular solids. In the majority of such experiments, a metal substrate is cooled to temperatures between 15 and 100 K. First an inert rare gas spacer of several monolayer thickness (ML) is condensed on the metal surface. Afterwards, a monolayer or sub-monolayer of the biomolecular target is deposited. Spacer films of inert rare gas (usually Ar or Kr) reduce molecule-metal substrate interactions and image-charge polarization (Michaud and Sanche 1994). In the case of Ar films, the inert nature and large band gap ensure that electron scattering within the spacer layer is essentially elastic (Levesque et al. 2005a, b; Michaud et al. 2012) below the energy threshold of exciton creation (11.75 eV). These cryogenic conditions are needed in order to supress the vibrational and phonon excitations of the molecular solid and the substrate, and to observe preferentially the interactions of electrons with molecules in their ground state. The resolution of the electron spectrometer can vary from 1 to 60 meV full width at half maximum (FWHM) depending on the incident current I₀, the incident and scattered angle (θ₀ and θ_d, respectively) and on the optimization of the working conditions of the two hemispherical electrostatic deflectors.

Fig. 1.2

Schematic representation of a High-Resolution Electron Energy Loss Spectrometer (HREELS) and solid phase target. The arrangement is composed of two electrostatic hemispheres: a monochromator and an analyzer. In this setup, monoenergetic electrons produced by the monochromator are incident at 15° from the normal of a platinum substrate surface, which is covered by a rare gas spacer layer held at 19 K. Biomolecules are condensed on the spacer layer. The analyzer measures the intensity of electrons inelastically scattered at 45° in the opposite azimuth. The total electron current transmitted through these layers can also be measured

2.2.1 Excitation Mechanisms

There exist two main classes of electron scattering with a medium or molecules: direct and resonant scattering. Direct scattering is mainly controlled by the exchange force and permanent and induced electrostatic potentials. The permanent or induced dipolar term is often the major contribution in the expansion of these potentials. It arises from long-range Coulombic interactions that operate at electron-molecule distances of between ~10 and 100 Å (Lafosse and Azria 2011). Resonant scattering takes place on a much shorter range, at around ~1–3 Å (Lafosse and Azria 2011). Contributions from each of these mechanisms in HREEL spectroscopy depends considerably on the experimental conditions; the incident energy E₀, the incident (θ₀) and analyzing angle (θ_d). With dipolar scattering, the incident electron induces vibrational or electronic excitations via interaction with the dynamic dipole of the molecules or the solid. Since the electron interacts with a long-range Coulomb potential, it scatters with a small change in its wave vector (Δk ≪ k) causing the electrons to scatter predominantly in the specular direction (Lafosse and Azria 2011). For the resonant mechanism, the vibrational or electronic excitations are induced via short-range interactions of the incoming electron with the atomic or molecular potential of the surface or near-surface components (Schulz 1976). With this type of interaction in a randomly oriented molecular film, the LEE wave vector experiences large momentum changes, with no particular backscattered direction being favored. Since dipolar (i.e., optical) selection rules no longer prevail in resonance scattering, multiple excitation losses are enhanced relative to dipolar scattering and electron resonances can be observed. These consist in the temporary capture of the incoming electron by a previously empty atomic or molecular orbital (Sanche and Schulz 1972) to form a transient negative ion (TNI). There exist mainly two types of resonances: shape and core-excited resonance (Sanche and Schulz 1972; Schulz 1973). The shape or single particle resonance occurs usually at low energies (0–5 eV), when the incoming electron occupies a previously empty orbital of the molecule in its ground state (Caron and Sanche 2011). It is called “shape” resonance, because the electron is captured by the shape of the effective potential barrier created by the electron and the molecule (Schulz 1973). In a core-excited resonance, the capture of the incoming electron involves also electronic excitation of the target molecule (Schulz 1973). A core-excited resonance is also called a “two-electrons one-hole state”, since it involves the movement of an electron from a lower energy orbital to a higher one. In either type of resonances, the TNI is formed at a specific energy corresponding to that of the anion’s transient state involved. At resonance energies, CSs for electron interactions can be considerably enhanced.

During the life-time of the TNI, the nuclei may move apart from the equilibrium position due to the perturbation induced by the extra electron (Arumainayagam et al. 2010). The TNI has multiple outcomes or decay channels. In the autodetachment channel, this perturbation can result in a vibrationally excited neutral molecule (Arumainayagam et al. 2010). If the TNI is sufficiently long-lived and its inter-atomic potential energy surface is repulsive, the nuclei may move apart sufficiently for fragmentation of the anion, a process known as DEA, in which the electron is captured permanently by one fragment (AB + e⁻ → AB⁻ → A⁻ + B) (Sanche 2010).

TNIs are of considerable interest in radiobiology, since multiple studies have shown that the decay of these resonances can cause fragmentation of biomolecules including lethal DNA damages, particularly local multiply-damage sites (Boudaı̈ffa et al. 2000; Sanche 2010; Chen et al. 2016; Shao et al. 2017). Thus, resonance scattering is probably one of the most relevant physical mechanisms to investigate in radiobiology.

2.2.2 Condensed-Phase HREELS and Scattering Models

In its condensed-phase version, HREELS allows the study of elastic scattering and energy losses by electrons scattered inside or at the surface of a solid. There exist principally two modes of measurement. It is possible to measure the magnitude of a given energy loss by sweeping the energy of both the monochromator and the analyzer, while maintaining a constant potential difference between them corresponding to the probed energy loss (Michaud et al. 1991; Lepage et al. 1998). The recorded current is termed an excitation function for the given energy-loss process (e.g., a vibration or an electronic mode). Excitation functions provide information on the energy dependence of interaction probabilities (Lepage et al. 1998), which are required to detect the presence of TNI at certain incident energies, but reliable absolute CSs cannot be extracted from such measurements (Allan 2007).

In the electron energy loss (EEL) modes of HREELS, spectra are recorded by sweeping the potential of the analyzer relative to the grounded target and keeping constant the potential of the monochromator or vice versa. When the incident electron energy (E₀) is kept constant, the analyzer measures electrons that have experienced a range of energy losses. Absolute CSs are usually measured in this mode. An example of a vibrational HREEL spectrum is shown in Fig. 1.3.

Fig. 1.3

(Reproduced from Lemelin et al. (2017), with the permission of AIP Publishing.)

A representative electron-energy-loss (EEL) spectrum recorded with 3.5-eV incident electrons on 2.4 monolayers (ML) of Dimethyl Phosphate (DMP) deposited on 3 ML of Ar. The thin solid line passing through the data points corresponds to the sum of Gaussian functions appearing at the bottom, which are associated with each vibrational peak. The dashed line accounts for the background current produced by the Ar and Pt substrates

The sample molecules can be condensed as a multilayer film or isolated on a rare gas spacer. To condense molecules on the substrate, there exist two alternative methods, which depend on the phase of the sample at ambient temperature (T) and pressure (P). For samples that are gases or liquids under ambient conditions, the vapor is introduced into a gas-handling manifold (Michaud and Sanche 1984a). Thereafter, a controlled quantity of vapor, determined by a pressure change in the manifold can be expanded into the UHV chamber and condensed onto a substrate. Alternatively, for samples that are solid at ambient temperature and pressure, a double-stage oven has been developed by Lévesque et al. (2003) for film deposition. In a secondary chamber, a crucible containing the sample in powder form, is heated up to the point of sublimation. Sublimated molecules escape the crucible via an aperture and condense upon a ceramic tip that is positioned beside the crucible. Thereafter, the tip is brought into the UHV analysis chamber and positioned in front of the metal surface, at a distance of 5 mm. The tip is then heated to desorb the molecules, which condense onto the cooled substrate (Levesque et al. 2003).

For extracting absolute CSs from LEE scattering data, two models have been developed to analyze results from either multilayer or (sub-) monolayer films. Dependent on film thickness, HREEL data are analyzed by a multiple scattering model (Michaud and Sanche 1987a; Michaud et al. 2003) or a single collision model (Levesque et al. 2005b; Bazin et al. 2010). In the latter, the elastically scattered current measured by the analyzer at an angle of θ_d, with respect to the surface normal, is assumed to have a diffuse reflectivity. Since this model only considers single collisions within a monolayer or submonolayer film, it can be shown that for an incident electron beam current I₀ of energy E₀, with a near normal incidence θ₀, the analyzer measures in the backscattered direction θ_d, a current of electrons with an energy E that have experienced an energy loss of E − E₀ into the film such that (Levesque et al. 2005b; Michaud et al. 2012):

$$ I\left( {\theta_{d} ,E_{0} ,E - E_{0} } \right) \cong \frac{{I_{0} \left( {\theta_{d} ,E_{0} } \right)}}{{cos\theta_{0} }}\sigma_{r} (E_{0} ,E - E_{0} )n_{s} $$

(1.1)

where σ_r(E₀, E − E₀) is the CS for an electron of energy E₀ to deposit an energy E-E₀ in the film and be backscattered into the vacuum; n_s is the surface number density of the target molecules (related to the thickness of the film). The term I₀(θ_d, E₀) is defined as an effective incident electron current and can be considered as that fraction of the total incident electron current I₀ that would be backscattered in the direction of the analyzer at θ_d by a material with a diffuse elastic reflectivity of one. This latter experimental parameter allows the normalization of EEL spectra and permits the energy integral over an energy loss feature to be expressed in terms of an absolute reflectivity value (Levesque et al. 2005b). To determine this value experimentally, a technique, which uses the linear relationship between the reflected and transmitted current has been developed and is described in detail elsewhere (Levesque et al. 2005b; Michaud et al. 2012). Briefly, the value of I₀(θ_d, E₀) can be determined from the conversion law between the backscattered and transmitted current (Levesque et al. 2005b; Michaud et al. 2012) and by extrapolation to zero thickness from measurements taken over a range of film thicknesses. Hence, from n_s and I₀(θ_d, E₀) values, it is possible to normalize EEL spectra (I(θ_d, E₀, E − E₀)) and extract integral CSs for inelastically scattered electrons. To determine the absolute CS values, multiple EEL spectra I(θ_d, E₀, E − E₀) are recorded at different E₀. Subsequently, each energy-loss spectrum is fitted with multiple Gaussian functions to delimit the various excitation energy regions (vibrational and electronic excitations) (Levesque et al. 2005b; Michaud et al. 2012) as is illustrated in the representative EEL spectrum of Fig. 1.3 (the solid black line represents the fit from the sum of the Gaussians). Then, the absolute CS value σ_ri(E₀, E − E₀), for a given excitation, is calculated using the area under the corresponding Gaussian function i with the amplitude of a_i(E₀) and δ_i FWHM using:

$$ \sigma_{ri} \left( {E_{0} } \right) = \frac{{a_{i} \left( {E_{0} } \right)\delta_{i} \pi^{{\frac{1}{2}}} }}{{2(\ln 2)^{{\frac{1}{2}}} }} $$

(1.2)

By varying E₀, it is possible to obtain the energy dependence of the absolute CSs for each excitation. The energy and the δ_i assigned to each Gaussian must stay constant between spectra and only the amplitude a_i(E₀) can vary in order to produce each fit. It is important to note that the CSs extracted with the single collision model are integral and absolute values, if the backscattered intensity is isotropic and the electron only experiences single collisions; this is the case for the results that are presented starting in Sect. 1.2.3.2. Under near normal electron incidence and with azimuthally disordered film conditions (Levesque et al. 2003, 2005a, b), multiple studies (Michaud and Sanche 1984b, 1987b; Lepage et al. 2000) have shown that the backscattered intensity can be considered isotropic for the systems used in the studies discussed here. By measuring EEL spectra in a fixed direction and by normalizing to the effective current I₀(θ_d, E₀), the single collision model (Eq. (1.1)) leads to CS values corresponding to electrons backscattered over the whole half-angular space (Levesque et al. 2005b). Thereby, the CSs presented in this chapter are considered to be integral and absolute values.

2.3 Absolute Cross Sections for Condensed Biomolecules

2.3.1 Amorphous Ice

One of the most important and abundant molecules in cells and biological tissues, is water. CSs for LEE scattering by water molecules have therefore been measured in the condensed phase (Michaud and Sanche 1987a, b; Bader et al. 1988; Michaud et al. 2003) and the values implemented into MC simulations (Meesungnoen et al. 2003, 2015; Uehara and Nikjoo 2006; Dingfelder et al. 2009; Plante and Cucinotta 2009; Plante 2011; Francis et al. 2011, 2012; Plante et al. 2012; Douglass et al. 2015). We present and discuss in this section the results of Michaud et al. (Michaud and Sanche 1987a, b; Michaud et al. 2003). These authors generated absolute integral CSs for elastic collisions, phonon excitations, vibrational and electronic excitations and ionization, in the range 1–100 eV from analysis of HREEL data (Michaud and Sanche 1987a, b; Michaud et al. 2003). The absolute inelastic scattering CSs for incident electrons below 30 eV lie within the range of 5.6–9.8 × 10⁻¹⁷ cm² (Michaud and Sanche 1987a, b; Bader et al. 1988; Michaud et al. 2003). Since the electrons were incident on 30-ML films of water, a multiple-scattering analysis in a two-stream approximation was required to extract the CSs. The method is described by Michaud and Sanche (Michaud and Sanche 1987a). The energy-dependence of the elastic CS in the range 1–100 eV exhibits three broad structures at around 6.5, 14.5 and 40 eV as well as a small shoulder near 80 eV, as seen in Fig. 1.4a). These authors also measured the CSs for the translational phonon mode ν_T″, the energy dependence of which exhibits a strong rise at low energy similar to the elastic CSs. The librational modes ν_L′ and ν_L″ have also been resolved and the 0–100 eV dependence of their CSs shows a rise at low energy (Fig. 1.4a)). Maxima around 8.5 and 7 eV are also observed for ν_L′ and ν_L″ respectively. At higher incident energy, librational CSs exhibit an oscillatory structure similar to that of the elastic CSs. The CSs for quasielastic scattering of electron in amorphous ice, represented as the sum of the CSs for elastic scattering and that for excitation of translational phonon modes (ν_T′ and ν_T″) is shown in Fig. 1.5.

Fig. 1.4

(Reproduced with permission from Michaud et al. (2003), © 2018 Radiation Research Society.)

Integral cross sections for a elastic scattering, translational (ν_T′ and ν_T″) and librational phonons modes (ν_L′ and ν_L″) and b vibrational modes ν₂, ν_1,3, ν₃, ν_1,3 + ν_L′ and 2 ν_1,3 of amorphous ice extracted from multiple scattering analysis of electron energy loss spectra. The white dots and triangle are measured integral cross sections for electron scattering from water in the gas phase: a elastic CSs ···○··· Danjo and Nishimura (1985); ···▽··· Johnstone and Newell (1991) and b cross sections for the ν₂, ν_1,3 modes; ···○··· Seng and Linder (1976); ···▽··· Shyn et al. (1988)

Fig. 1.5

(Adapted from Michaud et al. (2003), © 2018 Radiation Research Society.)

Energy dependence of the integral cross sections of water given by the sum of the elastic and translational phonon ν_T′ and ν_T″ modes

From their analysis Michaud et al., also obtained the vibrational CSs shown in Fig. 1.4b) for the 1–100 eV energy range (Michaud et al. 2003). As seen, the vibrational mode ν_1,3, ν₂, ν₃, ν_1,3 + ν_L′ and 2ν_1,3 exhibits a strong enhancement around 8 eV. This maximum is due to decay of the transient ²B₂ anion state into these modes. The energy position of this resonance is higher than the same resonance in the gas phase (i.e., 6–8 eV), which is thought to be due to the presence of hydrogen bonding in condensed phase (Michaud et al. 2003).

The sum of the CSs for other inelastic processes associated with greater energy losses than vibrational excitation (i.e., dissociative attachment (DA), electronic and ionization) is shown in Fig. 1.6 in the 1–100 eV energy range. There is a small maximum around 5.2 eV, in the energy dependence of these CSs, ascribed to the formation of the ²B₁ transient negative ion state. Following this feature, there is a steady rise above 7.5 eV attributed to the electronic excitation and ionization processes.

Fig. 1.6

(Reproduced from Michaud et al. (2003), © 2018 Radiation Research Society.)

Integral cross sections for dissociative electron attachment (DA), electronic excitation (electr) and ionization (ion) of amorphous ice

Although the two-stream analysis of Michaud et al. considers electron scattering from individual isolated targets, the CSs derived from their work necessarily contains interference effects that modify the CS values. Since in amorphous ice, constructive or destructive interference is short range, the extracted values can be regarded as ensemble-averaged cross sections per scattering site, in the sense defined by Lekner and Cohen (Lekner 1967; Cohen and Lekner 1967) and Davis et al. (1971). Here, the scattering sites can be seen as those in the two-stream multiple scattering analysis. The extracted CSs include interference and screening effects originating from the surrounding molecules (Michaud and Sanche 1987a), which should be most pronounced in the elastic and quasi-elastic scattering CSs. In a first approximation, the ensemble-averaged integral quasieleastic scattering CS per scatterer can be expressed as

$$ \sigma_{qe} \left( {E_{0} } \right) = \frac{{m^{2} }}{{4\pi^{2} h^{4} }}\mathop \int \limits_{0}^{2\pi } \mathop \int \limits_{0}^{\pi } \left| {V\left( K \right)} \right|^{2} S\left( K \right) \sin \theta d\theta d\varphi $$

(1.3)

where m is the reduced mass of the particle, S(K) is the static structure factor of amorphous ice and V(K) is the electron-molecule attraction potential. In the case of amorphous ice, the expression clearly shows that the gas-phase CSs are modulated by a structure factor taking into account short-range order diffraction. In fact, Michaud et al. have been able to correlate the results of Fig. 1.5 to the energy dependence of the structure factor (Michaud et al. 2003), showing that diffraction is occurring. Moreover, the structure factor decreases considerably with energy and, due to coherence, strongly reduces the quasi-elastic scattering CS below about 3 eV. In addition, Michaud et al. pointed out that a forward elastic scattering term is not contributing to the electron-beam attenuation in the two-stream analysis, which would make the derived elastic CSs, and thus the measured total CSs, smaller than they should be in amorphous ice. From this argument, Nikjoo et al. (2016) suggested to increase the published elastic CSs by factors derived from transport mean free paths, to produce values closer to those of the gas phase. Such factors are probably not needed for two reasons: (1) Eq. (1.3) can account for large reductions in the quasi-elastic CSs at low energies and (2) the higher momentum terms in the expansion of the scattered electron wavefunction are absent in the condensed phase due to the presence of neighboring molecules. This condition necessarily reduces the elastic and quasi-elastic scattering probabilities at each scattering site. Finally, we note that in similar investigations with disordered solid Xe films, the structure factor has been observed experimentally to reduce the gas-phase CS values by about an order of magnitude between 3 and 9 eV (Bader et al. 1982).

If CS values of amorphous ice are to be used for modelling liquid water, then they probably have to be increased to account for the reduction of coherence due to enhancement of thermal phonon and vibrational excitation in the liquid phase, the different geometrical arrangement of the molecules and hydrogen bonding. A reasonable amplification factor of 2 was introduced empirically by Meesungnoen et al. (2002), when they applied the CSs of amorphous ice to their simulation of LEE elastic scattering in a water solution.

2.3.2 DNA Backbone: Deoxyribose and Phosphate Group

Figure 1.1 shows the structure of a DNA strand. The DNA backbone is comprised of two molecules: deoxyribose generally called the sugar group and the phosphate group. The most studied molecular analog of deoxyribose is tetrahydrofuran (THF—C₄H₈O) (Lepage et al. 1998; Antic et al. 1999, 2000; Breton et al. 2004; Bouchiha et al. 2006; Sulzer et al. 2006; Jäggle et al. 2006; Park et al. 2006). THF is a convenient model, since it represents the furyl ring at the center of the deoxyribose molecule, as seen in Fig. 1.7a). Lemelin et al. (2016b) measured absolute vibrational CSs for 1–19 eV electron scattering from THF using HREELS and the simple collision model described in Sect. 1.2.2.2. The vibrational CSs values were found to lie within the 10⁻¹⁷ cm² range. Figure 1.8 shows the energy dependence of the CSs. Highlighted in color are four features observed by the authors around 2.5, 4.5, 9.5 and 12.5 eV, which were all attributed to resonances. The maximum around 2.5 eV had not previously been predicted in theoretical calculations, but has been inferred in gas-phase studies (Allan 2007). Thus, its observation in this solid-phase study confirmed its existence and was attributed to the formation of a shape resonance. Considering the broadness of the other structures, the authors attributed these to shape or core-excited shape resonances. Pure core-excited resonances produce sharp features in scattering CSs; thus, they are rarely seen in vibrational CSs (Sanche and Schulz 1972). The three resonances at higher energy were also predicted or observed in other previous theoretical or experimental studies on LEEs interactions with THF (Lepage et al. 1998; Antic et al. 1999; Breton et al. 2004; Zecca et al. 2005; Trevisan et al. 2006; Winstead and McKoy 2006; Tonzani and Greene 2006; Allan 2007).

Fig. 1.7

Chemical structure of model molecules representing the sugar a Tetrahydrofuran (THF) and the phosphate group b Dimethyl Phosphate (DMP) of DNA

Fig. 1.8

(Reproduced from Lemelin et al. (2016b), with the permission of AIP Publishing.)

Energy dependence of the absolute cross sections for various vibrational modes of tetrahydrofuran (THF)

Absolute CSs were also measured for electronic excitations of THF by HREELS (Lemelin et al. 2016a). Spectra for energy losses between 6 and 11.5 eV were recorded for incident energies between 11 and 16 eV and a representative spectrum is shown in Fig. 1.9. Since unlike vibrational spectra, there were no readily identifiable energy loss peaks in the electronic spectra, fitting these latter with Gaussians functions to represent discrete electronic states, was unjustified. Instead, each spectrum was divided in five regions of 1 eV width and one remaining region of width 0.5 eV. Then, absolute CS values for each energy loss interval could be obtained from the area of the corresponding region using Eq. (1.1). The values of the CSs for each region lie within the 10⁻¹⁷ cm² range and are plotted as functions of E₀ in Fig. 1.10. No electron-resonance effects can be discerned in this figure. Furthermore, the CS values are lower than those measured for DNA bases or bases derivatives (see next subsection). These results are consistent with previous theoretical and experimental studies, which suggest that initial capture of an electron by DNA occurs on a base rather than on the backbone; subsequently, electron transfer to the backbone, can break a DNA strand (Barrios et al. 2002; Martin et al. 2004; Aflatooni et al. 2006; Sanche 2010; Caron and Sanche 2011).

Fig. 1.9

(Reproduced from Lemelin et al. (2016a), with the permission of AIP Publishing.)

EEL spectrum for electronic excitations of tetrahydrofuran recorded with incident electrons of 14 eV. No structure was clearly observed and fitting this spectrum with Gaussian distributions was not attempted. The spectrum is divided into 6 regions within which cross section values were extracted

Fig. 1.10

(Reproduced from Lemelin et al. (2016a), with the permission of AIP Publishing.)

Incident-electron-energy dependence of absolute cross sections for electronic excitations of THF in the 6 regions defined in the EEL spectrum of Fig. 1.9. The last graph represents the total cross section from the sum of energies loses from all regions

A useful model of the phosphate group of DNA is dimethyl phosphate (DMP) shown in Fig. 1.7b). DMP consists of a phosphate group linked to two CH₃ which is rather like the DNA phosphate group that is linked to a CH and a CH₂. Absolute vibrational CSs have been measured for condensed DMP (Lemelin et al. 2017) using HREELS with the same technique and method described earlier (single collision treatment). They were acquired for electrons with incident energy of 1–18 eV. An example of EEL spectra of DMP is shown in Fig. 1.3. Each vibrational structure was identified and each spectrum was fitted to extract CSs. The energy dependence of absolute vibrational CSs are presented in Fig. 1.11. It is possible to discern two strong electron resonances at low energies near 2 and 4 eV and two others of weaker magnitudes at higher energies near 7 and 12 eV. These structures can be compared to other resonances predicted or observed in prior theoretical and experimental studies with various phosphate group models (Pan and Sanche 2006; König et al. 2006; Aflatooni et al. 2006; Tonzani and Greene 2006; Burrow et al. 2008; Winstead and McKoy 2008; Bryjko et al. 2010; Bhaskaran and Sarma 2015). These resonances are likely pure shape resonances due to the broadness of the structures in the CS data.

Fig. 1.11

(Reproduced from Lemelin et al. (2017), with the permission of AIP Publishing.)

Variation with electron collisional energy of the vibrational excitation cross sections of DMP

2.3.3 DNA and RNA Bases Analogs

The DNA bases (or analogs) thymine, cytosine, adenine and pyrimidine have been studied with HREELS. Their absolute inelastic CSs, generated from the HREELS spectra, with the method described in Sect. 1.2.2.2 using the single collision model (Eq. (1.1)) are presented in this section.

Figure 1.12 shows the energy dependence of absolute vibrational CSs of condensed thymine for electrons with incident energies between 1 and 12 eV (Levesque et al. 2003). As seen, there is a common 2 eV wide structure around 4 eV for all of the vibrational modes of thymine. The maximum CS values is about 1.6 × 10⁻¹⁶ cm² for the breathing mode (EEL of ~95 meV) at 4 eV and all the other CSs lie within the 10⁻¹⁷ cm² range. The feature at 4 eV is explained by the creation of a TNI by temporary trapping the incoming electron into the π* orbital of thymine at 4.05 eV (Aflatooni et al. 1998) and its decay into vibrational excitations. The absolute CSs for electronic excitations of thymine have also been measured (Levesque et al. 2005a). The authors observed four electronic electron energy losses between 3.5 and 9 eV. The energy dependence of the absolute CSs associated with these modes are presented in Fig. 1.13. They observe two resonances: at low-energy around 5 eV with a CS of 2.9 × 10⁻¹⁷ cm² and at 8 eV with a maximum CS reaching 1.36 × 10⁻¹⁶ cm². These structures are related to the formation of TNIs and they correspond to the resonances at the same energies that have been reported in the O⁻ yield function from DEA to thymine in the gas phase (Huels et al. 1998). Thus, TNIs associated with the fragmentation of thymine can also decay into its electronic states.

Fig. 1.12

(Reproduced with permission from Lévesque et al. (2003), with permission from Elsevier.)

Absolute cross sections for different vibrational excitation modes of thymine as a function of electron incident energy

Fig. 1.13

(Reproduced from Lévesque et al. (2005a), with the permission of AIP Publishing.)

Electron energy dependence of absolute cross sections for various electronic excitations (E_i) of thymine induce by 4–12 eV electron scattering

In the case of cytosine (Michaud et al. 2012), absolute vibrational CSs have been reported for vibrational modes. The CS values are shown as a function of electron energy in Fig. 1.14, where four structures appear at 1.5, 3.5, 5.5 and 12 eV. These were also interpreted as arising from TNI formation by comparison with the features found in electron transmission spectra (Aflatooni et al. 1998) and DEA yield functions (Denifl et al. 2004; Aflatooni et al. 2006). The first two enhancements at 1.5 and 3.5 eV correspond to resonances found at 1.5 and 4.5 eV in gas-phase transmission data. These resonances were ascribed to shape resonances. DEA studies on gas-phase cytosine also revealed three related resonances in the ranges of 1.5–2.1 eV, 5.2–6.8 eV, and 9.5–10.9 eV. It was then concluded that the TNIs responsible for these enhancements process have certain probabilities to decay into vibrational modes of cytosine. In addition, the absolute CSs for electronic excitations of cytosine have been measured (Bazin et al. 2010) for electron with energies between 5 and 18 eV. The authors observed eight electronic modes in HREEL spectra, from which they extracted the absolute CSs. They are all shown in Fig. 1.15. In the energy dependence of the CSs, they observe two resonances: a common maximum around 6 eV for the two lower excited states and another one near 10 eV. These TNIs correspond to the core-excited electron resonances found at the same energies (5.2–6.8 eV and 9.5–10.9 eV) in the gas-phase DEA channel (Denifl et al. 2004). The authors also measured the absolute CSs for four of the highest occupied orbitals of cytosine lying around 8.55, 9.21, 9.83 and 11.53 eV. The sum of their CSs are presented in Fig. 1.15 in the bottom right panel. This sum reaches a maximum of 8.1 × 10⁻¹⁶ cm² for incident electrons of 13 eV. As it appears in this graph, the theoretical calculations for the total ionization CSs are smaller below 15 eV, than the experimental values for electronic excitation. This result illustrates the relative importance of TNIs and their decay into electronic excitation at low energy.

Fig. 1.14

(Reproduced from Michaud et al. (2012), with the permission of AIP Publishing.)

Absolute cross sections for vibrational excitations of cytosine induced by 0.5–10 eV electron scattering

Fig. 1.15

(Reproduced from Bazin et al. (2010), with the permission of AIP Publishing.)

Electron impact energy dependence of the cross sections to excite various electronic modes of cytosine within the range 4–15 eV

The base adenine is another important DNA constituent. Its vibrational excitation CSs measured (Panajotović et al. 2007) in the condensed phase by HREELS are shown in Fig. 1.16, where it is possible to observe a wide resonance for each vibrational mode in the range 3–5 eV. Also, a weak shoulder around 7 eV is present in the energy dependence of the vibrational absolute CSs for ring deformations and bending of hydrogen atoms. Shown in Fig. 1.17 is the energy dependence of the absolute CSs for electronic excitation by 8–12 eV electrons; a resonance can be seen around 10 eV in all decay channels.

Fig. 1.16

Reproduced from Panajotović et al. (2007), with the permission of the Royal Society of Chemistry.)

Incident-electron-energy dependence of absolute cross sections for vibrational excitations of adenine within the range 1.5–12 eV. (

Fig. 1.17

(Reproduced from Panajotović et al. (2007), with the permission of the Royal Society of Chemistry.)

Energy dependence of absolute cross sections for various electronic excitations of adenine induced by 8–12 eV electron scattering

The pyrimidine molecule has also been studied with HREELS in order to extract absolute vibrational and electronic excitation CSs (Levesque et al. 2005b). Pyrimidine is a relevant biomolecule or model to investigate its three nucleobases derivatives: cytosine, thymine and uracil. The energy dependence of the absolute vibrational CSs of pyrimidine is presented in Fig. 1.18 for five vibrational modes. As seen, the CSs exhibit a common 2 eV wide maximum in the 4–5 eV range. A shape resonance around 4 eV has been identified in electron transmission experiments of gas phase pyrimidine (Nenner and Schulz 1975) and compares well with energies of the structures in Fig. 1.18. In the ν_9a, ν_18b and ν_CH excitation modes, there is also a structure around 6 eV, which compares favorably with the energy of a resonance observed in the same transmission experiment (Nenner and Schulz 1975), as well as in the vibrational CSs of benzene (a closely related molecule to pyrimidine) found around 8 eV in the gas phase. This maximum has also been ascribed to the formation of a shape resonance (Burrow et al. 1987; Allan 1989; Arfa and Tronc 1990; Allan and Andric 1996). Finally, the numerical values of electronic excitation CSs of pyrimidine are presented in Table 1.1; there is no observable structure in energy dependence (Levesque et al. 2005b).

Fig. 1.18

(Reproduced from Lévesque et al. (2005b), with the permission of AIP Publishing.)

Absolute vibrational excitation cross sections of pyrimidine induced by electron scattering in the range 2–12 eV

Table 1.1 Cross sections (10⁻¹⁷ cm²) at different incident energies E₀ (eV) for electrons exciting electronic states (E_i) of pyrimidine (Reproduced from Lévesque et al. (2005b), with the permission of AIP Publishing.)

3 Nanodosimetry Using Absolute Cross Sections from HREELS Measurements

A simple application of LEE absolute CSs is presented in this section. This example demonstrates the relevance and potential for the determination of local doses by use of the absolute CSs values presented in the previous section. As mentioned in the introduction, new modalities such as TRT are currently being developed to target cancer cells with radiolabeled molecules and create local toxic and lethal doses to these cancer cells, while preserving healthy cells (Hayes 2017; Rezaee et al. 2017). TRT needs nanodosimetric modelling, which requires CSs (Itikawa and Mason 2005; Vinodkumar et al. 2006; Champion 2010; Anzai et al. 2012; Jones et al. 2012) to predict the energy deposited by LEEs and link that energy to radiobiological effectiveness (Nikjoo and Lindborg 2010).

An exclusive application of LEE absolute CSs was performed by Michaud et al. (2013). The goal was to present a simple method to assess the energy deposited near the site of a common targeting radioisotope (i.e., ¹²⁵I), using cytosine as a simple model for DNA. Figure 1.19 shows the geometry of a 1-nm-radius (R) cytosine shell with a ¹²⁵I nuclei lying at the center, which was used for calculations. The absolute vibrational, electronic and ionization CSs of cytosine were entered into these calculations to estimate the energy deposited by LEEs into the cytosine shell following the decay of a ¹²⁵I nuclei.

Fig. 1.19

(Reproduced with permission from Michaud et al. (2013), Copyright 2018 by the American Physical Society.)

Model for calculating nanoscopic doses imparted by LEEs, emitted from a radionuclide, to nearby biomolecules. In this example, a one-nm-radius spherical shell of cytosine is irradiated by a ¹²⁵I nuclei at its center

The authors based their estimate of deposited dose on the energy spectrum of Auger electrons N(E₀) released by the decay of ¹²⁵I as shown in Table 1.2. To generate the dose absorbed by the cytosine shell on such a nanoscopic scale, they employed the MIRD schema and the following equation (Loevinger et al. 1991):

Table 1.2 Frequency distribution N(E₀) as a function of the energy in eV (E₀) of the Auger electrons for a single nuclear decay of a single ¹²⁵I atom (Reproduced with permission from Michaud et al. (2013), Copyright 2018 by the American Physical Society.)

$$ S_{k \leftarrow h} = \frac{1}{{4\pi R^{2} m_{cy} }}\mathop \sum \limits_{{E_{0,i} }} N\left( {E_{0} } \right)\sigma_{i} \left( {E_{0} } \right)\epsilon_{i} . $$

(1.4)

Here S_k←h is the absorbed dose of target region k produced by a unit nuclear decay in the source region h (i.e., at the center of the cytosine shell) and ε_i is the energy of the excitation mode i of cytosine (i.e., vibrational, electronic excitation or ionization). $\sigma_{i} \left( {E_{0} } \right)$ is the integral CS to deposit energy ε_i into the excitations mode i and m_cy is the molecular mass of cytosine. The product $\sigma_{i} \left( {E_{0} } \right)\epsilon_{i}$ corresponds to the stopping CS (SCS) (Inokuti 1996). The SCSs can be calculated from the absolute CSs presented earlier in this chapter for cytosine; its energy dependence is presented in Fig. 1.20. The SCSs in this figure are divided in three categories for each type of excitations: vibrational, electronic and ionization. Using these SCSs as well as the frequency distribution of LEEs (N(E₀)) in Eq. (1.4), it is possible to calculate the dose absorbed by the cytosine shell for the decay of a ¹²⁵I at its center. The authors found that taking into account only the distribution of 0–18 eV electrons emanating from iodine, from a single decay of the isotope, 2.5, 31 and 45.5 kGy were absorbed by the shell due to vibrational and electronic excitations and ionization, respectively. Of course, the work of Michaud et al. only gives information on the energy deposited in the cytosine shell and does not correlate this quantity to possible damages made to the molecule in DNA, nor does it predicts the biological effects of this dose. Rather, this work provides an example of the nanodosimetry possible using absolute CSs and clearly demonstrates that, over a short range, LEEs can deposit an enormous dose.

Fig. 1.20

(Reproduced with permission from Michaud et al. (2013), Copyright 2018 by the American Physical Society.)

Stopping cross sections for the vibrational and electronic excitations and ionizations of cytosine. These values were calculated from absolute cross sections of each process given in Figs. 1.14 and 1.15

The method was further elaborated by Rezaee et al. (2014), in a model of double-stranded DNA having the geometry shown in Fig. 1.19. These authors could correlate the absorbed dose deposited by LEEs to damage (Rezaee et al. 2014) in a 1 nm radius shell of double-stranded DNA with a ¹²⁵I nuclei at its center. They used all experimentally measured absolute CSs then available (supplemented with theoretical data for unavailable CS) for DNA bases, THF and phosphate groups to model DNA strands of 8 nucleotides (4 base pairs). For a single decay of ¹²⁵I, the total dose absorbed by the 1 nm radius shell of hydrated and dry DNA was found to be about 272 and 205 kGy respectively, and resulted from the deposition of energy by LEEs via vibrational excitation, electronic excitation, and ionization. For hydrated DNA, the molecule was assumed to contain 20 water molecules per nucleotide. The energy range of LEEs considered was 5–18 eV.

In the same article, Rezaee et al. (2014) report damage CSs (DmCS) calculated from the energy dependence of the yields for the formation of SSBs and DSBs, which could be correlated to the efficiency of 5–18 eV Auger electrons (produced by the ¹²⁵I nuclei decay) to induce DNA strand breaks, in their 4-base DNA shell model. For a single nuclear decay of the radionuclide, the number of SSBs and DSBs induced by LEEs of energies between 5 and 18 eV was 0.5–0.02 respectively. This study amply demonstrated the short-range efficiency of LEEs in producing lethal cellular lesions. It also suggested that in nanometric volumes, the absorbed dose is no longer an appropriate physical parameter to represent biological effectiveness. In fact, the absorbed dose of LEEs in this study is 5 orders of magnitude larger than the dose absorbed in macro- and microscopic volumes, while the number of molecular lesions per unit dose is less than those in larger (macro- and microscopic) volumes (Goodhead 1994, 2006). However, the type of damage produced could have a greater impact at the biological level (e.g., cluster damages). In fact, since radiation interacts with matter in a stochastic way, a deterministic parameter like the absorbed dose has no meaning at the molecular level (Rezaee et al. 2014). For this reason, Rezaee et al. (2014) concluded that nanodosimetry and future radiotherapeutic modalities like TRT need to use both stopping and damage CSs, as biologically related physical parameters that can estimate the energy deposition and predict the damages at the nanometric level. Finally, these authors argued that their results illustrated how LEEs are as efficient as high-LET electrons and suggested that LEEs contribute considerably to the biological effects of radionuclides (Rezaee et al. 2014).

4 Future Trends

In Sect. 1.2.3, we presented absolute CSs for isolated fundamental units of DNA (i.e., each constituent was isolated from the others). When such species are combined into larger biomolecules, modifications of electron-molecule interactions are to be expected and thus also CSs values. Hence, the next logical step requires measurements of absolute CSs for LEEs scattering from larger biomolecules under more complex conditions. For example, it would be revealing to measure with HREELS the absolute CSs for a base linked to the deoxyribose (e.g., thymidine, cytidine, adenosine, etc.), and to compare the obtained CSs to those measured for each isolated constituent. It would give information on the effects of chemical bounding on the scattering process. Similarly, it would be interesting to investigate the effects of other molecules known to exist close to DNA in cells, for example water.

Rezaee et al. (2014) have previously discussed the effect of the presence of water molecules surrounding DNA. They refer to several studies (Rezaee et al. 2012; Boulanouar et al. 2013; Alizadeh and Sanche 2013), which have demonstrated that damage to DNA induced by LEEs is enhanced by the presence of water and oxygen. In recent years, a number of theoretical studies have incorporated additional water molecules into their calculations. For example, the review article of Kohanoff et al. (2017) discusses the effects microsolvation or solvation on electron-thymine interactions (Smyth and Kohanoff 2011; Smyth et al. 2014). It was shown (Smyth and Kohanoff 2011; Smyth et al. 2014) that as small a number as 5 water molecules linked to thymine by H-bonds, are sufficient to raise the energy required for dissociation of the molecule after the LEE attachment, relative to the gas phase. This phenomena has been observed experimentally with microhydrated uracil and thymine (Kočišek et al. 2016). One hypothesis to explain this result is that the DEA channel is supressed due to the redistribution of internal energy (caging) by the fast energy transfer to solvent, which leads to the stabilization of the intact anion (Kočišek et al. 2016). Hence, it becomes crucial to study the effect of water on CSs for various DNA constituents by HREELS or other methods. Data obtained with biomolecules surrounded by water molecules will surely be more relevant and more representative of the biological reality.

In cells, DNA is also surrounded by and linked to proteins. Thus, the close proximity of proteins to DNA also provides an interest in studying experimentally, the variation in inelastic LEE-scattering CSs caused by protein constituents close to DNA, such as certain amino acids. Moreover, any estimate of the DNA damage produced would necessarily have to include that caused by the radiation-induced radicals in the amino acids. Thus, LEE-damage CSs are also needed for amino acids. CSs for gas-phase amino acids have already been reported (Scheer et al. 2007); Glycine has been the most studied amino acid (Gohlke et al. 2002; Ptasinska et al. 2003; Lafosse et al. 2006; Esmaili et al. 2017, 2018). However, the configuration of amino acids in biological media can differ considerably from that in the gas phase. Indeed, these molecules adopt the zwitterion configuration in the presence of water (McNaught 1997; Lafosse et al. 2006). This configuration is highly polarized and hence expected to induce significant changes to the gas-phase LEE CSs. Obviously, electron CSs for amino acid in the condensed phase are needed, particularly in the presence of water.

Ultimately, one would like to measure absolute LEE-CSs for an entire DNA strand with HREELS. This is not an easy task, but Vilar et al. (2008) were able to measure and identify sharp vibrational excitation in the HREEL spectra of well-organized self-assembled monolayers (SAM) of single DNA strand. However, no data treatment was attempted to extract either differential or absolute CSs from these measurements. To extract absolute CSs from HREEL data using the single collision model, molecules must be randomly oriented on an inert surface (as explained in Sect. 1.2.2.2), preferably as a single or sub-monolayer film, which is definitely not the case of a DNA SAM. Hence, with this configuration, it is not possible to extract absolute CSs for DNA from HREEL spectra with our present formulation of scattering within molecular and atomic solids. With present HREEL systems, it is not possible to sublimate DNA (under UHV) without breaking or damaging the molecule. In order to ultimately obtain condensed phase LEE-CSs for a DNA strand, more sophisticated methods of volatilisation must be implemented to create randomly oriented films of undamaged and condensed DNA strands. Laser-Induced Acoustic Desorption (LIAD) may be suitable for constructing such films, since it can sublimate large neutral biomolecules into the gas phase without damage (Golovlev et al. 1997; Shea et al. 2007). This method consists of depositing a solution of sample molecules (e.g., oligonucleotides) on a thin titanium foil and introducing this latter into an UHV chamber, where its reverse side is irradiated with a pulsed ND:YAG laser (Bald et al. 2008). The acoustic waves generated by the short laser pulse, travel to the coated side of the titanium foil, leading to the soft desorption of neutral and intact complex biomolecules (Golovlev et al. 1997; Shea et al. 2007). Bald et al. (2008) used LIAD method to vaporize thymidine in order to measure anion yields from DEA to this molecule in the gas-phase. They showed that no fragmentation was induced by LIAD. Thus, LIAD may have the potential to vaporize oligonucleotides, which could then be condensed onto a substrate. If LIAD is incorporated into a HREELS system, it could provide a powerful instrument to measure absolute CSs for LEE scattering from DNA.

5 Conclusion

HREELS is a powerful tool for studying the interactions of LEEs with biomolecules. This type of spectroscopy permits the extraction of absolute CSs for LEE energy losses to phononic, vibrational and electronic excitations. These CSs are required in nanodosimetric models related to the interaction of LEEs with biological media, as presented in this chapter. Dosimetric modelling is particularly needed for clinical modalities, where radionuclides are injected directly into a tumour or intravenously with a carrier molecule capable of targeting cancer cells or/and their nucleus. In these cases, to deliver a toxic and lethal dose directly and almost exclusively to cancer cells, the energy imparted at the nanoscopic level by the secondary species (e.g., LEEs) must be estimated. In this chapter, we have presented absolute CSs for the scattering of LEEs from DNA fundamental units and water molecules in the condensed phase.

Apart from the measurements of absolute LEE CSs for DNA subunits by HREELS, CSs for lethal cellular damages such as cross links, SSBs, DSBs and other cluster lesions can be measured experimentally using other techniques. These include X-rays photoelectrons spectroscopy (Klyachko et al. 1999; Briggs and Seah 2003), electron stimulated desorption (Abdoul-carime et al. 2000; Dugal et al. 2000), atomic force microscopy (AFM) (Bald and Keller 2014; Keller et al. 2015; Rackwitz et al. 2016, 2017; Schürmann et al. 2017) and electrophoresis (Rezaee et al. 2012). The increased availability of such CSs implemented in MC simulations should help reaching a fundamental understanding of the consequences of the passage of radiation into cells and knowing more precisely the energy deposited and damage induced at the molecular level in cells.

While the CSs presented here are of crucial importance for radiotherapy, they may also have a positive impact in other related fields. Indeed, these absolute CSs could be used in radioprotection to estimate the risk of any radiation source on human health. This includes estimating the energy deposited in modalities using ionizing radiation for imaging body structures, tissues and biochemical processes (e.g. X-ray radiography or positron emission tomography (Brix et al. 2005; Einstein et al. 2007; Eisenberg et al. 2011; Fazel et al. 2016)). CSs for LEE interactions with biomolecules are also of relevance to space radiobiology. Cosmic radiations are among the greatest obstacles to manned interplanetary missions and the assessment and prediction of doses absorbed by astronauts are based on dosimetric models, including track-structure Monte Carlo simulations (Nikjoo et al. 2006, 2016; Dingfelder 2006; Plante and Cucinotta 2009; Durante and Cucinotta 2011; Kennedy 2014; Durante 2014). Exposure to high-energy galactic cosmic rays in space corresponds to a low dose rate (Zeitlin et al. 2013; Hassler et al. 2014), making it difficult to determine the biological effects from this parameter alone (Cucinotta et al. 2011; Chancellor et al. 2014; Norbury et al. 2016; Slaba et al. 2016). LEE CSs values should aid in this fundamental comprehension, arising from models, to correlate the energy deposition at the nanoscopic level within cells to the biological effects of low-dose exposures.