2.1

Choice of a well-defined transient quantum probe

One of the most fundamental aspects of a biomolecule (BM) damage induced by ionising radiations concerns the dissociative electron attachment processes occurring in confined ionization spaces (Equation 1).

Such molecular damage involve generally a hierarchy of secondary electron populations for which the energy varies from the thermal value (kT ~ 0.025 eV) to the sub-excitation and relativistic levels i.e. few eV and MeV respectively. In this way, the prethermal processes and early spatial distribution of transient couplings between secondary low energy electron and biomolecules may play a crucial role in radiation induced damage at early time. The nano-scale insight of primary radical processes triggered by ionizing radiation requires the real-time probing of non-equilibrium states for which the lifetimes are typically in the sub-picosecond regime.

Ultrafast radical events occurring in less than 1ps (10^-12s) after an energy deposition induced by a ionizing radiation represent a specific domain for which the quantum character of short-lived events becomes preeminent. This is particularly important when biomolecular damage take place in the prethermal regime of secondary electrons ³. Consequently, one important challenge concerns the spatio-temporal description of events induced by the initial energy deposition of an electromagnetic ray or energetic particle in the medium and the subsequent effects on a solvated biomolecule. For that we are developing a multi-parametric approach that includes some energetic, spatial and temporal considerations (Figure 1). Previous Gauduel’s experimental researches devoted to low and high energy radiation effects on water molecules have suggested the crucial role of ultra-fast quantum effects for which short-lived configuration of very low energy quasi-delocalized secondary electrons would be involved ^16,17. For instance, in the framework of a nonlinear two-photon excitation process of water molecules by femtosecond UV pulses (pulse duration ~50 fs, E_Excit = 2 x 4 eV), multiple non-equilibrium configurations of delocalized electron are generated in less than 5 x 10^-13 s at 294K. One of these short-lived configurations can be analyzed in term of eigenstate and used as quantum probe for the development of preliminary investigations on prethermal chemistry and biomolecular damage induced by the interaction of ionizing radiations (photons or accelerated particles) with a water bath ^18-25. The specific spatio-temporal coherence which is required to get an efficient coupling between a very short-lived quantum probe and a biomolecule needs more complete studies which can be performed by ultrafast near-infrared spectroscopy, using different pump-probe configurations. The multi-parametric data extracted from ultrafast spectroscopic experiments are used for advanced physico-chemical understandings at early time. Some of these parameters will be presented in the next section.

Figure 1.

Ultrafast spectroscopic strategy used for the real time observation of an efficient coupling between a very shortlived quantum probe and a biomolecule in a liquid water bath. The spatio-temporal coherence linking a quantum probe and a biomolecular sensor is investigated at the femtosecond time scale and nanometric level.

For this multi-parametric approach, the transient quantum probe which is taken into consideration corresponds to a well-defined p-state of trapped electron (Figure 2). This eigenstate is generated in less than 150fs and represents a localized electron for which the energy is about -1.0 eV below the bottom of water conduction band (excited prehydrated electron). This state exhibits an absorption spectral signature in the near-infrared and its lifetime (~ 250 fs in pure water at 294K) is directly governed by a non-adiabatic 2p(e^-_prehyd) → 1s(e^-_hyd) transition ¹⁸. Considering semi-quantum Molecular Dynamics simulations, the predicted gyration radius of p-state electron is around 6 A in water bath ²⁶.

Figure 2.

Energy level diagram of a prethermal coupling between the quantum p-state of a localized electron and a disulfide biomolecule. Within an aqueous environment, the short-lived coupling between this quantum configuration of a trapped electron and a biomolecule competes with an ultrafast nonadiabatic p-s transition leading to the formation of a fully relaxed electron in water bath (1s configuration)¹⁸. The left part of the figure gives a representation of 2p and 1s state wavefunctions calculated by semi-quantum molecular dynamic simulations ²⁶.

2.2

Temporal and spatial coherence for an efficient coupling between a quantum probe and a biomolecular target

In the framework of an energy/space/time profile, the temporal and spatial coherences that are required to obtain an efficient coupling between the quantum probe 2p-state electron and a biomolecular target (cystamine molecule) are investigated by using Ti:Sa laser amplifier system generating amplified femtosecond pulses in the mJ energy domain and a pump-probe configuration: a femtosecond two-photons excitation in the ultraviolet (pump beam of 2 x 4 eV, pump beam power density ~ 10¹¹ Wcm^-2 at 0.31 μm) and an infrared probe centered at 0.99 eV (1.25 μm). The transient quantum probe (2p-state excited electron) is triggered by a two-photon excitation of chloride ion in water bath, via an ultrashort lived excited CTTS state (CTTS**) ^27,28. The resulting formation of a quantum p-state electron can be investigated in real time, considering its very short-lived signature in the near infrared (Figure 3). The choice of a disulfide biomolecular target (chlorhydrate of cystamine) permits to use the chloride counterion to initiate the two-photon excitation process and compare spectroscopic data with those obtained with a control sample (aqueous sodium or magnesium chloride solution for instance). The biomolecular target (cystamine (NH₃-(CH₂)₂-SS-(CH₂)₂-NH₃)) represents the reactive center of oxidized glutathione (GSSG).

Figure 3.

Ultrafast infrared spectroscopy of an efficient coupling between the quantum 2p state of an excited electron and a biomolecular target (chlorhydrate of cystamine) in water bath (see also Figure 2). Femtosecond infrared absorption signals are investigated at 0.99eV (1.25 μm). The molecular ratio of aqueous ionic solution (NaCl) and biomolecular target (Cystamine) equal 110. The short-lived quantum probe (p-state electron) is generated by a two photon UV excitation of an halide ion (Cl-), via a transient CTTS state (Charge Transfer To Solvent).

The direct coupling which takes place between the quantum probe (p state electron) and a disulfide biomolecule can be investigated from femtosecond infrared signal dynamics, considering the real-time contribution of quantum probe formation and the ultrafast collapse of this probe on the molecular target (ultrafast infrared p-state electron attachment, Equation 1). This collapse induces an early partition between a reactive trajectory ({e^-_IR}_Reac) and a nonreative trajectory that corresponds to a nonadiabatic relaxation of the quantum probe ({e^-_IR}_p-s). The branching ratio between these two ultrafast electronic trajectories has been expressed in term of probabilities, as reported in the equation of Figure 3.

In the equation of Figure 3, P_Reac, P_p->s represent respectively the probability of an ultrafast collapse of a 2p-like excited electron on a cystamine molecule and an electron solvation process via a nonadiabatic relaxation process (2p → 1s transition). In this equation, the adjusted parameter represents the spectral contribution of different electronic state “i” trajectories probed at 0.99eV. The subpicosecond competition involving the ultrafast electron attachment on cystamine and the energy gap relaxation from the first excited state to the ground state of trapped electron is characterized by a high branching ratio (P_Reac = 1-P_p->s ~ 0.91 ± 0.02). This ultrafast radical process would involve some distorsions of p-like orbitals of prehydrated electron in the vicinity of a sulfur-sulfur bond of cystamine. The sub-picosecond lifetime of the infrared quantum p state electron (e^-_p state) represents a temporal limit for that an early SS bond energy rearrangement facilitates an ultrafast electron tunnelling in the prethermal regime, through a potential barrier separating the infrared p-state electron of an unpaired electron. In this way, the effective radius r_eff of an ultrafast coupling between a non-equilibrium p-like excited electron and a cystamine molecule (RSSR) is defined by Equation 2. This effective radius r_eff equals 9.6 ± 0.2 angströms for a molecular concentration of cystamine of 0.5 M in water bath (molecular ratio = 110).

The effect of this efficient coupling between a quantum probe and the disulfide biomolecule leads to the formation of a native RS∴SR^- radical anion ²⁹. It can be underlined that the additional antibonding electron contributes to the formation of an anionic radical characterized by a 2center-3 electron bond in less than 650 fs (Figure 4).

Figure 4.

Femtoseond UV spectroscopy of a (2σ /σ*) transition inside a nascent 2c, 3e anionic radical following an ultrafast electron attachment on a disulfide molecule. The real time SS bond weakening triggered by an antibonding electron is characterized by a decrease of the gap energy inside the 2σ /σ* transition and involves a red shift of the transient UV absorption signal. A delayed intramolecular SS bond breaking can take place in the sub-nanosecond window.

The concomitant formation of an anionic radical and a weakening of a nascent 2σ /σ* bond energy may induce a disulfide bond breaking at longer time (molecular damage). This femtobioradical investigation performed in aqueous environment gives correlated information on spatial and temporal biomolecular damages triggered by a very short lived quantum scalpel for which the gyration radius is around 6 angströms. The ultrafast sub-nanometric spatial accuracy obtained by femtosecond infrared spectroscopy permits ⁱ⁾ to precise that the effective radius r_eff for getting an ultrafast coupling is greater than this gyration radius, ⁱⁱ⁾ to define an effective interaction cross section (ICS) of 3x10^-6 μm². This interesting parameter can only be discriminated within a very short-time window (t<< 1 ps). It characterizes an efficient and transient coupling between the polarizable fleeting quantum probe (2p state electron) and a disulfide biomolecule. The potential effects of local environments on this effective interaction cross section at early time require additional investigations which are actually performed.

3.1

High energy deposition and early inhomogeneous phenomena induced by relativistic particle

The interactions of relativistic MeV electrons with water molecules induce ultrafast energy scattering processes and fractionated ionization clusters (Figures 2 and 3). These ionization processes involve a hierarchy of electron populations for which the energy varies from relativistic levels to the thermal value (kT ~0.025 eV). Typically, in less than 10^-16s, different energy quanta in the 200-20 eV range may be delivered in nanometric tracks or spurs. Due to the uncertainty relation between time and energy, the fastest ionising events in confined clusters take place in less than 0.33 x 10^-16 s. Consequently, a quantum energy of 20 eV deposited by relativistic particles occurs on 10^-6 cm (~100 A) and involves nanometric ionization clusters configurations (Figure 5).

Figure 5.

Femtolysis experiments of water molecules in liquid phase with ultrashort high energy electron bunches: schematic representation of a spatial distribution of inhomogeneous energy deposition processes and ionisation tracks in the longitudinal direction of a beam propagation.. In the radial direction of this radiation beam, early radiation events take place within the chemical core i.e. at the interface of the physical core and penumbra zone.

As early radiation damages can be highly dependent on ⁱ⁾ the survival probability of very low-energy secondary electrons and ⁱⁱ⁾ the spatial distribution of primary radicals produced from water molecules, a thorough knowledge of native tracks requires the real-time probing of radiation events in the 10^-15 – 10^-11 s range. In aqueous environments, this temporal domain concerns mainly prethermal events for which the quantum states of short-lived excited electrons involve femtosecond nonadiabatic processes.

3.2

Ultrashort relativistic electron bunches and generation of native ionization tracks

From the technical point of view, a 820 nm TW titanium-doped sapphire laser beam with an on-target energy of 960 mJ in 30 fs FWHM pulses can be focused onto the sharp edge of a 2 mm diameter supersonic helium gas jet. With intensities on the order of 2.7 × 10¹⁹ W/cm² in vacuum, the femtosecond laser pulse ionises the gas and excites relativistic plasma waves in the underdense plasma. The electrons of the plasma are accelerated by the intense electric field in the forward direction producing a well collimated electron beam with an initial duration of the same order of the TW laser pulse. Typically, a total charge of the electron beam determined by an integrating current transformer equals 2.5 ± 0.2 nC and corresponds to a mean number of (1.55 ± 0.15) x 10¹⁰ electrons. The specific qualities and properties of ultra-short relativistic particle bunches foreshadow the development of advanced research to deepen the biophysical understanding of ultrafast radiation events in native ionization tracks. Recent femtolysis experiments (Femtosecond _radiolysis) of aqueous targets performed with pulsed electron bunches of 2.5-15 MeV were devoted to the investigation of early radical processes in nascent ionisation tracks. For an effective temperature of the femtosecond electron beam of about 4.5 MeV, the integrated energy flux in aqueous samples equals 5.8 x 10¹⁰ MeV cm^-2. Using a highly-time-resolved pump (femtosecond electron bunch) – optical probe (femtosecond photon pulse) orthogonal configuration, the real-time investigation of primary radiation processes can be performed in the radial direction of femtosecond electron bunches (Figure 5). Using a highly-time-resolved pump (femtosecond electron bunch) – optical probe (femtosecond photon pulse) orthogonal configuration and a detection system based on cooled 16-bit CCD camera (Andor Technology), the real-time investigation of primary radiation processes is performed in the radial direction of femtosecond electron bunches. In the vaccum chamber, the femtosecond high-energy electron pulse passes through a 10 mm/10 mm suprasil cell containing liquid samples. The synchronization of the two laser pulses within a 30 fs precision was performed by shadowgraphy of the plasma created by the pump laser. This arrangement permitted to give a very accurate synchronization and was free of jitter. Absorption spectroscopic measurements were performed at L = 5-6 mm downstream from the helium gas jet and 1mm depth path in the suprasil cell containing liquid water at 294K. With these conditions, the electron beam was visualized with a radiochromic film and the electron beam divergence measured in function of the energy.

3.3

Towards a nanoscale approach of early radiation events in nascent ionization tracks

Laser-plasma accelerator based high energy radiation femtochemistry gives new insights into the time dependence of early events occurring in native ionisation clusters (Figure 6). Indeed, as expressed in Equation 3, the short-time dynamics of the ubiquitous e^-_aq radical (1s ground state) is mainly governed by its transient recombination with surrounding water products (hydronium ion H₃O⁺ and radical hydroxyl OH).

Figure 6.

Dynamics of early radiation events occurring inside ionization tracks triggered by femtosecond bunches of relativistic electrons (E: 2.5 – 15 MeV). The radiation processes are investigated at 820 nm (1.5 eV). The absorption signal amplitude and time dependence assigned to the 1s ground state hydrated electrons is significantly influenced by the presence of a biomolecule (cystamine) in the aqueous phase. Normalized signal curves are reported in the upper part of the figure and relative amplitudes of near-infrared signals are shown in the lower part.

In this analytical expression, two adjustable parameters are considered: 1D geminate recombination time which is equivalent to a jump time (T_J) and a recombination probability γ. This random 1D walking electrons satisfies both the experimental absorption signal dynamics in the 0-75 ps range and the time-dependence 1/(t)^1/2 of dispersive recombination processes inside non-homogeneous ionization clusters (multi-scales phenomena). The least-squares fit of 820 nm signal dynamics emphasize that dispersive geminate recombinations between e^-_aq and neoformed OH radical or H₃O⁺ ion take place immediately after a femtosecond energy deposition in the water bath. Such non synchronized events are mainly observed between 0 and 20 ps (upper part of Figure 6).

Femtolysis experiments emphasize that in native ionisation tracks, ultrafast geminate recombinations are dependent on the transient distribution of electron-hole pairs and the spatial configurations of electron-prototropic entities. A limit case corresponds to very short-range electron-proton couplings for which hydronium ion (H₃O⁺) undergoes one jump (1D motion by a finite process). In this way, considering a diffusion coefficient of H₃O⁺ expressed as D ~ λd²/6 and an experimental jump frequency λ = 1/Tj = 0.5 x 10¹² s^-1, the initial proton jump distance would be around 2.8 Å. This early electron recombination process dynamic is significantly influenced by the nature of the surrounding environment. Indeed, laser-plasma accelerator based HERF may allow the direct observation of primary radiation events in function of local environments induced by the presence of ionic entities or bio-molecules in aqueous bath (Figure 6).

Indeed, when the high density of hydrogen bonding is significantly broken by a ionic strength of sodium chloride (H₂O/NaCl = 9), the contribution of early recombination processes is significantly reduced by specific field effects of anions and cations on the sub-structure of native ionization tracks. HERF studies strongly suggest the preeminence of quantum effects during the sub-picosecond recombination of non-independent radical pairs within a fluctuating hydrogen bonds network. The dynamics of early events can be also modulated significantly by the presence of molecules of biological interest such as cystamine. In the chemical core induced by femtosecond electron bunches, this disulfide compound favors a bimolecular reaction: an electron-biomolecule attachment from 1s-ground state hydrated electrons. For a molecular ratio of 91.7 (0.4 M) in an aqueous environment, this bimolecular reaction exhibits a pseudo-first order dynamics, (exp (-t/τ) with τ = 45 ps. As previously observed with femtosecond low energy photon pulses, this diffusion-controlled process leads to the formation of sulfur-centered radical anions RS∴SR^- characterized by a two-centre-three electron bond. Consequently, small bio-molecules can be used as a sensor of specific environments triggered by ultrashort relativistic electron bunches and characterized by confined ionisation spaces.

Advanced laser accelerator based femtolysis experiments would permit to extend our understanding of very short-time radical events in the prethermal regime of nascent ionization tracks, typically in the 10^-14 -10^-12 s window, and at the nanoscopic level. Following a dose delivery of 15 Gy in less than 500 fs, an ultrafast collapse takes place between low energy electron (precursors of fully hydrated electrons) and cystamine molecules localized in the chemical core i.e. at the interface between the physical core and penumbra zone. The decrease of the early signal amplitude assigned to the population of hydrated electron in native ionization tracks (lower part of Figure 6) argues for a prethermal p state one-electron attachment on a disulfide biomolecule (cystamine) in less than 0.85 x 10^-12 s. Consequently, in sub-nanometric ionization tracks, the anionic radical formation (RS∴SR^-)_aq would occur faster than the radiationless relaxation (2p → 1s transition) of excited prehydrated electrons (Equation 1 and Figure 2). A major stride of a short-range biomolecular alteration triggered by an ultrafast electron attachment in the prethermal regime of ionization clusters will be the quantitative characterization of two parameters ay very short time (t<< 1ps): the effective reaction radius and interaction cross section of the fleeting quantum probe(2p state electron) with a biomolecule. Real-time infrared spectroscopic measurements in the spectral range 1.1-1.6 μm, based on laser plasma accelerator technologies and HERF concepts, are in progress.