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Abstract We obtain generalizations of the classical Menchov–Rademacher theorem to the case of continuous orthogonal systems. These results are applied to show the existence of Moller wave operators in Schrödinger evolution. 

How can an electron induce oxidative damage in DNA DNA damage caused by the dissociative electron attachment (DEA) has been well-studied in the gas and solid phases. However, understanding of this process at the fundamental level in solution is still a challenge. The electrons, after losing their kinetic energy via ionization and excitation events, are thermalized and undergo a multistep hydration process with a time constant of ca. ≤ 1 ps, to becoming fully trapped as a hydrated or solvated electron (esol- or eaq-). Prior to the formation of esol-, the electron exists in its presolvated (or prehydrated) state (epre-) with no kinetic energy. We used picosecond pulse radiolysis to generate electrons in water or in liquid diethylene glycol (DEG) to observe the dynamics of capture of these electrons by DNA/RNA bases, nucleosides, and nucleotides. In diethylene glycol, we demonstrate that unlike esol- and epre-, eqf- effectively attaches itself to the RNA-nucleoside, ribothymidine, forming the excited state of the anion that undergoes the N1-C1 ́ glycosidic bond dissociation. Thanks to DEA, this process induced in fact by eqf- leads to an oxidation of the parent molecule similar to the hydroxyl radical (•OH), leading to the same glycosidic bond (N1-C1 ́) cleavage. 

Among the radicals (hydroxyl radical (•OH), hydrogen atom (H•), and solvated electron (esol−)) that are generated via water radiolysis, •OH has been shown to be the main transient species responsible for radiation damage to DNA via the indirect effect. Reactions of these radicals with DNA-model systems (bases, nucleosides, nucleotides, polynucleotides of defined sequences, single stranded (ss) and double stranded (ds) highly polymeric DNA, nucleohistones) were extensively investigated. The timescale of the reactions of these radicals with DNA-models range from nanoseconds (ns) to microseconds (µs) at ambient temperature and are controlled by diffusion or activation. However, those studies carried out in dilute solutions that model radiation damage to DNA via indirect action do not turn out to be valid in dense biological medium, where solute and water molecules are in close contact (e.g., in cellular environment). In that case, the initial species formed from water radiolysis are two radicals that are ultrashort-lived and charged: the water cation radical (H2O•+) and prethermalized electron. These species are captured by target biomolecules (e.g., DNA, proteins, etc.) in competition with their inherent pathways of proton transfer and relaxation occurring in less than 1 picosecond. In addition, the direct-type effects of radiation, i.e., ionization of macromolecule plus excitations proximate to ionizations, become important. The holes (i.e., unpaired spin or cation radical sites) created by ionization undergo fast spin transfer across DNA subunits. The exploration of the above-mentioned ultrafast processes is crucial to elucidate our understanding of the mechanisms that are involved in causing DNA damage via direct-type effects of radiation. Only recently, investigations of these ultrafast processes have been attempted by studying concentrated solutions of nucleosides/tides under ambient conditions. Recent advancements of laser-driven picosecond electron accelerators have provided an opportunity to address some long-term puzzling questions in the context of direct-type and indirect effects of DNA damage. In this review, we have presented key findings that are important to elucidate mechanisms of complex processes including excess electron-mediated bond breakage and hole transfer, occurring at the single nucleoside/tide level.