GHz EPR Research Articles

EPR Investigations to Study the Impact of Mito-Metformin on the Mitochondrial Function of Prostate Cancer Cells.

Background: Mito-metformin10 (MM10), synthesized by attaching a triphenylphosphonium cationic moiety via a 10-carbon aliphatic side chain to metformin, is a mitochondria-targeted analog of metformin that was recently demonstrated to alter mitochondrial function and proliferation in pancreatic ductal adenocarcinoma. Here, we hypothesized that this compound may decrease the oxygen consumption rate (OCR) in prostate cancer cells, increase the level of mitochondrial ROS, alleviate tumor hypoxia, and radiosensitize tumors. Methods: OCR and mitochondrial superoxide production were assessed by EPR (9 GHz) in vitro in PC-3 and DU-145 prostate cancer cells. Reduced and oxidized glutathione were assessed before and after MM10 exposure. Tumor oxygenation was measured in vivo using 1 GHz EPR oximetry in PC-3 tumor model. Tumors were irradiated at the time of maximal reoxygenation. Results: 24-hours exposure to MM10 significantly decreased the OCR of PC-3 and DU-145 cancer cells. An increase in mitochondrial superoxide levels was observed in PC-3 but not in DU-145 cancer cells, an observation consistent with the differences observed in glutathione levels in both cancer cell lines. In vivo, the tumor oxygenation significantly increased in the PC-3 model (daily injection of 2 mg/kg MM10) 48 and 72 h after initiation of the treatment. Despite the significant effect on tumor hypoxia, MM10 combined to irradiation did not increase the tumor growth delay compared to the irradiation alone. Conclusions: MM10 altered the OCR in prostate cancer cells. The effect of MM10 on the superoxide level was dependent on the antioxidant capacity of cell line. In vivo, MM10 alleviated tumor hypoxia, yet without consequence in terms of response to irradiation.

D‐Band EPR and ENDOR Spectroscopy of 15N‐Labeled Photosystem I

For billions of years, nature has optimized the photosynthetic machinery that converts light energy into chemical energy. Key primary reactions of photosynthesis occur in large membrane protein–cofactor complexes. The light-induced sequential electron transfer reactions occur through a chain of donor/acceptor cofactors embedded in the protein matrix resulting in a long-lived transmembrane charge-separated state. EPR is the method of choice to study electron transfer and the interaction of protein environment with redox-active cofactors. However, the spectra of organic cofactor radicals typically are not fully resolved and severely overlap at conventional X-band EPR. Even at Q-band EPR, this overlap is present and often a serious problem. As a result, there is a large variation of the reported EPR data and limited understanding of electronic structures of several redox-active cofactors. These serious problems can often be overcome by the excellent spectral resolution provided by high-frequency EPR (HF EPR). Here, we study the electronic structure of the primary electron donor P700 and the secondary electron acceptor A1 of Photosystem I (PSI) using 130 GHz (D-band) EPR and Electron–Nuclear-Double-Resonance (ENDOR) spectroscopy. PSI was isotopically labeled with 15N (I = ½) to avoid quadrupolar interactions in the most abundant nitrogen isotope 14N (I = 1) and simplify the ENDOR spectra. ENDOR spectroscopy is central for determining the hyperfine coupling of nitrogen atoms of the two chlorophyll molecules comprising oxidized P700 and the involvement of protein nitrogen atoms with reduced A1. While HF ENDOR of A1− allows identification of two nitrogen atoms, HF ENDOR of P700+ still does not permit unique assignment of the recorded hyperfine couplings.

Bidirectional Quantum Teleportation with GHZ States and EPR Pairs via Entanglement Swapping

A novel bidirectional quantum teleportation schema with GHZ states and EPR pairs via entanglement swapping is proposed. Two GHZ states and two pure EPR pairs build the quantum physical system. Within this quantum system, two entangled GHZ states serve for the quantum channel, and via the entanglement swapping the new entanglements are generated from the involved qbuits after the measurements are performed on both sides. CNOT operation, single qubit measurement and the appropriate unitary transformation are executed on each side, the pure EPR states are simultaneously teleported to each other. The presented protocol bears the economical and efficient advantage compared with the conventional protocols.

Understanding the g-tensors of perchlorotriphenylmethyl and Finland-type trityl radicals.

The 285 GHz EPR spectra of perchlorotriphenylmethyl and tetrathiatriarylmethyl radicals in frozen solution have been accurately measured. The relationship between their molecular structures and their g-tensors has been investigated with the aid of DFT calculations, revealing that the degree of spin density delocalization away from the central methylene carbon is an important determining factor of the g-anisotropy. In particular, the small amount of spin densities on the Cl or S heteroatoms at the 2 and 6 positions with respect to the central carbon have the strongest influence. Furthermore, the amount of spin densities on these heteroatoms and thus the anisotropy can be modulated by the protonation (esterification) state of the carboxylate groups at the 4 position. These results provide unique insights into the g-anisotropy of persistent trityl radicals and how it can be tuned.

High-frequency EPR study of the unusual multiferroic NH4CuCl3

We detail orientation and temperature dependent high-frequency 240 GHz EPR experiments undertaken on NH4CuCl3 from 11 to 290 K. At 290 K, the system is axially symmetric, producing a single Lorentzian peak with g‖=2.2674 and g⊥=2.0520. The linewidth, ΔHpp varies according to a A+Bcos2θ dependence, which is ascribed to the Dzyaloshinsky-Moriya antisymmetric interaction. Additionally, ΔHpp∝g-ge, a consequence of spin-orbit coupling. Temperature measurements along each principal g axis showed little temperature variation in g until around 50 K, at which point g‖ began to increase and g⊥ began to decrease with decreasing temperatures, with 〈g〉 remaining essentially constant. ΔHpp was found to significantly vary with respect to temperature for both principal g directions, with the line rapidly narrowing with decreasing temperatures from 290 to 45 K, while slowly beginning to broaden again until 11 K. We propose that an Orbach relaxation process is responsible for the linewidth behavior from 290 to 45 K, with Δ on the order of 370±15cm-1, and is related to the librational mode of the ammonium ion.

Tracking amyloid oligomerization with monomer resolution using a 13-amino acid peptide with a backbone-fixed spin label.

Amyloid oligomers are suspected as toxic agents in neurodegenerative disease, and are transient and often heterogeneous, making them difficult to detect. Here we show an approach to track the development of amyloid oligomers in situ by room temperature, continuous wave (cw) 9 and 95 GHz EPR. Three amyloid peptides with the 2,2,6,6-tetramethyl-N-oxyl-4-amino-4-carboxylic acid (TOAC) spin label were synthesized by solid phase peptide synthesis: T0EZ (TKVKVLGDVIEVGG) with TOAC (T) at the N-terminus, T5EZ with TOAC in the middle (KVKVTGDVIEVG) and T12EZ with TOAC at the C-terminus (KVKVLGDVIEVTG). These sequences are derived from the K11V (KVKVLGDVIEV) amyloid peptide, which self-aggregates to oligomers with a β-sheet configuration (A. Laganowsky, et al., Science, 2012, 335, 1228-1231). To monitor oligomerization, the rotational correlation time (τr) is measured by cw-EPR. For the backbone-fixed TOAC label that is devoid of local mobility τr should reflect the rotation and thereby the size of the peptide, resp. oligomer. For T5EZ a good match between the measured τr and the size of the peptide is obtained, showing the validity of the approach. One of the three peptides (T0EZ) aggregates (circular dichroism), whereas the other two do not. Since also the respective MTSL (S-(1-oxyl-2,2,5,5-tetramethyl-2,5-dihydro-1H-pyrrol-3-yl)methyl methanesulfonothioate) labelled peptides fail to aggregate, molecular crowding due to the label, rather than the helix-inducing properties of TOAC, seems to be responsible. Following in situ oligomer formation of T0EZ by the change in rotational correlation time, two oligomers are observed, a 5-6 mer and a 15-18 mer. The EPR approach, particularly 95 GHz EPR, enables following oligomerization of one monomer at a time, suggesting that the cw-EPR approach presented is a novel tool to follow amyloid oligomerization with high resolution.

Oxidative Stress and Obesity: Detection of Free Radicals in Leptin Resistant and Catalase Transgenic Mice

There is a homeostatic balance between the production of natural antioxidants and free radicals in the body. Catalase is an enzyme which behaves as an antioxidant by decomposing peroxide into oxygen and water. Oxidative stress occurs when free radicals are in excess in relation to antioxidants. Deficiencies in antioxidant mechanisms have been linked to obesity, type II diabetes, and cardiovascular disease. More than 33% of adults and 16% of children are obese, and to combat this crisis a better understanding of these mechanisms is needed. We hypothesized that an increase in catalase expression and activity should lead to a decrease in obesogenic pathways. Free radical concentrations were measured using electron paramagnetic resonance spectrometry in four different genotypes of mice: wild‐type, cat‐tg (catalase transgenic), ob/ob, and a new model bob‐cat (leptin resistant and catalase transgenic). Liver and adipose tissue were bathed in an EPR spin probe CMH, and incubated for 30 minutes. Tissues were then measured using the Bruker X‐Band 9.8 GHz EPR Spectrometer at Marshall University. It was observed that the wild‐type sample contained the highest concentration of free radicals, followed by cat‐tg. Bob‐cat contained the lowest concentration, slightly less than ob/ob. It was expected that cat‐tg would have a lower concentration than wild‐type. However, obtaining even lower measurements from ob/ob and bob‐cat shows that more work must be done to fully elucidate these processes.Support or Funding InformationSummer Undergraduate Research Fellowship 2017 (SURF)This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

The Magic of Disaccharide Glass Matrices for Protein Function as Decoded by High-Field EPR and FTIR Spectroscopy

The structural and dynamical interaction of proteins with their microenvironment in disordered matrices plays a decisive role for their function; EPR spectroscopy is a powerful tool for shading light onto the molecular mechanisms of this protein–matrix interplay. To clarify the molecular mechanisms of disaccharide bioprotection, we studied the structure and dynamics of spin-labeled systems and photosynthetic reaction centers (RCs) in sucrose and trehalose matrices at different hydration levels by means of cw and pulse high-field 95 GHz (W-band) EPR as well as by FTIR. In this minireview, we summarize and discuss EPR and FTIR experiments showing that the anhydrobiotic state of the RC–trehalose system (1) is not the result of matrix-induced changes of the local structure of the charge-separated radical-pair cofactors, $${\text{P}}_{865}^{ \cdot + }$$ and $${\text{Q}}_{\text{A}}^{ \cdot - }$$ , and (2) is not the result of changes of local dynamics and local hydrogen bonding of QA in its binding pocket. Rather, the extreme impairment of RC dynamics caused by incorporation into the dehydrated trehalose matrix, which also protects it against thermal denaturation, originates in the high rigidity, already at room temperature, of the dry trehalose glass matrix coating the RC protein surface. This surface hydrogen-bonding scaffold shifts the correlation time of thermal conformational fluctuations into the non-biological time domain. Another intriguing aspect of disaccharide bioprotection is the superior efficiency of trehalose versus sucrose matrices in stabilizing the anhydrobiotic state of proteins. To clarify the molecular basis of this specificity, glassy trehalose–water and sucrose–water binary systems, incorporating a nitroxide radical as spin probe, have been studied by high-field W-band EPR spectroscopy at different water contents. Analysis of the EPR spectra revealed a different structural and dynamical organization in the sucrose and trehalose matrix, only the trehalose being homogeneous in terms of residual water and nitroxide distribution.

Exploring the Fe(III) binding sites of human serum transferrin with EPR at 275 GHz.

We report 275 GHz EPR spectra of human serum transferrin. At this high microwave frequency the zero-field splitting between the magnetic sublevels of the high-spin [Formula: see text] sites can be accurately determined. We find the zero-field splitting to be a sensitive probe of the structure of the transferrin iron-binding sites. Signals arising from iron bound to the transferrin N-lobe can clearly be distinguished from signals from iron bound to the C-lobe. Moreover, our spectra show that the structure of the iron site in the N-lobe is influenced by the presence and conformation of the C-lobe. The spectra of a series of N-lobe mutants altering the second-shell interaction of Arg124 with the synergistic anion carbonate reflect conformational changes induced at the iron site.

A chemically competent thiosulfuranyl radical on the Escherichia coli class III ribonucleotide reductase.

The class III ribonucleotide reductases (RNRs) are glycyl radical (G•) enzymes that provide the balanced pool of deoxynucleotides required for DNA synthesis and repair in many facultative and obligate anaerobic bacteria and archaea. Unlike the class I and II RNRs, where reducing equivalents for the reaction are delivered by a redoxin (thioredoxin, glutaredoxin, or NrdH) via a pair of conserved active site cysteines, the class III RNRs examined to date use formate as the reductant. Here, we report that reaction of the Escherichia coli class III RNR with CTP (substrate) and ATP (allosteric effector) in the absence of formate leads to loss of the G• concomitant with stoichiometric formation of a new radical species and a “trapped” cytidine derivative that can break down to cytosine. Addition of formate to the new species results in recovery of 80% of the G• and reduction of the cytidine derivative, proposed to be 3′-keto-deoxycytidine, to dCTP and a small amount of cytosine. The structure of the new radical has been identified by 9.5 and 140 GHz EPR spectroscopy on isotopically labeled varieties of the protein to be a thiosulfuranyl radical [RSSR2]•, composed of a cysteine thiyl radical stabilized by an interaction with a methionine residue. The presence of a stable radical species on the reaction pathway rationalizes the previously reported [3H]-(kcat/KM) isotope effect of 2.3 with [3H]-formate, requiring formate to exchange between the active site and solution during nucleotide reduction. Analogies with the disulfide anion radical proposed to provide the reducing equivalent to the 3′-keto-deoxycytidine intermediate by the class I and II RNRs provide further evidence for the involvement of thiyl radicals in the reductive half-reaction catalyzed by all RNRs.

Deterministic Joint Remote Preparation of an Arbitrary Two-Qubit State Using the Cluster State

Recently, deterministic joint remote state preparation (JRSP) schemes have been proposed to achieve 100% success probability. In this paper, we propose a new version of deterministic JRSP scheme of an arbitrary two-qubit state by using the six-qubit cluster state as shared quantum resource. Compared with previous schemes, our scheme has high efficiency since less quantum resource is required, some additional unitary operations and measurements are unnecessary. We point out that the existing two types of deterministic JRSP schemes based on GHZ states and EPR pairs are equivalent.

Liquid state DNP of water at 9.2 T: an experimental access to saturation

We have performed liquid state ("Overhauser") Dynamic Nuclear Polarization (DNP) experiments at high magnetic field (9.2 T, corresponding to 260 GHz EPR and 400 MHz (1)H-NMR resonance frequency) on aqueous solutions of (14)N-TEMPOL nitroxide radicals. Integrated signal enhancements exceeding -80 were observed for the water protons at microwave superheated temperatures (160 °C) and still -14 at ambient temperatures (45 °C) relevant to biological applications. Different contributions contributing to the DNP enhancement such as saturation factor, leakage factor and sample temperature under microwave irradiation could be determined independently for a high spin concentration of 1 M, allowing the calculation of the coupling factors as a function of temperature and a quantitative comparison of this parameter with values derived from field dependent relaxation measurements or predictions from MD simulation.

Orientation selection in distance measurements between nitroxide spin labels at 94 GHz EPR with variable dual frequency irradiation

Pulsed electron-electron double resonance (PELDOR, also known as DEER) has become a method of choice to measure distances in biomolecules. In this work we show how the performance of the method can be improved at high EPR frequencies (94 GHz) using variable dual frequency irradiation in a dual mode cavity in order to obtain enhanced resolution toward orientation selection. Dipolar evolution traces of a representative RNA duplex and an α-helical peptide were analysed in terms of possible bi-radical structures by considering the inherent ambiguity of symmetry-related solutions.

Liquid State DNP on Metabolites at 260 GHz EPR/400 MHz NMR Frequency

We have performed liquid state (“Overhauser”) dynamic nuclear polarization (DNP) experiments at high magnetic field (9.2 T, corresponding to 260 GHz EPR and 400 MHz 1H-NMR resonance frequency) on solutions of pyruvate, lactate and alanine in water with TEMPOL nitroxide radicals as polarizing agent. We present experimental results showing DNP enhancement on metabolite methyl protons, varying for the different target metabolites. It is shown that the enhancements are achieved through direct coupling between the radicals and the target metabolites in solution, i.e., the effect is not mediated by the solvent water protons. The coupling factors between the TEMPOL radicals and the metabolites observed are a factor of 3–5 smaller compared to direct polarization transfer from TEMPOL to water protons.

Spectroscopic Studies of the Iron and Manganese Reconstituted Tyrosyl Radical in Bacillus Cereus Ribonucleotide Reductase R2 Protein

Ribonucleotide reductase (RNR) catalyzes the rate limiting step in DNA synthesis where ribonucleotides are reduced to the corresponding deoxyribonucleotides. Class Ib RNRs consist of two homodimeric subunits: R1E, which houses the active site; and R2F, which contains a metallo cofactor and a tyrosyl radical that initiates the ribonucleotide reduction reaction. We studied the R2F subunit of B. cereus reconstituted with iron or alternatively with manganese ions, then subsequently reacted with molecular oxygen to generate two tyrosyl-radicals. The two similar X-band EPR spectra did not change significantly over 4 to 50 K. From the 285 GHz EPR spectrum of the iron form, a g 1-value of 2.0090 for the tyrosyl radical was extracted. This g 1-value is similar to that observed in class Ia E. coli R2 and class Ib R2Fs with iron-oxygen cluster, suggesting the absence of hydrogen bond to the phenoxyl group. This was confirmed by resonance Raman spectroscopy, where the stretching vibration associated to the radical (C-O, ν7a = 1500 cm−1) was found to be insensitive to deuterium-oxide exchange. Additionally, the 18O-sensitive Fe-O-Fe symmetric stretching (483 cm−1) of the metallo-cofactor was also insensitive to deuterium-oxide exchange indicating no hydrogen bonding to the di-iron-oxygen cluster, and thus, different from mouse R2 with a hydrogen bonded cluster. The HF-EPR spectrum of the manganese reconstituted RNR R2F gave a g 1-value of ∼2.0094. The tyrosyl radical microwave power saturation behavior of the iron-oxygen cluster form was as observed in class Ia R2, with diamagnetic di-ferric cluster ground state, while the properties of the manganese reconstituted form indicated a magnetic ground state of the manganese-cluster. The recent activity measurements (Crona et al., (2011) J Biol Chem 286: 33053–33060) indicates that both the manganese and iron reconstituted RNR R2F could be functional. The manganese form might be very important, as it has 8 times higher activity.

Overhauser DNP with15N labelled Frémy's salt at 0.35 Tesla

The effectiveness of dynamic nuclear polarization (DNP) as a tool to enhance the sensitivity of liquid state NMR critically depends on the choice of the optimal polarizer molecule. In this study the performance of (15)N labelled Frémy's salt as a polarizing agent in Overhauser DNP is investigated in detail at X-band (0.35 T, 9.7 GHz EPR, 15 MHz (1)H NMR) and compared to that of TEMPONE-D,(15)N employed in previous studies. Both radicals provide similar maximum enhancements of the solvent water protons under similar conditions but a different saturation behaviour. The factors determining the enhancement and effective saturation were measured independently by EPR, ELDOR and NMRD and are shown to fulfil the Overhauser equation. In particular, following the theory of EPR saturation we provide analytical solutions for the dependence of the enhancement on the microwave field strength in terms of saturation transfer between two coupled hyperfine lines undergoing spin exchange. The negative charge of the radical in Frémy's salt solutions can explain the peculiar properties of this polarizing agent and indicates different suitable application areas for the two types of nitroxide radicals.

A 9 GHz EPR Imager for Thin Materials: Application to Surface Detection

A 9 GHz EPR imager that is capable of the imaging surface area of thin materials has been built. The EPR imager resolved samples spaced 1 mm apart. The developed TE(111) cavity was able to detect easily ~1.0 mM aqueous TEMPOL solution in ~1.0 mm (i.d.) glass capillary placed just above the cavity. The sensitivity measured using the TEMPOL solution showed ~0.3 of that for the modified JEOL cavity, which was in a qualitative agreement with the calculations considering the difference in the filling factors of the cavities. The relatively low measured sensitivity of the TE(111) cavity is due to utilization of the microwave field from ~3 mm aperture (hole) in the cavity wall. More importantly, the TE(111) cavity does not require inserting the sample into the cavity and placing samples into EPR tubes.

Q-Band EPR Spectroscopy of Photogenerated Quartet State Organic Nitreno Radicals

Q-band 34 GHz EPR spectra are reported for quartet state 2-(para-nitrenophenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl and 3-(para-nitrenophenyl)-1,5,6-triphenylverdazyl reactive intermediates generated from the corresponding azido precursors under frozen matrix photochemical conditions, in situ in a Q-band resonator. Comparison of the Q-band spectra to those generated under conventional X-band (9-10 GHz) conditions shows the much superior resolution of transitions in the g > 2 region of the former. Spectral transitions assigned by line shape simulation yield the zero field splittings for the nitreno-radical species.

Correlation of the EPR properties of perchlorotriphenylmethyl radicals and their efficiency as DNP polarizers

Water soluble perchlorinated trityl (PTM) radicals were found to be effective 95 GHz DNP (dynamic nuclear polarization) polarizers in ex situ (dissolution) (13)C DNP (Gabellieri et al., Angew Chem., Int. Ed. 2010, 49, 3360). The degree of the nuclear polarization obtained was reported to be dependent on the position of the chlorine substituents on the trityl skeleton. In addition, on the basis of the DNP frequency sweeps it was suggested that the (13)C NMR signal enhancement is mediated by the Cl nuclei. To understand the DNP mechanism of the PTM radicals we have explored the 95 GHz EPR characteristics of these radicals that are relevant to their performance as DNP polarizers. The EPR spectra of the radicals revealed axially symmetric g-tensors. A comparison of the spectra with the (13)C DNP frequency sweeps showed that although the solid effect mechanism is operational the DNP frequency sweeps reveal some extra width suggesting that contributions from EPR forbidden transitions involving (35,37)Cl nuclear flips are likely. This was substantiated experimentally by ELDOR (electron-electron double resonance) detected NMR measurements, which map the EPR forbidden transitions, and ELDOR experiments that follow the depolarization of the electron spin upon irradiation of the forbidden EPR transitions. DFT (density functional theory) calculations helped to assign the observed transitions and provided the relevant spin Hamiltonian parameters. These results show that the (35,37)Cl hyperfine and nuclear quadrupolar interactions cause a considerable nuclear state mixing at 95 GHz thus facilitating the polarization of the Cl nuclei upon microwave irradiation. Overlap of Cl nuclear frequencies and the (13)C Larmor frequency further facilitates the polarization of the (13)C nuclei by spin diffusion. Calculation of the (13)C DNP frequency sweep based on the Cl nuclear polarization showed that it does lead to an increase in the width of the spectra, improving the agreement with the experimental sweeps, thus supporting the existence of a new heteronuclear assisted DNP mechanism.

Nitric Oxide Synthase Stabilizes the Tetrahydrobiopterin Cofactor Radical by Controlling Its Protonation State

Nitric oxide synthase (NOS), a homodimeric enzyme with a flavin reductase domain and a P450-type heme-containing oxygenase domain, catalyzes the formation of NO from L-arginine, NADPH, and O(2) in a two-step reaction sequence. In the first step, a tetrahydrobiopterin (H(4)B) cofactor bound near one of the heme propionate groups acts as an electron donor to the P450-type heme active site, yielding a one-electron oxidized radical that is subsequently re-reduced. In solution, H(4)B undergoes two-electron oxidation, showing that the enzyme significantly alters the proton- and electron-transfer properties of the cofactor. Multifrequency EPR and ENDOR spectroscopy were used to determine magnetic parameters, and from them the (de)protonation state of the H(4)B radical in the oxygenase domain dimer of inducible NO synthase that was trapped by rapid freeze quench. From 9.5 and 330-416 GHz EPR and from 34 GHz (1)H ENDOR spectroscopy, the g tensor of the radical and the hyperfine tensors of several N and H nuclei in the radical were obtained. Density functional theory calculations at the PBE0/EPR-II level for H(4)B radical models predict different spin density distributions and g and hyperfine tensors for different protonation states. Comparison of the predicted and experimental values leads to the conclusion that the radical is cationic H(4)B(*+), suggesting that NOS stabilizes this protonated form to utilize the cofactor in a unique dual one-electron redox role, where it can deliver an electron to the active site for reductive oxygen activation and also remove an electron from the active site to generate NO and not NO(-). The protein environment also prevents further oxidation and subsequent loss of function of the cofactor, thus enabling the enzyme to perform the unusual catalytic one-electron chemistry.