Detangling Solvatochromic Effects by the Effective Fragment Potential Method.

Understanding molecular interactions in complex systems opens avenues for the efficient design of new materials with target properties. Energy decomposition methods provide a means to obtain a detailed picture of intermolecular interactions. This work introduces a molecular modeling approach for decomposing the solvatochromic shifts of the electronic excited states into the contributions of the individual molecular fragments of the environment surrounding the chromophore. The developed approach is implemented for the QM/EFP (quantum mechanics/effective fragment potential) model that provides a rigorous first-principles-based description of the electronic states of the chromophores in complex polarizable environments. On the example of two model systems, water pentamer and hydrated uracil, we show how the decomposition of the solvatochromic shifts into the contributions of individual solvent water molecules provides a detailed picture of the intermolecular interactions in the ground and excited states of these systems. The analysis also demonstrates the nonadditivity of solute-solvent interactions and the significant contribution of solute polarization to the total values of solvatochromic shifts.

Capturing CO2 in Quadrupolar Binding Pockets: Broadband Microwave Spectroscopy of Pyrimidine-(CO2)n, n = 1,2.

Pyrimidine has two in-plane CH(δ+)/N̈(δ-)/CH(δ+) binding sites that are complementary to the (δ-/2δ+/δ-) quadrupole moment of CO2. We recorded broadband microwave spectra over the 7.5-17.5 GHz range for pyrimidine-(CO2)n with n = 1 and 2 formed in a supersonic expansion. Based on fits of the rotational transitions, including nuclear hyperfine splitting due to the two 14N nuclei, we have assigned 313 hyperfine components across 105 rotational transitions for the n = 1 complex and 208 hyperfine components across 105 rotational transitions for the n = 2 complex. The pyrimidine-CO2 complex is planar, with CO2 occupying one of the quadrupolar binding sites, forming a structure in which the CO2 is stabilized in the plane by interactions with the C-H hydrogens adjacent to the nitrogen atom. This structure is closely analogous to that of the pyridine-CO2 complex studied previously by (Doran, J. L. J. Mol. Struct. 2012, 1019, 191-195). The fit to the n = 2 cluster gives rotational constants consistent with a planar cluster of C2v symmetry in which the second CO2 molecule binds in the second quadrupolar binding pocket on the opposite side of the ring. The calculated total binding energy in pyrimidine-CO2 is -13.7 kJ mol-1, including corrections for basis set superposition error and zero-point energy, at the CCSD(T)/ 6-311++G(3df,2p) level, while that in pyrimidine-(CO2)2 is almost exactly double that size, indicating little interaction between the two CO2 molecules in the two binding sites. The enthalpy, entropy, and free energy of binding are also calculated at 300 K within the harmonic oscillator/rigid-rotor model. This model is shown to lack quantitative accuracy when it is applied to the formation of weakly bound complexes.

Impact of Peripheral Hydrogen Bond on Electronic Properties of the Primary Acceptor Chlorophyll in the Reaction Center of Photosystem I.

Photosystem I (PS I) is a photosynthetic pigment-protein complex that absorbs light and uses the absorbed energy to initiate electron transfer. Electron transfer has been shown to occur concurrently along two (A- and B-) branches of reaction center (RC) cofactors. The electron transfer chain originates from a special pair of chlorophyll a molecules (P700), followed by two chlorophylls and one phylloquinone in each branch (denoted as A-1, A0, A1, respectively), converging in a single iron-sulfur complex Fx. While there is a consensus that the ultimate electron donor-acceptor pair is P700+A0-, the involvement of A-1 in electron transfer, as well as the mechanism of the very first step in the charge separation sequence, has been under debate. To resolve this question, multiple groups have targeted electron transfer cofactors by site-directed mutations. In this work, the peripheral hydrogen bonds to keto groups of A0 chlorophylls have been disrupted by mutagenesis. Four mutants were generated: PsaA-Y692F; PsaB-Y667F; PsaB-Y667A; and a double mutant PsaA-Y692F/PsaB-Y667F. Contrary to expectations, but in agreement with density functional theory modeling, the removal of the hydrogen bond by Tyr → Phe substitution was found to have a negligible effect on redox potentials and optical absorption spectra of respective chlorophylls. In contrast, Tyr → Ala substitution was shown to have a fatal effect on the PS I function. It is thus inferred that PsaA-Y692 and PsaB-Y667 residues have primarily structural significance, and their ability to coordinate respective chlorophylls in electron transfer via hydrogen bond plays a minor role.

Molecular and Structural Characterization of Isomeric Compounds in Atmospheric Organic Aerosol Using Ion Mobility-Mass Spectrometry.

Secondary organic aerosol (SOA) formed through multiphase atmospheric chemistry makes up a large fraction of airborne particles. The chemical composition and molecular structures of SOA constituents vary between different emission sources and aging processes in the atmosphere, which complicates their identification. In this work, we employ drift tube ion mobility spectrometry with quadrupole time-of-flight mass spectrometry (IM-MS) detection for rapid gas-phase separation and multidimensional characterization of isomers in two biogenic SOAs produced from ozonolysis of isomeric monoterpenes, d-limonene (LSOA) and α-pinene (PSOA). SOA samples were ionized using electrospray ionization (ESI) and characterized using IM-MS in both positive and negative ionization modes. The IM-derived collision cross sections in nitrogen gas (DTCCSN2 ) for individual SOA components were obtained using multifield and single-field measurements. A novel application of IM multiplexing/high-resolution demultiplexing methodology was employed to increase sensitivity, improve peak shapes, and augment mobility baseline resolution, which revealed several isomeric structures for the measured ions. For LSOA and PSOA samples, we report significant structural differences of the isomer structures. Molecular structural calculations using density functional theory combined with the theoretical modeling of CCS values provide insights into the structural differences between LSOA and PSOA constituents. The average DTCCSN2 values for monomeric SOA components observed as [M + Na]+ ions are 3-6% higher than those of their [M - H]- counterparts. Meanwhile, dimeric and trimeric isomer components in both samples showed an inverse trend with the relevant values of [M - H]- ions being 3-7% higher than their [M + Na]+ counterparts, respectively. The results indicate that the structures of Na+-coordinated oligomeric ions are more compact than those of the corresponding deprotonated species. The coordination with Na+ occurs on the oxygen atoms of the carbonyl groups leading to a compact configuration. Meanwhile, deprotonated molecules have higher DTCCSN2 values due to their elongated structures in the gas phase. Therefore, DTCCSN2 values of isomers in SOA mixtures depend strongly on the mode of ionization in ESI. Additionally, PSOA monomers and dimers exhibit larger DTCCSN2 values (1-4%) than their LSOA counterparts owing to more rigid structures. A cyclobutane ring is present with functional groups pointing in opposite directions in PSOA compounds, as compared to noncyclic flexible LSOA structures, forming more compact ions in the gas phase. Lastly, we investigated the effects of direct photolysis on the chemical transformations of selected individual PSOA components. We use IM-MS to reveal structural changes associated with aerosol aging by photolysis. This study illustrates the detailed molecular and structural descriptors for the detection and annotation of structural isomers in complex SOA mixtures.

Copper(I)-Pyrazolate Complexes as Solid-State Phosphors: Deep-Blue Emission through a Remote Steric Effect.

We describe a novel manifestation of rigidochromic behavior in a series of tetranuclear Cu(I)-pyrazolate (Cu4pz4) macrocycles, with implications for solid-state luminescence at deep-blue wavelengths (<460 nm). The Cu4pz4 emissions are remarkably sensitive to structural effects far from the luminescent core: when 3,5-di-tert-butylpyrazoles are used as bridging ligands, adding a C4 substituent can induce a blue shift of more than 100 nm. X-ray crystal and computational analyses reveal that C4 units influence the conformational behavior of adjacent tert-butyl groups, with a subsequent impact on the global conformation of the Cu4pz4 complex. Emissions are mediated primarily through a cluster-centered triplet (3CC) state; compression of the Cu4 cluster into a nearly close-packed geometry prevents the reorganization of its excited-state structure and preserves the 3CC energy at a high level. The remote steric effect may thus offer alternative strategies toward the design of phosphors with rigid excited-state geometries.

Interaction of Polymers with Enzalutamide Nanodroplets-Impact on Droplet Properties and Induction Times.

Amorphous solid dispersions (ASDs), which consist of a drug dispersed in a polymeric matrix, are increasingly being applied to improve the in vivo performance of poorly water-soluble drugs delivered orally. The polymer is a critical component, playing several roles including facilitating drug release from the ASD, as well as delaying crystallization from the supersaturated solution generated upon dissolution. Certain ASD formulations dissolve to produce amorphous drug-rich nanodroplets. The interaction of the polymer with these nanodroplets is poorly understood but is thought to be important for inhibiting crystallization in these systems. In this study, the impact of ionic polymers on the crystallization kinetics of enzalutamide from supersaturated solutions containing different amounts of amorphous nanodroplets was evaluated by determination of nucleation induction times. The amount of the polymer associated with the drug nanodroplets was also determined. When comparing two polymers, hydroxypropylmethyl cellulose acetate succinate (HPMCAS) and Eudragit E PO, it was found that the crystallization tendency and physical properties of the drug nanodroplets varied in the presence of these two polymers. Both polymers distributed between the aqueous phase and the drug-rich nanodroplets. A greater amount of Eudragit E PO was associated with the drug-rich nanodroplets. Despite this, Eudragit E PO was a less-effective crystallization inhibitor than HPMCAS in systems containing nanodroplets. In conclusion, in supersaturated solutions containing amorphous nanodroplets, the extent of association of a polymer with the drug nanodroplet does not solely predict crystallization inhibition.

Multiagent Consensus Equilibrium in Molecular Structure Determination.

Multiagent consensus equilibrium (MACE) is demonstrated for the integration of experimental observables as constraints in molecular structure determination and for the systematic merging of multiple computational architectures. MACE is founded on simultaneously determining the equilibrium point between multiple experimental and/or computational agents; the returned state description (e.g., atomic coordinates for molecular structure) represents the intersection of each manifold and is not equivalent to the average optimum state for each agent. The moment of inertia, determined directly from microwave spectroscopy measurements, serves to illustrate the mechanism through which MACE evaluations merge experimental and quantum chemical modeling. MACE results reported combine gradient descent optimization of each ab initio agent with an agent that predicts the chemical structure based on root-mean-square deviation of the predicted inertia tensor with experimentally measured moments of inertia. Successful model fusion for several small molecules was achieved as well as the larger molecule solketal. Fusing a model of moment of inertia, an underdetermined predictor of structure, with low cost computational methods yielded structure determination performance comparable to standard computational methods such as MP2/cc-pVTZ and greater agreement with experimental observables.

Polarizable embedding for simulating redox potentials of biomolecules.

Redox reactions play a key role in various biological processes, including photosynthesis and respiration. Quantitative and predictive computational characterization of redox events is therefore highly desirable for enriching our knowledge on mechanistic features of biological redox-active macromolecules. Here, we present a computational protocol exploiting polarizable embedding hybrid quantum-classical approach and resulting in accurate estimates of redox potentials of biological macromolecules. A special attention is paid to fundamental aspects of the theoretical description such as the effects of environment polarization and of the long-range electrostatic interactions on the computed energetic parameters. Environment (protein and the solvent) polarization is shown to be crucial for accurate estimates of the redox potential: hybrid quantum-classical results with and without account for environment polarization differ by 1.4 V. Long-range electrostatic interactions are shown to contribute significantly to the computed redox potential value even at the distances far beyond the protein outer surface. The approach is tested on simulating reduction potential of cryptochrome 1 protein from Arabidopsis thaliana. The theoretical estimate (0.07 V) of the midpoint reduction potential is in good agreement with available experimental data (-0.15 V).

The effects of site asymmetry on near-degenerate state-to-state vibronic mixing in flexible bichromophores.

Laser-induced fluorescence excitation and dispersed fluorescence spectra of a model flexible bichromophore, 1,1-diphenylethane (DPE), have been recorded under jet-cooled conditions in the gas phase in the region near the first pair of near-degenerate excited states (S1 and S2). The S1 and S2 origin transitions have been identified at 37 397 and 37 510 cm-1, a splitting of 113 cm-1. This splitting is four times smaller than the excitonic splitting calculated by ab initio methods at the EOM-CCSD/cc-pVDZ level of theory (410 cm-1), which necessarily relies on the Born-Oppenheimer approximation. Dispersed fluorescence spectra provide a state-to-state picture of the vibronic coupling. These results are compared with the results of a multimode vibronic coupling model capable of treating chromophores in asymmetric environments. This model was used to predict the splitting between S1 and S2 origins close to the experiment, reduced from its pure excitonic value by Franck-Condon quenching. Quantitative accuracy is achieved by the model, lending insight into the state-to-state mixing that occurs between individual S1 and S2 vibronic levels. The S2 origin is determined to be mixed with S1(v) levels by two mechanisms common to internal conversion in almost any setting; namely, (i) mixing involving near-degenerate levels with large vibrational quantum number changes that are not governed by Δv = 1 Herzberg-Teller (HT) selection rules, and (ii) mixing with levels with larger energy gaps that do follow these selection rules. In DPE, the asymmetric ring flapping vibrational mode R¯ dominates the HT coupling.

Phase Behavior of Drug-Hydroxypropyl Methylcellulose Amorphous Solid Dispersions Produced from Various Solvent Systems: Mechanistic Understanding of the Role of Polymer using Experimental and Theoretical Methods.

The vast majority of studies evaluating amorphous solid dispersions (ASDs) utilize solvent evaporation techniques as the preparation method. However, the impact of the solvent/cosolvent system properties on the polymer conformation and the phase behavior of the resultant drug/polymer blends is poorly understood. Herein, we investigate the influence of solvent properties on the phase behavior of ASDs containing itraconazole (ITZ) and hydroxypropylmethyl cellulose (HPMC) prepared using spin coating from binary/ternary cosolvent systems containing alkyl alcohols, dichloromethane (DCM), and water. The compatibility of the polymer with the cosolvent system was probed using high-resolution imaging techniques supported by molecular dynamics simulations. Solvent evaporation and evaporation rate profiles were tracked gravimetrically to understand the impact of the solvent composition on the evaporation process. Short-chain alcohols, including methanol (MeOH) and ethanol (EtOH), were found to induce drug-polymer demixing in the presence of water, with EtOH being less sensitive to moisture than MeOH owing to its ability to form an azeotrope with water. In contrast, water-induced mixing was observed when higher alcohols, including n-propanol (PrOH) and n-butanol (BuOH), were used as a cosolvent, due to the improved solubility of HPMC in the higher alcohols in the presence of water. Isopropanol (IPA) produced phase separated ASDs under wet and dry conditions with an increase in miscibility with faster evaporation rates in the presence of water. This solvent-triggered phase behavior highlights the importance of conducting a thorough screening of various solvents prior to the preparation of ASDs via solvent evaporation approaches such as spray drying.

Crystallization Inhibition Properties of Cellulose Esters and Ethers for a Group of Chemically Diverse Drugs: Experimental and Computational Insight.

Amorphous solid dispersions are widely used to enhance the oral bioavailability of poorly water-soluble drugs. Polymeric additives are commonly used to delay crystallization of the drug from the supersaturated solutions formed upon ASD dissolution by influencing the nucleation and growth of crystals. However, there is limited evidence regarding the mechanisms by which polymers stabilize supersaturated drug solutions. The current study used experiments and computational modeling to explore polymer-drug interactions in aqueous solutions. Nucleation induction times for supersaturated solutions of nine drugs in the presence of five newly synthesized cellulose-based polymers were evaluated. The polymers had carboxylic acids substituents with additional variations in the side-chain structure: (1) one with a single side chain and a carboxylic acid termination, (2) three with a branched side chain terminated with a carboxylic and an alcohol group (varying the cellulose linkage and the length of the hydrocarbon side chain), and (3) one with a branched side chain with two carboxylic acid end groups. The polymers with a short side chain and one carboxylic acid were effective, whereas the polymers with the two carboxylic acids or a long hydrocarbon chain were less effective. Atomic force microscopy experiments, evaluating polymer adsorption onto amorphous drug films, indicated that the effective polymers were uniformly spread across the surface. These results were supported by molecular dynamics simulations of a polymer chain in the presence of a drug aggregate in an aqueous environment, whereby the effective materials had a higher probability of establishing close contacts and more negative estimated free energies of interaction. The insights provided by this study provide approaches to design highly effective polymers to improve oral drug delivery.

Triplet-Triplet Coupling in Chromophore Dimers: Theory and Experiment.

Knowledge of triplet state energies and triplet-triplet (T-T) interactions in aggregated organic molecules is essential for understanding photochemistry and dynamics of many natural and artificial systems. In this work, we combine direct phosphorescence measurements of triplet state energies, which are challenging due to the spin-forbidden nature of respective transitions and applicable to only a limited number of systems, with quantum chemical computational tools that can provide valuable qualitative and quantitative information about triplet states of interacting molecules. Using hexatriene, protoporphyrin, pheophorbide, and chlorophyll dimers as model systems, we demonstrate a complicated dependence of T-T coupling on a relative orientation of chromophores, governed by a nodal structure of overlapping electronic wave functions, that modulates interpigment interactions by orders of magnitude. It is also shown that geometrical relaxation of the triplet state is one of the critical factors for predictive modeling of T-T interactions in molecular aggregates.

Exchange-repulsion energy in QM/EFP.

The effective fragment potential (EFP) is a quantum mechanics (QM)-based model designed to accurately describe intermolecular interactions. Hybrid QM/EFP calculations combine quantum mechanical methods with an EFP embedding to study complex systems in which many-body effects are relevant. As in EFP-only calculations, non-bonded interactions between the QM region and EFP fragments are computed as a sum of electrostatic, polarization, dispersion, and exchange-repulsion energies. The exchange-repulsion term is a computational bottleneck of the EFP calculations. Here, we present a general procedure for computing the QM/EFP exchange-repulsion interactions based on one-electron contributions to the QM Hamiltonian, by using Gaussian functions to represent localized molecular orbitals of the effective fragments. The accuracy of the exchange-repulsion and total QM/EFP interaction energies is evaluated on a diverse set of dimers, including complexes from the S22 dataset of non-covalent interactions. In most cases, the QM/EFP energies are at least as accurate as corresponding EFP energies. A simple and computationally efficient form of the introduced QM/EFP exchange-repulsion term will facilitate further developments and applications of QM/EFP methods.

Effective Fragment Potential Method for H-Bonding: How To Obtain Parameters for Nonrigid Fragments.

Accuracy of the effective fragment potential (EFP) method was explored for describing intermolecular interaction energies in three dimers with strong H-bonded interactions, formic acid, formamide, and formamidine dimers, which are a part of HBC6 database of noncovalent interactions. Monomer geometries in these dimers change significantly as a function of intermonomer separation. Several EFP schemes were considered, in which fragment parameters were prepared for a fragment in its gas-phase geometry or recomputed for each unique fragment geometry. Additionally, a scheme in which gas-phase fragment parameters are shifted according to relaxed fragment geometries is introduced and tested. EFP data are compared against the coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) method in a complete basis set (CBS) and the symmetry adapted perturbation theory (SAPT). All considered EFP schemes provide a good agreement with CCSD(T)/CBS for binding energies at equilibrium separations, with discrepancies not exceeding 2 kcal/mol. However, only the schemes that utilize relaxed fragment geometries remain qualitatively correct at shorter than equilibrium intermolecular distances. The EFP scheme with shifted parameters behaves quantitatively similar to the scheme in which parameters are recomputed for each monomer geometry and thus is recommended as a computationally efficient approach for large-scale EFP simulations of flexible systems.

Multipole Moments in the Effective Fragment Potential Method.

In the effective fragment potential (EFP) method the Coulomb potential is represented using a set of multipole moments generated by the distributed multipole analysis (DMA) method. Misquitta, Stone, and Fazeli recently developed a basis space-iterated stockholder atom (BS-ISA) method to generate multipole moments. This study assesses the accuracy of the EFP interaction energies using sets of multipole moments generated from the BS-ISA method, and from several versions of the DMA method (such as analytic and numeric grid-based), with varying basis sets. Both methods lead to reasonable results, although using certain implementations of the DMA method can result in large errors. With respect to the CCSD(T)/CBS interaction energies, the mean unsigned error (MUE) of the EFP method for the S22 data set using BS-ISA-generated multipole moments and DMA-generated multipole moments (using a small basis set and the analytic DMA procedure) is 0.78 and 0.72 kcal/mol, respectively. The MUE accuracy is on the same order as MP2 and SCS-MP2. The MUEs are lower than in a previous study benchmarking the EFP method without the EFP charge transfer term, demonstrating that the charge transfer term increases the accuracy of the EFP method. Regardless of the multipole moment method used, it is likely that much of the error is due to an insufficient short-range electrostatic term (i.e., charge penetration term), as shown by comparisons with symmetry-adapted perturbation theory.

Dispersion Interactions in QM/EFP.

The dispersion energy term between quantum-mechanical (QM) and classical (represented by effective fragment potentials, EFP) subsystems is developed and implemented. A new formulation is based on long-range perturbation theory and uses dynamic polarizability tensors of the effective fragments and electric field integrals and orbital energies of the quantum-mechanical subsystem. No parametrization is involved. The accuracy of the QM-EFP dispersion energy is tested on a number of model systems; the average mean unsigned error is 0.8 kcal/mol or 13% with respect to the symmetry adapted perturbation theory on the S22 data set of noncovalent interactions. The computational cost of the dispersion energy computation is low compared to the self-consistent field calculation of the QM subsystem. The dispersion energy is sensitive to the level of theory employed for the QM part and to the electrostatic interactions in the system. The latter means that the dispersion interactions in the QM/EFP method are not purely two-body but have more complex many-body behavior.

Mechanistic Design of Chemically Diverse Polymers with Applications in Oral Drug Delivery.

Polymers play a key role in stabilizing amorphous drug formulations, a recent strategy employed to improve solubility and bioavailability of drugs delivered orally. However, the molecular mechanism of stabilization is unclear, therefore, the rational design of new crystallization-inhibiting excipients remains a substantial challenge. This article presents a combined experimental and computational approach to elucidate the molecular features that improve the effectiveness of cellulose polymers as solution crystallization inhibitors, a crucial first step toward their rational design. Polymers with chemically diverse substituents including carboxylic acids, esters, ethers, alcohols, amides, amines, and sulfides were synthesized. Measurements of nucleation induction times of the model drug, telaprevir, show that the only effective polymers contained carboxylate groups in combination with an optimal hydrocarbon chain length. Computational results indicate that polymer conformation as well as solvation free energy are important determinants of effectiveness at inhibiting crystallization and show that simulations are a promising predictive tool in the screening of polymers. This study suggests that polymers need to have an adequate hydrophilicity to promote solvation in an aqueous environment, and sufficient hydrophobic regions to drive interactions with the drug. Particularly, the right balance between key substituent groups and lengths of hydrocarbon side chains is needed to create effective materials.

Ground-State Charge Transfer: Lithium-Benzene and the Role of Hartree-Fock Exchange.

Most approximations to the exchange-correlation functional of Kohn-Sham density functional theory lead to delocalization errors that undermine the description of charge-transfer phenomena. We explore how various approximate functionals and charge-distribution schemes describe ground-state atomic-charge distributions in the lithium-benzene complex, a model system of relevance to carbon-based supercapacitors. To understand the trends, we compare Hartree-Fock (HF) and correlated post-HF calculations, confirming that the HOMO-LUMO gap is narrower in semilocal functionals but widened by hybrid functionals with large fractions of HF exchange. For semilocal functionals, natural bond orbital (NBO) and Mulliken schemes yield opposite pictures of how charge transfer occurs. In PBE, for example, when lithium and benzene are <1.5 Å apart, NBO yields a positive charge on the lithium atom, but the Mulliken scheme yields a negative charge. Furthermore, the partial charges in conjugated materials depend on the interplay between the charge-distribution scheme employed and the underlying exchange-correlation functional, being critically sensitive to the admixture of HF exchange. We analyze and explain why this happens, discuss implications, and conclude that hybrid functionals with an admixture of about one-fourth of HF exchange are particularly useful in describing charge transfer in the lithium-benzene model.

Thermodynamics and Kinetics for the Free Radical Oxygen Protein Oxidation Pathway in a Model for ß-Structured Peptides.

Oxidative stress plays a role in many biological phenomena, but involved mechanisms and individual reactions are not well understood. Correlated electronic structure calculations with the MP2, MP4, and CCSD(T) methods detail thermodynamic and kinetic information for the free radical oxygen protein oxidation pathway studied in a trialanine model system. The pathway includes aerobic, anaerobic and termination reactions. The course of the oxidation process depends on local conditions and availability of specific reactive oxygen species (ROS). A chemical mechanism is proposed for how oxidative stress promotes ß-structure formation in the amyloid diseases. The work can be used to aid experimentalists as they explore individual reactions and mechanisms involving oxygen free radicals and oxidative stress in ß-structured proteins.