Solvent Reorganization Effects Research Articles

Thermochemical Study of the Interaction of Cytosine and Uracil with Peptides in a Buffered Saline: Complex Formation with beta-Endorphin 30-31 (Human), L-Glutathion (Reduced) and α-L-Alanyl-L-Tyrosine.

The complex formation of uracil and cytosine with glycyl-L-glutamic acid (β-endorphin 30-31), γ-L-glutamyl-L-cysteinyl-glycine (glutathione reduced), α-L-alanyl-L-tyrosine, and α-L-alanyl-α-L-alanine in a buffered saline has been studied using dissolution calorimetry. The values of the reaction constant, the change in Gibbs energy, enthalpy, and entropy were obtained. It is shown that the ratio of the enthalpy and entropy factors depends on the charge of the peptide ion, and the number of H-bond acceptors in the peptide structure. The contributions of interaction between charged groups and polar fragments, hydrogen bonding, and stacking interaction are discussed, taking into account the effect of solvent reorganization around the reactant molecules.

Thermodynamics and Kinetics of Electron Transfer of Electrode-Immobilized Small Laccase from Streptomyces coelicolor.

The thermodynamic and kinetic properties for heterogeneous electron transfer (ET) were measured for the electrode-immobilized small laccase (SLAC) from Streptomyces coelicolor subjected to different electrostatic and covalent protein-electrode linkages, using cyclic voltammetry. Once immobilized electrostatically onto a gold electrode using mixed carboxyl- and hydroxy-terminated alkane-thiolate SAMs or covalently exploiting the same SAM subjected to N-hydroxysuccinimide+1-Ethyl-3-(3-dimethylaminopropyl)carbodiimide (NHS-EDC) chemistry, the SLAC-electrode electron flow occurs through the T1 center. The E°' values (from +0.2 to +0.1 V vs. SHE at pH 7.0) are lower by more than 0.2 V compared to the protein either in solution or immobilized with different anchoring strategies using uncharged SAMs. For the present electrostatic and covalent binding, this effect can, respectively, be ascribed to the negative charge of the SAM surfaces and to deletion of the positive charge of Lys/Arg residues due to amide bond formation which both selectively stabilize the more positively charged oxidized SLAC. Observation of enthalpy/entropy compensation within the series indicates that the immobilized proteins experience different reduction-induced solvent reorganization effects. The E°' values for the covalently attached SLAC are sensitive to three acid base equilibria, with apparent pKa values of pKa1ox = 5.1, pKa1red = 7.5, pKa2ox = 8.4, pKa2red = 10.9, pKa2ox = 8.9, pKa2red = 11.3 possibly involving one residue close to the T1 center and two residues (Lys and/or Arg) along with moderate protein unfolding, respectively. Therefore, the E°' value of immobilized SLAC turns out to be particularly sensitive to the anchoring mode and medium conditions.

The influence of the Cys46/Cys55 disulfide bond on the redox and spectroscopic properties of human neuroglobin

Neuroglobin is a monomeric globin containing a six-coordinate heme b, expressed in the nervous system, which exerts an important neuroprotective role. In the human protein (hNgb), Cys46 and Cys55 form an intramolecular disulfide bond under oxidizing conditions, whose cleavage induces a helix-to-strand rearrangement of the CD loop that strengthens the bond between the heme iron and the distal histidine. Hence, it is conceivable that the intramolecular disulfide bridge modulates the functionality of human neuroglobin by controlling exogenous ligand binding. In this work, we investigated the influence of the Cys46/Cys55 disulfide bond on the redox properties and on the pH-dependent conformational equilibria of hNgb, using UV–vis spectroelectrochemistry, cyclic voltammetry, electronic absorption spectroscopy and magnetic circular dichroism (MCD). We found that the SS bridge significantly affects the heme Fe(III) to Fe(II) reduction enthalpy (ΔH°′rc) and entropy (ΔS°′rc), mostly as a consequence of changes in the reduction-induced solvent reorganization effects, without affecting the axial ligand-binding interactions and the polarity and electrostatics of the heme environment. Between pH3 and 12, the electronic properties of the heme of ferric hNgb are sensitive to five acid-base equilibria, which are scarcely affected by the Cys46/Cys55 disulfide bridge. The equilibria occurring at extreme pH values induce heme release, while those occurring between pH5 and 10 alter the electronic properties of the heme without modifying its axial coordination and low spin state. They involve the sidechains of non-coordinating aminoacids close to the heme and at least one heme propionate.

Vibronic approach to the calculation of the decay rate of the photoexcited charge-transfer state of Guanine–Cytosine stacked dimer in water solution

We compute the rate of the charge recombination (CR) process from the minimum of the charge transfer (CT) Guanine–Cytosine stacked dimer in water solution to the ground electronic state (GS). We adopt the quantum non-adiabatic theory of electron transfer reactions, where key ingredients to determine the CR rate are the electronic coupling and the so-called Franck–Condon density of states (FCWD). In order to compute the FCWD, we exploited recent developments in the field of the time-independent and time-dependent simulations of vibronic spectra of large systems, based on model harmonic potential energy surfaces (PESs). Both mean-field solvent effects on the PESs and the solvent reorganization effects on the CR rate were described by implicit polarizable continuum model. We show that an improper treatment of the contributions of the inter-base modes to the FCWD results in artefacts which can change the estimate of the CR rates by orders of magnitude and we devise a computational protocol in internal coordinates able to determine “effective normal modes” that separate the stiff (intra-base) modes and the inter-base ones. The results for the CR rate are qualitatively consistent with available experimental data. By computing the CR rate for four different stacking geometries, we show that all the parameters ruling the CR rate, namely the CT character of the excited state (ES), the equilibrium position of stiff modes (and therefore the FCWD), the electronic coupling and the energy gap between the GS and ES are all strongly dependent on the fluctuation of the dimer structure along the inter-base modes. On this ground, we discuss some possible future theoretical developments to achieve a non-phenomenological fully first-principle estimate of the CR rate that can be directly compared with experiment.

Understanding the influence of capillary waves on solvation at the liquid-vapor interface.

This work investigates the question if surface capillary waves (CWs) affect interfacial solvation thermodynamic properties that determine the propensity of small molecules toward the liquid-vapor interface. We focus on (1) the evaluation of these properties from molecular simulations in a practical manner and (2) understanding them from the perspective of theories in solvation thermodynamics, especially solvent reorganization effects. Concerning the former objective, we propose a computational method that exploits the relationship between an external field acting on the liquid-vapor interface and the magnitude of CWs. The system considered contains the solvent, an externally applied field (f) and the solute molecule fixed at a particular location. The magnitude of f is selected to induce changes in CWs. The difference between the solvation free energies computed in the presence and in the absence of f is then shown to quantify the contribution of CWs to interfacial solvation. We describe the implementation of this method in the canonical ensemble by using a Lennard-Jones solvent and a non-ionic solute. Results are shown for three types of solutes that differ in the nature of short-ranged repulsive (hard-core) interactions. Overall, we observe that CWs have a negligible or very small effect on the interfacial solvation free energy of a solute molecule fixed near the liquid-vapor interface for the above systems. We also explain how the effects of pinning or dampening of CWs caused by a fixed solute are effectively compensated and do not contribute to the solvation free energy.

Thermodynamics and kinetics of reduction and species conversion at a hydrophobic surface for mitochondrial cytochromes c and their cardiolipin adducts

Cytochrome c (cytc) and its adduct with cardiolipin (CL) were immobilized on a hydrophobic SAM-coated electrode surface yielding a construct which mimics the environment experienced by the complex at the inner mitochondrial membrane where it plays a role in cell apoptosis. Under these conditions, both species undergo an equilibrium between a six-coordinated His/His-ligated and a five-coordinated His/- ligated forms stable in the oxidized and in the reduced state, respectively. The thermodynamics of the oxidation-state dependent species conversion were determined by temperature-dependent diffusionless voltammetry experiments. CL binding stabilizes the immobilized reduced His/- ligated form of cytc which was found previously to catalytically reduce dioxygen. Here, this adduct is also found to show pseudoperoxidase activity, catalysing reduction of hydrogen peroxide. These effects would impart CL with an additional role in the cytc-mediated peroxidation leading to programmed cell death. Moreover, immobilized cytc exchanges electrons more slowly upon CL binding possibly due to changes in solvent reorganization effects at the protein-SAM interface.

Solvent reorganization plays a temperature-dependent role in antibiotic selection by a thermostable aminoglycoside nucleotidyltransferase-4'.

The aminoglycoside nucleotidyltransferase-4' (ANT) is an enzyme that causes resistance to a large number of aminoglycoside antibiotics by nucleotidylation of the 4'-site on these antibiotics. The effect of solvent reorganization on enzyme-ligand interactions was investigated using a thermophilic variant of the enzyme resulting from a single-site mutation (T130K). Data showed that the binding of aminoglycosides to ANT causes exposure of polar groups to solvent. However, solvent reorganization becomes the major contributor to the enthalpy of the formation of enzyme-aminoglycoside complexes only above 20 °C. The change in heat capacity (ΔCp) shows an aminoglycoside-dependent pattern such that it correlates with the affinity of the ligand for the enzyme. Differences in ΔCp values determined in H2O and D2O also correlated with the ligand affinity. The temperature-dependent increase in the offset temperature (Toff), the temperature difference required to observe equal enthalpies in both solvents, is also dependent on the binding affinity of the ligand, and the steepest increase was observed with the tightest binding aminoglycoside, neomycin. Overall, these data, together with earlier observations with a different enzyme, the aminoglycoside N3-acetyltransferase-IIIb [Norris, A. L., and Serpersu, E. H. (2011) Biochemistry 50, 9309], show that solvent reorganization or changes in soft vibrational modes of the protein are interchangeable with respect to the role of being the major contributor to complex formation depending on temperature. These data suggest that such effects may more generally apply to enzyme-ligand interactions, and studies at a single temperature may provide only a part of the whole picture of thermodynamics of enzyme-ligand interactions.

Theoretical calculation of the photo-induced electron transfer rate between a gold atom and a gold cation solvated in CCl 4

A theoretical calculation was performed to evaluate the photo-induced electron transfer (PIET) rate between a gold atom and a gold ion solvated in carbon tetrachloride (CCl 4) in the framework of Marcus electron transfer (ET) theory, including both solvent reorganization effects and electronic wavefunction coupling between the ET diabatic states. A novel component of this work involves calculation of the electronic coupling strength using a recently developed constrained real-time time-dependent density-functional-theory (CRT-TDDFT) method. It is found that the PIET rate reaches its maximum value at the electronic resonance wavelength regardless of the inter-particle separation, suggesting a strong correlation between PIET and light absorption. In comparison with thermally activated electron transfer (TAET) at room temperature, light irradiation is demonstrated to be much more efficient than thermal fluctuations in promoting long-range ET, at least for the most common situations, when the light travelling substantially exceeds thermal energy. This work is the first step towards a quantum theory of plasmon enhanced electron transfer, and the theory can also be used to calculate electron transfer rates quite generally for condensed phase problems.

Control of reduction thermodynamics in [2Fe–2S] ferredoxins: Entropy–enthalpy compensation and the influence of surface mutations

The reaction thermodynamics for the one-electron reduction of the [2Fe–2S] cluster of both human ferredoxin and various surface point mutants, in which each of the negatively charged residues Asp72, Glu73, Asp76, and Asp79 were converted to Ala, have been determined by variable temperature spectroelectrochemical measurements. The above are conserved residues that have been implicated in interactions between the vertebrate-type ferredoxins and their redox partners. In all cases, and similar to other 2Fe-ferredoxins, the reduction potentials are negative as a result of both an enthalpic and entropic stabilization of the oxidized state. Although all Hs Fd mutants, with the exception of Asp72Ala, show slightly higher E°′ values than that of wild type Hs Fd, according to expectations for a purely electrostatic model, they exhibit changes in the ∆ H°′ rc values that are electrostatically counter-intuitive. The observation of enthalpy–entropy compensation within the protein series indicates that the mutation-induced changes in ∆ H°′ rc and ∆ S°′ rc are dominated by reduction-induced solvent reorganization effects. Protein-based entropic effects are likely to be responsible for the low E°′ value of D72A.

A VB/MM View of the Identity SN2 Valence-Bond State Correlation Diagram in Aqueous Solution

The valence-bond state correlation diagram (VBSCD), which was developed by Shaik and co-workers is an excellent tool to understand reactivity patterns in chemical reactions. The strength of the model is in its ability to describe the whole spectrum of reaction types and unify them under a single general paradigm. Moreover, it allows one to understand, conceptualize, and predict chemical reactivity in a general as well as specific manner. As such, VBSCD is a valuable model. The model has been largely tested on various systems in the gas phase both qualitatively and quantitatively. However, its application to reactions in solution was given less attention because of the difficulties to represent solvent reorganization and estimate non-equilibrium solvation effects, which, on the basis of the model, are expected to be fundamental. The recently developed valence-bond molecular mechanics (VB/MM) method overcomes these difficulties because it involves explicit solvent molecules and thus allows quantitative examination of these solvent effects. This work presents a study of the identity S(N)2 reaction X(-) + H(3)CX --> XCH(3) + X(-); (X = F, Cl, Br, I) in aqueous solution. The various parameters that form the VBSCD model are calculated and compared with the corresponding model's estimated values. A relatively good agreement between the calculated and estimated values is found. It is shown that when facing quantitative considerations, the picture may not be as simplistic as in the qualitative study; yet, the fundamental nature of the description is unaffected. This indicates that combined together, the VB/MM approach and the VBSCD model offer a very powerful tool to study reactions in complex systems and understand their reactivity patterns.

Immobilization of horseradish peroxidase on self-assembled (3-mercaptopropyl)trimethoxysilane film: Characterization, direct electrochemistry, redox thermodynamics and biosensing

Highly organized (3-mercaptopropyl)trimethoxysilane (3-MPT) films have been prepared via self-assembled coupled with sol–gel linking technology. Horseradish peroxidase (HRP) is successfully immobilized onto the densely packed three-dimensional (3D) 3-MPT network and the direct electrochemistry of HRP is achieved without any electron mediators or promoters. Redox thermodynamics of HRP on the 3-MPT films, which is obtained from the temperature dependence of the reduction potential, suggests that the positive shift of redox potentials of HRP at the interface of 3-MPT originates from the solvent reorganization effects and conformational change of the polypeptide chain of HRP. Based on the direct electrochemistry and electrocatalytic ability of HRP, a sensitive third-generation amperometric H 2O 2 biosensor is developed with two linear dependence ranges of 5.0 × 10 −7 to 1.0 × 10 −4 and 1.0 × 10 −4 to 2.0 × 10 −2 mol L −1.

Redox reactivity of the heme Fe3+/Fe2+ couple in native myoglobins and mutants with peroxidase-like activity

The reaction enthalpy and entropy for the one-electron reduction of the ferric heme in horse heart and sperm whale aquometmyoglobins (Mb) have been determined exploiting a spectroelectrochemical approach. Also investigated were the T67R, T67K, T67R/S92D and T67R/S92D Mb-H variants (the latter containing a protoheme-L: -histidine methyl ester) of sperm whale Mb, which feature peroxidase-like activity. The reduction potential (E degrees ') in all species consists of an enthalpic term which disfavors Fe(3+) reduction and a larger entropic contribution which instead selectively stabilizes the reduced form. This behavior differs from that of the heme redox enzymes and electron transport proteins investigated so far. The reduction thermodynamics in the series of sperm whale Mb variants show an almost perfect enthalpy-entropy compensation, indicating that the mutation-induced changes in DeltaH(o')(rc) and DeltaS(o')(rc) are dominated by reduction-induced solvent reorganization effects. The modest changes in E degrees ' originate from the enthalpic effects of the electrostatic interactions of the heme with the engineered charged residues. The small influence that the mutations exert on the reduction potential of myoglobin suggests that the increased peroxidase activity of the variants is not related to changes in the redox reactivity of the heme iron, but are likely related to a more favored substrate orientation within the distal heme cavity.

Free Energy of Transition for the Individual Alkaline Conformers of Yeast Iso-1-cytochrome c,

Direct protein electrochemistry was used to obtain the thermodynamic parameters of transition from the native (state III) to the alkaline (state IV) conformer for untrimethylated Saccharomyces cerevisiae iso-1-cytochrome c expressed in E. coli and its single and multiple lysine-depleted variants. In these variants, one or more of the lysine residues involved in axial Met substitution (Lys72, Lys73, and Lys79) was mutated to alanine. The aim of this work is to determine the thermodynamic affinity of each of the substituting lysines for the heme iron and evaluate the interplay of enthalpic and entropic factors. The equilibrium constants for the deprotonation reaction of Lys72, 73, and 79 were computed for the minimized MD average structures of the wild-type and mutated proteins, applying a modified Tanford-Kirkwood calculation. Solvent accessibility calculations for the substituting lysines in all variants were also performed. The transition enthalpy and entropy values within the protein series show a compensatory behavior, typical of a process involving extensive solvent reorganization effects. The experimental and theoretical data indicate that Lys72 most readily deprotonates and replaces M80 as the axial heme iron ligand, whereas Lys73 and Lys79 show comparably higher pKa values and larger transition free energies. A good correlation is found within the series between the lowest calculated Lys pKa value and the corresponding experimental pKa value, which can be interpreted as indicative of the deprotonating lysine itself acting as the triggering group for the conformational transition. The triple Lys to Ala mutant, in which no lysine residues are available for heme iron binding, features transition thermodynamics consistent with a hydroxide ion replacing the axial methionine ligand.

Redox properties of the Fe3+/Fe2+ couple in Arthromyces ramosus class II peroxidase and its cyanide adduct

The thermodynamics of the one-electron reduction of the ferric heme in free and cyanide-bound Arthromyces ramosus peroxidase (ARP), a class II plant peroxidase, were determined through spectro-electrochemical experiments. The data were compared with those for class III horseradish peroxidase C (HRP) and its cyanide adduct, and were interpreted in terms of ligand binding features, electrostatic effects and solvent accessible surface area of the heme group and of catalytically relevant residues in the heme distal site. The E(o)' values for free and cyanide-bound ARP (-0.183 and -0.390 V, respectively, at 25 degrees C and pH 7) are higher than those for HRP and HRP-CN. ARP features an enthalpic stabilization of the ferrous state and a remarkably negative reduction entropy, which are both unprecedented for heme peroxidases. Once the compensatory contributions of solvent reorganization are partitioned from the measured reduction enthalpy, the resulting protein-based deltaH(o)'(rc(int)) value for ARP turns out to be less positive than that for HRP by +10 kJ mol(-1). The smaller stabilization of the oxidized heme in ARP most probably results from the less pronounced anionic character of the proximal histidine, and the decreased polarity in the heme distal site as compared with HRP, as indicated by the X-ray structures. The surprisingly negative deltaS(o)'(rc) value for ARP is the result of peculiar reduction-induced solvent reorganization effects.

Reduction thermodynamics of the T1 Cu site in plant and fungal laccases

The thermodynamic parameters for reduction of the type-1 (T1) copper site in Rhus vernicifera and Trametes versicolor laccases and for the derivative of the former protein from which the type-2 copper has been selectively removed (T2D) have been determined with UV-vis spectroelectrochemistry. In all cases, the enthalpic term turns out to be the main determinant of the Eo' of the T1 site. Also the difference between the reduction potentials of the two laccases is enthalpy-based and reflects differences in the coordination features of the T1 sites and their protein environment. The T1 sites in native R. vernicifera laccase and its T2D derivative show the same Eo', as a result of compensatory differences in the reduction thermodynamics. This suggests that removal of the type-2 (T2) copper results in modification of the reduction-induced solvent reorganization effects, with no influence in the structure of the multicopper protein site. This conclusion is supported by NMR data recorded on the native, the T2D, and Hg-substituted T1 derivatives of R. vernicifera laccase, which show that the T1 and T2/T3 sites are largely noninteracting.

Axial ligation and polypeptide matrix effects on the reduction potential of heme proteins probed on their cyanide adducts

The enthalpic and entropic changes accompanying the reduction reaction of the six-coordinate cyanide adducts of cytochrome c, microperoxidase-11 and a few plant peroxidases were measured electrochemically. Once the compensating changes in reduction enthalpy and entropy due to solvent reorganization effects are factorized out, it is found that cyanide binding stabilizes enthalpically the ferriheme following the order: cyochrome c > peroxidase > microperoxidase-11. The effect is inversely correlated to the solvent accessibility of the heme. Comparison of the reduction thermodynamics for the cyanide adducts of cytochrome c and plant peroxidases with those for microperoxidase-11 and myoglobin, respectively, yielded an estimate of the consequences of protein encapsulation and of the anionic character of the proximal histidine on the reduction potential of the heme-cyanide group. Insertion of the heme-CN group into the folded peptide chain of cyt c induces an enthalpy-based decrease in E degrees ' of approximately 100 mV, consistent with the lower net charge of the oxidized as compared to the reduced iron center, whereas a full imidazolate character of the proximal histidine stabilizes enthalpically the ferriheme by approximately 400 mV. The latter value should be best considered as an upper limit since it also includes some solvation effects arising from the nature of the protein systems being compared.

Intramolecular Charge-Transfer State Formation of 4-(N,N-Dimethylamino)benzonitrile in Acetonitrile Solution: RISM-SCF Study

Intramolecular charge-transfer (ICT) state formation of 4-(N,N-dimethylamino)benzonitrile in acetonitrile solution is studied by the reference interaction site model self-consistent field (RISM-SCF) method. Geometry optimizations are performed for each electronic state in solution with the complete-active-space SCF wave functions. Dynamic electron correlation effects are taken into account by using the multiconfigurational quasidegenerate perturbation theory. Two-dimensional free energy surfaces are constructed as the function of the twisting and wagging angles of the dimethylamino group for the ground and locally excited (LE) states. The calculated absorption and fluorescence energies are in good agreement with experiments. The validity of the twisted ICT (TICT) model is confirmed in explaining the dual fluorescence, and the possibility of the planar ICT model is ruled out. To examine the mechanism of the TICT state formation, a "crossing" seam between the LE and charge-transfer (CT) state surfaces is determined. The inversion of two electronic states occurs at a relatively small twisting angle. The effect of solvent reorganization is also examined. It is concluded that the intramolecular twisting coordinate is more important than the solvent fluctuation for the TICT state formation, because the energy difference between the two states is minimally dependent on the solvent configuration.

Electrostatic Effects on the Thermodynamics of Protonation of Reduced Plastocyanin

The L12E, L12K, Q88E, and Q88K variants of spinach plastocyanin have been electrochemically investigated. The effects of insertion of net charges near the metal site on the thermodynamics of protonation and detachment from the copper(I) ion of the His87 ligand have been evaluated. The mutation-induced changes in transition enthalpy cannot be explained by electrostatic considerations. The existence of enthalpy/entropy (H/S) compensation within the protein series indicates that solvent-reorganization effects control the differences in transition thermodynamics. Once these compensating contributions are factorized out, the resulting modest differences in transition enthalpies turn out to be those that can be expected on purely electrostatic grounds. Therefore, this work shows that the acid transition in cupredoxins involves a reorganization of the H-bonding network within the hydration sphere of the molecule in the proximity of the metal center that dominates the observed transition thermodynamics and masks the differences that are due to protein-based effects.

Solvent-based deuterium isotope effects on the redox thermodynamics of cytochrome c

The reduction thermodynamics of cytochrome c (cytc), determined electrochemically, are found to be sensitive to solvent H/D isotope effects. Reduction of cytochrome c is enthalpically more favored in D(2)O with respect to H(2)O, but is disfavored on entropic grounds. This is consistent with a reduction-induced strengthening of the H-bonding network within the hydration sphere of the protein. No significant changes in E degrees ' occur, since the above variations are compensative. As a main result, this work shows that the oxidation-state-dependent differences in protein solvation, including electrostatics and solvent reorganization effects, play an important role in determining the individual enthalpy and entropy changes of the reduction process. It is conceivable that this is a common thermodynamic feature of all electron transport metalloproteins. The isotope effects turn out to be sensitive to buffer anions which specifically bind to cytc. Evidence is gained that the solvation thermodynamics of both redox forms of cytc are sensibly affected by strongly hydrated anions.

Enthalpy/entropy compensation phenomena in the reduction thermodynamics of electron transport metalloproteins.

Compensation phenomena between the enthalpy and entropy changes of the reduction reaction for all classes of electron transport metalloproteins, namely cytochromes, iron-sulfur, and blue copper proteins, are brought to light. This is the first comprehensive report on such effects for biological redox reactions. Following Grunwald's approach for the interpretation of H/ S compensation for solution reactions, it is concluded that reduction-induced solvent reorganization effects involving the hydration shell of the molecule dominate the reduction thermodynamics in these species, although they have no net effect on the E degrees values, owing to exact compensation. Thus the reduction potentials of these species are primarily determined by the selective enthalpic stabilization of one of the two oxidation states due to ligand binding interactions and electrostatics at the metal site and by the entropic effects of reduction-induced changes in protein flexibility.