Conformational Flexibility Controls Proton Transfer between the

We set the sampling windows at intervals of 0.1 Å and a force constant for the .... that kOH+Thr = 5.1 × 108 M-1 s-1 57 and kOH+Met = 1.0 × 1010 M-...
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J. Phys. Chem. B 2001, 105, 1250-1259

Conformational Flexibility Controls Proton Transfer between the Methionine Hydroxy Sulfuranyl Radical and the N-Terminal Amino Group in Thr-(X)n-Met Peptides Dariusz Pogocki,†,‡ Elena Ghezzo-Scho1 neich,† and Christian Scho1 neich*,† Department of Pharmaceutical Chemistry, UniVersity of Kansas, 2095 Constant AVenue, Lawrence, Kansas 66047, and Institute of Nuclear Chemistry and Technology, Dorodna 16, 03-195 Warsaw, Poland ReceiVed: September 23, 2000; In Final Form: NoVember 16, 2000

For Thr-(X)n-Met peptides, we have correlated the efficiency of proton transfer and an intramolecular radical reaction between a methionyl hydroxy sulfuranyl radical and the N-terminus with the flexibility of the spacer sequence -(X)n-, X ) Gly and Pro and n ) 0-4. Hydroxy sulfuranyl radicals accept a proton from the N-terminus to yield a cyclic (S∴Ν)+ three-electron-bonded intermediate which ultimately expels acetaldehyde. Acetaldehyde formation was used to quantify the efficiency of proton transfer and cyclization, whereas peptide flexibility was calculated by molecular modeling methods. For X ) Gly, proton transfer and cyclization proceeds in a concerted manner, and peptide flexibility mainly controls the proton transfer step. For X ) Pro, no low-energy conformation was located, which allows concerted proton transfer and cyclization, indicating that proton transfer occurs over longer distances, likely via bridging water molecules. These sequence-dependent differences are reflected in different β-values for the proton-transfer step, β ) 0.66 ( 0.02 Å-1 for X ) Gly and β ≈ 0.12 ( 0.1 Å-1 for X ) Pro.

1. Introduction

SCHEME 1

Protein oxidation is a characteristic feature of oxidative stress, during which biological tissue experiences increased levels of various reactive oxygen species such as superoxide, peroxides, peroxynitrite, peroxyl, and hydroxyl radicals.1-12 Depending on their nature and reactivity, these species react more or less selectively with the various amino acid residues of proteins and peptides though, generally, the aromatic and sulfur-containing residues show the highest reactivity.9,10 Importantly, a single hit of a protein by a reactive species may ultimately convert more than one amino acid residue, suggesting chain mechanisms and radical migration along the peptide backbone.13 For example, hydrogen abstraction by the hydroxyl radical from any aliphatic amino acid side chain ultimately generates a peroxyl radical, which may attack other labile C-H bonds within the protein.13 Hence, stable oxidation products may form quite remote from the site of an initial attack, potentially even in protein domains which show little surface exposure. Though it can be assumed that such intramolecular processes would benefit from the conformational flexibility of a protein, only few mechanistic studies on how the sequence may control relatively fast free radical processes in peptides and proteins have been carried out. In fact, most knowledge on the effect of peptide sequence on reactivity originates from work on electron-transfer reactions.14 However, as electron transfer often proceeds through the bonds of the peptide skeleton, these studies may not be representative for other “chemical” reactions occurring between functional groups separated by specific peptide sequences. In this paper, we report on the effect of peptide sequence on proton transfer and cyclization between a sulfur-centered radical * Corresponding author. Email: [email protected]. Phone: (785) 8644880. FAX: (785) 864-5736. † University of Kansas. ‡ Institute of Nuclear Chemistry and Technology.

from Met and the amino group of the N-terminal Thr residue in Thr-(X)n-Met model peptides, with X ) Gly and Pro and n ) 0-4. Earlier, we had shown that the reaction of a hydroxyl radical with Thr-Met yields hydroxy sulfuranyl radical 1 (Scheme 1),15 which, under appropriate experimental conditions, accepts a proton from the N-terminal amino group and cyclizes to intermediate 2a.15 Qualitative evidence for 2a was obtained by means of time-resolved pulse radiolysis experiments.15 Electron transfer within 2a and ring-opening lead to the nitrogen-

10.1021/jp003450m CCC: $20.00 © 2001 American Chemical Society Published on Web 01/09/2001

Thr-(X)n-Met Peptides centered radical cation 3, which suffers heterolytic cleavage into acetaldehyde and the carbon-centered radical 4. The kinetics of most other competitive processes of 1 are more or less known. Therefore, in a series of Thr-(X)n-Met model peptides, the efficiency of acetaldehyde formation from 1 can be utilized to obtain absolute estimates for the rate constants of reaction 2 and a correlation of the efficiency of reaction 2 with peptide dynamics. While acetaldehyde yields can be defined experimentally, the dynamics of the peptide-derived intermediates were investigated theoretically using molecular modeling calculations. 2. Materials and Methods 2.1. Materials. The peptide Thr-Met was obtained from Research Plus, Inc. (Bayonne, NJ). The Biotechnology Core Facility of Kansas State University provided all the other peptides, synthesized by the solid-phase method using FMOC protected amino acids. The peptides were purified via HPLC and characterized by matrix-assisted laser desorption ionization mass spectrometry. Acetaldehyde and (2,4-dinitrophenyl) hydrazine (2,4-DNPH) were purchased from Merck. Acetonitrile and hydrogen peroxide (30% solution in water) were from Fisher Scientific (Pittsburgh, PA). 2.2. Reactions. A Rayonet (Branford, CT) photochemical reactor was used to produce hydroxyl radicals through the photolytic cleavage of hydrogen peroxide at 254 nm.16 Stock solutions of hydrogen peroxide and peptide in 1 mM phosphate buffer, pH 6.0, were separately saturated with N2. Subsequently, hydrogen peroxide was added to the peptide solution to reach a final concentration of both reagents of 200 µM. Immediately after hydrogen peroxide addition, the sealed solutions were irradiated with eight (253.7 nm) lamps for 15, 30, 45, or 60 s. Nonirradiated reaction samples were used as controls. 2.3. HPLC Product Analysis. Quantification of peptide loss and product formation was performed by reverse-phase HPLC using a Shimadzu instrument equipped with a UV-vis detector and an SGE 250 × 4.6 mm Hypersil C18 column. For the quantification of peptide loss, a final concentration of 10 units/ ml of catalase was added after photolysis in order to prevent any reaction between H2O2 and peptides. The peptides were separated from their reaction products using different gradients of mobile phase A (water/acetonitrile 99.5/0.5, v/v, containing 0.1% trifluoroacetic acid) and mobile phase B (30/70 water/ acetonitrile, v/v, containing 0.1% trifluoroacetic acid), adjusting the conditions for each individual peptide in order to achieve good resolution in short times. Acetaldehyde was derivatized prior to analysis by coupling with 2,4-DNPH, as described previously,17 yielding the corresponding hydrazone. The hydrazone was eluted with mixtures of water/acetonitrile 60/40 (mobile phase A) and 10/90 (mobile phase B), running a linear gradient from 20% B to 60% B within 10 min. The absorbance of the 2,4-DNPH adducts was monitored at 345 nm. 2.4. Molecular Simulations and Computational Details. All the simulations were done in the extended atom model. As the potential energy function, the CHARMM potential18,19 was employed in its HyperChem implementation.20 To simulate the presence of water solvent, we utilized a scale factor () equal to 80, which screened the charge-charge interactions. Such a simplification has been shown to give results that quantitatively agreed with solvent simulations.21 The modeling of zwitterionic nonoxidized peptides was done with the default Bio85+ set of parameters that is an equivalent of the PARAM19 parameter set.22 However, to model the hydroxy sulfuranyl radicalcontaining peptides, we parametrized the hydroxy sulfuranyl

J. Phys. Chem. B, Vol. 105, No. 6, 2001 1251 TABLE 1: Potential Energy Parameters Used to Simulate the Hydroxy Sulfuranyl Radical of Met (a) Bond Parameters bond type

force constant (kcal mol-1Å-2)

bond length (Å)

S•-O C-S• O-H

205 450 450

2.050 1.804 0.978

(b) Bond Angle Parameters angle type

force constant (kcal mol-1 rad-2)

bond angle (rad)

C-S•-O C-C-S• C-S•-C S•-O-H

38 50 52 57

1.548 1.918 1.743 1.808

(c) Electrostatic Charge Distribution atom type

charge (1 electron)

CH2 CH2 S•-O-H S•-O-H S•-O-H CH3

+0.000 +0.055 +0.190 -0.740 +0.440 +0.055

radical (>S•-OH) of Met. These parameters were deconvoluted from the MP2/6-31+G(2d) gas-phase calculation performed for the hydroxy sulfuranyl radical of dimethyl sulfide.23 Bond lengths, bond angles, and dihedral angels were taken from published geometrical data.23 The force constants of bond stretching and bond angle bending were evaluated using the harmonic oscillator approximation from the ab initio calculated infrared frequencies scaled by the factor 0.98, which was determined by comparison of known experimental frequencies24 with the ab initio results23 for dimethyl sulfide. The force constants of deformation of dihedral angles, improper dihedral angles, and nonbonded interaction for the hydroxy sulfuranyl sulfur and oxygen were copied from a set of parameters for the thioether sulfur and the hydroxyl oxygen.18,22 The partial charges were averaged from the charge distributions calculated using Merz-Kollman25,26 and Chelp27,28 models, implemented into the Gaussian’98W suite of programs29 and then normalized to yield zero charge within the side chain of the hydroxy sulfuranyl radical of Met. Parameters for the hydroxy sulfuranyl radical of Met are summarized in Table 1. In the majority of the calculations, the hydroxy sulfuranyl radical was taken in its R-configuration. However, free inversion of the starting configuration was allowed, since no additional forces to prevent it were added. The statistical distribution of distances separating the reactive centers (nitrogen and sulfur) were calculated by means of umbrella sampling calculations.30-35 The sampling was done utilizing the Langevin dynamics (LD) model32-34,36-39 without explicit waters, with a collision frequency of ca. 50 ps-1 for all heavy atoms. We set the sampling windows at intervals of 0.1 Å and a force constant for the umbrella potential of 20 kcal mol-1Å-2 (83.7 kJ mol-1Å-2). Each window simulation was run with the 1.5 fs time step for 50 ps, preceded by 9 ps of heating from 0 to 300 K and 10 ps of equilibration. The longtime free LD simulations were done with 20 ns propagation time, which is comparable with the lifetime of hydroxy sulfuranyl radicals in aqueous solution. The remaining parameters (time step, heating, and equilibration times) were identical to those in the umbrella sampling computations. For the force

1252 J. Phys. Chem. B, Vol. 105, No. 6, 2001 TABLE 2: Formation of Acetaldehyde in the Reaction of Hydroxy Radicals with Peptides peptide

kCH3CHOa [10-7 Ms-1 s-1]

fAc ) ([Ac]/[-peptide])

TM TPM TP2M TP3M TP4M TGM TG4M

0.99 ( 0.05 0.23 ( 0.02 0.26 ( 0.01 0.18 ( 0.01 0.14 ( 0.01 1.10 ( 0.02 0.77 ( 0.01

0.21 ( 0.026 0.05 ( 0.007 0.06 ( 0.005 0.04 ( 0.005 0.03 ( 0.006 0.23 ( 0.016 0.16 ( 0.029

a 200 µM peptide, 200 µM H O , 1 mM phosphate buffer pH 6.0, 2 2 N2-saturated, eight 253.7 nm lamps.

SCHEME 2

field calculations, we used either 4.5 or 5 trial versions of the HyperChem PC molecular modeling package.40 The data analysis was done using self-written procedures within the SigmaPlot 3.0241 program using its math features.42 For the nonlinear regression, the Marquardt-Levenberg algorithm43-47 provided by SigmaPlot has been utilized. 3. Results and Discussion In the following, experimental data on the N-terminal fragmentation of Thr-(X)n-Met will provide the basis for a theoretical consideration of the parameters controlling the various steps of the process. Hence, we will first introduce the experimental data of acetaldehyde formation, followed by a summary of important individual reactions to consider and, finally, a theoretical analysis of each individual step. 3.1. Formation of Acetaldehyde. The reaction of •OH radicals with Thr-(X)n-Met peptides in 1 mM phosphate buffer leads to significant amounts of acetaldehyde, summarized in Table 2. The efficiency of acetaldehyde formation, fAc, is calculated according to fAc ) [acetaldehyde]/[lost peptide]. For Thr-Met, we obtain fAc ) 0.21; i.e., acetaldehyde formation accounts for 21% of the peptide-derived products. [In the absence of phosphate buffer, we obtain fAc ≈ 0.5, consistent with our earlier radiation chemical results.15] The residual fraction of hydroxy sulfuranyl radical 1 ultimately yields R-(alkylthio)alkyl radicals 5a and 5b (reaction 5) and, to a smaller extent, radical 6 and CO2 (reaction 6)48 (see Scheme 2). A significantly lower fAc is observed for Thr-Pro-Met, i.e., when Thr and Met are separated by a single Pro residue, whereas no significant difference is observed between Thr-Met and Thr-Gly-Met. Within error limits, there is no difference between fAc for Thr-Pro-Met and Thr-Pro-Pro-Met, while any further increase of the number of the Pro residues results in a gradual decrease of fAc. Ultimately, Thr-(Pro)4-Met shows

Pogocki et al. a negligible yield of acetaldehyde, fAc ) 0.03, in contrast to Thr-(Gly)4-Met (fAc ) 0.16). 3.2. Summary of Mechanisms Important for Theoretical Considerations. For a detailed theoretical consideration of the processes leading to the N-terminal fragmentation of Thr-(X)nMet, the reactions presented in Schemes 1 and 2 have to be supplemented by a set of competitive processes, summarized in Scheme 3. Dependent on pH, hydroxy sulfuranyl radical 1 can decompose via the following additional routes: (i) the reaction with solvent protons leads to the elimination of water (kH) and monomeric sulfur-centered radical cation 717,49,50 (reaction 7), (ii) the carboxylate-catalyzed elimination of HO(kSO) yields the SO-bonded cyclic intermediate 851(reaction 8),52-54 and (iii) the elimination of HO- through reaction with a second thioether moiety (kSO) yields dimeric sulfur-sulfur bonded radical cation 949 (reaction 9).55,56 It should be noted that, practically, reaction 7 and 9 will be of minor importance under our experimental conditions of 2 × 10-4 M peptide at pH 6. Ultimately, the sulfuranyl radical 8 will decompose via ring opening (reaction 10), followed by deprotonation to yield the R-(alkylthio)alkyl radicals 5a and 5b (reaction 11). 3.3. Multistep Process Leading to the N-Terminal Fragmentation of Thr-(X)n-Met. The proposed fragmentation mechanism involves (i) the initial formation of hydroxy sulfuranyl radical 1 (reaction 1), followed by (ii) intramolecular proton transfer from the N-terminal amino group (reaction 2), (iii) formation of a sulfur-nitrogen bonded intermediate 2a, and (iv) heterolytic cleavage of the Thr side chain (reaction 4). The latter process derives “activation” from the radical stabilization energy (RSE) of the product R-aminoalkyl radicals. In view of the expected relatively small variation between the RSEs of R-aminoalkyl radicals of the different peptides, we consider the driving force for acetaldehyde production from 3 to be independent of the length of the peptide. Similarly, the initial photochemical yields of HO• are independent of the nature of the peptide. Thus, eq 1 predicts the yields of acetaldehyde formation for each individual peptide j as the product of the initial concentration of HO• (ξ), multiplied by the efficiency of the three reaction steps i-iii. Each step is represented by its individual efficiency, YSOH, YPT, and YET, which depends on the peptide sequence and the nature of the bridging amino acid residues (Pro or Gly) j YCH ) ξ × YjSOH × YjPT × YjET 3CHO

(1)

j Here, ξ represents the initial yield of •OH radicals, YSOH the efficiency of the addition of hydroxyl radicals to the sulfur of Met (relative to reactions with other functional groups in the peptide), YjPT the efficiency of the proton transfer from the protonated amino group of Thr to the hydroxy sulfuranyl radical function, and YjET the efficiency of the electron transfer from the amino group to the sulfur-centered radical cation of Met for an individual peptide j. We assume that YjET will be higher for the cyclic N-S bonded species 2a compared to the open form 2b; hence, peptides with a higher flexibility (and higher propensity to form 2a) will show higher YjET values. The efficiency of each reaction step for every individual peptide can be calculated from appropriate competition kinetics, as described below. Addition of HO• to Met (YSOH). The C-terminal Met in any given peptide competes for hydroxyl radicals with several possible target sites of the peptide. If we assume that these target sites are equally accessible for HO• in each of the small peptides and that this accessibility does not depend on the peptide

Thr-(X)n-Met Peptides

J. Phys. Chem. B, Vol. 105, No. 6, 2001 1253

SCHEME 3

j conformation, YSOH can be derived from eq 2

YjSOH ) kOH+Met kOH+Met + kOH+Thr + n × kOH+(-Pro-) + mj × kOH+(-Gly-) + kOH+CR-H j

(2) where kOH+Met represents the rate constant for the addition of HO• to Met, kOH+Thr is the rate constant for the attack of Thr by HO•, kOH+(-Pro-) is the rate constant for the reaction of HO• with the internal Pro residue(s), kOH+(-Gly-) is the rate constant for the reaction of HO• with the internal Gly residue(s), nj and mj are the numbers of internal Pro and Gly residues, respectively, in the peptide molecule, and kOH+CR-H is the rate constant for the abstraction of CR-protons from the terminal Met and Thr by HO•. Not all individual rate constants for the reaction of HO• with every possible target sites of our model peptides are precisely known. However, they can be approximated in the following way: For the isolated amino acids Thr and Met, we know that kOH+Thr ) 5.1 × 108 M-1 s-1 57 and kOH+Met ) 1.0 × 1010 M-1 s-1 58. Since, the β-CH bond of Thr and the thioether function of Met are the most reactive groups, these rate constants are good approximations for the reaction of HO• with Thr and Met in the small peptides. The rate constant for the attack of HO• on the CR-H bond of an internal Gly residue in peptides (kOH+(-Gly-) ≈ 4.7 × 108 M-1 s-1) can be computed on the

basis of subtraction of the rate constant for Gly-Gly-Gly (kOH+Gly-Gly-Gly ) 7.3 × 108 M-1 s-1)57 by the rate constant for Gly-Gly (kOH+Gly-Gly ) 2.6 × 108 M-1 s-1).57 Similarly, the rate constant for HO• attack on the internal Pro residue (kOH+(-Pro-) ≈ 1.7 × 109 M-1 s-1) can be obtained by subtraction of the rate constant for Gly (pH ) 1, kOH+Gly ) 1.7 × 107 M-1 s-1)57 from that of Gly-Pro (pH ) 2kOH+Gly-Pro ) 1.7 × 109 M-1 s-1).57 The rate constant for the abstraction of the CR-H from the C-terminal Met (kOH+CR-H ≈1.3 × 108 M-1 s-1) can be approximated from the rate constant for Gly-Gly (kOH+Gly-Gly ) 2.6 × 108 M-1 s-1)57 divided by 2 (the number of the C-terminal R-protons in Gly-Gly). Efficiency of the Proton Transfer (YPT). The efficiency of the proton transfer from the amino group of Thr to the hydroxy sulfuranyl radical, YjPT, can be expressed by eq 3

YjPT )

YjPT kjPT + kjSO

(3)

where kjPT represents the rate constant of the proton transfer from the amino group to the hydroxy sulfuranyl radical and kjSO the rate constant of competitive carboxylate-assisted elimination of HO- from the hydroxy sulfuranyl radical (cf. reaction 8 in Scheme 3), yielding the sulfur-oxygen bonded radical cation 8. This is the only competitive elimination of HO- taken into account here, as under the given experimental conditions (pH ) 6, peptide concentration ) 2 × 10-4 M) other

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competitive processes of hydroxy sulfuranyl radical decay are negligible. For example, typical values for the proton-assisted decay of the hydroxy sulfuranyl radical at pH 6 would be kH[H+] ) 1 × 104 s-1 (kH ) 1 × 1010 M-1 s-1)59-61 and kSS[S] ) 2 × 104 s-1 (kSS ) 1.0 × 108 M-1 s-1),51,59-61 whereas the intramolecular carboxylate-assisted decay may occur with kSO as high 107-108 s-1 (by analogy to thiopropionic acids51). Estimation of kSO. Our simulations show that the mean distances 〈rC-S〉 between carboxylate carbons and the side chain sulfur in the terminal Met residues, calculated in 20 ns free LD of hydroxy sulfuranyl radicals in TM, TPM, TP2M, and TGM, are 4.74 ( 0.93, 4.89 ( 0.24, 4.95 ( 0.16, and 4.96 ( 0.25 Å, respectively. Hence, there is little variation of the distance regardless of the sequence N-terminal to Met, and correspondingly, kSO will most likely vary only slightly with the expansion of the N-terminal peptide sequence. Therefore, we approximate TM TM that kjSO ≈ kTM SO . The relative ratio, Ω ) kSO /kPT , for Thr-Met can then be computed from our experimental data presented earlier,15 where two independent methods give quite consistent values with an average of Ω ) 0.46 (see Appendix). The efficiency of the proton-transfer reaction for the j-th peptide can then be calculated from eq 4

YjPT )

kjPT kjPT + 0.46 × kTM PT

(4)

Estimation of kPT. The rate constant of intramolecular proton transfer is a value that should demonstrate a formal dependence on the distance between the donor and the acceptor of the proton (here, the nitrogen of the N-terminal amino group and the oxygen of the hydroxy sulfuranyl radical of the C-terminal Met). Similar to electron transfer,14 the resonance splitting of the donor and the acceptor proton energy levels determines the rate of the nonadiabatic proton transfer, which depends exponentially on the transfer distance.62 Thus, in a first approximation, the distance dependence of the proton-transfer rate constant, kPT, can be described by the exponential expression 5

kPT ) k0 × e-β×(rDA-r0)

(5)

where k0 represents the rate constant for the limiting case that donor and acceptor sites are in van der Waals contact, r0 is their center to center separation distance for k0, and β [Å-1] is a coefficient relating the exponential dependence of kPT to the internuclear donor-acceptor separation rDA. Electron-Transfer Efficiency (YET). The mathematical description of the electron-transfer efficiency (YET) between the sulfurcentered radical cation and the deprotonated amino group is complex. This rate constant kET cannot be measured directly and cannot not be well separated experimentally from other competing processes. Electron transfer should be sufficiently fast to compete with deprotonation of the sulfur-centered radical cation in the ring-open structure 2b that occurs with an estimated rate constant of k(-H+) ≈ 2.4 × 105 s-1.58 Since deprotonation of 2b is the only irreversible process competing with electron transfer (see Scheme 3), YET, can be calculated from eq 6

YjET )

kjET kjET + k(-H+)

(6)

Practically, we can consider two limiting cases: the electron transfer occurs (i) through space or (ii) through the system of the coupled orbitals of the peptide bonds.

Case i: If the N-terminal amino group and the hydroxy sulfuranyl radical of Met stay long enough in close contact, both electron and proton transfer will occur simultaneously in a concerted process. Electron transfer will then likely occur in the N∴S three-electron-bonded transient structure 2a. In such case, we should not observe any dependence on the N-S distance, as for all peptides reacting via this mechanism, the N-S-distance shall be more or less the same. Consequently, the value of YET should be constant and close to unity. In support of this hypothesis, a lower limit of kET was estimated from our earlier studies for free Met.61 Taking electron transfer as ratelimiting step in the formation of R-aminoalkyl radicals during decarboxylation, we obtained kET g 3.8 × 106 s-1.61 Thus, eq 6 yields YET g 0.94, within the N∴S three-electron-bonded transient 2a. If the amino and hydroxy sulfuranyl radical groups are separated by a longer distance, water molecules can mediate the proton transfer63-66and probably the electron transfer as well. In this case, the factors YPT and YET would be undistinguishable, due to the similar shape of the function describing the distance dependence. Case ii: Electron transfer through the peptide bonds establishes a reasonable alternative to the transfer through space. However, it is less probable that this process can play the role of the “bottleneck” in the considered mechanism. Perhaps the strongest argument against it is derived from a comparison with the results of a mechanistic investigation of the electron transfer in Tyr-(Pro)n-Met model peptides (n ) 0-3).67 The rate constants of the electron-transfer reaction TyrOH-(Pro)n-Met/ S∴Br f TyrO•-(Pro)n-Met + Br- + H+ were found to decrease almost linearly with the number of Pro residues, since each of the peptide bonds contributes an increment to the “resistance” of the electron-transfer conductor. Instead, in our system, the most significant decrease of acetaldehyde formation occurs already with the introduction of only one Pro residue (but not Gly); however, no difference in fAc is observed between TPM and TP2M (see Table 2). We conclude that our system is more likely described by “through-space” electron transfer. 3.4. Statistical Distribution of the N-S Distance between the N-Terminal Nitrogen and the Met Sulfur. Mean RelatiVe Constant of Intramolecular Proton Transfer. Due to its conformational flexibility, a peptide molecule in aqueous solution can adopt several conformations. Some of them could favor a particular reaction pathway and disfavor other possible pathways. Thus, in the following, we modeled the properties of the investigated peptides, taking into account the distribution of the distances separating reactive centers involved in proton and electron transfer. To interpret the acetaldehyde formation more quantitatively, we carried out LD simulations.32-34,37,39 For this purpose, we used the r(N-S) distance between the N-terminal Thr nitrogen and the sulfur of the C-terminal Met as a convenient measure of the distance separating the reactive centers. Although the proton transfer actually involves the N-H bond of Thr and the oxygen of the hydroxy sulfuranyl radical of Met (i.e., in structure 1), the r(N-S) distance is more convenient, since r(N-S) can be measured both for the hydroxy sulfuranyl radical and the nonoxidized, native peptides. The statistical distribution of the r(N-S) distances over the 99 lowenergy conformers for each peptide was obtained from umbrella sampling LD calculations with the umbrella potential of 20 kcal mol -1Å-2 put on r(N-S) at intervals of 0.1 Å. The umbrella sampling search of probability distribution along the r(N-S) coordinate for Thr-(Gly)n-Met (n ) 0, 1, 4) was done starting from the all-trans conformations. To take into consideration the

Thr-(X)n-Met Peptides

J. Phys. Chem. B, Vol. 105, No. 6, 2001 1255

Figure 1. Distribution of distances r(N-S) between the N-terminal nitrogen of Thr and the C-terminal sulfur of Met in statistical samples of Thr(Pro)n-Met (n ) 0-4) and Thr-(Gly)n-Met (n ) 0, 1, 4) conformers, obtained via umbrella sampling simulation. The inset shows the mean relative rate constant of intramolecular proton transfer 〈kjPT〉 vs the coefficient β.

TABLE 3: Average 〈r(N-S)〉 Distances between the N-terminal Thr Nitrogen and the Sulfur of the C-terminal Met in Statistical Samples of Thr-(Pro)n-Met (n ) 0-4) and Thr-(Gly)n-Met (n ) 0, 1, 4) Conformers Obtained in LD Simulations peptide

native peptide 〈r(N-S)〉 [Å]

hydroxy sulfuranyl radical 〈r(N-S)〉a [Å]

TM TPM TP2M TP3M TP4M TGM TG4M

6.96 ( 0.04 9.83 ( 0.10 9.16 ( 0.02 13.24 ( 0.05 16.28 ( 0.07 7.24 ( 0.03 8.05 ( 0.08

6.19 ( 0.11 (4.52 ( 0.12) 8.50 ( 0.17 (7.41 ( 0.17) 10.35 ( 0.07 (9.09 ( 0.09) 6.21 ( 0.15 (6.11 ( 0.12) 4.78 ( 0.23

a Data in parentheses for the cis configuration of the first peptide bond.

possible presence of Pro units in the cis configuration, we started the umbrella sampling LD simulations of oligoproline-bridged peptides from two different points: (i) the extended all-trans conformations [PLPII, (all-trans/(Pro2(ω(trans))] and (ii) the equally probable conformations with the first peptide bond in the cis configuration [Pro2(ω(cis))].21,68-73 We did not see significant differences in the r(N-S) distribution between the alltrans and the Pro2(ω(cis)) populations of the native oligoprolinebridged conformers, probably due to the high flexibility of the C-terminal Met side chain. The normalized statistical distributions of the r(N-S) distances for the native peptides are shown in Figure 1, and the mean distances 〈r(N-S)〉 averaged over the

conformers of the examined peptides are presented in the second column of Table 3. The third column of Table 3 summarizes 〈r(N-S)〉 for the hydroxy sulfuranyl radicals of the Thr-(X)nMet peptides. Notably, some differences between simulations starting from all-trans and X2(ω(cis)) conformation exist for the hydroxy sulfuranyl radicals of the shorter peptides (see also Figure 2). The statistical distributions of the distances within the samples are rather wide, as exemplified in Figures 1 and 2, clearly showing that the mean 〈r(N-S)〉 values alone could not reflect properly the overall distribution of the intramolecular distances. Therefore, the distance-dependent mean relative rate constant of intramolecular proton transfer 〈kjPT〉 for each peptide was calculated according to expression 7

〈kjPT〉 k0 × eβ×r0

)

ij ) e-β×r ∑i W(r(N-S)

ij (N-S)

(7)

ij where W(r(N-S) ) represents the statistical weight corresponding to r(N-S) in the i-th molecular conformation of the j-th peptide, using the r(N-S) distances for each peptide for β in the range between 0 and 1.0 Å-1 (Figure 1, inset). (Because k0 and r0 are constant, the denominator on the left side of eq 7 is also constant for a given value of β.) We shall stress that the formalism utilized in eq 7 can also be used for calculations of the distance-dependent mean relative

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Figure 2. Shift of the statistical distribution of the r(N-S) distances in samples of the tripeptides Thr-Gly-Met (A) and Thr-Pr--Met (B) during the 20 ns free LD simulations of their respective hydroxy sulfuranyl radicals. The strait line (s) shows the statistical distribution in the nonoxidized compounds (from umbrella sampling), and the doted (‚‚‚) and dashed (- - -) lines show distributions for the cis and trans conformation of the first peptide bond in the hydroxy sulfuranyl radical of the respective peptide.

rate constant of intramolecular electron transfer 〈kjET〉 for each peptide with proper k0 and r0

〈kjET〉 k0 × eβ×r0

)

ij ) e-β×r ∑i W(r(N-S)

ij (N-S)

(8)

In general, the simulations indicate that peptides containing the -(Pro)n- bridge are rather unlikely to attain low-energy conformations, which allow the two terminal functions (amino and sulfur) to come into a close contact, required for the formation of the N∴S three-electron-bonded transient. Also, any significant conformational rearrangement that could allow such a contact might not be expected within the nanosecond lifetime of the hydroxy sulfuranyl radical. The fastest rearrangement of the oligoproline backbone that would result in a significant change of the r(N-S) distance would require at least a microsecond-to-millisecond lifetime of the radical 1. For example, on the basis of MD simulations of oligoproline peptides in aqueous solutions carried out by Sneddon and Brooks21 and Poznan´ski and co-workers,71,73 the frequency of the fastest (βfR) transition of the oligoproline backbone, evaluated from the potential of mean force, has been restricted to the range of 103-106 s-1. Contrary to this, the flexible peptides Thr-(Gly)n-Met (n ) 0, 1, 4) adopt low-energy conformations that can allow with relative ease an approach of reactive centers as close as the van der Waals contact. Even within the nanosecond lifetime of the hydroxy sulfuranyl radical 1, already short distances between the reactive centers in the flexible peptides can be significantly reduced further. The longtime (20 ns) free LD simulations of the hydroxy sulfuranyl radical derived from Thr-(Gly)n-Met show a significant shift of conformational distributions to lower r(N-S). This is displayed in Figure 2A, where the statistical distributions of the r(N-S) distances in samples of Thr-Gly-Met, together with results

of long-time LD for the respective hydroxy sulfuranyl radical, are shown. For comparison, the analogous calculations for ThrPro-Met are presented in Figure 2B. For Thr-Pro-Met, a significant shift of r(N-S) suggests that in this system r(N-S) never approaches distances even close to the sum of the van der Waals radii of both atoms (ca. 3.3 Å74). The average distances 〈r(N-S)〉 for the hydroxy sulfuranyl radicals of the chosen peptides, obtained in 20 ns free LD, are summarized in Table 3, compared with data obtained during the umbrella sampling simulation for the native zwitterionic peptides. 3.5. Nature of the Distance-Dependent Step. Considering all the differences between the more rigid and the more flexible series of the examined peptides, we can now correlate our experimental with the computational data. The yields of j acetaldehyde, YCH , were calculated according to eq 1, 3CHO employing eq 2 for the efficiency of hydroxy sulfuranyl radical j formation, YSOH , and eq 4 for the efficiency of the proton j transfer, YPT. Equation 4 was resolved for the mean relative rate constants of intramolecular proton transfer 〈kjPT〉, calculated according to expression 7. For the flexible peptides Thr(Gly)n-Met (n ) 0, 1, 4), YET was set constant, since we assumed for all peptides of this series that electron transfer occurs within the N∴S three-electron-bonded transient 2a (see discussion in 3.2). For calculations of YET for the oligoprolinebridged peptides two limiting cases were considered assuming (a) that proton transfer is the distance-dependent limiting step or (b) that electron transfer is the distance-dependent limiting step. For case a, YET was set constant for all peptides, and YjPT was calculated as above; for case b, YPT was set constant for all peptides, and YjET was calculated from eq 6, resolved for the mean relative rate constants of intramolecular electron transfer 〈kjET〉, calculated according to eq 8 (β ) 0-1.0 Å-1; r0 ) 2.55-3.3 Å; these boundary distances reflect the average N-S distance in the N∴S three-electron-bonded transient 2a75 and the sum of the van der Waals radii of the N and S atoms,74 respectively). For each value of β, the calculated set of j j was compared with the experimental kCH , with the YCH 3CHO 3CHO j error of kCH3CHO as a weight of the fit. The standard error of coefficient ξ × YET (or ξ × YPT) and the coefficient of regression R were used as the criteria for the best correlation of the experiment with the calculation. As shown in Figure 3, the best correlation coefficient of regression for the flexible peptides (Thr-(Gly)n-Met (n ) 0, 1, 4)), R ) 0.98 has been accomplished for β ) 0.66 ( 0.02 Å-1 and ξ × YET ) 1.68 ( 0.03. For oligoproline-bridged peptides, the following best-correlation coefficients of regression (R ) 0.92) have been obtained: for limiting case a, β ) 0.11 ( 0.02 Å-1 and ξ × YET ) 0.55 ( 0.02; for limiting case b, β ) 0.13 ( 0.02 Å-1 and ξ × YPT ) 0.46 ( 0.03. A comparison of β clearly shows that for both types of peptides, β characterizes different processes. The following considerations suggest that electron transfer cannot be the distance-dependent rate-limiting process. In such a case, the parameter β would depend on the distance separating the donor and acceptor of the electron. Hence, we would need to assume that the different β-values indicate that electron transfer must proceed through different types of media. The simplest quantum-mechanical interpretation of β for electron transfer is that for a free electron tunneling through a rectangular barrier of the potential β ≈ (V0)1/2, where V0 represents the altitude of the barrier.62 The difference in the decay constant β for the electron transfer in various peptides has been interpreted as the difference between through-peptide and through-solvent transfer. Because the tunneling barrier for water is higher than

Thr-(X)n-Met Peptides

J. Phys. Chem. B, Vol. 105, No. 6, 2001 1257

Figure 3. Correlation of experimental kCH3CHO with theoretical YCH3CHO, where coefficient β was optimized for the two series of peptides (see text), Thr-(Gly)n-Met (n ) 0, 1, 4) (O, - - -) and Thr-(Pro)n-Met (n ) 0-4): (9, s) case a, (3, ‚‚‚) case b. Inset: Standard error of ξ × YET and ξ × YPT vs the coefficient β for each correlation.

that for the peptide backbone, the through-solvent pathway will have a more rapid distance decay then the through-peptide path. However, the calculated β-values for tunneling through water and through the peptide backbone were found to be close to 1.4 and 0.9 Å-1, respectively.76-79 Similarly, the conformational interpretation of intramolecular electron transfer between Tyr and Met(S∴Br) in Met5-enkephalins80 as well as in Tyr(Pro)n-Met71 has suggested that the β-value of electron transfer must be located in the range of 1.0-1.5 Å-1. As our results locate the value of coefficient β sufficiently below the 0.9 Å-1 range, we can conclude that the observed distance-dependent process cannot be electron transfer. We propose that β characterizes the transfer of a proton and that the different β values for both series of peptides indicate different media through which the proton is transferred. For example, the difference in β may be interpreted as the difference between the through-vacuum and the through-solvent proton transfer. If the donor-acceptor distance is shorter or comparable to the thickness of one hydration shell of water (ca. 3.5 Å34), there is no room for any water molecule between the reacting centers. This is the case for the peptides Thr-Met, Thr-GlyMet, and Thr-(Gly)4-Met, where proton-transfer will proceed through vacuum and/or through direct contact between the donor and the acceptor centers. On the other hand, if the donoracceptor distance is sufficiently long, the centers are separated by one or more solvation shells. This is the case for the Thr(Pro)n-Met peptides. For all peptides, the rate of proton transfer limits the yield of the three-electron-bonded [>S∴NH2]+ peptide intermediate 2a. Consequently, it limits the efficiency of the overall process of acetaldehyde production. The high value of YET for the Thr-(Gly)n-Met (represented by ξ × YET ≈1.7, assuming that ξ is similar for both series of peptides) seems to characterize the high efficiency of the adiabatic electron transfer within the N∴S three-electron-bonded structure 2a. In the oligoproline-bridged peptides, the lower value of β characterizes the decay of the rate of proton transfer mediated by the bulk of water. The proton transfer most probably occurs with participation of water molecules in a so-called “proton

shuttling” mechanism, which is known to be operative within liquid or solid water.63-66 Nevertheless, such a process can be sufficiently fast to compete with the carboxylate-group-assisted elimination of HO- from the hydroxy sulfuranyl radicals (reaction 8), as the expected rate constant of proton transfer should be comparable with the first-order rate constants for proton exchange in carboxylic acids of ca. 108 s-1.64 The small “distance-independent” factor YET for Thr-(Pro)n-Met (represented by ξ × YET ≈ 0.6) could be interpreted as superposition of two opposite effects resulting from the different dependence of electron-transfer mechanisms on the distance. On one hand, the growth of the number of Pro residues in the peptides results in the decrease of kET through the peptide backbone, on the other hand, it promotes an increase of kET through space, due to the growing flexibility of the peptides. 4. Summary and Conclusions Our experimental and molecular modeling results clearly show that the efficiency of acetaldehyde formation during HO• radical-induced oxidation of Thr-(X)n-Met peptides depends mainly on the conformational flexibility of the oligopeptide backbone. A relatively high efficiency of acetaldehyde formation is observed for peptides (Thr-(Gly)n-Met), which can adopt conformations with relative ease, allowing a close contact between the reactive centers, methionine hydroxy sulfuranyl radical 1 and the N-terminal amino group of Thr. Thus, conformational flexibility controls the efficiency of proton transfer between the reactive centers and, hence, the formation of the N∴S three-electron-bonded transient products. If the reactive centers approach a distance comparable to the sum of their van der Waals radii and smaller than the thickness of one hydration shell of water, the rate constant of proton transfer shows a strong, exponential dependence on the distance separating reactive centers (β ≈ 0.66). The formation of the N∴S threeelectron-bonded transient 2a creates optimal conditions for a highly effective adiabatic electron transfer.

1258 J. Phys. Chem. B, Vol. 105, No. 6, 2001

Pogocki et al.

The restriction of conformational flexibility in the oligoproline-bridged peptides (Thr-(Pro)n-Met) results in a drastic decrease of the acetaldehyde yield. In that case, both proton and electron transfer have to proceed over the longer distances through the bulk of water (proton transfer and electron transfer) or through the peptide backbone (electron transfer). Hence, proton transfer is not expected to yield the N∴S three-electronbonded transient 2a in a concerted manner. Therefore, subsequent electron transfer has to occur over a larger distance and is more than 3 times less efficient compared to the adiabatic process in the Thr-(Gly)n-Met peptides. We note that a simulation performed using the LD-generated statistical distribution of peptide conformers includes the averaged effects of the solvent without requiring the explicit presence of solvent molecules. Hence, the solvent influence on the dynamic behavior of the solute (by random collisions imposing a frictional drag on the motion of the solute through the solvent) is simulated by the frictional force proportional to the collision frequency.32-34,39 The distribution of structures obtained through the LD simulation could be slightly different then that from the molecular dynamics (MD) with explicit water molecules, due to the consideration of hydrogen bonding between a peptide and the solvent. On the other hand, the projected discrepancy between the LD and the MD simulation is probably lower than the uncertainty arising from the simplifying assumption of the “united atom” representation, which allows to perform CHARMM-force field simulations on a PC computer. Acknowledgment. This research was supported by the NIH (PO1 AG 12993). We thank Dr. Krzysztof Kuczera for many helpful discussions.

formation of R-aminoalkyl radicals.15 In support, the decay of 2a is accompanied by the parallel formation of a broad absorption band with λmax < 260 nm, characteristic for R-aminoalkyl radicals.15,48,81 Thus, the yield of 2a, G2a, should be equal to the final yield of R-aminoalkyl radicals, ∆GRN ≈ 1.9, calculated by division of the radiation chemical yield at 260 (4) -1 -1 -1 nm (∆GRN × (4) 260 ≈ 4800 M cm ) by 260 ≈ 2560 M -1 15 cm and the extinction coefficient for 2a at λ ) 380 nm, -1 -1 (from the equation  (2a) 380 ≈ ((G × 380 ≈ 2740 M cm 380)0.2µs - (G × 380)1.4µs)/∆GRN)). The residual absorption at 1.4 µs after the pulse can be assigned to the superposition of the long-lived species 8 and 9. The contribution of 9 to absorption at λ ) 380 nm at 1.4 µs after the pulse can be estimated from its known absorption at λ ) 480 nm at longer times after the pulse, i.e., 2.5 µs. Multiplying G × 480 ≈ 11 800 M-1cm-1 15 by 380/480 ) 0.13 (calculated from the spectrum of a pulse-irradiated N2O-saturated solution of 2 × 10-3 M AcMet-OMe at pH 1 (380 ≈ 1100 M-1cm-1, 480 ≈ 8600 M-1cm-1 61), which is convenient due to the low efficiency of any N∴S bond formation and lack of decarboxylation for AcMet-OMe),61 and by the time correction coefficient G1.4µs/G2.5µs 1.4µs ) 0.64 (calculated from pseudo-first-order kinetics, GSS ) 2.5µs k [S]×1.1µs 8 -1 -1 15 SS , with kSS ) 2 × 10 M s ), we obtain G GSS /e × 380 ≈ 980 M-1cm-1 of the residual absorption of the sulfursulfur-bonded radical 9 at λ ) 380 nm at 1.4 µs after the pulse. Thus, GSO ) 0.96 is calculated by subtraction of G × (9) 380 ≈ 980 M-1cm-1 from G ×  ≈ 4100 M-1cm-1 and division by the absorption coefficient of the SO-bonded radicals ((8) 380 ≈ 3250 M-1cm-1).54 Finally, inserting GSO ≈ 0.96 and GSN ≈ 1.9, we derive eq 10

kSO/kPT ) GSO/GSN

(10)

Appendix TM Calculation of Ω ) kTM SO /kPT . In the first method, we use the yields of acetaldehyde (GCH3CHO) measured radiationchemically for different TM concentrations.15 [The G-value is defined as a number of species (transient or stable) per 100 eV absorbed energy of ionizing radiation (G ) 1.0 corresponds to 0.1036 µM/J converted or generated species).] Equation 9 relates GCH3CHO to the initial yield of HO•

0.93 × GOH TM GCH 3CHO

≈

TM TM kTM SS [TM] + kSO + kPT

kTM PT

(9)

TM where kSS represents the rate constant of bimolecular hydroxy sulfuranyl radical decay through reaction with a nonoxidized peptide (reaction 9; Scheme 3). From the intercept of a plot of TM )/∂([TM]) we obtain Ω ) 0.41 ( 0.03. ∂(GOH/GCH 3CHO In the second approach, we compare the pulse radiolytically determined G-values of the transient species in this system: the decomposition of the hydroxy sulfuranyl radical leads to the TM formation of species 2a, 8, and 9, with the rate constants kSS , TM TM kSO , and kPT , respectively (see Scheme 3). These transients -1 -1 15 absorb in the UV/VIS region with (9) 480 ≈ 6540 M cm , (8) (2a) -1 -1 54 -1 -1 50 380 ≈ 3250 M cm , and 390 ≈ 2700 M cm . Pulse irradiation15 of an N2O-saturated aqueous solution, pH 5.9, containing 2 × 10-3 M of TM yields an optical spectrum with λmax around 380 nm, with G × 380 ≈ 9300 M-1cm-1 at ca. 200 ns after the pulse, which subsequently decays to (G × 380 ≈ 4100 M-1cm-1) over the following 1.4 µs. This rapid decay (t1/2 ≈ 320 ns) is assigned to the unimolecular transformation of 2a into acetaldehyde (reaction 3 and 4) with simultaneous

and we obtain Ω ) 0.51. References and Notes (1) Flitter, W.; Rowley, D. A.; Halliwell, B. FEBS Lett. 1983, 158, 310. (2) Stadtman, E. R. Free Radical Biol. Med. 1990, 315. (3) Vogt, M. Free Radical Biol. Med. 1995, 18, 93. (4) Sayre, L. M.; Zagorski, M. G.; Surewicz, W. K.; Krafft, G. A.; Perry, G. Chem. Res. Toxicol. 1997, 10, 518. (5) Oxygen Radicals in Biology and Medicine; Plenum Press: New York, 1988. (6) Scho¨neich, C.; Zhao, F.; Wilson, G. S.; Borchardt, R. T. Biochim. Biophys. Acta 1993, 1158, 307. (7) Sies, H. OxidatiVe Stress: Oxidants and Antioxidants; Academic Press: New York, 1991. (8) Ferradini, C. J. Chim. Phys. 1991, 88, 873. (9) Riley, P. A. Int. J. Radiat. Biol. 1994, 65, 27. (10) von Sonntag, C. The Chemical Basis of Radiation Biology; Taylor & Francis: London, 1987; pp 1-515. (11) Stadtman, E. R. Biochemistry 1990, 29, 6323. (12) Stadtman, E. R. Science 1992, 267, 1220. (13) Neuzil, J.; Gebicki, J. M.; Stocker, R. Biochem. J. 1993, 293, 601. (14) Bobrowski, K. In Properties and Reactions of Radiation induced Transients. Selected Topics; Mayer, J., Ed.; Polish Scientific Publishers PWN: Warszawa, Poland, 1999; pp 177-204. (15) Scho¨neich, C.; Zhao, F.; Madden, K. P.; Bobrowski, K. J. Am. Chem. Soc. 1994, 116, 4641. (16) Schiffman, A.; Nelson, D. D., Jr.; Nesbitt, D. J. J. Chem. Phys. 1993, 98, 6935. (17) Scho¨neich, C.; Bobrowski, K. J. Am. Chem. Soc. 1993, 115, 6538. (18) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S. K. M. J. Comput. Chem. 1983, 4, 187. (19) Reiher, W. E. Ph.D. Dissertation, Harvard University, Cambridge MA, 1985. (20) HyperChem® Computational Chemistry; Hypercube Inc.: Waterloo, Canada, 1994; pp 139-185. (21) Sneddon, S. F.; Brooks, C. L. I. J. Am. Chem. Soc. 1992, 114, 8220.

Thr-(X)n-Met Peptides (22) MacKarell, A. D., Jr. PARAM19. (www.pharmacy.umab.edu/∼alex/ research.html, accessed 1999) (23) McKee, M. L. J. Phys. Chem. 1993, 97, 10971. (24) Dewar, M. S. J.; Ford, G. P. J. Am. Chem. Soc. 1977, 99, 1685. (25) Singh, U. Ch.; Kollman, P. A. J. J. Comput. Chem. 1984, 5, 129. (26) Besler, B. H.; Merz, K. M.; Kollman, P. A. J. J. Comput. Chem. 1990, 11, 431. (27) Chirlian, L. E.; Francl, M. M. J. Comput. Chem. 1987, 8, 894. (28) Breneman, C. M.; Wiberg, K. B. J. J. Comput. Chem. 1990, 11, 361. (29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komoromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Rev. A.7; Gaussian Inc.: Pittsburgh, PA, 1998. (30) Torrie, G. M.; Valleau, J. P. J. Comput. Phys. 1977, 23, 187. (31) Beveridge, D. L.; DiCapua, F. M. In Computer Simulation of Biological Systems. Theoretical and Experimental Applications.; van Gunsteren, W. F., Weiner, P. K., Eds.; ESCOM: Leiden, The Netherlands, 1989; pp 1-26. (32) Frenkel, D.; Smit, B. Understanding Molecular Simulation. From Algorithms to Applications.; Academic Press: San Diego, 1996; pp 1-443. (33) Leach, A. R. Molecular Modeling. Principles and Applications.; Longman: Harlow, U.K., 1996; pp 1-595. (34) Field, M. J. A Practical Introduction to the Simulation of Molecular Systems; Cambridge University Press: Cambridge, 1999; pp 1-313. (35) Billeter, S. R.; van Gunsteren, W. F. J. Am. Chem. Soc. 2000, 104, 3276. (36) Levy, R. M.; Karplus, M.; McKee, M. L. Chem. Phys. Lett. 1979, 65, 4. (37) Widmalm, G.; Pastor, R. W. J. Chem. Soc., Faraday Trans. 1992, 88, 1747. (38) He, S.; Scheraga, H. A. J. Chem. Phys. 1998, 108, 287. (39) Hinchliffe, A. Chemical Modeling. From Atoms to Liquids.; John Wiley & Sons: Chichester, U.K., 1999; pp 1-395. (40) HyperChem® Computational Chemistry.; Hypercube Inc.: Waterloo, Canada, 1994. (41) Kerle, K.; Norby, J.; Rubenstein, S.; Schwallie-Farmer, C.; Senchyna, T.; Turke, T. M.; Youtz, P.; Zhu, Q. SigmaPlot for Windows, 3.02; Jandel Corporation: San Rafael, CA, 1995. (42) Kuo, J. SigmaPlot. Scientific Graphic Software. Transformation & CurVe Fitting; Jandel Scientific: San Rafael, CA, 1994. (43) Marquardt, D. W. J. Soc. Ind. Appl. Math. 1963, 11, 431. (44) Shrager, R. I. J. Assoc. Comput. Machinery 1970, 17, 446. (45) Shrager, R. I. Commun. ACM 1972, 15, 41. (46) Nash, J. C. Compact Numerical Methods for Computers: Linear Algebra and Function Minimization; John Wiley & Sons: New York, 1979. (47) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes; Cambridge University Press: Cambridge, 1986. (48) Bobrowski, K.; Scho¨neich, C.; Holcman, J.; Asmus, K.-D. J. Chem. Soc., Perkin Trans. 2 1991, 975. (49) Bonifacˇic´, M.; Mo¨ckel, H.; Asmus, K.-D. J. Chem. Soc., Perkin Trans. 2 1975, 675.

J. Phys. Chem. B, Vol. 105, No. 6, 2001 1259 (50) Janata, E.; Veltwisch, D.; Asmus, K.-D. Radiat. Phys. Chem. 1980, 16, 43. (51) Bobrowski, K.; Pogocki, D.; Scho¨neich, C. J. Phys. Chem. A 1998, 102, 10512. (52) Glass, R. S.; Hojjatie, M.; Wilson, G. S.; Mahling, S.; Go¨bl, M.; Asmus, K.-D. J. Am. Chem. Soc. 1984, 106, 5382. (53) Mahling, S.; Asmus, K.-D.; Glass, R. S.; Hojjatie, M.; Wilson, G. S. J. Org. Chem. 1987, 52, 3717. (54) Steffen, L. K.; Glass, R. S.; Sabahi, M.; Wilson, G. S.; Scho¨neich, C.; Mahling, S.; Asmus, K.-D. J. Am. Chem. Soc. 1991, 113, 2141. (55) Chaudhri, S. A.; Go¨bl, M.; Freyholdt, T.; Asmus, K.-D. J. Am. Chem. Soc. 1984, 106, 5988. (56) Bonifacˇic´, M.; Asmus, K.-D. J. Org. Chem. 1986, 51, 1216. (57) Buxton, G. V.; Greenstock, C. L.; Helman, W. P.; Ross, A. B. J. Phys. Chem. Ref. Data 1988, 17, 513. (58) Hiller, K.-O.; Masloch, B.; Go¨bl, M.; Asmus, K.-D. J. Am. Chem. Soc. 1981, 103, 2734. (59) Bobrowski, K.; Scho¨neich, C. J. Chem. Soc., Chem. Commun. 1993, 795. (60) Bobrowski, K.; Pogocki, D.; Scho¨neich, C. J. Phys. Chem. 1993, 97, 13677. (61) Pogocki, D. Ph.D. Dissertation, Institute of Nuclear Chemistry and Technology, Warsaw, Poland, 1996. (62) Kuznetsov, A. M. Charge Transfer in Chemical Reaction Kinetics; Press Polytechniques et Universitaries Romades: Lausanne, Switzerland, 1997; pp 1-107. (63) Eigen, M. Angew. Chem., Int. Ed. Engl. 1964, 3, 1. (64) Grunwald, E.; Eustace, D. In Proton-Transfer Reactions; Caldin, E., Gold, V., Eds.; John Wiley & Sons: New York, 1975; pp 103-120. (65) Scheiner, S.; Duan, X. In Modeling the Hydrogen Bond; Smith, D. A., Ed.; ACS: Washington, DC, 1994; pp 125-138. (66) Braiman, M. S.; Mogi, T.; Marti, T.; Stern, L. J.; Khorana, H. G.; Rothschild, K. J. Biochemistry 1988, 27, 8516. (67) Bobrowski, K.; Wierzchowski, K. L.; Holcman, J.; Ciurak, M. Int. J. Radiat. Biol. 1990, 57, 919. (68) Thomas, W. A.; Williams, M. K. J. Chem. Soc., Chem. Commun. 1972, 994. (69) Evans, C. A.; Rabenstein, D. L. J. Am. Chem. Soc. 1974, 96, 7312. (70) Siemion, I. Z. Biostereochemia (Biostereochemistry); Pan´stwowe Wydawnictwo Naukowe: Warszawa, Poland, 1985; pp 1-431. (71) Poznan´ski, J. Ph.D. Dissertation, Institute of Biochemistry and Biophysics, Polish Academy of Sciences, Warsaw, Poland, 1995. (72) Poznan´ski, J.; Ejchart, A.; Wierzchowski, K. L.; Ciurak, M. Biopolymers 1993, 33, 781. (73) Bobrowski, K.; Poznan´ski, J.; Holcman, J.; Wierzchowski, K. L. J. Phys. Chem. B 1999, 10316. (74) Bondi, A. J. J. Phys. Chem. 1964, 68, 441. (75) Carmichael, I. Acta Chem. Scand. 1997, 51, 567. (76) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265. (77) Sneddon, S. F.; Morgan, R. S.; Brooks, C. L. I. Biophys. J. 1988, 53, 83. (78) Sneddon, S. F.; Brooks, C. L. I. Int. J. Quantum Biol. Symp. 1988, 15, 23. (79) Alexandrov, I. V.; Khairutdinov, R. F.; Zamaraev, K. I. Chem. Phys. 1978, 32, 123. (80) Vesterman, B.; Bobrowski, K.; Betins, J.; Nikiforovich, G. V.; Wierzchowski, K. L. Biochim. Biophys. Acta 1991, 1079, 39. (81) Hiller, K.-O.; Asmus, K.-D. J. Phys. Chem. 1983, 87, 3682.