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1.
The gas-phase structures of protonated and alkali metal cationized arginine (Arg) and arginine methyl ester (ArgOMe) are investigated with infrared spectroscopy and ab initio calculations. Infrared spectra, measured in the hydrogen-stretch region, provide compelling evidence that arginine changes from its nonzwitterionic to zwitterionic form with increasing metal ion size, with the transition in structure occurring between lithium and sodium. For sodiated arginine, evidence for both forms is obtained from spectral deconvolution, although the zwitterionic form is predominant. Comparisons of the photodissociation spectra with spectra calculated for low-energy candidate structures provide additional insights into the detailed structures of these ions. Arg*Li+, ArgOMe*Li+, and ArgOMe*Na+ exist in nonzwitterionic forms in which the metal ion is tricoordinated with the amino acid, whereas Arg*Na+ and Arg*K+ predominately exist in a zwitterionic form where the protonated side chain donates one hydrogen bond to the N terminus of the amino acid and the metal ion is bicoordinated with the carboxylate group. Arg*H+ and ArgOMe*H+ have protonated side chains that form the same interaction with the N terminus as zwitterionic, alkali metal cationized arginine, yet both are unambiguously determined to be nonzwitterionic. Calculations indicate that for clusters with protonated side chains, structures with two strong hydrogen bonds are lowest in energy, in disagreement with these experimental results. This study provides new detailed structural assignments and interpretations of previously observed fragmentation patterns for these ions.  相似文献   

2.
We utilized gas phase hydrogen/deuterium (H/D) exchange reactions and ab initio calculations to investigate the complexation between a model peptide (Arg-Gly-AspRGD) with various alkali metal ions. The peptide conformation is drastically altered upon alkali metal ion complexation. The associated conformational changes depend on both the number and type of complexing alkali metal ions. Sodium has a smaller ionic diameter and prefers a multidentate interaction that involves all three amino acids of the peptide. Conversely, potassium and cesium form different types of complexes with the RGD. The [RGD + 2Cs − H]+ species exhibit the slowest H/D exchange reactivity (reaction rate constant of 6 × 10−13 cm3molecule−1s−1 for the fastest exchanging labile hydrogen with ND3). The reaction rate constant of the protonated RGD is two orders of magnitude faster than that of the [RGD + 2Cs − H]+. Addition of the first cesium to the RGD reduces the H/D exchange reaction rate constant (i.e., D0) by a factor of seven whereas sodium reduces this value by a factor of thirty. Conversely, addition of the second alkali metal ions has the opposite effect; the rate of D0 disappearance for all [RGD + 2Met − H]+ species (MetNa, K, and Cs) decreases with the alkali metal ion size.  相似文献   

3.
Gas-phase hydrogen/deuterium exchange reactions between noncovalent polyamine complexes and D2O, CH3OD, or ND3 are undertaken in a quadrupole ion trap mass spectrometer. Structural features of the protonated polyamines can be differentiated by the rates and overall extent of exchange, specifically the presence of propylene units and/or a cyclic structure noticeably decreases exchange compared to the exchange observed for acyclic polyamines with only ethylene bridges between amino groups. Significant differences are observed for singly protonated vs. doubly protonated complexes, where the doubly protonated complexes undergo more efficient exchange at a higher rate than the analogous singly protonated complexes. Molecular modeling calculations suggest that more diffuse conformations may exist for the higher charge states, thus facilitating H/D exchange. In addition, H/D exchange reactions between the alkali metal cationized complexes and ND3 are nearly quenched, compared to the significant exchange seen for singly protonated complexes. A conformational change or the loss of a low energy reaction pathway may explain the limited exchange reactions seen when a bulky cation replaces a proton in the complex.  相似文献   

4.
One water molecule stabilizes the cationized arginine zwitterion   总被引:1,自引:0,他引:1  
Singly hydrated clusters of lithiated arginine, sodiated arginine, and lithiated arginine methyl ester are investigated using infrared action spectroscopy and computational chemistry. Whereas unsolvated lithiated arginine is nonzwitterionic, these results provide compelling evidence that attachment of a single water molecule to this ion makes the zwitterionic form of arginine, in which the side chain is protonated, more stable. The experimental spectra of lithiated and sodiated arginine with one water molecule are very similar and contain spectral signatures for protonated side chains, whereas those of lithiated arginine and singly hydrated lithiated arginine methyl ester are different and contain spectral signatures for neutral side chains. Calculations at the B3LYP/6-31++G** level of theory indicate that solvating lithiated arginine with a single water molecule preferentially stabilizes the zwitterionic forms of this ion by 25-32 kJ/mol and two essentially isoenergetic zwitterionic structure are most stable. In these structures, the metal ion either coordinates with the N-terminal amino group and an oxygen atom of the carboxylate group (NO coordinated) or with both oxygen atoms of the carboxylate group (OO coordinated). In contrast, the OO-coordinated zwitterionic structure of sodiated arginine, both with and without a water molecule, is clearly lowest in energy for both ions. Hydration of the metal ion in these clusters weakens the interactions between the metal ion and the amino acid, whereas hydrogen-bond strengths are largely unaffected. Thus, hydration preferentially stabilizes the zwitterionic structures, all of which contain strong hydrogen bonds. Metal ion size strongly affects the relative propensity for these ions to form NO or OO coordinated structures and results in different zwitterionic structures for lithiated and sodiated arginine clusters containing one water molecule.  相似文献   

5.
The structures of lithiated lysine, ornithine, and related molecules, both with and without a water molecule, are investigated using both density functional theory and blackbody infrared radiative dissociation experiments. The lowest-energy structure of lithiated lysine without a water molecule is nonzwitterionic; the metal ion interacts with both nitrogen atoms and the carbonyl oxygen. Structures in which lysine is zwitterionic are higher in energy by more than 29 kJ/mol. In contrast, the singly hydrated clusters with the zwitterionic and nonzwitterionic forms of lysine are more similar in energy, with the nonzwitterionic form more stable by only approximately 7 kJ/mol. Thus, a single water molecule can substantially stabilize the zwitterionic form of an amino acid. Analogous molecules that have methyl groups attached to either the N-terminus (NMeLys) or the side-chain amine (Lys(Me)) have proton affinities greater than that of lysine. In the lithiated clusters with a water molecule attached, the zwitterionic forms of NMeLys and Lys(Me) are calculated to be approximately 4 and approximately 11 kJ/mol more stable than the nonzwitterionic forms, respectively. Calculations of the potential-energy pathway for interconversion between the different forms of lysine in the lithiated complex indicate multiple stable intermediates with an overall barrier height of approximately 83 kJ/mol between the lowest-energy nonzwitterionic form and the most accessible zwitterionic form. Experimentally determined binding energies of water are similar for all these complexes and range from 57 to 64 kJ/mol. These results suggest that loss of a water molecule from the lysine complexes is both energetically and entropically favored compared to interconversion between the nonzwitterionic and zwitterionic structures. Comparisons to calculated binding energies of water to the various structures show that the experimental results are most consistent with the nonzwitterionic forms.  相似文献   

6.
The gas-phase structures of protonated and alkali-metal-cationized lysine (Lys) and epsilon-N-methyllysine (Lys(Me)) are investigated using infrared multiple photon dissociation (IRMPD) spectroscopy utilizing light generated by a free electron laser, in conjunction with ab initio calculations. IRMPD spectra of Lys.Li(+) and Lys.Na(+) are similar, but the spectrum for Lys.K(+) is different, indicating that the structure of lysine in these complexes depends on the metal ion size. The carbonyl stretch of a carboxylic acid group is clearly observed in each of these spectra, indicating that lysine is nonzwitterionic in these complexes. A detailed comparison of these spectra to those calculated for candidate low-energy structures indicates that the bonding motif for the metal ion changes from tricoordinated for Li and Na to dicoordinated for K, clearly revealing the increased importance of hydrogen-bonding relative to metal ion solvation with increasing metal ion size. Spectra for Lys(Me).M(+) show that Lys(Me), an analogue of lysine whose side chain contains a secondary amine, is nonzwitterionic with Li and zwitterionic with K and both forms are present for Na. The proton affinity of Lys(Me) is 16 kJ/mol higher than that of Lys; the higher proton affinity of a secondary amine can result in its preferential protonation and stabilization of the zwitterionic form.  相似文献   

7.
Gas-phase structures of noncovalent complexes between the glycopeptide antibiotics vancomycin, eremomycin, ristocetin, and pseudo aglyco-ristocetin and the cell-wall mimicking peptides N-acetyl-D-Alanyl-D-Alanine, N-acetyl-Glycyl-D-Alanine, and N,N′-di-acetyl L-Lysyl-D-Alanyl-D-Alanine have been probed by hydrogen/deuterium (H/D) exchange using ND3 as reagent gas. The noncovalent complexes were transferred from solution to the vacuum using electrospray ionization. The H/D exchange of the solvent-free ions was studied in a Fourier transform ion cyclotron resonance mass spectrometer. The H/D exchange behavior of the free antibiotics and the free peptides were compared with the exchange observed for the antibiotic–peptide complexes. A general increase was found in the degree of deuterium incorporation upon complex formation with the ligand, which indicates that the peptide binding makes more sites on the antibiotic capable of taking part in the H/D exchange. Apart from H/D exchange, adduct formation with ND3 was observed, but only for the singly protonated peptides and the doubly protonated [ristocetin+N-acetyl-D-Alanyl-D-Alanine]. This marked difference in chemical reactivity of closely related systems such as [ristocetin+N-acetyl-Glycyl-D-Alanine] and [ristocetin+N-acetyl-D-Alanyl-D-Alanine] indicates that the gas-phase structures of these noncovalent complexes are quite sensitive to small changes in the primary structures of the peptides. The gas-phase structures of the antibiotic–peptide complexes are probably different from the solution-phase structures, with the peptides no longer bound to the characteristic solution-phase binding pockets of the antibiotics.  相似文献   

8.
The relative stabilities of zwitterionic and canonical forms of neutral arginine and of its protonated derivative were studied by using ab initio electronic structure methods. Trial structures were first identified at the PM3 level of theory with use of a genetic algorithm to systematically vary geometrical parameters. Further geometry optimizations of these structures were performed at the MP2 and B3LYP levels of theory with basis sets of the 6-31++G** quality. The final energies were determined at the CCSD/6-31++G** level and corrected for thermal effects determined at the B3LYP level. Two new nonzwitterionic structures of the neutral were identified, and one of them is the lowest energy structure found so far. The five lowest energy structures of neutral arginine are all nonzwitterionic in nature and are clustered within a narrow energy range of 2.3 kcal/mol. The lowest energy zwitterion structure is less stable than the lowest nonzwitterion structure by 4.0 kcal/mol. For no level of theory is a zwitterion structure suggested to be the global minimum. The calculated proton affinity of 256.3 kcal/mol and gas-phase basicity of 247.8 kcal/mol of arginine are in reasonable agreement with the measured values of 251.2 and 240.6 kcal/mol, respectively. The calculated vibrational characteristics of the low-energy structures of neutral arginine provide an alternative interpretation of the IR-CRLAS spectrum (Chapo et al. J. Am. Chem. Soc. 1998, 120, 12956-12957).  相似文献   

9.
The structures of lithiated and sodiated glutamine, both with and without a water molecule, are investigated using experiment and theory. Loss of water from these complexes and from lithiated and sodiated complexes of asparagine methyl ester, asparagine ethyl ester, and glutamine methyl ester is probed with blackbody infrared radiative dissociation experiments performed over a wide temperature range. Threshold dissociation energies, E(o), for loss of a water molecule from these complexes are obtained from master equation modeling of these data. The values of E(o) are 63 +/- 1 and 53 +/- 1 kJ/mol for the lithiated and sodiated glutamine complexes, respectively. These values are similar to those for the nonzwitterionic model complexes and are in excellent agreement with calculated values. In contrast, water binding to the zwitterionic form is calculated to be significantly higher. These results indicate that glutamine in these lithiated and sodiated complexes with a water molecule are nonzwitterionic. Complexes with the asparagine side chain have slightly higher E(o) values than those with the glutamine side chain, a result consistent with more effective solvation of the metal ion due to the slightly longer side chain of glutamine. Calculations indicate that lithiated and sodiated glutamine are nonzwitterionic, with the metal ion interacting with the amine nitrogen and carbonyl oxygen from the amino acid backbone and the amide oxygen of the side chain. Addition of a water molecule does not affect the lowest-energy structure of lithiated glutamine, whereas, for sodiated glutamine, the lowest-energy zwitterionic and nonzwitterionic structures are essentially isoenergetic.  相似文献   

10.
The gas-phase interaction of sodiated amino acids and sodiated amino acid methyl esters with various deuterium donors is investigated by combining results of H/D exchange reactions with those from density functional theory and molecular dynamics calculations. Discrepancy between experimentally and theoretically obtained structures for sodium cationized amino acids is explained by deuterium donor caused perturbation of the most stable amino acid conformation. Detailed study of H/D exchange mechanism on sodiated amino acids shows that the H/D exchange reaction is preceded by a multistep quasi-isoenergetic transition (perturbation) from a charge solvated to zwitterionic structure in the amino acid. Although the computation refers to the system AlaNa(+) and D(2)O, these mechanisms apply to all amino acids, except those where a functional side-chain group takes part in the perturbation process. The suggested perturbation mechanism applies also for other deuterium donors such as CD(3)OD or even ND(3) and indicates that a single water molecule suffices to convert the sodiated amino acid from charge solvated to zwitterionic form.  相似文献   

11.
The structures of isolated alkaline earth metal cationized amino acids are investigated using infrared multiple photon dissociation (IRMPD) spectroscopy and theory. These results indicate that arginine, glutamine, proline, serine, and valine all adopt zwitterionic structures when complexed with divalent barium. The IRMPD spectra for these ions exhibit bands assigned to carboxylate stretching modes, spectral signatures for zwitterionic amino acids, and lack bands attributable to the carbonyl stretch of a carboxylic acid functional group. Structural and spectral assignments are strengthened through comparisons with absorbance spectra calculated for low-energy structures and the IRMPD spectra of analogous ions containing monovalent alkali metals. Many bands are significantly red-shifted from the corresponding bands for amino acids complexed with monovalent metal ions, owing to increased charge transfer to divalent metal ions. The IRMPD spectra of arginine complexed with divalent strontium and barium are very similar and indicate that arginine adopts a zwitterionic form in both ions. Calculations indicate that nonzwitterionic forms of arginine are lowest in free energy in complexes with smaller alkaline earth metal cations and that zwitterionic forms are preferentially stabilized with increasing metal ion size. B3LYP and MP2 calculations indicate that zwitterionic forms of arginine are lowest in free energy for M = Ca, Sr, and Ba.  相似文献   

12.
The modes of metal-ion and water binding in doubly hydrated complexes of lithiated and sodiated glutamine (Gln) are probed using blackbody infrared radiative dissociation experiments and density functional theory calculations. Threshold dissociation energies, E0, for loss of a water molecule from these complexes are obtained from master-equation modeling of these data. The values of E0 are 36 +/- 1 and 38 +/- 2 kJ/mol for the lithiated and sodiated glutamine complexes, respectively, and are consistent with calculated water binding energies for the nonzwitterionic form of these complexes. Calculated water binding energies for the zwitterionic forms of these complexes are significantly higher. In contrast, calculations indicate that the zwitterionic form of Gln in these complexes is more stable than the nonzwitterionic form by 8 and 15 kJ/mol when lithiated and sodiated, respectively. Doubly hydrated lithiated and sodiated complexes of asparagine methyl ester (AsnOMe), asparagine ethyl ester (AsnOEt), and glutamine methyl ester (GlnOMe) were also studied for comparison to Gln. Although these clusters lack the acidic group of Gln and therefore have different water coordination behavior, these results further support the conclusion that Gln is nonzwitterionic in these clusters. Surprisingly, the complexes containing sodium are more stable than those containing lithium, a result that is attributed to subtle differences in how these two metal ions bind to the amino acid esters in these complexes.  相似文献   

13.
Density functional theory has been employed to model the structure and the relative stabilities of alpha/beta-alanine conformers and their protonated and alkali metal cationized complexes. In general, we find that the behavior of the beta-alanine (beta-Ala) system is quite similar to that of alpha-alanine (alpha-Ala). However, the presence of the methylene group (-CH2-) at the beta position in beta-Ala leads to a few key differences. First, the intramolecular hydrogen bonding patterns are different between free alpha- and beta-Ala. Second, the stability of zwitterionic species (in either the free ligand or alkali metal cationized complexes) is often enhanced in beta-Ala. Third, the preferred mode of alkali metal cation (M+) binding may also differ in alpha- and beta-Ala. Natural energy decomposition analysis has been applied here to gain further insight into the effects of the ligand, cation size, and mode of binding on the nature of interaction in these M+-Ala complexes.  相似文献   

14.
The mode of metal ion and water binding to the amino acid valine is investigated using both theory and experiment. Computations indicate that without water, the structure of valine is nonzwitterionic. Both Li(+) and Na(+) are coordinated to the nitrogen and carbonyl oxygen (NO coordination), whereas K(+) coordinates to both oxygens (OO coordination) of nonzwitterionic valine. The addition of a single water molecule does not significantly affect the relative energies calculated for the cationized valine clusters. Experimentally, the rates of water evaporation from clusters of Val.M(+)(H(2)O)(1), M = Li, Na, and K, are measured using blackbody infrared radiative dissociation. The dissociation rate from the valine complex is compared to water evaporation rates from model complexes of known structure. These results indicate that the metal ion in the lithiated and the sodiated clusters is NO-coordinated to nonzwitterionic valine, while that in the potassiated cluster has OO coordination, in full agreement with theory. The zwitterionic vs nonzwitterionic character of valine in the potassiated cluster cannot be distinguished experimentally. Extensive modeling provides strong support for the validity of inferring structural information from the kinetic data.  相似文献   

15.
Gas-phase ion/molecule reactions and collision-induced dissociation (CID) were conducted on [M + 4H]4+ of insulin chain B. This Fourier transform mass spectrometry work involved ions from the oxidized peptide (with two cysteic acid residues) and its reduced form (with two cysteine residues). Kinetic behavior during deprotonation and hydrogen/deuterium exchange reactions indicates that insulin B (ox) ions have two distinct structural types. In contrast, insulin B (red) ions have only one major reacting population, which has a more compact structure than the oxidized ions. No significant differences in fragmentation patterns for the two insulin B (ox) populations were observed when CID was performed as a function of deprotonating reaction time. However, markedly different fragmentation was found between [M + 4H]4+ of insulin B (ox) and (red). Therefore, the presence of cysteic acid groups in insulin B (ox) significantly impacts dissociation and presumably structure. This suggests that some insulin B (ox) ions are zwitterionic, with the five basic sites protonated and one cysteic acid group deprotonated. Molecular dynamics calculations revealed several viable structures that are consistent with the experimental results. For example, the most stable form of the reduced ion, which is unprotonated at the His10, is very compact and has lost the alpha-helix of native insulin. Low energy structures for the oxidized ions include a zwitterion with an intraionic interaction between anionic Cyx7 and cationic His10, as well as a nonzwitterionic conformer that lacks a proton at Phe1; both structures retain the alpha-helix. These structures may account for the two experimentally observed isomers, although others are possible. In addition, experiments on oxidized insulin B were conducted from methanolic solution, which may denature the conformation, and pure aqueous solution, which may leave a native conformation. These differences in solvent composition had no effect on the gas-phase results.  相似文献   

16.
MSn experiments involving low energy collisionally activated dissociation (CAD) in a quadrupole ion trap were used to characterize the fragmentation of alkali, alkaline earth and transition metal complexes of five cyclic peptides, and the results were compared with those obtained for protonated cyclic peptides. Complexes with metal ions produced enhanced abundances of the most diagnostic fragments for elucidating the primary structures. For cyclosporin A, nickel and lithium complexes gave additional sequence information compared with the protonated peptide. For depsipeptides, sodium and lead complexes were superior to the protonated peptide or other metal complexes for sequencing residues, and CAD of the lead complexes led to preferential cleavage of two residues at a time. For cyclic lipopeptides, complexes with silver, nickel and strontium ions provided enhanced abundances of key fragment ions.  相似文献   

17.
The complexes formed by alkali metal cations (Cat(+) = Li(+), Na(+), K(+), Rb(+)) and singly charged tryptic peptides were investigated by combining results from the low-energy collision-induced dissociation (CID) and ion mobility experiments with molecular dynamics and density functional theory calculations. The structure and reactivity of [M + H + Cat](2+) tryptic peptides is greatly influenced by charge repulsion as well as the ability of the peptide to solvate charge points. Charge separation between fragment ions occurs upon dissociation, i.e. b ions tend to be alkali metal cationised while y ions are protonated, suggesting the location of the cation towards the peptide N-terminus. The low-energy dissociation channels were found to be strongly dependant on the cation size. Complexes containing smaller cations (Li(+) or Na(+)) dissociate predominantly by sequence-specific cleavages, whereas the main process for complexes containing larger cations (Rb(+)) is cation expulsion and formation of [M + H](+). The obtained structural data might suggest a relationship between the peptide primary structure and the nature of the cation coordination shell. Peptides with a significant number of side chain carbonyl oxygens provide good charge solvation without the need for involving peptide bond carbonyl groups and thus forming a tight globular structure. However, due to the lack of the conformational flexibility which would allow effective solvation of both charges (the cation and the proton) peptides with seven or less amino acids are unable to form sufficiently abundant [M + H + Cat](2+) ion. Finally, the fact that [M + H + Cat](2+) peptides dissociate similarly as [M + H](+) (via sequence-specific cleavages, however, with the additional formation of alkali metal cationised b ions) offers a way for generating the low-energy CID spectra of 'singly charged' tryptic peptides.  相似文献   

18.
The gas-phase structures of alkali-metal cationized glutamine are investigated by using both infrared multiple photon dissociation (IRMPD) action spectroscopy, utilizing light generated by a free electron laser, and theory. The IRMPD spectra contain many similarities that are most consistent with glutamine adopting nonzwitterionic forms in all ions, but differences in the spectra indicate that the specific nonzwitterionic forms adopted depend on metal-ion identity. For ions containing small alkali metals, the metal ion is solvated predominantly by the amino group, the carbonyl oxygen of the carboxylic acid group, and the carbonyl oxygen of the amide group. With increasing alkali-metal-ion size, additional structures are present in which the carboxylic acid group donates a hydrogen bond to the amino group and the metal ion is solvated only by the amide and carboxylic acid groups. The effects of alkylation of the amino and amide groups on the proton affinity of isolated glutamine and the relative zwitterion stability of sodiated glutamine were examined computationally. Methylation of the amino group increases the proton affinity of isolated glutamine and preferentially stabilizes the zwitterionic form of sodiated glutamine by roughly 20 kJ/mol. Ethylation and isopropylation of the amide group each increase the proton affinity of isolated glutamine by roughly 13 kJ/mol but preferentially stabilize the zwitterionic form of sodiated glutamine by less than 3 kJ/mol. These results indicate that effects of proton affinity on relative zwitterion stability compete with effects of metal-ion solvation.  相似文献   

19.
Mass analysis of proteolytic fragment peptides following hydrogen/deuterium exchange offers a general measure of solvent accessibility/hydrogen bonding (and thus conformation) of solution-phase proteins and their complexes. The primary problem in such mass analyses is reliable and rapid assignment of mass spectral peaks to the correct charge state and degree of deuteration of each fragment peptide, in the presence of substantial overlap between isotopic distributions of target peptides, autolysis products, and other interferant species. Here, we show that at sufficiently high mass resolving power (m/Δm50% ≥ 100,000), it becomes possible to resolve enough of those overlaps so that automated data reduction becomes possible, based on the actual elemental composition of each peptide without the need to deconvolve isotopic distributions. We demonstrate automated, rapid, reliable assignment of peptide masses from H/D exchange experiments, based on electrospray ionization FT-ICR mass spectra from H/D exchange of solution-phase myoglobin. Combined with previously demonstrated automated data acquisition for such experiments, the present data reduction algorithm enhances automation (and thus expands generality and applicability) for high-resolution mass spectrometry-based analysis of H/D exchange of solution-phase proteins.  相似文献   

20.
A model was developed to describe the deuterium uptake of gas phase polypeptide ions via H/D exchange with D2O. Ab initio calculations established, for energetic reasons, that the exchange must take place via a “relay” mechanism involving both a charged site and a nearby basic site. Molecular dynamics simulations indicated that the D2O molecule did not penetrate the core of the example peptide, protonated bradykinin (Bk+H)+, and hence the relay mechanism must occur on the peptide surface. Two factors were deemed to be important: (1) The surface accessibility of the charged sites and the basic sites and (2) the distances between them. An algorithm was developed that accounted for these features using the absolute exchange rate as a free parameter. Excellent agreement was obtained with experiment when equal weight was given to an ensemble of low energy conformations of (Bk+H)+, assumed to have a salt bridge primary structure. Single conformations, or other protonated forms, did not allow good agreement with experiment for any value of the absolute exchange rate constant.  相似文献   

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