Determination of the Rate Constants k1 and k2 of the Linderstrøm-Lang Model for Protein Amide Hydrogen Exchange

Pedersen, Torben Graves; Thomsen, Niels Kirk; Andersen, Kim; Madsen, Jes; Poulsen, Flemming M.

doi:10.1006/jmbi.1993.1176

Cited by 55 publications

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“…However, determination of the closing rate, k cl , requires the rate constants for proton transfer in the open state, k H and k OH . These rate constants can be influenced by steric and electrostatic features of the open state, which are not known (20,30). Therefore, to estimate ␦ ⌬G op 0 , we have made the following two assumptions: (i) the rate constants k H for His␣103(G10) and k OH for His␣122(H5) are pH-independent, and their values are similar to those in model compounds (10 9 -10 10 M Ϫ1 s Ϫ1 ) (27,31), and (ii) these rate constants are the same in deoxy and in ligated Hb A.…”

Section: Allosteric Free Energy Changes At His␣103(g10) and His␣122(hmentioning

confidence: 99%

A signature of the T → R transition in human hemoglobin

Mihailescu

Russu

2001

Proc. Natl. Acad. Sci. U.S.A.

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Allosteric effects in hemoglobin arise from the equilibrium between at least two energetic states of the molecule: a tense state, T, and a relaxed state, R. The two states differ from each other in the number and energy of the interactions between hemoglobin subunits. In the T state, constraints between subunits oppose the structural changes resulting from ligand binding. In the R state, these constraints are released, thus enhancing ligand-binding affinity. In the present work, we report the presence of four sites in hemoglobin that are structurally stabilized in the R relative to the T state. These sites are His␣103(G10) and His␣122(H5) in each ␣ subunit of hemoglobin. They are located at the ␣1␤1 and ␣2␤2 interfaces of the hemoglobin tetramer, where the histidine side chains form hydrogen bonds with specific residues from the ␤ chains. We have measured the solvent exchange rates of side chain protons of His␣103(G10) and His␣122(H5) in both deoxygenated and ligated hemoglobin by NMR spectroscopy. The exchange rates were found to be higher in the deoxygenated-T than in ligated-R state. Analysis of exchange rates in terms of the local unfolding model revealed that the structural stabilization free energy at each of these two histidines is larger by Ϸ1.5 kcal͞(mol tetramer) in the R relative to the T state. The location of these histidines at the intradimeric ␣1␤1 and ␣2␤2 interfaces also suggests a role for these interfaces in the allosteric equilibrium of hemoglobin.T he Hb molecule has been a paradigm for understanding the molecular events underlying biological function. Cooperative oxygen-binding and allosteric effects have been rationalized by global thermodynamic models that postulate states of the molecule with specific energetic features (1-3). In the two-state model proposed by Monod, Wyman, and Changeux (2), the two energetic states are the tense (T) and the relaxed (R) states. The two states differ from each other in their affinity for ligand and in the interactions between subunits. Binding of oxygen to the deoxygenated (deoxy)-T state occurs with low affinity. However, the binding of the ligand destabilizes the T state and makes it more likely to switch to the high-affinity oxygenated (oxy)-R state. Thus, as ligation proceeds, the gradual enrichment in Hb molecules in the R state accounts for cooperativity in ligand binding. The success of this model in explaining the function of Hb has promoted its general application to a large variety of systems, including allosteric protein systems and nucleic acidbinding proteins (reviewed in refs. 4 and 5). However, the structural basis of this thermodynamic model is not yet fully understood.The first insights into the molecular structures representing the T and R thermodynamic states of Hb have been provided by crystallographic results on deoxy and ligated Hb obtained by Perutz (6, 7). The deoxy-T and ligated-R structures maintain the same ␣ 1 ␤ 1 and ␣ 2 ␤ 2 interfaces within ␣␤ dimers but differ greatly at the ␣ 1 ␤ 2 and ␣ 2 ␤ 1 interfaces between the two d...

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Section: Allosteric Free Energy Changes At His␣103(g10) and His␣122(hmentioning

confidence: 99%

A signature of the T → R transition in human hemoglobin

Mihailescu

Russu

2001

Proc. Natl. Acad. Sci. U.S.A.

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“…The EX2 limit is almost always observed in the pH range between 4 and 7 (Bai et al, 1995) because formation of hydrogen-bonded structure is usually much faster than intrinsic exchange (Englander & Kallenbach, 1984). In kinetic experiments, where pH values ranging between 9 and 1 1 are often necessary to achieve hydrogen-exchange timescales (-1 ms) comparable to those for protein folding or unfolding (Baldwin, 1993), hydrogen exchange may be in the EX1 regime (Englander & Mayne, 1992) or in the range between the EX1 and EX2 limits (Pedersen et al, 1993). The pH dependence of kob., can be used to distinguish between EX1 and EX2 mechanisms, provided krl and k, are invariant as a function of pH (Pedersen et al, 1993).…”

Section: Kc/mentioning

confidence: 99%

“…In kinetic experiments, where pH values ranging between 9 and 1 1 are often necessary to achieve hydrogen-exchange timescales (-1 ms) comparable to those for protein folding or unfolding (Baldwin, 1993), hydrogen exchange may be in the EX1 regime (Englander & Mayne, 1992) or in the range between the EX1 and EX2 limits (Pedersen et al, 1993). The pH dependence of kob., can be used to distinguish between EX1 and EX2 mechanisms, provided krl and k, are invariant as a function of pH (Pedersen et al, 1993).It is possible to correct for the effects of pH, temperature, and protein sequence (to a first approximation nearest neighbor effects) by normalizing against exchange rates for model peptides (k,,,<,<,). In the EX2 limit, with the assumption k,, -kmc,dr Equation 3 can be recast to a form that describes an equilibrium constant relating the concentrations of open and closed conformations:…”

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confidence: 99%

A fragment of staphylococcal nuclease with an OB‐fold structure shows hydrogen‐exchange protection factors in the range reported for “molten globules”

1996

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Hydrogen-exchange rates for an OB-fold subdomain fragment of staphylococcal nuclease have been measured at pH 4.7 and 4 "C, conditions close to the minimum of acidlbase catalyzed exchange. The strongest protection from solvent exchange is observed for residues from a five-stranded P-barrel in the NMR structure of the protein. Protection factors, calculated from the experimental hydrogen-exchange rates, range between 1 and 190. Similarly small protection factors have in many cases been attributed to "molten globule" conformations that are supposed to lack a specific tertiary structure. The present results suggest that marginal protection from solvent exchange does not exclude welldefined structure.Keywords: hydrogen exchange; kinetic intermediate; molten globule; NMR structure; protection factors; protein folding A common application of hydrogen-exchange methodology is the characterization of species that are not amenable to direct NMR study. These include short-lived kinetic folding intermediates (Roder et al., 1988; Udgaonkar & Baldwin, 1988), equilibrium folding intermediates with large line-broadening contributions due to conformational exchange or aggregation (Hughson et al., 1990) proteinchaperone complexes that are otherwise too large for NMR analysis (Zahn et al., 1994), and subglobal unfolding units whose concentrations are too small to allow direct NMR detection (Bai et al., 1995). Hydrogen-exchange data are usually analyzed in terms of the Linderstrom-Lang (1955) Exchange is believed to occur due to transient "breaking" of hydrogen bonds, through either local or global fluctuations in protein structure. In the EX1 limit, the rate of closing (kc/) is much slower than the intrinsic "chemical" rate of exchange (kch), and the observed rate (kobs) is limited by the opening rate (kc,p):In the EX2 limit, kc, is much faster than kc,, and kohs is limited by the fraction of conformations in the open state:In the EX1 limit, hydrogen exchange is pH-independent, whereas in the EX2 limit, kc, and hence kobs increase IO-fold with each pH unit (Baldwin, 1993). The EX2 limit is almost always observed in the pH range between 4 and 7 (Bai et al., 1995) because formation of hydrogen-bonded structure is usually much faster than intrinsic exchange (Englander & Kallenbach, 1984). In kinetic experiments, where pH values ranging between 9 and 1 1 are often necessary to achieve hydrogen-exchange timescales (-1 ms) comparable to those for protein folding or unfolding (Baldwin, 1993), hydrogen exchange may be in the EX1 regime (Englander & Mayne, 1992) or in the range between the EX1 and EX2 limits (Pedersen et al., 1993). The pH dependence of kob., can be used to distinguish between EX1 and EX2 mechanisms, provided krl and k, are invariant as a function of pH (Pedersen et al., 1993).It is possible to correct for the effects of pH, temperature, and protein sequence (to a first approximation nearest neighbor effects) by normalizing against exchange rates for model peptides (k,,,<,<,). In the EX2 limit, with the assump...

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“…1 1 . In lysozyme (Radford et al, 1992;Pedersen et al, 1993) and leucine zipper peptides (Goodman & Kim, 1991), there are helices in which buried protons exchange more slowly than solvent-exposed protons.…”

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confidence: 99%

A statistical mechanical model for hydrogen exchange in globular proteins

Miller

Dill

1995

Protein Sci.

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We develop a statistical mechanical theory for the mechanism of hydrogen exchange in globular proteins. Using the H P lattice model, we explore how the solvent accessibilities of chain monomers vary as proteins fluctuate from their stable native conformations. The model explains why hydrogen exchange appears to involve two mechanisms under different conditions of protein stability: (1) a "global unfolding" mechanism by which all protons exchange at a similar rate, approaching that of the denatured protein, and (2) a "stable-state" mechanism by which protons exchange at rates that can differ by many orders of magnitude. There has been some controversy about the stable-state mechanism: does exchange take place inside the protein by solvent penetration, or outside the protein by the local unfolding of a subregion? The present model indicates that the stable-state mechanism of exchange occurs through an ensemble of conformations, some of which may bear very little resemblance to the native structure. Although most fluctuations are small-amplitude motions involving solvent penetration or local unfolding, other fluctuations (the conformational distant relatives) can involve much larger transient excursions to completely different chain folds.

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Determination of the Rate Constants k1 and k2 of the Linderstrøm-Lang Model for Protein Amide Hydrogen Exchange

Cited by 55 publications

References 0 publications

A signature of the T → R transition in human hemoglobin

A signature of the T → R transition in human hemoglobin

A fragment of staphylococcal nuclease with an OB‐fold structure shows hydrogen‐exchange protection factors in the range reported for “molten globules”

A statistical mechanical model for hydrogen exchange in globular proteins

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