Protein hydrogen exchange mechanism: local fluctuations

Experiments were done to study the dynamic structural motions that determine protein hydrogen exchange (HX) behavior. The replacement of a solvent-exposed lysine residue with glycine (Lys8Gly) in a helix of recombinant cytochrome c does not perturb the native structure, but it entropically potentiates main-chain flexibility and thus can promote local distortional motions and large-scale unfolding. The mutation accelerates amide hydrogen exchange of the mutated residue by about 50-fold, neighboring residues in the same helix by less, and residues elsewhere in the protein not at all, except for Leu98, which registers the change in global stability. The pattern of HX changes shows that the coupled structural distortions that dominate exchange can be several residues in extent, but they expose to exchange only one amide NH at a time. This "local fluctuation" mode of hydrogen exchange may be generally recognized by disparate near-neighbor rates and a low dependence on destabilants (denaturant, temperature, pressure). In contrast, concerted unfolding reactions expose multiple neighboring amide NHs with very similar computed protection factors, and they show marked destabilant sensitivity. In both modes, ionic hydrogen exchange catalysts attack from the bulk solvent without diffusing through the protein matrix.     

A direct test of the reductionist approach to structural studies of calmodulin activity: relevance of peptide models of target proteins

Ca(2+)-saturated calmodulin (CaM) directly associates with and activates CaM-dependent protein kinase I (CaMKI) through interactions with a short sequence in its regulatory domain. Using heteronuclear NMR (13)C-(15)N-(1)H correlation experiments, the backbone assignments were determined for CaM bound to a peptide (CaMKIp) corresponding to the CaM-binding sequence of CaMKI. A comparison of chemical shifts for free CaM with those of the CaM.CaMKIp complex indicate large differences throughout the CaM sequence. Using NMR techniques optimized for large proteins, backbone resonance assignments were also determined for CaM bound to the intact CaMKI enzyme. NMR spectra of CaM bound to either the CaMKI enzyme or peptide are virtually identical, indicating that calmodulin is structurally indistinguishable when complexed to the intact kinase or the peptide CaM-binding domain. Chemical shifts of CaM bound to a peptide (smMLCKp) corresponding to the calmodulin-binding domain of smooth muscle myosin light chain kinase are also compared with the CaM.CaMKI complexes. Chemical shifts can differentiate one complex from another, as well as bound versus free states of CaM. In this context, the observed similarity between CaM.CaMKI enzyme and peptide complexes is striking, indicating that the peptide is an excellent mimetic for interaction of calmodulin with the CaMKI enzyme.     

Direct evidence for the cooperative unfolding of cytochrome c in lipid membranes from H-(2)H exchange kinetics

The interaction of cytochrome c (cyt c) with anionic lipid membranes is known to disrupt the tightly packed native structure of the protein. This process leads to a lipid-inserted denatured state, which retains a native-like alpha-helical structure but lacks any specific tertiary interactions. The structural and dynamic properties of cyt c bound to vesicles containing an anionic phospholipid (DOPS) were investigated by amide H-(2)H exchange using two-dimensional NMR spectroscopy and electrospray ionisation mass spectrometry. The H-(2)H exchange kinetics of the core amide protons in cyt c, which in the native protein undergo exchange via an uncorrelated EX2 mechanism, exchange in the lipid vesicles via a highly concerted global transition that exposes these protected amide groups to solvent. The lack of pH dependence and the observation of distinct populations of deuterated and protonated species by mass spectrometry confirms that exchange occurs via an EX1 mechanism with a common rate of 1(+/-0.5) h(-1), which reflects the rate of transition from the lipid-inserted state, H(l), to an unprotected conformation, D(i), associated with the lipid interface.     

Backbone and side chain dynamics of mutant calmodulin-peptide complexes

The mechanism of long-range coupling of allosteric sites in calcium-saturated calmodulin (CaM) has been explored by characterizing structural and dynamics effects of mutants of calmodulin in complex with a peptide corresponding to the smooth muscle myosin light chain kinase calmodulin-binding domain (smMLCKp). Four CaM mutants were examined: D95N and D58N, located in Ca2+-binding loops; and M124L and E84K, located in the target domain-binding site of CaM. Three of these mutants have altered allosteric coupling either between Ca2+-binding sites (D58N and D95N) or between the target- and Ca2+-binding sites (E84K). The structure and dynamics of the mutant calmodulins in complex with smMLCKp were characterized using solution NMR. Analysis of chemical shift perturbations was employed to detect largely structural perturbations. 15N and 2H relaxation was employed to detect perturbations of the dynamics of the backbone and methyl-bearing side chains of calmodulin. The least median squares method was found to be robust in the detection of perturbed sites. The main chain dynamics of calmodulin are found to be largely unresponsive to the mutations. Three mutants show significantly perturbed dynamics of methyl-bearing side chains. Despite the pseudosymmetric location of Ca2+-binding loop mutations D58N and D95N, the dynamic response of CaM is asymmetric, producing long-range perturbation in D58N and almost none in D95N. The mutations located at the target domain-binding site have quite different effects. For M124L, a local perturbation of the methyl dynamics is observed, while the E84K mutation produces a long-range propagation of dynamic perturbations along the target domain-binding site.     

Hydrogen exchange kinetics of core peptide protons in Streptomyces subtilisin inhibitor

The hydrogen isotope exchange kinetics of the 10 slowest exchanging resonances in the 1H NMR spectrum of Streptomyces subtilisin inhibitor (SSI) have been determined at pH 7-11 and 30-60 degrees C. These resonances are assigned to peptide amide protons in the beta-sheet core that comprises the extensive protein-protein interface of the tightly bound SSI dimer. The core protons are atypical in that their exchange rates are orders of magnitude slower than those for all other SSI protons. When they do exchange at temperatures greater than 50 degrees C, they do so as a set and with a very high temperature coefficient. The pH dependence of the exchange rate constants is also atypical. Exchange rates are approximately first order in hydroxyl ion dependence at pH less than 8.5 and greater than 9.5 and pH independent between pH 8.5 and 9.5. The pH dependence and temperature dependence of the SSI proton exchange rates are interpreted by the two-process model [Woodward, C. K., & Hilton, B. D. (1980) Biophys. J. 32, 561-575]. The results suggest that in the average solution structure of SSI, an unusual mobility of secondary structural elements at the protein surface is, in a sense, compensated by an unusual rigidity and inaccessibility of the beta-sheet core at the dimer interface.     

1H NMR study on amide proton exchange of calmodulin-mastoparan complex

Amide proton exchange rates of Ca2(+)-saturated calmodulin and Ca2(+)-saturated calmodulin-mastoparan complex were studied by 1H NMR spectroscopy. Exchange rates of Gly25, Gly61, Gly98, Gly134, Ile27, Ile100, and Asn137 were determined for Ca2(+)-saturated calmodulin and for Ca2(+)-saturated calmodulin-mastoparan complex, and were found to be less than 10(-4)s-1. All these residues of which the amide proton resonances appear at lower fields were considered to form hydrogen bonds, based on the results of X-ray analysis. Exchange rates of Ile27 and Asn137 became an order of magnitude smaller when mastoparan bound to Ca2(+)-saturated calmodulin, while those of the four glycines and Ile100 did not change appreciably. The reduction in accessibility of Asn137 to water cased by mastoparan binding suggests that a part of the mastoparan binding site is probably located in or near the hydrophobic cluster of the C-terminal-half domain. The reduction in accessibility of Ile27 also suggests that another part of the mastoparan binding site is located in or near the hydrophobic cleft of the N-terminal-half domain.     

Early formation of a beta hairpin during folding of staphylococcal nuclease H124L as detected by pulsed hydrogen exchange

Pulsed hydrogen exchange methods were used to follow the formation of structure during the refolding of acid-denatured staphylococcal nuclease containing a stabilizing Leu substitution at position 124 (H124L SNase). The protection of more than 60 backbone amide protons in uniformly (15)N-labeled H124L SNase was monitored as a function of refolding time by heteronuclear two-dimensional NMR spectroscopy. As found in previous studies of staphylococcal nuclease, partial protection was observed for a subset of amide protons even at the earliest folding time point (10 msec). Protection indicative of marginally stable hydrogen-bonded structure in an early folding intermediate was observed at over 30 amide positions located primarily in the beta-barrel and to a lesser degree in the alpha-helical domain of H124L SNase. To further characterize the folding intermediate, protection factors for individual amide sites were measured by varying the pH of the labeling pulse at a fixed refolding time of 16 msec. Protection factors >5.0 were observed only for amide positions in a beta-hairpin formed by strands 2 and 3 of the beta-barrel domain and a single site near the C-terminus. The results indicate that formation of stable hydrogen-bonded structure in a core region of the beta-sheet is among the earliest structural events in the folding of SNase and may serve as a nucleation site for further structure formation.     

Structural,energetic, and dynamic responses of the native state ensemble of staphylococcal nuclease to cavity‐creating mutations

The effects of cavity‐creating mutations on the structural flexibility, local and global stability, and dynamics of the folded state of staphylococcal nuclease (SNase) were examined with NMR spectroscopy, MD simulations, H/D exchange, and pressure perturbation. Effects on global thermodynamic stability correlated well with the number of heavy atoms in the vicinity of the mutated residue. Variants with substitutions in the C‐terminal domain and the interface between α and β subdomains showed large amide chemical shift variations relative to the parent protein, moderate, widespread, and compensatory perturbations of the H/D protection factors and increased local dynamics on a nanosecond time scale. The pressure sensitivity of the folded states of these variants was similar to that of the parent protein. Such observations point to the capacity of the folded proteins to adjust to packing defects in these regions. In contrast, cavity creation in the β‐barrel subdomain led to minimal perturbation of the structure of the folded state, However, significant pressure dependence of the native state amide resonances, along with strong effects on native state H/D exchange are consistent with increased probability of population of excited state(s) for these variants. Such contrasted responses to the creation of cavities could not be anticipated from global thermodynamic stability or crystal structures; they depend on the local structural and energetic context of the substitutions. © 2012 Wiley Periodicals, Inc.     

The native state conformational ensemble of the SH3 domain from alpha-spectrin.

The folding/unfolding equilibrium of the alpha-spectrin SH3 domain has been measured by NMR-detected hydrogen/deuterium exchange and by differential scanning calorimetry. Protection factors against exchange have been obtained under native conditions for more than half of the residues in the domain. Most protected residues are located at the beta-strands, the short 3(10) helix, and part of the long RT loop, whereas the loops connecting secondary structure elements show no measurable protection. Apparent stability constants per residue and their corresponding Gibbs energies have been calculated from the exchange experiments. The most stable region of the SH3 domain is defined by the central portions of the beta-strands. The peptide binding region, on the other hand, is composed of a highly stable region (residues 53-57) and a highly unstable region, the loop between residues 34-41 (n-Src loop). All residues in the domain have apparent Gibbs energies lower than the global unfolding Gibbs energy measured by differential scanning calorimetry, indicating that under our experimental conditions the amide exchange of all residues in the SH3 domain occurs primarily via local unfolding reactions. A structure-based thermodynamic analysis has allowed us to predict correctly the thermodynamics of the global unfolding of the domain and to define the ensemble of conformational states that quantitatively accounts for the observed pattern of hydrogen exchange protection. These results demonstrate that under native conditions the SH3 domain needs to be considered as an ensemble of conformations and that the hydrogen exchange data obtained under those conditions cannot be interpreted by a two-state equilibrium. The observation that specific regions of a protein are able to undergo independent local folding/unfolding reactions indicates that under native conditions the scale of cooperative interactions is regional rather than global.     

GuHCl and NaCl-dependent hydrogen exchange in MerP reveals a well-defined core with an unusual exchange pattern

We have analysed hydrogen exchange at amide groups to characterise the energy landscape of the 72 amino acid residue protein MerP. From the guanidine hydrochloride (GuHCl) dependence of exchange in the pre-transitional region we have determined free energy values of exchange (DeltaG(HX)) and corresponding m-values for individual amide protons. Detailed analysis of the exchange patterns indicates that for one set of amide protons there is a weak dependence on denaturant, indicating that the exchange is dominated by local fluctuations. For another set of amide protons a linear, but much stronger, denaturant dependence is observed. Notably, the plots of free energy of exchange versus [GuHCl] for 16 amide protons show pronounced upward curvature, and a close inspection of the structure shows that these residues form a well-defined core in the protein. The hydrogen exchange that was measured at various concentrations of NaCl shows an apparent selective stabilisation of this core. Detailed analysis of this exchange pattern indicates that it may originate from selective destabilisation of the unfolded state by guanidinium ions and/or selective stabilisation of the core in the native state by chloride ions.     

Dynamics of cAPK type IIbeta activation revealed by enhanced amide H/2H exchange mass spectrometry (DXMS)

cAMP-dependent protein kinase (cAPK) is a key component in numerous cell signaling pathways. The cAPK regulatory (R) subunit maintains the kinase in an inactive state until cAMP saturation of the R-subunit leads to activation of the enzyme. To delineate the conformational changes associated with cAPK activation, the amide hydrogen/deuterium exchange in the cAPK type IIbeta R-subunit was probed by electrospray mass spectrometry. Three states of the R-subunit, cAMP-bound, catalytic (C)-subunit bound, and apo, were incubated in deuterated water for various lengths of time and then, prior to mass spectrometry analysis, subjected to digestion by pepsin to localize the deuterium incorporation. High sequence coverage (>99%) by the pepsin-digested fragments enables us to monitor the dynamics of the whole protein. The effects of cAMP binding on RIIbeta amide hydrogen exchange are restricted to the cAMP-binding pockets, while the effects of C-subunit binding are evident across both cAMP-binding domains and the linker region. The decreased amide hydrogen exchange for residues 253-268 within cAMP binding domain A and for residues 102-115, which include the pseudosubstrate inhibitory site, support the prediction that these two regions represent the conserved primary and peripheral C-subunit binding sites. An increase in amide hydrogen exchange for a broad area within cAMP-binding domain B and a narrow area within cAMP-binding domain A (residues 222-232) suggest that C-subunit binding transmits long-distance conformational changes throughout the protein.     

Structural Tightening and Interdomain Communication in the Catalytic Cycle of Phosphoglycerate Kinase

Changes in amide-NH chemical shift and hydrogen exchange rates as phosphoglycerate kinase progresses through its catalytic cycle have been measured to assess whether they correlate with changes in hydrogen bonding within the protein. Four representative states were compared: the free enzyme, a product complex containing 3-phosphoglyceric acid (3PG), a substrate complex containing ADP and a transition-state analogue (TSA) complex containing a 3PG-AlF₄⁻-ADP moiety. There are an overall increases in amide protection from hydrogen exchange when the protein binds the substrate and product ligands and an additional increase when the TSA complex is formed. This is consistent with stabilisation of the protein structure by ligand binding. However, there is no correlation between the chemical shift changes and the protection factor changes, indicating that the protection factor changes are not associated with an overall shortening of hydrogen bonds in the protected ground state, but rather can be ascribed to the properties of the high-energy, exchange-competent state. Therefore, an overall structural tightening mechanism is not supported by the data. Instead, we observed that some cooperativity is exhibited in the N-domain, such that within this domain the changes induced upon forming the TSA complex are an intensification of those induced by binding 3PG. Furthermore, chemical shift changes induced by 3PG binding extend through the interdomain region to the C-domain β-sheet, highlighting a network of hydrogen bonds between the domains that suggests interdomain communication. Interdomain communication is also indicated by amide protection in one domain being significantly altered by binding of substrate to the other, even where no associated change in the structure of the substrate-free domain is indicated by chemical shifts. Hence, the communication between domains is also manifested in the accessibility of higher-energy, exchange-competent states. Overall, the data that are consistent with structural tightening relate to defined regions and are close to the 3PG binding site and in the hinge regions of 3-phosphoglycerate kinase.     

Probing backbone hydrogen bonds in the hydrophobic core of GCN4

Backbone amide hydrogen bonds play a central role in protein secondary and tertiary structure. Previous studies have shown that substitution of a backbone ester (-COO-) in place of a backbone amide (-CONH-) can selectively destabilize backbone hydrogen bonds in a protein while maintaining a similar conformation to the native backbone structure. The majority of these studies have focused on backbone substitutions that were accessible to solvent. The GCN4 coiled coil domain is an example of a stable alpha-helical dimer that possesses a well-packed hydrophobic core. Amino acids in the a and d positions of the GCN4 helix, which pack the hydrophobic core, were replaced with the corresponding alpha-hydroxy acids in the context of a chemoselectively ligated heterodimer. While the overall structure and oligomerization state of the heterodimer were maintained, the overall destabilization of the ester analogues was greater (average DeltaDeltaG of 3+ kcal mol(-1)) and more variable than previous studies. Since burial of the more hydrophobic ester should stabilize the backbone and reduce the DeltaDeltaG, the increased destabilization must come from another source. However, the observed destabilization is correlated with the protection factors for individual amide hydrogens from previous hydrogen exchange experiments. Therefore, our results suggest that backbone engineering through ester substitution is a useful approach for probing the relative strength of backbone hydrogen bonds.     

Amide proton exchange rates of a bound pepsin inhibitor determined by isotope-edited proton NMR experiments

From a series of isotope-edited proton NMR spectra, amide proton exchange rates were measured at 20 degrees C, 30 degrees C, and 40 degrees C for a tightly bound 15N-labeled tripeptide inhibitor of porcine pepsin (IC50 = 1.7 X 10(-) M). Markedly different NH exchange rates were observed for the three amide protons of the bound inhibitor. The P1 NH exchanged much more slowly than the P2 NH and P3 NH. These results are discussed in terms of the relative solvent accessibility in the active site and the role of the NH protons of the inhibitor for hydrogen bonding to the enzyme. In this study a useful approach is demonstrated for obtaining NH exchange rates on ligands bound to biomacromolecules, the knowledge of which could be of potential utility in the design of therapeutically useful nonpeptide enzyme inhibitors from peptide leads.     

Investigation of the structural stability of the human acidic fibroblast growth factor by hydrogen-deuterium exchange

The conformational stability of the human acidic fibroblast growth factor (hFGF-1) is investigated using amide proton exchange and temperature-dependent chemical shifts, monitored by two-dimensional NMR spectroscopy. The change in free energy of unfolding (DeltaG(u)) of hFGF-1 is estimated to be 5.00 +/- 0.09 kcal.mol(-)(1). Amide proton-exchange rates of 74 residues (in hFGF-1) have been unambiguously measured, and the exchange process occurs predominately according to the conditions of the EX2 limit. The exchange rates of the fast-exchanging amide protons exposed to the solvent have been measured using the clean SEA-HSQC technique. The amide proton protection factor and temperature coefficient estimates show reasonably good correlation. Residues in beta-strands II and VI appear to constitute the stability core of the protein. Among the 12 beta-strands constituting the beta-barrel architecture of hFGF-1, beta-strand XI, located in the heparin binding domain, exhibits the lowest average protection factor value. Amide protons involved in the putative folding nucleation site in hFGF-1, identified by quench-flow NMR studies, do not represent the slow-exchanging core. Residues in portions of hFGF-1 experiencing high conformational flexibility mostly correspond to those involved in receptor recognition and binding.     

Dissecting interdomain communication within cAPK regulatory subunit type IIbeta using enhanced amide hydrogen/deuterium exchange mass spectrometry (DXMS)

cAMP-dependent protein kinase (cAPK) is a heterotetramer containing a regulatory (R) subunit dimer bound to two catalytic (C) subunits and is involved in numerous cell signaling pathways. The C-subunit is activated allosterically when two cAMP molecules bind sequentially to the cAMP-binding domains, designated A and B (cAB-A and cAB-B, respectively). Each cAMP-binding domain contains a conserved Arg residue that is critical for high-affinity cAMP binding. Replacement of this Arg with Lys affects cAMP affinity, the structural integrity of the cAMP-binding domains, and cAPK activation. To better understand the local and long-range effects that the Arg-to-Lys mutation has on the dynamic properties of the R-subunit, the amide hydrogen/deuterium exchange in the RIIbeta subunit was probed by electrospray mass spectrometry. Mutant proteins containing the Arg-to-Lys substitution in either cAMP-binding domain were deuterated for various times and then, prior to mass spectrometry analysis, subjected to pepsin digestion to localize the deuterium incorporation. Mutation of this Arg in cAB-A (Arg230) causes an increase in amide hydrogen exchange throughout the mutated domain that is beyond the modest and localized effects of cAMP removal and is indicative of the importance of this Arg in domain organization. Mutation of Arg359 (cAB-B) leads to increased exchange in the adjacent cAB-A domain, particularly in the cAB-A domain C-helix that lies on top of the cAB-B domain and is believed to be functionally linked to the cAB-B domain. This interdomain communication appears to be a unidirectional pathway, as mutation of Arg230 in cAB-A does not effect dynamics of the cAB-B domain.     

Structural and kinetic characterization of early folding events in beta-lactoglobulin

We have defined the structural and dynamic properties of an early folding intermediate of beta-lactoglobulin known to contain non-native alpha-helical structure. The folding of beta-lactoglobulin was monitored over the 100 micros--10 s time range using ultrarapid mixing techniques in conjunction with fluorescence detection and hydrogen exchange labeling probed by heteronuclear NMR. An initial increase in Trp fluorescence with a time constant of 140 micros is attributed to formation of a partially helical compact state. Within 2 ms of refolding, well protected amide protons indicative of stable hydrogen bonded structure were found only in a domain comprising beta-strands F, G and H, and the main alpha-helix, which was thus identified as the folding core of beta-lactoglobulin. At the same time, weak protection (up to approximately 10-fold) of amide protons in a segment spanning residues 12--21 is consistent with formation of marginally stable non-native alpha-helices near the N-terminus. Our results indicate that efficient folding, despite some local non-native structural preferences, is insured by the rapid formation of a native-like alpha/beta core domain.     

Hydrogen exchange shows peptide binding stabilizes motions in Hck SH2.

Src-homology-2 domains are small, 100 amino acid protein modules that are present in a number of signal transduction proteins. Previous NMR studies of SH2 domain dynamics indicate that peptide binding decreases protein motions in the pico- to nanosecond, and perhaps slower, time range. We suggest that amide hydrogen exchange and mass spectrometry may be useful for detecting changes in protein dynamics because hydrogen exchange rates are relatively insensitive to the time domains of the dynamics. In the present study, hydrogen exchange and mass spectrometry were used to probe hematopoietic cell kinase SH2 that was either free or bound to a 12-residue high-affinity peptide. Hydrogen exchange rates were determined by exposing free and bound SH2 to D(2)O, fragmenting the SH2 with pepsin, and determining the deuterium level in the peptic fragments. Binding generally decreased hydrogen exchange along much of the SH2 backbone, indicating a widespread reduction in dynamics. Alterations in the exchange of the most rapidly exchanging amide hydrogens, which was detected following acid quench and analysis by mass spectrometry, were used to locate differences in low-amplitude motion when SH2 was bound to the peptide. In addition, the results indicate that hydrogen exchange from the folded form of SH2 is an important process along the entire SH2 backbone.     

Fast folding of a prototypic polypeptide: the immunoglobulin binding domain of streptococcal protein G.

The folding of the small (56 residues) highly stable B1 immunoglobulin binding domain (GB1) of streptococcal protein G has been investigated by quenched-flow deuterium-hydrogen exchange. This system represents a paradigm for the study of protein folding because it exhibits no complicating features superimposed upon the intrinsic properties of the polypeptide chain. Collapse to a semicompact state exhibiting partial order, reflected in protection factors for ND-NH exchange up to 10-fold higher than that expected for a random coil, occurs within the dead time (< or = 1 ms) of the quenched flow apparatus. This is followed by the formation of the fully native state, as monitored by the fractional proton occupancy of 26 backbone amide groups spread throughout the protein, in a single rapid concerted step with a half-life of 5.2 ms at 5 degrees C.     

Mapping protein energy landscapes with amide hydrogen exchange and mass spectrometry: I. A generalized model for a two-state protein and comparison with experiment

Protein amide hydrogen exchange (HDX) is a convoluted process, whose kinetics is determined by both dynamics of the protein and the intrinsic exchange rate of labile hydrogen atoms fully exposed to solvent. Both processes are influenced by a variety of intrinsic and extrinsic factors. A mathematical formalism initially developed to rationalize exchange kinetics of individual amide hydrogen atoms is now often used to interpret global exchange kinetics (e.g., as measured in HDX MS experiments). One particularly important advantage of HDX MS is direct visualization of various protein states by observing distinct protein ion populations with different levels of isotope labeling under conditions favoring correlated exchange (the so-called EX1 exchange mechanism). However, mildly denaturing conditions often lead to a situation where the overall HDX kinetics cannot be clearly classified as either EX1 or EX2. The goal of this work is to develop a framework for a generalized exchange model that takes into account multiple processes leading to amide hydrogen exchange, and does not require that the exchange proceed strictly via EX1 or EX2 kinetics. To achieve this goal, we use a probabilistic approach that assigns a transition probability and a residual protection to each equilibrium state of the protein. When applied to a small protein chymotrypsin inhibitor 2, the algorithm allows complex HDX patterns observed experimentally to be modeled with remarkably good fidelity. On the basis of the model we are now in a position to begin to extract quantitative dynamic information from convoluted exchange kinetics.