Models for hydrogen exchange from folded proteins. II.

The kinetics of hydrogen exchange from folded proteins can be molded as a function of two continuous distributions of rate constants, kcx and kn, representing exchange from the folded and unfolded conformations, respectively. This model can account for the temperature dependence of soybean trypsin inhibitor at pH 3 and pH 6.5. The physical significance of this model, especially the shape and breadth of the kn distribution, are discussed.     

The pH dependence of hydrogen exchange in proteins

The static accessibility modified discrete charge model for electrostatic interactions in proteins is extended to the prediction of the pH dependence of hydrogen exchange reactions. The exchange rate profiles of buried amide protons are shown to follow the calculated pH dependence of the electrostatic component of protein stability. Rate profiles are calculated for individual buried amide protons in ribonuclease S and bovine pancreatic trypsin inhibitor. The electrostatic free energy of stabilization of the protein and the energy required to bring the catalytic ion to an exchange site are expressed as an apparent, pH-dependent contribution to the activation energy. Changes in the electrostatic stabilization of the proteins affect the calculated exchange rate for buried amide protons by more than 1000, while local field effects raise or lower the predicted exchange rates by less than 100. The pH dependence of exchangeable protons at the protein surface, such as the C-2 imidazole protons, is shown to follow the estimated energy required to introduce the catalytic ion at the exchange site. These calculations are discussed in terms of current models for proton exchange which incorporate the dynamic nature of the structure to explain exchange data from the interior of a protein.     

Solvent accessibility in folded proteins. Studies of hydrogen exchange in trypsin.

In a native protein, the exchange of a peptide amide proton with solvent occurs by one of two pathways, either directly from the folded protein, or via unfolding, exchange taking place from the unfolded protein. From the thermal unfolding rate constants, the contribution of unfolding to the over-all kinetics as a function of solvent and temperature has been determined. Exchange involving unfolding of the protein is characterized by a high activation energy, in the range of 50 to 60 Cal per mol. The activiation energy (Eapp) of the rates of exchange directly from the folded protein is approximately 20 to 25 Cal per mol. Because for the proton transfer step, Eapp approximately equal to 20 Cal per mol, the activation energy for any contributing protein conformational process(es) is approximately equal to 0 to 5 Cal per mol. Most, if not all, of the peptide amide protons in a folded protein can exchange directly with solvent without the protein unfolding. The number of "slowly" exchanging protons at a given condition of pH and temperature is not related to a discrete structural unit, but rather to the distribution of observed rates within the broader distribution of actual rates. The large attenuation of hydrogen exchange rates in folded proteins, resulting in a distribution of first order rates over 6 orders of magnitude, is primarily due to the effects of restricted solvent accessibility of labile protons in the three-dimensional structure. Any protein conformational process, such as protein fluctuations, invoked to explain the solvent accessibility must be of low activation energy and attenuated by ethanol and other co-solvents (Woodward, C. K., Ellis, L. M., and Rosenberg, A. (1974) J. Biol. Chem. 250, 440-444).     

Hydrogen exchange kinetics of human hemoglobins. The pH dependence of solvent accessibility in cyanomet-, oxy-, and deoxyhemoglobin.

The hydrogen exchange kinetics of human oxy-, deoxy-, and cyanomethemoglobin have been measured as a function of pH by the tritium tracer method. At 5 degrees C and in phosphate buffer both liganded and unliganded forms of ferrohemoglobin exhibit deviations from the regular pH dependence of exchange that is characteristic of cyanomethemoglobin. In oxyhemoglobin, the deviation from the normal exchange pattern is centered at pH 7.4 and is in the direction of increased exchange or solvent accessibility. The effect in deoxyhemogloin, while occurring at the same pH and being of the same order of magnitude, is in the opposite direction, thus suggesting a pH-induced conformational transition leading to a less accessible structure. The width of these pH-induced deviations in solvent accessibility is approximately 1 pH unit in both cases. We propose a model in which specific interactions between charged groups in both froms of ferrohemoglobin account for these deviations.     

The nature of folded states of globular proteins.

We suggest, using dynamical simulations of a simple heteropolymer modelling the alpha-carbon sequence in a protein, that generically the folded states of globular proteins correspond to statistically well-defined metastable states. This hypothesis, called the metastability hypothesis, states that there are several free energy minima separated by barriers of various heights such that the folded conformations of a polypeptide chain in each of the minima have similar structural characteristics but have different energies from one another. The calculated structural characteristics, such as bond angle and dihedral angle distribution functions, are assumed to arise from only those configurations belonging to a given minimum. The validity of this hypothesis is illustrated by simulations of a continuum model of a heteropolymer whose low temperature state is a well-defined beta-barrel structure. The simulations were done using a molecular dynamics algorithm (referred to as the "noisy" molecular dynamics method) containing both friction and noise terms. It is shown that for this model there are several distinct metastable minima in which the structural features are similar. Several new methods of analyzing fluctuations in structures belonging to two distinct minima are introduced. The most notable one is a dynamic measure of compactness that can in principle provide the time required for maximal compactness to be achieved. The analysis shows that for a given metastable state in which the protein has a well-defined folded structure the transition to a state of higher compactness occurs very slowly, lending credence to the notion that the system encounters a late barrier in the process of folding to the most compact structure. The examination of the fluctuations in the structures near the unfolding----folding transition temperature indicates that the transition state for the unfolding to folding process occurs closer to the folded state.     

Conformation of corticotropin. An infrared spectrometry study of hydrogen exchange kinetics.

1H--2H exchange kinetics of the peptide hydrogens in corticotropin have been examined in 2H2O and CF3C2H2O2H solutions by means of infrared absorption measurements. In aqueous solution, around pH 3, the experimental data suggest a partially ordered structure, since in the two corticotropins 1--24 and 1--32 about 6 slowly exchanging peptide protons are numbered. These might belong to the N-terminal part of the molecule. The C-terminal 25--32 octapeptide segment appears to be unordered and slightly destabilizes the overall hormone conformation. For corticotropin1--24 in CF3C2H2O2H, the qualitative interpretation of infrared spectra and the quantitative analysis of exchange data give evidence of a strong stabilization: a predominantly alpha-helical structure is induced by trifluoroethanol.     

Concentration-dependent hydrogen exchange kinetics of 3H-labeled S-peptide in ribonuclease S.

The hydrogen exchange kinetics of the S-peptide in ribonuclease S can be measured by first tritiating the S-peptide in the absence of S-protein and then allowing it to recombine rapidly with S-protein. Afterwards the exchange reactions of this specific segment of ribonuclease S can be studied. The exchange kinetics of bound S-peptide are complex, indicating that different protons exchange at markedly different rates. The terminal exchange reaction, involving at least five highly protected protons, has been studied as a function of pH.At low concentrations of ribonuclease S the exchange kinetics become concentration-dependent, owing to the dissociation of the S-peptide. Although the fraction of free S-peptide is always very small, its rate of exchange is several orders of magnitude faster than that of bound S-peptide, and the concentration dependence of the exchange kinetics is readily measurable. It provides a highly sensitive method for determining small dissociation constants (K_D). Values of K_D ranging from 10^?6m at pH 2.7, 0 °C, to 2 × 10^?10m at pH 7.0, 0 °C, are reported here. Our value for K_D at pH 7.0, 0 °C, confirms the data and extrapolation to 0 °C of Hearn et al. (1971).At high concentrations of ribonuclease S the terminal exchange reaction is independent of concentration. It probably results from a local unfolding reaction of the bound S-peptide. Above pH 4 the strong pH dependence of K_D closely resembles that of the apparent equilibrium constant for this local unfolding reaction. The latter may be one step in the dissociation process and we present such a model for ribonuclease S dissociation.Measurement of concentration-dependent exchange kinetics should provide a useful method of determining small dissociation constants in other systems: for example, in studies of protein-nucleic acid interactions.     

Equilibrium amide hydrogen exchange and protein folding kinetics

The classical Linderstrøm-Lang hydrogen exchange (HX) model is extended to describe the relationship between the HX behaviors (EX1 and EX2) and protein folding kinetics for the amide protons that can only exchange by global unfolding in a three-state system including native (N), intermediate (I), and unfolded (U) states. For these slowly exchanging amide protons, it is shown that the existence of an intermediate (I) has no effect on the HX behavior in an off-pathway three-state system (IUN). On the other hand, in an on-pathway three-state system (UIN), the existence of a stable folding intermediate has profound effect on the HX behavior. It is shown that fast refolding from the unfolded state to the stable intermediate state alone does not guarantee EX2 behavior. The rate of refolding from the intermediate state to the native state also plays a crucial role in determining whether EX1 or EX2 behavior should occur. This is mainly due to the fact that only amide protons in the native state are observed in the hydrogen exchange experiment. These new concepts suggest that caution needs to be taken if one tries to derive the kinetic events of protein folding from equilibrium hydrogen exchange experiments.     

The role of packing interactions in stabilizing folded proteins.

In order to investigate the role of nonpolar side chains in determining protein stability, we have carried out a molecular dynamics simulation study of the thermodynamics of interconverting isoleucine and valine side chains in the core of ribonuclease T1. The free energy change in the unfolded state, which we take to be fully solvated, was small and agrees qualitatively with experimental studies of alkane solvation. In the two Ile----Val mutations studied, the protein was able to relax around the smaller side chains, while in the case of the two Val----Ile mutations, the ability of the core to accommodate the extra methylene group depended on where the mutation took place. We argue that the experimentally observed decrease in stability for mutating isoleucine into valine results from a loss of favorable packing interactions of the side chain in the folded form of the protein. This supports the view that packing interactions in the folded state are an important contributor to the overall stability of the folded protein and that the core of the native protein is packed efficiently and almost completely.     

Hydrogen-tritium exchange kinetics of soybean trypsin inhibitor (Kunitz). Solvent accessibility in the folded conformation.

The hydrogen exchange kinetics of Kunitz soybean trypsin inhibitor (STI) has been studied at pH 2, 3, and 6.5. From the temperature dependence of proton exchange at low pH, THE CONTRIBUTION OF MAJOR, REVERSIBLE PROTEIN UNFOLDING To the hydrogen exchange kinetics has been determined. Exchange directly from the folded conformation is characterized by an apparent activation energy (E*app) of approximately 25 kcal/mol, close to that of the chemical exchange step. At pH 6.5 the protein is more temperature stable than at low pH, and exchange of all but congruent to 8 protons can be observed to exchange with E*app congruent to 27 kcal/mol. This implies that all but congruent to 8 protons are accessible to exchange with solvent in the solution structure of folded STI. Estimates can be made of the average number of water molecules per molecule of STI consistent with a solvent accessibility model of hydrogen exchange kinetics. These estimates indicate that very few water molecules within the protein matrix are necessary to explain the exchange data. Calculations are done for the STI hydrogen exchange kinetics at pH 3, 30 degrees, approximating STI structure by a sphere of radius = 18 A. These calculations indicate an average of congruent to 4 water molecules in the shell from 13 to 16 A. from the center of the molecule, while less than 1 water molecule is indicated in the innermost 13 A. These calculations also suggest that there are congruent to 190 water molecules associated with the outermost 1.5-2 A of the sphere. While these values are consistent with a hydrophobic region in the central protein matrix, they indicate more solvent accessibility in the outer 1/3 of the molecule than the static accessibility estimates made from X-ray coordinates. Our results suggest that any protein movements or fluctuations responsible for solvent accessibility in proton exchange processes are localized in the outer regions of the globular structure.     

The kinetics of transdermal ethanol exchange.

The kinetics of ethanol transport from the blood to the skin surface are incompletely understood. We present a mathematical model to predict the transient exchange of ethanol across the skin while it is being absorbed from the gut and eliminated from the body. The model simulates the behavior of a commercial device that is used to estimate the blood alcohol concentration (BAC). During the elimination phase, the stratum corneum of the skin has a higher ethanol concentration than the blood. We studied the effect of varying the maximum BAC and the absorption rate from the gut on the relationship between BAC and equivalent concentration in the gas phase above the skin. The results showed that the ethanol concentration in the gas compartment always took longer to reach its maximum, had a lower maximum, and had a slower apparent elimination rate than the BAC. These effects increased as the maximum BAC increased. Our model's predictions are consistent with experimental data from the literature. We performed a sensitivity analysis (using Latin hypercube sampling) to identify and rank the importance of parameters. The analysis showed that outputs were sensitive to solubility and diffusivity within the stratum corneum, to stratum corneum thickness, and to the volume of gas in the sampling chamber above the skin. We conclude that ethanol transport through the skin is primarily governed by the washin and washout of ethanol through the stratum corneum. The dynamics can be highly variable from subject to subject because of variability in the physical properties of the stratum corneum.     

The thermodynamics of solvent exchange

A model for solvation in mixed solvents, which was developed for the free energy and preferential interaction [J. A. Schellman (1987), Biopolymers, Vol. 26, pp. 549–559; (1990), Biophysical Chemistry, Vol. 37, pp. 121–140; (1993), Biophysical Chemistry, Vol. 45, pp. 273–279], is extended in this paper to cover the thermal properties: enthalpy, entropy, and heat capacity. An important result is that the enthalpy of solvation H? responds directly to the fraction of site occupation. This differs from the free energy ? and preferential interaction Γ₃₂, which are measures of the excess binding above a random distribution of solvent molecules. In other words, the enthalpy is governed by K while ? and Γ₃₂ are governed by (K ? 1) where K is the equilibrium constant on a mole fraction scale [Schellman (1987)]. The solvation heat capacity C?p consists of two term: (1) the intrinsic heat capacity of species in solution with no change in composition, and (2) a term that accounts for the change in composition that accompanies solvent exchange. Binding to biological macromolecules is heterogeneous but experiementalists must use binding isotherms that assume the homogeneity of sites. Equations are developed for the interpretation of the experimental parameters (number of sites n_exp, equilibrium constant K_exp, and enthalpy, Δh_exp), when homogeneous formulas are applied to the heterogeneous case. It is shown that the experimental parameters for the occupation and enthalpy are simple functions of the moments of the distribution of equilibrium constants over the sites. In general, n_exp is greater than the true number of sites and K_exp is greater than the average of the equilibrium constants. The free energy and preferential interaction can be fit to a homogenious formula, but the parameters of the curve are not easily represented in terms of the moments of distributions over the sites. The strengths and deficiencies of this type of thermodynamic model are discussed. © 1994 John Wiley & Sons, Inc.     

On the pH dependence of amide proton exchange rates in proteins.

We have analyzed the pH dependencies of published amide proton exchange rates (kex) in three proteins: bovine pancreatic trypsin inhibitor (BPTI), bull seminal plasma proteinase inhibitor IIA (BUSI IIA), and calbindin D9K. The base-catalyzed exchange rate constants (kOH) of solvent exposed amides in BPTI are lower for residues with low peptide carbonyl exposure, showing that the environment around the carbonyl oxygen influences kOH. We also examined the possible importance of an exchange mechanism that involves formations of imidic acid intermediates along chains of hydrogen-bonded peptides in the three proteins. By invoking this "relayed imidic acid exchange mechanism," which should be essentially acid-catalyzed, we can explain the surprisingly high pHmin (the pH value at which kex reaches a minimum) found for the non-hydrogen-bonded amide protons in the beta-sheet in BPTI. The successive increase of pHmin along a chain of hydrogen-bonded peptides from the free amide to the free carbonyl, observed in BPTI, can be explained as an increasing contribution of the proposed mechanism in this direction of the chain. For BUSI IIA (pH 4-5) and calbindin D9K (pH 6-7) the majority of amide protons with negative pH dependence of kex are located in chains of hydrogen-bonded peptides; this situation is shown to be consistent with the proposed mechanism.     

A statistical mechanical model for hydrogen exchange in globular proteins.

We develop a statistical mechanical theory for the mechanism of hydrogen exchange in globular proteins. Using the HP 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.     

Import of stably folded proteins into peroxisomes.

By virtue of their synthesis in the cytoplasm, proteins destined for import into peroxisomes are obliged to traverse the single membrane of this organelle. Because the targeting signal for most peroxisomal matrix proteins is a carboxy-terminal tripeptide sequence (SKL or its variants), these proteins must remain import competent until their translation is complete. We sought to determine whether stably folded proteins were substrates for peroxisomal import. Prefolded proteins stabilized with disulfide bonds and chemical cross-linkers were shown to be substrates for peroxisomal import, as were mature folded and disulfide-bonded IgG molecules containing the peroxisomal targeting signal. In addition, colloidal gold particles conjugated to proteins bearing the peroxisomal targeting signal were translocated into the peroxisomal matrix. These results support the concept that proteins may fold in the mammalian cytosol, before their import into the peroxisome, and that protein unfolding is not a prerequisite for peroxisomal import.     

Amide hydrogen exchange shows that malate dehydrogenase is a folded monomer at pH 5

Although there is general agreement that native mitochondrial malate dehydrogenase (MDH) exists as a dimer at pH 7, its aggregation state at pH 5 is less certain. The present amide hydrogen exchange study was performed to determine whether MDH remains a dimer at pH 5. To detect pH-induced changes in solvent accessibility, MDH was exposed to D(2)O at pH 5 or 7, then fragmented with pepsin into peptides that were analyzed by mass spectrometry. Even after adjustments for the effect of pH on the intrinsic rate of hydrogen exchange, large increases in deuterium levels were found at pH 5 only in peptic fragments derived from the subunit binding surface of MDH. In parallel experiments, elevated deuterium levels were also found in the same regions of MDH monomer trapped inside a mutant form of the chaperonin GROEL: This selective increase in hydrogen exchange rates, which was attributed to increased solvent accessibility of these regions, provides new evidence that MDH is a monomer at pH 5.