Hydrophobic‐hydrophilic forces in protein folding

The process of protein folding is obviously driven by forces exerted on the atoms of the amino‐acid chain. These forces arise from interactions with other parts of the protein itself (direct forces), as well as from interactions with the solvent (solvent‐induced forces). We present a statistical–mechanical formalism that describes both these direct and indirect, solvent‐induced thermodynamic forces on groups of the protein. We focus on 2 kinds of protein groups, commonly referred to as hydrophobic and hydrophilic. Analysis of this result leads to the conclusion that the forces on hydrophilic groups are in general stronger than on hydrophobic groups. This is then tested and verified by a series of molecular dynamics simulations, examining both hydrophobic alkanes of different sizes and hydrophilic moieties represented by polar‐neutral hydroxyl groups. The magnitude of the force on assemblies of hydrophilic groups is dependent on their relative orientation: with 2 to 4 times larger forces on groups that are able to form one or more direct hydrogen bonds.     

Application of a chaperone-based refolding method to two- and three-dimensional off-lattice protein models

A model of protein-chaperone interaction as a two-phase (unfolding/refolding) iterative annealing mechanism able to promote structural segregation of hydrophobic and hydrophilic monomers and thereby facilitate access to nativelike states has recently been applied successfully to two 22-mers of the Honeycutt and Thirumalai BLN (hydrophobic, hydrophilic, neutral) heteropolymer model. This technique is here applied to a much wider data set: 94 8-mers of the off-lattice protein model originally presented in two dimensions by Stillinger and Head-Gordon, and later extended into three dimensions by Irb?ck and Potthast; the model chaperone is shown to be equally successful, and by progressive elaboration of the chaperone model as in the earlier BLN model work, to be utilizing very similar underlying mechanisms. It is demonstrated that on average, contacts with the model chaperone give rise to a consistent movement in structure space in the direction of more nativelike structures; this method of global minimization does not therefore rely fundamentally on random search. Insofar as the responses to the chaperone of the two- and three-dimensional forms of the substrate model do differ, this can be interpreted as reflecting the different handling of hydrophilic monomers in the models-in particular, whether there is active repulsion between these and monomers of hydrophobic character. The chaperone-induced refolding method is also tested on a set of 220 9-mer chains of each version of the substrate model, where it is seen that the two-dimensional model, with its more clearly distinguished roles for the hydrophobic and hydrophilic monomers, shows a more favorable scaling behavior.     

Increasing protein stability by altering long-range coulombic interactions.

It is difficult to increase protein stability by adding hydrogen bonds or burying nonpolar surface. The results described here show that reversing the charge on a side chain on the surface of a protein is a useful way of increasing stability. Ribonuclease T1 is an acidic protein with a pI approximately 3.5 and a net charge of approximately -6 at pH 7. The side chain of Asp49 is hyperexposed, not hydrogen bonded, and 8 A from the nearest charged group. The stability of Asp49Ala is 0.5 kcal/mol greater than wild-type at pH 7 and 0.4 kcal/mol less at pH 2.5. The stability of Asp49His is 1.1 kcal/mol greater than wild-type at pH 6, where the histidine 49 side chain (pKa = 7.2) is positively charged. Similar results were obtained with ribonuclease Sa where Asp25Lys is 0.9 kcal/mol and Glu74Lys is 1.1 kcal/mol more stable than the wild-type enzyme. These results suggest that protein stability can be increased by improving the coulombic interactions among charged groups on the protein surface. In addition, the stability of RNase T1 decreases as more hydrophobic aromatic residues are substituted for Ala49, indicating a reverse hydrophobic effect.     

Exhaustive enumeration of protein conformations using experimental restraints.

We present an efficient new algorithm that enumerates all possible conformations of a protein that satisfy a given set of distance restraints. Rapid growth of all possible self-avoiding conformations on the diamond lattice provides construction of alpha-carbon representations of a protein fold. We investigated the dependence of the number of conformations on pairwise distance restraints for the proteins crambin, pancreatic trypsin inhibitor, and ubiquitin. Knowledge of between one and two contacts per monomer is shown to be sufficient to restrict the number of candidate structures to approximately 1,000 conformations. Pairwise RMS deviations of atomic position comparisons between pairs of these 1,000 structures revealed that these conformations can be grouped into about 25 families of structures. These results suggest a new approach to assessing alternative protein folds given a very limited number of distance restraints. Such restraints are available from several experimental techniques such as NMR, NOESY, energy transfer fluorescence spectroscopy, and crosslinking experiments. This work focuses on exhaustive enumeration of protein structures with emphasis on the possible use of NOESY-determined distance restraints.     

Chemically crosslinked protein dimers: stability and denaturation effects.

Nine single substitution cysteine mutants of staphylococcal nuclease (nuclease) were preferentially crosslinked at the introduced cysteine residues using three different bifunctional crosslinking reagents; 1,6-bismaleimidohexane (BMH), 1,3-dibromo-2-propanol (DBP), and the chemical warfare agent, mustard gas (bis(2-chloroethyl)sulfide; mustard). BMH and mustard gas are highly specific reagents for cysteine residues, whereas DBP is not as specific. Guanidine hydrochloride (GuHCl) denaturations of the resulting dimeric proteins exhibited biphasic unfolding behavior that did not fit the two-state model of unfolding. The monofunctional reagent, epsilon-maleimidocaproic acid (MCA), was used as a control for the effects of alkylation. Proteins modified with MCA unfolded normally, showing that this unusual unfolding behavior is due to crosslinking. The data obtained from these crosslinked dimers was fitted to a three-state thermodynamic model of two successive transitions in which the individual subunits cooperatively unfold. These two unfolding transitions were very different from the unfolding of the monomeric protein. These differences in unfolding behavior can be attributed in large part to changes in the denatured state. In addition to GuHCl titrations, the crosslinked dimers were also thermally unfolded. In contrast to the GuHCl denaturations, analysis of this data fit a two-state model well, but with greatly elevated van't Hoff enthalpies in many cases. However, clear correlations between the thermal and GuHCl denaturations exist, and the differences in thermal unfolding can be rationalized by postulating interactions of the denatured crosslinked proteins.     

Charge centers and formation of the protein folding core

Electrostatic interactions are important for protein folding. At low resolution, the electrostatic field of the whole molecule can be described in terms of charge center(s). To study electrostatic effects, the centers of positive and negative charge were calculated for 20 small proteins of known structure, for which hydrogen exchange cores had been determined experimentally. Two observations seem to be important. First, in all 20 proteins studied 30-100% of the residues forming hydrogen exchange core(s) were clustered around the charge centers. Moreover, in each protein more than half of the core sequences are located near the centers of charge. Second, the general architecture of all-alpha proteins from the set seems to be stabilized by interactions of residues surrounding the charge centers. In most of the alpha-beta proteins, either or both of the centers are located near a pair of consecutive strands, and this is even more characteristic for alpha/Beta and all-beta structures. Consecutive strands are very probable sites of early folding events. These two points lead to the conclusion that charge centers, defined solely from the structure of the folded protein may indicate the location of a protein's hydrogen exchange/folding core. In addition, almost all the proteins contain well-conserved continuous hydrophobic sequences of three or more residues located in the vicinity of the charge centers. These hydrophobic sequences may be primary nucleation sites for protein folding. The results suggest the following scheme for the order of events in folding: local hydrophobic nucleation, electrostatic collapse of the core, global hydrophobic collapse, and slow annealing to the native state. This analysis emphasizes the importance of treating electrostatics during protein-folding simulations.     

Energetics of aliphatic deletions in protein cores

Although core residues can sometimes be replaced by shorter ones without introducing significant changes in protein structure, the energetic consequences are typically large and destabilizing. Many efforts have been devoted to understand and predict changes in stability from analysis of the environment of mutated residues, but the relationships proposed for individual proteins have often failed to describe additional data. We report here 17 apoflavodoxin large-to-small mutations that cause overall protein destabilizations of 0.6-3.9 kcal.mol(-1). By comparing two-state urea and three-state thermal unfolding data, the overall destabilizations observed are partitioned into effects on the N-to-I and on the I-to-U equilibria. In all cases, the equilibrium intermediate exerts a "buffering" effect that reduces the impact of the overall destabilization on the N-to-I equilibrium. The performance of several structure-energetics relationships, proposed to explain the energetics of hydrophobic shortening mutations, has been evaluated by using an apoflavodoxin data set consisting of 14 mutations involving branching-conservative aliphatic side-chain shortenings and a larger data set, including similar mutations implemented in seven model proteins. Our analysis shows that the stability changes observed for any of the different types of mutations (LA, IA, IV, and VA) in either data set are best explained by a combination of differential hydrophobicity and of the calculated volume of the modeled cavity (as previously observed for LA and IA mutations in lysozyme T4). In contrast, sequence conservation within the flavodoxin family, which is a good predictor for charge-reversal stabilizing mutations, does not perform so well for aliphatic shortening ones.     

Folding of a designed simple ankyrin repeat protein

Ankyrin repeats (AR) are 33-residue motifs containing a beta-turn, followed by two alpha-helices connected by a loop. AR occur in tandem arrangements and stack side-by-side to form elongated domains involved in very different cellular tasks. Recently, consensus libraries of AR repeats were constructed. Protein E1_5 represents a member of the shortest library, and consists of only a single consensus repeat flanked by designed N- and C-terminal capping repeats. Here we present a biophysical characterization of this AR domain. The protein is compactly folded, as judged from the heat capacity of the native state and from the specific unfolding enthalpy and entropy. From spectroscopic data, thermal and urea-induced unfolding can be modeled by a two-state transition. However, scanning calorimetry experiments reveal a deviation from the two-state behavior at elevated temperatures. Folding and unfolding at 5 degrees C both follow monoexponential kinetics with k(folding) = 28 sec(-1) and k(unfolding) = 0.9 sec(-1). Kinetic and equilibrium unfolding parameters at 5 degrees C agree very well. We conclude that E1_5 folds in a simple two-state manner at low temperatures while equilibrium intermediates become populated at higher temperatures. A chevron-plot analysis indicates that the protein traverses a very compact transition state along the folding/unfolding pathway. This work demonstrates that a designed minimal ankyrin repeat protein has the thermodynamic and kinetic properties of a compactly folded protein, and explains the favorable properties of the consensus framework.     

SIMPLE estimate of the free energy change due to aliphatic mutations: superior predictions based on first principles

The bioinformatics revolution of the last decade has been instrumental in the development of empirical potentials to quantitatively estimate protein interactions for modeling and design. Although computationally efficient, these potentials hide most of the relevant thermodynamics in 5-to-40 parameters that are fitted against a large experimental database. Here, we revisit this longstanding problem and show that a careful consideration of the change in hydrophobicity, electrostatics, and configurational entropy between the folded and unfolded state of aliphatic point mutations predicts 20-30% less false positives and yields more accurate predictions than any published empirical energy function. This significant improvement is achieved with essentially no free parameters, validating past theoretical and experimental efforts to understand the thermodynamics of protein folding. Our first principle analysis strongly suggests that both the solute-solute van der Waals interactions in the folded state and the electrostatics free energy change of exposed aliphatic mutations are almost completely compensated by similar interactions operating in the unfolded ensemble. Not surprisingly, the problem of properly accounting for the solvent contribution to the free energy of polar and charged group mutations, as well as of mutations that disrupt the protein backbone remains open.     

Automatic recognition of hydrophobic clusters and their correlation with protein folding units.

A method is described to objectively identify hydrophobic clusters in proteins of known structure. Clusters are found by examining a protein for compact groupings of side chains. Compact clusters contain seven or more residues, have an average of 65% hydrophobic residues, and usually occur in protein interiors. Although smaller clusters contain only side-chain moieties, larger clusters enclose significant portions of the peptide backbone in regular secondary structure. These clusters agree well with hydrophobic regions assigned by more intuitive methods and many larger clusters correlate with protein domains. These results are in striking contrast with the clustering algorithm of J. Heringa and P. Argos (1991, J Mol Biol 220:151-171). That method finds that clusters located on a protein's surface are not especially hydrophobic and average only 3-4 residues in size. Hydrophobic clusters can be correlated with experimental evidence on early folding intermediates. This correlation is optimized when clusters with less than nine hydrophobic residues are removed from the data set. This suggests that hydrophobic clusters are important in the folding process only if they have enough hydrophobic residues.     

Investigation of the pH‐dependence of dye‐doped protein–protein interactions

Proteins can dramatically change their conformation under environmental conditions such as temperature and pH. In this context, Glycoprotein's conformational determination is challenging. This is due to the variety of domains which contain rich chemical characters existing within this complex. Here we demonstrate a new, straightforward and efficient technique that uses the pH‐dependent properties of dyes‐doped Pig Gastric Mucin (PGM) for predicting and controlling protein–protein interaction and conformation. We utilize the PGM as natural host matrix which is capable of dynamically changing its conformational shape and adsorbing hydrophobic and hydrophilic dyes under different pH conditions and investigate and control the fluorescent properties of these composites in solution. It is shown at various pH conditions, a large variety of light emission from these complexes such as red, green and white is obtained. This phenomenon is explained by pH‐dependent protein folding and protein–protein interactions that induce different emission spectra which are mediated and controlled by means of dye–dye interactions and surrounding environment. This process is used to form the technologically challenging white light‐emitting liquid or solid coating for LED devices.     

Polar and nonpolar atomic environments in the protein core: Implications for folding and binding

Hydrophobic interactions are believed to play an important role in protein folding and stability. Semi-empirical attempts to estimate these interactions are usually based on a model of solvation, whose contribution to the stability of proteins is assumed to be proportional to the surface area buried upon folding. Here we propose an extension of this idea by defining an environment free energy that characterizes the environment of each atom of the protein, including solvent, polar or nonpolar atoms of the same protein or of another molecule that interacts with the protein. In our model, the difference of this environment free energy between the folded state and the unfolded (extended) state of a protein is shown to be proportional to the area buried by nonpolar atoms upon folding. General properties of this environment free energy are derived from statistical studies on a database of 82 well-refined protein structures. This free energy is shown to be able to discriminate misfolded from correct structural models, to provide an estimate of the stabilization due to oligomerization, and to predict the stability of mutants in which hydrophobic residues have been substituted by site-directed mutagenesis, provided that no large structural modifications occur. © 1994 Wiley-Liss, Inc.     

Funnel-like organization in sequence space determines the distributions of protein stability and folding rate preferred by evolution

To understand the physical and evolutionary determinants of protein folding, we map out the complete organization of thermodynamic and kinetic properties for protein sequences that share the same fold. The exhaustive nature of our study necessitates using simplified models of protein folding. We obtain a stability map and a folding rate map in sequence space. Comparison of the two maps reveals a common organizational principle: optimality decreases more or less uniformly with distance from the optimal sequence in the sequence space. This gives a funnel-shaped optimality surface. Evolutionary dynamics of a sequence population on these two maps reveal how the simple organization of sequence space affects the distributions of stability and folding rate preferred by evolution.     

Side-chain conformational entropy in protein folding.

An important, but often neglected, contribution to the thermodynamics of protein folding is the loss of entropy that results from restricting the number of accessible side-chain conformers in the native structure. Conformational entropy changes can be found by comparing the number of accessible rotamers in the unfolded and folded states, or by estimating fusion entropies. Comparison of several sets of results using different techniques shows that the mean conformational free energy change (T delta S) is 1 kcal.mol-1 per side chain or 0.5 kcal.mol-1 per bond. Changes in vibrational entropy appear to be negligible compared to the entropy change resulting from the loss of accessible rotamers. Side-chain entropies can help rationalize alpha-helix propensities, predict protein/inhibitor complex structures, and account for the distribution of side chains on the protein surface or interior.     

The importance of explicit chain representation in protein folding models: an examination of Ising-like models

A class of models that represents a protein chain as a sequence of "folded" and "unfolded" residues has recently been used to correlate rates and mechanisms of protein folding with the protein native structure. In order to better understand the conditions under which these "Ising-like" models apply, we compare results from this model to those obtained from an off-lattice model which uses the same potential function. We find that Ising-like models by construction impose folding via a highly sequential nucleation-condensation mechanism, which in turn leads to more rugged energy landscapes, fewer "pathways" to the native state, and in the specific case examined here, the cold shock protein A from Escherichia coli, a qualitative difference in the most likely order of events in folding.     

Optimal local propensities for model proteins

Lattice models of proteins were used to examine the role of local propensities in stabilizing the native state of a protein, using techniques drawn from spin-glass theory to characterize the free-energy landscapes. In the strong evolutionary limit, optimal conditions for folding are achieved when the contributions from local interactions to the stability of the native state is small. Further increasing the local interactions rapidly decreases the foldability. © 1995 Wiley-Liss, Inc.     

Effect of denaturant and protein concentrations upon protein refolding and aggregation: a simple lattice model.

We present a study of the competition between protein refolding and aggregation for simple lattice model proteins. The effect of solvent conditions (i.e., the denaturant concentration and the protein concentration) on the folding and aggregation behavior of a system of simple, two-dimensional lattice protein molecules has been investigated via (dynamic Monte Carlo simulations. The population profiles and aggregation propensities of the nine most populated intermediate configurations exhibit a complex dependence on the solution conditions that can be understood by considering the competition between intra- and interchain interactions. Some of these configurations are not even seen in isolated chain simulations; they are observed to be highly aggregation prone and are stabilized primarily by the aggregation reaction in multiple-chain systems. Aggregation arises from the association of partially folded intermediates rather than from the association of denatured random-coil states. The aggregation reaction dominates over the folding reaction at high protein concentration and low denaturant concentration, resulting in low refolding yields at those conditions. However, optimum folding conditions exist at which the refolding yield is a maximum, in agreement with some experimental observations.     

Testing a new Monte Carlo algorithm for protein folding

We demonstrate that the recently proposed pruned-enriched Rosenbluth method (PERM) (Grassberger, Phys. Rev. E 56:3682, 1997) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare it to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences. Proteins 32:52–66, 1998. © 1998 Wiley-Liss, Inc.