Alignment of a sparse protein signature with protein sequences: application to fold prediction for three small globulins.

A novel algorithm has been developed for scoring the match between an imprecise sparse signature and all the protein sequences in a sequence database. The method was applied to a specific problem: signatures were derived from the probable folding nucleus and positions obtained from the determined interactions that occur during the folding of three small globular proteins and points of inter-element contact and sequence comparison of the actual three-dimensional structures of the same three proteins. In the case of two of these, lysozyme and myoglobin, the residues in the folding nucleus corresponded well to the key residues spotted by examination of the structures and in the remaining case, barnase, they did not. The diagnostic performance of the two types of signatures were compared for all three proteins. The significance of this for the application of an understanding of the protein folding mechanisms for structure prediction is discussed. The algorithm is generic and could be applied to other user-defined problems of sequence analysis.     

RNA and protein folding: common themes and variations

Visualizing the navigation of an ensemble of unfolded molecules through the bumpy energy landscape in search of the native state gives a pictorial view of biomolecular folding. This picture, when combined with concepts in polymer theory, provides a unified theory of RNA and protein folding. Just as for proteins, the major folding free energy barrier for RNA scales sublinearly with the number of nucleotides, which allows us to extract the elusive prefactor for RNA folding. Several folding scenarios can be anticipated by considering variations in the energy landscape that depend on sequence, native topology, and external conditions. RNA and protein folding mechanism can be described by the kinetic partitioning mechanism (KPM) according to which a fraction (Phi) of molecules reaches the native state directly, whereas the remaining fraction gets kinetically trapped in metastable conformations. For two-state folders Phi approximately 1. Molecular chaperones are recruited to assist protein folding whenever Phi is small. We show that the iterative annealing mechanism, introduced to describe chaperonin-mediated folding, can be generalized to understand protein-assisted RNA folding. The major differences between the folding of proteins and RNA arise in the early stages of folding. For RNA, folding can only begin after the polyelectrolyte problem is solved, whereas protein collapse requires burial of hydrophobic residues. Cross-fertilization of ideas between the two fields should lead to an understanding of how RNA and proteins solve their folding problems.     

Use of a potential of mean force to analyze free energy contributions in protein folding.

A method for calculation of the free energy of residues as a function of residue burial is proposed. The method is based on the potential of mean force, with a reaction coordinate expressed by residue burial. Residue burials are calculated from high-resolution protein structures. The largest individual contributions to the free energy of a residue are found to be due to the hydrophobic interactions of the nonpolar atoms, interactions of the main chain polar atoms, and interactions of the charged groups of residues Arg and Lys. The contribution to the free energy of folding due to the uncharged side chain polar atoms is small. The contribution to the free energy of folding due to the main chain polar atoms is favorable for partially buried residues and less favorable or unfavorable for fully buried residues. Comparison of the accessible surface areas of proteins and model spheres shows that proteins deviate considerably from a spherical shape and that the deviations increase with the size of a protein. The implications of these results for protein folding are also discussed.     

Understanding the determinants of stability and folding of small globular proteins from their energetics

The results of minimal model calculations indicate that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By means of molecular dynamics simulations around the native conformation, which describe the protein and the surrounding solvent at the all-atom level, an accurate and compact energetic map of the native state of the protein is generated. This map is further simplified by means of an eigenvalue decomposition. The components of the eigenvector associated with the lowest eigenvalue indicate which hot sites are likely to be responsible for the stability and for the rapid folding of the protein. The comparison of the results of the model with the findings of mutagenesis experiments performed for four small proteins show that the eigenvalue decomposition method is able to identify between 60% and 80% of these (hot) sites.     

Folding-unfolding energy change of a simple sphere model protein and an energy landscape of the folding process

We have calculated the free energy of a spherical model of a protein or part of a protein generated in the way of protein folding. Two spherical models are examined; one is a homogeneous model consisting of only one residue type—hydrophobic. The other is a heterogeneous model consisting of two residue types—strong hydrophobic and weak hydrophobic. Both models show a folding transition state, and the latter model reproduces the trend of the experimental folded-unfolded energy change. The heterogeneous model suggests that in the folding process of a protein of more than 70 residues, a specific region of the protein folds first to form a stable region, then the other residues follow the folding process. The energy landscape of folding of a small protein is approximately a funnel model, whereas a flatter energy landscape is suggested for larger proteins of more than 55–70 residues. Proteins 33:408–416, 1998. © 1998 Wiley-Liss, Inc.     

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.     

Kinetic coupling between protein folding and prolyl isomerization. II. Folding of ribonuclease A and ribonuclease T1.

The folding and unfolding kinetics within the transition region were measured for RNase A and for RNase T1. The data were used to evaluate the theoretical models for the influence of prolyl isomerization on the observed folding kinetics. These two proteins were selected, since the folding reaction of RNase A is faster than prolyl isomerization, whereas in RNase T1, folding is slower than isomerization in the transition region. Folding of RNase T1 was investigated for three variants with different numbers of cis prolyl residues. The results indicate that in the transition region the folding rates are indeed strongly dependent on the number of prolyl residues. The variant of RNase T1 that contains only one cis prolyl residue folds about ten times faster than two variants that contain two cis prolyl residues. For both RNase A and RNase T1, the apparent rates of folding and unfolding as well as the corresponding amplitudes depend on the concentration of denaturant in a manner that was predicted by the model calculations. When refolding was started from the fast-folding species, additional kinetic phases could be observed in the transition region for both proteins. The obtained values could be used to calculate the microscopic rate constants of folding and isomerization on the basis of theoretical models.     

Frequencies of amino acid strings in globular protein sequences indicate suppression of blocks of consecutive hydrophobic residues

Patterns of hydrophobic and hydrophilic residues play a major role in protein folding and function. Long, predominantly hydrophobic strings of 20-22 amino acids each are associated with transmembrane helices and have been used to identify such sequences. Much less attention has been paid to hydrophobic sequences within globular proteins. In prior work on computer simulations of the competition between on-pathway folding and off-pathway aggregate formation, we found that long sequences of consecutive hydrophobic residues promoted aggregation within the model, even controlling for overall hydrophobic content. We report here on an analysis of the frequencies of different lengths of contiguous blocks of hydrophobic residues in a database of amino acid sequences of proteins of known structure. Sequences of three or more consecutive hydrophobic residues are found to be significantly less common in actual globular proteins than would be predicted if residues were selected independently. The result may reflect selection against long blocks of hydrophobic residues within globular proteins relative to what would be expected if residue hydrophobicities were independent of those of nearby residues in the sequence.     

Conserved residues and their role in the structure, function, and stability of acyl-coenzyme A binding protein

In the family of acyl-coenzyme A binding proteins, a subset of 26 sequence sites are identical in all eukaryotes and conserved throughout evolution of the eukaryotic kingdoms. In the context of the bovine protein, the importance of these 26 sequence positions for structure, function, stability, and folding has been analyzed using single-site mutations. A total of 28 mutant proteins were analyzed which covered 17 conserved sequence positions and three nonconserved positions. As a first step, the influence of the mutations on the protein folding reaction has been probed, revealing a folding nucleus of eight hydrophobic residues formed between the N- and C-terminal helices [Kragelund, B. B., et al. (1999) Nat. Struct. Biol. (In press)]. To fully analyze the role of the conserved residues, the function and the stability have been measured for the same set of mutant proteins. Effects on function were measured by the extent of binding of the ligand dodecanoyl-CoA using isothermal titration calorimetry, and effects on protein stability were measured with chemical denaturation followed by intrinsic tryptophan and tyrosine fluorescence. The sequence sites that have been conserved for direct functional purposes have been identified. These are Phe5, Tyr28, Tyr31, Lys32, Lys54, and Tyr73. Binding site residues are mainly polar or charged residues, and together, four of these contribute approximately 8 kcal mol-1 of the total free energy of binding of 11 kcal mol-1. The sequence sites conserved for stability of the structure have likewise been identified and are Phe5, Ala9, Val12, Leu15, Leu25, Tyr28, Lys32, Gln33, Tyr73, Val77, and Leu80. Essentially, all of the conserved residues that maintain the stability are hydrophobic residues at the interface of the helices. Only one conserved polar residue, Gln33, is involved in stability. The results indicate that conservation of residues in homologous proteins may result from a summed optimization of an effective folding reaction, a stable native protein, and a fully active binding site. This is important in protein design strategies, where optimization of one of these parameters, typically function or stability, may influence any of the others markedly.     

Parser for protein folding units

General patterns of protein structural organization have emerged from studies of hundreds of structures elucidated by X-ray crystallography and nuclear magnetic resonance. Structural units are commonly identified by visual inspection of molecular models using qualitative criteria. Here, we propose an algorithm for identification of structural units by objective, quantitative criteria based on atomic interactions. The underlying physical concept is maximal interactions within each unit and minimal interaction between units (domains). In a simple harmonic approximation, interdomain dynamics is determined by the strength of the interface and the distribution of masses. The most likely domain decomposition involves units with the most correlated motion, or largest interdomain fluctuation time. The decomposition of a convoluted 3-D structure is complicated by the possibility that the chain can cross over several times between units. Grouping the residues by solving an eigenvalue problem for the contact matrix reduces the problem to a one-dimensional search for all reasonable trial bisections. Recursive bisection yields a tree of putative folding units. Simple physical criteria are used to identify units that could exist by themselves. The units so defined closely correspond to crystallographers' notion of structural domains. The results are useful for the analysis of folding principles, for modular protein design and for protein engineering. © 1994 Wiley-Liss, Inc.     

Engineering strand-specific DNA nicking enzymes from the type IIS restriction endonucleases BsaI, BsmBI, and BsmAI

To determine the extent to which protein folding rates and free energy landscapes have been shaped by natural selection, we have examined the folding kinetics of five proteins generated using computational design methods and, hence, never exposed to natural selection. Four of these proteins are complete computer-generated redesigns of naturally occurring structures and the fifth protein, called Top7, has a computer-generated fold not yet observed in nature. We find that three of the four redesigned proteins fold much faster than their naturally occurring counterparts. While natural selection thus does not appear to operate on protein folding rates, the majority of the designed proteins unfold considerably faster than their naturally occurring counterparts, suggesting possible selection for a high free energy barrier to unfolding. In contrast to almost all naturally occurring proteins of less than 100 residues but consistent with simple computational models, the folding energy landscape for Top7 appears to be quite complex, suggesting the smooth energy landscapes and highly cooperative folding transitions observed for small naturally occurring proteins may also reflect the workings of natural selection.     

Native protein sequences are designed to destabilize folding intermediates

Hydrophobic core mutants of sperm whale apomyoglobin were constructed to investigate the amino acid sequence features that determine the folding properties. Replacements of all of the Ile residues with Leu and of all of the Ile and Val residues with Leu decreased the thermodynamic stability of the folded states against the unfolded states but increased the stability of the folding intermediates against the unfolded states, indicating that the amino acid composition of the protein core is important for the protein stability and folding cooperativity. To examine the effect of the arrangement of these hydrophobic residues, mutant proteins were further constructed: 12 sites out of the 18 Leu, 9 Ile, and 8 Val residues of the wild-type myoglobin were randomly replaced with each other so that the amino acid compositions were similar to that of the wild-type protein. Four mutant proteins were obtained without selection of the protein properties. These residue replacements similarly resulted in the stabilization of both the intermediate and folded states against the unfolded states, as compared to the wild-type protein. Thus, the arrangements of the hydrophobic residues in the native amino acid sequence are selected to destabilize the folding intermediate rather than to stabilize the folded state. The present results suggest that the two-state transition of protein folding or the transient formation of the unstable intermediate, which seems to be required for effective production of the functional proteins, has been a major driving force in the molecular evolution of natural globular proteins.     

Thermodynamics, kinetics, and salt dependence of folding of YopM, a large leucine-rich repeat protein

Small globular proteins have many contacts between residues that are distant in primary sequence. These contacts create a complex network between sequence-distant segments of secondary structure, which may be expected to promote the cooperative folding of globular proteins. Although repeat proteins, which are composed of tandem modular units, lack sequence-distant contacts, several of considerable length have been shown to undergo cooperative two-state folding. To explore the limits of cooperativity in repeat proteins, we have studied the unfolding of YopM, a leucine-rich repeat (LRR) protein of over 400 residues. Despite its large size and modular architecture (15 repeats), YopM equilibrium unfolding is highly cooperative, and shows a very strong dependence on the concentration of urea. In contrast, kinetic studies of YopM folding indicate a mechanism that includes one or more transient intermediates. The urea dependence of the folding and unfolding rates suggests a relatively small transition state ensemble. As with the urea dependence, we have found an extreme dependence of the free energy of unfolding on the concentration of salt. This salt dependence likely results from general screening of a large number of unfavorable columbic interactions in the folded state, rather than from specific cation binding.     

Salt-bridges in the microenvironment of stable protein structures

Salt-bridges (sb) play an important role in the folding and stability of proteins. This is deduced from the evaluation of net energy in the microenvironments (ME, residues that are 4 Å away from positive and negative partners of salt-bridge and interact with them). MEs act as a determinant of net-energy due to the intrinsic features in the sequence. The stability of extremophilic proteins is due to the presence of favorable residues at the ME without any unfavorable residues. We studied a dataset of four structures from the protein data bank (PDB) and a homology model (1HM5) to gain insights on this issue. Data shows that the presence of isolated charges and polar residues in the core of extremophilic proteins helps in the formation of stable salt-bridges with reduced desolvation. Thus, site-specific mutations with favorable residues at the ME will help to develop thermo stable proteins with strong salt bridges.     

Consistency in structural energetics of protein folding and peptide recognition.

We report a new free energy decomposition that includes structure-derived atomic contact energies for the desolvation component, and show that it applies equally well to the analysis of single-domain protein folding and to the binding of flexible peptides to proteins. Specifically, we selected the 17 single-domain proteins for which the three-dimensional structures and thermodynamic unfolding free energies are available. By calculating all terms except the backbone conformational entropy change and comparing the result to the experimentally measured free energy, we estimated that the mean entropy gain by the backbone chain upon unfolding (delta Sbb) is 5.3 cal/K per mole of residue, and that the average backbone entropy for glycine is 6.7 cal/K. Both numbers are in close agreement with recent estimates made by entirely different methods, suggesting a promising degree of consistency between data obtained from disparate sources. In addition, a quantitative analysis of the folding free energy indicates that the unfavorable backbone entropy for each of the proteins is balanced predominantly by favorable backbone interactions. Finally, because the binding of flexible peptides to receptors is physically similar to folding, the free energy function should, in principle, be equally applicable to flexible docking. By combining atomic contact energies, electrostatics, and sequence-dependent backbone entropy, we calculated a priori the free energy changes associated with the binding of four different peptides to HLA-A2, 1 MHC molecule and found agreement with experiment to within 10% without parameter adjustment.     

Specific interactions for ab initio folding of protein terminal regions with secondary structures

Proteins fold into unique three-dimensional structures by specific, orientation-dependent interactions between amino acid residues. Here, we extract orientation-dependent interactions from protein structures by treating each polar atom as a dipole with a direction. The resulting statistical energy function successfully refolds 13 out of 16 fully unfolded secondary-structure terminal regions of 10-23 amino acid residues in 15 small proteins. Dissecting the orientation-dependent energy function reveals that the orientation preference between hydrogen-bonded atoms is not enough to account for the structural specificity of proteins. The result has significant implications on the theoretical and experimental searches for specific interactions involved in protein folding and molecular recognition between proteins and other biologically active molecules.     

Identification of side-chain clusters in protein structures by a graph spectral method.

This paper presents a novel method to detect side-chain clusters in protein three-dimensional structures using a graph spectral approach. Protein side-chain interactions are represented by a labeled graph in which the nodes of the graph represent the Cbeta atoms and the edges represent the distance between the Cbeta atoms. The distance information and the non-bonded connectivity of the residues are represented in the form of a matrix called the Laplacian matrix. The constructed matrix is diagonalized and clustering information is obtained from the vector components associated with the second lowest eigenvalue and cluster centers are obtained from the vector components associated with the top eigenvalues. The method uses global information for clustering and a single numeric computation is required to detect clusters of interest. The approach has been adopted here to detect a variety of side-chain clusters and identify the residue which makes the largest number of interactions among the residues forming the cluster (cluster centers). Detecting such clusters and cluster centers are important from a protein structure and folding point of view. The crucial residues which are important in the folding pathway as determined by PhiF values (which is a measure of the effect of a mutation on the stability of the transition state of folding) as obtained from protein engineering methods, can be identified from the vector components corresponding to the top eigenvalues. Expanded clusters are detected near the active and binding site of the protein, supporting the nucleation condensation hypothesis for folding. The method is also shown to detect domains in protein structures and conserved side-chain clusters in topologically similar proteins.     

Statistical mechanics of protein folding by cluster distance geometry

This is our second type of model for protein folding where the configurational parameters and the effective potential energy function are chosen in such a way that all conformations are described and the canonical partition function can be evaluated analytically. Structure is described in terms of distances between pairs of sequentially contiguous blocks of eight residues, and all possible conformations are grouped into 71 subsets in terms of bounds on these distances. The energy is taken to be a sum of pairwise interactions between such blocks. The 210 energy parameters were adjusted so that the native folds of 32 small proteins are favored in free energy over the denatured state. We then found 146 proteins having negligible sequence similarity to any of the training proteins, yet the free energy of the respective correct native states were favored over the denatured state.     

Exploring structures in protein folding funnels with free energy functionals: the transition state ensemble

We use free energy functionals that account for the partial ordering of residues in the transition state ensemble to characterize the free energy surfaces for fast folding proteins. We concentrate on chymotrypsin inhibitor and lambda-repressor. We show how the explicit cooperativity that can arise from many body forces, such as side-chain ordering or hydrophobic surface burial, determines the crossover from folding with a large delocalized nucleus and the specific small classical nucleus of the type envisioned in nucleation growth scenarios. We compare the structural correlations present in the transition state ensemble obtained from free energy functionals with those inferred from experiment using extrathermodynamic free energy relations for folding time obtained via protein engineering kinetics experiments. We also use the free energy functionals to examine both the size of barriers and multidimensional representations of the free energy profiles in order to address the question of appropriate reaction coordinates for folding.     

Understanding the folding and stability of a designed WW domain protein with replica exchange molecular dynamics simulations

WW domain proteins are usually regarded as simple models for understanding the folding mechanism of β-sheet. CC45 is an artificial protein that is capable of folding into the same structure as WW domain. In this article, the replica exchange molecular dynamics simulations are performed to investigate the folding mechanism of CC45. The analysis of thermal stability shows that β-hairpin 1 is more stable than β-hairpin 2 during the unfolding process. Free energy analysis shows that the unfolding of this protein substantially proceeds through solvating the smaller β-hairpin 2, followed by the unfolding of β-hairpin 1. We further propose the unfolding process of CC45 and the folding mechanism of two β-hairpins. These results are similar to the previous folding studies of formin binding protein 28 (FBP28). Compared with FBP28, it is found that CC45 has more aromatic residues in N-terminal loop, and these residues contact with C-terminal loop to form the outer hydrophobic core, which increases the stability of CC45. Knowledge about the stability and folding behaviour of CC45 may help in understanding the folding mechanisms of the β-sheet and in designing new WW domains.