The optimal fraction of hydrophobic residues required to ensure protein collapse

The hydrophobic interaction is the main driving force for protein folding. Here, we address the question of what is the optimal fraction, f of hydrophobic (H) residues required to ensure protein collapse. For very small f (say f<0.1), the protein chain is expected to behave as a random coil, where the H residues are "wrapped" locally by polar (P) residues. However, for large enough f this local coverage cannot be achieved and the thermodynamic alternative to avoid contact with water is burying the H residues in the interior of a compact chain structure. The interior also contains P residues that are known to be clustered to optimize their electrostatic interactions. This means that the H residues are clustered as well, i.e. they effectively attract each other like the H-monomers in Dill's HP lattice model. Previously, we asked the question: assuming that the H monomers in the HP model are distributed randomly along the chain, what fraction of them is required to ensure a compact ground state? We claimed there that f approximately p(c), where p(c) is the site percolation threshold of the lattice (in a percolation experiment, each site of an initially empty lattice is visited and a particle is placed there with a probability p. The interest is in the critical (minimal) value, p(c), for which percolation occurs, i.e. a cluster connecting the opposite sides of the lattice is created). Due to the above correspondence between the HP model and real proteins (and assuming that the H residues are distributed at random) we suggest that the experimental f should lead to percolating clusters of H residues over the highly dense protein core, i.e. clusters of the core size. To check this theory, we treat a simplified model consisting of H and P residues represented by their alpha-carbon atoms only. The structure is defined by the C(alpha)-C(alpha) virtual bond lengths, angles and dihedral angles, and the X-ray structure is best-fitted onto a face-centered cubic lattice. Percolation experiments are carried out for 103 single-chain proteins using six different hydrophobic sets of residues. Indeed, on average, percolating clusters are generated, which supports our theory; however, some sets lead to a better core coverage than others. We also calculate the largest actual hydrophobic cluster of each protein and show that, on average, these clusters span the core, again in accord with our theory. We discuss the effect of protein size, deviations from the average picture, and implications of this study for defining reliable simplified models of proteins.     

Effect of site-directed point mutations on protein misfolding: A simulation study

A Monte Carlo simulation based sequence design method is proposed to investigate the role of site-directed point mutations in protein misfolding. Site-directed point mutations are incorporated in the designed sequences of selected proteins. While most mutated sequences correctly fold to their native conformation, some of them stabilize in other nonnative conformations and thus misfold/unfold. The results suggest that a critical number of hydrophobic amino acid residues must be present in the core of the correctly folded proteins, whereas proteins misfold/unfold if this number of hydrophobic residues falls below the critical limit. A protein can accommodate only a particular number of hydrophobic residues at the surface, provided a large number of hydrophilic residues are present at the surface and critical hydrophobicity of the core is preserved. Some surface sites are observed to be equally sensitive toward site-directed point mutations as the core sites. Point mutations with highly polar and charged amino acids increases the misfold/unfold propensity of proteins. Substitution of natural amino acids at sites with different number of nonbonded contacts suggests that both amino acid identity and its respective site-specificity determine the stability of a protein. A clash-match method is developed to calculate the number of matching and clashing interactions in the mutated protein sequences. While misfolded/unfolded sequences have a higher number of clashing and a lower number of matching interactions, the correctly folded sequences have a lower number of clashing and a higher number of matching interactions. These results are valid for different SCOP classes of proteins.     

Detection of secondary structure elements in proteins by hydrophobic cluster analysis.

Hydrophobic cluster analysis (HCA) is a protein sequence comparison method based on alpha-helical representations of the sequences where the size, shape and orientation of the clusters of hydrophobic residues are primarily compared. The effectiveness of HCA has been suggested to originate from its potential ability to focus on the residues forming the hydrophobic core of globular proteins. We have addressed the robustness of the bidimensional representation used for HCA in its ability to detect the regular secondary structure elements of proteins. Various parameters have been studied such as those governing cluster size and limits, the hydrophobic residues constituting the clusters as well as the potential shift of the cluster positions with respect to the position of the regular secondary structure elements. The following results have been found to support the alpha-helical bidimensional representation used in HCA: (i) there is a positive correlation (clearly above background noise) between the hydrophobic clusters and the regular secondary structure elements in proteins; (ii) the hydrophobic clusters are centred on the regular secondary structure elements; (iii) the pitch of the helical representation which gives the best correspondence is that of an alpha-helix. The correspondence between hydrophobic clusters and regular secondary structure elements suggests a way to implement variable gap penalties during the automatic alignment of protein sequences.     

A new approach to the design of uniquely folded thermally stable proteins

A new computer program (CORE) is described that predicts core hydrophobic sequences of predetermined target protein structures. A novel scoring function is employed, which for the first time incorporates parameters directly correlated to free energies of unfolding (deltaGu), melting temperatures (Tm), and cooperativity. Metropolis-driven simulated annealing and low-temperature Monte Carlo sampling are used to optimize this score, generating sequences predicted to yield uniquely folded, stable proteins with cooperative unfolding transitions. The hydrophobic core residues of four natural proteins were predicted using CORE with the backbone structure and solvent exposed residues as input. In the two smaller proteins tested (Gbeta1, 11 core amino acids; 434 cro, 10 core amino acids), the native sequence was regenerated as well as the sequence of known thermally stable variants that exhibit cooperative denaturation transitions. Previously designed sequences of variants with lower thermal stability and weaker cooperativity were not predicted. In the two larger proteins tested (myoglobin, 32 core amino acids; methionine aminopeptidase, 63 core amino acids), sequences with corresponding side-chain conformations remarkably similar to that of native were predicted.     

Energy minimization method using automata network for sequence and side-chain conformation prediction from given backbone geometry

Globular proteins have high packing densities as a result of residue side chains in the core achieving a tight, complementary packing. The internal packing is considered the main determinant of native protein structure. From that point of view, we present here a method of energy minimization using an automata network to predict a set of amino acid sequences and their side-chain conformations from a desired backbone geometry for de novo design of proteins. Using discrete side-chain conformations, that is, rotamers, the sequence generation problem from a given backbone geometry becomes one of combinatorial problems. We focused on the residues composing the interior core region and predicted a set of amino acid Sequences and their side-chain conformations only from a given backbone geometry. The kinds of residues were restricted to six hydrophobic amino acids (Ala, Ile, Met, Leu, Phe, and Val) because the core regions are almost always composed of hydrophobic residues. The obtained sequences were well packed as was the native sequence. The method can be used for automated sequence generation in the de novo design of proteins. © 1994 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.     

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.     

Improving computational protein design by using structure‐derived sequence profile

Designing a protein sequence that will fold into a predefined structure is of both practical and fundamental interest. Many successful, computational designs in the last decade resulted from improved understanding of hydrophobic and polar interactions between side chains of amino acid residues in stabilizing protein tertiary structures. However, the coupling between main‐chain backbone structure and local sequence has yet to be fully addressed. Here, we attempt to account for such coupling by using a sequence profile derived from the sequences of five residue fragments in a fragment library that are structurally matched to the five‐residue segments contained in a target structure. We further introduced a term to reduce low complexity regions of designed sequences. These two terms together with optimized reference states for amino‐acid residues were implemented in the RosettaDesign program. The new method, called RosettaDesign‐SR, makes a 12% increase (from 34 to 46%) in fraction of proteins whose designed sequences are more than 35% identical to wild‐type sequences. Meanwhile, it reduces 8% (from 22% to 14%) to the number of designed sequences that are not homologous to any known protein sequences according to psi‐blast. More importantly, the sequences designed by RosettaDesign‐SR have 2–3% more polar residues at the surface and core regions of proteins and these surface and core polar residues have about 4% higher sequence identity to wild‐type sequences than by RosettaDesign. Thus, the proteins designed by RosettaDesign‐SR should be less likely to aggregate and more likely to have unique structures due to more specific polar interactions. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Statistical distribution of hydrophobic residues along the length of protein chains. Implications for protein folding and evolution.

We consider in this paper the statistical distribution of hydrophobic residues along the length of protein chains. For this purpose we used a binary hydrophobicity scale which assigns hydrophobic residues a value of one and non-hydrophobes a value of zero. The resulting binary sequences are tested for randomness using the standard run test. For the majority of the 5,247 proteins examined, the distribution of hydrophobic residues along a sequence cannot be distinguished from that expected for a random distribution. This suggests that (a) functional proteins may have originated from random sequences, (b) the folding of proteins into compact structures may be much more permissive with less sequence specificity than previously thought, and (c) the clusters of hydrophobic residues along chains which are revealed by hydrophobicity plots are a natural consequence of a random distribution and can be conveniently described by binomial statistics.     

Polar residues in the protein core of Escherichia coli thioredoxin are important for fold specificity

Most globular proteins contain a core of hydrophobic residues that are inaccessible to solvent in the folded state. In general, polar residues in the core are thermodynamically unfavorable except when they are able to form intramolecular hydrogen bonds. Compared to hydrophobic interactions, polar interactions are more directional in character and may aid in fold specificity. In a survey of 263 globular protein structures, we found a strong positive correlation between the number of polar residues at core positions and protein size. To probe the importance of buried polar residues, we experimentally tested the effects of hydrophobic mutations at the five polar core residues in Escherichia coli thioredoxin. Proteins with single hydrophobic mutations (D26I, C32A, C35A, T66L, and T77V) all have cooperative unfolding transitions like the wild type (wt), as determined by chemical denaturation. Relative to wt, D26I is more stable while the other point mutants are less stable. The combined 5-fold mutant protein (IAALV) is less stable than wt and has an unfolding transition that is substantially less cooperative than that of wt. NMR spectra as well as amide deuterium exchange indicate that IAALV is likely sampling a number of low-energy structures in the folded state, suggesting that polar residues in the core are important for specifying a well-folded native structure.     

The role of the N region in signal sequence and signal-anchor function.

To determine the role of sequences other than the hydrophobic core in mediating signal sequence function, we examined the behavior of fusion proteins and deletion mutants in cell-free systems. We demonstrate that neither the N nor the C region of the preprolactin signal sequence is necessary for translocation. However, insertion of sequences with either a net charge of +2.5 or -6.0 between the N region and the hydrophobic core of the signal converted it into a signal-anchor. The topologies adopted (types I and II, respectively) were opposite those predicted from the distribution of charges surrounding the hydrophobic core of the signals. When these mutant signals were located in the interior of an otherwise secreted protein, both sequences functioned as stop-transfer sequences. Related mutations were assayed in fusion proteins in which the IgM transmembrane domain functioned as an amino-terminal signal-anchor. For these molecules, the distribution of charged residues surrounding the hydrophobic core had no influence on the topology adopted. Our results suggest that features other than simple charge distribution play an important role in determining membrane topology in vitro.     

Residue cluster additivity of thermodynamic stability in the hydrophobic core of mesophile vs. hyperthermophile rubredoxins

The branched sidechain residues 24 and 33 in the hydrophobic core of rubredoxin differ between the Clostridium pasteurianum (Cp) and Pyrococcus furiosus (Pf) sequences. Their X-ray structures indicate that these two sidechains are in van der Waals contact with each other, while neither appears to significantly interact with the other nonconserved residues. The simultaneous interchange of residues 24 and 33 between the Cp and Pf rubredoxin sequences yield a complementary pair of hybrid proteins for which the sum of their thermodynamic stabilities equals that of the parental rubredoxins. The 1.2 kcal/mol change arising from this two residues interchange accounts for 21% of the differential thermodynamic stability between the mesophile and hyperthermophile proteins. The additional interchange of the sole nonconserved aromatic residue in the hydrophobic core yields a 0.78 kcal/mol deviation from thermodynamic additivity.     

De novo design of the hydrophobic cores of proteins.

We have developed and experimentally tested a novel computational approach for the de novo design of hydrophobic cores. A pair of computer programs has been written, the first of which creates a "custom" rotamer library for potential hydrophobic residues, based on the backbone structure of the protein of interest. The second program uses a genetic algorithm to globally optimize for a low energy core sequence and structure, using the custom rotamer library as input. Success of the programs in predicting the sequences of native proteins indicates that they should be effective tools for protein design. Using these programs, we have designed and engineered several variants of the phage 434 cro protein, containing five, seven, or eight sequence changes in the hydrophobic core. As controls, we have produced a variant consisting of a randomly generated core with six sequence changes but equal volume relative to the native core and a variant with a "minimalist" core containing predominantly leucine residues. Two of the designs, including one with eight core sequence changes, have thermal stabilities comparable to the native protein, whereas the third design and the minimalist protein are significantly destabilized. The randomly designed control is completely unfolded under equivalent conditions. These results suggest that rational de novo design of hydrophobic cores is feasible, and stress the importance of specific packing interactions for the stability of proteins. A surprising aspect of the results is that all of the variants display highly cooperative thermal denaturation curves and reasonably dispersed NMR spectra. This suggests that the non-core residues of a protein play a significant role in determining the uniqueness of the folded structure.     

A tripartite structure of the signals that determine protein insertion into the endoplasmic reticulum membrane

Multilineage colony stimulating factor is a secretory protein with a cleavable signal sequence that is unusually long and hydrophobic. Using molecular cloning techniques we exchanged sequences NH2- or COOH-terminally flanking the hydrophobic signal sequence. Such modified fusion proteins still inserted into the membrane but their signal sequence was not cleaved. Instead the proteins were now anchored in the membrane by the formerly cleaved signal sequence (signal-anchor sequence). They exposed the NH2 terminus on the exoplasmic and the COOH terminus on the cytoplasmic side of the membrane. We conclude from our results that hydrophilic sequences flanking the hydrophobic core of a signal sequence can determine cleavage by signal peptidase and insertion into the membrane. It appears that negatively charged amino acid residues close to the NH2 terminal side of the hydrophobic segment are compatible with translocation of this segment across the membrane. A tripartite structure is proposed for signal-anchor sequences: a hydrophobic core region that mediates targeting to and insertion into the ER membrane and flanking hydrophilic segments that determine the orientation of the protein in the membrane.     

Identification of amino acids involved in protein structural uniqueness: implication for de novo protein design

Structural uniqueness is characteristic of native proteins and is essential to express their biological functions. The major factors that bring about the uniqueness are specific interactions between hydrophobic residues and their unique packing in the protein core. To find the origin of the uniqueness in their amino acid sequences, we analyzed the distribution of the side chain rotational isomers (rotamers) of hydrophobic amino acids in protein tertiary structures and derived deltaS(contact), the conformational-entropy changes of side chains by residue-residue contacts in each secondary structure. The deltaS(contact) values indicate distinct tendencies of the residue pairs to restrict side chain conformation by inter-residue contacts. Of the hydrophobic residues in alpha-helices, aliphatic residues (Leu, Val, Ile) strongly restrict the side chain conformations of each other. In beta-sheets, Met is most strongly restricted by contact with Ile, whereas Leu, Val and Ile are less affected by other residues in contact than those in alpha-helices. In designed and native protein variants, deltaS(contact) was found to correlate with the folding-unfolding cooperativity. Thus, it can be used as a specificity parameter for designing artificial proteins with a unique structure.     

Increased sequence hydrophobicity reduces conformational specificity: A mutational case study of the Arc repressor protein

The amino-acid sequences of soluble, globular proteins must have hydrophobic residues to form a stable core, but excess sequence hydrophobicity can lead to loss of native state conformational specificity and aggregation. Previous studies of polar-to-hydrophobic mutations in the β-sheet of the Arc repressor dimer showed that a single substitution at position 11 (N11L) leads to population of an alternate dimeric fold in which the β-sheet is replaced by helix. Two additional hydrophobic mutations at positions 9 and 13 (Q9V and R13V) lead to population of a differently folded octamer along with both dimeric folds. Here we conduct a comprehensive study of the sequence determinants of this progressive loss of fold specificity. We find that the alternate dimer-fold specifically results from the N11L substitution and is not promoted by other hydrophobic substitutions in the β-sheet. We also find that three highly hydrophobic substitutions at positions 9, 11, and 13 are necessary and sufficient for oligomer formation, but the oligomer size depends on the identity of the hydrophobic residue in question. The hydrophobic substitutions increase thermal stability, illustrating how increased hydrophobicity can increase folding stability even as it degrades conformational specificity. The oligomeric variants are predicted to be aggregation-prone but may be hindered from doing so by proline residues that flank the β-sheet region. Loss of conformational specificity due to increased hydrophobicity can manifest itself at any level of structure, depending upon the specific mutations and the context in which they occur.     

Substitution rates in α-helical transmembrane proteins

It has been shown previously that some membrane proteins have a conserved core of amino acid residues. This idea not only serves to orient helices during model building exercises but may also provide insight into the structural role of residues mediating helix-helix interactions. Using experimentally determined high-resolution structures of alpha-helical transmembrane proteins we show that, of the residues within the hydrophobic transmembrane spans, the residues at lipid and subunit interfaces are more evolutionarily variable than those within the lipid-inaccessible core of a polypeptide's transmembrane domain. This supports the idea that helix-helix interactions within the same polypeptide chain and those at the interface between different polypeptide chains may arise in distinct ways. To show this, we use a new method to estimate the substitution rate of an amino acid residue given an alignment and phylogenetic tree of closely related proteins. This method gives better sensitivity in the otherwise-conserved transmembrane domains than a conventional similarity analysis and is relatively insensitive to the sequences used.     

Frequencies of hydrophobic and hydrophilic runs and alternations in proteins of known structure

Patterns of alternation of hydrophobic and polar residues are a profound aspect of amino acid sequences, but a feature not easily interpreted for soluble proteins. Here we report statistics of hydrophobicity patterns in proteins of known structure in a current protein database as compared with results from earlier, more limited structure sets. Previous studies indicated that long hydrophobic runs, common in membrane proteins, are underrepresented in soluble proteins. Long runs of hydrophobic residues remain significantly underrepresented in soluble proteins, with none longer than 16 residues observed. These long runs most commonly occur as buried alpha helices, with extended hydrophobic strands less common. Avoiding aggregation of partially folded intermediates during intracellular folding remains a viable explanation for the rarity of long hydrophobic runs in soluble proteins. Comparison between database editions reveals robustness of statistics on aqueous proteins despite an approximately twofold increase in nonredundant sequences. The expanded database does now allow us to explain several deviations of hydrophobicity statistics from models of random sequence in terms of requirements of specific secondary structure elements. Comparison to prior membrane-bound protein sequences, however, shows significant qualitative changes, with the average hydrophobicity and frequency of long runs of hydrophobic residues noticeably increasing between the database editions. These results suggest that the aqueous proteins of solved structure may represent an essentially complete sample of the universe of aqueous sequences, while the membrane proteins of known structure are not yet representative of the universe of membrane-associated proteins, even by relatively simple measures of hydrophobic patterns.     

A putative signal peptidase recognition site and sequence in eukaryotic and prokaryotic signal peptides

Presecretory signal peptides of 39 proteins from diverse prokaryotic and eukaryotic sources have been compared. Although varying in length and amino acid composition, the labile peptides share a hydrophobic core of approximately 12 amino acids. A positively charged residue (Lys or Arg) usually precedes the hydrophobic core. Core termination is defined by the occurrence of a charged residue, a sequence of residues which may induce a beta-turn in a polypeptide, or an interruption in potential alpha-helix or beta-extended strand structure. The hydrophobic cores contain, by weight average, 37% Leu: 15% Ala: 10% Val: 10% Phe: 7% Ile plus 21% other hydrophobic amino acids arranged in a non-random sequence. Following the hydrophobic cores (aligned by their last residue) a highly non-random and localized distribution of Ala is apparent within the initial eight positions following the core: (formula; see text) Coincident with this observation, Ala-X-Ala is the most frequent sequence preceding signal peptidase cleavage. We propose the existence of a signal peptidase recognition sequence A-X-B with the preferred cleavage site located after the sixth amino acid following the core sequence. Twenty-two of the above 27 underlined Ala residues would participate as A or B in peptidase cleavage. Position A includes the larger aliphatic amino acids, Leu, Val and Ile, as well as the residues already found at B (principally Ala, Gly and Ser). Since a preferred cleavage site can be discerned from carboxyl and not amino terminal alignment of the hydrophobic cores it is proposed that the carboxyl ends are oriented inward toward the lumen of the endoplasmic reticulum where cleavage is thought to occur. This orientation coupled with the predicted beta-turn typically found between the core and the cleavage site implies reverse hairpin insertion of the signal sequence. The structural features which we describe should help identify signal peptides and cleavage sites in presumptive amino acid sequences derived from DNA sequences.     

The role of internal packing interactions in determining the structure and stability of a protein

Cassette mutagenesis has been used to investigate how internal packing interactions help to specify a protein's three-dimensional structure and stability. Three interacting residues in the hydrophobic core of the N-terminal domain of lambda repressor were randomized combinatorially. The randomization was restricted to the five amino acids Val, Leu, Ile, Met and Phe, thereby generating a sterically diverse set of core sequences composed solely of hydrophobic residues. We have isolated 78 of the 125 possible sequences generated by this randomization. Approximately 70% of the isolated sequences show some level of biological activity, and thus still carry sufficient information to encode the basic structure of lambda repressor. An assay based on the temperature dependence of activity in vivo has been used to estimate the relative activities and thermal stabilities of the set of mutants. In addition, nine mutants have been purified and their stabilities and DNA binding activities characterized in vitro. Of the 56 active sequences, only two, in addition to the wild-type, maintain the wild-type level of stability and activity. All three of these proteins satisfy stringent requirements for specifically shaped residues at each position. All of the remaining active sequences have reduced stabilities and/or reduced DNA binding affinities. These and previous results suggest that there are two levels of structural information encoded in core residues. At the first level, the basic structural information appears to reside largely in the hydrophobic character of these residues. The majority of sequences that simply maintain hydrophobicity at core positions are able to adopt the overall lambda repressor fold and maintain moderate stability. At the second, more detailed level, specific steric features of these residues and their packing interactions clearly act as important determinants of the protein's precise structure and stability. These results imply that many of the basic structural features of a protein could be predicted from relatively simple, degenerate sequence patterns.