Dynamic Monte Carlo simulations of globular protein folding/unfolding pathways. II. Alpha-helical motifs

Dynamic Monte Carlo simulations of the folding pathways of alpha-helical protein motifs have been undertaken in the context of a diamond lattice model of globular proteins. The first question addressed in the nature of the assembly process of an alpha-helical hairpin. While the hairpin could, in principle, be formed via the diffusion-collision-adhesion of isolated performed helices, this is not the dominant mechanism of assembly found in the simulations. Rather, the helices that form native hairpins are constructed on-site, with folding initiating at or near the turn in almost all cases. Next, the folding/unfolding pathways of four-helix bundles having tight bends and one and two long loops in the native state are explored. Once again, an on-site construction mechanism of folding obtains, with a hairpin forming first, followed by the formation of a three-helix bundle, and finally the fourth helix of the native bundle assembles. Unfolding is essentially the reverse of folding. A simplified analytic theory is developed that reproduces the equilibrium folding transitions obtained from the simulations remarkably well and, for the dominant folding pathway, correctly identifies the intermediates seen in the simulations. The analytic theory provides the free energy along the reaction co-ordinate and identifies the transition state for all three motifs as being quite close to the native state, with three of the four helices assembled, and approximately one turn of the fourth helix in place. The transition state is separated from the native conformation by a free-energy barrier of mainly energetic origin and from the denatured state by a barrier of mainly entropic origin. The general features of the folding pathway seen in all variants of the model four-helix bundles are similar to those observed in the folding of beta-barrel, Greek key proteins; this suggests that many of the qualitative aspects of folding are invariant to the particular native state topology and secondary structure.     

Characteristic features of amino acid residues in coiled-coil protein structures

Detailed analyses of protein structures provide an opportunity to understand conformation and function in terms of amino acid sequence and composition. In this work, we have systematically analyzed the characteristic features of the amino acid residues found in alpha-helical coiled-coils and, in so doing, have developed indices for their properties, conformational parameters, surrounding hydrophobicity and flexibility. As expected, there is preference for hydrophobic (Ala, Leu), positive (Lys, Arg) and negatively (Glu) charged residues in coiled-coil domains. However, the surrounding hydrophobicity of residues in coiled-coil domains is significantly less than that for residues in other regions of coiled-coil proteins. The analysis of temperature factors in coiled-coil proteins shows that the residues in these domains are more stable than those in other regions. Further, we have delineated the medium- and long-range contacts in coiled-coil domains and compared the results with those obtained for other (non-coiled-coil) parts of the same proteins and non-coiled-coil helical segments of globular proteins. The residues in coiled-coil domains are largely influenced by medium-range contacts, whereas long-range interactions play a dominant role in other regions of these same proteins as well as in non-coiled-coil helices. We have also revealed the preference of amino acid residues to form cation-pi interactions and we found that Arg is more likely to form such interactions than Lys. The parameters developed in this work can be used to understand the folding and stability of coiled-coil proteins in general.     

Identification of Helical Packing Motifs Common to Bacteriorhodopsin and G Protein-Coupled Receptors

A sequence analysis and comparison of transmembrane helices in bacteriorhodopsin (BR) and G protein-coupled receptors (GPCRs) is presented to identify potential regions of homology across protein families. The results show a common pattern of residues is conserved within the interhelical contact regions of BR that fit a knob-into-hole structural motif previously postulated for globular proteins and photosynthetic reaction centers. Based on an alignment of conserved prolines in transmembrane helices, it is inferred that analogous helix packing arrangements are possible in the rhodopsin-like GPCRs. Molecular models of GPCR helices V and VI indicate these interactions occur between aromatic and hydrophobic residues flanking the highly conserved prolines in these sequences. A similar packing arrangement is shown to occur in the X-ray structure of the melittin which also displays a unique pairing of proline-linked helices. The contact pattern identified is further applied to predict the packing of pairs of proline-containing helices in the pheromone-like and cAMP GPCRs. A potential role in stabilizing structure formation is also suggested for the contacts. The results and conclusions are supported by recent biophysical studies of zinc binding to kappa-opioid receptor mutants.     

Identification of Helical Packing Motifs Common to Bacteriorhodopsin and G Protein-Coupled Receptors

A sequence analysis and comparison of transmembrane helices in bacteriorhodopsin (BR) and G protein-coupled receptors (GPCRs) is presented to identify potential regions of homology across protein families. The results show a common pattern of residues is conserved within the interhelical contact regions of BR that fit a knob-into-hole structural motif previously postulated for globular proteins and photosynthetic reaction centers. Based on an alignment of conserved prolines in transmembrane helices, it is inferred that analogous helix packing arrangements are possible in the rhodopsin-like GPCRs. Molecular models of GPCR helices V and VI indicate these interactions occur between aromatic and hydrophobic residues flanking the highly conserved prolines in these sequences. A similar packing arrangement is shown to occur in the X-ray structure of the melittin which also displays a unique pairing of proline-linked helices. The contact pattern identified is further applied to predict the packing of pairs of proline-containing helices in the pheromone-like and cAMP GPCRs. A potential role in stabilizing structure formation is also suggested for the contacts. The results and conclusions are supported by recent biophysical studies of zinc binding to kappa-opioid receptor mutants.     

Dynamics and hydration of the alpha-helices of apolipophorin III

Apolipophorin III (apoLp-III) is an exchangeable apolipoprotein whose structure is represented as a bundle of five amphipathic alpha-helices. In order to study the properties of the helical domains of apolipophorin III, we designed and obtained five single-tryptophan mutants of Locusta migratoria apoLp-III. The proteins were studied by UV absorption spectroscopy, time-resolved and steady-state fluorescence spectroscopy, and circular dichroism. Fluorescence anisotropy, near-UV CD and solute fluorescence quenching studies indicate that the Trp residues in helices 1 (N-terminal) and 5 (C-terminal) have the highest conformational flexibility. These two residues also showed the highest degree of hydration. Trp residues in helices 3 and 4 display the lowest mobility, as assessed by fluorescence anisotropy and near UV CD. The Trp residue in helix 2 is protected from the solvent but shows high mobility. As inferred from the properties of the Trp residues, helices 1 and 5 appear to have the highest conformational flexibility. Helix 2 has an intermediate mobility, whereas helices 3 and 4 appear to constitute a highly ordered domain. From the configuration of the helices in the tertiary structure of the protein, we estimated the relative strength of the five interhelical interactions of apoLp-III. These interactions can be ordered according to their apparent stabilizing strengths as: helix 3-helix 4 > helix 2-helix 3 > helix 4-helix 1 approximately helix 2-helix 5 > helix 1-helix 5. A new model for the conformational change that is expected to occur upon binding of the apolipoprotein to lipid is proposed. This model is significantly different from the currently accepted model (Breiter, D. R., Kanost, M. R., Benning, M. M., Wesemberg, G., Law, J. H., Wells, M. A., Rayment, I., and Holden, M. (1991) Biochemistry 30, 603-608). The model presented here predicts that the relaxation of the tertiary structure and the concomitant exposure of the hydrophobic core take place through the disruption of the weak interhelical contacts between helices 1 and 5. To some extent, the weakness of the helix 1-helix 5 interaction would be due to the parallel arrangement of these helices.     

Towards accurate residue-residue hydrophobic contact prediction for alpha helical proteins via integer linear optimization

A new optimization-based method is presented to predict the hydrophobic residue contacts in alpha-helical proteins. The proposed approach uses a high resolution distance dependent force field to calculate the interaction energy between different residues of a protein. The formulation predicts the hydrophobic contacts by minimizing the sum of these contact energies. These residue contacts are highly useful in narrowing down the conformational space searched by protein structure prediction algorithms. The proposed algorithm also offers the algorithmic advantage of producing a rank ordered list of the best contact sets. This model was tested on four independent alpha-helical protein test sets and was found to perform very well. The average accuracy of the predictions (separated by at least six residues) obtained using the presented method was approximately 66% for single domain proteins. The average true positive and false positive distances were also calculated for each protein test set and they are 8.87 and 14.67 A, respectively.     

Cotranslational, cosecretory protein folding and its renaturation from a denatured state

On the basis of the available experimental data on structure, biosynthesis and secretion of globular proteins it is concluded that an alpha-helix is a starting conformation at formation of the native structure of any globular protein (alpha-helical model for initiation of protein folding). The structural invariant (clusterization of hydrophobic side chains on the alpha-helix surface) in the amino acid sequences of globular proteins is found which is predicted by alpha-helical model for the initiation of protein folding. The model predicts the pyramidization of the atoms C and N of peptide groups during the formation of spatial structure of proteins and a number of other effects that can be put to the experimental test. In the work the mechanism for protein translocation across membrane lipid bilayer is also suggested.     

Influence of medium- and long-range interactions in different folding types of globular proteins

Recognition of protein fold from amino acid sequence is a challenging task. The structure and stability of proteins from different fold are mainly dictated by inter-residue interactions. In our earlier work, we have successfully used the medium- and long-range contacts for predicting the protein folding rates, discriminating globular and membrane proteins and for distinguishing protein structural classes. In this work, we analyze the role of inter-residue interactions in commonly occurring folds of globular proteins in order to understand their folding mechanisms. In the medium-range contacts, the globin fold and four-helical bundle proteins have more contacts than that of DNA-RNA fold although they all belong to all-alpha class. In long-range contacts, only the ribonuclease fold prefers 4-10 range and the other folding types prefer the range 21-30 in alpha/beta class proteins. Further, the preferred residues and residue pairs influenced by these different folds are discussed. The information about the preference of medium- and long-range contacts exhibited by the 20 amino acid residues can be effectively used to predict the folding type of each protein.     

Importance of context in protein folding: secondary structural propensities versus tertiary contact-assisted secondary structure formation

Molecular dynamics simulations can be used to reveal the detailed conformational behaviors of peptides and proteins. By comparing fragment and full-length protein simulations, we can investigate the role of each peptide segment in the folding process. Here, we take advantage of information regarding the helix formation process from our previous simulations of barnase and protein A as well as new simulations of four helical fragments from these proteins at three different temperatures, starting with both helical and extended structures. Segments with high helical propensity began the folding process by tethering the chain through side chain interactions involving either polar interactions, such as salt bridges, or hydrophobic staples. These tethers were frequently nonnative (i.e., not i --> i + 4 spacing) and provided a scaffold for other residues, thereby limiting the conformational search. The helical structure then propagated on both sides of the tether. Segments with low stability and propensity formed later in the folding process and utilized contacts with other portions of the protein when folding. These helices formed via a tertiary contact-assisted mechanism, primarily via hydrophobic contacts between residues distant in sequence. Thus, segments with different helical propensities appear to play different roles during protein folding. Furthermore, the active role of nonlocal side chains in helix formation highlights why we must move beyond simple hierarchical models of protein folding.     

Optimal potentials for predicting inter-helical packing in transmembrane proteins

A set of pairwise contact potentials between amino acid residues in transmembrane helices was determined from the known native structure of the transmembrane protein (TMP) bacteriorhodopsin by the method of perceptron learning, using Monte Carlo dynamics to generate suitable "decoy" structures. The procedure of finding these decoys is simpler than for globular proteins, since it is reasonable to assume that helices behave as independent, stable objects and, therefore, the search in the conformational space is greatly reduced. With the learnt potentials, the association of the helices in bacteriorhodopsin was successfully simulated. The folding of a second TMP (the helix-dimer glycophorin A) was then accomplished with only a refinement of the potentials from a small number of decoys.     

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.     

Comparison of helix interactions in membrane and soluble alpha-bundle proteins

Helix-helix interactions are important for the folding, stability, and function of membrane proteins. Here, two independent and complementary methods are used to investigate the nature and distribution of amino acids that mediate helix-helix interactions in membrane and soluble alpha-bundle proteins. The first method characterizes the packing density of individual amino acids in helical proteins based on the van der Waals surface area occluded by surrounding atoms. We have recently used this method to show that transmembrane helices pack more tightly, on average, than helices in soluble proteins. These studies are extended here to characterize the packing of interfacial and noninterfacial amino acids and the packing of amino acids in the interfaces of helices that have either right- or left-handed crossing angles, and either parallel or antiparallel orientations. We show that the most abundant tightly packed interfacial residues in membrane proteins are Gly, Ala, and Ser, and that helices with left-handed crossing angles are more tightly packed on average than helices with right-handed crossing angles. The second method used to characterize helix-helix interactions involves the use of helix contact plots. We find that helices in membrane proteins exhibit a broader distribution of interhelical contacts than helices in soluble proteins. Both helical membrane and soluble proteins make use of a general motif for helix interactions that relies mainly on four residues (Leu, Ala, Ile, Val) to mediate helix interactions in a fashion characteristic of left-handed helical coiled coils. However, a second motif for mediating helix interactions is revealed by the high occurrence and high average packing values of small and polar residues (Ala, Gly, Ser, Thr) in the helix interfaces of membrane proteins. Finally, we show that there is a strong linear correlation between the occurrence of residues in helix-helix interfaces and their packing values, and discuss these results with respect to membrane protein structure prediction and membrane protein stability.     

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.     

The Topology of the Energy Landscapes of Macromolecules in the Torsion Angle Space and the Principle of the Minimum Energy Dissipation Rate in Conformational Relaxation

This article discusses some basic problems of structural biology and molecular dynamics simulation methods that need to be taken into account when considering, the protein folding problem, and prediction of 3D-structures for biopolymers. A multidimensional Fourier series expansions were formulated for the energy landscapes of the systems with conformational mobility, These energy landscape representations are correct from the viewpoint of the topology of the macromolecule configuration spaces. The problem of the single global minimum on the energy landscape for proteins is discussed and is formulated in tems of phase rules for the component of Fourier expansions. This rule is formally similar to the problem of diffraction on a multidimensional cubic lattice. The calibration of biopolymer force fields and their correspondence to topologically correct energy landscapes are discussed. Equations of motion were obtained in a matrix form for the relaxation of a representative point position on a multidimensional potential energy surface. The solutions of the equations for conformational relaxation were shown to obey the principle of the minimum energy dissipation rate at a given relaxation rate of potential energy (or folding rate).     

The solution structure of ribosomal protein L18 from Bacillus stearothermophilus

A medium resolution solution structure has been obtained for L18 from Bacillus stearothermophilus (BstL18), a ribosomal protein that stabilizes the tertiary structure of 5S rRNA and mediates its interaction with the rest of the large subunit. The N-terminal 22 amino acid residues of BstL18 are unstructured in solution. Its remaining 98 residues form a globular domain that has the same topology as the globular domains of other L18s, but the orientation of helices is different. This conformational peculiarity should not prevent BstL18 from functioning in the ribosome the same way as other L18s.     

Insight into polyproline II helical bundle stability in an antifreeze protein denatured state

The use of polyproline II (PPII) helices in protein design is currently hindered by limitations in our understanding of their conformational stability and folding. Recent studies of the snow flea antifreeze protein (sfAFP), a useful model system composed of six PPII helices, suggested that a low denatured state entropy contributes to folding thermodynamics. Here, circular dichroism spectroscopy revealed minor populations of PPII like conformers at low temperature. To get atomic level information on the conformational ensemble and entropy of the reduced, denatured state of sfAFP, we have analyzed its chemical shifts and {¹H}-¹⁵N relaxation parameters by NMR spectroscopy at four experimental conditions. No significant populations of stable secondary structure were detected. The stiffening of certain N-terminal residues at neutral versus acidic pH and shifted pK_a values leads us to suggest that favorable charge-charge interactions could bias the conformational ensemble to favor the formation the C1-C28 disulfide bond during nascent folding, although no evidence for preferred contacts between these positions was detected by paramagnetic relaxation enhancement under denaturing conditions. Despite a high content of flexible glycine residues, the mobility of the sfAFP denatured ensemble is similar for denatured α/β proteins both on fast ps/ns as well as slower μs/ms timescales. These results are in line with a conformational entropy in the denatured ensemble resembling that of typical proteins and suggest that new structures based on PPII helical bundles should be amenable to protein design.     

Helix packing moments reveal diversity and conservation in membrane protein structure

Helical membrane proteins are more tightly packed and the packing interactions are more diverse than those found in helical soluble proteins. Based on a linear correlation between amino acid packing values and interhelical propensity, we propose the concept of a helix packing moment to predict the orientation of helices in helical membrane proteins and membrane protein complexes. We show that the helix packing moment correlates with the helix interfaces of helix dimers of single pass membrane proteins of known structure. Helix packing moments are also shown to help identify the packing interfaces in membrane proteins with multiple transmembrane helices, where a single helix can have multiple contact surfaces. Analyses are described on class A G protein-coupled receptors (GPCRs) with seven transmembrane helices. We show that the helix packing moments are conserved across the class A family of GPCRs and correspond to key structural contacts in rhodopsin. These contacts are distinct from the highly conserved signature motifs of GPCRs and have not previously been recognized. The specific amino acid types involved in these contacts, however, are not necessarily conserved between subfamilies of GPCRs, indicating that the same protein architecture can be supported by a diverse set of interactions. In GPCRs, as well as membrane channels and transporters, amino acid residues with small side-chains (Gly, Ala, Ser, Cys) allow tight helix packing by mediating strong van der Waals interactions between helices. Closely packed helices, in turn, facilitate interhelical hydrogen bonding of both weakly polar (Ser, Thr, Cys) and strongly polar (Asn, Gln, Glu, Asp, His, Arg, Lys) amino acid residues. We propose the use of the helix packing moment as a complementary tool to the helical hydrophobic moment in the analysis of transmembrane sequences.     

Computational design of proteins stereochemically optimized in size, stability, and folding speed

Artificial proteins potentially barrier-free in the folding kinetics are approached computationally under the guidance of protein-folding theories. The smallest and fastest folding globular protein triple-helix-bundle (THB) is so modified as to minimize or eliminate its presumed barriers in folding speed. As the barriers may reside in the ordering of either secondary or tertiary structure, the elements of both secondary and tertiary structure in the protein are targeted for prenucleation with suitable stereochemically constrained amino acid residues. The required elements of topology and sequence for the THB are optimized independently; first the topology is optimized with simulated annealing in polypeptides of highly simplified alphabet; next, the sequence in side chains is optimized using the standard inverse design methods. The resultant three best-adapted THBs, variable in topology and distinctive in sequences, are assessed by comparing them with a few benchmark proteins. The results of mainly molecular dynamics (MD) comparisons, undertaken in explicit water at different temperatures, show that the designed sequences are favorably placed against the chosen benchmarks as THB proteins potentially thermostable in the native folds. Folding simulation experiments with MD establish that the designed sequences are rapid in the folding of individual helices, but not in the evolution of tertiary structure; energetic cum topological frustrations remain but could be the artifacts of the starting conformations that were chosen in the THBs in the folding simulations. Overall, a practical high-throughput approach for de novo protein design has been developed that may have fruitful application for any type of tertiary structure.     

Comparison between long-range interactions and contact order in determining the folding rate of two-state proteins: application of long-range order to folding rate prediction.

The contact order is believed to be an important factor for understanding protein folding mechanisms. In our earlier work, we have shown that the long-range interactions play a vital role in protein folding. In this work, we analyzed the contribution of long-range contacts to determine the folding rate of two-state proteins. We found that the residues that are close in space and are separated by at least ten to 15 residues in sequence are important determinants of folding rates, suggesting the presence of a folding nucleus at an interval of approximately 25 residues. A novel parameter "long-range order" has been proposed to predict protein folding rates. This parameter shows as good a relationship with the folding rate of two-state proteins as contact order. Further, we examined the minimum limit of residue separation to determine the long-range contacts for different structural classes. We observed an excellent correlation between long-range order and folding rate for all classes of globular proteins. We suggest that in mixed-class proteins, a larger number of residues can serve as folding nuclei compared to all-alpha and all-beta proteins. A simple statistical method has been developed to predict the folding rates of two-state proteins using the long-range order that produces an agreement with experimental results that is better or comparable to other methods in the literature.