Equilibrium transitions between side‐chain conformations in leucine and isoleucine

Despite recent improvements in computational methods for protein design, we still lack a quantitative, predictive understanding of the intrinsic probabilities for amino acids to adopt particular side‐chain conformations. Surprisingly, this question has remained unsettled for many years, in part because of inconsistent results from different experimental approaches. To explicitly determine the relative populations of different side‐chain dihedral angles, we performed all‐atom hard‐sphere Langevin Dynamics simulations of leucine (Leu) and isoleucine (Ile) dipeptide mimetics with stereo‐chemical constraints and repulsive‐only steric interactions between non‐bonded atoms. We determine the relative populations of the different χ₁ and χ₂ dihedral angle combinations as a function of the backbone dihedral angles ? and ψ. We also propose, and test, a mechanism for inter‐conversion between the different side‐chain conformations. Specifically, we discover that some of the transitions between side‐chain dihedral angle combinations are very frequent, whereas others are orders of magnitude less frequent, because they require rare coordinated motions to avoid steric clashes. For example, to transition between different values of χ₂, the Leu side‐chain bond angles κ₁ and κ₂ must increase, whereas to transition in χ₁, the Ile bond angles λ₁ and λ₂ must increase. These results emphasize the importance of computational approaches in stimulating further experimental studies of the conformations of side‐chains in proteins. Moreover, our studies emphasize the power of simple steric models to inform our understanding of protein structure, dynamics, and design. Proteins 2015; 83:1488–1499. © 2015 Wiley Periodicals, Inc.     

New Insights into the Interdependence between Amino Acid Stereochemistry and Protein Structure

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ? and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.     

New Insights into the Interdependence between Amino Acid Stereochemistry and Protein Structure

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ϕ and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.     

Using quantum mechanics to improve estimates of amino acid side chain rotamer energies

Amino acid side chains adopt a discrete set of favorable conformations typically referred to as rotamers. The relative energies of rotamers partially determine which side chain conformations are more often observed in protein structures and accurate estimates of these energies are important for predicting protein structure and designing new proteins. Protein modelers typically calculate side chain rotamer energies by using molecular mechanics (MM) potentials or by converting rotamer probabilities from the protein database (PDB) into relative free energies. One limitation of the knowledge‐based energies is that rotamer preferences observed in the PDB can reflect internal side chain energies as well as longer‐range interactions with the rest of the protein. Here, we test an alternative approach for calculating rotamer energies. We use three different quantum mechanics (QM) methods (second order Møller‐Plesset (MP2), density functional theory (DFT) energy calculation using the B3LYP functional, and Hartree‐Fock) to calculate the energy of amino acid rotamers in a dipeptide model system, and then use these pre‐calculated values in side chain placement simulations. Energies were calculated for over 36,000 different conformations of leucine, isoleucine, and valine dipeptides with backbone torsion angles from the helical and strand regions of the Ramachandran plot. In a subset of cases these energies differ significantly from those calculated with standard molecular mechanics potentials or those derived from PDB statistics. We find that in these cases the energies from the QM methods result in more accurate placement of amino acid side chains in structure prediction tests. Proteins 2008. © 2007 Wiley‐Liss, Inc.     

BuildBeta—A system for automatically constructing beta sheets

We describe a method that can thoroughly sample a protein conformational space given the protein primary sequence of amino acids and secondary structure predictions. Specifically, we target proteins with β‐sheets because they are particularly challenging for ab initio protein structure prediction because of the complexity of sampling long‐range strand pairings. Using some basic packing principles, inverse kinematics (IK), and β‐pairing scores, this method creates all possible β‐sheet arrangements including those that have the correct packing of β‐strands. It uses the IK algorithms of ProteinShop to move α‐helices and β‐strands as rigid bodies by rotating the dihedral angles in the coil regions. Our results show that our approach produces structures that are within 4–6 Å RMSD of the native one regardless of the protein size and β‐sheet topology although this number may increase if the protein has long loops or complex α‐helical regions. Proteins 2010. © Published 2009 Wiley‐Liss, Inc.     

Helix kinks are equally prevalent in soluble and membrane proteins

Helix kinks are a common feature of α‐helical membrane proteins, but are thought to be rare in soluble proteins. In this study we find that kinks are a feature of long α‐helices in both soluble and membrane proteins, rather than just transmembrane α‐helices. The apparent rarity of kinks in soluble proteins is due to the relative infrequency of long helices (≥20 residues) in these proteins. We compare length‐matched sets of soluble and membrane helices, and find that the frequency of kinks, the role of Proline, the patterns of other amino acid around kinks (allowing for the expected differences in amino acid distributions between the two types of protein), and the effects of hydrogen bonds are the same for the two types of helices. In both types of protein, helices that contain Proline in the second and subsequent turns are very frequently kinked. However, there are a sizeable proportion of kinked helices that do not contain a Proline in either their sequence or sequence homolog. Moreover, we observe that in soluble proteins, kinked helices have a structural preference in that they typically point into the solvent. Proteins 2014; 82:1960–1970. © 2014 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.     

Comparing side chain packing in soluble proteins,protein‐protein interfaces,and transmembrane proteins

We compare side chain prediction and packing of core and non‐core regions of soluble proteins, protein‐protein interfaces, and transmembrane proteins. We first identified or created comparable databases of high‐resolution crystal structures of these 3 protein classes. We show that the solvent‐inaccessible cores of the 3 classes of proteins are equally densely packed. As a result, the side chains of core residues at protein‐protein interfaces and in the membrane‐exposed regions of transmembrane proteins can be predicted by the hard‐sphere plus stereochemical constraint model with the same high prediction accuracies (>90%) as core residues in soluble proteins. We also find that for all 3 classes of proteins, as one moves away from the solvent‐inaccessible core, the packing fraction decreases as the solvent accessibility increases. However, the side chain predictability remains high (80% within ) up to a relative solvent accessibility, , for all 3 protein classes. Our results show that % of the interface regions in protein complexes are “core”, that is, densely packed with side chain conformations that can be accurately predicted using the hard‐sphere model. We propose packing fraction as a metric that can be used to distinguish real protein‐protein interactions from designed, non‐binding, decoys. Our results also show that cores of membrane proteins are the same as cores of soluble proteins. Thus, the computational methods we are developing for the analysis of the effect of hydrophobic core mutations in soluble proteins will be equally applicable to analyses of mutations in membrane proteins.     

Sequence and conformational preferences at termini of α‐helices in membrane proteins: Role of the helix environment

α‐helices are amongst the most common secondary structural elements seen in membrane proteins and are packed in the form of helix bundles. These α‐helices encounter varying external environments (hydrophobic, hydrophilic) that may influence the sequence preferences at their N and C‐termini. The role of the external environment in stabilization of the helix termini in membrane proteins is still unknown. Here we analyze α‐helices in a high‐resolution dataset of integral α‐helical membrane proteins and establish that their sequence and conformational preferences differ from those in globular proteins. We specifically examine these preferences at the N and C‐termini in helices initiating/terminating inside the membrane core as well as in linkers connecting these transmembrane helices. We find that the sequence preferences and structural motifs at capping (Ncap and Ccap) and near‐helical (N' and C') positions are influenced by a combination of features including the membrane environment and the innate helix initiation and termination property of residues forming structural motifs. We also find that a large number of helix termini which do not form any particular capping motif are stabilized by formation of hydrogen bonds and hydrophobic interactions contributed from the neighboring helices in the membrane protein. We further validate the sequence preferences obtained from our analysis with data from an ultradeep sequencing study that identifies evolutionarily conserved amino acids in the rat neurotensin receptor. The results from our analysis provide insights for the secondary structure prediction, modeling and design of membrane proteins. Proteins 2014; 82:3420–3436. © 2014 Wiley Periodicals, Inc.     

An amino acid code to define a protein's tertiary packing surface

One difficult aspect of the protein‐folding problem is characterizing the nonspecific interactions that define packing in protein tertiary structure. To better understand tertiary structure, this work extends the knob‐socket model by classifying the interactions of a single knob residue packed into a set of contiguous sockets, or a pocket made up of 4 or more residues. The knob‐socket construct allows for a symbolic two‐dimensional mapping of pockets. The two‐dimensional mapping of pockets provides a simple method to investigate the variety of pocket shapes to understand the geometry of protein tertiary surfaces. The diversity of pocket geometries can be organized into groups of pockets that share a common core, which suggests that some interactions in pockets are ancillary to packing. Further analysis of pocket geometries displays a preferred configuration that is right‐handed in α‐helices and left‐handed in β‐sheets. The amino acid composition of pockets illustrates the importance of nonpolar amino acids in packing as well as position specificity. As expected, all pocket shapes prefer to pack with hydrophobic knobs; however, knobs are not selective for the pockets they pack. Investigating side‐chain rotamer preferences for certain pocket shapes uncovers no strong correlations. These findings allow a simple vocabulary based on knobs and sockets to describe protein tertiary packing that supports improved analysis, design, and prediction of protein structure. Proteins 2016; 84:201–216. © 2015 Wiley Periodicals, Inc.     

Detecting local residue environment similarity for recognizing near‐native structure models

We developed a new representation of local amino acid environments in protein structures called the Side‐chain Depth Environment (SDE). An SDE defines a local structural environment of a residue considering the coordinates and the depth of amino acids that locate in the vicinity of the side‐chain centroid of the residue. SDEs are general enough that similar SDEs are found in protein structures with globally different folds. Using SDEs, we developed a procedure called PRESCO (Protein Residue Environment SCOre) for selecting native or near‐native models from a pool of computational models. The procedure searches similar residue environments observed in a query model against a set of representative native protein structures to quantify how native‐like SDEs in the model are. When benchmarked on commonly used computational model datasets, our PRESCO compared favorably with the other existing scoring functions in selecting native and near‐native models. Proteins 2014; 82:3255–3272. © 2014 Wiley Periodicals, Inc.     

Helix‐sheet packing in proteins

The three‐dimensional structure of a protein is organized around the packing of its secondary structure elements. Although much is known about the packing geometry observed between α‐helices and between β‐sheets, there has been little progress on characterizing helix–sheet interactions. We present an analysis of the conformation of αβ₂ motifs in proteins, corresponding to all occurrences of helices in contact with two strands that are hydrogen bonded. The geometry of the αβ₂ motif is characterized by the azimuthal angle θ between the helix axis and an average vector representing the two strands, the elevation angle ψ between the helix axis and the plane containing the two strands, and the distance D between the helix and the strands. We observe that the helix tends to align to the two strands, with a preference for an antiparallel orientation if the two strands are parallel; this preference is diminished for other topologies of the β‐sheet. Side‐chain packing at the interface between the helix and the strands is mostly hydrophobic, with a preference for aliphatic amino acids in the strand and aromatic amino acids in the helix. From the knowledge of the geometry and amino acid propensities of αβ₂ motifs in proteins, we have derived different statistical potentials that are shown to be efficient in picking native‐like conformations among a set of non‐native conformations in well‐known decoy datasets. The information on the geometry of αβ₂ motifs as well as the related statistical potentials have applications in the field of protein structure prediction. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

An ensemble of lipoxygenase structures reveals novel conformations of the Fe coordination sphere

The regio‐ and stereo‐specific oxygenation of polyunsaturated fatty acids is catalyzed by lipoxygenases (LOX); both Fe and Mn forms of the enzyme have been described. Structural elements of the Fe and Mn coordination spheres and the helical catalytic domain in which the metal center resides are highly conserved. However, animal, plant, and microbial LOX each have distinct features. We report five crystal structures of a LOX from the fungal plant pathogen Fusarium graminearum. This LOX displays a novel amino terminal extension that provides a wrapping domain for dimerization. Moreover, this extension appears to interfere with the iron coordination sphere, as the typical LOX configuration is not observed at the catalytic metal when the enzyme is dimeric. Instead novel tetra‐, penta‐, and hexa‐coordinate Fe²⁺ ligations are apparent. In contrast, a monomeric structure indicates that with repositioning of the amino terminal segment, the enzyme can assume a productive conformation with the canonical Fe²⁺ coordination sphere.     

What stabilizes the 314‐helix in β3‐peptides? A conformational analysis using molecular simulation

β‐Peptides are analogs of natural α‐peptides and form a variety of remarkably stable structures. Having an additional carbon atom in the backbone of each residue, their folded conformation is not only influenced by the side‐chain sequence but also and foremost by their substitution pattern. The precise mechanism by which the side chains interact with the backbone is, however, hitherto not completely known. To unravel the various effects by which the side chains influence the backbone conformation, we quantify to which extent the dihedral angles of a β³‐substited peptide with an additional methyl group on the central C_α‐atom can be regarded as independent degrees of freedom and analyze the distributions of these dihedral angles. We also selectively capture the steric effect of substituents on the C_α‐ and C_β‐atoms of the central residue by alchemically changing them into dummy atoms, which have no nonbonded interactions. We find that the folded state of the β³‐peptide is primarily stabilized by a steric exclusion of large parts of the unfolded state (entropic effect) and only subsequently by mutual dependence of the ψ‐dihedral angles (enthalpic effect). The folded state of β‐peptides is stabilized by a different mechanism than that of α‐peptides. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Steric restrictions in protein folding: an alpha-helix cannot be followed by a contiguous beta-strand

Using only hard-sphere repulsion, we investigated short polyalanyl chains for the presence of sterically imposed conformational constraints beyond the dipeptide level. We found that a central residue in a helical peptide cannot adopt dihedral angles from strand regions without encountering a steric collision. Consequently, an alpha-helical segment followed by a beta-strand segment must be connected by an intervening linker. This restriction was validated both by simulations and by seeking violations within proteins of known structure. In fact, no violations were found within an extensive database of high-resolution X-ray structures. Nature's exclusion of alpha-beta hybrid segments, fashioned from an alpha-helix adjoined to a beta-strand, is built into proteins at the covalent level. This straightforward conformational constraint has far-reaching consequences in organizing unfolded proteins and limiting the number of possible protein domains.     

Synthesis and conformational analysis of macrocyclic peptides consisting of both α‐helix and polyproline helix segments

Macrocycles are interesting molecules because their topological features and constrained properties significantly affect their chemical, physical, biological, and self‐assembling properties. In this report, we synthesized unique macrocyclic peptides composed of both an α‐helix and a polyproline segment and analyzed their conformational properties. We found that the molecular stiffness of the rod‐like polyproline segment and the relative orientation of the two different helical segments strongly affect the efficiency of the macrocyclization reaction. Conformational analyses showed that both the α‐helix and the polyproline II helix coexisted within the macrocyclic peptides and that the polyproline segment exerts significant effect on the overall helical stability and conformation of the α‐helical segment. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 279–286, 2014.     

Intrinsic α‐helical and β‐sheet conformational preferences: A computational case study of alanine

A fundamental question in protein science is what is the intrinsic propensity for an amino acid to be in an α-helix, β-sheet, or other backbone dihedral angle (-ψ) conformation. This question has been hotly debated for many years because including all protein crystal structures from the protein database, increases the probabilities for α-helical structures, while experiments on small peptides observe that β-sheet-like conformations predominate. We perform molecular dynamics (MD) simulations of a hard-sphere model for Ala dipeptide mimetics that includes steric interactions between nonbonded atoms and bond length and angle constraints with the goal of evaluating the role of steric interactions in determining protein backbone conformational preferences. We find four key results. For the hard-sphere MD simulations, we show that (1) β-sheet structures are roughly three and half times more probable than α-helical structures, (2) transitions between α-helix and β-sheet structures only occur when the backbone bond angle τ (N–C_α–C) is greater than 110°, and (3) the probability distribution of τ for Ala conformations in the “bridge” region of-ψ space is shifted to larger angles compared to other regions. In contrast, (4) the distributions obtained from Amber and CHARMM MD simulations in the bridge regions are broader and have increased τ compared to those for hard sphere simulations and from high-resolution protein crystal structures. Our results emphasize the importance of hard-sphere interactions and local stereochemical constraints that yield strong correlations between -ψ conformations and τ.     

Helix stability of oligoglycine,oligoalanine, and oligo‐β‐alanine dodecamers reflected by hydrogen‐bond persistence

Helices are important structural/recognition elements in proteins and peptides. Stability and conformational differences between helices composed of α‐ and β‐amino acids as scaffolds for mimicry of helix recognition has become a theme in medicinal chemistry. Furthermore, helices formed by β‐amino acids are experimentally more stable than those formed by α‐amino acids. This is paradoxical because the larger sizes of the hydrogen‐bonding rings required by the extra methylene groups should lead to entropic destabilization. In this study, molecular dynamics simulations using the second‐generation force field, AMOEBA (Ponder, J.W., et al., Current status of the AMOEBA polarizable force field. J Phys Chem B, 2010. 114 (8): p. 2549–64.) explored the stability and hydrogen‐bonding patterns of capped oligo‐β‐alanine, oligoalanine, and oligoglycine dodecamers in water. The MD simulations showed that oligo‐β‐alanine has strong acceptor+2 hydrogen bonds, but surprisingly did not contain a large content of 3₁₂‐helical structures, possibly due to the sparse distribution of the 3₁₂‐helical structure and other structures with acceptor+2 hydrogen bonds. On the other hand, despite its backbone flexibility, the β‐alanine dodecamer had more stable and persistent <3.0 Å hydrogen bonds. Its structure was dominated more by multicentered hydrogen bonds than either oligoglycine or oligoalanine helices. The 3₁ (PII) helical structure, prevalent in oligoglycine and oligoalanine, does not appear to be stable in oligo‐β‐alanine indicating its competition with other structures (stacking structure as indicated by MD analyses). These differences are among the factors that shape helical structural preferences and the relative stabilities of these three oligopeptides. Proteins 2014; 82:3043–3061. © 2014 Wiley Periodicals, Inc.     

Conformational preferences of amino acid side chains in collagen

Conformational energy computations were carried out on collagenlike triple-stranded conformations of several poly(tripeptide)s with the general structure CH₃CO? (Gly? X? Y)₃? NHCH₃. The sequences considered had various amino acid residues in position X or Y of the central tripeptide, with either Pro or Ala as a neighbor, i.e., Gly-X-Pro, Gly-X-Ala, Gly-Pro-Y, and Gly-Ala-Y. Minimum-energy conformations were computed for the side chains, and their distributions were compared for the four sequences. The residues used were Abu (= α-aminobutyric acid), Leu, Phe, Ser, Asp, Asn, Val, Ile, and Thr. The conformational energy of a ? Ch₂? CH₃ side chain in Abu was mapped as a function of the dihedral angle χ¹. Intrastrand interactions with neighboring residues do not affect the conformations of a side chain in position Y, and they have a minor effect on it in the X-Ala sequence, but they strongly restrict the conformational freedom of the side chain in the X-Pro sequence. Conversely, interstrand interactions do not affect side chains in position X, but they strongly restrict the conformational freedom of a side chain in position Y if there is a nearby Pro residue in a neighboring strand. Hydrogen bonds with the backbone can be formed in some conformations of long polar side chains, such as Asp, Asn, or Gln. All amino acid residues can be accommodated in collagen. Because of the interactions mentioned above, steric and energetic constraints can be correlated with observed preferences of certain amino acids for positions X or Y in collagen. Hence, these preferences may be explained, in part, in terms of differences in the conformational freedom of the side chains in the triple-stranded structure.