Addition of side chain interactions to modified Lifson-Roig helix-coil theory: application to energetics of phenylalanine-methionine interactions

Efficient enumeration and visualization of helix-coil ensembles

Helix-coil models are routinely used to interpret circular dichroism data of helical peptides or predict the helicity of naturally-occurring and designed polypeptides. However, a helix-coil model contains significantly more information than mean helicity alone, as it defines the entire ensemble-the equilibrium population of every possible helix-coil configuration-for a given sequence. Many desirable quantities of this ensemble are either not obtained as ensemble averages or are not available using standard helicity-averaging calculations. Enumeration of the entire ensemble can allow calculation of a wider set of ensemble properties, but the exponential size of the configuration space typically renders this intractable. We present an algorithm that efficiently approximates the helix-coil ensemble to arbitrary accuracy by sequentially generating a list of the M highest populated configurations in descending order of population. Truncating this list of (configuration, population) pairs at a desired accuracy provides an approximating sub-ensemble. We demonstrate several uses of this approach for providing insight into helix-coil ensembles and folding mechanisms, including landscape visualization.

Thermodynamics-Based Molecular Modeling of α-Helices in Membranes and Micelles

The Folding of Membrane-Associated Peptides (FMAP) method was developed for modeling α-helix formation by linear peptides in micelles and lipid bilayers. FMAP 2.0 identifies locations of α-helices in the amino acid sequence, generates their three-dimensional models in planar bilayers or spherical micelles, and estimates their thermodynamic stabilities and tilt angles, depending on temperature and pH. The method was tested for 723 peptides (926 data points) experimentally studied in different environments and for 170 single-pass transmembrane (TM) proteins with available crystal structures. FMAP 2.0 detected more than 95% of experimentally observed α-helices with an average error in helix end determination of around 2, 3, 4, and 5 residues per helix for peptides in water, micelles, bilayers, and TM proteins, respectively. Helical and nonhelical residue states were predicted with an accuracy from 0.86 to 0.96, and the Matthews correlation coefficient was from 0.64 to 0.88 depending on the environment. Experimental micelle- and membrane-binding energies and tilt angles of peptides were reproduced with a root-mean-square deviation of around 2 kcal/mol and 7°, respectively. The TM and non-TM states of hydrophobic and pH-triggered α-helical peptides in various lipid bilayers were reproduced in more than 95% of cases. The FMAP 2.0 web server (https://membranome.org/fmap) is publicly available to explore the structural polymorphism of antimicrobial, cell-penetrating, fusion, and other membrane-binding peptides, which is important for understanding the mechanisms of their biological activities.

Expanding the range of binding energies and oxidizability of biologically relevant S-aromatic interactions: imidazolium and phenolate binding to sulfoxide and sulfone

Oxidation and protonation/deprotonation strongly impact intermolecular noncovalent interactions. For example, S-aromatic interactions are stabilized up to three-fold in the gas phase on oxidation of the sulfur ligand or protonation/deprotonation of the aromatic. To probe if such stabilizing effects are additive and to model interactions of oxidized methionine (MetOn) with protonated histidine and deprotonated tyrosine residues in proteins, we examined Me2SOn (n = 1, 2) binding to imidazolium, phenolate and their 4-methylated forms. Ab initio MP2(full)/6-311++G(d,p) gas-phase calculations reveal that the Me2SOn-imidazolium complexes adopt edge-on geometry with σ-type (N/C-HarO) H-bonding and interaction energies of -17.2 to -31.1 kcal mol-1. The less stable (-13.8 to -21.0 kcal mol-1) Me2SOn-phenolates possess en-face geometry stabilized by π-type (C-Hπar) H-bonding. Comparing these energies with those reported for the Me2S-neutral aromatics affirms the additive effects of ligand protonation/deprotonation and oxidation on gas-phase stability. However, this is not the case in water although the aqueous complexes retain their preferred gas-phase σ- and π-type H-bonded structures. Binding free energies (kcal mol-1) calculated from molecular dynamics simulations in bulk water (preceded by CHARMM36 force field calibration where necessary) reveal that Me2SO-imidazolium (-4.4) is more stable than Me2SO-phenolate (-2.4) but Me2SO2-imidazolium (-0.6) is less stable than Me2SO2-phenolate (-3.8). Vertical ionization potentials (IPV) calculated for the gas-phase complexes indicate that the Me2SOn-phenolates, but not the Me2SOn-imidazoles, are oxidizable under biological conditions. Charge transfer from the phenolate increases its IPV by ∼20%, decreasing its susceptibility to oxidation. Overall, this work provides fundamental data to predict the behaviour of protein-based MetOn-aromatic-ion interactions.

Modeling Protein S-Aromatic Motifs Reveals Their Structural and Redox Flexibility

S-aromatic motifs are important noncovalent forces for protein stability and function but remain poorly understood. Hence, we performed quantum calculations at the MP2(full)/6-311++G(d,p) level on complexes between Cys (H₂S, MeSH) and Met (Me₂S) models with models of Phe (benzene, toluene), Trp (indole, 3-methylindole), Tyr (phenol, 4-methylphenol), and His (imidazole, 4-methylimidazole). The most stable gas-phase conformers exhibit binding energies of -2 to -6 kcal/mol, and the S atom lies perpendicular to the ring plane. This reveals preferential interaction with the ring π-system, except in the imidazoles where S binds edge-on to an N atom. Complexation tunes the gas-phase vertical ionization potentials of the ligands over as much as 1 eV, and strong σ- or π-type H-bonding supports charge transfer to the H-bond donor, rendering it more oxidizable. When the S atom acts as an H-bond acceptor (N/O-H_ar···S), calibration of the CHARMM36 force field (by optimizing pair-specific Lennard-Jones parameters) is required. Implementing the optimized parameters in molecular dynamics simulations in bulk water, we find stable S-aromatic complexes with binding free energies of -0.6 to -1.1 kcal/mol at ligand separations up to 8 Å. The aqueous S-aromatics exhibit flexible binding conformations, but edge-on conformers are less stable in water. Reflecting this, only 0.3 to 10% of the S-indole, S-phenol, and S-imidazole structures are stabilized by N/O-H_ar···S or S-H···O_ar/N_ar σ-type H-bonding. The wide range of energies and geometries found for S-aromatic interactions and their tunable redox properties expose the versatility and variability of the S-aromatic motif in proteins and allow us to predict a number of their reported properties.

Predicting structural and energetic changes in Met–aromatic motifs on methionine oxidation to the sulfoxide and sulfone

Methionine oxidation increases its affinity for aromatics in the gas phase but lowers it for most complexes in water.

Design of Stable α-Helical Peptides and Thermostable Proteins in Biotechnology and Biomedicine

α-Helices are the most frequently occurring elements of the secondary structure in water-soluble globular proteins. Their increased conformational stability is among the main reasons for the high thermal stability of proteins in thermophilic bacteria. In addition, α-helices are often involved in protein interactions with other proteins, nucleic acids, and the lipids of cell membranes. That is why the highly stable α-helical peptides used as highly active and specific inhibitors of protein-protein and other interactions have recently found more applications in medicine. Several different approaches have been developed in recent years to improve the conformational stability of α-helical peptides and thermostable proteins, which will be discussed in this review. We also discuss the methods for improving the permeability of peptides and proteins across cellular membranes and their resistance to intracellular protease activity. Special attention is given to the SEQOPT method (http://mml.spbstu.ru/services/seqopt/), which is used to design conformationally stable short α-helices.

A Structuring Repeat for Peptide Design: Long Beta Ribbons

Beta sheets are inherently length-limited; adding residues to the ends of model β-sheets does not necessarily grow the β-sheet. Here, we present a method for extending β-sheets to any length with a stabilizing repeat unit containing cross-strand Trp residues. Beta ribbons as long as 35 residues (approaching 100 Å in length) are reported and characterized.

Protein thermostability engineering

Using structure and sequence based analysis we can engineer proteins to increase their thermal stability.

De novo design of stable α-helices

Recent studies have elucidated key principles governing folding and stability of α-helices in short peptides and globular proteins. In this chapter we review briefly those principles and describe a protocol for the de novo design of highly stable α-helixes using the SEQOPT algorithm. This algorithm is based on AGADIR, the statistical mechanical theory for helix-coil transitions in monomeric peptides, and the tunneling algorithm for global sequence optimization.

Solution characterization of [methyl-(13)C]methionine HIV-1 reverse transcriptase by NMR spectroscopy

HIV reverse transcriptase (RT) is a primary target for drug intervention in the treatment of AIDS. We report the first solution NMR studies of [methyl-(13)C]methionine HIV-1 RT, aimed at better understanding the conformational and dynamic characteristics of RT, both in the presence and absence of the non-nucleoside RT inhibitor (NNRTI) nevirapine. The selection of methionine as a structural probe was based both on its favorable NMR characteristics, and on the presence of two important active site methionine residues, M184(66) and M230(66). Observation of the M184 resonance is subunit dependent; in the p66 subunit the solvent-exposed residue produces a readily observed signal with a characteristic resonance shift, while in the globular p51 subunit, the M184(51) resonance is shifted and broadened as M184 becomes buried in the protein interior. In contrast, although structural data indicates that the environment of M230 is also strongly subunit dependent, the M230 resonances from both subunits have very similar shift and relaxation characteristics. A comparison of chemical shift and intensity data with model-based predictions gives reasonable agreement for M184(66), while M230(66), located on the beta-hairpin "primer grip", is more mobile and solvent-exposed than suggested by crystal structures of the apo enzyme which have a "closed" fingers-thumb conformation. This mobility of the primer grip is presumably important for binding of non-nucleoside RT inhibitors (NNRTIs), since the NNRTI binding pocket is not observed in the absence of the inhibitors, requiring instead that the binding pocket be dynamically accessible. In the presence of the nevirapine, both the M184(66) and M230(66) resonances are significantly perturbed, while none of the methionine resonances in the p51 subunit is sensitive to this inhibitor. Site-directed mutagenesis indicates that both M16 and M357 produce two resonances in each subunit, and for both residues, the intensity ratio of the component peaks is strongly subunit dependent. Conformational features that might explain the multiple peaks are discussed.

Statistical mechanical model for helix-sheet-coil transitions in homopolypeptides

In this paper, we propose a simple statistical mechanical model to study the conformation transition between the alpha helix, beta sheet, and random coil in homopolypeptides. In our model, five parameters are introduced to obtain the partition function. There are two factors for helical propagation and initiation, which are the same as those used in the Zimm-Bragg model, and three newly introduced parameters for beta structures: the strand propagation factor for residues in beta strands and two correction factors for the initiation effect of the beta strand and beta sheet. Our model shows that the variation of these parameters may induce conformation transition from alpha helix or random coil to beta sheet. The sharpness of the transition depends on the initiation factors.

Statistical estimation of statistical mechanical models: helix-coil theory and peptide helicity prediction

Analysis of biopolymer sequences and structures generally adopts one of two approaches: use of detailed biophysical theoretical models of the system with experimentally-determined parameters, or largely empirical statistical models obtained by extracting parameters from large datasets. In this work, we demonstrate a merger of these two approaches using Bayesian statistics. We adopt a common biophysical model for local protein folding and peptide configuration, the helix-coil model. The parameters of this model are estimated by statistical fitting to a large dataset, using prior distributions based on experimental data. L(1)-norm shrinkage priors are applied to induce sparsity among the estimated parameters, resulting in a significantly simplified model. Formal statistical procedures for evaluating support in the data for previously proposed model extensions are presented. We demonstrate the advantages of this approach including improved prediction accuracy and quantification of prediction uncertainty, and discuss opportunities for statistical design of experiments. Our approach yields a 39% improvement in mean-squared predictive error over the current best algorithm for this problem. In the process we also provide an efficient recursive algorithm for exact calculation of ensemble helicity including sidechain interactions, and derive an explicit relation between homo- and heteropolymer helix-coil theories and Markov chains and (non-standard) hidden Markov models respectively, which has not appeared in the literature previously.

Geometry of nonbonded interactions involving planar groups in proteins

Although hydrophobic interaction is the main contributing factor to the stability of the protein fold, the specificity of the folding process depends on many directional interactions. An analysis has been carried out on the geometry of interaction between planar moieties of ten side chains (Phe, Tyr, Trp, His, Arg, Pro, Asp, Glu, Asn and Gln), the aromatic residues and the sulfide planes (of Met and cystine), and the aromatic residues and the peptide planes within the protein tertiary structures available in the Protein Data Bank. The occurrence of hydrogen bonds and other nonconventional interactions such as C-H...pi, C-H...O, electrophile-nucleophile interactions involving the planar moieties has been elucidated. The specific nature of the interactions constraints many of the residue pairs to occur with a fixed sequence difference, maintaining a sequential order, when located in secondary structural elements, such as alpha-helices and beta-turns. The importance of many of these interactions (for example, aromatic residues interacting with Pro or cystine sulfur atom) is revealed by the higher degree of conservation observed for them in protein structures and binding regions. The planar residues are well represented in the active sites, and the geometry of their interactions does not deviate from the general distribution. The geometrical relationship between interacting residues provides valuable insights into the process of protein folding and would be useful for the design of protein molecules and modulation of their binding properties.

The CXXC motif at the N terminus of an alpha-helical peptide

An active site containing a CXXC motif is always found in the thiol-disulphide oxidoreductase superfamily. A survey of crystal structures revealed that the CXXC motif had a very high local propensity (26.3 +/- 6.2) for the N termini of alpha-helices. A helical peptide with the sequence CAAC at the N terminus was synthesized to examine the helix-stabilizing capacity of the CXXC motif. Circular dichroism was used to confirm the helical nature of the peptide and study behavior under titration with various species. With DTT, a redox potential of E(o) = -230 mV was measured, indicating that the isolated peptide is reducing in nature and similar to native human thioredoxin. The pK(a) values of the individual Cys residues could not be separated in the titration of the reduced state, giving a single transition with an apparent pK(a) of 6.74 (+/-0.06). In the oxidized state, the N-terminal pK(a) is 5.96 (+/-0.05). Analysis of results with the modified helix-coil theory indicated that the disulfide bond stabilized the alpha-helical structure by 0.5 kcal/mol. Reducing the disulfide destabilizes the helix by 0.9 kcal/mol.

Fundamental processes of protein folding: measuring the energetic balance between helix formation and hydrophobic interactions

Theories of protein folding often consider contributions from three fundamental elements: loops, hydrophobic interactions, and secondary structures. The pathway of protein folding, the rate of folding, and the final folded structure should be predictable if the energetic contributions to folding of these fundamental factors were properly understood. alphatalpha is a helix-turn-helix peptide that was developed by de novo design to provide a model system for the study of these important elements of protein folding. Hydrogen exchange experiments were performed on selectively 15N-labeled alphatalpha and used to calculate the stability of hydrogen bonds within the peptide. The resulting pattern of hydrogen bond stability was analyzed using a version of Lifson-Roig model that was extended to include a statistical parameter for tertiary interactions. This parameter, x, represents the additional statistical weight conferred upon a helical state by a tertiary contact. The hydrogen exchange data is most closely fit by the XHC model with an x parameter of 9.25. Thus the statistical weight of a hydrophobic tertiary contact is approximately 5.8x the statistical weight for helix formation by alanine. The value for the x parameter derived from this study should provide a basis for the understanding of the relationship between hydrophobic cluster formation and secondary structure formation during the early stages of protein folding.

Anticooperativity in a Glu-Lys-Glu salt bridge triplet in an isolated alpha-helical peptide

Salt bridges between oppositely charged side chains are well-known to stabilize protein structure, though their contributions vary considerably. Here we study Glu-Lys and Lys-Glu salt bridges, formed when the residues are spaced i, i + 4 surface of an isolated alpha-helix in aqueous solution. Both are stabilizing by -0.60 and -1.02 kcal/mol, respectively, when the interacting residues are fully charged. When the side chains are spaced i, i + 4, i + 8, forming a Glu-Lys-Glu triplet, the second salt bridge provides no additional stabilization to the helix. We attribute this to the inability of the central Lys to form two salt bridges simultaneously. Analysis of these salt bridges in protein structures shows that the Lys-Glu interaction is dominant, with the side chains of the Glu-Lys pair far apart.

Investigation of the nature of the methionine-pi interaction in beta-hairpin peptide model systems

There are frequent contacts between aromatic rings and sulfur atoms in proteins. However, it is unclear to what degree this putative interaction is stabilizing and what the nature of the interaction is. We have investigated the aryl-sulfur interaction by placing a methionine residue diagonal to an aromatic ring on the same face of a beta-hairpin, which places the methionine side chain in close proximity to the aryl side chain. The methionine (Met)-aryl interaction was compared with an equivalent hydrophobic and cation-pi interaction in the context of the beta-hairpin. The interaction between phenylalanine (Phe), tryptophan (Trp), or cyclohexylalanine (Cha) and Met stabilized the beta-hairpin by -0.3 to -0.5 kcal mole(-1), as determined by double-mutant cycles. The peptides were subjected to thermal denaturations that suggest a hydrophobic driving force for the interactions between Met and Trp or Cha. The observed interaction of Met or norleucine (Nle) with Trp or Cha are quite similar, implying a hydrophobic driving force for the Met-pi interaction. However, the thermodynamic data suggest that there may be some differences between the interaction of Met with Trp and Phe and that there may be a small thermodynamic component to the Met...Phe interaction.

Pairwise Coupling in an Arg-Phe-Met Triplet Stabilizes α-Helical Peptide via Shared Rotamer Preferences

The hydrophobic Arg-Phe and Phe-Met side chain interactions stabilize the alpha-helix by -0.29 and -0.59 kcal/mol, respectively, when placed i, i + 4 in an alanine-based peptide. When both interactions are present simultaneously, however, they stabilize the helix by an additional -0.75 kcal/mol, nearly as much as the sum of its parts. We attribute this coupling to a shared rotamer preference, as the central Phe is t in both bonds. The energetic cost of restricting the Phe residue into a t conformation is only paid once in the triplet, rather than twice when the interactions are separate. Coupling is thus demonstrated to have large effects on protein stability.

Thermodynamics Of α‐Helix Formation

The alpha-helix was the first proposed and experimentally confirmed secondary structure. The elegant simplicity of the alpha-helical structure, stabilized by hydrogen bonding between the backbone carbonyl oxygen and the peptide amide four residues away, has captivated the scientific community. In proteins, alpha-helices are also stabilized by the so-called capping interactions that occur at both the C- and the N-termini of the helix. This chapter provides a brief historical overview of the thermodynamic studies of the energetics of helix formation, and reviews recent progress in our understanding of the thermodynamics of helix formation.

Aromatic interactions in peptides: Impact on structure and function

Aromatic interactions, including pi-pi, cation-pi, aryl-sulfur, and carbohydrate-pi interactions, have been shown to be prevalent in proteins through protein structure analysis, suggesting that they are important contributors to protein structure. However, the magnitude and significance of aromatic interactions is not defined by such studies. Investigation of aromatic interactions in the context of structured peptides has complemented studies of protein structure and has provided a wealth of information regarding the role of aromatic interactions in protein structure and function. Recent advances in this area are reviewed.

Effects of temperature and pH on the helicity of a peptide adsorbed to colloidal silica

The conformation of a cationic alpha-helical peptide (DDDDAAAARRRRR) adsorbed to anionic colloidal silica has been investigated by circular dichroism (CD) spectroscopy as a function of temperature and pH in order to examine how the structure of an adsorbed molecule responds to two simultaneous perturbations. Increased temperature destabilizes the helicity of the peptide in solution, while pH changes alter the substrate surface charge and the corresponding strength of the interaction with the peptide. Near neutral pH, the helicity of the adsorbed peptide, which is determined from the intensity of the CD signal at 222 nm, decreases with increasing temperature, similarly to the temperature-dependent behavior observed for the peptide in aqueous solution. By contrast, at basic pH and a strongly negative surface charge, the helicity of the adsorbed peptide increases with temperature. In order to elucidate the origin of the reversal of the temperature dependence of helicity, a statistical model for the conformation of the adsorbed peptide has been formulated based on the Lifson-Roig model for the helix-coil transition of the peptide in solution. The model provides insight into the trends in fractional helicity and reveals that the temperature dependence of the helicity of the adsorbed peptide results from a competition between the intramolecular interactions that promote helicity and the intermolecular interactions with the surface. The statistical model also enables estimation of the free energy contributions from specific aspects of the adsorption process. Through identification of a connection between the conformation of adsorbed peptide and the interactions of the peptide with the surface, this work suggests a route for the control of adsorbate conformation through peptide and surface engineering.

Effect of Side Chains on Turns and Helices in Peptides of β3-Aminoxy Acids

We have investigated, using NMR, IR, and CD spectroscopy and X-ray crystallography, the conformational properties of peptides 1-10 of beta(3)-aminoxy acids (NH(2)OCHRCH(2)COOH) having different side chains on the beta carbon atom (e.g., R = Me, Et, COOBn, CH(2)CH(2)CH=CH(2), i-Bu, i-Pr). The beta N-O turns and beta N-O helices that involve a nine-membered-ring intramolecular hydrogen bond between NH(i)(+2) and CO(i), which have been found previously in peptides of beta(2,2)-aminoxy acids (NH(2)OCH(2)CMe(2)COOH), are also present in those beta(3)-aminoxy peptides. X-ray crystal structures and NMR spectral analysis reveal that, in the beta N-O turns and beta N-O helices induced by beta(3)-aminoxy acids, the N-O bond could be either anti or gauche to the C(alpha)-C(beta) bond depending on the size of the side chain; in contrast, only the anti conformation was found in beta(2,2)-aminoxy peptides. Both diamide 1 and triamide 9 exist in different conformations in solution and in the solid state: parallel sheet structures in the solid state and predominantly beta N-O turn and beta N-O helix conformations in nonpolar solvents. Theoretical studies on a series of model diamides rationalize very well the experimentally observed conformational features of these beta(3)-aminoxy peptides.

Probing helix formation in unsolvated peptides

Ion mobility measurements have been used to examine helix formation in unsolvated glycine-based peptides containing three alanine residues. Nine sequence isomers of Ac-[12G3A]K+H(+) were studied (Ac = acetyl, G = glycine, A = alanine, and K = lysine). The amount of helix present for each peptide was examined using two metrics, and it is strongly dependent on the proximity and the location of the alanine residues. Peptides with three adjacent alanines have the highest helix abundances, and those with well-separated alanines have the lowest. The helix abundances for most of the peptides can be fit reasonably well using a modified Lifson-Roig theory. However, Lifson-Roig theory fails to account for several key features of the experimental results. The most likely explanation for the correlation between helix abundances and the number of adjacent alanines is that neighboring alanines promote helix nucleation.

Effects of As(III) binding on alpha-helical structure

As(III) displays a wide range of effects in cellular chemistry. Surprisingly, the structural consequences of arsenic binding to peptides and proteins are poorly understood. This study utilizes model alpha-helical peptides containing two cysteine (Cys) residues in various sequential arrangements and spatial locations to study the structural effects of arsenic binding. With i, and i + 1, i + 2, or i + 3 arrangements, CD spectroscopy shows that As(III) coordination causes helical destabilization when Cys residues are located at central or C-terminal regions of the helix. Interestingly, arsenic binding to i, i + 3 positions results in the elimination of helical structure and the formation of a relatively stable alternate fold. In contrast, helical stabilization is observed for peptides containing i, i + 4 Cys residues, with corresponding pseudo pairwise interaction energies (Delta G(pw) degrees) of -1.0 and -0.7 kcal/mol for C-terminal and central placements, respectively. Binding affinities and association rate constants show that As(III) binding is comparatively insensitive to the location of the Cys residues within these moderately stable helices. These data demonstrate that As(III) binding can be a significant modulator of helical secondary structure.

Simple cation-pi interaction between a phenyl ring and a protonated amine stabilizes an alpha-helix in water

Cation-pi interactions have been proposed to be important contributors to protein structure and function. In particular, these interactions have been suggested to provide significant stability at the solvent-exposed surface of a protein. We have investigated the magnitude of cation-pi interactions between phenylalanine (Phe) and lysine (Lys), ornithine (Orn), and diaminobutanoic acid (Dab) in the context of an alpha-helix and have found that only the Phe...Orn interaction provides significant stability to the helix, stabilizing it by -0.4 kcal/mol. This interaction energy is in the same range as a salt bridge in an alpha-helix, and equivalent to the recently reported Trp...Arg interaction in an alpha-helix, despite the fact that Trp...guanidinium interactions have been proposed to be stronger than Phe...ammonium interactions. These results indicate that even the simplest cation-pi interaction can provide significant stability to protein structure and demonstrate the subtle factors that can influence the observed interaction energies in designed systems.

Recent advances in helix-coil theory

Peptide helices in solution form a complex mixture of all helix, all coil or, most frequently, central helices with frayed coil ends. In order to interpret experiments on helical peptides and make theoretical predictions on helices, it is therefore essential to use a helix-coil theory that takes account of this equilibrium. The original Zimm-Bragg and Lifson-Roig helix-coil theories have been greatly extended in the last 10 years to include additional interactions. These include preferences for the N-cap, N1, N2, N3 and C-cap positions, capping motifs, helix dipoles, side chain interactions and 3(10)-helix formation. These have been applied to determine energies for these preferences from experimental data and to predict the helix contents of peptides. This review discusses these newly recognised structural features of helices and how they have been included in helix-coil models.

[Structures of peptides related to the inactivation gate on sodium channels]

The peptides related to inactivation of sodium channels were synthesized by the solid-phase method for the purpose of proposing a more precise concept than so far obtained for the inactivation and to determine the main factors that control inactivation. The three-dimensional structures of the peptides were determined using 1H-NMR spectroscopy. It was newly discovered that hydrogen bonding was formed between the amide proton of Ile in the IFM (IFM1488-1490) motif of the III-IV linker and the hydroxyl oxygen atom of the side chain of Thr located adjacent to the IFM motif. This hydrogen bonding characterizes the structure around the IFM motif. By calculating the solvent-accessible surface area of the peptide corresponding to the III-IV linker, it was found that a hydrophobic cluster was formed. The hydrophobic cluster stabilizes the structure of the IFM motif. Moreover, the solvent-accessible surface area of the IFM motif correlated with the sustained currents of the incompletely inactivated sodium channels. The free energy of stabilization by hydrophobic interactions (delta G, -3.9 kcal mol-1), which is calculated from the solvent-accessible surface area for the IFM motif (195 A2), was in good agreement with that calculated for the equilibrium between the open and the inactivated states of the sodium channels (-4.1 kcal mol-1). The structure of the III-IV linker peptide in a phosphate buffer also formed a hydrophobic cluster, as well as in SDS micelles, although no hydrogen bonding was formed. This distinction results in the following conformational change in the IFM motif: in SDS micelles, the side chains of Ile and Phe in the IFM motif were directed to the hydrophobic cluster, whereas those in a phosphate buffer were directed opposite to the cluster and solvent exposed. The secondary structures of IIIS4-S5 and IVS4-S5, which are considered to form a receptor site, assumed alpha-helical conformations around the N-terminal half of the sequences. The residue A1329 in MPD3, which is considered to interact with F1489 of the IFM motif, was found to locate within the alpha-helix. A hydrophobic cluster was formed on one side of the helix of MP-D4, which also plays an important role in the inactivation. A new concept for the process of fast inactivation is presented. In response to the voltage-dependent activation and the movement of the S4 segments, the two hydrophobic clusters due to the IVS4-S5 and the III-IV linker interact with each other. This interaction increases the hydrophobicity around the IFM motif. The increased hydrophobicity causes the conformational switching of the IF1488-1489 residues to allow F1489 to interact with A1329 of IIIS4-S5 and/or with N1662 in IVS4-S5. As a consequence of this process, the inactivation gate closes.

Stabilizing interactions between aromatic and basic side chains in alpha-helical peptides and proteins. Tyrosine effects on helix circular dichroism

Here we investigate the structures and energetics of interactions between aromatic (Phe or Tyr) and basic (Lys or Arg) amino acids in alpha-helices. Side chain interaction energies are measured using helical peptides, by quantifying their helicities with circular dichroism at 222 nm and interpreting the results with Lifson-Roig-based helix/coil theory. A difficulty in working with Tyr is that the aromatic ring perturbs the CD spectrum, giving an incorrect helicity. We calculated the effect of Tyr on the CD at 222 nm by deriving the intensities of the bands directly from the electronic and magnetic transition dipole moments through the rotational strengths corresponding to each excited state of the polypeptide. This gives an improved value of the helix preference of Tyr (from 0.48 to 0.35) and a correction to the helicity for the peptides containing Tyr. We find that Phe-Lys, Lys-Phe, Phe-Arg, Arg-Phe, and Tyr-Lys are all stabilizing by -0.10 to -0.18 kcal.mol-1 when placed i, i + 4 on the surface of a helix in aqueous solution, despite the great difference in polarity between these residues. Interactions between these side chains have previously been attributed to cation-pi bonds. A survey of protein structures shows that they are in fact predominantly hydrophobic interactions between the CH2 groups of Lys or Arg and the aromatic rings.

Contribution of aromatic interactions to alpha-helix stability

The influence of natural and unnatural i, i + 4 aromatic side chain-side chain interactions on alpha-helix stability was determined in Ala-Lys host peptides by circular dichroism (CD). All interactions investigated provided some stability to the helix; however, phenylalanine-phenylalanine (F-F) and phenylalanine-pentafluorophenylalanine (F-f5F) interactions resulted in the greatest enhancement in helicity, doubling the helical content over i, i + 5 control peptides at internal positions. Quantification of these interactions using AGADIR multistate helix-coil algorithm revealed that the F-F and F-f5F interaction energies are equivalent at internal positions in the sequence (deltaGF-F = deltaGF-f5F = -0.27 kcal/mol), despite the differences in their expected geometries. As the strength of a face-to-face stacked phenyl-pentafluorophenyl interaction should surpass an edge-to-face or offset-stacked phenyl-phenyl interaction, we believe this result reflects the inability of the side chains in F-f5F to attain a fully stacked geometry within the context of an alpha-helix. Positioning the interactions at the C-terminus led to much stronger interactions (deltaGF-F = -0.8 kcal/mol; deltaGF-f5F = -0.55 kcal/mol) likely because of favorable chi(1) rotameric preferences for aromatic residues at C-capping regions of alpha-helices, suggesting that aromatic side chain-side chain interactions are an effective alpha-helix C-capping method.

Origin of the different strengths of the (i,i+4) and (i,i+3) leucine pair interactions in helices

Pairs of leucine side chains, spaced either (i,i+3) or (i,i+4), are known to stabilize alanine-based peptide helices, Experiments with new peptide sequences confirm that the (i,i+4) pair interaction is markedly stronger than the (i,i+3) pair interaction. This result is not expected from reported Monte Carlo simulations, which predict that the (i,i+3) interaction is slightly stronger. The interaction strength can be predicted from recently reported measurements of buried non-polar surface area, obtained from structures in the Protein Data Bank: the agreement is reasonable for the (i,i+3) LL interaction but underestimates the (i,i+4) LL interaction. Solvation of peptide groups in the helix backbone may contribute to the different strengths of the two LL pair interactions because different chi(1) leucine rotamers are used and the (i,i+3) pair shields two peptide groups whereas the (i,i+4) pair shields only one. A rough estimate of the backbone solvation effect, based on the difference between the helix propensities of leucine and alanine, agrees with the size of the difference between the (i,i+3) and (i,i+4) leucine pair interactions.

Amino acid intrinsic alpha-helical propensities III: positional dependence at several positions of C terminus

In this study, we have analyzed experimentally the helical intrinsic propensities of non-charged and non-aromatic residues at different C-terminal positions (C1, C2, C3) of an Ala-based peptide. The effect was found to be complex, resulting in extra stabilization or destabilization, depending on guest amino acid and position under consideration. Polar (Ser, Thr, Cys, Asn, and Gln) amino acids and Gly were found to have significantly larger helical propensities at several C-terminal positions compared with the alpha-helix center (-1.0 kcal/mole in some cases). Some of the nonpolar residues, especially beta-branched ones (Val and Ile) are significantly more favorable at position C3 (-0.3 to -0.4 kcal/mole), although having minor differences at other C-terminal positions compared with the alpha-helix center. Leu has moderate (-0.1 to -0.2 kcal/mole) stabilization effects at position C2 and C3, whereas being relatively neutral at C1. Finally, Met was found to be unfavorable at C1 and C2 ( +0.2 kcal/mole) and favorable at C3 (-0.2 kcal/mole). Thus, significant differences found between the intrinsic helical propensities at the C-terminal positions and those in the alpha-helix center must be accounted for in helix/coil transition theories and in protein design.

Stabilizing nonpolar/polar side-chain interactions in the alpha-helix

A simplistic, yet often used, view of protein stability is that amino acids attract other amino acids with similar polarity, whereas nonpolar and polar side chains repel. Here we show that nonpolar/polar interactions, namely Val or Ile bonding to Lys or Arg in alpha-helices, can in fact be stabilizing. Residues spaced i, i + 4 in alpha-helices are on the same face of the helix, with potential to favorably interact and stabilize the structure. We observe that the nonpolar/polar pairs Ile-Lys, Ile-Arg, and Val-Lys occur in protein helices more often than expected when spaced i, i + 4. Partially helical peptides containing pairs of nonpolar/polar residues were synthesized. Controls with i, i + 5 spacing have the residues on opposite faces of the helix and are less helical than the test peptides with the i, i + 4 interactions. Experimental circular dichroism results were analyzed with helix-coil theory to calculate the free energy for the interactions. All three stabilize the helix with DeltaG between -0.14 and -0.32 kcal x mol(-1). The interactions are hydrophobic with contacts between Val or Ile and the alkyl groups in Arg or Lys. Side chains such as Lys and Arg can thus interact favorably with both polar and nonpolar residues.

Solution structures of the cytoplasmic linkers between segments S4 and S5 (S4-S5) in domains III and IV of human brain sodium channels in SDS micelles

The two cytoplasmic linkers connecting segment S4 and segment S5 (S4-S5 linker) of both domain III (III/S4-S5) and IV (IV/S4-S5) of the sodium channel alpha-subunit are considered to work as a hydrophobic receptor for the inactivation particle because of the three hydrophobic amino acids of Ile-Phe-Met (IFM motif) in the III-IV linker of the sodium channel alpha-subunit. To date, the solution structures of the peptides related to III/S4-S5 (MP-D3: A1325-M1338) and IV/S4-S5 (MP-D4: T1648-L1666) of human brain sodium channels have been investigated using CD and (1)H NMR spectroscopies. SDS micelles were employed as a solvent. The micelles mimic either biological membranes or the interior of a protein and can be a relevant environment at the inactivated state of the channels. It was found that the secondary structures of both MP-D3 and MP-D4 assume alpha-helical conformations around the N-terminal half-side of the sequences, i.e. the residues between V1326 and L1331 in MP-D3 and between L1650 and S1656 in MP-D4. Residue A1329 in MP-D3, which is considered to interact with F1489 of the IFM motif, was found to be located within the alpha-helix. Residues F1651, M1654, M1655, L1657 and A1669 in MP-D4, which also play an important role in inactivation, formed a hydrophobic cluster on one side of the helix. This cluster was concluded to interact with the hydrophobic cluster due to the III-IV linker before the inactivation gate closes.

Determination of alpha-helix N1 energies after addition of N1, N2, and N3 preferences to helix/coil theory

Surveys of protein crystal structures have revealed that amino acids show unique structural preferences for the N1, N2, and N3 positions in the first turn of the alpha-helix. We have therefore extended helix-coil theory to include statistical weights for these locations. The helix content of a peptide in this model is a function of N-cap, C-cap, N1, N2, N3, C1, and helix interior (N4 to C2) preferences. The partition function for the system is calculated using a matrix incorporating the weights of the fourth residue in a hexamer of amino acids and is implemented using a FORTRAN program. We have applied the model to calculate the N1 preferences of Gln, Val, Ile, Ala, Met, Pro, Leu, Thr, Gly, Ser, and Asn, using our previous data on helix contents of peptides Ac-XAKAAAAKAAGY-CONH2. We find that Ala has the highest preference for the N1 position. Asn is the most unfavorable, destabilizing a helix at N1 by at least 1.4 kcal mol(-1) compared to Ala. The remaining amino acids all have similar preferences, 0.5 kcal mol(-1) less than Ala. Gln, Asn, and Ser, therefore, do not stabilize the helix when at N1.

A helix initiation motif, XLLRA, is stabilized by hydrogen bond, hydrophobic and van der Waals interactions

Five partially overlapping synthetic peptides containing the N-terminal portion of the leucine zipper (LZ)-like domain of human immunodeficiency virus envelope glycoprotein gp41 were used to deduce the helix initiation site. Circular dichroism (CD) data suggested a strong helix-inducing motif, LLRA. The coupling constant and nuclear Overhauser effect (NOE) results obtained from nuclear magnetic resonance experiments in 20% trifluoroethanol aqueous solution at 280 K for the four decapeptides under study suggested that the motif XLLRA, where X is a group or an amino acid residue capable of forming hydrogen bond to arginine, constitutes a helix nucleation core. A similar conclusion was reached for a pentadecapeptide in water, suggesting that the result was not dependent on both chain length and the helix promoting medium. Detailed analysis of NOE and CD data from the four decapeptides indicated that the acetyl group and asparagine had a strong tendency to be helix N-capping, in confirmation of previous studies. Molecular modeling using restraints derived from NOE data showed that van der Waals, hydrophobic interactions and hydrogen bonds contribute synergetically to the stability of the core structure. The concept of nucleation core consisting of a few amino acids may be generally applied in proton design and folding studies.

Bayesian segmentation of protein secondary structure

We present a novel method for predicting the secondary structure of a protein from its amino acid sequence. Most existing methods predict each position in turn based on a local window of residues, sliding this window along the length of the sequence. In contrast, we develop a probabilistic model of protein sequence/structure relationships in terms of structural segments, and formulate secondary structure prediction as a general Bayesian inference problem. A distinctive feature of our approach is the ability to develop explicit probabilistic models for alpha-helices, beta-strands, and other classes of secondary structure, incorporating experimentally and empirically observed aspects of protein structure such as helical capping signals, side chain correlations, and segment length distributions. Our model is Markovian in the segments, permitting efficient exact calculation of the posterior probability distribution over all possible segmentations of the sequence using dynamic programming. The optimal segmentation is computed and compared to a predictor based on marginal posterior modes, and the latter is shown to provide significant improvement in predictive accuracy. The marginalization procedure provides exact secondary structure probabilities at each sequence position, which are shown to be reliable estimates of prediction uncertainty. We apply this model to a database of 452 nonhomologous structures, achieving accuracies as high as the best currently available methods. We conclude by discussing an extension of this framework to model nonlocal interactions in protein structures, providing a possible direction for future improvements in secondary structure prediction accuracy.

Folding propensities of synthetic peptide fragments covering the entire sequence of phage 434 Cro protein

The phage 434 Cro protein, the N-terminal domain of its repressor (R1-69) and that of phage lambda (lambda6-85) constitute a group of small, monomeric, single-domain folding units consisting of five helices with striking structural similarity. The intrinsic helix stabilities in lambda6-85 have been correlated to its rapid folding behavior, and a residual hydrophobic cluster found in R1-69 in 7 M urea has been proposed as a folding initiation site. To understand the early events in the folding of 434 Cro, and for comparison with R1-69 and lambda6-85, we examined the conformational behavior of five peptides covering the entire 434 Cro sequence in water, 40% (by volume) TFE/water, and 7 M urea solutions using CD and NMR. Each peptide corresponds to a helix and adjacent residues as identified in the native 434 Cro NMR and crystal structures. All are soluble and monomeric in the solution conditions examined except for the peptide corresponding to the 434 Cro helix 4, which has low water solubility. Helix formation is observed for the 434 Cro helix 1 and helix 2 peptides in water, for all the peptides in 40% TFE and for none in 7 M urea. NMR data indicate that the helix limits in the peptides are similar to those in the native protein helices. The number of side-chain NOEs in water and TFE correlates with the helix content, and essentially none are observed in 7 M urea for any peptide, except that for helix 5, where a hydrophobic cluster may be present. The low intrinsic folding propensities of the five helices could account for the observed stability and folding behavior of 434 Cro and is, at least qualitatively, in accord with the results of the recently described diffusion-collision model incorporating intrinsic helix propensities.