Mean-square hydrophobic moment for partially helical polypeptides

A mean-square helical hydrophobic moment, 〈h²〉, is defined for polypeptides in analogy to the mean-square dipole moment, 〈μ²〉, for polymer chains. For a freely jointed polymer chain, 〈μ²〉 is given by Σm, where m_i denotes the dipole moment associated with bond i. In the absence of any correlations in the hydrophobic moments of individual amino acid residues in the helix, 〈h²〉 is specified by ΣH, where H_i denotes the hydrophobicity of residue i. The tendency for correlations in orientations of residue hydrophobic moments in helices therefore dictates the size of 〈h²〉/〈H²〉, where 〈H²〉 denotes the average value of ΣH for all helices. The value of 〈h²〉/〈H²〉 will be greater than one in amphiphilic helices. A necessary prerequisite for this diagnostic usage of 〈h²〉/〈H²〉 is that the residue hydrophobic moment be oriented prependicular to the principal axis of the helix. Matrix-generation schemes are formulated that permit rapid evaluation of 〈h²〉 and 〈H²〉. The behavior of 〈h²〉/〈H²〉 is illustrated by calculations performed for model sequential copolypeptides.     

Analysis and prediction of the packing of α-helices against a β-sheet in the tertiary structure of globular proteins

The packing of α-helices and β-sheets in six $\text{α}\text{β}$ proteins (e.g. flavodoxin) has been analysed. The results provide the basis for a computer algorithm to predict the tertiary structure of an $\text{α}\text{β}$ protein from its amino acid sequence and actual assignment of secondary structure.The packing of an individual α-helix against a β-sheet generally involves two adjacent ± 4 rows of non-polar residues on the α-helix at the positions i, i + 4, i + 8, i + 1, i + 5, i + 9. The pattern of interacting β-sheet residues results from the twisted nature of the sheet surface and the attendant rotation of the side-chains. At a more detailed level, four of the α-helical residues (i + 1, i + 4, i + 5 and i + 8) form a diamond that surrounds one particular β-sheet residue, generally isoleucine, leucine or valine. In general, the α-helix sits 10 Å above the sheet and lies parallel to the strand direction.The prediction follows a combinational approach. First, a list of possible β-sheet structures (10⁶ to 10¹⁴) is constructed by the generation of all β-sheet topologies and β-strand alignments. This list is reduced by constraints on topology and the location of non-polar residues to mediate the sheet/helix packing, and then rank-ordered on the extent of hydrogen bonding. This algorithm was uniformly applied to 16 $\text{α}\text{β}$ domains in 13 proteins. For every structure, one member of the reduced list was close to the crystal structure; the root-mean-square deviation between equivalenced C^α atoms averaged 5.6 Å for 100 residues. For the $\text{α}\text{β}$ proteins with pure parallel β-sheets, the total number of structures comparable to or better than the native in terms of hydrogen bonds was between 1 and 148. For proteins with mixed β-sheets, the worst case is glyceraldehyde-3-phosphate dehydrogenase, where as many as 3800 structures would have to be sampled. The evolutionary significance of these results as well as the potential use of a combinatorial approach to the protein folding problem are discussed.     

Kinetic steps for α-helix formation

The kinetics of α-helix formation in polyalanine and polyglycine eicosamers (20-mers) were examined using torsional-coordinate molecular dynamics (MD). Of one hundred fifty-five MD experiments on extended (Ala)₂₀ carried out for 0.5 ns each, 129 (83%) formed a persistent α-helix. In contrast, the extended state of (Gly)₂₀ only formed a right-handed α-helix in two of the 20 MD experiments (10%), and these helices were not as long or as persistent as those of polyalanine. These simulations show helix formation to be a competition between the rates of (a) forming local hydrogen bonds (i.e. hydrogen bonds between any residue i and its i + 2, i + 3, i + 4, or i + 5th neighbor) and (b) forming nonlocal hydrogen bonds (HBs) between residues widely separated in sequence. Local HBs grow rapidly into an α-helix; but nonlocal HBs usually retard helix formation by “trapping” the polymer in irregular, “balled-up” structures. Most trajectories formed some nonlocal HBs, sometimes as many as eight. But, for (Ala)₂₀, most of these eventually rearranged to form local HBs that lead to α-helices. A simple kinetic model describes the rate of converting nonlocal HBs into α-helices. Torsional-coordinate MD speeds folding by eliminating bond and angle degrees of freedom and reducing dynamical friction. Thus, the observed 210 ps half-life for helix formation is likely to be a lower bound on the real rate. However, we believe the sequential steps observed here mirror those of real systems. Proteins 33:343–357, 1998. © 1998 Wiley-Liss, Inc.     

A systematic study of labelling an α-helix in a protein with a lanthanide using IDA-SH or NTA-SH tags

The previously published IDA-SH and NTA-SH tags are small synthetic lanthanide-binding tags derived from cysteine, which afford site-specific lanthanide labelling by disulfide-bond formation with a cysteine residue of the target protein. Following attachment to a single cysteine in an α-helix, sizeable pseudocontact shifts (PCS) can be observed, if the lanthanide is immobilized by additional coordination to a negatively charged amino-acid side chain that is located in a neighboring turn of the helix. To identify the best labelling strategy for PCS measurements, we performed a systematic study, where IDA-SH or NTA-SH tags were ligated to a cysteine residue in position i of an α-helix, and aspartate or glutamate residues were placed in the positions i ? 4 or i + 4. The largest anisotropy components of the magnetic susceptibility tensor were observed for an NTA-SH tag in position i with a glutamate residue in position i ? 4. While the NTA-SH tag produced sizeable PCSs regardless of the presence of nearby carboxyl groups of the protein, the IDA-SH tag generated a good lanthanide binding site only if an aspartate was placed in position i + 4. The findings provide a firm basis for the design of site-directed mutants that are suitable for the reliable generation of PCSs in proteins with paramagnetic lanthanides.     

Utilization of 13C-labeled amino acids to probe the α-helical local secondary structure of a membrane peptide using electron spin echo envelope modulation (ESEEM) spectroscopy

Electron spin echo envelope modulation (ESEEM) spectroscopy in combination with site-directed spin labeling (SDSL) has been established as a valuable biophysical technique to provide site-specific local secondary structure of membrane proteins. This pulsed electron paramagnetic resonance (EPR) method can successfully distinguish between α-helices, β-sheets, and 3₁₀-helices by strategically using ²H-labeled amino acids and SDSL. In this study, we have explored the use of ¹³C-labeled residues as the NMR active nuclei for this approach for the first time. ¹³C-labeled d₅-valine (Val) or ¹³C-labeled d₆-leucine (Leu) were substituted at a specific Val or Leu residue (i), and a nitroxide spin label was positioned 2 or 3 residues away (denoted i-2 and i-3) on the acetylcholine receptor M2δ (AChR M2δ) in a lipid bilayer. The ¹³C ESEEM peaks in the FT frequency domain data were observed for the i-3 samples, and no ¹³C peaks were observed in the i-2 samples. The resulting spectra were indicative of the α-helical local secondary structure of AChR M2δ in bicelles. This study provides more versatility and alternative options when using this ESEEM approach to study the more challenging recombinant membrane protein secondary structures.     

Conformational studies on poly(N-δ-trimethyl-l-ornithine)

$\text{Poly}\text{(N-δ-}\text{trimethyl-}\text{l}\text{-ornithine}$), (Me₃Orn)_n, is usually not able to attain the α-helical conformation in aqueous solution independent of its pH value; however, it becomes α-helical at low concentrations of sodium perchlorate over a wide pH range according to the circular dichorism (c.d.) spectra. Cl^?, SO₄^2? and H₂PO₄^? do not induce α-helix formation. One can conclude that a distinct topology of the anions bound by the side chains is responsible for the α-helix-inducing effect of some water-structure-breaking anions such as perchlorate. This means that the anions are inserted between the ?N⁺ of the side groups shielding the positive charges repelling one another. The insertion of the anions requires that the water molecules surrounding the ions can be stripped off, which is easily possible if they are water-structure-breaking ones. At higher perchlorate concentrations, the c.d. spectrum changes. It is characterized by a negative shoulder near 208 nm and a pronounced minimum at ≈ 226 nm. With increasing temperature, the c.d. spectrum of the α-helix occurs. Finally the α-helix undergoes a conformational change to the random coil. The apparent transition enthalpy ΔH_vH is remarkably lower than that of the homologue (Me₃Lys)_n, obviously due to a lower cooperativity of the transition. In contrast to poly(l-ornithine), (Orn)_n, the c.d. spectrum of (Me₃Orn)_n remains almost unchanged after adding anionic surfactants such as sodium octyl sulphate (SOS) or sodium dodecyl sulphate (SDS). In organic solvents like methanol or isopropanol, in contrast to (Orn)_a and (Lys)_n, no α-helix formation occurs. However, in mixtures of these alcohols or dioxane with water, α-helix formation is induced by perchlorate, as in pure water. The thermal stability of the α-helix in these systems is increased.     

Proline-induced constraints in alpha-helices

The disrupting effect of a prolyl residue on an α-helix has been analyzed by means of conformational energy computations. In the preferred, nearly α-helical conformations of Ac-Ala₄-Pro-NHMe and of Ac-Ala₇-Pro-Ala₇-NHMe, only the residue preceding Pro is not α-helical, while all other residues can occur in the α-helical A conformation; i.e., it is sufficient to introduce a conformational change of only one residue in order to accommodate proline in a distorted α-helix. Other low-energy conformations exist in which the conformational state of three residues preceding proline is altered considerably; on the other hand, another conformation in which these three residues retain the near-α-helical A-conformational state (with up to 26° changes of their dihedral angles ? and ψ, and a 48° change in one ω from those of the ideal α-helix) has a considerably higher energy. These conclusions are not altered by the substitution of other residues in the place of the Ala preceding Pro. The conformations of the peptide chain next to prolyl residues in or near an α-helix have been analyzed in 58 proteins of known structure, based on published atomic coordinates. Of 331 α-helices, 61 have a Pro at or next to their N-terminus, 21 have a Pro next to their C-terminus, and 30 contain a Pro inside the helix. Of the latter, 16 correspond to a break in the helix, 9 are located inside distorted first turns of the helix, and 5 are parts of irregular helices. Thus, the reported occurrence of prolyl residues next to or inside observed α-helices in proteins is consistent with the computed steric and energetic requirements of prolyl peptides.     

NMR solution structure of human cannabinoid receptor-1 helix 7/8 peptide: Candidate electrostatic interactions and microdomain formation

We report the NMR solution structure of a synthetic 40-mer (T³⁷⁷-E⁴¹⁶) that encompasses human cannabinoid receptor-1 (hCB1) transmembrane helix 7 (TMH7) and helix 8 (H8) [hCB1(TMH7/H8)] in 30% trifluoroethanol/H₂O. Structural features include, from the peptide’s amino terminus, a hydrophobic α-helix (TMH7); a loop-like, 11 residue segment featuring a pronounced Pro-kink within the conserved NPxxY motif; a short amphipathic α-helix (H8) orthogonal to TMH7 with cationic and hydrophobic amino-acid clusters; and an unstructured C-terminal end. The hCB1(TMH7/H8) NMR solution structure suggests multiple electrostatic amino-acid interactions, including an intrahelical H8 salt bridge and a hydrogen-bond network involving the peptide’s loop-like region. Potential cation-π and cation-phenolic OH interactions between Y³⁹⁷ in the TMH7 NPxxY motif and R⁴⁰⁵ in H8 are identified as candidate structural forces promoting interhelical microdomain formation. This microdomain may function as a flexible molecular hinge during ligand-induced hCB1 conformer transitions.     

Helix-helix interactions and their impact on protein motifs and assemblies

Protein secondary structure elements are arranged in distinct structural motifs such as four-α-helix bundle, 8α/8β TIM-barrel, Rossmann dinucleotide binding fold, assembly of a helical rod. Each structural motif is characterized by a particular type of helix-helix interactions. A unique pattern of contacts is formed by interacting helices of the structural motif. In each type of fold, edges of the helix surface, which participate in the formation of helix-helix contacts with preceding and following helices, differ. This work shows that circular arrangements of the four, eight, and sixteen α-helices, which are found in the four-α-helical motif, TIM-barrel 8α/8β fold, and helical rod of 16.3¯ helices per turn correspondingly, can be associated with the mutual positioning of the edges of the helix surfaces. Edges (i, i+1)−(i+1, i+2) of the helix surface are central for the interhelical contacts in a four-α-helix bundle. Edges (i, i+1)−(i+2, i+3) are involved in the assembly of four-α-helix subunits into helical rod of a tobacco mosaic virus and a three-helix fragment of a Rossmann fold. In 8α/8β TIM-barrel fold, edges (i, i+1)−(i+5, i+6) are involved in the octagon arrangement. Approximation of a cross section of each motif with a polygon (n-gon, n=4, 8, 16) shows that a good correlation exists between polygon interior angles and angles formed by the edges of helix surfaces.     

ω-Helices in Proteins

A modification of the α-helix, termed the ω-helix, has four residues in one turn of a helix. We searched the ω-helix in proteins by the HELFIT program which determines the helical parameters—pitch, residues per turn, radius, and handedness—and p = rmsd/(N ? 1)^1/2 estimating helical regularity, where “rmsd” is the root mean square deviation from the best fit helix and “N” is helix length. A total of 1,496 regular α-helices 6–9 residues long with p ≤ 0.10 Å were identified from 866 protein chains. The statistical analysis provides a strong evidence that the frequency distribution of helices versus n indicates the bimodality of typical α-helix and ω-helix. Sixty-two right handed ω-helices identified (7.2% of proteins) show non-planarity of the peptide groups. There is amino acid preference of Asp and Cys. These observations and analyses insist that the ω-helices occur really in proteins.     

Pituitary corticotropin-inhibiting peptide: Properties and use in study of corticotropin action

The biological properties of the naturally occurring pituitary peptide α_h^7–38-adrenocorticotropin (ACTH) have been investigated. α_h^7–38-ACTH is devoid of steroidogenic activity but inhibits competitively ACTH-induced steroidogenesis in vitro as well as in vivo. The long-term actions of ACTH on normal and tumor adrenal cells in culture are also antagonized by α_h^7–38-ACTH. The apparent K_i for the inhibition of cyclic AMP production by α_h^7–38-ACTH (301 ± 62 nm) was significantly higher than the apparent K_i for the inhibition of corticosterone synthesis (21.6 ± 6.8 nm). Analysis of the inhibition of ACTH-induced steroidogenesis and cyclic AMP production in normal rat adrenocortical cells indicates that two separate receptors may be involved in mediating these responses.     

Behavior of amphipathic helices on analysis via matrix methods, with application to glucagon, secretin, and vasoactive intestinal peptide

A configuration partition function, which incorporates concepts embodied in the amphipathic helix hypothesis, has been formulated for a polypeptide in the presence of zwitterionic phospholipid. An enhanced probability is assigned to helix formation in any region of the polypeptide chain where side chains bearing charges of opposite sign will be situated on the same side of the α-helix but displaced from one another by one turn. This situation will arise when residues i ? 4 (or i ? 3) and i bear charges of opposite sign and residue i ? 4 (or i ? 3) through i are in a helical state. Illustrative calculations are performed for polypeptide chains in which the generalized nonionic amino acid residue serving as host has Zimm-Bragg parameters of σ = 10^?4, s = 1. These calculations define conditions under which two interacting charged pairs can cooperate in a synergistic helix augmentation even when the two pairs are separated by significantly more than four generalized nonionic amino acid residues. Furthermore, the two interacting charged pairs, as well as the intervening amino acid residues, may become helical as one unit. Significant augmentation in helicity is observed with plausible values for the enhanced probablity assigned to helix formation for an interacting pair. This model predicts correctly that glucagon and secretin, but not vasoactive intestinal peptide, undergo a coil-to-helix trnsition in the presence of zwitterionic phospholipid. This prediction is made with plausible values for the parameter used to express the helicity enhancement. The experimental observation with zwitterionic phospholipids is the direct opposite of that seen for these three peptides in the presence of anionic lipids and detergents. In anionic lipids the amount of induced helicity is in the following order: glucagon < secretin < vasoactive intestinal peptide. Results obtained with these three peptides demonstrate that the nature of the head group of the lipid is important for lipid–protein interaction and that the resulting conformational changes can be rationalized by matrix methods.     

Fluctuations of an alpha-helix.

Fluctuations in backbone dihedral angles in the α-helical conformation of homopolypeptides are studied based on an assumption that the conformational energy function of a polypeptide consisting of n amino-acid residues can be approximated by a 2n-dimensional parabola around the minimum point in the range of fluctuations. A formula is derived that relates 〈Δθ_iΔθ_j〉, the mean value of the product of deviations of dihedral angles ?_i and ψ_i (collectively designated by θ_i) from their energy minimum values, with a matrix inverse to the second derivative matrix F ,_n of the conformational energy function at the minimum point. A method of calculating the inverse matrix F _n^?1 explicitly is given. The method is applied to calculating 〈Δθ_iΔθ_j〉 for the α-helices of poly(L -alanine) and polyglycine. The autocorrelations 〈(Δ?_i)²〉 and 〈(Δψ_i)²〉 at 300°K are found to be about 66 deg² and 49 deg², respectively, for poly(L -alanine), and 84 deg² and 116 deg², respectively, for polyglycine. The length of correlations of fluctuations along the chain is found for both polypeptides to be about eight residues long.     

Vibrational analysis of peptides,polypeptides, and proteins. XVIII. Conformational sensitivity of the α-helix spectrum: αI- and αII-Poly(L-alanine)

The α_II-helix (? = ?70.47°, ψ = ?35.75°) is a structure having the same n and h as the (standard) α_I-helix (? = ?57.37°, ψ = ?47.49°). Its conformational angles are commonly found in proteins. Using an improved α-helix force field, we have compared the vibrational frequencies of these two structures. Despite the small conformational differences, there are significant predicted differences in frequencies, particularly in the amide A, amide I, and amide II bands, and in the conformation-sensitive region below 900 cm^?1. This analysis indicates that α_II-helices are likely to be present in bacteriorhodopsin [Krimm, S. & Dwivedi, A. M. (1982) Science 216 , 407–408].     

A stone's throw and its launch window: timing precision and its implications for language and hominid brains

The Chou-Fasman conformational parameters, P, for amino acid residues in proteins are shown to be a linear function of intermolecular force and steric parameters. For α- helix, coil and turn parameters, steric effects are predominant; whereas for β-sheet parameters, intramolecular forces are predominant. Turn and coil parameters show little or no difference in their dependence which is different from that of α-helix and in some ways almost reciprocal. Factors which increase the probability of finding an amino acid residue in an α-helix usually decrease the probability of finding it in coil or turn. Values of P were calculated for several of the less common amino acids.     

Directional structural features of globular proteins

We describe a novel presentation of the conformation of the backbone atoms for proteins of known structure. Given the C^α atom cartesian co-ordinates from X-ray crystallography, a matrix is calculated, where the ijth element of the matrix is the cosine of the angle between the direction of the chain at residue i and the direction of the chain at residue j. These “direction matrices” have distinctive patterns which correspond to α-helix, extended structure, straight or bent segments, “superhelix”, and many other important structural features. We discuss the direction matrices for a number of proteins, and make some generalizations on the basic principles of protein folding.     

A new solid-state microelectrode for measuring intra-cellular chloride activities

Solid-state microelectrodes for measuring intracellular Cl^? activity (aⁱCl) were made by sealing the tips of tapered glass capillaries (tip diameter 0.3 μm), coating them under vacuum with a 0.2–0.3 μm thick layer of spectroscopic grade silver, and sealing them (except for the terminal 2–5 μm of the tip) inside tapered glass shields. 106 microelectrodes had an average slope of 55.0 ± 0.6 mV (S.E.) per decade change in α_Cl. Tip resistance was (77.1 ± 3.1 × 10⁹ω (n=30). Electrode response was rapid (10–20 s), was unaffected by HCO₃^?, H₂PO₄^2? or protein, and remained essentially unchanged over a 24-h period. αⁱ_Cl in frog sartorius muscle fibers and epithelial cells of bullfrog small intestine was measured in vitro. In both tissues, αⁱ_Cl significantly exceeded the value corresponding to equilibrium distribution of Cl^? across the cell membrane.     

ΔμH+ dependency of in vitro protein translocation into Escherichia coli inner-membrane vesicles varies with the signal-sequence core-region composition

Signal sequences frequently contain α-helix-destabilizing amino acids in the hydrophobic core. Nuclear magnetic resonance studies on the conformation of signal sequences in membrane mimetic environments revealed that these residues cause a break in the α-helix. In the precursor of the Escherichia coli outer membrane protein PhoE (pre-PhoE), a glycine residue at position -10 (Gly^?10) is thought to be responsible for the break in the α-helix. We investigated the role of this glycine residue in the translocation process by employing site-directed mutagenesis. SDS-PAGE analysis showed drastic variations in the electrophoretic mobilities of the mutant precursor proteins, suggesting an important role of the glycine residue in determining the conformation of the signal sequence. In vivo, no drastic differences in the translocation kinetics were observed as compared with wild-type PhoE, except when a charged residue (Arg) was substituted for Gly^?10. However, the in vitro translocation of all mutant proteins into inverted inner-membrane vesicles was affected. Two classes of precursors could be distinguished. Translocation of one class of mutant proteins (Ala, Cys and Leu for Gly^?10) was almost independent of the presence of a ΔμH⁺, whereas translocation of the other class of precursors (wild type or Ser) was strongly decreased in the absence of the ΔμH⁺. Apparently, the ΔμH⁺ dependency of in vitro protein translocation varies with the signal-sequence core-region composition. Furthermore, a proline residue at position -10 resulted in a signal sequence that did not prevent the folding of the precursor in an in vitro trimerization assay.     

Statistical mechanical treatment of α-helices and extended structures in proteins with inclusion of short- and medium-range interactions

A statistical mechanical model of protein conformation with medium-range interactions between theith and (i+k)^th residues (k<-4) is presented. Two two-state models, an α-helix-coil and an extended-structure-coil model, are formulated using the same form of the partition function, but the two models are applied independently to predict the locations of α-helical, extended, and coil segments; in the relatively few cases (<2%) where the predictions from the two models are in conflict, the prediction is scored as an incorrect one. Two independent sets of statistical weights (one set for each model) are derived to describe the interactions between the 20 amino acid residues for each range of interactionk; they are evaluated by minimizing an objective function so that the probability profiles for the α-helix or extended structure, respectively, in proteins computed from these statistical weights correlate optimally with the experimentally observed native conformations of these proteins. Examination of the resulting statistical weights shows that those for the interactions between hydrophobic residues and between a hydrophobic and a hydrophilic residue have reasonable magnitudes compared to what would be expected from the spatial arrangements of the side chains in the α-helix and the extended structure, and that those for the α-helix-coil model correlate well with experimentally determined values of the Zimm-Bragg parameterss and σ of the helix-coil transition theory. From the point of view of a method to predict the conformational states (i.e., α-helix, extended structure, and coil) of each residue, the statistical weights (as inall empirical prediction schemes) depend very much on the proteins used for the data base, since the presently available set of proteins of known structure is still too small for very high predictability; as a result, the correctness of the prediction is not very good for proteins not included in the data base. However, the correctness of the prediction, at least for the 37 proteins utilized as the data base in this study, is 91% and 87% for the α-helix-coil and the extended-structure-coil models, respectively; further, 79% of all the residues are predicted correctly when both the α-helix-coil and extended-structure-coil models are applied independently.     

Carbon-13 nuclear magnetic resonance studies of polyamino acids: the helix-coil transition of poly-L-lysine

The helix-coil transition of poly-l-lysine hydrochloride ((Lys)_n) in aqueous solution has been studied by ¹³C Fourier-transform nuclear magnetic resonance spectroscopy. As reference compounds dodeca-l-lysine hydrobromide ((Lys)^?₁₂, tri-l-lysine hydrochloride ((Lys)₃), and l-lysine hydrochloride (Lys), have been also studied by the same method. It is found that ¹³C spin-lattice relaxation times t₁ of the carbonyl and the side-chain carbons decrease sharply at pD 10.2 which is the midpoint of the transition from the random-coil to the α-helix. Similarly the T₁ values of the carbonyl groups of (Lys)^?₁₂ decrease at this point in a more moderate way, while no change is observed for those of the side-chain carbons. This is interpreted in terms of the reduced α-helicity involved for (Lys)^?₁₂.The variation of ¹³C chemical shifts with pD for (Lys)_n and (Lys)^?₁₂ show the same trend:downfield shifts at higher pD. Furthermore, nonterminal and C-terminal residues of (Lys)₃ show similar behavior. Thus it is concluded that the ¹³C chemical shift changes are caused mainly by the pD changes and not by the conformational transition. Conversion from α-helix to β-structure by elevation of temperature at pD 11.2 results in narrowing and downfield shifts of the ¹³C resonances of (Lys)_n.