Conformational constraints of amino acid side chains in alpha-helices

The conformational freedom of amino acid side chains is strongly reduced when the side chains occur on an α-helix. A quantitative evaluation of this freedom has been carried out by means of conformational energy computations for all naturally occurring amino acids and for α-aminobutyric acid when they are placed in the middle of a right-handed poly(L-alanine) α-helix. One of the three possible rotameric states for rotation around the C^α ? C^β bond (viz. g⁺) is excluded completely on the helix because of steric hindrance, and the relative populations of the other two rotamers (t and g^?) are altered because of steric interactions and the reduction of hydrogen-bonding possibilities. The computed tendencies of the changes in distributions of rotamers, on going from an ensemble of all backbone conformations to the α-helix, agree with the observed tendencies in proteins. Minimum-energy side-chain conformations in an α-helix have been tabulated for use in conformational energy computations on polypeptides.     

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.     

Studying the Structural and Folding Features of Long‐Sequence Trichobrachin Peptides

In this theoretical study, the folding processes of long‐sequence trichobrachin peptides (i.e., TB IIb peptides) were investigated by molecular dynamics methods. The formation of various helical structures (i.e., 3₁₀‐, α‐, and left‐handed α‐helices) was studied with regard to the entire sequence of peptides, as well as to each amino acid. The results pointed out that TB IIb molecules showed a propensity to form helical conformations, and they could be characterized by 3₁₀‐helical structure rather than by α‐helical structure. The formation of local (i.e., i←i+3 and i←i+4) as well as of non‐local (i.e., i←i+n, where n>4; and all i→i+n) H‐bonds was also examined. The results revealed that the occurrence of local, helix‐stabilizing H‐bonds was in agreement with the appearance of helical conformations, and the non‐local H‐bonds did not produce relevant effects on the evolution of helical structures. Based on the data obtained by our structural investigation, differences were observed between the TB IIb peptides, according to the type of amino acid located in the 17th position of their sequences. In summary, the folding processes were explored for TB IIb molecules, and our theoretical study led to the conclusion that these long‐sequence peptaibols showed characteristic structural and folding features.     

Equilibrium folding and unfolding pathways for a model protein

The folding–unfolding process of reduced bovine pancreatic trypsin inhibitor was investigated with an idealized model employing approximate free energies. The protein is regarded to consist of only C^α and C^β atoms. The backbone dihedral angles are the only conformational variables and are permitted to take discrete values at every 10°. Intraresidue energies consist of two terms: an empirical part taken from the observed frequency distributions of (?,ψ) and an additional favorable energy assigned to the native conformation of each residue. Interresidue interactions are simplified by assuming that there is an attractive energy operative only between residue pairs in close contact in the native structure. A total of 230,000 molecular conformations, with no atomic overlaps, ranging from the native state to the denatured state, are randomly generated by changing the sampling bias. Each conformation is classified according to its conformational energy, F; a conformational entropy, S(F) is estimated for each value of F from the number of samples. The dependence of S(F) on energy reveals that the folding–unfolding transition for this idealized model is an “all-or-none” type; this is attributable to the specific long-range interactions. Interresidue contact probabilities, averaged over samples representing various stages of folding, serve to characterize folding intermediates. Most probable equilibrium pathways for the folding–unfolding transition are constructed by connecting conformationally similar intermediates. The specific details obtained for bovine pancreatic trypsin inhibitor are as follows: (1) Folding begins with the appearance of nativelike medium-range contacts at a β-turn and at the α-helix. (2) These grow to include the native pair of interacting β-strands. This state includes intact regular secondary conformations, as well as the interstrand sheet contacts, and corresponds to an activated state with the highest free energy on the pathway. (3) Additional native long-range contacts are completely formed either toward the amino terminus or toward the carboxyl terminus. (4) In a final step, the missing contacts appear. Although these folding pathways for this model are not consistent with experimental reports, it does indicate multiple folding pathways. The method is general and can be applied to any set of calculated conformational energies and furthermore permits investigation of gross folding features.     

Structural versatility of peptides from Cα, α-disubstituted glycines: Crystal-state conformational analysis of homopeptides from Cα-methyl,Cα-benzylglycine [(αMe)Phe]n

The molecular and crystal structures of one derivative and three homopeptides (from the di-to the tetrapeptide level) of the chiral, C^{α, α}-disubstituted glycine C^α-methyl, C^α-benzylglycine [(αMe)Phe], have been determined by x-ray diffraction. The derivative is mClAc-D -(αMe)Phe-OH, and the peptides are pBrBz-[D -(αMe)Phe]₂-NHMe, pBrBz-[D -(αMe)Phe]₃-OH hemihydrate, and pBrBz-[D -(αMe)Phe]₄-OtBu sesquihydrate. All (αMe)Phe residues prefer ?,ψ torsion angles in the helical region of the conformational map. The dipeptide methylamide and the tripeptide carboxylic acid adopt a β-turn conformation with a 1 ← 4 C?O…?H? N intramolecular H bond. The structure of the tripeptide carboxylic acid is further stabilized by a 1 ← 4 C?O…?H? O intramolecular H bond, forming an “oxy-analogue” of a β-turn. The tetrapeptide ester is folded in a regular (incipient) 3₁₀-helix. In general, the relationship between (αMe)Phe chirality and helix screw sense is opposite to that exhibited by protein amino acids. A comparison is made with the conclusions extracted from published work on homopeptides from other C^α-methylated α-amino acids. © 1993 John Wiley & Sons, Inc.     

Conformational analysis of the type II and type III collagen α-1 chain N-telopeptides by 1H-NMR spectroscopy and restrained molecular mechanics calculations

The type II and type III collagen α-1 chain N-telopeptides are a nonadecamer with the sequence pEMAGGFDEKAGGAQLGVMQ-NH₂ and a tetradecamer with the sequence pEYEAYDVKSGVAGG-NH₂, respectively. Their conformations have been studied in CD₃OH/H₂O (60/40) solution by means of two-dimensional proton nmr spectroscopy. Based on double quantum filtered correlation spectroscopy, total correlation spectroscopy, rotating frame nuclear Overhauser enhancement (ROE) spectroscopy, and nuclear Over-hauser enhancement (NOE) spectroscopy experiments, all resonances were assigned and the conformational properties were analyzed in terms of vicinal NH-H_α coupling constants, sequential and medium-range NOEs (ROEs), and amide proton temperature coefficients. The NOE distance constraints as well as dihedral constraints based on the vicinal NH-H_α coupling constants were used as input parameters for restrained molecular mechanics, consisting of restrained molecular dynamics and restrained energy minimization calculations. The type II N-telopeptide's conformation is dominated by a fused βγ-turn between Phe⁶ and Ala¹⁰, stabilized by three hydrogen bonds and a salt bridge between the side-chain end groups of Glu⁸ and Lys⁹. The first 5 amino acids are extended with a much higher degree of conformational freedom. The 2 Gly residues following the turns were found to be highly flexible (hinge-like), leaving the spatial position of the second half of the molecule relative to the fused βγ-turn undefined. In the type III telopeptide, a series of sequential NH(i)-NH(i + 1) ROEs were observed between the amino acids Tyr² and Ser⁹, indicating that a fraction of the conformational space is helical. However, the absence of medium-range ROEs and the lack of regularity of the effects associated with α-helices suggest the presence of a nascent rather than a complete helix. © 1993 John Wiley & Sons, Inc.     

Optimization of amino acid type-specific <Superscript>13</Superscript>C and <Superscript>15</Superscript>N labeling for the backbone assignment of membrane proteins by solution- and solid-state NMR with the UPLABEL algorithm

We present a computational method for finding optimal labeling patterns for the backbone assignment of membrane proteins and other large proteins that cannot be assigned by conventional strategies. Following the approach of Kainosho and Tsuji (Biochemistry 21:6273–6279 (1982)), types of amino acids are labeled with ¹³C or/and ¹⁵N such that cross peaks between ¹³CO(i – 1) and ¹⁵NH(i) result only for pairs of sequentially adjacent amino acids of which the first is labeled with ¹³C and the second with ¹⁵N. In this way, unambiguous sequence-specific assignments can be obtained for unique pairs of amino acids that occur exactly once in the sequence of the protein. To be practical, it is crucial to limit the number of differently labeled protein samples that have to be prepared while obtaining an optimal extent of labeled unique amino acid pairs. Our computer algorithm UPLABEL for optimal unique pair labeling, implemented in the program CYANA and in a standalone program, and also available through a web portal, uses combinatorial optimization to find for a given amino acid sequence labeling patterns that maximize the number of unique pair assignments with a minimal number of differently labeled protein samples. Various auxiliary conditions, including labeled amino acid availability and price, previously known partial assignments, and sequence regions of particular interest can be taken into account when determining optimal amino acid type-specific labeling patterns. The method is illustrated for the assignment of the human G-protein coupled receptor bradykinin B2 (B₂R) and applied as a starting point for the backbone assignment of the membrane protein proteorhodopsin.     

D-isomeric replacements within the 6-9 core sequence of Ac-[Nle4]-alpha-MSH4-11-NH2: a topological model for the solution conformation of alpha-melanotropin

Analogs of Ac-[Nle⁴]-α-MSH_4–11-NH₂ and Ac-[Nle⁴, D -Phe⁷]-α-MSH_4–11-NH₂ were prepared with D -isomeric replacements at the His⁶, Arg⁸, and Trp⁹ residues. The requirement for an indole moiety at position 9 also was evaluated by replacement with L -leucine in both parent fragment analogs. D -isomeric replacements at positions 6 and 8 in either series were detrimental to biological potency in frog (Rana pipiens) and lizard skin (Anolis carolinensis) in vitro melanotropic assays. However, Ac-[Nle⁴, D -Trp⁹]-α-MSH_4–11-NH₂ and Ac-[Nle⁴, D -Phe⁷, D -Trp⁹]-α-MSH_4–11-NH₂ were equipotent and 10 × more potent than Ac-[Nle⁴]-α-MSH_4–11-NH₂, respectively, in the lizard skin bioassay, and 30 and 1900 times more potent in the frog skin bioassay. Ac-[Nle⁴, D -Phe⁷, D -Trp⁹]-α-MSH_4–11-NH₂ was 3 × more potent than α-MSH in the frog skin bioassay. Proton nmr studies in aqueous solution revealed a marked preservation of the backbone conformation of these linear analogs. Chemical-shift variations due to the through-space anisotropic influence of the core aromatic amino acid residues permitted evaluation of side-chain topology. The observed topology was consistent with nonhydrogen-bonded β-like structure (? = ?139°, ψ = +135° for L -amino acids; ? = +139°, ψ = ?135° for D -amino acids) as the predominant solution conformation. The biological and conformational data suggest that high melanotropic potency requires a close spatial arrangement of the His⁶, Phe⁷, and Arg⁸ side chains.     

A pentapeptide model for an early folding step in the refolding of staphylococcal nuclease: The role of its turn propensity

Recently the folding of a staphylococcal nuclease (P117G) variant was examined with the hydrogen-deuterium (H-D) exchange technique. Many of the residues that showed significant protection are located in protection are located in β-sheet regions. About half the residues protected belong to an antiparallel β-hairpin structure (residues 21–35) in the native structure. The β-hairpin structure is formed by strands 2 and 3 of sheet 2 connected by the sequence²⁷ Y KGQP³¹ in a type I′ reverse turn conformation with a 4 → 1 hydrogen bonding between Q30 NH and Y27 C=O. We have targeted the conformational characterization of the peptide model Ac-YKGQP-NH₂ with ¹II two-dimensional nmr techniques in aqueous solution with a view to assessing its propensity to sample turn conformational forms and thus initiate the formation of β-hairpin structure. Based upon the observed dαn (i, i + 1), dαn (i, i + 3), and dnn (i, i + 1) nuclear Overhauser effect connectivities, temperature coefficients for amide protons and conformational analysis with quantum mechanical perturbative configuration interaction over localized orbitals method, we conclude that the model peptide samples turn conformational forms with reduced conformational entropy. We suggest that the turn can nucleate the formation of the β-hairpin structure in the refolding of nuclease. Observation of turn propensity for this sequence is consistent with the folding mechanism of the Greek key motif (present in Staphylococcal nuclease) proposed in the literature. © 1997 John Wiley & Sons, Inc.     

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.     

Asparagine and glutamine differ in their propensities to form specific side chain-backbone hydrogen bonded motifs in proteins

Short range side chain‐backbone hydrogen bonded motifs involving Asn and Gln residues have been identified from a data set of 1370 protein crystal structures (resolution ≤ 1.5 Å). Hydrogen bonds involving residues i ? 5 to i + 5 have been considered. Out of 12,901 Asn residues, 3403 residues (26.4%) participate in such interactions, while out of 10,934 Gln residues, 1780 Gln residues (16.3%) are involved in these motifs. Hydrogen bonded ring sizes (C_n, where n is the number of atoms involved), directionality and internal torsion angles are used to classify motifs. The occurrence of the various motifs in the contexts of protein structure is illustrated. Distinct differences are established between the nature of motifs formed by Asn and Gln residues. For Asn, the most highly populated motifs are the C₁₀ (CO^δ_i …NH_{i + 2}), C₁₃ (CO^δ_i …NH_{i + 3}) and C₁₇ (N^δH_i …CO_{i ? 4}) structures. In contrast, Gln predominantly forms C₁₆ (CO^ε_i …NH_{i ? 3}), C₁₂ (N^εH_i …CO_{i ? 2}), C₁₅ (N^εH_i …CO_{i ? 3}) and C₁₈ (N^εH_i …CO_{i ? 4}) motifs, with only the C₁₈motif being analogous to the Asn C₁₇structure. Specific conformational types are established for the Asn containing motifs, which mimic backbone β‐turns and α‐turns. Histidine residues are shown to serve as a mimic for Asn residues in side chain‐backbone hydrogen bonded ring motifs. Illustrative examples from protein structures are considered. Proteins 2012; © 2011 Wiley Periodicals, Inc.     

Structural versatility of peptides from Cα,α-dialkylated glycines. I. A conformational energy computation and x-ray diffraction study of homo-peptides from Cα,α-diethylglycine

Conformational energy computations on a derivative and a homo-dipeptide of C^α,α-diethylglycine were performed. In both cases the N- and C-terminal groups are blocked as acetamido and methylamido moieties, respectively. It was found that the C^α,α-diethylglycine residues are conformationally restricted and that the minimum energy conformation corresponds to the fully extended C₅ structure when the N? C^α? C′ bond angle is smaller than 108° (as experimentally observed). The results of the theoretical analysis are in agreement with the crystal-state structural propensity of the complete series of N-trifluoroacetylated homo-peptides of this C^α,α-dialkylated residue from monomer to pentamer, determined by x-ray diffraction and also described in this work. Interestingly, for the first time, a crystallographically planar peptide backbone was observed (in the protected tripeptide). A comparison with peptides of C^α,α-dimethylglycine, C^α-methyl, C^α-ethylglycine, and C^α,α-di-n-propylglycine indicates that the fully extended conformation becomes more stable than the helical structures when both amino acid side-chain C^β atoms are substituted.     

Experimental conformational study of two peptides containing α-aminoisobutyric acid. Crystal structure of N-acetyl-α-aminoisobutyric acid methylamide

Some theoretical studies have predicted that the conformational freedom of the α-aminoisobutyric acid (H-Aib-OH) residue is restricted to the α-helical region of the Ramachandran map. In order to obtain conformational experimental data, two model peptide derivatives, MeCO-Aib-NHMe 1 and Bu^tCO-LPro-Aib-NHMe 2 , have been investigated. The Aib dipeptide 1 crystallizes in the monoclinic system (a = 12.71 Å, b = 10.19 Å, c = 7.29 Å, β = 110.02°, Cc space group) and its crystal structure was elucidated by x-ray diffraction analysis. The azimuthal angles depicting the molecular conformation (? = ?55.5°, ψ = ?39.3°) fall in the α-helical region of the Ramachandran map and molecules are hydrogen-bonded in a three-dimensional network. In CCl₄ solution, ir spectroscopy provides evidence for the occurrence of the so-called ₅ and C₇ conformers stabilized by the intramolecular i → i and i + 2 → i hydrogen bonds, respectively. The tripeptide 2 was studied in various solvents [CCl₄, CD₂Cl₂, CDCl₃, (CD₃)₂SO, and D₂O] by ir and pmr spectroscopies. It was shown to accommodate predominantly the βII folded state stabilized by the i + 3 → i hydrogen bond. All these experimental findings indicate that the Aib residue displays the same conformational behavior as the other natural chiral amino acid residues.     

HN(CA)N and HN(COCA)N experiments for assignment of large disordered proteins

Two new 3D HN-based experiments are proposed for backbone assignment of large disordered proteins. The spectra obtained with the new pulse schemes are free of redundant diagonal peaks (H_iN_i–N_i) and provide sequential correlations (H_iN_i–N_i+1 and H_iN_i–N_i?1) not only between adjacent non-proline residues but also between non-proline and proline residues. The experiments have been demonstrated on an intrinsically disordered protein with 306 amino acids including 64 proline residues. Using the two experiments, we obtained nearly complete assignments of backbone amides and proline ¹⁵N spins except for 4 proline and 4 non-proline residues.     

Synthesis,Structure, and Biological Applications of α‐Fluorinated β‐Amino Acids and Derivatives

This review gives a broad overview of the state of play with respect to the synthesis, conformational properties, and biological activity of α‐fluorinated β‐amino acids and derivatives. General methods are described for the preparation of monosubstituted α‐fluoro‐β‐amino acids (Scheme 1). Nucleophilic methods for the introduction of fluorine predominantly involve the reaction of DAST with alcohols derived from α‐amino acids, whereas electrophilic sources of fluorine such as NFSI have been used in conjunction with Arndt? Eistert homologation, conjugate addition or organocatalyzed Mannich reactions. α,α‐Difluoro‐β‐amino acids have also been prepared using DAST; however, this area of synthesis is largely dominated by the use of difluorinated Reformatsky reagents to introduce the difluoro ester functionality (Scheme 9). α‐Fluoro‐β‐amino acids and derivatives analyzed by X‐ray crystal and NMR solution techniques are found to adopt preferred conformations which are thought to result from stereoelectronic effects associated with F located close to amines, amides, and esters (Figs. 2–6). α‐Fluoro amide and β‐fluoro ethylamide/amine effects can influence the secondary structure of α‐fluoro‐β‐amino acid‐containing derivatives including peptides and peptidomimetics (Figs. 7–9). α‐Fluoro‐β‐amino acids are also components of a diverse range of bioactive anticancer (e.g., 5‐fluorouracil), antifungal, and antiinsomnia agents as well as protease inhibitors where such fluorinated analogs have shown increased potency and spectrum of activity.     

Effect of side chains on the conformational energy and rotational strength of the n-pi transition for some alpha-helical poly-alpha-amino acids

Calculations of the dependence of the conformational energy and the rotational strength of the amide n–π* electronic transition (in a series of α-helical polyhel-α- amino acids with different side chains) on conformation have been carried out. The conformational energies were computed by procedures developed in this laboratory; the computation of rotational strengths was carried out by the method of Schellman and Oriel, with a slight modification. Polyamino acids with both nonpolar and polar side chains were considered; in the latter case, it was assumed that the only influence of the polar side chain was on the backbone conformation and on the electrostatic field which perturbs the amide chromophore of the backbone. Only conformations in the range of backbone dihedral angles of the right- and left-handed a-helices were considered, and the assumption of regularity (i.e., uniformity of dihedral angles in every residue) was made. The rotational strength per residue was found to vary markedly with chain length (in oligomers of up to 40 residues long); both the conformational energy per residue and the rotational strength per residue were found to vary significantly with the backbone conformation, which in turn depends on the nature of the side chain. The geometry of the hydrogen bond in the α-helical backbone is the most important factor which influences the dependence of the rotational strength on conformation. The implications of these results, for the interpretation of experimental circular dichroism and optical rotatory dispersion data, are discussed.     

1H, 15N and 13C resonance assignments of yeast Saccharomyces cerevisiae calmodulin in the Ca2+-free state

Calmodulin (CaM) is a small Ca²⁺-binding protein, which has been found in all of eucaryotic cells examined. CaMs isolated from various species have highly conserved amino acid sequence (more than 90% identical), and show the same biological functions. CaM isolated from the baker's yeast (Saccharomyces cerevisiae) (yCaM), however, shares only 60% identity in the amino acid sequence with CaM from vertebrate, and shows quite distinct conformational and biochemical properties compared with those of CaM from other species. The conformational details of yCaM, however, have not been revealed yet. We achieved the chemical shift assignments of yCaM (146 amino acids) in the apo-state using uniformly ¹⁵N- and ¹³C-labeled protein. Consequently, the resonances of 95% atoms in the backbone amides were successfully assigned.     

Characterization of multiple bends in proteins

The concept of bends or chain reversals [nonhelical dipeptide sequences in which the distance R₃ (i,i+3) between the C^α atoms of residues i and i+3 is ≦ 7.0 Å] has been extended to define double bends as tripeptide sequences, not in an α-helix, in which two successive distances R₃(i,i+3) and R₃ (i+1, i+4) are both ≦7.0 Å, with analogous definitions for higher-order multiple bends. A sample of 23 proteins, consisting of 4050 residues, contains 235 single, 58 double, and 11 higher-order multiple bends. Multiple bends may occur as combinations of the “standard” type I, II, and III chain reversals (as well as their mirror images), but usually they require distortions from these well-defined conformations. The frequency of occurrence of amino acids often differs significantly between single and multiple bends. The probability distribution of R₃ distances does not differ in single and multiple bends. However, R₄ (the distance between the C^α atoms of residues i and i+4) in multiple bends is generally shorter than in tripeptide sequences containing single bends. The value of R₄ in many multiple bends is near those for α-helices. In some other multiple bends, R₄ is even shorter, indicating that these structures are very compact. The signs of the dihedral angles about the virtual bonds connecting C^α atoms and the values of curvature and torsion, as defined by means of differential geometry, indicate that there is a preference for single and multiple bends to be right-handed (like an α-helical sequence, for example) and that there is a strong tendency to conserve the handedness in both single-bend components of many multiple bends. These often have a strong resemblance to distorted single turns of an α-helix and do not constitute chain reversals. Double bends, in which the signs of two successive virtual-bond dihedral angles differ, have conformations that are very different from an α-helix. They act as chain reversals occuring over three residues. These chain reversals have not been described previously. Multiple bends may play an important role in protein folding because they occur fairly frequently in proteins and cause major changes in the direction of the polypeptide chain.     

Conversion from a virtual-bond chain to a complete polypeptide backbone chain

A method for generating a complete polypeptide backbone structure from a set of C^α coordinates is presented. Initial trial values of ? and ψ for a selected residue are chosen (essentially from an identification of the conformational region of the virtual-bond backbone, e.g., and α-helical region), and values of ? and ψ for the remaining residues (both towards the N- and C-terminus) are then computed, subject to the constraint that the chain have the same virtual-bond angles and virtual-bond dihedral angles as the given set of C^α coordinates. The conversion from C^α coordinates to full backbone dihedral angles (?,ψ) involves the solution of a set of algebraic equations relating the virtual-bond angles and virtual-bond dihedral angles to standard peptide geometry and backbone dihedral angles. The procedure has been tested successfully on C^α coordinates taken from standard-geometry full-atom structures of bovine pancreatic trypsin inhibitor (BPTI). Some difficulty was encountered with error-sensitive residues, but on the whole the backbone generation was successful. Application of the method to C^α coordinates for BPTI derived from simplified model calculations (involving nonstandard geometry) showed that such coordinates may be inconsistent with the requirement that ?_Pro be near ?75°. In such a case, i.e., for residues for which the algebraic method failed, a leastsquares minimizer was then used in conjunction with the algebraic method; the mean-square deviation of the calculated C^α coordinates from the given ones was minimized by varying the backbone dihedral angles. Thus, these inconsistencies were circumvented and a full backbone structure whose C^α coordinates had an rms deviation of 0.26 Å from the given set of C^α coordinates was obtained.     

A genetic code Boolean structure. II. The genetic information system as a Boolean information system

A Boolean structure of the genetic code where Boolean deductions have biological and physicochemical meanings was discussed in a previous paper. Now, from these Boolean deductions we propose to define the value of amino acid information in order to consider the genetic information system as a communication system and to introduce the semantic content of information ignored by the conventional information theory. In this proposal, the value of amino acid information is proportional to the molecular weight of amino acids with a proportional constant of about 1.96×10²⁵ bits per kg. In addition to this, for the experimental estimations of the minimum energy dissipation in genetic logic operations, we present two postulates: (1) the energy E _i (i = 1, 2, ..., 20) of amino acids in the messages conveyed by proteins is proportional to the value of information, and (2) amino acids are distributed according to their energy E _i so the amino acid population in proteins follows a Boltzmann distribution. Specifically, in the genetic message carried by the DNA from the genomes of living organisms, we found that the minimum energy dissipation in genetic logic operations was close to kTLn(2) joules per bit.