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.     

Solvent Effects on the Shape of a Tetramer

Abstract

The solvent effect on the shape of a tetramer with increasing temperature is analyzed. For this purpose models of an isolated chain and a chain immersed in a solvent have been simulated by Molecular Dynamics. A solvent model represented by stochastic forces has been tested against molecular dynamics results. The behaviour of the mean-square end-to-end distance 〈R ²〉 and 〈l ₁ ³ S ²〉 with increasing temperature are shown. where l ₁ is the longest eigenvalue of the moment of inertia tensor and S is the radius of gyration. All the chain models studied show different behaviour of these quantities at low temperature compared to high temperature where the shape of the tetramer is temperature insensitive. The main solvent effect is to pospone the transition to higher temperature. The stochastic solvent model qualitatively agrees with molecular dynamics results.     

Solution properties of synthetic polypeptides. V. Helix–coil transition in poly(β-benzyl L-aspartate)

Simple approximate expressions have been derived from the theory of Zimm and Bragg for use in the analysis of experimental data on the helix-coil transition in polypeptide. On the basis of the resulting expressions practical procedures are proposed to determine two basic parameters characterizing a thermally induced transition, i.e., helix initiation parameter σ and enthalpy change for helix formation, ΔH. They have been applied to the data for poly(β-benzyl L -aspartate) (PBLA) with the result: σ = 1.6 × 10^?4 and ΔH = ?450 cal/mole for PBLA in m-cresol; σ = 0.6 × 10^?4 and ΔH = 260 cal/mole for PBLA in chloroform containing 5.7 vol-% of dichloroacetic acid. This result gives evidence that σ may change not only from one polypeptide to another but also for a given polypeptide in different solvents. The change in limiting viscosity number [η] accompanying the transition was measured in the same solvents. The curve of [η] versus helical content had a relatively monotonic shape for the chloroformdichloroacetic acid solutions as compared with that for the m-cresol solutions, indicating that [η] depended largely on σ. Provided that [η] is a direct measure of the mean-square radius of gyration, 〈S²〉, the results are consistent with the theoretical predictions of Nagai and of Miller and Flory for 〈S²〉.     

Spatial configuration of single-stranded polynucleotides. Calculations of average dimensions and Nmr coupling constants

The probability distributions of the torsional angles (Φ′, ω′, ω, Φ, and ψ), which fix the structure of nucleotide backbone, have been calculated using the results of energy calculations based on extended Huckel theory (EHT), complete neglect of differential overlap (CNDO), perturbative configuration interaction using localized orbitals (PCILO), and classical potential functions (CPF) methods. Statistical average values of the vicinal ¹H? ¹H, ¹H? ³¹P, and ¹³C? ³¹P nmr coupling constants 〈J〉 have been calculated from the generalized Karplus relations using the probability distribution in the Φ′, Φ, and ψ space. Experimental 〈J〉 values for polyribouridylic acid (polyU) support the theoretical predictions for these torsional angles. Using Monte Carlo technique, random coils of single-stranded polynucleotides have been simulated and the mean-square end-to-end distance 〈r²〉 has been calculated. Molecular orbital methods (EHT, CNDO, and PCILO) suggest considerable flexibility around O? P bonds, leading to fairly small values for the characteristic ratio (C_∞ ～ 4). Observed values of the unperturbed characteristic ratio for polynucleotides are quite large (C_∞ ～ 18) suggesting a relatively rigid nucleotide backbone. The results based on molecular orbital calculations can be reconciled with the experimental values by introducing an additional stabilization of ～2 kcal mol^?1 for the predicted minimum energy ragion (Φ′ ～ 240°, ω′ ～ 290°, ω 290°, Φ 180°, and ψ 60°). Such a stabilization may arise from the association of water molecules and metal ions with the phosphate group and (or) Coulomb interaction between neighboring phosphate groups. The calculations provide a semiquantitative estimate of torsional rigidity in the nucleotide backbone.     

Intrinsic viscosities of cyclic and linear lamda DNA

The ratio of the intrinsic viscosities of the linear and circular forms of λ DNA, [η]L /[η]c, has been measured as a function of ionic strength in the range [Na⁺] = 0.6. M–0.03MCorrections were made for the presence of uncyclizable linear contaminant in circular preparations. By combining data in the literature on the ionic strength dependence of linear DNA of various molecular weights with that obtained here, it was possible to determine the expansion parameter εL as a function of [Na⁺]. εL is defined by the relation 〈L²〉 = b²N^1+εL, where 〈L¹〉 is the mean-square end-to-end distance of a chain of N segments of length b. The empirical relation εL = 0.05 ? 0.11 log [Na⁺] for native NaDNA at 25°C is found. When εL = 0, [η]L /[η]c extrapolates to 1.6, in good agreement with the theoretical prediction of 1.55. As εL increases, [η]L /[η]c increases, in agreement with a theory of Bloomfield and Zimm.     

Solvent‐dependent conformation of amylose tris(phenylcarbamate) as deduced from scattering and viscosity data

The z‐average mean‐square radius of gyration 〈S²〉_z, the particle scattering function P(k), the second virial coefficient, and the intrinsic viscosity [η] have been determined for amylose tris(phenylcarbamate) (ATPC) in methyl acetate (MEA) at 25°C, in ethyl acetate (EA) at 33°C, and in 4‐methyl‐2‐pentanone (MIBK) at 25°C by light and small‐angle X‐ray scattering and viscometry as functions of the weight‐average molecular weight in a range from 2 × 10⁴ to 3 × 10⁶. The first two solvents attain the theta state, whereas the last one is a good solvent for the amylose derivative. Analysis of the 〈S²〉_z, P(k), and [η] data based on the wormlike chain yields h (the contour length or helix pitch per repeating unit) = 0.37 ± 0.02 and λ^?1 (the Kuhn segment length) = 15 ± 2 nm in MEA, h = 0.39 ± 0.02 and λ^?1 = 17 ± 2 nm in EA, and h = 0.42 ± 0.02 nm and λ^?1 = 24 ± 2 nm in MIBK. These h values, comparable with the helix pitches (0.37–0.40 nm) per residue of amylose triesters in the crystalline state, are somewhat larger than the previously determined h of 0.33 ± 0.02 nm for ATPC in 1,4‐dioxane and 2‐ethoxyethanol, in which intramolecular hydrogen bonds are formed between the C?O and NH groups of the neighbor repeating units. The slightly extended helices of ATPC in the ketone and ester solvents are most likely due to the replacement of those hydrogen bonds by intermolecular hydrogen bonds between the NH groups of the polymer and the carbonyl groups of the solvent. © 2009 Wiley Periodicals, Inc. Biopolymers 91: 729–736, 2009. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com     

Linkage studies of the h gene with plant weight in flax genotrophs

Summary The association of the H-h (hairy-hairless septa) character with plant weight was studied in the coupling and repulsion phases in F₂ of reciprocal crosses between large (L) and small (S) genotrophs of flax variety Stormont Cirrus. F₂ plants of reciprocal crosses in coupling (L^H x S^h) and in repulsion (L^h x S^H) giving H-h segregations were grown with their parents at two sowing times. Significant positive and negative associations between h and plant weight were obtained. A model is proposed based on the hypothesis that the H phenotype had changed to the h phenotype at the time of induction by a heterochromatic region extending over this locus. In the heterozygote, stable equilibria of the homozygotes are destroyed and transfer of heterochromatin, or number of reiterated sequences, or a decrease in one homologue and an increase in the other, occur in this region between homologous chromosomes. The amount and direction of the association is dependent upon the frequency of transfer: 0% transfer gives complete positive association; 50% transfer, no association; 100% transfer, complete negative association. This mechanism or heterochromatic transfer preserves the Mendelian ratio of 31 of Hh in the F₂. It is also supposed that there must be other controlling elements present as well.     

Measurement of diffusion coefficients of meningococcal polysaccharide by optical mixing spectroscopy. I. A preliminary characterization on the aggregation of the group C polysaccharide

The angular distribution of scattered intensity and decay times of concentration fluctuations have been measured by means of digital photon counting and single-clipped photon correlation for solutions of Group C meningococcal polysaccharides at 31°C. The z-average diffusion coefficient 〈D〉_z and its second moment 〈D²〉_z have been determined from the time-dependent correlation function using the cumulant expansion technique. Very low observed values of 〈D〉_z and the tremendous width of the polydispersity index, which is the z-average normalized variance, suggest a higher degree of aggregation than the monomer–dimer type self-association at finite concentrations.     

Triangular matrix representation of dimensionless helical hydrophobic moment ratios

If the hydrophobicity of the ith residue in an α-helix is denoted by H_i, one can (following Eisenberg) define a corresponding vector, h_i = a_iH_i. Here a_i is a unit vector directed radially from the helix axis through C_i^α. The vector sum of the h_i for the N residues in an α-helix is denoted by h, and h² is the square of the magnitude of h. In the absence of any correlation in the h_i we obtain h² = ∑ H_i², where the sum extends over all N residues in the helix. The dimensionless ratio h²/∑ H_i² has the value 1 when the h_i are uncorrected. However, if hydrophobic residues occur on the opposite surface of a helix from the hydrophilic residues, h²/∑ H_i² > 1. The h²/∑ H_i² for the n(n − 1)/2 helices that might occur in a chain of n residues are conveniently displayed as the elements in a symmetric n × n matrix. The jkth and kjth elements are h²/∑ H_i² for the helix that initiates at residue j and terminates at residue k. All of the h²/∑ H_i² are retained in either of the triangular matrices that together together constitute the symmetric matrix. The largest element in the triangular matrix for glucagon is the entry for a helix that is nearly identical with the major helix found by Wüthrich when the peptide is bound to a zwitterionic micelle. Three related hormonal peptides have their maximum h²/∑ H_i² in the same region of their respectively triangular matrices. The triangular matrix for α-tropomyosin shows that the h²/∑ H_i² are larger in the portion of the chain that forms the more stable helix in the in-register dimer.     

Temperature‐induced partially unfolded state of hUBF HMG Box‐5: Conformational and dynamic investigations of the Box‐5 thermal intermediate ensemble

Human upstream binding factor (hUBF) HMG Box‐5 is a highly conserved protein domain, containing 84 amino acids and belonging to the family of the nonspecific DNA‐binding HMG boxes. Its native structure adopts a twisted L shape, which consists of three α‐helices and two hydrophobic cores: the major wing and the minor wing. In this article, we report a reversible three‐state thermal unfolding equilibrium of hUBF HMG Box‐5, which is investigated by differential scanning calorimetry (DSC), circular dichroism spectroscopy, fluorescence spectroscopy, and NMR spectroscopy. DSC data show that Box‐5 unfolds reversibly in two separate stages. Spectroscopic analyses suggest that different structural elements exhibit noncooperative transitions during the unfolding process and that the major form of the Box‐5 thermal intermediate ensemble at 55°C shows partially unfolded characteristics. Compared with previous thermal stability studies of other boxes, it appears that Box‐5 possesses a more stable major wing and two well separated subdomains. NMR chemical shift index and sequential ¹H^N_i‐¹H^N_i+1 NOE analyses indicate that helices 1 and 2 are native‐like in the thermal intermediate ensemble, while helix 3 is partially unfolded. Detailed NMR relaxation dynamics are compared between the native state and the intermediate ensemble. Our results implicate a fluid helix‐turn‐helix folding model of Box‐5, where helices 1 and 2 potentially form the helix 1‐turn‐helix 2 motif in the intermediate, while helix 3 is consolidated only as two hydrophobic cores form to stabilize the native structure. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Nonradiative energy transfer in oligopeptide chains generated by a monte-cralo mehod including long-range interactions

A Monte-Carlo method including long-range interactions is used to oligopeptide chains in random-coil state. The chains are composed of 4, 9, or 14 repeating units and are labeled with the luminopheres tyrosine or tryptophan. Interactions with a solvent (water) are taken into account in the calculations through modifications of the semiempirical potential-energy functions. The chains represent oligopeptides composed of hydrophobic or hydrophilic amino acid residues. Various properties relavent to the interpretaiton of nonradiative enrgy-transfer experiments, such as the average value of the orientation factor for dipole-dipole interaction of the luminophores, 〈k²〉, the distribution function of the distances between the luminophores f(r_l), the efficiences of energy transfer in the static and dyamic averaging regimes, 〈T〉_s amnd 〈T〉_d, as well as the fluorescence decay I(t) of the donor luminophore in various averaging conditions, are computed. It is shown that, for all chains considered, 〈k²〉 is not vary far form 0.67 and that 〈T〉_s and 〈T〉_d have completely different values. Due to the small extent of correlation between the distances r_l and the mutual orientations of the lumninophores, the decay kinetics 〈I(t)_s corresponding to a static averaging regime can be expressed in terms of distribution functions f(r_l). These results are in agrrement with those obtained previously for the unperturbed chain model.     

Spatial configurations of polynucleotide chains. 3. Polydeoxyribonucleotides

The virtual bond scheme set forth in preceding papers for treating the average properties of polyriboadenylic acid (poly rA) is here applied to the calculation of the unperturbed mean-square end-to-end distance of polydeoxyriboadenylic acid (poly dA). The modifications in structure and in charge distribution resulting from the replacement of the hydroxyl group at C_2′ in the ribose residue by hydrogen in deoxyribose produce only minor modifications in the conformational energies associated with the poly dA chain as compared to those found for poly rA. The main difference is manifested in the energy associated with rotations about the C_3′–O_3′ bond of the deoxyribose residue in the C_2′-endo conformation; accessible rotations are confined to the range between 0° and 30° relative to the trans conformation, whereas in the ribose unit the accessible regions comprise two ranges centered at approximately 35° and 85°. The characteristic ratio 〈r²〉0/nl² calculated on the basis of the conformational energy estimates is ≈9 for the poly dA chain with all deoxyribose residues in the C_3′-endo conformation and ≈21 with all residues in the C_2′-endo form. Satisfactory agreement is achieved between the theoretical values and experimental results on apurinic acid by treating the poly dA chain as a random copolymer of C_3′-endo and C_2′-endo conformational isomers present in a ratio of ～1 to 9.     

The influence of H2, CO2 and dilution rate on the continuous fermentation of acetone-butanol

Summary The effect of product gases, H₂ and CO₂, on solvent production was studied using a continuous culture of alginate-immobilized Clostridium acetobutylicum. Initially, in order to find the optimum dilution rate for aceton--butanol production in this system, fermentations were carried out at various dilution rates. With 10% H₂ and 10% CO₂ in the sparging gas, a dilution rate of 0.07 h^–1 was found to maximize volumetric productivity (0.58 g·l^–1·h^–1), while the maximum specific productivity of 0.27 g^–·h^–1 occured at 0.12 h^–1. Continuous cultures with vigorous sparging of N₂ produced only acids. It was concluded that in the case of continuous fermentation H₂ is essential for good solvent production, although good solvent production is possible in an H₂-absent environment in the case of batch fermentations. When the fermentation was carried out at atmospheric pressure under H₂-enriched conditions, the presence of CO₂ in the sparging gas did not slow down glucose metabolism; rather it changed the direction of the phosphoroclastic reaction and as a result increased the butanol/acetone ratio.     

Configuration-dependent properties of randomly coiling polynucleotide chains. I. A comparison of theoretical energy estimates

Various theoretical estimates of the conformational energy associated with polynucleotides in solution have been compared with each other and also with the experimentally observed conformations found in X-ray crystallographic investigations of low-molecular-weight nucleic acid analogs. In view of the disparities between these data, certain configuration-dependent properties (i.e., the mean-square unperturbed end-to-end distance 〈r²〉₀ and the average vicinal nmr coupling constant 〈J〉) appropriate to randomly coiling polynucleotides described by either the energy estimates or by the crystallographically preferred conformations have also been calculated and compared with the known solution behavior of polynucleotide chains. Both the theoretical energy surfaces and the X-ray data show good agreement with the nmr coupling constant indications of the preferred rotations about the O-C and C-C bonds of the chain backbone. The principal discrepancies between the theoretical methods and X-ray data arise in their ability to predict successfully the preferred rotations about the two phosphodiester bonds of the chain backbone and the unperturbed dimensions of randomly coiling polynucleotide chains.     

Statistical mechanical deconvolution of thermal transitions in macromolecules. I. Theory and application to homogeneous systems

The theoretical basis for the statistical mechanical deconvolution of a thermally induced macromolecular melting profile is presented. It is demonstrated that all the thermodynamic quantities characterizing a multistate macromolecular transition can be obtained from the average excess enthalpy function, 〈ΔH〉, of the system, without any assumption of the particular model or mechanism of the reaction. Experimentally, 〈ΔH〉 is obtained from scanning calorimetric data by direct integration of the excess apparent molar heat capacity function, ΦCp. Once 〈ΔH〉 is known as a continuous function of the temperature, the partition function, Q, of the system can be calculated by means of the equation From the partition function all the thermodynamic quantities of the system can be obtained. It is shown that the number of discrete macroscopic energy states, the enthalpy and entropy changes between them, and the relative population of each state as a function of temperature can be calculated in a recursive form.     

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.     

Biohydrogen production from carbon monoxide and water byRhodopseudomonas palustris P4

A reactor-scale hydrogen (H₂) productionvia the water-gas shift reaction of carbon monoxide (CO) and water was studied using the purple nonsulfur bacterium,Rhodopseudomonas palustris P4. The experiment was conducted in a two-step process: an aerobic/chemoheterotrophic cell growth step and a subsequent anaerobic H₂ production step. Important parameters investigated included the agitation speed, inlet CO concentration and gas retention time. P4 showed a stable H₂ production capability with a maximum activity of 41 mmol H₂ g cell⁻¹h⁻¹ during the continuous reactor operation of 400 h. The maximal volumetric H₂ production rate was estimated to be 41 mmol H₂ L¹h⁻¹, which was about nine-fold and fifteen-fold higher than the rates reported for the photosynthetic bacteriaRhodospirillum rubrum andRubrivivax gelatinosus, respectively. This is mainly attributed to the ability of P4 to grow to a high cell density with a high specific H₂ production activity. This study indicates that P4 has an outstanding potential for a continuous H₂ productionvia the water-gas shift reaction once a proper bioreactor system that provides a high rate of gas-liquid mass transfer is developed.     

Actual and potential rates of hydrogen photoproduction by continuous culture of the purple non-sulphur bacterium Rhodobacter capsulatus

The influence of (NH₄)₂SO₄ concentration and dilution rate (D) on actual and potential H₂ photoproduction has been studied in ammonium-limited chemostat cultures of Rhodobacter capsulatus B10. The actual H₂ production in a photobioreactor was maximal (approx. 80 ml h⁻¹l⁻¹) at D = 0.06 h⁻¹ and 4 mM (NH₄)₂SO₄. However, it was lower than the potential H₂ evolution (calculated from hydrogen evolution rates in incubation vials), which amounted to 100–120 ml h⁻¹ l⁻¹ at D = 0.03–0.08 h⁻¹. Taking into account the fact that H₂ production in the photobioreactor under these conditions was not limited by light or lactate, another limiting (inhibiting) factor should be sought. One possibility is an inhibition of H₂ production by the H₂ accumulated in the gas phase. This is apparent from the non-linear kinetics of H₂ evolution in the vials or from its inhibition by the addition of H₂; initial rates were restored in both cases after the vials had been refilled with argon. The actual H₂ production in the photobioreactor at D = 0.06 h⁻¹ was shown to increase from approximately 80 ml h⁻¹ l⁻¹ to approximately 100 ml h⁻¹ l⁻¹ under an argon flow at 100 ml min⁻¹. Under maximal H₂ production rates in the photobioreactor, up to 30% of the lactate feedstock was utilised for H₂ production and 50% for biomass synthesis. Received: 22 April 1997 / Received revision: 14 July 1997 / Accepted: 27 July 1997     

Effect of O(2′)-methylation on the stability of polynucleotide helices

The effect of ribose(O2′)-methylation on the stability of (O2′)-methylated polyribonucleotide helices has been studied by conformational energy calculations. The preferred orientation of the methyl group is found to further stabilize the helical phosphodiester conformation (g^?,g^?) due to the enhanced short-range interactions arising between the methyl groups and the adjacent ribose moieties. The experimentally observed increase in melting temperature of (O2′)-alkylated polyribonucleotides is thus attributable to the enhanced stability of the helical backbone conformation.     

A Monte Carlo study of the excluded-volume effect on the amylosic chain conformation

A Monte Carlo procedure was used to determine the effect of excluded volume on the conformational dimensions of amylosic chains. The excluded volume was introduced into the model by assuming that hard spheres, which cannot overlap each other, exist at the center of mass of each glucose unit in the chain sequence. Monte Carlo chains, which were generated to be distributed consistent with the potential energy of nonbonded nearest-neighbor interactions, underwent self-intersections, and the attrition rate in the generation of self-avoiding chains was found to obey an exponential decay law with increasing chain length x. Thus, in order to generate effectively a large number of self-avoiding chains with long sequences, we used the Wall–Erpenbeck s-p method of chain enrichment [F. T. Wall and J. J. Erpenbeck (1959) J. Chem. Phys. 30 , 634–637]. By examination of the radial distribution of the end-to-end distance and the chain-length dependence of the quantity 〈r²〉/xl² (〈r²〉 is the mean square end-to-end distance and l is the virtual bond length), it was found that unperturbed amylosic chains change in overall conformation from a non-Gaussian chain having a helical character to Gaussian as x is increased, whereas perturbed chains do not show Gaussian behavior even at x = 500. For the perturbed chains, 〈r²〉 can be expressed by the equation 〈r²〉 = ax^b in the range of 100 ≤ x ≤ 500, where a and b > 1 are constants. From comparisons of the persistence vectors and perspective drawings of representative unperturbed and perturbed chains, we felt the local conformation of the amylosic chains, i.e., the local helical character, is also affected by the long-range excluded-volume interaction.