Computer simulation of the conformational properties of retro–inverso peptides. I. Empirical force field calculations of rigid and flexible geometries of N-acetylglycine-N′- methylamide,bis(acetamido) methane,and N,N′- dimethylmalonamide and their corresponding Cα-methylated analogs

Rigid and flexible geometry calculations are described for N-acetylglycine-N′-methylamide, N-acetylalanine-N′-methylamide, and their retro-inverso analogs, bis(acetamido) methane, 1,1-bis(acetamido) ethane, N,N′-dimethylmalonamide, and N,N′-dimethyl-2-methyl-malonamide. The significance of relaxing all degrees of freedom, especially angular flexibility is demonstrated. The flexible geometry approach yields energy maps similar to those from rigid geometry, but the energy barriers between minima are substantially reduced, leading in general, to more probable transitions and a higher volume of accessible conformational space. Whereas the glycine and alanine derivatives exhibit their lowest energy minima in the C region, the gem-diaminoalkyl and malonyl residues show their lowest minima in the “α-helical” regions. With respect to the effect of side chains (H versus CH₃), the greatest conformational influence appears with the gem-diaminoalkyl residues. These results indicate significantly different conformational behavior of retro peptides and the implications of these pairwise incorporations of retro-inverso residues in peptide chains, are discussed.     

Construction of Equi-replicated Balanced Block Designs with Block Sizes Exceeding the Number of Treatments

In this note it is shown that the block design with incidence matrix Ñ = [NN… N], where N = c_1hN_h + c_oh (11′–N_h). c_oh and c_1h are any non-negative integers and N_h,h = 1, 2,…,p, are incidence matrices of balanced incomplete block designs with the same number of treatments t, is a balanced block design with the block sizes exceeding the number of treatments. In derivation the matrix M₀, introduced by CALIński (1971) is utilized.     

Equi-replicated balanced block designs generated by a balanced matrix

In this paper it is shown that if N= \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} c_ihN_ih, where c_ih are some non-negative integer numbers and N_ih are such incidence matrices that A_h = \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} i N_ih is a balanced matrix defined by SHAH (1959), for h = 1, 2,…, p, then a block design with an incidence matrix Ñ = [N, N,…,N] is an equi-replicated balanced block design. Here the balance of a block design is defined in terms of the matrix M₀ introduced by CALI?SKI (1971).     

An Unbalanced Mixed Model with Random Effects Having Unequal Variances

Consider the mixed model where x_ijk's are known constants, β_k are unknown parameters and a_i, e_ij are random variables independently and normally distributed with zero means and variances σd_i and σ² respectively, where it is assumed that the d_i's are known (d_i >0). This paper presents procedures for estimating the variance components σ, σ², for testing the hypothesis σ = 0, and for making transformations to random variables with uncorrelated errors and constant variances in order to estimate as well as to test hypothesis concerning the β_k's in the model.     

Conformation study of poly(γ-methyl-L-glutamate) in helicogenic solvents by small-angle X-ray scattering

Small-angle x-ray scattering of poly(γ-methyl-L -glutamate), [Glu(OMe)]_n, in m-cresol and in pyridine was measured to determine the mass per unit length, M_q, and the radius of gyration of the cross section, 〈S〉^1/2. It was confirmed from the values of M_q that [Glu(OMe)]_n exists in an α-helical conformation in these solvents. It was elucidated from the calculations on 〈S〉^1/2 that the side chains come in moderately close contact with the main chain in these solvents. It was indicated from the analysis of the outer portion of the scattering curves that the side-chain conformation varied depending on the solvent.     

Conformation of poly(L-arginine). I. Effects of anions

The conformational transition of poly(L -agrignine) by binding with various mono-, di-, and polyvalent anions, especially with SO, was studied by CD measurements. The intramolecular random coil-to-α-helix conformational transition and the subsequent transition to the β-turn-like structure was caused by binding with SO. The binding data obtained from equilibrium dialysis experiments showed that the α-helical conformation of poly(L -arginine) is stabilized at a 1:3 stoichiometric ratio of bound SO to arginine residue; at higher free SO concentrations, the α-helix converts to the β-turn-like structure accompanied by a decrease in amount of bound SO. The same conformaitonal transition of poly(L -arginine) also occurred in the solutions of other divalent anions (SO, CO, and HPO) and polyvalent anions (P₂O, P₃O). Among the monovalent anions examined, CIO and dodecyl sulfate were effective in including α-helical conformation, while the other monovalent anions (OH^?, Cl^?, F^?, H₂PO, HCO and CIO) failed to induce poly(L -arginine) to assume the α-helical conformation. Thus, we noticed that, except for dodecyl sufate, the terahedral structure is common to the α-helix-forming anions. A well-defined model to the α-helical poly(L -arginine)/anion complex was proposed, in which both the binding stoichiometry of anions to the arginine residue and the tetrahedral structure of anions were taken into consideration. Based on these results, it was concluded that the tetrahedral-type anions stabilize the α-helical conformation of poly(L -arginine) by crosslinking between two guanidinium groups of nearby side chains on the same α-helix through the ringed structures stabilized by hydrogen bonds as well as by electrostatic interaction. Throughout the study it was noticed that the structural behavior of poly(L -arginine) toward anions is distinct from that of poly(L -lysine).     

Conformation of poly(L-homoarginine)

Poly(L -arginine) assumes the α-helix in the presence of the tetrahedral-type anions or some polyanions by forming the “ringed-structure bridge” between guanidinium groups and anions which is stabilized by a pair of hydrogen bonds and electrostatic interaction [Ichimura, S., Mita, K. & Zama, M. (1978) Biopolymers 17 , 2769–2782; Mita, K., Ichimura, S. & Zama, M. (1978) Biopolymers 17 , 2783–2798]. This paper describes the parallel CD studies on the conformational effects on poly (L -homoarginine) of various mono-, di-, polyvalent anions and some polyanions, as well as alcohol and sodium dodecylsulfate. The random coil to α-helix transition of poly(L -homoarginine) occurred only in NaClO₄ solution or in the presence of high content of ethanol or methanol. The divalent and polyvalent anions of the tetrahedral type (SO, HPO, and P₂O), which are strong α-helix-forming agents for poly(L -arginine), failed to induce the α-helical conformation of poly(L -homoarginine). By complexing with poly(L -glutamic acid) or with polyacrylate, which is also a strong α-helix-forming agent for poly(L -arginine), poly(L -homoarginine) only partially formed the α-helical conformation. Monovalent anions (OH^?, Cl^?, F^?, and H₂PO) did not change poly(L -homoarginine) to the α-helix, and in the range of pH 2–11, the polypeptide remained in an unordered conformation. In sodium dodecylsulfate, poly(L -homoarginine) exhibited the remarkably enlarged CD spectrum of an extended conformation, while poly(L -arginine) forms the α-helix by interacting with the agent. Thus poly(L -homoarginine), compared with poly(L -arginine), has a much lower ability to form the α-helical conformation by interacting with anions. The stronger hydrophobicity of homoarginine residue in comparison with the arginine residue would provide unfavorable conditions to maintain the α-helical conformation.     

Etude experimentale de L′auto-association des molécules modèles dipeptidiques. III. Influence de la dimerisation stéréosélective sur les spectres de résonance magnétique protonique

Proton magnetic resonance spectra of model dipeptide molecules R₁–C′₁O₁–N₂H₂–CHR₂–C′₂O₂–N₃H₃–R₃ in CCl₄ solutions exhibit splited signals when investigating on mixtures of L and D enantiomers differing from the racemic composition. The major effect is observed on amide proton signals which are the ones most sensitive to the ratio of aggregation. The stereoselective dimerization of enantiomeric molecules in the so-called C₅ conformational state is shown to be responsible for such a phenomenon, the intensity of which depends on the bulkiness of the side chain R₂. A theoretical approach is proposed which gives predictions in close agreement with our own experimental findings.     

Crystal structure of Boc-Leu-Aib-Pro-Val-Aib-Aib-Glu(OBzl)-Gln-Phl × H2O,the C-terminal nonapeptide of the voltage-dependent ionophore alamethicin

Boc-L -Leu-Aib-Pro-Val-Aib-Aib-Glu(OBzl)-Gln-Phl (Boc = t-butyloxycarbonyl, Aib = α-aminoisobutyric acid, Bzl = benzyl, Phl = phenylalaninol), C₅₉H₉₀N₁₀O₁₄, the protected C-terminal nonapeptide with the sequence 12–20 of alamethicin, crystallizes in the orthorhombic space group P2₁2₁2₁ with a = 15.666, b = 16.192, c = 26.876 Å, and Z = 4. The molecular conformation is right-handed helical with three α-(5 → 1 hydrogen bonds) and three β-turns (4 → 1 hydrogen bonds). All but two of the hydrogen bonds are significantly longer than the usual value and show bifurcation to some extent. The α/3-helical nonapeptide molecules are arranged head-to-tail along the a direction. The resulting linear antiparallel chains are linked by a weak intermolecular hydrogen bridge, thus forming a two-dimensional layer structure in the ab plane. The conformation of this nonapeptide is almost identical with that of the corresponding C-terminal part found by x-ray crystallography of the eicosapeptide alamethicin.     

Conformational analysis of acetyl-L-phenylalanine p-acetyl and p-valeryl anilides

Empirical force-field calculations and ir and ¹H-nmr spectra indicate that five-membered (C₅) and seven-membered (C) hydrogen-bonded rings are the preferred conformations of acetyl-L -Phe p-acetyl and p-valeryl anilides in nonpolar media. The C₅/C ratio was found to be dependent on the dryness of the solute and the solvent. This fact and the results from conformational-energy calculations suggest that a molecule of water participates in the stabilization of the C conformation.     

On the blue color of triiodide ions in starch and starch fractions. I. Characterization and assignment of absorption and circular dichroism spectra of triiodide ions in amylose

Four fundamental Raman lines were observed at 159, 111, 55 and 27 cm^-1 corresponding to the I bound (I) in amyloses with DP from 20 to 100, regardless of the degree of polymerization of I and the excitation wavelength. The spectral resolution was based on the molar extinction coefficient and molar ellipticity spectra of I. Eight bands, named, S₁, S₂, ?, S₈ from long to short wavelength, were isolated. These were found regardless of the DP. By a resonance excitation Raman study, the characteristics of S₃ and S₄, comprising the shoulder around 480 nm, were found to be different from those of S₁ and S₂, comprising the blue band. The assignment of the spectra was based on the electronic states of the monomeric I in the exciton-coupled dimeric unit. It was concluded that the blue band (S₁,S₂) belonged to the long-axis transitions and the shoulder band (S₃,S₄) to the short-axis ones on the monmeric coordinate system.     

Physical association of two simple alkylators to some DNA sequences

Molecular mechanics calculations have been used to determine the preferred physical association sites of the known alkylating agent dimethyl aziridinium ion (Az⁺) and a CH prototype test probe with B-form, tetrameric DNA sequences. Electrostatic interactions are most important in determining these preferential physical association sites. In turn, the intermolecular energy minima depend on the charge distribution assigned to the DNA sequence. However, for three reported DNA charge distributions, only two distinct sets of energy minima were obtained for the CH-like ion interacting with (G-C)₄, (A-T)₄, and [(G-C)·(A-T)]₂ deoxyribonucleic acids. These minima correspond to physical association geometries in which the CH-like ion is near known alkylation sites. The results of the Az⁺ … [(G-C)·(A-T)]₂ interaction are virtually identical to those found for the CH-like ion. Aqueous solvation energetics have little effect on the physical association of Az⁺ with [(G-C)·(A-T)]₂.     

Apparent molar volumes of some amino acids and peptides in aqueous urea solutions

Densities of solutions of several α-amino acids and peptides in 3 and 6m aqueous urea solvents have been determined at 298.15 K. These data have been used to evaluate the infinite-dilution apparent molar volumes of the solutes and the volume changes due to transfer (V ) of the α-amino acids and peptides at infinite dilution from water to aqueous urea solutions. The sign and magnitude of the V values have been rationalized in the framework of Friedman's cosphere-overlap model. The V values for the glycyl group (? CH₂CONH? ) and alkyl side chains have been estimated.     

Étude expérimentale de l'auto-association des molécules modèles dipeptidiques. II. Association stéréosélective des molécules énantiomères

Modes of aggregation fo alanine-, norvaline- and valine-contaiing dpepetides with the general formula R₁? C₁O₁? N₂H₂? CHR₂? C₂O₂? N₃H₃? R₃ have been studied in CCl₄ solution by using infrared and nuclear magnetic resonance spectroscopies. Solutions of the pure L isomer and of the racemic mixture do not give identical data. At a given concentration, the racemic mixtrue is more aggregated than the pure enantiomer, and the difference, negligible in the case of alanine derivative, increases wiht the bulkiness of the side cahin R₂. The results show that a selective interaction takes place between enantiomeric molecules, resulting ina dimer associating tow inverse configurated C₅ conformers. The stabilizaion of this dimer proceeds from two symmetrical and intermolecular H₃ … O₁ hydrogen bondings.     

Polyiodine units in starch–iodine complex: INDO CI study of spectra and comparison with experiments

The starch–iodine blue complex formation does not involve negatively charged iodine species like I, I, or I; rather, neutral iodine units are involved. The heat of reaction is determined to be about ?110 kJ for every mole of I-I unit in the amylose helix, which suggests that the dissociation of I₂ (binding energy 149 kJ/mol) does not take place during the complex formation. Quantum mechanical (INDO CI) calculations indicate that the linear as well as nonlinear polyiodine units, I₆, with interiodine distance of 3.0 Å are responsible for characteristic absorbance bands of the starch–iodine complex. Based on our previous article [(1989) J. Polym. Sci. A 27 , 4161] and the present studies we identify (C₆H₁₀O₅)_16.5I₆ to be the polymeric unit responsible for the characteristic blue color of the complex.     

Nmr studies on complex formation of poly(L-lysine HBr) with carbonate ion in aqueous solution

Diemer formation of poly(L -lysine HBr) in carbonate buffer at pD 10.5 was reported in our previous paper [Biopolymers(1981) 20 , 345–357]. The mechanism of the dimer formation was investigated employing carbon-13 and proton nmr. pD dependence of the ¹³C-nmr spectrum of poly(L -lysine HBr) in the presence of carbonate ion clearly shows that a complex formation between the CO ion and protonated ε-amino group is involved in the stabilization of the dimer form. The lifetime of the complex is longer than 10^?2 s. A stoichiometric evaluation suggests that CO bridges two lysyl side chains. A molecular model of the dimer form designated as a single antiparallel β-ribbon was proposed and discussed in the light of hydrodynamic and ir spectroscopic properties reported earlier. Concentration change experiments indicate that CO binds not only to the dimer formation is inferred as stabilization of the single antiparallel β-ribbon as an intermediate structure in the conversion between the α-helix and β-sheet. The α-CH proton signal of the lysine residue located in the ordered structure (α-helix and β-form) was observed to be separate from that in the random-coil region.     

Interchain hydrogen bonds via bound water molecules in the collagen triple helix

If the collagen triple helix is so built as to have one set of NH ? O hydrogen bonds of the type N₃H₃(A) ? O₂(B), then it is possible to have a linkage between N₁H₁(B) and O₁(A) through the intermediary of a water molecule with an oxygen O leading to the formation of the hydrogen bonds N₁(B) ? O and O (A). In the same configuration, another water molecule with an oxygen O can link two earbonyl oxygens of chains A and B forming the hydrogen bonds O O₁(A) and O O₀ (B). The two water oxygens also become receptors at the same time for CH ? O hydrogen bonds. Thus, the neighboring chains in the triple helix are held together by secondary valence bond linkages occurring regularly sit intervals of about 3 Å along the length of the protofibril. The additional water molecules occur on the periphery of the proto-fibril and will contribute their full share towards stabilizing the structure in the solid state. In solution, they will be disturbed by the medium unless they are protected by long side groups. It appears that this type of two-bonded structure, in which one NH ? O bond is to a water molecule, can explain several observations on the stability and hydrogen exchange properties of collagen itself and related synthetic polypeptides. The nature of the water bonds and their strength are found to be better in the one-bonded structure proposed from Madras than in the one having the coordinates of Rich and Crick.     

The thermodynamics of solvent exchange

A model for solvation in mixed solvents, which was developed for the free energy and preferential interaction [J. A. Schellman (1987), Biopolymers, Vol. 26, pp. 549–559; (1990), Biophysical Chemistry, Vol. 37, pp. 121–140; (1993), Biophysical Chemistry, Vol. 45, pp. 273–279], is extended in this paper to cover the thermal properties: enthalpy, entropy, and heat capacity. An important result is that the enthalpy of solvation H? responds directly to the fraction of site occupation. This differs from the free energy ? and preferential interaction Γ₃₂, which are measures of the excess binding above a random distribution of solvent molecules. In other words, the enthalpy is governed by K while ? and Γ₃₂ are governed by (K ? 1) where K is the equilibrium constant on a mole fraction scale [Schellman (1987)]. The solvation heat capacity C?p consists of two term: (1) the intrinsic heat capacity of species in solution with no change in composition, and (2) a term that accounts for the change in composition that accompanies solvent exchange. Binding to biological macromolecules is heterogeneous but experiementalists must use binding isotherms that assume the homogeneity of sites. Equations are developed for the interpretation of the experimental parameters (number of sites n_exp, equilibrium constant K_exp, and enthalpy, Δh_exp), when homogeneous formulas are applied to the heterogeneous case. It is shown that the experimental parameters for the occupation and enthalpy are simple functions of the moments of the distribution of equilibrium constants over the sites. In general, n_exp is greater than the true number of sites and K_exp is greater than the average of the equilibrium constants. The free energy and preferential interaction can be fit to a homogenious formula, but the parameters of the curve are not easily represented in terms of the moments of distributions over the sites. The strengths and deficiencies of this type of thermodynamic model are discussed. © 1994 John Wiley & Sons, Inc.     

How Large is the Probability for the Estimate of a Variance Component to be Negative?

For a balanced one-way classification, where the normally distributed observations obey a random model y_ij=μ+b_i+c_ij with two variance components var (b_i) = δ and var (c_ij) = δ, the probability is given that the analysis of variance estimate of δ will be negative. This probability depends on δ/δ and the degrees of freedom in the ANOVA table. Tables for this probability are given. If the normally distributed observations obey an intra-class correlation model, the probability that the Mean Square between groups is smaller than the Mean Square within groups can also be evaluated from the given tables.     

Evaluating four mathematical models for nitrous oxide production by autotrophic ammonia‐oxidizing bacteria

There is increasing evidence showing that ammonia‐oxidizing bacteria (AOB) are major contributors to N₂O emissions from wastewater treatment plants (WWTPs). Although the fundamental metabolic pathways for N₂O production by AOB are now coming to light, the mechanisms responsible for N₂O production by AOB in WWTP are not fully understood. Mathematical modeling provides a means for testing hypotheses related to mechanisms and triggers for N₂O emissions in WWTP, and can then also become a tool to support the development of mitigation strategies. This study examined the ability of four mathematical model structures to describe two distinct mechanisms of N₂O production by AOB. The production mechanisms evaluated are (1) N₂O as the final product of nitrifier denitrification with NO as the terminal electron acceptor and (2) N₂O as a byproduct of incomplete oxidation of hydroxylamine (NH₂OH) to NO. The four models were compared based on their ability to predict N₂O dynamics observed in three mixed culture studies. Short‐term batch experimental data were employed to examine model assumptions related to the effects of (1) NH concentration variations, (2) dissolved oxygen (DO) variations, (3) NO accumulations and (4) NH₂OH as an externally provided substrate. The modeling results demonstrate that all these models can generally describe the NH, NO, and NO data. However, none of these models were able to reproduce all measured N₂O data. The results suggest that both the denitrification and NH₂OH pathways may be involved in N₂O production and could be kinetically linked by a competition for intracellular reducing equivalents. A unified model capturing both mechanisms and their potential interactions needs to be developed with consideration of physiological complexity. Biotechnol. Bioeng. 2013; 110: 153–163. © 2012 Wiley Periodicals, Inc.