Conformational analysis of [Met5]-enkephalin: Solvation and ionization considerations

[Met5]-Enkephalin has the sequence Tyr-Gly-Gly-Phe-Met. Only the extended conformation of the peptide has been observed by X-ray crystallography. Nuclear magnetic resonance spectroscopy supports the presence of a turn at Gly 3 and Phe 4 in dimethyl sulfoxide. In this study, the peptide conformational states and thermodynamic properties are understood in terms of ionization state and solvent environment. In the calculation, final conformations obtained from multiple independent Monte Carlo simulated annealing conformational searches are starting points for molecular dynamics simulations. In an aqueous environment given by the use of solvation free energy and the zwitterionic state, dominant structural motifs computed are G-P Type II bend, G-G Type II bend, and G-G Type I bend motifs, in order of increasing free energy. In the calculation of the peptide with neutral N- and C-termini and solvation free energy, the extended conformer dominates (by at least a factor of 2.5), and the conformation of another low free energy conformer superimposes well on the pharmacophoric groups of morphine. Neutralization of charge and solvation induce and stabilize the extended conformation, respectively. A mechanism of inter-conversion between the extended conformer and three bent conformers is supported by /-scatter plots, and by the conformer relative free energies. An estimate of the entropy change of receptor unbinding is 8.3 cal K-1 mol-1, which gives rise to a -2.5 kcal/mol entropy contribution to the free energy of unbinding at 25 °C. The conformational analysis methodology described here should be useful in studies on short peptides and flexible protein surface loops that have important biological implications.     

Observations of trends for singular values and eigenvectors from library searching ultraviolet-visible spectra with spectral subtraction

A promising procedure for computerized library searching and identification of ultraviolet-visible spectra for one- and two-component mixtures is evaluated. The procedure is based on singular value decomposition and utilizes band position and shape. Searching more than one library spectrum at a time is possible. Library spectra which have similar spectra (collinear) with the sample and each other are indicated by two measures. First, a large condition index must be obtained, and second, two or more large variance-decomposition proportions in the same row need to be associated with the large condition index. The searching procedure has a significant degree of differentiation between the actual sample and potential candidates and is compared with the dot product, Euclidean distance and the correlation coefficient.     

A proposal for the molecular basis of μ and δ opiate receptor differentiation based on modeling of two types of cyclic enkephalins and a narcotic alkaloid

Summary The molecular basis underlying the divergent receptor selectivity of two cyclic opioid peptides Tyr-c[N -d-Orn²-Gly-Phe-Leu-] (c-ORN) and [d-Pen², l-Cys⁵]-enkephalinamide (c-PEN) was investigated using a molecular modeling approach. Ring closure and conformational searching procedures were used to determine low-energy cyclic backbone conformers. Following reinsertion of amino acid side chains, the narcotic alkaloid 7-[(1R)-1-methyl-1-hydroxy-3-phenylpropyl]-6,14-endoethenotetrahydro oripavine (PEO) was used as a flexible template for bimolecular superpositions with each of the determined peptide ring conformers using the coplanarity and cocentricity of the phenolic rings as the minimum constraint. A vector space of PEO, accounting for all possible orientations for the C₂₁-aromatic ring of PEO served as a geometrical locus for the aromatic ring of the Phe⁴ residue in the opioid peptides. Although a vast number of polypeptide conformations satisfied the criteria of the opiate pharmacophore, they could be grouped into three classes differing in magnitude and sign of the torsional angle values of the tyrosyl side chain. Only class III conformers for both c-ORN and c-PEN, having tyramine dihedral angles ₁ =–150° ± 30° and ₂=–155° ± 20°, had significant structural and conformational properties that were mutually compatible while respecting the PEO vector space. Comparison of these properties in the context of the divergent receptor selectivity of the studied opioid peptides suggests that the increased distortion of the peptide backbone in the closure region of c-PEN together with the pendant ,-dimethyl group, combine to generate a steric volume which is absent in c-ORN and that may be incompatible with a restrictive topography of the receptor. The nature and stereo-chemistry of substituents adjacent to the closure region of the peptides could also modulate receptor selection by interacting with a charged () or neutral () subsite.     

On the convergence of the LJ search method

The convergence of the Luus-Jaakola search method for unconstrained optimization problems is established.Notation E _n Euclideann-space - f Gradient off(x) - ² f Hessian matrix - (·) ^T Transpose of (·) - I Index set {1, 2, ...,n} - [x _i1 ^*(j) ] Point around which search is made in the (j + 1)th iteration, i.e., [x _1l ^*(j) ,x _2l ^*(j) ,...,x _n1 ^*(j) ] - r _i ⁽ⁱ⁾ Range ofx _il ^*(i) in the (j + 1)th iteration - l ₁ min_i {r _i ⁽⁰⁾ } - l ₂ min_i {r _i ⁽⁰⁾ } - A _j Region of search in thejth iteration, i.e., {x E _n:x _il ^*(j-1) –0.5r _i ^(j-1) x _ix _il ^*(j-1) +0.5r _i ^(j-1) ,i I} - S _j Closed sphere with center origin and radius _j - Reduction factor in each iteration - 1– - (·) Gamma function Many discussions with Dr. S. N. Iyer, Professor of Electrical Engineering, College of Engineering, Trivandrum, India, are gratefully acknowledged. The author has great pleasure to thank Dr. K. Surendran, Professor, Department of Electrical Engineering, P.S.G. College of Technology, Coimbatore, India, for suggesting this work.     

Properties of the random search in global optimization

From theorems which we prove about the behavior of gaps in a set ofN uniformly random points on the interval [0, 1], we determine properties of the random search procedure in one-dimensional global optimization. In particular, we show that the uniform grid search is better than the random search when the optimum is chosen using the deterministic strategy, that a significant proportion of large gaps are contained in the uniformly random search, and that the error in the determination of the point at which the optimum occurs, assuming that it is unique, will on the average be twice as large using the uniformly random search compared with the uniform grid. In addition, some of the properties of the largest gap are verified numerically, and some extensions to higher dimensions are discussed. The latter show that not all of the conclusions derived concerning the inadequacies of the one-dimensional random search extend to higher dimensions, and thaton average the random search is better than the uniform grid for dimensions greater than 6.This paper is based on work started in the Statistics Department of Princeton University when the first author was visiting as a Research Associate. Part of this research was supported by the Office of Naval Research, Contract No. 0014-67-A-0151-0017, and by the US Army Research Office—Durham, Contract No. DA-31-124-ARO-D-215.2 The authors wish to thank B. Omodei for his careful work in preparing the programs for the results of Figs. 1–2 and Table 1. The computations were performed on the IBM 360/50 of the Australian National University's Computer Centre. Thanks are also due to R. Miles for suggestions regarding the extension of the results to multidimensional regions, and to P. A. P. Moran and R. Brent for suggestions regarding the evaluation of the integral ₀ ¹ ... ^0/1 (x ₁ ² + ... +x _n ^/2 )^1/2 dx ₁ ...dx _n.     

On the nonlinear stochastic realization problem

In this paper we construct a first solution of the stochastic realization problem in a nonlinear setting. The great bulk of previous work on stochastic realization has been in the linear Gaussian setting. Such Markovian representations are used e.g., to apply certain filtering and stochastic control techniques. Our methods consist of an amalgamation of methods introduced by Nelson with the Lax-Phillips type geometric approach to linear Gaussian stochastic realization which has been developed by Lindquist and Picci and by Ruckebusch. The result of this that we are able to realize any purely nondeterministic process satisfying suitable continuity conditions as an instantaneous function of a Markov process.     

北海航道班轮运输排班模型的构建与求解

首先,以拟开通的大连港至鹿特丹港北海航道班轮航线为研究对象,以油耗和运营成本最小化为优化目标,将官方已有记载的北海航道通过的货船航速数据输入Eureqa软件,得到航行最高速度f(x)与进入北海航道时间t的拟合度最好的函数公式.在此基础上,构建了北海航道班轮运输排班的数学模型;其次,在仿真实例分析中,选用了5000TEU的集装箱船作为计算参数,将捕食搜索算法运用到数学模型求解之中,并且运用MATLAB软件进行求解,在最快航速受限的前提下,得到单艘班轮最佳往返时间和相同型号班轮的最低配置数目以及在服务周期内班轮公司所要付出的最低运营成本;最后,通过比较研究,得出结论是:最快航速的提高,对于降低北海航线班轮运输的运营成本将起较大作用.     

The maximum number of columns in supersaturated designs with

Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle .