Some approaches to the multiple-minima problem in the calculation of polypeptide and protein structures

Various methods are used to surmount the multiple-minima problem that is encountered in the multidimensional conformational energy surface of a polypeptide. A summary is given here of two of these methods: (i) The build-up procedure that is modified to include statistical data on the positional frequencies of occurrence of amino acid residues along the chain, and (ii) the diffusion equation method that smoothes out the potential surface, leaving only the potential well containing the global minimum.     

An algorithm for packing regular multistrand polypeptide structures by energy minimization

An algorithm has been developed for packing polypeptide chains by energy minimization subject to regularity conditions, in which regularity is maintained without the addition of pseudoenergy terms by defining the energy as a function of appropriately chosen independent variables. The gradient of the energy with respect to the independent variables is calculated analytically. The speed and efficiency of convergence of the algorithm to a local energy minimum are comparable to those of existing algorithms for minimizing the energy of a single polypeptide chain. The algorithm has been used to reinvestigate the minimum-energy regular structures of three-stranded (L -Ala)₈, three-stranded (L -Val)₆, five-stranded (L -Ile)₆, and the regular and truncated three-stranded (Gly-L -Pro-L -Pro)₄ triple helices. Local minima with improved packing energies, but with essentially unchanged geometrical properties, were obtained in all cases. The algorithm was also used to reinvestigate the structures proposed previously for the I and II forms of crystalline silk fibroin. The silk II structure was reproduced with slightly improved packing and little other change. The orthorhombic silk I structure showed more change and considerably improved packing energy, but the new regular monoclinic silk I structure had considerably higher energy. The results support the structure proposed previously for silk II and the orthorhombic structure, but not the monoclinic structure proposed for silk I. © 1994 by John Wiley & Sons, Inc.     

TDI三聚体的合成研究

以一种碱金属羧酸盐K-1000作为甲苯二异氰酸酯(TDI)三聚反应的催化剂合成了以TDI三聚体为主要成分的多异氰酸酯固化剂。对合成工艺条件进行了探讨。结果表明,将反应温度控制在35℃,催化剂K-1000用量为0.06%时,用苯甲酰氯作为阻聚剂可得到性能基本稳定的TDI三聚体产品。     

Statistical mechanical treatment of protein conformation. III. Prediction of protein conformation based on a three-state model.

The method proposed for the evaluation of statistical weights in paper I, and the three-state model [alpha-helical (alpha), extended (epsilon), and other (c) states] formulated in paper II, have been used to develop a procedure to predict the backbone conformations of proteins, based on the concept of the predominant role played by shortrange interactions in determining protein conformation. Conformational probability profiles, in which the probabilities of formation of three consecutive alpha-helical conformations (triad) and of four consecutive extended conformations (tetrad) have been defined relative to their average values over the whole molecule, are calculated for 19 proteins, of which 16 had been used in paper I to evaluate the set of statistical weights of the 20 naturally occurring amino acids. By comparing these conformational probability profiles to experimental x-ray observations, the following results have been obtained: 80% of the alpha-helical regions and 72% of the extended conformational regions have been predicted correctly for the 19 proteins. The percentage of residues predicted correctly is in the range of 53 to 90% for the alpha-helical conformation and in the range of 63 to 88% for the extended conformation for the 19 proteins in the two-state models [alpha-helical (alpha) and other (c) states, and extended (epsilon) and other (c) states]. In the three-state model, the percentage of residues predicted correctly is in the range of 47% to 77 for 19 proteins. These results suggest that the assumption of the dominance of short-range interactions, on which the predictive scheme is based, is a reasonable one. The present predictive method is compared with that of other authors.     

Variable step molecular dynamics: An exploratory technique for peptides with fixed geometry

A new algorithm is presented for performing molecular dynamics simulations of peptides with fixed geometry, with the aim of simulating conformational changes and of exploring conformational space. The principle of the method is to expand the potential energy as a Taylor's series in the coordinates around the current point, retaining the force and its first two derivatives, and obtain a series solution of the resulting differential equations using a method due to Lyapunov. By choosing the time step so that the second term in the series is small compared to the first, the true solution can in principle be approximated to any desired degree of accuracy. The algorithm has been used to solve numerically Lagrange's equations of motion for N-acetyl alanine amide and N-acetyl methionide amide, regarded as fixed at their C-termini, under the influence of the ECEPP/2 potential energy function, and time steps of 15–30 fsec have been achieved with little variation in the total energy. Possible directions for future development are discussed.     

Spatial geometric arrangements of disulfide-crosslinked loops in nonplanar proteins

The method presented earlier [T. Kikuchi, G. Némethy, and H.A. Scheraga, (1986) J. Comput. Chem. 7 , 67] for the classification of patterns of the three-dimensional folding of a covalently crosslinked polypeptide chain has been extended to nonplanar proteins. The procedure described earlier was applicable only to proteins termed planar, i.e., with a connexity of the crosslinks (e.g., disulfide bonds) that can be represented in a planar diagram. The procedure described in the present work is applicable to any (planar or nonplanar) pattern of crosslinking. The classification is based on a systematic and objective method of enumeration of spatial geometric arrangements of loops (SGAL) using no information other than the location of the disulfide bonds in the amino acid sequence. Various SGAL classes correspond to the presence of different ways of mutual penetration of loops, called thrustings and entanglements. Information on SGAL classes can be of use in structural predictions of folding patterns of proteins.     

Revised algorithms for the build-up procedure for predicting protein conformations by energy minimization

The build-up procedure for predicting low-energy conformations of polypeptides has been extended to cover the case of peptides in aqueous solutions. The revised procedure consists of five steps to be applied to each stage of the build-up. I. All low-energy minima of each of the two fragments to be joined are combined as starting points for energy minimization of the enlarged fragment, and those minima of the enlarged fragment within a certain upper bound of the lowest energy are retained. II. Whenever one of the combinations in Step I leads to an atomic overlap, the minimization is started again using a pseudoenergy function which remains finite everywhere and becomes equal to the standard energy function when no atoms overlap. III. The minima generated in Steps I and II are culled by ignoring side-chain conformations and retaining only those minima whose backbone conformations differ significantly. IV. The rotameric states of the side chains are optimized, by testing their energy of interaction with the rest of the molecule, and subjecting the whole molecule to a further round of energy minimization if the test indicates that this would reduce the energy. V. The energies of all minima are recomputed with inclusion of a term for solvation and with a smaller upper bound as the criterion for retention. The original build-up procedure consisted of Steps I and III only. Examples are presented showing the effectiveness of the new Steps II and IV in locating low-energy minima, and the problems that remain to be solved, chiefly concerning Step V, are discussed.     

Acceleration of convergence in Monte Carlo simulations of aqueous solutions using the metropolis algorithm. Hydrophobic hydration of methane

Convergence problems encountered in the computer simulations of aqueous solutions are discussed. Solute–solvent radial distribution functions are shown to converge very poorly when the standard Metropolis Monte Carlo procedure is applied. To overcome this difficulty, several modifications are made in the Metropolis method. Optimum maximum step sizes are determined for simulations of liquid water. A scheme is employed for preferential sampling of both the solvent and the solute molecules. To test these modifications, a simulation is carried out for pure liquid water, treating a single water molecule as a “solute.” The convergence of the radial distribution functions is found to be accelerated significantly. A further test is made by simulating an aqueous solution of methane, consisting of one methane molecule (using the EPEN /2 potential for methane–water interactions) and 124 water molecules (using the MCY potential for water–water interactions). Again, the convergence of solute–solvent radial distribution functions is found to be accelerated. The computation of partial molar thermodynamic quantities, however, still suffers from convergence difficulties. This problem is discussed in detail. The EPEN /2 potential is found to yield structural and thermodynamic features of hydrophobic hydration that are consistent with available experimental and theoretical results for aqueous solutions of methane.     

铝球弹丸高速正撞击薄铝板穿孔研究

 低地球轨道上的航天器易受到微流星体及空间碎片的超高速撞击，导致其严重的损伤甚至灾难性的失效。撞击损伤特性研究是航天器防护设计的一个重要问题。通过铝球弹丸超高速正撞击薄铝板的实验研究和数值模拟，证明了AUTODYN-2D软件数值模拟预测薄铝板超高速撞击穿孔直径的有效性。通过对弹丸直径、弹丸撞击速度和薄铝板厚度影响薄铝板超高速撞击穿孔直径的数值模拟，以及利用实验结果和数值模拟结果拟合的曲线，得到了铝球弹丸超高速撞击薄铝板的穿孔规律以及影响薄铝板超高速撞击穿孔直径的主要因素。