利用粒子群算法在菱形网格上预测蛋白质结构

本文在菱形网格上研究讨论了二维HP模型。首先,将蛋白质结构预测问题转化成一个数学问题,并简化成氨基酸序列中每个氨基酸与网格格点的匹配问题。为了解决这个数学问题,我们改进并扩展了经典的粒子群算法。为了验证算法和模型的有效性,我们对一些典型的算例进行数值模拟。通过与方格网上得到的蛋白质构象进行比较,菱形网上的蛋白质构象更自然,更接近真实。我们进一步比较了菱形网格上的紧致构象和非紧致构象。结果显示我们的模型和算法在菱形网格上预测氨基酸序列的蛋白质结构是有效的有意义的。     

How are model protein structures distributed in sequence space?

The figure-to-structure maps for all uniquely folding sequences of short hydrophobic polar (HP) model proteins on a square lattice is analyzed to investigate aspects considered relevant to evolution. By ranking structures by their frequencies, few very frequent and many rare structures are found. The distribution can be empirically described by a generalized Zipf's law. All structures are relatively compact, yet the most compact ones are rare. Most sequences falling to the same structure belong to "neutral nets." These graphs in sequence space are connected by point mutations and centered around prototype sequences, which tolerate the largest number (up to 55%) of neutral mutations. Profiles have been derived from these homologous sequences. Frequent structures conserve hydrophobic cores only while rare ones are sensitive to surface mutations as well. Shape space covering, i.e., the ability to transform any structure into most others with few point mutations, is very unlikely. It is concluded that many characteristic features of the sequence-to-structure map of real proteins, such as the dominance of few folds, can be explained by the simple HP model. In analogy to protein families, nets are dense and well separated in sequence space. Potential implications in better understanding the evolution of proteins and applications to improving database searches are discussed.     

Analysis on folding of misgurin using two-dimensional HP model

Misgurin is an antimicrobial peptide from the loach, while the hydrophobic-polar (HP) model is a way to study the folding conformations and native states in peptide and protein although several amino acids cannot be classified either hydrophobic or polar. Practically, the HP model requires extremely intensive computations, thus it has yet to be used widely. In this study, we use the two-dimensional HP model to analyze all possible folding conformations and native states of misgurin with conversion of natural amino acids according to the normalized amino acid hydrophobicity index as well as the shortest benchmark HP sequence. The results show that the conversion of misgurin into HP sequence with glycine as hydrophobic amino acid at pH 2 has 1212 folding conformations with the same native state of minimal energy -6; the conversion of glycine as polar amino acid at pH 2 has 13,386 folding conformations with three native states of minimal energy -5; the conversion of glycine as hydrophobic amino acid at pH 7 has 2538 folding conformations with three native states of minimal energy -5; and the conversion of glycine as polar amino acid at pH 7 has 12,852 folding conformations with three native states of minimal energy -4. Those native states can be ranked according to the normalized amino acid hydrophobicity index. The detailed discussions suggest two ways to modify misgurin.     

Enhanced hybrid search algorithm for protein structure prediction using the 3D-HP lattice model

The problem of protein structure prediction in the hydrophobic-polar (HP) lattice model is the prediction of protein tertiary structure. This problem is usually referred to as the protein folding problem. This paper presents a method for the application of an enhanced hybrid search algorithm to the problem of protein folding prediction, using the three dimensional (3D) HP lattice model. The enhanced hybrid search algorithm is a combination of the particle swarm optimizer (PSO) and tabu search (TS) algorithms. Since the PSO algorithm entraps local minimum in later evolution extremely easily, we combined PSO with the TS algorithm, which has properties of global optimization. Since the technologies of crossover and mutation are applied many times to PSO and TS algorithms, so enhanced hybrid search algorithm is called the MCMPSO-TS (multiple crossover and mutation PSO-TS) algorithm. Experimental results show that the MCMPSO-TS algorithm can find the best solutions so far for the listed benchmarks, which will help comparison with any future paper approach. Moreover, real protein sequences and Fibonacci sequences are verified in the 3D HP lattice model for the first time. Compared with the previous evolutionary algorithms, the new hybrid search algorithm is novel, and can be used effectively to predict 3D protein folding structure. With continuous development and changes in amino acids sequences, the new algorithm will also make a contribution to the study of new protein sequences.     

Designability of protein structures: a lattice-model study using the Miyazawa-Jernigan matrix

We study the designability of all compact 3 x 3 x 3 and 6 x 6 lattice-protein structures using the Miyazawa-Jernigan (MJ) matrix. The designability of a structure is the number of sequences that design the structure, i.e., sequences that have that structure as their unique lowest-energy state. Previous studies of hydrophobic-polar (HP) models showed a wide distribution of structure designabilities. Recently, questions were raised concerning the use of a two-letter (HP) code in such studies. Here, we calculate designabilities using all 20 amino acids, with empirically determined interaction potentials (MJ matrix) and compare with HP model results. We find good qualitative agreement between the two models. In particular, highly designable structures in the HP model are also highly designable in the MJ model-and vice versa-with the associated sequences having enhanced thermodynamic stability.     

Minimum energy configurations of the 2-dimensional HP-model of proteins by self-organizing networks.

We use self-organizing maps (SOM) as an efficient tool to find the minimum energy configurations of the 2-dimensional HP-models of proteins. The usage of the SOM for the protein folding problem is similar to that for the Traveling Salesman Problem. The lattice nodes represent the cities whereas the neurons in the network represent the amino acids moving towards the closest cities, subject to the HH interactions. The valid path that maximizes the HH contacts corresponds to the minimum energy configuration of the protein. We report promising results for the cases when the protein completely fills a lattice and discuss the current problems and possible extensions. In all the test sequences up to 36 amino acids, the algorithm was able to find the global minimum and its degeneracies.     

Reading the three-dimensional structure of lattice model-designed proteins from their amino acid sequence.

While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the detailed, biological active, three-dimensional structure of a protein whose sequence is known. Using insight obtained from lattice model simulations of the folding of small proteins (fewer than 100 residues), in particular of the fact that this phenomenon is essentially controlled by conserved contacts (Mirny et al., Proc Natl Acad Sci USA 1995;92:1282) among (few) strongly interacting ("hot") amino acids (Tiana et al., J Chem Phys 1998;108:757-761), which also stabilize local elementary structures formed early in the folding process and leading to the (postcritical) folding core when they assemble together (Broglia et al., Proc Natl Acad Sci USA 1998;95:12930, Broglia & Tiana, J Chem Phys 2001;114:7267), we have worked out a successful strategy for reading the three-dimensional structure of lattice model-designed proteins from the knowledge of only their amino acid sequence and of the contact energies among the amino acids.     

Amino acid sequence of Paracoccus denitrificans cytochrome c550.

The amino acid sequence of Paracoccus (formerly Micrococcus) denitrificans cytochrome c550 has been established by a combination of standard chemical techniques and interpretation of a 2.5 A resolution x-ray electron density map. Peptides derived from a trypsin digest were chemically sequenced, and then ordered by fitting them to the density map. The amino acid compositions of chymotryptic peptides confirmed the x-ray map ordering the tryptic peptides. The amino acid sequence of this respiratory, prokaryotic cytochrome with 134 residues is discussed in relation to those of eukaryotic respiratory cytochrome c (103 to 113 amino acids), and prokaryotic, photosynthetic c2 (103 to 124 amino acids). At the primary structure level, c and c550 differ no more from cytochromes c2 than the various cytochromes c2 do from one another. It is suggested that the respiratory electron transport chain in prokaryotes and eukaryotes is a relatively late evolutionary offshoot of the photosynthetic electron transport chain in purple non-sulfur bacteria.     

Heterochromatin protein 1, a known suppressor of position-effect variegation, is highly conserved in Drosophila.

The Su(var)205 gene of Drosophila melanogaster encodes heterochromatin protein 1 (HP1), a protein located preferentially within beta-heterochromatin. Mutation of this gene has been associated with dominant suppression of position-effect variegation. We have cloned and sequenced the gene encoding HP1 from Drosophila virilis, a distantly related species. Comparison of the predicted amino acid sequence with Drosophila melanogaster HP1 shows two regions of strong homology, one near the N-terminus (57/61 amino acids identical) and the other near the C-terminus (62/68 amino acids identical) of the protein. Little homology is seen in the 5' and 3' untranslated portions of the gene, as well as in the intronic sequences, although intron/exon boundaries are generally conserved. A comparison of the deduced amino acid sequences of HP1-like proteins from other species shows that the cores of the N-terminal and C-terminal domains have been conserved from insects to mammals. The high degree of conservation suggests that these N- and C-terminal domains could interact with other macromolecules in the formation of the condensed structure of heterochromatin.     

Prediction of the location of structural domains in globular proteins

The location of structural domains in proteins is predicted from the amino acid sequence, based on the analysis of a computed contact map for the protein, the average distance map (ADM). Interactions between residues i and j in a protein are subdivided into several ranges, according to the separation |i-j| in the amino acid sequence. Within each range, average spatial distances between every pair of amino acid residues are computed from a data base of known protein structures. Infrequently occurring pairs are omitted as being statistically insignificant. The average distances are used to construct a predicted ADM. The ADM is analyzed for the occurrence of regions with high densities of contacts (compact regions). Locations of rapid changes of density between various parts of the map are determined by the use of scanning plots of contact densities. These locations serve to pinpoint the distribution of compact regions. This distribution, in turn, is used to predict boundaries of domains in the protein. The technique provides an objective method for the location of domains both on a contact map derived from a known three-dimensional protein structure, the real distance map (RDM), and on an ADM. While most other published methods for the identification of domains locate them in the known three-dimensional structure of a protein, the technique presented here also permits the prediction of domains in proteins of unknown spatial structure, as the construction of the ADM for a given protein requires knowledge of only its amino acid sequence.     

A SOM projection technique with the growing structure for visualizing high-dimensional data

The Self-Organizing Map (SOM) is an efficient tool for visualizing high-dimensional data. In this paper, an intuitive and effective SOM projection method is proposed for mapping high-dimensional data onto the two-dimensional grid structure with a growing self-organizing mechanism. In the learning phase, a growing SOM is trained and the growing cell structure is used as the baseline framework. In the ordination phase, the new projection method is used to map the input vector so that the input data is mapped to the structure of the SOM without having to plot the weight values, resulting in easy visualization of the data. The projection method is demonstrated on four different data sets, including a 118 patent data set and a 399 checical abstract data set related to polymer cements, with promising results and a significantly reduced network size.     

Manifold learning for robot navigation

In this paper we introduce methods to build a SOM that can be used as an isometric map for mobile robots. That is, given a dataset of sensor readings collected at points uniformly distributed with respect to the ground, we wish to build a SOM whose neurons (prototype vectors in sensor space) correspond to points uniformly distributed on the ground. Manifold learning techniques have already been used for dimensionality reduction of sensor space in navigation systems. Our focus is on the isometric property of the SOM. For reliable path-planning and information sharing between several robots, it is desirable that the robots build an internal representation of the sensor manifold, a map, that is isometric with the environment. We show experimentally that standard Non-Linear Dimensionality Reduction (NLDR) algorithms do not provide isometric maps for range data and bearing data. However, the auxiliary low dimensional manifolds created can be used to improve the distribution of the neurons of a SOM (that is, make the neurons more evenly distributed with respect to the ground). We also describe a method to create an isometric map from a sensor readings collected along a polygonal line random walk.     

Interaction of heterochromatin protein 2 with HP1 defines a novel HP1-binding domain

Heterochromatin Protein 2 (HP2) is a nonhistone chromosomal protein from Drosophila melanogaster localized principally in the pericentric heterochromatin, telomeres, and fourth chromosome, all regions associated with HP1. Mutations in HP2 can suppress position effect variegation, indicating a role in gene silencing and heterochromatin formation [Shaffer, C. D. et al. (2002) Proc. Natl. Acad. Sci.U.S.A. 99, 14332-14337]. In vitro coimmunoprecipitation experiments with various peptides from HP2 have identified a single HP1-binding domain. Conserved domains in HP2, including those within the HP1-binding region, have been identified by recovering and sequencing Su(var)2-HP2 from D. willistoni and D. virilis, as well as examining available sequence data from D. pseudoobscura. A PxVxL motif, shown to be an HP1-binding domain in many HP1-interacting proteins, is observed but is not well-conserved in location and sequence and does not mediate HP2 binding to HP1. The sole HP1-binding domain is composed of two conserved regions of 12 and 16 amino acids separated by 19 amino acids. Site-directed mutagenesis within the two conserved regions has shown that the 16 amino acid domain is critical for HP1 binding. This constitutes a novel domain for HP1 interaction, providing a critical link for heterochromatin formation in Drosophila.     

Protein map: an alignment-free sequence comparison method based on various properties of amino acids

In this paper, we propose a new protein map which incorporates with various properties of amino acids. As a powerful tool for protein classification, this new protein map both considers phylogenetic factors arising from amino acid mutations and provides computational efficiency for the huge amount of data. The ten amino acid physico-chemical properties (the chemical composition of the side chain, two polarity measures, hydropathy, isoelectric point, volume, aromaticity, aliphaticity, hydrogenation, and hydroxythiolation) are utilized according to their relative importance. Moreover, during the course of calculation of genetic distances between pairs of proteins, this approach does not require any alignment of sequences. Therefore, the proposed model is easier and quicker in handling protein sequences than multiple alignment methods, and gives protein classification greater evolutionary significance at the amino acid sequence level.     

A high-order graph generating self-organizing structure

A large class of neural network models have their units organized in a lattice with fixed topology or generate their topology during the learning process. These network models can be used as neighborhood preserving map of the input manifold, but such a structure is difficult to manage since these maps are graphs with a number of nodes that is just one or two orders of magnitude less than the number of input points (i.e., the complexity of the map is comparable with the complexity of the manifold) and some hierarchical algorithms were proposed in order to obtain a high-level abstraction of these structures. In this paper a general structure capable to extract high order information from the graph generated by a large class of self-organizing networks is presented. This algorithm will allow to build a two layers hierarchical structure starting from the results obtained by using the suitable neural network for the distribution of the input data. Moreover the proposed algorithm is also capable to build a topology preserving map if it is trained using a graph that is also a topology preserving map.     

Structure of Streptomyces erythraeus lysozyme at 6 A resolution

A 6 A resolution electron density map has been calculated for a bacterial lysozyme produced by Streptomyces erythraeus. This lysozyme differs from the vertebrate lysozyme in its size, amino acid composition, and specificity. The structure was determined by the method of isomorphous replacement. Three heavy atom derivatives were obtained by soaking crystals of the lysozyme in HgCl2, K2PtCl4, and UO2(NO3)26H2O. The resulting electron density map clearly shows the molecular boundary. The molecule is ellipsoidal in shape with average dimensions 50 A X 35 A X 35 A. High resolution analysis and sequence analysis of the molecule are in progress.     

Prediction of probable pathways of folding in globular proteins

A method is described for the prediction of probable folding pathways of globular proteins, based on the analysis of distance maps. It is applicable to proteins of unknown spatial structure but known amino acid sequence as well as to proteins of known structure. It is based on an objective procedure for the determination of the boundary of compact regions that contain high densities of interresidue contacts on the distance map of a globular protein. The procedure can be used both with contact maps derived from a known three-dimensional protein structure and with predicted contact maps computed by means of a statistical procedure from the amino acid sequence alone. The computed contact map can also be used to predict the location of compact short-range structures, viz. -helices and -turns, thereby complementing other statistical predictive procedures. The method provides an objective basis for the derivation of a theoretically predicted pathway of protein folding, proposed by us earlier [Tanaka and Scheraga (1977) Macromolecules10, 291–304; Némethy and Scheraga (1979) Proc. Natl. Acad. Sci., U.S.A.76, 6050–6054].