Adsorption of polypeptides on solid surfaces. I. Effect of chain stiffness

The general method of obtaining the partition function and thermodynamic characteristics of polymer chains near an adsorbing surface, simulated by random walks on a lattice, is developed. The method takes into account the effect of short-range interactions in polymer chains, in particular, the chain stiffness and secondary structure. The theory of adsorption of chains of different stiffness is developed, and the process of adsorption which occurs when the external conditions change is shown to be always a second-order phase transition. The critical adsorption energy decreases and the sharpness of transition grows when the chain stiffness increases. A simple model of a chain with “virtual” steps is proposed which simplifies the treatment; the results obtained are in good agreement with exact theories. A general scheme of analysis of adsorption of chains with a given secondary structure is set forth and the analogy between the stiffness of a noncooperative chain and the presence of helical segments in a polypeptide chain is discussed.     

The structure of adsorbed cyclic chains

In order to determine the structure of polymer films formed of cyclic chains (rings) we developed and studied a simple coarse-grained model. Our main goal was to check how the percolation and jamming thresholds in such a system were related to the thresholds obtained for linear flexible chains system, i.e., how the geometry of objects influenced both thresholds. All atomic details were suppressed and polymers were represented as a sequence of identical beads and the chains were embedded to a square lattice (a strictly 2D model). The system was athermal and the excluded volume was the only potential introduced. A random sequential adsorption algorithm was chosen to determine the properties of a polymer monolayer. It was shown that the percolation threshold of cyclic chains was considerably higher than those of linear flexible chains while the jamming thresholds for both chain architectures are very similar. The shape of adsorbed cyclic chains was found to be more prolate when compared to average single chain.     

Contact interactions method: a new algorithm for protein folding simulations.

Computer simulations of simple exact lattice models are an aid in the study of protein folding process; they have sometimes resulted in predictions experimentally proved. The contact interactions (CI) method is here proposed as a new algorithm for the conformational search in the low-energy regions of protein chains modeled as copolymers of hydrophobic and polar monomers configured as self-avoiding walks on square or cubic lattices. It may be regarded as an extension of the standard Monte Carlo method improved by the concept of cooperativity deriving from nonlocal contact interactions. A major difference with respect to other algorithms is that criteria for the acceptance of new conformations generated during the simulations are not based on the energy of the entire molecule, but cooling factors associated with each residue define regions of the model protein with higher or lower mobility. Nine sequences of length ranging from 20 to 64 residues were used on the square lattice and 15 sequences of length ranging from 46 to 136 residues were used on the cubic lattice. The CI algorithm proved very efficient both in two and three dimensions, and allowed us to localize energy minima not localized by other searching algorithms described in the literature. Use of this algorithm is not limited to the conformational search, because it allows the exploration of thermodynamic and kinetic behavior of model protein chains.     

A procedure for the automatic determination of hydrophobic cores in protein structures.

An algorithm is described for automatically detecting hydrophobic cores in proteins of known structure. Three pieces of information are considered in order to achieve this goal. These are: secondary structure, side-chain accessibility, and side-chain-side-chain contacts. Residues are considered to contribute to a core when they occur in regular secondary structure and have buried side chains that form predominantly nonpolar contacts with one another. This paper describes the algorithm's application to families of proteins with conserved topologies but low sequence similarities. The aim of this investigation is to determine the efficacy of the algorithm as well as to study the extent to which similar cores are identified within a common topology.     

Construction of Resolvable Designs with Nested Treatment Structure

The construction of resolvable incomplete block and row-column designs is investigated when the treatments have a nested structure. Some theoretical results are derived for lattice designs. Efficient designs for unequal-sized treatment groups are obtained by defining a multiple objective function and carrying out a computer search using an interchange algorithm.     

Improved genetic algorithm for the protein folding problem by use of a Cartesian combination operator.

We have devised a Cartesian combination operator and coding scheme for improving the performance of genetic algorithms applied to the protein folding problem. The genetic coding consists of the C alpha Cartesian coordinates of the protein chain. The recombination of the genes of the parents is accomplished by: (1) a rigid superposition of one parent chain on the other, to make the relation of Cartesian coordinates meaningful, then, (2) the chains of the children are formed through a linear combination of the coordinates of their parents. The children produced with this Cartesian combination operator scheme have similar topology and retain the long-range contacts of their parents. The new scheme is significantly more efficient than the standard genetic algorithm methods for locating low-energy conformations of proteins. The considerable superiority of genetic algorithms over Monte Carlo optimization methods is also demonstrated. We have also devised a new dynamic programming lattice fitting procedure for use with the Cartesian combination operator method. The procedure finds excellent fits of real-space chains to the lattice while satisfying bond-length, bond-angle, and overlap constraints.     

Plausible molecular and crystal structures of chitosan/HI type II salt

Chitosan/HI type II salt prepared from crab tendon was investigated by X-ray fiber diffraction. Two polymer chains and 16 iodide ions (I(-)) crystallized in a tetragonal unit cell with lattice parameters of a = b = 10.68(3), c (fiber axis) = 40.77(13) A, and a space group P4(1). Chitosan forms a fourfold helix with a 40.77 A fiber period having a disaccharide as the helical asymmetric unit. One of the O-3... O-5 intramolecular hydrogen bonds at the glycosidic linkage is weakened by interacting with iodide ions, which seems to cause the polymer to take the 4/1-helical symmetry rather than the extended 2/1-helix. The plausible orientations of two O-6 atoms in the helical asymmetric unit were found to be gt and gg. Two chains are running through at the corner and the center of the unit cell along the c-axis. They are linked by hydrogen bonds between N-21 and O-61 atoms. Two out of four independent iodide ions are packed between the corner chains while the other two are packed between the corner and center chains when viewing through the ab-plane. The crystal structure of the salt is stabilized by hydrogen bonds between these iodide ions and N-21, N-22, O-32, O-61, O-62 of the polymer chains.     

The structure of percolated polymer systems: a computer simulation study

We studied the percolation process in a system consisting of long flexible polymer chains and solvent molecules. The polymer chains were approximated by linear sequences of beads on a two-dimensional triangular lattice. The system was athermal and the excluded volume was the only potential. The properties of the model system across the entire range of polymer concentrations were determined by Monte Carlo simulations employing a cooperative motion algorithm (CMA). The scaling behavior and the structure of the percolation clusters are presented and discussed.     

Study of PE and iPP orientations on the surface of carbon nanotubes by using molecular dynamic simulations

In this study, the early stage of interfacial crystallisation behaviour of low molecular weight polyethylene (PE) and isotactic polypropylene (iPP) oligomer on the surface of carbon nanotubes (CNTs) with different diameters, chiralities and topography structures was studied using MD simulations. We started to simulate the effect of CNTs chirality and diameter on PE molecular chain orientation, and then the effect of CNTs topography structure on PE and iPP molecular chain orientation was investigated. Finally, some experiments were carried out to prove the simulated results. Our study shows that for CNTs with a diameter comparable with the radius of gyration (R_g) of a polymer chain, an easy orientation of PE chains along CNTs axis is observed for all the systems of the CNTs with different chiralities due to a geometric confinement effect. For CNTs with a much larger diameter, multiple orientation of PE chains is induced on its surface due to the lattice matching between graphite lattice and PE molecular chains. In this case, the chirality of CNTs dominates the orientation of graphite lattice, which determines the orientation of PE chains arrangement on CNTs surface. More importantly, it was found that the groove structure formed by CNT bundles is very useful for the stabilisation of polymer chain, and thus facilitates the orientation of molecular chain along the long axis of CNTs. As a result, a novel nanohybrid shish–kebab (NHSK) structure with CNTs acting as central shish while polymer lamellae as kebab can be successfully obtained for both PE with zigzag conformation and iPP with helical conformation. This simulation result was well supported by the experimental observation. Our study could provide not only a deep understanding of the origin of the polymer chain orientation on CNTs surface but also the guidance for the preparation of polymer/CNTs nanocomposites with novel NHSK structure.     

Monte carlo study of the percolation in two-dimensional polymer systems

The structure of a two-dimensional film formed by adsorbed polymer chains was studied by means of Monte Carlo simulations. The polymer chains were represented by linear sequences of lattice beads and positions of these beads were restricted to vertices of a two-dimensional square lattice. Two different Monte Carlo methods were employed to determine the properties of the model system. The first was the random sequential adsorption (RSA) and the second one was based on Monte Carlo simulations with a Verdier-Stockmayer sampling algorithm. The methodology concerning the determination of the percolation thresholds for an infinite chain system was discussed. The influence of the chain length on both thresholds was presented and discussed. It was shown that the RSA method gave considerably lower thresholds for longer chains. This behavior can be explained by a different pool of chain conformations used in the calculations in both methods under consideration.

IRECS: a new algorithm for the selection of most probable ensembles of side-chain conformations in protein models

We introduce a new algorithm, IRECS (Iterative REduction of Conformational Space), for identifying ensembles of most probable side-chain conformations for homology modeling. On the basis of a given rotamer library, IRECS ranks all side-chain rotamers of a protein according to the probability with which each side chain adopts the respective rotamer conformation. This ranking enables the user to select small rotamer sets that are most likely to contain a near-native rotamer for each side chain. IRECS can therefore act as a fast heuristic alternative to the Dead-End-Elimination algorithm (DEE). In contrast to DEE, IRECS allows for the selection of rotamer subsets of arbitrary size, thus being able to define structure ensembles for a protein. We show that the selection of more than one rotamer per side chain is generally meaningful, since the selected rotamers represent the conformational space of flexible side chains. A knowledge-based statistical potential ROTA was constructed for the IRECS algorithm. The potential was optimized to discriminate between side-chain conformations of native and rotameric decoys of protein structures. By restricting the number of rotamers per side chain to one, IRECS can optimize side chains for a single conformation model. The average accuracy of IRECS for the chi1 and chi1+2 dihedral angles amounts to 84.7% and 71.6%, respectively, using a 40 degrees cutoff. When we compared IRECS with SCWRL and SCAP, the performance of IRECS was comparable to that of both methods. IRECS and the ROTA potential are available for download from the URL http://irecs.bioinf.mpi-inf.mpg.de.     

On lattice protein structure prediction revisited

Protein structure prediction is regarded as a highly challenging problem both for the biology and for the computational communities. In recent years, many approaches have been developed, moving to increasingly complex lattice models and off-lattice models. This paper presents a Large Neighborhood Search (LNS) to find the native state for the Hydrophobic-Polar (HP) model on the Face-Centered Cubic (FCC) lattice or, in other words, a self-avoiding walk on the FCC lattice having a maximum number of H-H contacts. The algorithm starts with a tabu-search algorithm, whose solution is then improved by a combination of constraint programming and LNS. The flexible framework of this hybrid algorithm allows an adaptation to the Miyazawa-Jernigan contact potential, in place of the HP model, thus suggesting its potential for tertiary structure prediction. Benchmarking statistics are given for our method against the hydrophobic core threading program HPstruct, an exact method which can be viewed as complementary to our method.     

Algorithmic generation of freely jointed hard sphere chains and properties of their inertial tensors

A statistical algorithm, capable of generating a large number of freely jointed hard sphere chains, is presented. This is the first of a series of algorithms being developed to model unfolded proteins by different modes of hard sphere chains. The aim of these studies is to systematically investigate the effects of different factors, such as atomic radii, bond angles, torsion angles, chain length, etc., on the conformation of unfolded proteins and other random polymers. As continuous models, various types of hard sphere chains enable one to isolate the aforementioned factors one at a time for investigation and thus are advantageous over discrete lattice models. In particular, the freely jointed hard sphere chain model allows one to evaluate the excluded volume effect. As a first step in this endeavor, the average determinant D(N, r) and the average trace T(N, r) of the inertial tensor A of the random chains were calculated at various sphere radii r and chain lengths N. It is found that both the average determinant D(N, r) and the average trace T(N, r) scale linearly with chain length N after logarithmic transformation. However, the critical exponent of D(N, r) increases with r faster than that of T(N, r) as a result of the non-commutativity between the det operator and the average operator < >. The significance of the algorithm and the results obtained on understanding random polypeptide chains are discussed.     

Fast and simple Monte Carlo algorithm for side chain optimization in proteins: application to model building by homology.

An unknown protein structure can be predicted with fair accuracy once an evolutionary connection at the sequence level has been made to a protein of known 3-D structure. In model building by homology, one typically starts with a backbone framework, rebuilds new loop regions, and replaces nonconserved side chains. Here, we use an extremely efficient Monte Carlo algorithm in rotamer space with simulated annealing and simple potential energy functions to optimize the packing of side chains on given backbone models. Optimized models are generated within minutes on a workstation, with reasonable accuracy (average of 81% side chain chi 1 dihedral angles correct in the cores of proteins determined at better than 2.5 A resolution). As expected, the quality of the models decreases with decreasing accuracy of backbone coordinates. If the back-bone was taken from a homologous rather than the same protein, about 70% side chain chi 1 angles were modeled correctly in the core in a case of strong homology and about 60% in a case of medium homology. The algorithm can be used in automated, fast, and reproducible model building by homology.     

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。     

Protein folding. Effect of packing density on chain conformation

Recent lattice polymer simulations by Chan & Dill suggest that compactness may be a significant driving force in the formation of secondary structure. We have addressed the robustness of this conclusion for non-lattice polymers using a rotational isomeric model of proteins. Boundary conditions are used to enforce compactness and excluded volume effects are explicitly incorporated. As in the cubic lattice studies, compactness is seen to influence secondary structure content. This effect is modest for densities comparable to native proteins but dramatic for chains that are approximately 30% more dense than native proteins. alpha-Helical structure is common but beta-sheet structure is rare. It appears that lattices impart to compact chains an organizational bias that favors beta-sheet structure. The strengths and weakness of various simplified representations of polypeptide chains are also discussed.     

Predicting the structures of 18 peptides using Geocore

We describe an extensive test of Geocore, an ab initio peptide folding algorithm. We studied 18 short molecules for which there are structures in the Protein Data Bank; chains are up to 31 monomers long. Except for the very shortest peptides, an extremely simple energy function is sufficient to discriminate the true native state from more than 10(8) lowest energy conformations that are searched explicitly for each peptide. A high incidence of native-like structures is found within the best few hundred conformations generated by Geocore for each amino acid sequence. Predictions improve when the number of discrete phi/psi choices is increased.     

Modelling Studies of Crystalline PEEK

Abstract

The x-ray diffraction spectrum of the engineering thermoplastic poly (aryl-ether-ether-ketone), commonly known as PEEK, has been reported in the literature. The unit cell dimensions are consistent with two aryl units per unit cell, while the chemical repeat has three, suggesting that there is not a strict lateral register between chains. The polymer chain packing of crystalline PEEK has been investigated using lattice energy calculations and it is concluded that lateral chain ordering effects are rather unimportant in determining the crystal structure. The crystallographic equivalence of ether and ketone linkages arises due to essentially random chain stacking.