Geometry optimization and conformational analysis of (C60)N clusters using a dynamic lattice-searching method.

A newly developed unbiased global optimization method, named dynamic lattice searching (DLS), is used to locate putative global minima for all (C6O)N clusters with Girifalco potential up to N=150. A simple greedy strategy is adopted for the basic frame, so DLS has a very high convergence speed and may converge at various configurations. As most structures are packed by basic tetrahedra, some sequences are defined by both configurations and the size of the basic tetrahedra. A sequence-based conformational analysis is carried out with the defined sequences by counting the hit number over 10,000 independent DLS runs for all the cases up to N = 5. It was found that the hit rate of a sequence is related to the size of the basic tetrahedra. U.e of this method proved that the Leary tetrahedral sequence is dominant in a certain range of cluster sizes, although the sequence has no potential energy advantage. The calculation results are also consistent with those of annealing experiments at high temperature, both in magic numbers and height of the peaks in the mass spectrum.     

A dynamic lattice searching method for fast optimization of Lennard-Jones clusters

A highly efficient unbiased global optimization method called dynamic lattice searching (DLS) was proposed. The method starts with a randomly generated local minimum, and finds better solution by a circulation of construction and searching of the dynamic lattice (DL) until the better solution approaches the best solution. The DL is constructed adaptively based on the starting local minimum by searching the possible location sites for an added atom, and the DL searching is implemented by iteratively moving the atom located at the occupied lattice site with the highest energy to the vacant lattice site with the lowest energy. Because the DL can greatly reduce the searching space and the number of the time-consuming local minimization procedures, the proposed DLS method runs at a very high efficiency, especially for the clusters of larger size. The performance of the DLS is investigated in the optimization of Lennard-Jones (LJ) clusters up to 309 atoms, and the structure of the LJ(500) is also predicted. Furthermore, the idea of dynamic lattice can be easily adopted in the optimization of other molecular or atomic clusters. It may be a promising approach to be universally used for structural optimizations in the chemistry field.     

Serial replica exchange

Parallel tempering (or the replica exchange method (REM)) is a powerful method for speeding up the sampling of conformational states of systems with rough energy landscapes, like proteins, where stable conformational states can be separated by large energy barriers. The usual implementation of the REM is performed on local computer clusters (or parallel processors) where the different replicas must be run synchronously. Here, we present serial replica exchange (SREM), a method that is equivalent to the standard REM in terms of efficiency yet runs asynchronously on a distributed network of computers. A second advantage is the method's greatly enhanced fault tolerance, which enables the study of biological systems on worldwide distributed computing environments, such as Folding@Home. For proof of concept, we apply the SREM to a single alanine dipeptide molecule in explicit water. We show that the SREM reproduces the thermodynamic and structural properties determined by the REM.     

Structural variation of silver clusters from Ag13 to Ag160

The structures of silver clusters from Ag(121) to Ag(160) were optimized with a modified dynamic lattice searching (DLS) method, named as DLS with constructed core (DLSc). The interaction among silver atoms is modeled by the Gupta potential. Structural characteristic of silver clusters with the growth of cluster size is investigated with the newly optimized structures and our previous results from Ag(13) to Ag(120). A set of amorphous structures was obtained in the size range of 13-48, together with several ordered structures. The putative stable motif is an icosahedron from Ag(49) to Ag(61) and then changes to a decahedron in the size range of 62-160. Some of the results are consistent with experiments. Furthermore, it was also found that, for clusters with decahedral motif, the stable structure is a result of the competition among the different Marks decahedral motifs. On the other hand, different from the Lennard-Jones cluster, there are some silver clusters with the face-centered cubic (fcc) motif in the size range of 13-160. But the fcc motif can only be obtained for some specific sizes.     

A dynamic lattice searching method with constructed core for optimization of large Lennard-Jones clusters

A variation of the previous dynamic lattice searching (DLS) method, named as DLS with constructed core (DLSc), was proposed for structural optimization of Lennard-Jones (LJ) clusters. In the new method, the starting random structure is generated with an icosahedron or a decahedron as a core. For a cluster with n shells, the atoms in the inner n - 2 shells are set as a fixed core, and the remaining atoms in the outer 2 shells are optimized by DLS. With applications of DLSc to optimization of LJ100-200 and LJ660-670, it was found that all the putative global minima can be obtained by using the DLSc method, and the method was proved to be high efficient compared with the previous DLS, because the searching space is reduced by the use of the fixed core. However, although DLSc is still an unbiased approach for smaller LJ clusters, it turned out to be biased for large ones. Further works are still needed to make it to be a more general method for cluster optimization problem.     

Cage and tube structures of medium-sized zinc oxide clusters (ZnO)n (n=24, 28, 36, and 48)

Following our recent work which revealed that the lowest-energy structures of (ZnO)n (n=9-18) follow cage and tube structural growth patterns with stacks of small subunits of (ZnO)2 and (ZnO)3 [Wang et al., J. Phys. Chem. C 111, 4956 (2007)], we have extended the search for the most stable structures to some larger clusters, i.e., (ZnO)n (n=24, 28, 36, and 48) by using gradient-corrected density-functional theory (DFT). A number of starting configurations belonging to different structural motifs were generated from handmade constructions with chemical intuition and then optimized via DFT calculations. Within the size range studied, cage and tube structures were found to be the most preferred structural motifs for the (ZnO)n clusters.     

A dynamic lattice searching method with interior operation for unbiased optimization of large Lennard-Jones clusters

For improving the efficiency of dynamic lattice searching (DLS) method for unbiased optimization of large Lennard-Jones (LJ) clusters, a variant of the interior operation (IO) proposed by Takeuchi was combined with DLS. The method is named as DLS-IO. In the method, the IO moves outer atoms with higher energy toward the coordinates center, i.e., (0, 0, 0), of a cluster and a local minimization (LM) follows each IO. This makes the interior atoms more compact and the outer atoms more uniformly distributed with lower potential energy. Therefore, the starting structure for DLS operations is closer to the global optimum compared with the randomly generated structures. On the other hand, a method to identify the central atom is proposed for the central vacancy problem. Optimizations of LJ(500), LJ(561), LJ(660), LJ(665), and LJ(670) were investigated with the DLS-IO, and the structural transition during the optimization was analyzed. It was found that the method is efficient and unbiased for optimization of large LJ clusters, and it may be a promising approach to be universally used for structural optimizations.     

Efficient evaluation of sampling quality of molecular dynamics simulations by clustering of dihedral torsion angles and Sammon mapping

A direct conformational clustering and mapping approach for peptide conformations based on backbone dihedral angles has been developed and applied to compare conformational sampling of Met-enkephalin using two molecular dynamics (MD) methods. Efficient clustering in dihedrals has been achieved by evaluating all combinations resulting from independent clustering of each dihedral angle distribution, thus resolving all conformational substates. In contrast, Cartesian clustering was unable to accurately distinguish between all substates. Projection of clusters on dihedral principal component (PCA) subspaces did not result in efficient separation of highly populated clusters. However, representation in a nonlinear metric by Sammon mapping was able to separate well the 48 highest populated clusters in just two dimensions. In addition, this approach also allowed us to visualize the transition frequencies between clusters efficiently. Significantly, higher transition frequencies between more distinct conformational substates were found for a recently developed biasing-potential replica exchange MD simulation method allowing faster sampling of possible substates compared to conventional MD simulations. Although the number of theoretically possible clusters grows exponentially with peptide length, in practice, the number of clusters is only limited by the sampling size (typically much smaller), and therefore the method is well suited also for large systems. The approach could be useful to rapidly and accurately evaluate conformational sampling during MD simulations, to compare different sampling strategies and eventually to detect kinetic bottlenecks in folding pathways.     

DNA closed nanostructures: a structural and Monte Carlo simulation study

DNA nanoconstructs are obtained in solution by using six unique 42-mer DNA oligonucleotides, whose sequences have been designed to form a pseudohexagonal structure. The required flexibility is provided by the insertion of two non-base-paired thymines in the middle of each sequence that work as flexible hinges and constitute the corners of the nanostructure when formed. We show that hexagonally shaped nanostructures of about 7 nm diameter and their corresponding linear open constructs are formed by self-assembly of the specifically designed linear oligonucleotides. The structural and dynamical characterization of the nanostructure is obtained in situ for the first time by using dynamic light scattering (DLS), a noninvasive method that provides a fast dynamic and structural analysis and allows the characterization of the different synthetic DNA nanoconstructs in solution. A validation of the LS results is obtained through Monte Carlo (MC) simulations and atomic force microscopy (AFM). In particular, a mesoscale molecular model for DNA, developed by Knotts et al., is exploited to perform MC simulations and to obtain information about the conformations as well as the conformational flexibilities of these nanostructures, while AFM provides a very detailed particle analysis that yields an estimation of the particle size and size distribution. The structural features obtained by MC and AFM are in good agreement with DLS, showing that DLS is a fast and reliable tool for characterization of DNA nanostructures in solution.     

Bismuth-doped tin clusters: experimental and theoretical studies of neutral Zintl analogues

The electron count of gas-phase clusters is increased gradually by element substitution in order to mimic the total number of electrons of known stable closo-clusters. A combination of elements from the fourth and fifth group of the periodic table such as Sn and Bi is well-suited for this approach. Hence, these small Sn-Bi clusters are investigated by employing the electric field deflection method. For clusters in the series Sn(M-N)Bi(N) (M = 5-13, N = 1-2), the beam profiles obtained in cryogenic experiments are dominated by beam broadening, indicating the presence of a permanent electric dipole moment that is sensitive to the (rigid) cluster structure. An intensive search for the global minimum structure employing a density functional theory/genetic algorithm method is performed. Dielectric properties for the identified low-energy isomers are computed. The structural and dielectric properties are used in beam profile simulations in order to discuss the experimental data. Comparison of theoretical and experimental results enables identification of the growing pattern of these small bimetallic clusters. For multiply doped clusters, it is concluded that the dopant atoms do not form direct Bi-Bi bonds, but more interestingly, a rearrangement of the cluster skeleton becomes apparent. The structural motifs are different from pure tin clusters but rather are rationalized using the corresponding structures of tin anions or are based on the Wade-Mingos concept. Further evidence for this idea is deduced from nuclear independent chemical shift calculations, which show nearly identical behavior for negatively charged pure and neutral bimetallic clusters. All of these findings are consistent with the idea of neutral Zintl analogues in the gas phase.     

De novo structural prediction of transition metal complexes: application to technetium

De novo structural prediction of transition metal complexes is investigated. Technetium complexes are chosen given their importance in medical imaging and nuclear waste remediation and for the chemical diversity they display. A new conformational searching algorithm (LIGB) for transition metals is described that allows one to search for different conformational and geometric isomers within a single simulation. In the preponderance of cases, both conformational searching techniques (LIGB and high-temperature molecular dynamics/simulated annealing) provide comparable results, while LIGB is superior for macrocyclic complexes. A genetic algorithm-optimized PM3(tm) parametrization for Tc is compared with the standard implementation and found to yield a significant improvement in predictive ability for the most prevalent Tc structural motifs. The utility of a coupled molecular mechanics-semiempirical quantum mechanics protocol is demonstrated for very rapid, efficient, and effective de novo prediction of transition metal complex geometries.     

Dynamic lattice searching methods for optimization of clusters

Global optimization of clusters is a subject of intense interest in computational chemistry. Especially for large clusters, locating the global minima is a challenging problem. Two strategies are generally used for the problem, i.e., the stochastic optimization and the static modeling strategy. The former is known as unbiased global optimization method, while the latter is more efficient but biased. This review describes the development of a dynamic lattice searching (DLS) approach. In DLS, the lattices are constructed dynamically and optimization is achieved by searching these lattices. Therefore, DLS possesses the characteristics of both the stochastic and static methods. With the aim of improving the efficiency of DLS for optimization of large clusters, several variants of the method have been developed. The results show that DLS methods may be promising tools for fast modeling of large clusters. With this review, greater interests are expected for global optimization of atomic or molecular clusters.     

Activity-aware clustering of high throughput screening data and elucidation of orthogonal structure-activity relationships

From a medicinal chemistry point of view, one of the primary goals of high throughput screening (HTS) hit list assessment is the identification of chemotypes with an informative structure-activity relationship (SAR). Such chemotypes may enable optimization of the primary potency, as well as selectivity and phamacokinetic properties. A common way to prioritize them is molecular clustering of the hits. Typical clustering techniques, however, rely on a general notion of chemical similarity or standard rules of scaffold decomposition and are thus insensitive to molecular features that are enriched in biologically active compounds. This hinders SAR analysis, because compounds sharing the same pharmacophore might not end up in the same cluster and thus are not directly compared to each other by the medicinal chemist. Similarly, common chemotypes that are not related to activity may contaminate clusters, distracting from important chemical motifs. We combined molecular similarity and Bayesian models and introduce (I) a robust, activity-aware clustering approach and (II) a feature mapping method for the elucidation of distinct SAR determinants in polypharmacologic compounds. We evaluated the method on 462 dose-response assays from the Pubchem Bioassay repository. Activity-aware clustering grouped compounds sharing molecular cores that were specific for the target or pathway at hand, rather than grouping inactive scaffolds commonly found in compound series. Many of these core structures we also found in literature that discussed SARs of the respective targets. A numerical comparison of cores allowed for identification of the structural prerequisites for polypharmacology, i.e., distinct bioactive regions within a single compound, and pointed toward selectivity-conferring medchem strategies. The method presented here is generally applicable to any type of activity data and may help bridge the gap between hit list assessment and designing a medchem strategy.     

Structural dynamics of free proteins in diffraction

Among the macromolecular patterns of biological significance, right-handed α-helices are perhaps the most abundant structural motifs. Here, guided by experimental findings, we discuss both ultrafast initial steps and longer-time-scale structural dynamics of helix-coil transitions induced by a range of temperature jumps in large, isolated macromolecular ensembles of an α-helical protein segment thymosin β(9) (Tβ(9)), and elucidate the comprehensive picture of (un)folding. In continuation of an earlier theoretical work from this laboratory that utilized a simplistic structure-scrambling algorithm combined with a variety of self-avoidance thresholds to approximately model helix-coil transitions in Tβ(9), in the present contribution we focus on the actual dynamics of unfolding as obtained from massively distributed ensemble-convergent MD simulations which provide an unprecedented scope of information on the nature of transient macromolecular structures, and with atomic-scale spatiotemporal resolution. In addition to the use of radial distribution functions of ultrafast electron diffraction (UED) simulations in gaining an insight into the elementary steps of conformational interconversions, we also investigate the structural dynamics of the protein via the native (α-helical) hydrogen bonding contact metric which is an intuitive coarse graining approach. Importantly, the decay of α-helical motifs and the (globular) conformational annealing in Tβ(9) occur consecutively or competitively, depending on the magnitude of temperature jump.     

Conformational search using a molecular dynamics–minimization procedure: Applications to clusters of coulombic charges,Lennard–Jones particles,and waters

A new conformational search method, molecular dynamics–minimization (MDM), is proposed, which combines a molecular dynamics sampling strategy with energy minimizations in the search for low-energy molecular structures. This new method is applied to the search for low energy configurations of clusters of coulombic charges on a unit sphere, Lennard–Jones clusters, and water clusters. The MDM method is shown to be efficient in finding the lowest energy configurations of these clusters. A closer comparison of MDM with alternative conformational search methods on Lennard–Jones clusters shows that, although MDM is not as efficient as the Monte Carlo–minimization method in locating the global energy minima, it is more efficient than the diffusion equation method and the method of minimization from randomly generated structures. Given the versatility of the molecular dynamics sampling strategy in comparison to Monte Carlo in treating molecular complexes or molecules in explicit solution, one anticipates that the MDM method could be profitably applied to conformational search problems where the number of degrees of freedom is much greater. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 60–70, 1998     

Search for global-minimum geometries of medium-sized germanium clusters. II. Motif-based low-lying clusters Ge21-Ge29

We performed a constrained search for the geometries of low-lying neutral germanium clusters Ge(N) in the size range of 21 < or = N < or = 29. The basin-hopping global optimization method is employed for the search. The potential-energy surface is computed based on the plane-wave pseudopotential density functional theory. A new series of low-lying clusters is found on the basis of several generic structural motifs identified previously for silicon clusters [S. Yoo and X. C. Zeng, J. Chem. Phys. 124, 054304 (2006)] as well as for smaller-sized germanium clusters [S. Bulusu et al., J. Chem. Phys. 122, 164305 (2005)]. Among the generic motifs examined, we found that two motifs stand out in producing most low-lying clusters, namely, the six/nine motif, a puckered-hexagonal-ring Ge6 unit attached to a tricapped trigonal prism Ge9, and the six/ten motif, a puckered-hexagonal-ring Ge6 unit attached to a bicapped antiprism Ge10. The low-lying clusters obtained are all prolate in shape and their energies are appreciably lower than the near-spherical low-energy clusters. This result is consistent with the ion-mobility measurement in that medium-sized germanium clusters detected are all prolate in shape until the size N approximately 65.     

Self-assembly of organic molecules at metal surfaces

Self-assembly represents a promising strategy for surface functionalisation as well as creating nanostructures with well-controlled, tailor-made properties and functionality. Molecular self-assembly at solid surfaces is governed by the subtle interplay between molecule–molecule and molecule–substrate interactions that can be tuned by varying molecular building blocks, surface chemistry and structure as well as substrate temperature.In this review, basic principles behind molecular self-assembly of organic molecules on metal surfaces will be discussed. Controlling these formation principles allows for creating a wide variety of different molecular surface structures ranging from well-defined clusters, quasi one-dimensional rows to ordered, two-dimensional overlayers. An impressive number of studies exist, demonstrating the ability of molecular self-assembly to create these different structural motifs in a predictable manner by tuning the molecular building blocks as well as the metallic substrate.Here, the multitude of different surface structures of the natural amino acid cysteine on two different gold surfaces observed with scanning tunnelling microscopy will be reviewed. Cysteine on Au(110)-(1×2) represents a model system illustrating the formation of all the above mentioned structural motifs without changing the molecular building blocks or the substrate surface. The only parameters in this system are substrate temperature and molecular coverage, controlling both the molecular adsorption state (physisorption versus chemisorption) and molecular surface mobility. By tuning the adsorption state and the molecular mobility, distinctly different molecular structures are formed, exemplifying the variety of structural motifs that can be achieved by molecular self-assembly.     

Adsorption on montmorillonite prevents oligomerization of Bt Cry1Aa toxin

The adsorption of the insecticidal Cry1Aa protein from Bacillus thuringiensis (Bt-toxin) on a model clay surface was studied to understand the structural changes of the protein induced by the clay surface. We studied the adsorption of the monomeric and soluble oligomeric forms of the Cry1Aa toxin as a function of pH and ionic strength conditions on montmorillonite, which is an electronegative phyllosilicate. Cry1Aa secondary structure was determined from the amide I' FTIR absorption profiles. Accessibility to the solvent was determined by NH/ND exchange to characterize conformational flexibility of the different states of the Cry1Aa protein. The size distribution of Cry1Aa solutions was obtained by dynamic light scattering (DLS). From combined DLS and FTIR measurements, we conclude that montmorillonite traps the Cry1Aa toxin in its monomeric state, preventing the oligomerization of the protein. The oligomeric forms were adsorbed onto the clay without significant structural changes.     

Potential of peptides selected from random phage-displayed libraries to mimic conformational epitopes: a study on scorpion toxin Cn2 and the neutralizing monoclonal antibody BCF2

Many conformational epitopes cannot be mapped by the use of a phage display approach due to the lack of amino acid similarity with the selected peptides. Exploring the potential of the method, we selected mimotopes of the discontinuous, highly conformational epitope of scorpion neurotoxin Cn2, whose 3D structure is known, using its generic neutralizing monoclonal antibody BCF2. With an exhaustive selection procedure, we isolated from a 12-mer phage library a large collection of mimotopes that reproduce the antigenic and immunogenic specificity of the Cn2-epitope. The selected peptides presented three sequence motifs, the most abundant of which, RD(N)XXGF, appeared in 15 different sequence contexts displayed by 97 out of 206 clones. In the most reactive mimotope, displayed by 24 (25%) clones, the motif was flanked by two Cys residues allowing the adoption of a cyclic conformation. Motifs QL(H,M)L(M) and (S/T)WHLP were selected with less efficiency. Comparison of the motifs with the primary and three-dimensional structure of Cn2 as well as with a model of the Cn2-BCF2(Fv) complex suggests that RD(N)XXGF, which does not share sequence similarity with the epitope, mimics its central structural element, turn 7-11, by using an alternative amino acid combination nevertheless keeping the nature of its interactions with BCF2. The QL(H,M)L(M) is assumed to mimic the hydrophobic part of the epitope. The principles of the conformational mimicry by phage-displayed peptides are discussed.