A comparison of neighbor search algorithms for large rigid molecules

Fast determination of neighboring atoms is an essential step in molecular dynamics simulations or Monte Carlo computations, and there exists a variety of algorithms to efficiently compute neighbor lists. However, most of these algorithms are general, and not specifically designed for a given type of application. As a result, although their average performance is satisfactory, they might be inappropriate in some specific application domains. In this article, we study the case of detecting neighbors between large rigid molecules, which has applications in, e.g., rigid body molecular docking, Monte Carlo simulations of molecular self-assembly or diffusion, and rigid body molecular dynamics simulations. More precisely, we compare the traditional grid-based algorithm to a series of hierarchy-based algorithms that use bounding volumes to rapidly eliminate large groups of irrelevant pairs of atoms during the neighbor search. We compare the performance of these algorithms based on several parameters: the size of the molecules, the average distance between them, the cutoff distance, as well as the type of bounding volume used in the culling hierarchy (AABB, OBB, wrapped, or layered spheres). We demonstrate that for relatively large systems (> 100,000 atoms) the algorithm based on the hierarchy of wrapped spheres shows the best results and the traditional grid-based algorithm gives the worst timings. For small systems, however, the grid-based algorithm and the one based on the wrapped sphere hierarchy are beneficial.     

GeneMCL in microarray analysis

Accurately and reliably identifying the actual number of clusters present with a dataset of gene expression profiles, when no additional information on cluster structure is available, is a problem addressed by few algorithms. GeneMCL transforms microarray analysis data into a graph consisting of nodes connected by edges, where the nodes represent genes, and the edges represent the similarity in expression of those genes, as given by a proximity measurement. This measurement is taken to be the Pearson correlation coefficient combined with a local non-linear rescaling step. The resulting graph is input to the Markov Cluster (MCL) algorithm, which is an elegant, deterministic, non-specific and scalable method, which models stochastic flow through the graph. The algorithm is inherently affected by any cluster structure present, and rapidly decomposes a graph into cohesive clusters. The potential of the GeneMCL algorithm is demonstrated with a 5,730 gene subset (IGS) of the Van't Veer breast cancer database, for which the clusterings are shown to reflect underlying biological mechanisms.     

A Central Partition of Molecular Conformational Space. III. Combinatorial Determination of the Volume Spanned by a Molecular System

In the first work of this series (Gabarro-Arpa, Comp. Biol. Chem. 27 (2003) 153–159) it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the space into a hierarchical set of cells that can be encoded by the face lattice poset of the arrangement. The model however, lacked explicit rotational symmetry, which made impossible to distinguish rotated structures in conformational space. This problem was solved in a second work (Gabarro-Arpa, Proc. 26th Ann. Int. Conf. of the IEEE EMBS (San Franciso, 2004) 3007–3010) by sorting the elementary 3-dimensional components of the molecular system into a set of morphological classes that can be properly oriented in a standard 3-D reference frame. This also made possible to find a solution to the problem that is being addressed in the present work: for a molecular system immersed in a heat bath we want to enumerate the subset of cells in conformational space that are visited by the molecule in its thermal wandering. If each visited cell is a vertex on a graph with edges to the adjacent cells, here it is explained how such graph can be built.     

Practical modeling of molecular systems with symmetries

A new method for efficient modeling of macromolecular systems with symmetries is presented. The method is based on a hierarchical representation of the molecular system and a novel fast binary tree‐based neighbor list construction algorithm. The method supports all types of molecular symmetry, including crystallographic symmetry. Testing the proposed neighbor list construction algorithm on a number of different macromolecular systems containing up to about 200,000 of atoms shows that (1) the current binary tree‐based neighbor list construction algorithm scales linearly in the number of atoms for the central subunit, and sublinearly for its replicas, (2) the overall computational overhead of the method for a system with symmetry with respect to the same system without symmetry scales linearly with the cutoff value and does not exceed 50% for all but one tested macromolecules at the cutoff distance of 12 Å. (3) the method may help produce optimized molecular structures that are much closer to experimentally determined structures when compared with the optimization without symmetry, (4) the method can be applied to models of macromolecules with still unknown detailed structure. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Maximum symmetrical split of molecular graphs. Application to organic synthesis design

Whereas the potential symmetry of a molecule may be a feature of importance in synthesis design, this one is often difficult to detect visually in the structural formula. In the present article, we describe an efficient algorithm for the perception of this molecular property. We have addressed this problem in terms of graph theory and defined it as the Maximum Symmetrical Split of a molecular graph. A solution is obtained by deleting in such a graph a minimum number of edges and vertices so that the resulting subgraph consists of exactly two isomorphic connected components that correspond to a pair of synthetically equivalent synthons. In view to reduce the search space of the problem, we have based our algorithm on CSP techniques. In this study, we have found that the maximum symmetrical split is an original kind of Constraint Satisfaction Problem. The algorithm has been implemented into the RESYN_Assistant system, and its performance has been tested on a set of varied molecules which were the targets of previously published synthetic studies. The results show that potential symmetry is perceived quickly and efficiently by the program. The graphical display of this perception information may help a chemist to design reflexive or highly convergent syntheses.     

An algorithm for three-dimensional Voronoi S-network

The paper presents an algorithm for calculating the three-dimensional Voronoi-Delaunay tessellation for an ensemble of spheres of different radii (additively-weighted Voronoi diagram). Data structure and output of the algorithm is oriented toward the exploration of the voids between the spheres. The main geometric construct that we develop is the Voronoi S-network (the network of vertices and edges of the Voronoi regions determined in relation to the surfaces of the spheres). General scheme of the algorithm and the key points of its realization are discussed. The principle of the algorithm is that for each determined site of the network we find its neighbor sites. Thus, starting from a known site of the network, we sequentially find the whole network. The starting site of the network is easily determined based on certain considerations. Geometric properties of ensembles of spheres of different radii are discussed, the conditions of applicability and limitations of the algorithm are indicated. The algorithm is capable of working with a wide variety of physical models, which may be represented as sets of spheres, including computer models of complex molecular systems. Emphasis was placed on the issue of increasing the efficiency of algorithm to work with large models (tens of thousands of atoms). It was demonstrated that the experimental CPU time increases linearly with the number of atoms in the system, O(n).     

Novel Indices for the Topological Complexity of Molecules

Abstract

The development of molecular complexity measures is reviewed. Two novel sets of indices termed topological complexities are introduced proceeding from the idea that topological complexity increases with the overall connectivity of the molecular graph. The latter is assessed as the connectivity of all connected subgraphs in the molecular graph, including the graph itself. First-order, second-order, third-order, etc., topological complexities ⁱ TC are defined as the sum of the vertex degrees in the connected subgraphs with one, two, three, etc., edges, respectively. Zero-order complexity is also specified for the simplest subgraphs–the graph vertices. The overall topological complexity TC is then defined as the sum of the complexities of all orders. These new indices mirror the increase in complexity with the increase in the number of atoms and, at a constant number of atoms, with the increase in molecular branching and cyclicity. Topological complexities compare favorably to molecular connectivities of Kier and Hall, as demonstrated in detail for the classical QSPR test-the boiling points of alkanes. Related to the wide application of molecular connectivities to QSAR studies, a similar importance of the new indices is anticipated.     

Modular multi-level circuits from immobilized DNA-based logic gates

One of the fundamental goals of molecular computing is to reproduce the tenets of digital logic, such as component modularity and hierarchical circuit design. An important step toward this goal is the creation of molecular logic gates that can be rationally wired into multi-level circuits. Here we report the design and functional characterization of a complete set of modular DNA-based Boolean logic gates (AND, OR, and AND-NOT) and further demonstrate their wiring into a three-level circuit that exhibits Boolean XOR (exclusive OR) function. The approach is based on solid-supported DNA logic gates that are designed to operate with single-stranded DNA inputs and outputs. Since the solution-phase serves as the communication medium between gates, circuit wiring can be achieved by designating the DNA output of one gate as the input to another. Solid-supported logic gates provide enhanced gate modularity versus solution-phase systems by significantly simplifying the task of choosing appropriate DNA input and output sequences used in the construction of multi-level circuits. The molecular logic gates and circuits reported here were characterized by coupling DNA outputs to a single-input REPORT gate and monitoring the resulting fluorescent output signals.     

Self-assembly of irregular graphs whose edges are DNA helix axes

A variety of computational models have been introduced recently that are based on the properties of DNA. In particular, branched junction molecules and graphlike DNA structures have been proposed as computational devices, although such models have yet to be confirmed experimentally. DNA branched junction molecules have been used previously to form graph-like three-dimensional DNA structures, such as a cube and a truncated octahedron, but these DNA constructs represent regular graphs, where the connectivities of all of the vertexes are the same. Here, we demonstrate the construction of an irregular DNA graph structure by a single step of self-assembly. A graph made of five vertexes and eight edges was chosen for this experiment. DNA branched junction molecules represent the vertexes, and duplex molecules represent the edges; in contrast to previous work, specific edge molecules are included as components. We demonstrate that the product is a closed cyclic single-stranded molecule that corresponds to a double cover of the graph and that the DNA double helix axes represent the designed graph. The correct assembly of the target molecule has been demonstrated unambiguously by restriction analysis.     

Molecular and Crystal Magnetic Engineering of Polymetallic Coupling System: From Magnetic Molecules to Molecular Magnets

One of the main challenges in the field of molecular materials is the design of molecular ferromagnets. General design strategy includes two steps, that is molecular magnetic engineering and crystal magnetic engineering. The first step is the synthesis of ferromagnetically coupled polymetallic systems. The second step is the assembly of polymetallic systems with muti‐dimensional structure and exhibiting a ferromagnetic transition. This paper summarized the strategies of molecular design and crystal engineering allowed to obtain such systems and our efforts in the fields of molecular magnetism and molecular‐based magnets.     

Boolean logic functions of a synthetic peptide network

Living cells can process rapidly and simultaneously multiple extracellular input signals through the complex networks of evolutionary selected biomolecular interactions and chemical transformations. Recent approaches to molecular computation have increasingly sought to mimic or exploit various aspects of biology. A number of studies have adapted nucleic acids and proteins to the design of molecular logic gates and computational systems, while other works have affected computation in living cells via biochemical pathway engineering. Here we report that de novo designed synthetic peptide networks can also mimic some of the basic logic functions of the more complex biological networks. We show that segments of a small network whose graph structure is composed of five nodes and 15 directed edges can express OR, NOR, and NOTIF logic.     

Understanding the Unusual Adsorption Behavior in Hierarchical Zeolite Nanosheets

Hierarchical zeolites are advanced materials possessing the catalytic and adsorption properties of conventional zeolites while eliminating their transport limitations through the introduction of mesopores. Recent experiments comparing the adsorption in hierarchical self‐pillared pentasils (SPP) and silicalite‐1 (MFI) revealed an interesting crossover in sorbate loading for branched or long‐chain alkanes but not for shorter linear alkanes, but an explanation for this behavior is not readily available through experimental probes due to the complications arising from the presence of multiple adsorption sites. Here we present a molecular simulation study on the adsorption of alkane isomers and show that a multi‐step mechanism, found here for all molecules, is responsible for the observed phenomena.     

Improving protein identification from peptide mass fingerprinting through a parameterized multi-level scoring algorithm and an optimized peak detection

We have developed a new algorithm to identify proteins by means of peptide mass fingerprinting. Starting from the matrix-assisted laser desorption/ionization-time-of-flight (MALDI-TOF) spectra and environmental data such as species, isoelectric point and molecular weight, as well as chemical modifications or number of missed cleavages of a protein, the program performs a fully automated identification of the protein. The first step is a peak detection algorithm, which allows precise and fast determination of peptide masses, even if the peaks are of low intensity or they overlap. In the second step the masses and environmental data are used by the identification algorithm to search in protein sequence databases (SWISS-PROT and/or TrEMBL) for protein entries that match the input data. Consequently, a list of candidate proteins is selected from the database, and a score calculation provides a ranking according to the quality of the match. To define the most discriminating scoring calculation we analyzed the respective role of each parameter in two directions. The first one is based on filtering and exploratory effects, while the second direction focuses on the levels where the parameters intervene in the identification process. Thus, according to our analysis, all input parameters contribute to the score, however with different weights. Since it is difficult to estimate the weights in advance, they have been computed with a generic algorithm, using a training set of 91 protein spectra with their environmental data. We tested the resulting scoring calculation on a test set of ten proteins and compared the identification results with those of other peptide mass fingerprinting programs.     

Quest for molecular graphs with maximal energy: a computer experiment

If lambda(1), lambda(2),..., lambda(n) are the eigenvalues of a graph G, then the energy of G is defined as E(G) = the absolute value of lambda(1) + the absolute value of lambda(2) +.... + the absolute value of lambda(n). If G is a molecular graph, representing a conjugated hydrocarbon, then E(G) is closely related to the respective total pi-electron energy. It is not known which molecular graph with n vertices has maximal energy. With the exception of m = n - 1 and m = n, it is not known which molecular graph with n vertices and m edges has maximal energy. To come closer to the solution of this problem, and continuing an earlier study (J. Chem. Inf. Comput. Sci. 1999, 39, 984-996, ref 7), we performed a Monte Carlo-type construction of molecular (n,m)-graphs, recording those with the largest (not necessarily maximal possible) energy. The results of our search indicate that for even n the maximal-energy molecular graphs might be those possessing as many as possible six-membered cycles; for odd n such graphs seem to prefer both six- and five-membered cycles.     

Bounds on Harary index

In this paper, we obtain the lower and upper bounds on the Harary index of a connected graph (molecular graph), and, in particular, of a triangle- and quadrangle-free graphs in terms of the number of vertices, the number of edges and the diameter. We give the Nordhaus–Gaddum-type result for Harary index using the diameters of the graph and its complement. Moreover, we compare Harary index and reciprocal complementary Wiener number for graphs.     

Separation of Amyl Alcohol Isomers in ZIF‐77

The separation of pentanol isomer mixtures is shown to be very efficient using the nanoporous adsorbent zeolitic imidazolate framework ZIF‐77. Through molecular simulations, we demonstrate that this material achieves a complete separation of linear from monobranched—and these from dibranched—isomers. Remarkably, the adsorption and diffusion behaviors follow the same decreasing trend, produced by the channel size of ZIF‐77 and the guest shape. This separation based on molecular branching applies to alkanes and alcohols and promises to encompass numerous other functional groups.     

MATCH: an atom-typing toolset for molecular mechanics force fields

We introduce a toolset of program libraries collectively titled multipurpose atom-typer for CHARMM (MATCH) for the automated assignment of atom types and force field parameters for molecular mechanics simulation of organic molecules. The toolset includes utilities for the conversion of multiple chemical structure file formats into a molecular graph. A general chemical pattern-matching engine using this graph has been implemented whereby assignment of molecular mechanics atom types, charges, and force field parameters are achieved by comparison against a customizable list of chemical fragments. While initially designed to complement the CHARMM simulation package and force fields by generating the necessary input topology and atom-type data files, MATCH can be expanded to any force field and program, and has core functionality that makes it extendable to other applications such as fragment-based property prediction. In this work, we demonstrate the accurate construction of atomic parameters of molecules within each force field included in CHARMM36 through exhaustive cross validation studies illustrating that bond charge increment rules derived from one force field can be transferred to another. In addition, using leave-one-out substitution it is shown that it is also possible to substitute missing intra and intermolecular parameters with ones included in a force field to complete the parameterization of novel molecules. Finally, to demonstrate the robustness of MATCH and the coverage of chemical space offered by the recent CHARMM general force field (Vanommeslaeghe, et al., J Comput Chem 2010, 31, 671), one million molecules from the PubChem database of small molecules are typed, parameterized, and minimized.     

Multiparticle moves in acceptance rate optimized monte carlo

Molecular Dynamics (MD) and Monte Carlo (MC) based simulation methods are widely used to investigate molecular and nanoscale structures and processes. While the investigation of systems in MD simulations is limited by very small time steps, MC methods are often stifled by low acceptance rates for moves that significantly perturb the system. In many Metropolis MC methods with hard potentials, the acceptance rate drops exponentially with the number of uncorrelated, simultaneously proposed moves. In this work, we discuss a multiparticle Acceptance Rate Optimized Monte Carlo approach (AROMoCa) to construct collective moves with near unit acceptance probability, while preserving detailed balance even for large step sizes. After an illustration of the protocol, we demonstrate that AROMoCa significantly accelerates MC simulations in four model systems in comparison to standard MC methods. AROMoCa can be applied to all MC simulations where a gradient of the potential is available and can help to significantly speed up molecular simulations. © 2015 Wiley Periodicals, Inc.     

On Wiener‐type polynomials of thorn graphs

We derive the expressions of the ordinary, the vertex‐weighted and the doubly vertex‐weighted Wiener polynomials of a type of thorn graph, for which the number of pendant edges attached to any vertex of the underlying parent graph is a linear function of its degree. We also define variable vertex‐weighted Wiener polynomials and calculate them for the same type of thorn graphs. Copyright © 2009 John Wiley & Sons, Ltd.