Conformational sampling by self-organization

A new stochastic algorithm for conformational sampling is described. The algorithm generates molecular conformations that are consistent with a set of geometric constraints, which include interatomic distance bounds and chiral volumes derived from the molecular connectivity table. The algorithm repeatedly selects individual geometric constraints at random and updates the respective atomic coordinates toward satisfying the chosen constraint. When compared to a conventional distance geometry algorithm based on the same set of geometric constraints, our method is faster and generates conformations that are more diverse and more energetically favorable.     

General Distribution Function for Periods of Downtime of a Single System Exceeding a Limiting Downtime

A reparable two-state system whose components upon failure are replaced is considered. The time to failure and the time to repair of the components are a pair of renewal processes. The distribution of the random variable D(τ, t), which is defined as the random sum of those repair times of the system in the interval of time (0, t) that are greater than or equal to a constant time τ, is derived.     

Ultrafast algorithm for designing focused combinational arrays

A novel greedy algorithm for the design of focused combinatorial arrays is presented. The method is applicable when the objective function is decomposable to individual molecular contributions and makes use of a heuristic that allows the independent evaluation and ranking of candidate reagents in each variation site in the combinatorial library. The algorithm is extremely fast and convergent and produces solutions that are comparable to and often better than those derived from the substantially more elaborate and computationally intensive stochastic sampling techniques. Typical examples of design objectives that are amendable to this approach include maximum similarity to a known lead (or set of leads), maximum predicted activity according to some structure-activity or receptor binding model, containment within certain molecular property bounds, and many others.     

A constant time algorithm for estimating the diversity of large chemical libraries

We describe a novel diversity metric for use in the design of combinatorial chemistry and high-throughput screening experiments. The method estimates the cumulative probability distribution of intermolecular dissimilarities in the collection of interest and then measures the deviation of that distribution from the respective distribution of a uniform sample using the Kolmogorov-Smirnov statistic. The distinct advantage of this approach is that the cumulative distribution can be easily estimated using probability sampling and does not require exhaustive enumeration of all pairwise distances in the data set. The function is intuitive, very fast to compute, does not depend on the size of the collection, and can be used to perform diversity estimates on both global and local scale. More importantly, it allows meaningful comparison of data sets of different cardinality and is not affected by the curse of dimensionality, which plagues many other diversity indices. The advantages of this approach are demonstrated using examples from the combinatorial chemistry literature.     

Variable selection for QSAR by artificial ant colony systems

Derivation of quantitative structure-activity relationships (QSAR) usually involves computational models that relate a set of input variables describing the structural properties of the molecules for which the activity has been measured to the output variable representing activity. Many of the input variables may be correlated, and it is therefore often desirable to select an optimal subset of the input variables that results in the most predictive model. In this paper we describe an optimization technique for variable selection based on artificial ant colony systems. The algorithm is inspired by the behavior of real ants, which are able to find the shortest path between a food source and their nest using deposits of pheromone as a communication agent. The underlying basic self-organizing principle is exploited for the construction of parsimonious QSAR models based on neural networks for several classical QSAR data sets.     

On the Stochastic Theory of Compartments: The General Time-dependent Two-compartment Reversible System with an Application to Manpower Planning

In this paper a general time-dependent stochastic model for the analysis of the two-compartment reversible system with non-homogeneous Poisson inputs and arbitrary residence times in each of the compartments is presented. The transition probabilities are suitably modified in order to be useful for estimation purposes of the parameters of the model. Various results are derived in terms of the distributions of the residence times only and are expressed in the form of convolution integrals which are readily evaluated by means of known computational algorithms. Finally, the theoretical results are applied to examples from the literature on manpower planning and some practical implications for the personnel and labour fields are considered.     

Variable selection for QSAR by artificial ant colony systems

Derivation of quantitative structure-activity relationships (QSAR) usually involves computational models that relate a set of input variables describing the structural properties of the molecules for which the activity has been measured to the output variable representing activity. Many of the input variables may be correlated, and it is therefore often desirable to select an optimal subset of the input variables that results in the most predictive model. In this paper we describe an optimization technique for variable selection based on artificial ant colony systems. The algorithm is inspired by the behavior of real ants, which are able to find the shortest path between a food source and their nest using deposits of pheromone as a communication agent. The underlying basic self-organizing principle is exploited for the construction of parsimonious QSAR models based on neural networks for several classical QSAR data sets.     

Fast determination of the optimal rotational matrix for macromolecular superpositions

Finding the rotational matrix that minimizes the sum of squared deviations between two vectors is an important problem in bioinformatics and crystallography. Traditional algorithms involve the inversion or decomposition of a 3 × 3 or 4 × 4 matrix, which can be computationally expensive and numerically unstable in certain cases. Here, we present a simple and robust algorithm to rapidly determine the optimal rotation using a Newton‐Raphson quaternion‐based method and an adjoint matrix. Our method is at least an order of magnitude more efficient than conventional inversion/decomposition methods, and it should be particularly useful for high‐throughput analyses of molecular conformations. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Advances in diversity profiling and combinatorial series design

Rapid advances in synthetic and screening technology have recently enabled the simultaneous synthesis and biological evaluation of large chemical libraries containing hundreds to tens of thousands of compounds, using molecular diversity as a means to design and prioritize experiments. This paper reviews some of the most important computational work in the field of diversity profiling and combinatorial library design, with particular emphasis on methodology and applications. It is divided into four sections that address issues related to molecular representation, dimensionality reduction, compound selection, and visualization.