The molecular matching problem

Molecular chemistry contains many difficult optimization problems that have begun to attract the attention of optimizers in the Operations Research community. Problems including protein folding, molecular conformation, molecular similarity, and molecular matching have been addressed. Minimum energy conformations for simple molecular structures such as water clusters, Lennard-Jones microclusters, and short polypeptides have dominated the literature to date. However, a variety of interesting problems exist and we focus here on a molecular structure matching (MSM) problem

Can Sgr A* flares reveal the molecular gas density PDF?

Illumination of dense gas in the Central Molecular Zone (CMZ) by powerful X-ray flares from Sgr A* leads to prominent structures in the reflected emission that can be observed long after the end of the flare. By studying this emission we learn about past activity of the supermassive black hole in our Galactic Center and, at the same time, we obtain unique information on the structure of molecular clouds that is essentially impossible to get by other means. Here we discuss how X-ray data can improve our knowledge of both sides of the problem. Existing data already provide: i) an estimate of the flare age, ii) a model-independent lower limit on the luminosity of Sgr A* during the flare and iii) an estimate of the total emitted energy during Sgr A* flare. On the molecular clouds side, the data clearly show a voids-and-walls structure of the clouds and can provide an almost unbiased probe of the mass/density distribution of the molecular gas with the hydrogen column densities lower than few $10^{23}\;{\rm cm^{-2}}$. For instance, the probability distribution function of the gas density $PDF(\rho)$ can be measured this way. Future high energy resolution X-ray missions will provide the information on the gas velocities, allowing, for example a reconstruction of the velocity field structure functions and cross-matching the X-ray and molecular data based on positions and velocities.Comment: 13 pages, 7 figures; Accepted for publication in MNRA

Efficient algorithms for local forest similarity and forest pattern matching

Ordered labelled trees are trees where each node has a label and the left-to-right order among siblings is significant. Ordered labelled forests are sequences of ordered labelled trees. Ordered labelled trees and forests are useful structures for hierarchical data representation. Given two ordered labelled forests F and G, the local forest similarity is to compute two sub-forests F\u27 and G\u27 of F and G respectively such that they are the most similar over all the possible F\u27 and G\u27. Given a target forest F and a pattern forest G, the forest pattern matching problem is to compute a sub-forest F\u27 of F which is the most similar to G over all the possible F\u27. This thesis presents novel efficient algorithms for the local forest similarity problem and forest pattern matching problem for sub-forest. An application of the algorithms is that it can be used to locate the structural regions in RNA secondary structures which is the necessity data in RNA secondary structure prediction and function investigation. RNA is a chain molecular, mathematically it is a string over a four letter alphabet; in computational molecular biology, labeled ordered trees are used to represent RNA secondary structures

Maximum common subgraph isomorphism algorithms for the matching of chemical structures

The maximum common subgraph (MCS) problem has become increasingly important in those aspects of chemoinformatics that involve the matching of 2D or 3D chemical structures. This paper provides a classification and a review of the many MCS algorithms, both exact and approximate, that have been described in the literature, and makes recommendations regarding their applicability to typical chemoinformatics tasks

Global Energy Matching Method for Atomistic-to-Continuum Modeling of Self-Assembling Biopolymer Aggregates

This paper studies mathematical models of biopolymer supramolecular aggregates that are formed by the self-assembly of single monomers. We develop a new multiscale numerical approach to model the structural properties of such aggregates. This theoretical approach establishes micro-macro relations between the geometrical and mechanical properties of the monomers and supramolecular aggregates. Most atomistic-to-continuum methods are constrained by a crystalline order or a periodic setting and therefore cannot be directly applied to modeling of soft matter. By contrast, the energy matching method developed in this paper does not require crystalline order and, therefore, can be applied to general microstructures with strongly variable spatial correlations. In this paper we use this method to compute the shape and the bending stiffness of their supramolecular aggregates from known chiral and amphiphilic properties of the short chain peptide monomers. Numerical implementation of our approach demonstrates consistency with results obtained by molecular dynamics simulations