92-08 Computational methods
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- biochemical conformations (2)
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Biochemical interactions are determined by the 3D-structure of the involved components - thus the identification of conformations is a key for many applications in rational drug design. {\sf ConFlow} is a new multilevel approach to conformational analysis with main focus on completeness in investigation of conformational space. In contrast to known conformational analysis, the starting point for design is a space-based description of conformational areas. A tight integration of sampling and analysis leads to an identification of conformational areas simultaneously during sampling. An incremental decomposition of high-dimensional conformational space is used to guide the analysis. A new concept for the description of conformations and their path connected components based on convex hulls and {\em Hypercubes}is developed. The first results of the {\sf ConFlow} application constitute a 'proof of concept' and are further more highly encouraging. In comparison to conventional industrial applications, {\sf ConFlow} achieves higher accuracy and a specified degree of completeness with comparable effort.
In this paper we describe a new algorithm for multiple semi-flexible superpositioning of drug-sized molecules. The algorithm identifies structural similarities of two or more molecules. When comparing a set of molecules on the basis of their three-dimensional structures, one is faced with two main problems. (1) Molecular structures are not fixed but flexible, i.e., a molecule adopts different forms. To address this problem, we consider a set of conformers per molecule. As conformers we use representatives of conformational ensembles, generated by the program ZIBMol. (2) The degree of similarity may vary considerably among the molecules. This problem is addressed by searching for similar substructures present in arbitrary subsets of the given set of molecules. The algorithm requires to preselect a reference molecule. All molecules are compared to this reference molecule. For this pairwise comparison we use a two-step approach. Clique detection on the correspondence graph of the molecular structures is used to generate start transformations, which are then iteratively improved to compute large common substructures. The results of the pairwise comparisons are efficiently merged using binary matching trees. All common substructures that were found, whether they are common to all or only a few molecules, are ranked according to different criteria, such as number of molecules containing the substructure, size of substructure, and geometric fit. For evaluating the geometric fit, we extend a known scoring function by introducing weights which allow to favor potential pharmacophore points. Despite considering the full atomic information for identifying multiple structural similarities, our algorithm is quite fast. Thus it is well suited as an interactive tool for the exploration of structural similarities of drug-sized molecules.
A new and time efficient model to evaluate the free energy of solvation has been developed. The solvation free energy is separated into an electrostatic term, a hydrogen bond term, and a rest-term, combining both entropic and van der Waals effects. The electrostatic contribution is evaluated with a simplified boundary element method using the partial charges of the MMFF94 force field. The number of hydrogen bonds and the solvent excluded surface area over the surface atoms are used in a linear model to estimate the non-electrostatic contribution. This model is applied to a set of 213 small and mostly organic molecules, yielding an rmsd of 0.87kcal/mol and a correlation with experimental data of r=0.951. The model is applied as a supplementary component of the free energy of binding to estimate binding constants of protein ligand complexes. The intermolecular interaction energy is evaluated by using the MMFF94 force field.
The problem of clustering data can be formulated as a graph partitioning problem. Spectral methods for obtaining optimal solutions have reveceived a lot of attention recently. We describe Perron Cluster Cluster Analysis (PCCA) and, for the first time, establish a connection to spectral graph partitioning. We show that in our approach a clustering can be efficiently computed using a simple linear map of the eigenvector data. To deal with the prevalent problem of noisy and possibly overlapping data we introduce the min Chi indicator which helps in selecting the number of clusters and confirming the existence of a partition of the data. This gives a non-probabilistic alternative to statistical mixture-models. We close with showing favorable results on the analysis of gene expressi on data for two different cancer types.
Recently, a novel approach for the analysis of molecular dynamics on the basis of a transfer operator has been introduced. Therein conformations are considered to be disjoint metastable clusters within position space of a molecule. These clusters are defined by almost invariant characteristic functions that can be computed via {\em Perron Cluster} analysis. The present paper suggests to replace crisp clusters with {\em fuzzy} clusters, i.e. to replace characteristic functions with membership functions. This allows a more sufficient characterization of transiton states between different confor conformations and therefore leads to a better understanding of molecular dynamics. Fur thermore, an indicator for the uniqueness of metastable fuzzy clusters and a fast algorithm for the computation of these clusters are described. Numerical examples are included.
As has been shown recently, the identification of metastable chemical conformations leads to a Perron cluster eigenvalue problem for a reversible Markov operator. Naive discretization of this operator would suffer from combinatorial explosion. As a first remedy, a pre-identification of essential degrees of freedom out of the set of torsion angles had been applied up to now. The present paper suggests a different approach based on neural networks: its idea is to discretize the Markov operator via self-organizing (box) maps. The thus obtained box discretization then serves as a prerequisite for the subsequent Perron cluster analysis. Moreover, this approach also permits exploitation of additional structure within embedded simulations. As it turns out, the new method is fully automatic and efficient also in the treatment of biomolecules. This is exemplified by numerical results.