Comparative analysis of dendritic architecture of identified neurons using the Hausdorff distance metric.

Dendritic trees often are complex, three-dimensional structures. Comparative morphologic studies have not yet provided a reliable measure to analyze and compare the geometry of different dendritic trees. Therefore, it is important to develop quantitative methods for analyzing the three-dimensional geometry of these complex trees. The authors developed a comparison measure based on the Hausdorff distance for comparing quantitatively the three-dimensional structure of different neurons. This algorithm was implemented and incorporated into a new software package that the authors developed called NeuroComp. The authors tested this algorithm to study the variability in the three-dimensional structure of identified central neurons as well as measuring the structural differences between homologue neurons. They took advantage of the uniform dendritic morphology of identified interneurons of an insect, the giant interneurons of the cockroach. More specifically, after establishing a morphometric data base of these neurons, the authors found that the algorithm is a reliable tool for distinguishing between dendritic trees of different neurons, whereas conventional metric analysis often is inadequate. The authors propose to use this method as a quantitative tool for the investigation of the effects of various experimental paradigms on three-dimensional dendritic architecture.

Fast detection of common geometric substructure in proteins.

We consider the problem of identifying common three-dimensional substructures between proteins. Our method is based on comparing the shape of the alpha-carbon backbone structures of the proteins in order to find three-dimensional (3D) rigid motions that bring portions of the geometric structures into correspondence. We propose a geometric representation of protein backbone chains that is compact yet allows for similarity measures that are robust against noise and outliers. This representation encodes the structure of the backbone as a sequence of unit vectors, defined by each adjacent pair of alpha-carbons. We then define a measure of the similarity of two protein structures based on the root mean squared (RMS) distance between corresponding orientation vectors of the two proteins. Our measure has several advantages over measures that are commonly used for comparing protein shapes, such as the minimum RMS distance between the 3D positions of corresponding atoms in two proteins. A key advantage is that this new measure behaves well for identifying common substructures, in contrast with position-based measures where the nonmatching portions of the structure dominate the measure. At the same time, it avoids the quadratic space and computational difficulties associated with methods based on distance matrices and contact maps. We show applications of our approach to detecting common contiguous substructures in pairs of proteins, as well as the more difficult problem of identifying common protein domains (i.e., larger substructures that are not necessarily contiguous along the protein chain).

Unit-vector RMS (URMS) as a tool to analyze molecular dynamics trajectories.

The Unit-vector RMS (URMS) is a new technique to compare protein chains and to detect similarities of chain segments. It is limited to comparison of C(alpha) chains. However, it has a number of unique features that include exceptionally weak dependence on the length of the chain and efficient detection of substructure similarities. Two molecular dynamics simulations of proteins in the neighborhood of their native states are used to test the performance of the URMS. The first simulation is of a solvated myoglobin and the second is of the protein MHC. In accord with previous studies the secondary structure elements (helices or sheets) are found to be moving relatively rigidly among flexible loops. In addition to these tests, folding trajectories of C peptides are analyzed, revealing a folding nucleus of seven amino acids.