Analysis and 3D reconstruction of heterogeneity in malignant brain tumors: an interdisciplinary case study using a novel computational visualization approach

OBJECTIVE: To explore how a multidisciplinary approach, combining modern visualization and image processing techniques with innovative experimental studies, can augment the understanding of tumor development. STUDY DESIGN: We analyzed histologic sections of a microscopic brain tumor and reconstructed these slices into a 3D representation. We processed these slices to: (1) identify tumor boundaries, (2) isolate proliferating tumor cells, and (3) segment the tumor into regions based on the density of proliferating cells. We then reconstructed the 3D shape of the tumor using a constrained deformable surface approach. RESULTS: This novel method allows the analyst to (1) see specific properties of histologic slices in the 3D environment with animation, (2) switch 2D "views" dynamically, and (3) see relationships between the 3D structure and structure on a plane. CONCLUSION: Using this method to analyze a specific "case," we were also able to shed light on the limitations of a widely held assumption about the shape of expanding microscopic solid tumors as well as find more indications that such tumors behave as adaptive biosystems. Implications of these case study results, as well as future applications of the method for tumor biology research, are discussed.     

Shape group studies of molecular similarity: relative shapes of Van der Waals and electrostatic potential surfaces of nicotinic agonists

In drug design, the usual strategy involves characterizing and comparing the shapes of molecules. We apply a simple method to accomplish this goal: determining the symmetry-independent shape groups (homology groups of algebraic topology) of a molecular surface.In this paper, we have adapted the method to describing the interrelation between Van der Waals and electrostatic potential surfaces. We describe rigorously the shape features in a series of molecules by using specific ranges of electrostatic potential over a Van der Waals surface. We consider a series of four nicotinic agonists as an example and discuss their expected activities as potential drugs on the basis of the shape similarities found.     

Theoretical Modeling of Surface Confined Chiral Nanoporous Networks: Cruciform Molecules as Versatile Building Blocks

Patterning of solid surfaces with functional organic molecules has been a convenient route to fabricate two‐dimensional materials with programmed architecture and activities. One example is the chiral nanoporous networks that can be created via controlled self‐assembly of star‐shaped molecules under 2D confinement. In this contribution we use computer modeling to predict the formation of molecular networks in adsorbed overlayers comprising cruciform molecular building blocks equipped with discrete interaction centers. To that end, we employ the Monte Carlo simulation method combined with a coarse‐grained representation of the adsorbed molecules which are treated as collections of interconnected segments. The interaction centers within the molecules are represented by active segments whose number and distribution are adjusted. Our particular focus is on those distributions that produce prochiral molecules able to occur in adsorbed configurations being mirror images of each other (surface enantiomers). We demonstrate that, depending on size, aspect ratio, and intramolecular distribution of active sites, the surface enantiomers can co‐crystallize or segregate into extended homochiral domains with largely diversified nanosized cavities. The insights from our theoretical studies can be helpful in designing 2D chiral porous networks with potential applications in enantioselective adsorption and asymmetric heterogeneous catalysis. Chirality 27:397–404, 2015. © 2015 Wiley Periodicals, Inc.     

ShapeRotator: An R tool for standardized rigid rotations of articulated three‐dimensional structures with application for geometric morphometrics

The quantification of complex morphological patterns typically involves comprehensive shape and size analyses, usually obtained by gathering morphological data from all the structures that capture the phenotypic diversity of an organism or object. Articulated structures are a critical component of overall phenotypic diversity, but data gathered from these structures are difficult to incorporate into modern analyses because of the complexities associated with jointly quantifying 3D shape in multiple structures. While there are existing methods for analyzing shape variation in articulated structures in two‐dimensional (2D) space, these methods do not work in 3D, a rapidly growing area of capability and research. Here, we describe a simple geometric rigid rotation approach that removes the effect of random translation and rotation, enabling the morphological analysis of 3D articulated structures. Our method is based on Cartesian coordinates in 3D space, so it can be applied to any morphometric problem that also uses 3D coordinates (e.g., spherical harmonics). We demonstrate the method by applying it to a landmark‐based dataset for analyzing shape variation using geometric morphometrics. We have developed an R tool (ShapeRotator) so that the method can be easily implemented in the commonly used R package geomorph and MorphoJ software. This method will be a valuable tool for 3D morphological analyses in articulated structures by allowing an exhaustive examination of shape and size diversity.     

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).     

Ab initio RNA folding by discrete molecular dynamics: from structure prediction to folding mechanisms

RNA molecules with novel functions have revived interest in the accurate prediction of RNA three-dimensional (3D) structure and folding dynamics. However, existing methods are inefficient in automated 3D structure prediction. Here, we report a robust computational approach for rapid folding of RNA molecules. We develop a simplified RNA model for discrete molecular dynamics (DMD) simulations, incorporating base-pairing and base-stacking interactions. We demonstrate correct folding of 150 structurally diverse RNA sequences. The majority of DMD-predicted 3D structures have <4 A deviations from experimental structures. The secondary structures corresponding to the predicted 3D structures consist of 94% native base-pair interactions. Folding thermodynamics and kinetics of tRNA(Phe), pseudoknots, and mRNA fragments in DMD simulations are in agreement with previous experimental findings. Folding of RNA molecules features transient, non-native conformations, suggesting non-hierarchical RNA folding. Our method allows rapid conformational sampling of RNA folding, with computational time increasing linearly with RNA length. We envision this approach as a promising tool for RNA structural and functional analyses.     

Quantitative analysis of molecular surfaces: areas, volumes, electrostatic potentials and average local ionization energies

We describe a procedure for performing quantitative analyses of fields f(r) on molecular surfaces, including statistical quantities and locating and evaluating their local extrema. Our approach avoids the need for explicit mathematical representation of the surface and can be implemented easily in existing graphical software, as it is based on the very popular representation of a surface as collection of polygons. We discuss applications involving the volumes, surface areas and molecular surface electrostatic potentials, and local ionization energies of a group of 11 molecules.

Lipophilicity force field profile: An expressive visualization of the lipophilicity molecular potential gradient

This paper proposes a new tool that allows us to see the following in the same frame: (1) 3D geometrical features of a molecule, and (2) pseudo-3D representation of the lipohilicity molecular potential. It thus becomes very easy to compare the lipohilicity molecular potential gradient of different molecules having the same pharmacological properties. An example of two structurally dissimilar anti-PAF molecules is given.     

Three-dimensional lipophilicity characterization of molecular pores and channel-like cavities

Molecular lipophilicity is a useful property for assessing molecular similarity or complementarity within the context of computer-aided drug design. As well, local contributions to solvent affinity help us to understand both dynamics and conformational stability in biomolecules. In this work, we discuss an approach to characterize the local contributions to hydrophobicity by using one- and two-dimensional representations of molecular channel-like cavities. The method monitors how a phenomenological lipophilicity potential (based on fragmental atom contributions) changes over a continuum of “molecular tubes” used for modeling channels and pores. Our results convey a relatively detailed picture of the spatial distribution of water affinity. The procedure can then be used as a complement to the hydrophobicity scales based on averaging contributions from single amino acids. In addition, we can study how the water affinity changes for inner and outer regious of the pores. As an application, we compute the 3D distribution of lipophilicity in the “pore conformation” of gramicidin A. The qualitative trends indicated by our results are broadly consistent with computer simulations of the gramicidin channel in the presence of hydrated ions. The behavior revealed by the simulations can then be incorporated to produce an improved, simple 2D model for water-channel interactions.     

NMR: prediction of molecular alignment from structure using the PALES software

Orientational restraints such as residual dipolar couplings promise to overcome many of the problems that traditionally limited liquid-state nuclear magnetic resonance spectroscopy. Recently, we developed methods to predict a molecular alignment tensor and thus residual dipolar couplings for a given molecular structure. This provides many new opportunities for the study of the structure and dynamics of proteins, nucleic acids, oligosaccharides and small molecules. This protocol details the use of the software PALES (Prediction of AlignmEnt from Structure) for prediction of an alignment tensor from a known three-dimensional (3D) coordinate file of a solute. The method is applicable to alignment of molecules in many neutral and charged orienting media and takes into account the molecular shape and 3D charge distribution of the molecule.     

FPV: fast protein visualization using Java 3D

MOTIVATION: Many tools have been developed to visualize protein structures. Tools that have been based on Java 3D((TM)) are compatible among different systems and they can be run remotely through web browsers. However, using Java 3D for visualization has some performance issues with it. The primary concerns about molecular visualization tools based on Java 3D are in their being slow in terms of interaction speed and in their inability to load large molecules. This behavior is especially apparent when the number of atoms to be displayed is huge, or when several proteins are to be displayed simultaneously for comparison. RESULTS: In this paper we present techniques for organizing a Java 3D scene graph to tackle these problems. We have developed a protein visualization system based on Java 3D and these techniques. We demonstrate the effectiveness of the proposed method by comparing the visualization component of our system with two other Java 3D based molecular visualization tools. In particular, for van der Waals display mode, with the efficient organization of the scene graph, we could achieve up to eight times improvement in rendering speed and could load molecules three times as large as the previous systems could. AVAILABILITY: EPV is freely available with source code at the following URL: http://www.cs.ucsb.edu/~tcan/fpv/     

Structural analysis of interphase X-chromatin based on statistical shape theory

The 3D folding structure formed by different genomic regions of a chromosome is still poorly understood. So far, only relatively simple geometric features, like distances and angles between different genomic regions, have been evaluated. This work is concerned with more complex geometric properties, i.e., the complete shape formed by genomic regions. Our work is based on statistical shape theory and we use different approaches to analyze the considered structures, e.g., shape uniformity test, 3D point-based registration, Fisher distribution, and 3D non-rigid image registration for shape normalization. We have applied these approaches to analyze 3D microscopy images of the X-chromosome where four consecutive genomic regions (BACs) have been simultaneously labeled by multicolor FISH. We have acquired two sets of four consecutive genomic regions with an overlap of three regions. From the experimental results, it turned out that for all data sets the complete structure is non-random. In addition, we found that the shapes of active and inactive X-chromosomal genomic regions are statistically independent. Moreover, we reconstructed the average 3D structure of chromatin in a small genomic region (below 4 Mb) based on five BACs resulting from two overlapping four BAC regions. We found that geometric normalization with respect to the nucleus shape based on non-rigid image registration has a significant influence on the location of the genomic regions.