Dataset Information

Fractal Dimensions of Macromolecular Structures.

ABSTRACT: Quantifying the properties of macromolecules is a prerequisite for understanding their roles in biochemical processes. One of the less-explored geometric features of macromolecules is molecular surface irregularity, or 'roughness', which can be measured in terms of fractal dimension (D). In this study, we demonstrate that surface roughness correlates with ligand binding potential. We quantified the surface roughnesses of biological macromolecules in a large-scale survey that revealed D values between 2.0 and 2.4. The results of our study imply that surface patches involved in molecular interactions, such as ligand-binding pockets and protein-protein interfaces, exhibit greater local fluctuations in their fractal dimensions than 'inert' surface areas. We expect approximately 22 % of a protein's surface outside of the crystallographically known ligand binding sites to be ligandable. These findings provide a fresh perspective on macromolecular structure and have considerable implications for drug design as well as chemical and systems biology.

SUBMITTER: Todoroff N

PROVIDER: S-EPMC4502991 | biostudies-literature | 2014 Sep

REPOSITORIES: biostudies-literature

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Fractal Dimensions of Macromolecular Structures.

Todoroff Nickolay N Kunze Jens J Schreuder Herman H Hessler Gerhard G Baringhaus Karl-Heinz KH Schneider Gisbert G

Molecular informatics 20140902 9

Quantifying the properties of macromolecules is a prerequisite for understanding their roles in biochemical processes. One of the less-explored geometric features of macromolecules is molecular surface irregularity, or 'roughness', which can be measured in terms of fractal dimension (<i>D</i>). In this study, we demonstrate that surface roughness correlates with ligand binding potential. We quantified the surface roughnesses of biological macromolecules in a large-scale survey that revealed <i>D ...[more]

PMID: 26213587

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Project description:Morphometrics are fundamental for the analysis of size and shape in fossils, particularly because soft parts or DNA are rarely preserved and hard parts such as shells are commonly the only source of information. Geometric morphometrics, that is, landmark analysis, is well established for the description of shape but it exhibits a couple of shortcomings resulting from subjective choices during landmarking (number and position of landmarks) and from difficulties in resolving shape at the level of micro-sculpture.With the aid of high-resolution 3D scanning technology and analyses of fractal dimensions, we test whether such shortcomings of linear and landmark morphometrics can be overcome. As a model group, we selected a clade of modern viviparid gastropods from Lake Lugu, with shells that show a high degree of sculptural variation. Linear and landmark analyses were applied to the same shells in order to establish the fractal dimensions. The genetic diversity of the gastropod clade was assessed.The genetic results suggest that the gastropod clade represents a single species. The results of all morphometric methods applied are in line with the genetic results, which is that no specific morphotype could be delimited. Apart from this overall agreement, landmark and fractal dimension analyses do not correspond to each other but represent data sets with different information. Generally, the fractal dimension values quantify the roughness of the shell surface, the resolution of the 3D scans determining the level. In our approach, we captured the micro-sculpture but not the first-order sculptural elements, which explains that fractal dimension and landmark data are not in phase.We can show that analyzing fractal dimensions of gastropod shells opens a window to more detailed information that can be considered in evolutionary and ecological contexts. We propose that using low-resolution 3D scans may successfully substitute landmark analyses because it overcomes the subjective landmarking. Analyses of 3D scans with higher resolution than used in this study will provide surface roughness information at the mineralogical level. We suggest that fractal dimension analyses of a combination of differently resolved 3D models will significantly improve the quality of shell morphometrics.

Project description:A failure of adaptive inference-misinterpreting available sensory information for appropriate perception and action-is at the heart of clinical manifestations of schizophrenia, implicating key subcortical structures in the brain including the hippocampus. We used high-resolution, three-dimensional (3D) fractal geometry analysis to study subtle and potentially biologically relevant structural alterations (in the geometry of protrusions, gyri and indentations, sulci) in subcortical gray matter (GM) in patients with schizophrenia relative to healthy individuals. In particular, we focus on utilizing Fractal Dimension (FD), a compact shape descriptor that can be computed using inputs with irregular (i.e., not necessarily smooth) surfaces in order to quantify complexity (of geometrical properties and configurations of structures across spatial scales) of subcortical GM in this disorder. Probabilistic (entropy-based) information FD was computed based on the box-counting approach for each of the seven subcortical structures, bilaterally, as well as the brainstem from high-resolution magnetic resonance (MR) images in chronic patients with schizophrenia (n = 19) and age-matched healthy controls (n = 19) (age ranges: patients, 22.7-54.3 and healthy controls, 24.9-51.6 years old). We found a significant reduction of FD in the left hippocampus (median: 2.1460, range: 2.07-2.18 vs. median: 2.1730, range: 2.15-2.23, p<0.001; Cohen's effect size, U3 = 0.8158 (95% Confidence Intervals, CIs: 0.6316, 1.0)), the right hippocampus (median: 2.1430, range: 2.05-2.19 vs. median: 2.1760, range: 2.12-2.21, p = 0.004; U3 = 0.8421 (CIs: 0.5263, 1)), as well as left thalamus (median: 2.4230, range: 2.40-2.44, p = 0.005; U3 = 0.7895 (CIs: 0.5789, 0.9473)) in schizophrenia patients, relative to healthy individuals. Our findings provide in-vivo quantitative evidence for reduced surface complexity of hippocampus, with reduced FD indicating a less complex, less regular GM surface detected in schizophrenia.

Dataset Information

Fractal Dimensions of Macromolecular Structures.

Publications

Fractal Dimensions of Macromolecular Structures.

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