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Background: Many molecules of interest are flexible and undergo significant shape deformation as part of their function, but most existing methods of molecular shape comparison treat them as rigid shapes, which may lead to incorrect measure of the shape similarity of flexible molecules. Currently, there still is a limited effort in retrieval and navigation for flexible molecular shape comparison, which would improve data retrieval by helping users locate the desirable molecule in a convenient way. Results: To address this issue, we develop a web-based retrieval and navigation tool, named 3DMolNavi, for flexible molecular shape comparison. This tool is based on the histogram of Inner Distance Shape Signature (IDSS) for fast retrieving molecules that are similar to a query molecule, and uses dimensionality reduction to navigate the retrieved results in 2D and 3D spaces. We tested 3DMolNavi in the Database of Macromolecular Movements (MolMovDB) and CATH. Compared to other shape descriptors, it achieves good performance and retrieval results for different classes of flexible molecules. Conclusions: The advantages of 3DMolNavi, over other existing softwares, are to integrate retrieval for flexible molecular shape comparison and enhance navigation for user's interaction. 3DMolNavi can be accessed via https:// engineering.purdue.edu/PRECISE/3dmolnavi/index.html. [ABSTRACT FROM AUTHOR]

Background: During the past decade, the computed tomography has been successfully applied to various fields especially in medicine. The estimation of view angles for projections is necessary in some special applications of tomography, for example, the structuring of viruses using electron microscopy and the compensation of the patient's motion over long scanning period. Methods: This work introduces a novel approach, based on the spherical multidimensional scaling (sMDS), which transforms the problem of the angle estimation to a sphere constrained embedding problem. The proposed approach views each projection as a high dimensional vector with dimensionality equal to the number of sampling points on the projection. By using SMDS, then each projection vector is embedded onto a 1D sphere which parameterizes the projection with respect to view angles in a globally consistent manner. The parameterized projections are used for the final reconstruction of the image through the inverse radon transform. The entire reconstruction process is noniterative and computationally efficient. Results: The effectiveness of the sMDS is verified with various experiments, including the evaluation of the reconstruction quality from different number of projections and resistance to different noise levels. The experimental results demonstrate the efficiency of the proposed method. Conclusion: Our study provides an effective technique for the solution of 2D tomography with unknown acquisition view angles. The proposed method will be extended to three dimensional reconstructions in our future work. All materials, including source code and demos, are available on https://engineering.purdue.edu/PRECISE/SMDS. [ABSTRACT FROM AUTHOR]

Background: Many molecules are flexible and undergo significant shape deformation as part of their function, and yet most existing molecular shape comparison (MSC) methods treat them as rigid bodies, which may lead to incorrect shape recognition. Results: In this paper, we present a new shape descriptor, named Diffusion Distance Shape Descriptor (DDSD), for comparing 3D shapes of flexible molecules. The diffusion distance in our work is considered as an average length of paths connecting two landmark points on the molecular shape in a sense of inner distances. The diffusion distance is robust to flexible shape deformation, in particular to topological changes, and it reflects well the molecular structure and deformation without explicit decomposition. Our DDSD is stored as a histogram which is a probability distribution of diffusion distances between all sample point pairs on the molecular surface. Finally, the problem of flexible MSC is reduced to comparison of DDSD histograms. Conclusions: We illustrate that DDSD is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. The presented algorithm is robust and does not require any prior knowledge of the flexible regions. [ABSTRACT FROM AUTHOR]

Background: The conventional superposition methods use an ordinary least squares (LS) fit for structural comparison of two different conformations of the same protein. The main problem of the LS fit that it is sensitive to outliers, i.e. large displacements of the original structures superimposed. Results: To overcome this problem, we present a new algorithm to overlap two protein conformations by their atomic coordinates using a robust statistics technique: least median of squares (LMS). In order to effectively approximate the LMS optimization, the forward search technique is utilized. Our algorithm can automatically detect and superimpose the rigid core regions of two conformations with small or large displacements. In contrast, most existing superposition techniques strongly depend on the initial LS estimating for the entire atom sets of proteins. They may fail on structural superposition of two conformations with large displacements. The presented LMS fit can be considered as an alternative and complementary tool for structural superposition. Conclusion: The proposed algorithm is robust and does not require any prior knowledge of the flexible regions. Furthermore, we show that the LMS fit can be extended to multiple level superposition between two conformations with several rigid domains. Our fit tool has produced successful superpositions when applied to proteins for which two conformations are known. The binary executable program for Windows platform, tested examples, and database are available from https://engineering.purdue.edu/PRECISE/LMSfit. [ABSTRACT FROM AUTHOR]

Background: Many molecules of interest are flexible and undergo significant shape deformation as part of their function, but most existing methods of molecular shape comparison (MSC) treat them as rigid bodies, which may lead to incorrect measure of the shape similarity of flexible molecules. Results: To address the issue we introduce a new shape descriptor, called Inner Distance Shape Signature (IDSS), for describing the 3D shapes of flexible molecules. The inner distance is defined as the length of the shortest path between landmark points within the molecular shape, and it reflects well the molecular structure and deformation without explicit decomposition. Our IDSS is stored as a histogram which is a probability distribution of inner distances between all sample point pairs on the molecular surface. We show that IDSS is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. Our approach reduces the 3D shape comparison problem of flexible molecules to the comparison of IDSS histograms. Conclusion: The proposed algorithm is robust and does not require any prior knowledge of the flexible regions. We demonstrate the effectiveness of IDSS within a molecular search engine application for a benchmark containing abundant conformational changes of molecules. Such comparisons in several thousands per second can be carried out. The presented IDSS method can be considered as an alternative and complementary tool for the existing methods for rigid MSC. The binary executable program for Windows platform and database are available from https://engineering.purdue.edu/PRECISE/IDSS. [ABSTRACT FROM AUTHOR]

Background: Techniques for inferring the functions of the protein by comparing their shape similarity have been receiving a lot of attention. Proteins are functional units and their shape flexibility occupies an essential role in various biological processes. Several shape descriptors have demonstrated the capability of protein shape comparison by treating them as rigid bodies. But this may give rise to an incorrect comparison of flexible protein shapes. Results: We introduce an efficient approach for comparing flexible protein shapes by adapting a local diameter (LD) descriptor. The LD descriptor, developed recently to handle skeleton based shape deformations [1], is adapted in this work to capture the invariant properties of shape deformations caused by the motion of the protein backbone. Every sampled point on the protein surface is assigned a value measuring the diameter of the 3D shape in the neighborhood of that point. The LD descriptor is built in the form of a one dimensional histogram from the distribution of the diameter values. The histogram based shape representation reduces the shape comparison problem of the flexible protein to a simple distance calculation between 1D feature vectors. Experimental results indicate how the LD descriptor accurately treats the protein shape deformation. In addition, we use the LD descriptor for protein shape retrieval and compare it to the effectiveness of conventional shape descriptors. A sensitivity-specificity plot shows that the LD descriptor performs much better than the conventional shape descriptors in terms of consistency over a family of proteins and discernibility across families of different proteins. Conclusion: Our study provides an effective technique for comparing the shape of flexible proteins. The experimental results demonstrate the insensitivity of the LD descriptor to protein shape deformation. The proposed method will be potentially useful for molecule retrieval with similar shapes and rapid structure retrieval for proteins. The demos and supplemental materials are available on https://engineering.purdue.edu/PRECISE/LDD. [ABSTRACT FROM AUTHOR]

Background: Many molecules of interest are flexible and undergo significant shape deformation as part of their function, but most existing methods of molecular shape comparison treat them as rigid shapes, which may lead to incorrect measure of the shape similarity of flexible molecules. Currently, there still is a limited effort in retrieval and navigation for flexible molecular shape comparison, which would improve data retrieval by helping users locate the desirable molecule in a convenient way., Results: To address this issue, we develop a web-based retrieval and navigation tool, named 3DMolNavi, for flexible molecular shape comparison. This tool is based on the histogram of Inner Distance Shape Signature (IDSS) for fast retrieving molecules that are similar to a query molecule, and uses dimensionality reduction to navigate the retrieved results in 2D and 3D spaces. We tested 3DMolNavi in the Database of Macromolecular Movements (MolMovDB) and CATH. Compared to other shape descriptors, it achieves good performance and retrieval results for different classes of flexible molecules., Conclusions: The advantages of 3DMolNavi, over other existing softwares, are to integrate retrieval for flexible molecular shape comparison and enhance navigation for user's interaction. 3DMolNavi can be accessed via https://engineering.purdue.edu/PRECISE/3dmolnavi/index.html.

Background: Many molecules are flexible and undergo significant shape deformation as part of their function, and yet most existing molecular shape comparison (MSC) methods treat them as rigid bodies, which may lead to incorrect shape recognition., Results: In this paper, we present a new shape descriptor, named Diffusion Distance Shape Descriptor (DDSD), for comparing 3D shapes of flexible molecules. The diffusion distance in our work is considered as an average length of paths connecting two landmark points on the molecular shape in a sense of inner distances. The diffusion distance is robust to flexible shape deformation, in particular to topological changes, and it reflects well the molecular structure and deformation without explicit decomposition. Our DDSD is stored as a histogram which is a probability distribution of diffusion distances between all sample point pairs on the molecular surface. Finally, the problem of flexible MSC is reduced to comparison of DDSD histograms., Conclusions: We illustrate that DDSD is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. The presented algorithm is robust and does not require any prior knowledge of the flexible regions.

Background: During the past decade, the computed tomography has been successfully applied to various fields especially in medicine. The estimation of view angles for projections is necessary in some special applications of tomography, for example, the structuring of viruses using electron microscopy and the compensation of the patient's motion over long scanning period., Methods: This work introduces a novel approach, based on the spherical multidimensional scaling (sMDS), which transforms the problem of the angle estimation to a sphere constrained embedding problem. The proposed approach views each projection as a high dimensional vector with dimensionality equal to the number of sampling points on the projection. By using SMDS, then each projection vector is embedded onto a 1D sphere which parameterizes the projection with respect to view angles in a globally consistent manner. The parameterized projections are used for the final reconstruction of the image through the inverse radon transform. The entire reconstruction process is non-iterative and computationally efficient., Results: The effectiveness of the sMDS is verified with various experiments, including the evaluation of the reconstruction quality from different number of projections and resistance to different noise levels. The experimental results demonstrate the efficiency of the proposed method., Conclusion: Our study provides an effective technique for the solution of 2D tomography with unknown acquisition view angles. The proposed method will be extended to three dimensional reconstructions in our future work. All materials, including source code and demos, are available on https://engineering.purdue.edu/PRECISE/SMDS.

Background: Many molecules of interest are flexible and undergo significant shape deformation as part of their function, but most existing methods of molecular shape comparison (MSC) treat them as rigid bodies, which may lead to incorrect measure of the shape similarity of flexible molecules., Results: To address the issue we introduce a new shape descriptor, called Inner Distance Shape Signature (IDSS), for describing the 3D shapes of flexible molecules. The inner distance is defined as the length of the shortest path between landmark points within the molecular shape, and it reflects well the molecular structure and deformation without explicit decomposition. Our IDSS is stored as a histogram which is a probability distribution of inner distances between all sample point pairs on the molecular surface. We show that IDSS is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. Our approach reduces the 3D shape comparison problem of flexible molecules to the comparison of IDSS histograms., Conclusion: The proposed algorithm is robust and does not require any prior knowledge of the flexible regions. We demonstrate the effectiveness of IDSS within a molecular search engine application for a benchmark containing abundant conformational changes of molecules. Such comparisons in several thousands per second can be carried out. The presented IDSS method can be considered as an alternative and complementary tool for the existing methods for rigid MSC. The binary executable program for Windows platform and database are available from https://engineering.purdue.edu/PRECISE/IDSS.

Background: Techniques for inferring the functions of the protein by comparing their shape similarity have been receiving a lot of attention. Proteins are functional units and their shape flexibility occupies an essential role in various biological processes. Several shape descriptors have demonstrated the capability of protein shape comparison by treating them as rigid bodies. But this may give rise to an incorrect comparison of flexible protein shapes., Results: We introduce an efficient approach for comparing flexible protein shapes by adapting a local diameter (LD) descriptor. The LD descriptor, developed recently to handle skeleton based shape deformations 1, is adapted in this work to capture the invariant properties of shape deformations caused by the motion of the protein backbone. Every sampled point on the protein surface is assigned a value measuring the diameter of the 3D shape in the neighborhood of that point. The LD descriptor is built in the form of a one dimensional histogram from the distribution of the diameter values. The histogram based shape representation reduces the shape comparison problem of the flexible protein to a simple distance calculation between 1D feature vectors. Experimental results indicate how the LD descriptor accurately treats the protein shape deformation. In addition, we use the LD descriptor for protein shape retrieval and compare it to the effectiveness of conventional shape descriptors. A sensitivity-specificity plot shows that the LD descriptor performs much better than the conventional shape descriptors in terms of consistency over a family of proteins and discernibility across families of different proteins., Conclusion: Our study provides an effective technique for comparing the shape of flexible proteins. The experimental results demonstrate the insensitivity of the LD descriptor to protein shape deformation. The proposed method will be potentially useful for molecule retrieval with similar shapes and rapid structure retrieval for proteins. The demos and supplemental materials are available on https://engineering.purdue.edu/PRECISE/LDD.

Background: The conventional superposition methods use an ordinary least squares (LS) fit for structural comparison of two different conformations of the same protein. The main problem of the LS fit that it is sensitive to outliers, i.e. large displacements of the original structures superimposed., Results: To overcome this problem, we present a new algorithm to overlap two protein conformations by their atomic coordinates using a robust statistics technique: least median of squares (LMS). In order to effectively approximate the LMS optimization, the forward search technique is utilized. Our algorithm can automatically detect and superimpose the rigid core regions of two conformations with small or large displacements. In contrast, most existing superposition techniques strongly depend on the initial LS estimating for the entire atom sets of proteins. They may fail on structural superposition of two conformations with large displacements. The presented LMS fit can be considered as an alternative and complementary tool for structural superposition., Conclusion: The proposed algorithm is robust and does not require any prior knowledge of the flexible regions. Furthermore, we show that the LMS fit can be extended to multiple level superposition between two conformations with several rigid domains. Our fit tool has produced successful superpositions when applied to proteins for which two conformations are known. The binary executable program for Windows platform, tested examples, and database are available from https://engineering.purdue.edu/PRECISE/LMSfit.