The Experts below are selected from a list of 276 Experts worldwide ranked by ideXlab platform

Antonio Mucherino - One of the best experts on this subject based on the ideXlab platform.

  • Systematic Exploration of Protein Conformational Space Using a Distance Geometry Approach
    Journal of Chemical Information and Modeling, 2019
    Co-Authors: Thérèse Malliavin, Carlile Lavor, Antonio Mucherino, Leo Liberti
    Abstract:

    The optimization approaches classically used during the determination of protein structure encounter various difficulties, especially when the size of the conformational space is large. Indeed, in such a case, algorithmic convergence criteria are more difficult to set up. Moreover, the size of the search space makes it difficult to achieve a complete exploration. The interval branch-and-prune (iBP) approach, based on the reformulation of the Distance Geometry problem (DGP) provides a theoretical frame for the generation of protein conformations, by systematically sampling the conformational space. When an appropriate subset of interatomic Distances is known exactly, this worst-case exponential-time algorithm is provably complete and fixed-parameter tractable. These guarantees, however, immediately disappear as Distance measurement errors are introduced. Here we propose an improvement of this approach: threading-augmented interval branch-and-prune (TAiBP), where the combinatorial explosion of the original iBP approach arising from its exponential complexity is alleviated by partitioning the input instances into consecutive peptide fragments and by using self-organizing maps (SOMs) to obtain clusters of similar solutions. A validation of the TAiBP approach is presented here on a set of proteins of various sizes and structures. The calculation inputs are a uniform covalent Geometry extracted from force field covalent terms, the backbone dihedral angles with error intervals, and a few long-range Distances. For most of the proteins smaller than 50 residues and interval widths of 20°, the TAiBP approach yielded solutions with RMSD values smaller than 3 Å with respect to the initial protein conformation. The efficiency of the TAiBP approach for proteins larger than 50 residues will require the use of nonuniform covalent Geometry and may have benefits from the recent development of residue-specific force-fields.

  • systematic exploration of protein conformational space using a Distance Geometry approach
    bioRxiv, 2019
    Co-Authors: Therese E Malliavin, Carlile Lavor, Antonio Mucherino, Leo Liberti
    Abstract:

    Abstract The optimization problem that arises for protein structure determination is undergoing a change of perspective due to the larger importance in biology taken by the disordered regions of biomolecules and intrinsically disordered proteins. Indeed, in such cases, the algorithm convergence criterion is more difficult to set up; moreover, the enormous size of the space makes it difficult to achieve a complete exploration. The interval Branch-and-Prune (iBP) approach, based on a reformulating of the Distance Geometry Problem (DGP) and proposed few years ago, provides a theoretical frame for the fast generation of protein conformations, by systematically sampling the conformational space. When an appropriate subset of inter-atomic Distances is known exactly, this worst-case exponential-time algorithm is provably complete and fixed-parameter tractable. These guarantees, however, quickly disappear as Distance measurement errors are introduced. Here we propose a variant of this approach: the threading-augmented interval Branch-and-Prune (TAiBP), where the combinatorial explosion of the original iBP approach arising from its exponential complexity is alleviated by partitioning the input instances into consecutive peptide fragments and by using Self-Organizing Maps (SOMs) to obtain clusters of similar solutions. A validation of the TAiBP approach is presented here on a set of proteins of various sizes and structures. The calculation inputs are: a uniform covalent Geometry extracted from force field covalent terms, the backbone dihedral angles with error intervals, and some long-range Distances. For most of the protein smaller than 50 residues and interval widthes of 20°, the TAiBP approach yielded solutions with RMSD values smaller than 3 A with respect to the initial protein conformation. The efficiency of TAiBP approach for proteins larger than 50 residues will require the use of non-uniform covalent Geometry, and may benefit from the recent development of residue-specific force-field.

  • Recent results on assigned and unassigned Distance Geometry with applications to protein molecules and nanostructures
    Annals of Operations Research, 2018
    Co-Authors: Simon J. L. Billinge, Douglas S. Gonçalves, Carlile Lavor, Phillip M. Duxbury, Antonio Mucherino
    Abstract:

    In the 2 years since our last 4OR review of Distance Geometry methods with applications to proteins and nanostructures, there has been rapid progress in treating uncertainties in the discretizable Distance Geometry problem; and a new class of Geometry problems started to be explored, namely vector Geometry problems. In this work we review this progress in the context of the earlier literature.

  • an approach to dynamical Distance Geometry
    GSI 2017 - International Conference on Geometric Science of Information, 2017
    Co-Authors: Antonio Mucherino, Douglas Soares Goncalves
    Abstract:

    We introduce the dynamical Distance Geometry problem (dynDGP), where vertices of a given simple weighted undirected graph are to be embedded at different times t. Solutions to the dynDGP can be seen as motions of a given set of objects. In this work, we focus our attention on a class of instances where motion inter-frame Distances are not available, and reduce the problem of embedding every motion frame as a static Distance Geometry problem. Some preliminary computational experiments are presented.

  • Recent advances on the interval Distance Geometry problem
    Journal of Global Optimization, 2017
    Co-Authors: Douglas S. Gonçalves, Carlile Lavor, Antonio Mucherino, Leo Liberti
    Abstract:

    We discuss a discretization-based solution approach for a classic problem in global optimization, namely the Distance Geometry problem (DGP). We focus our attention on a particular class of the DGP which is concerned with the identification of the conformation of biological molecules. Among the many relevant ideas for the discretization of the DGP in the literature, we identify the most promising ones and address their inherent limitations to application to this class of problems. The result is an improved method for estimating 3D structures of small proteins based only on the knowledge of some Distance restraints between pairs of atoms. We present computational results showcasing the usefulness of the new proposed approach. Proteins act on living cells according to their geometric and chemical properties: finding protein conformations can be very useful within the pharmaceutical industry in order to synthesize new drugs.

Leo Liberti - One of the best experts on this subject based on the ideXlab platform.

  • Unassigned Distance Geometry and molecular conformation problems
    Journal of Global Optimization, 2021
    Co-Authors: Phil Duxbury, Carlile Lavor, Leo Liberti, Luiz Leduino Salles-neto
    Abstract:

    3D protein structures and nanostructures can be obtained by exploiting Distance information provided by experimental techniques, such as nuclear magnetic resonance and the pair distribution function method. These are examples of instances of the unassigned Distance Geometry problem (uDGP), where the aim is to calculate the position of some points using a list of associated Distance values not previoulsy assigned to the pair of points. We propose new mathematical programming formulations and a new heuristic to solve the uDGP related to molecular structure calculations. In addition to theoretical results, computational experiments are also provided.

  • Distance Geometry and data science
    TOP, 2020
    Co-Authors: Leo Liberti
    Abstract:

    Data are often represented as graphs. Many common tasks in data science are based on Distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in vectorial form. In this survey we discuss the fundamental problem of mapping graphs to vectors, and its relation with mathematical programming. We discuss applications, solution methods, dimensional reduction techniques and some of their limits. We then present an application of some of these ideas to neural networks, showing that Distance Geometry techniques can give competitive performance with respect to more traditional graph-to-vector mappings.

  • Systematic Exploration of Protein Conformational Space Using a Distance Geometry Approach
    Journal of Chemical Information and Modeling, 2019
    Co-Authors: Thérèse Malliavin, Carlile Lavor, Antonio Mucherino, Leo Liberti
    Abstract:

    The optimization approaches classically used during the determination of protein structure encounter various difficulties, especially when the size of the conformational space is large. Indeed, in such a case, algorithmic convergence criteria are more difficult to set up. Moreover, the size of the search space makes it difficult to achieve a complete exploration. The interval branch-and-prune (iBP) approach, based on the reformulation of the Distance Geometry problem (DGP) provides a theoretical frame for the generation of protein conformations, by systematically sampling the conformational space. When an appropriate subset of interatomic Distances is known exactly, this worst-case exponential-time algorithm is provably complete and fixed-parameter tractable. These guarantees, however, immediately disappear as Distance measurement errors are introduced. Here we propose an improvement of this approach: threading-augmented interval branch-and-prune (TAiBP), where the combinatorial explosion of the original iBP approach arising from its exponential complexity is alleviated by partitioning the input instances into consecutive peptide fragments and by using self-organizing maps (SOMs) to obtain clusters of similar solutions. A validation of the TAiBP approach is presented here on a set of proteins of various sizes and structures. The calculation inputs are a uniform covalent Geometry extracted from force field covalent terms, the backbone dihedral angles with error intervals, and a few long-range Distances. For most of the proteins smaller than 50 residues and interval widths of 20°, the TAiBP approach yielded solutions with RMSD values smaller than 3 Å with respect to the initial protein conformation. The efficiency of the TAiBP approach for proteins larger than 50 residues will require the use of nonuniform covalent Geometry and may have benefits from the recent development of residue-specific force-fields.

  • systematic exploration of protein conformational space using a Distance Geometry approach
    bioRxiv, 2019
    Co-Authors: Therese E Malliavin, Carlile Lavor, Antonio Mucherino, Leo Liberti
    Abstract:

    Abstract The optimization problem that arises for protein structure determination is undergoing a change of perspective due to the larger importance in biology taken by the disordered regions of biomolecules and intrinsically disordered proteins. Indeed, in such cases, the algorithm convergence criterion is more difficult to set up; moreover, the enormous size of the space makes it difficult to achieve a complete exploration. The interval Branch-and-Prune (iBP) approach, based on a reformulating of the Distance Geometry Problem (DGP) and proposed few years ago, provides a theoretical frame for the fast generation of protein conformations, by systematically sampling the conformational space. When an appropriate subset of inter-atomic Distances is known exactly, this worst-case exponential-time algorithm is provably complete and fixed-parameter tractable. These guarantees, however, quickly disappear as Distance measurement errors are introduced. Here we propose a variant of this approach: the threading-augmented interval Branch-and-Prune (TAiBP), where the combinatorial explosion of the original iBP approach arising from its exponential complexity is alleviated by partitioning the input instances into consecutive peptide fragments and by using Self-Organizing Maps (SOMs) to obtain clusters of similar solutions. A validation of the TAiBP approach is presented here on a set of proteins of various sizes and structures. The calculation inputs are: a uniform covalent Geometry extracted from force field covalent terms, the backbone dihedral angles with error intervals, and some long-range Distances. For most of the protein smaller than 50 residues and interval widthes of 20°, the TAiBP approach yielded solutions with RMSD values smaller than 3 A with respect to the initial protein conformation. The efficiency of TAiBP approach for proteins larger than 50 residues will require the use of non-uniform covalent Geometry, and may benefit from the recent development of residue-specific force-field.

  • Recent advances on the interval Distance Geometry problem
    Journal of Global Optimization, 2017
    Co-Authors: Douglas S. Gonçalves, Carlile Lavor, Antonio Mucherino, Leo Liberti
    Abstract:

    We discuss a discretization-based solution approach for a classic problem in global optimization, namely the Distance Geometry problem (DGP). We focus our attention on a particular class of the DGP which is concerned with the identification of the conformation of biological molecules. Among the many relevant ideas for the discretization of the DGP in the literature, we identify the most promising ones and address their inherent limitations to application to this class of problems. The result is an improved method for estimating 3D structures of small proteins based only on the knowledge of some Distance restraints between pairs of atoms. We present computational results showcasing the usefulness of the new proposed approach. Proteins act on living cells according to their geometric and chemical properties: finding protein conformations can be very useful within the pharmaceutical industry in order to synthesize new drugs.

Carlile Lavor - One of the best experts on this subject based on the ideXlab platform.

  • Unassigned Distance Geometry and molecular conformation problems
    Journal of Global Optimization, 2021
    Co-Authors: Phil Duxbury, Carlile Lavor, Leo Liberti, Luiz Leduino Salles-neto
    Abstract:

    3D protein structures and nanostructures can be obtained by exploiting Distance information provided by experimental techniques, such as nuclear magnetic resonance and the pair distribution function method. These are examples of instances of the unassigned Distance Geometry problem (uDGP), where the aim is to calculate the position of some points using a list of associated Distance values not previoulsy assigned to the pair of points. We propose new mathematical programming formulations and a new heuristic to solve the uDGP related to molecular structure calculations. In addition to theoretical results, computational experiments are also provided.

  • Systematic Exploration of Protein Conformational Space Using a Distance Geometry Approach
    Journal of Chemical Information and Modeling, 2019
    Co-Authors: Thérèse Malliavin, Carlile Lavor, Antonio Mucherino, Leo Liberti
    Abstract:

    The optimization approaches classically used during the determination of protein structure encounter various difficulties, especially when the size of the conformational space is large. Indeed, in such a case, algorithmic convergence criteria are more difficult to set up. Moreover, the size of the search space makes it difficult to achieve a complete exploration. The interval branch-and-prune (iBP) approach, based on the reformulation of the Distance Geometry problem (DGP) provides a theoretical frame for the generation of protein conformations, by systematically sampling the conformational space. When an appropriate subset of interatomic Distances is known exactly, this worst-case exponential-time algorithm is provably complete and fixed-parameter tractable. These guarantees, however, immediately disappear as Distance measurement errors are introduced. Here we propose an improvement of this approach: threading-augmented interval branch-and-prune (TAiBP), where the combinatorial explosion of the original iBP approach arising from its exponential complexity is alleviated by partitioning the input instances into consecutive peptide fragments and by using self-organizing maps (SOMs) to obtain clusters of similar solutions. A validation of the TAiBP approach is presented here on a set of proteins of various sizes and structures. The calculation inputs are a uniform covalent Geometry extracted from force field covalent terms, the backbone dihedral angles with error intervals, and a few long-range Distances. For most of the proteins smaller than 50 residues and interval widths of 20°, the TAiBP approach yielded solutions with RMSD values smaller than 3 Å with respect to the initial protein conformation. The efficiency of the TAiBP approach for proteins larger than 50 residues will require the use of nonuniform covalent Geometry and may have benefits from the recent development of residue-specific force-fields.

  • systematic exploration of protein conformational space using a Distance Geometry approach
    bioRxiv, 2019
    Co-Authors: Therese E Malliavin, Carlile Lavor, Antonio Mucherino, Leo Liberti
    Abstract:

    Abstract The optimization problem that arises for protein structure determination is undergoing a change of perspective due to the larger importance in biology taken by the disordered regions of biomolecules and intrinsically disordered proteins. Indeed, in such cases, the algorithm convergence criterion is more difficult to set up; moreover, the enormous size of the space makes it difficult to achieve a complete exploration. The interval Branch-and-Prune (iBP) approach, based on a reformulating of the Distance Geometry Problem (DGP) and proposed few years ago, provides a theoretical frame for the fast generation of protein conformations, by systematically sampling the conformational space. When an appropriate subset of inter-atomic Distances is known exactly, this worst-case exponential-time algorithm is provably complete and fixed-parameter tractable. These guarantees, however, quickly disappear as Distance measurement errors are introduced. Here we propose a variant of this approach: the threading-augmented interval Branch-and-Prune (TAiBP), where the combinatorial explosion of the original iBP approach arising from its exponential complexity is alleviated by partitioning the input instances into consecutive peptide fragments and by using Self-Organizing Maps (SOMs) to obtain clusters of similar solutions. A validation of the TAiBP approach is presented here on a set of proteins of various sizes and structures. The calculation inputs are: a uniform covalent Geometry extracted from force field covalent terms, the backbone dihedral angles with error intervals, and some long-range Distances. For most of the protein smaller than 50 residues and interval widthes of 20°, the TAiBP approach yielded solutions with RMSD values smaller than 3 A with respect to the initial protein conformation. The efficiency of TAiBP approach for proteins larger than 50 residues will require the use of non-uniform covalent Geometry, and may benefit from the recent development of residue-specific force-field.

  • oriented conformal geometric algebra and the molecular Distance Geometry problem
    Advances in Applied Clifford Algebras, 2019
    Co-Authors: Carlile Lavor, Rafael Alves
    Abstract:

    The problem of 3D protein structure determination using Distance information from nuclear magnetic resonance (NMR) experiments is a classical problem in Distance Geometry. NMR data and the chemistry of proteins provide a way to define a protein backbone order such that the Distances related to the pairs of atoms $$\{i-3,i\},\{i-2,i\},\{i-1,i\}$$ are available, implying a combinatorial method to solve the problem, called branch-and-prune (BP). There are two main steps in BP algorithm: the first one (the branching phase) is to intersect three spheres centered at the positions for atoms $$ i-3,i-2,i$$ , with radius given by the atomic Distances $$ d_{i-3,i},d_{i-2,i},d_{i-1,i}$$ , respectively, to obtain two possible positions for atom i; and the second one (the pruning phase) is to check if additional spheres (related to Distances $$d_{j,i}$$ , $$jDistances $$d_{i-2,i},d_{i-1,i}$$ (associated to bond lenghts and bond angles), Distances $$d_{j,i}$$ , $$j\le i-3$$ , may not be precise. BP algorithm has difficulties to deal with uncertainties, and this paper proposes the oriented conformal geometric algebra to take care of intersection of spheres when their centers and radius are not precise.

  • Recent results on assigned and unassigned Distance Geometry with applications to protein molecules and nanostructures
    Annals of Operations Research, 2018
    Co-Authors: Simon J. L. Billinge, Douglas S. Gonçalves, Carlile Lavor, Phillip M. Duxbury, Antonio Mucherino
    Abstract:

    In the 2 years since our last 4OR review of Distance Geometry methods with applications to proteins and nanostructures, there has been rapid progress in treating uncertainties in the discretizable Distance Geometry problem; and a new class of Geometry problems started to be explored, namely vector Geometry problems. In this work we review this progress in the context of the earlier literature.

Nelson Maculan - One of the best experts on this subject based on the ideXlab platform.

  • clifford algebra and the discretizable molecular Distance Geometry problem
    Advances in Applied Clifford Algebras, 2015
    Co-Authors: Carlile Lavor, Rafael Alves, Weber Figueiredo, Antonio Petraglia, Nelson Maculan
    Abstract:

    Nuclear Magnetic Resonance experiments can provide Distances between pairs of atoms of a protein that are close enough and the problem is how to determine the 3D protein structure based on this partial Distance information, called Molecular Distance Geometry Problem. It is possible to define an atomic order 1, ..., n and solve the problem iteratively using an exact method, called Branch-and-Prune (BP). The main step of BP algorithm is to solve a quadratic system to get the two possible positions for i, i > 3, in terms of the positions of i−3, i−2, i−1 and the Distances di−1, i, di−2, i, di−3, i. Because of uncertainty in NMR data, some of the Distances di−3, i may not be precise and the main problem to apply BP is related to the difficulty of obtaining an analytical expression of the position of atom i in terms of the positions of the three previous ones and the corresponding Distances. We present such expression and although it is similar to one already existing in the literature, based on polyspherical coordinates, a new proof is given, based on Clifford algebra, and we also explain how such expression can be useful in BP using a parameterization which depends on di−3, i. The results suggest that a master equation might exist, what is generally not believed by many researchers.

  • Euclidean Distance Geometry and Applications
    SIAM Review, 2014
    Co-Authors: Leo Liberti, Carlile Lavor, Nelson Maculan, Antonio Mucherino
    Abstract:

    Euclidean Distance Geometry is the study of Euclidean Geometry based on the concept of Distance. This is useful in several applications where the input data consists of an incomplete set of Distances, and the output is a set of points in Euclidean space that realizes the given Distances. We survey some of the theory of Euclidean Distance Geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.

  • Euclidean Distance Geometry and Applications
    SIAM Review, 2014
    Co-Authors: Leo Liberti, Carlile Lavor, Nelson Maculan, Antonio Mucherino
    Abstract:

    Euclidean Distance Geometry is the study of Euclidean Geometry based on the concept of Distance. This is useful in several applications where the input data consist of an incomplete set of Distances and the output is a set of points in Euclidean space realizing those given Distances. We survey the theory of Euclidean Distance Geometry and its most important applications, with special emphasis on molecular conformation problems.

  • solving the molecular Distance Geometry problem with inaccurate Distance data
    Web Science, 2013
    Co-Authors: Michael Souza, Carlile Lavor, Albert Muritiba, Nelson Maculan
    Abstract:

    We present a new iterative algorithm for the molecular Distance Geometry problem with inaccurate and sparse data, which is based on the solution of linear systems, maximum cliques, and a minimization of nonlinear least-squares function. Computational results with real protein structures are presented in order to validate our approach.

  • Distance Geometry theory methods and applications
    2013
    Co-Authors: Antonio Mucherino, Carlile Lavor, Leo Liberti, Nelson Maculan
    Abstract:

    Preface.- 1. Universal Rigidity of Bar Frameworks in General Position (A. Alfakih).- 2. Mixed Volume and Distance Geometry Techniques for Counting Euclidean Embeddings of Rigid Graphs (I. Emiris, E. Tsigaridas, A. Varvitsiotis).- 3. (The discretizable molecular Distance Geometry Problem Seems Easier on Proteins (L. Liberti, C. Lavor, A. Mucherino).- 4. Spheres Unions and Intersections and Some of Their Applications in Molecular Modeling (M. Petitjean).- 5. Is the Distance Geometry Problem in NP? (N. Beeker, S. Gaubert, C. Glusa, L. Liberti).- 6. Solving Spatial Constraints with Generalized Distance Geometry (L. Yang).- 7. A Topological Interpretation of the Walk Distances (P. Chebotarev, M. Deza).- 8. Distance Geometry Methods for Protein Structure Determination (Z. Voller, Z. Wu).- 9. Solving the discretizable molecular Distance Geometry problem by multiple realization trees (P. Nucci, L. Nogueira, C. Lavor).- 10.-ASAP - An Eigenvector Synchronization Algorithm for the Graph Realization Problem (M. Cucuringu).- 11. Global Optimization for Atomic Cluster Distance Geometry Problems (M. Locatelli, F. Schoen).- 12. Solving molecular Distance Geometry problems using a continuous optimization approach (R. Lima, J.M. Martinez).- 13. DC Programming Approaches for Distance Geometry Problems (H. Thi, T. Dinh).- 14. Stochastic Proximity Embedding (D. Agrafiotis, D. Bandyopadhyay, E. Yang).- 15. Distance Geometry for Realistic Molecular Conformations.- 16. Distance Geometry in Structural Biology (T. Malliavin, A. Mucherino, M. Nilges).- 17. Using a Distributed SDP Approach to Solve Simulated Protein Molecular Conformation Problems (X. Fang, K-C. Toh).- 18. An Overview on Protein Structure Determintion by NMR - Historical and Future Perspectives of the Use of Distance Geometry Methods.-Index.

Subhajit Mazumdar - One of the best experts on this subject based on the ideXlab platform.

  • triangle diagram Distance Geometry and symmetries of feynman integrals
    Journal of High Energy Physics, 2020
    Co-Authors: Barak Kol, Subhajit Mazumdar
    Abstract:

    We study the most general triangle diagram through the Symmetries of Feynman Integrals (SFI) approach. The SFI equation system is obtained and presented in a simple basis. The system is solved providing a novel derivation of an essentially known expression. We stress a description of the underlying Geometry in terms of the Distance Geometry of a tetrahedron discussed by Davydychev-Delbourgo [1], a tetrahedron which is the dual on-shell diagram. In addition, the singular locus is identified and the diagram’s value on the locus’s two components is expressed as a linear combination of descendant bubble diagrams. The massless triangle and the associated magic connection are revisited.