AlgorithmXXX: Efficient Atlasing and Search of Configuration Spaces of Point-Sets Constrained by Distance Intervals

For configurations of point-sets that are pairwise constrained by distance intervals, the EASAL software implements a suite of algorithms that characterize the structure and geometric properties of the configuration space. The algorithms generate, describe, and explore these configuration spaces using generic rigidity properties, classical results for stratification of semi-algebraic sets, and new results for efficient sampling by convex parametrization. The article reviews the key theoretical underpinnings, major algorithms, and their implementation. The article outlines the main applications such as the computation of free energy and kinetics of assembly of supramolecular structures or of clusters in colloidal and soft materials. In addition, the article surveys select experimental results and comparisons.

[1]  R. McKenna,et al.  Comparative Analysis of Adeno-Associated Virus Capsid Stability and Dynamics , 2013, Journal of Virology.

[2]  Pramodita Sharma.  2012 , 2013, Les 25 ans de l’OMC: Une rétrospective en photos.

[3]  O. L. Weaver,et al.  Nucleation in short-range attractive colloids: ordering and symmetry of clusters. , 2012, Langmuir : the ACS journal of surfaces and colloids.

[4]  E. Coutsias,et al.  Topology of cyclo-octane energy landscape. , 2010, The Journal of chemical physics.

[5]  W. Heckl.  Molecular Self-Assembly , 2002 .

[6]  Jun Tan,et al.  Efficient calculation of configurational entropy from molecular simulations by combining the mutual‐information expansion and nearest‐neighbor methods , 2008, J. Comput. Chem..

[7]  F. Khan,et al.  Physicochemical study of cationic gemini surfactant butanediyl-1,4-bis(dimethyldodecylammonium bromide) with various counterions in aqueous solution , 2012 .

[8]  Meera Sitharam,et al.  Robustness measure for an adeno-associated viral shell self-assembly is accurately predicted by configuration space atlasing using EASAL , 2012, BCB.

[9]  E. Katchalski‐Katzir,et al.  Molecular surface recognition: determination of geometric fit between proteins and their ligands by correlation techniques. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[10]  J. Doye,et al.  Energy landscapes of colloidal clusters: thermodynamics and rearrangement mechanisms. , 2012, Nanoscale.

[11]  Janet E. Jones.  On the determination of molecular fields. III.—From crystal measurements and kinetic theory data , 1924 .

[12]  Matthew Kahle.  Sparse Locally-Jammed Disk Packings , 2012 .

[13]  John F. Canny,et al.  A new algebraic method for robot motion planning and real geometry , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[14]  Matthew Kahle,et al.  Random Geometric Complexes , 2009, Discret. Comput. Geom..

[15]  L. Guibas,et al.  Topological methods for exploring low-density states in biomolecular folding pathways. , 2008, The Journal of chemical physics.

[16]  S. Basu,et al.  COMPUTING ROADMAPS OF SEMI-ALGEBRAIC SETS ON A VARIETY , 1999 .

[17]  Harshinder Singh,et al.  Nearest‐neighbor nonparametric method for estimating the configurational entropy of complex molecules , 2007, J. Comput. Chem..

[18]  M. Brenner,et al.  Minimal energy clusters of hard spheres with short range attractions. , 2009, Physical review letters.

[19]  Jiguo Su,et al.  Uncovering the Properties of Energy-Weighted Conformation Space Networks with a Hydrophobic-Hydrophilic Model , 2009, International journal of molecular sciences.

[20]  Herbert Edelsbrunner,et al.  Local Search Heuristic for Rigid Protein Docking , 2004, WABI.

[21]  H. Grubmüller,et al.  Estimating Absolute Configurational Entropies of Macromolecules: The Minimally Coupled Subspace Approach , 2010, PloS one.

[22]  Juan Jesús Pérez,et al.  Complete maps of molecular‐loop conformational spaces , 2008, J. Comput. Chem..

[23]  S. Gortler,et al.  A geometrical approach to computing free-energy landscapes from short-ranged potentials , 2012, Proceedings of the National Academy of Sciences.

[24]  F. Stillinger,et al.  Jamming in hard sphere and disk packings , 2004 .

[25]  C. O’Hern,et al.  Structure of finite sphere packings via exact enumeration: implications for colloidal crystal nucleation. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  M. Karplus,et al.  Method for estimating the configurational entropy of macromolecules , 1981 .

[27]  H. Edelsbrunner,et al.  Accurate Protein Docking by Shape Complementarity Alone , 2022 .

[28]  Yuliy Baryshnikov,et al.  Min-type Morse theory for configuration spaces of hard spheres , 2011, ArXiv.

[29]  Janet E. Jones.  On the determination of molecular fields. —II. From the equation of state of a gas , 1924 .

[30]  Jose C. Flores-Canales,et al.  Fast and Flexible Geometric Method For Enhancing MC Sampling of Compact Configurations For Protein Docking Problem , 2014, 1408.2481.

[31]  Jean-Paul Watson,et al.  Topology of cyclo-octane energy landscape. , 2010, The Journal of chemical physics.

[32]  Lydia E. Kavraki,et al.  Probabilistic roadmaps for path planning in high-dimensional configuration spaces , 1996, IEEE Trans. Robotics Autom..

[33]  G. Carlsson,et al.  Statistical topology via Morse theory, persistence and nonparametric estimation , 2009, 0908.3668.

[34]  Yung-chen Lu.  Thom-Whitney Stratification Theory , 1976 .

[35]  M. Sitharam,et al.  Best of Both Worlds: Uniform sampling in Cartesian and Cayley Molecular Assembly Configuration Space , 2014, 1409.0956.

[36]  Dinesh Manocha,et al.  Topology preserving approximation of free configuration space , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[37]  Simonis Priscilla,et al.  アフリカのカミキリムシ科Prosopocera lactator(Cerambycidae)の緑がかった白スケール内の光子多結晶 , 2012 .

[38]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[39]  T. Conlon,et al.  Mutational Analysis of the Adeno-Associated Virus Type 2 (AAV2) Capsid Gene and Construction of AAV2 Vectors with Altered Tropism , 2000, Journal of Virology.

[40]  Miklós Bóna,et al.  Symmetry in Sphere-Based Assembly Configuration Spaces , 2016, Symmetry.

[41]  Léonard Jaillet,et al.  Path Planning with Loop Closure Constraints Using an Atlas-Based RRT , 2011, ISRR.

[42]  Ioan Andricioaei,et al.  On the calculation of entropy from covariance matrices of the atomic fluctuations , 2001 .

[43]  Meera Sitharam,et al.  Characterizing Graphs with Convex and Connected Cayley Configuration Spaces , 2010, Discret. Comput. Geom..

[44]  John F. Canny,et al.  Computing Roadmaps of General Semi-Algebraic Sets , 1991, Comput. J..

[45]  Meera Sitharam,et al.  EASAL (Efficient Atlasing, Analysis and Search of Molecular Assembly Landscapes) , 2012, BICoB.

[46]  D. Wales.  Energy landscapes of clusters bound by short-ranged potentials. , 2010, Chemphyschem : a European journal of chemical physics and physical chemistry.

[47]  Michael K. Gilson,et al.  ''Mining minima'': Direct computation of conformational free energy , 1997 .

[48]  C. Peirce.  An unpublished manuscript) , 2016 .

[49]  Michael A. Bevan,et al.  Free energy landscapes for colloidal crystal assembly , 2011 .

[50]  Bruce Tidor,et al.  Efficient calculation of molecular configurational entropies using an information theoretic approximation. , 2012, The journal of physical chemistry. B.

[51]  Michael K Gilson,et al.  Extraction of configurational entropy from molecular simulations via an expansion approximation. , 2007, The Journal of chemical physics.

[52]  J. Maxwell,et al.  XLV. On reciprocal figures and diagrams of forces , 1864 .

[53]  Guido Caldarelli,et al.  Uncovering the topology of configuration space networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Matthew Kahle,et al.  Computational topology for configuration spaces of hard disks , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  Ruth Nussinov,et al.  Efficient Unbound Docking of Rigid Molecules , 2002, WABI.

[56]  Lydia E. Kavraki,et al.  Analysis of probabilistic roadmaps for path planning , 1998, IEEE Trans. Robotics Autom..

[57]  Diego Prada-Gracia,et al.  Exploring the Free Energy Landscape: From Dynamics to Networks and Back , 2009, PLoS Comput. Biol..

[58]  James Clerk Maxwell,et al.  The Scientific Papers of James Clerk Maxwell: On Reciprocal Figures and Diagrams of Forces , 2011 .

[59]  R. Hoy.  Structure and dynamics of model colloidal clusters with short-range attractions. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  Ruth Nussinov,et al.  PatchDock and SymmDock: servers for rigid and symmetric docking , 2005, Nucleic Acids Res..