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A virtual pebble game to ensemble average graph rigidity

Luis C González, Hui Wang, Dennis R Livesay, Donald J Jacobs
2015 Algorithms for Molecular Biology  
The body-bar Pebble Game (PG) algorithm is commonly used to calculate network rigidity properties in proteins and polymeric materials.  ...  Results: The Virtual Pebble Game (VPG) algorithm is a MFA that retains spatial inhomogeneity in the density of constraints on all length scales.  ...  Acknowledgements Support for this work has come from NIH R01 GM073082, and partial support to Hui Wang through a Duke fellowship from Charlotte Research Institute, and a Ph.D. graduate student fellowship  ... 
doi:10.1186/s13015-015-0039-3 pmid:25904973 pmcid:PMC4406122 fatcat:27dzqynxm5hnvimmop47o2jpvy

Calculating Ensemble Averaged Descriptions of Protein Rigidity without Sampling

Luis C. González, Hui Wang, Dennis R. Livesay, Donald J. Jacobs, Jerome Mathe
2012 PLoS ONE  
We have developed a mean field Virtual Pebble Game (VPG) that represents the ensemble of networks by a single effective network.  ...  Mechanical network rigidity properties of a single conformation are efficiently calculated using the integer body-bar Pebble Game (PG) algorithm.  ...  That is, we have developed a Virtual Pebble Game (VPG) that allows for probabilistic descriptions of the network.  ... 
doi:10.1371/journal.pone.0029176 pmid:22383947 pmcid:PMC3285152 fatcat:sw3rlsem2fctletkwbwyx6576a

Generic rigidity percolation in two dimensions

D. J. Jacobs, M. F. Thorpe
1996 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Using the pebble game algorithm, the total number of floppy modes are counted exactly, and exhibit a cusp singularity in the second derivative at the transition from a rigid to a floppy structure.  ...  The fractal dimension of the spanning rigid clusters and the spanning stressed regions at the critical threshold are found to be d f ϭ1.86Ϯ0.02 and d BB ϭ1.80Ϯ0.03, respectively.  ...  ACKNOWLEDGMENTS We thank A. R. Day  ... 
doi:10.1103/physreve.53.3682 pmid:9964678 fatcat:wntkzmdvlbcnnf4usa6mnnm5ha

Rigidity and Self-Organization of Network Glasses and the Intermediate Phase [chapter]

M. F. Thorpe, M. V. Chubynsky
2001 Properties and Applications of Amorphous Materials  
These results, which involve a new graph theoretical approach called the pebble game, show that Maxwell counting is quite reliable in locating the transition from rigid to floppy.  ...  A systematic search is made to map out all rigid clusters. We show in Figure 2 (b) the end result of the pebble game applied to a simple structure. Many aspects of rigidity are displayed.  ... 
doi:10.1007/978-94-010-0914-0_7 fatcat:7wnnp4aoqvc4thcdxifctgqvpy

Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion

Dominik Budday, Sigrid Leyendecker, Henry van den Bedem
2018 Journal of Chemical Information and Modeling  
Analysis of a large, structurally diverse data set revealed that collectivity of protein motions, reported by the Shannon entropy, is significantly reduced for rigidity theory compared to normal mode approaches  ...  Here, we present an alternative, kinematic approach to rigidity analysis, which circumvents these drawbacks.  ...  ACKNOWLEDGMENTS The authors gratefully acknowledge financial support to D.B. from the Deutsche Telekom Stiftung. H.v.d.B. is supported by NIH GM123159.  ... 
doi:10.1021/acs.jcim.8b00267 pmid:30240209 pmcid:PMC6261933 fatcat:ibut7qudengubds7y6cabbbana

Constrained geometric simulation of diffusive motion in proteins

Stephen Wells, Scott Menor, Brandon Hespenheide, M F Thorpe
2005 Physical Biology  
The rigid regions in the protein are first determined, and then replaced by ghost templates which are used to guide the movements of the atoms in the protein.  ...  We describe a new computational method, FRODA (framework rigidity optimized dynamic algorithm), for exploring the internal mobility of proteins.  ...  We should like to thank Ming Lei and Maria Zavodszky for continuing discussions on geometric simulation.  ... 
doi:10.1088/1478-3975/2/4/s07 pmid:16280618 fatcat:hm4noep2dvaxtjvlgn7m4whw4u

Changes in Lysozyme Flexibility upon Mutation Are Frequent, Large and Long-Ranged

Deeptak Verma, Donald J. Jacobs, Dennis R. Livesay, Ruth Nussinov
2012 PLoS Computational Biology  
The average distance from mutation to a site with a change in flexibility is 17-20 Å .  ...  We investigate changes in human c-type lysozyme flexibility upon mutation via a Distance Constraint Model, which gives a statistical mechanical treatment of network rigidity.  ...  Key to the distance constraint model is the use of graph-rigidity algorithms, claimed in U.S. Patent 6,014,449, which has been assigned to the Board of Trustees Michigan State University.  ... 
doi:10.1371/journal.pcbi.1002409 pmid:22396637 pmcid:PMC3291535 fatcat:n5y6sluupfdubh3ffgmkyvqwqm

Nullspace Sampling with Holonomic Constraints Reveals Molecular Mechanisms of Protein Gαs

Dimitar V. Pachov, Henry van den Bedem, Charlotte M Deane
2015 PLoS Computational Biology  
However, NMA is limited to a second order expansion about a minimum of the potential energy function, which limits opportunities to observe diffusional motions.  ...  The motion centers on a dynamic hub near the nucleotide-binding site of Gαs, and radiates to helix α 4 . We find that comparative NMA-based ensembles underestimate the amplitudes of the motion.  ...  Acknowledgments We are grateful to Rasmus Fonseca for stimulating discussions and help with implementation. Author Contributions Conceived and designed the experiments: HvdB.  ... 
doi:10.1371/journal.pcbi.1004361 pmid:26218073 pmcid:PMC4517867 fatcat:gqcipv5vfzhdlizjyempiu4cle

A computational study of the use of an optimization-based method for simulating large multibody systems†

Cosmin Petra, Bogdan Gavrea, Mihai Anitescu, Florian Potra
2009 Optimization Methods and Software  
Such LCPs are generally solved by means of Lemketype algorithms and solvers such as the PATH solver proved to be robust.  ...  The present work aims at comparing the performance of several quadratic programming (QP) solvers for simulating large-scale frictional rigid-body systems.  ...  All the QPs appearing in such approaches have a sparsity structure with an incidence graph closely related to the graph with nodes in the center of the bodies and edges between bodies in potential contact  ... 
doi:10.1080/10556780902806094 fatcat:fzmt6zhh35esjf2sv5wvh2tyfu

Network rigidity at finite temperature: Relationships between thermodynamic stability, the nonadditivity of entropy, and cooperativity in molecular systems

Donald J. Jacobs, S. Dallakyan, G. G. Wood, A. Heckathorne
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
The DCM is compared to the Lifson-Roig model. It is found that network rigidity provides a mechanism for cooperativity in molecular structures including their ability to spontaneously self-organize.  ...  It is proposed that network rigidity plays a central role in balancing the energetic and entropic contributions to the free energy of bio-polymers, such as proteins.  ...  CC5141͒, and to the NIH ͑Grant No. GM48680-0952͒. We thank Dennis Livesay for many useful discussions. We also thank Professor Hansmann for sharing his raw MC simulation data with us.  ... 
doi:10.1103/physreve.68.061109 pmid:14754182 pmcid:PMC4667989 fatcat:it2uclmnsrb73pe3xfjponazm4

Flexibility Correlation between Active Site Regions Is Conserved across Four AmpC β-Lactamase Enzymes

Jenna R. Brown, Dennis R. Livesay, Alexandre G. de Brevern
2015 PLoS ONE  
Starting from a native protein structure, we generate a network rigidity topological framework (graph) where vertices correspond to atoms, and edges Correlated Active Site Flexibility in AmpC PLOS ONE  ...  In particular, the bulk of each structure is composed of a large rigid cluster, punctuated by three flexibly correlated regions located at the active site.  ...  Acknowledgments The distance constraint model relies on the pebble game graph-rigidity algorithm, which is claimed in U.S.  ... 
doi:10.1371/journal.pone.0125832 pmid:26018804 pmcid:PMC4446314 fatcat:pmsxaxe435h2tkstsxqf4gdenm

Thermodynamic Stability and Flexibility Characteristics of Antibody Fragment Complexes

Tong Li, Deeptak Verma, Malgorzata Tracka, Jose Casas-Finet, Dennis Livesay, Donald Jacobs
2013 Protein Peptide Letters  
Typically, a VL fragment has more co-rigid residue pairs when isolated compared to the scFv and Fab forms, where correlated flexibility appears upon complex formation.  ...  Global flexibility in the denatured ensemble typically decreases in the larger complexes due to domain-domain interfaces.  ...  Key to the distance constraint model is the use of graph-rigidity algorithms, claimed in U.S. Patent 6,014,449, which has been assigned to the Board of Trustees Michigan State University.  ... 
doi:10.2174/09298665113209990051 pmid:23855672 pmcid:PMC4667953 fatcat:7drty46yfrcild7doee2xq3faa

Change in protein flexibility upon complex formation: Analysis of Ras-Raf using molecular dynamics and a molecular framework approach

Holger Gohlke, Leslie A. Kuhn, David A. Case
2004 Proteins: Structure, Function, and Bioinformatics  
Similarly, FIRST assigns the ␤-sheet to the largest rigid cluster of the complex.  ...  The two methods show a very good agreement with respect to the identification of changes in flexibility in both binding partners on a local scale.  ...  ACKNOWLEDGEMENTS The present study was supported by NIH Grant RR12255 to D.C. and by NIH Mathematics in Biology grant GM67249 to L.K.  ... 
doi:10.1002/prot.20116 pmid:15211515 fatcat:rjgyixufnneg7oisa5agou5o54

Stochastic Kinetics of Viral Capsid Assembly Based on Detailed Protein Structures

Martin Hemberg, Sophia N. Yaliraki, Mauricio Barahona
2006 Biophysical Journal  
Starting from PDB files containing atomic coordinates, the algorithm builds a coarse grained description of protein oligomers based on graph rigidity.  ...  The dissociation rates are derived by interpreting the splitting of oligomers as a process of graph partitioning akin to the escape from a multidimensional well.  ...  Thorpe for permission to use the FIRST software, and for their responsiveness to our queries. We are also grateful to Gert Vriend for access to the WHAT IF software.  ... 
doi:10.1529/biophysj.105.076737 pmid:16473916 pmcid:PMC1432130 fatcat:bnxd24bv3zeupda2e2zaqn6mjm

New insight into long-range nonadditivity within protein double-mutant cycles

Andrei Y. Istomin, M. Michael Gromiha, Oleg K. Vorov, Donald J. Jacobs, Dennis R. Livesay
2007 Proteins: Structure, Function, and Bioinformatics  
Here, we test the hypothesis that the mutational effects tend to be nonadditive if two structurally well-separated mutated residues belong to the same rigid cluster within the wild type protein, and additive  ...  To the best of our knowledge, this result represents the first demonstration of a statistically significant preponderance for nonadditivity over long distances.  ...  Key to FIRST is the use of a graphrigidity algorithm that is claimed in U.S. Patent 6,014,449, which has been assigned to the Board of Trustees Michigan State University. Used with permission.  ... 
doi:10.1002/prot.21620 pmid:17803237 pmcid:PMC4667956 fatcat:q4rmzzk3zndpdaz6sdjd53funi
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