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Mandal R, Sollich P. Shear-induced orientational ordering in an active glass former. Proc Natl Acad Sci U S A 2021; 118:e2101964118. [PMID: 34551973 PMCID: PMC8488658 DOI: 10.1073/pnas.2101964118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/12/2021] [Indexed: 11/18/2022] Open
Abstract
Dense assemblies of self-propelled particles that can form solid-like states also known as active or living glasses are abundant around us, covering a broad range of length scales and timescales: from the cytoplasm to tissues, from bacterial biofilms to vehicular traffic jams, and from Janus colloids to animal herds. Being structurally disordered as well as strongly out of equilibrium, these systems show fascinating dynamical and mechanical properties. Using extensive molecular dynamics simulation and a number of distinct dynamical and mechanical order parameters, we differentiate three dynamical steady states in a sheared model active glassy system: 1) a disordered state, 2) a propulsion-induced ordered state, and 3) a shear-induced ordered state. We supplement these observations with an analytical theory based on an effective single-particle Fokker-Planck description to rationalize the existence of the shear-induced orientational ordering behavior in an active glassy system without explicit aligning interactions of, for example, Vicsek type. This ordering phenomenon occurs in the large persistence time limit and is made possible only by the applied steady shear. Using a Fokker-Planck description with parameters that can be measured independently, we make testable predictions for the joint distribution of single-particle position and orientation. These predictions match well with the joint distribution measured from direct numerical simulation. Our results are of relevance for experiments exploring the rheological response of dense active colloids and jammed active granular matter systems.
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Affiliation(s)
- Rituparno Mandal
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37 077 Göttingen, Germany;
| | - Peter Sollich
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37 077 Göttingen, Germany
- Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom
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2
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Sanbonmatsu KY. Large-scale simulations of nucleoprotein complexes: ribosomes, nucleosomes, chromatin, chromosomes and CRISPR. Curr Opin Struct Biol 2019; 55:104-113. [PMID: 31125796 DOI: 10.1016/j.sbi.2019.03.004] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2019] [Accepted: 03/01/2019] [Indexed: 12/11/2022]
Abstract
Recent advances in biotechnology such as Hi-C, CRISPR/Cas9 and ribosome display have placed nucleoprotein complexes at center stage. Understanding the structural dynamics of these complexes aids in optimizing protocols and interpreting data for these new technologies. The integration of simulation and experiment has helped advance mechanistic understanding of these systems. Coarse-grained simulations, reduced-description models, and explicit solvent molecular dynamics simulations yield useful complementary perspectives on nucleoprotein complex structural dynamics. When combined with Hi-C, cryo-EM, and single molecule measurements, these simulations integrate disparate forms of experimental data into a coherent mechanism.
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3
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Ma L, Li X, Liu C. From generalized Langevin equations to Brownian dynamics and embedded Brownian dynamics. J Chem Phys 2016. [DOI: 10.1063/1.4962419] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Lina Ma
- Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802-6400, USA
| | - Xiantao Li
- Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802-6400, USA
| | - Chun Liu
- Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802-6400, USA
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Karmakar S, Dasgupta C, Sastry S. Short-Time Beta Relaxation in Glass-Forming Liquids Is Cooperative in Nature. PHYSICAL REVIEW LETTERS 2016; 116:085701. [PMID: 26967425 DOI: 10.1103/physrevlett.116.085701] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Indexed: 05/17/2023]
Abstract
Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. Using molecular dynamics simulations for three model glass-forming liquids, we show that the short-time β relaxation is cooperative in nature. Using finite-size scaling analysis, we extract a growing length scale associated with beta relaxation from the observed dependence of the beta relaxation time on the system size. We find, in qualitative agreement with the prediction of the inhomogeneous mode coupling theory, that the temperature dependence of this length scale is the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time α-relaxation regime.
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Affiliation(s)
- Smarajit Karmakar
- Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India
| | - Chandan Dasgupta
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
| | - Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
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Müller EH, Scheichl R, Shardlow T. Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation. Proc Math Phys Eng Sci 2015; 471:20140679. [PMID: 27547075 DOI: 10.1098/rspa.2014.0679] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.
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Affiliation(s)
- Eike H Müller
- Department of mathematical Sciences , University of Bath Claverton Down , Bath BA2 7AY, UK
| | - Rob Scheichl
- Department of mathematical Sciences , University of Bath Claverton Down , Bath BA2 7AY, UK
| | - Tony Shardlow
- Department of mathematical Sciences , University of Bath Claverton Down , Bath BA2 7AY, UK
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6
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Arita Y, Mazilu M, Dholakia K. Laser-induced rotation and cooling of a trapped microgyroscope in vacuum. Nat Commun 2014; 4:2374. [PMID: 23982323 PMCID: PMC3763500 DOI: 10.1038/ncomms3374] [Citation(s) in RCA: 217] [Impact Index Per Article: 21.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2013] [Accepted: 07/30/2013] [Indexed: 11/15/2022] Open
Abstract
Quantum state preparation of mesoscopic objects is a powerful playground for the elucidation of many physical principles. The field of cavity optomechanics aims to create these states through laser cooling and by minimizing state decoherence. Here we demonstrate simultaneous optical trapping and rotation of a birefringent microparticle in vacuum using a circularly polarized trapping laser beam—a microgyroscope. We show stable rotation rates up to 5 MHz. Coupling between the rotational and translational degrees of freedom of the trapped microgyroscope leads to the observation of positional stabilization in effect cooling the particle to 40 K. We attribute this cooling to the interaction between the gyroscopic directional stabilization and the optical trapping field. Quantum state preparation of mesoscopic objects is a powerful tool for the study of physics at the limits. Here, Arita et al. realise the optical trapping of a microgyroscope rotating at MHz rates in vacuum where the coupling between the rotational and translational motion cools the particle to 40 K.
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Affiliation(s)
- Yoshihiko Arita
- SUPA, School of Physics & Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK.
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7
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Długosz M, Huber GA, McCammon JA, Trylska J. Brownian dynamics study of the association between the 70S ribosome and elongation factor G. Biopolymers 2011; 95:616-27. [PMID: 21394717 PMCID: PMC3125448 DOI: 10.1002/bip.21619] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2010] [Revised: 02/28/2011] [Accepted: 02/28/2011] [Indexed: 02/01/2023]
Abstract
Protein synthesis on the ribosome involves a number of external protein factors that bind at its functional sites. One key factor is the elongation factor G (EF-G) that facilitates the translocation of transfer RNAs between their binding sites, as well as advancement of the messenger RNA by one codon. The details of the EF-G/ribosome diffusional encounter and EF-G association pathway still remain unanswered. Here, we applied Brownian dynamics methodology to study bimolecular association in the bacterial EF-G/70S ribosome system. We estimated the EF-G association rate constants at 150 and 300 mM monovalent ionic strengths and obtained reasonable agreement with kinetic experiments. We have also elucidated the details of EF-G/ribosome association paths and found that positioning of the L11 protein of the large ribosomal subunit is likely crucial for EF-G entry to its binding site.
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Affiliation(s)
- Maciej Długosz
- Interdisciplinary Centre for Mathematical and Computational Modeling, University of Warsaw, Warsaw, Poland.
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Chen YL, Lin PK, Chou CF. Generalized Force−Extension Relation for Wormlike Chains in Slit Confinement. Macromolecules 2010. [DOI: 10.1021/ma102268b] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yeng-Long Chen
- Institute of Physics and Research Center for Applied Sciences, Academia Sinica, Nangang, Taipei 11529, Taiwan
| | - Po-keng Lin
- Institute of Physics and Research Center for Applied Sciences, Academia Sinica, Nangang, Taipei 11529, Taiwan
| | - Chia-Fu Chou
- Institute of Physics and Research Center for Applied Sciences, Academia Sinica, Nangang, Taipei 11529, Taiwan
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Saw S, Ellegaard NL, Kob W, Sastry S. Structural relaxation of a gel modeled by three body interactions. PHYSICAL REVIEW LETTERS 2009; 103:248305. [PMID: 20366240 DOI: 10.1103/physrevlett.103.248305] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2009] [Indexed: 05/16/2023]
Abstract
We report a molecular dynamics simulation study of a model gel whose interaction potential is obtained by modifying the three body Stillinger-Weber model potential for silicon. The modification reduces the average coordination number and suppresses the liquid-gas phase coexistence curve. The low density, low temperature equilibrium gel that can thus form exhibits interesting dynamical behavior, including compressed exponential relaxation of density correlations. We show that motion responsible for such relaxation has ballistic character, and arises from the motion of chain segments in the gel without the restructuring of the gel network.
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Affiliation(s)
- Shibu Saw
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bangalore 560 064, India
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11
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Winter U, Geyer T. Coarse grained simulations of a small peptide: Effects of finite damping and hydrodynamic interactions. J Chem Phys 2009. [DOI: 10.1063/1.3216573] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Sun X, Lin T, Gezelter JD. Langevin dynamics for rigid bodies of arbitrary shape. J Chem Phys 2008; 128:234107. [DOI: 10.1063/1.2936991] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sweet CR, Petrone P, Pande VS, Izaguirre JA. Normal mode partitioning of Langevin dynamics for biomolecules. J Chem Phys 2008; 128:145101. [PMID: 18412479 DOI: 10.1063/1.2883966] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
We propose a novel normal mode multiple time stepping Langevin dynamics integrator called NML. The aim is to approximate the kinetics or thermodynamics of a biomolecule by a reduced model based on a normal mode decomposition of the dynamical space. Our basis set uses the eigenvectors of a mass reweighted Hessian matrix calculated with a biomolecular force field. This particular choice has the advantage of an ordering according to the eigenvalues, which have a physical meaning of being the square of the mode frequency. Low frequency eigenvalues correspond to more collective motions, whereas the highest frequency eigenvalues are the limiting factor for the stability of the integrator. In NML, the higher frequency modes are overdamped and relaxed near their energy minimum while respecting the subspace of low frequency dynamical modes. Our numerical results confirm that both sampling and rates are conserved for an implicitly solvated alanine dipeptide model, with only 30% of the modes propagated, when compared to the full model. For implicitly solvated systems, NML gives a twofold improvement in efficiency over plain Langevin dynamics for sampling a small 22 atom (alanine dipeptide) model and in excess of an order of magnitude for sampling an 882 atom (bovine pancreatic trypsin inhibitor) model, with good scaling with system size subject to the number of modes propagated. NML has been implemented in the open source software PROTOMOL.
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Affiliation(s)
- Christopher R Sweet
- Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, Indiana, 46556, USA
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Długosz M, Antosiewicz JM, Trylska J. Association of aminoglycosidic antibiotics with the ribosomal A-site studied with Brownian dynamics. J Chem Theory Comput 2008; 4:549-559. [PMID: 19343095 DOI: 10.1021/ct700210n] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Brownian dynamics methodology was applied to simulate the encounter of aminoglycosidic antibiotics with the ribosomal A-site RNA. Studied antibiotics included neamine, neomycin, ribostamycin and paromomycin which differ in chemical structure, the number of pseudo-sugar rings and the net charge. The influence of structural, electrostatic and hydrodynamic properties of antibiotics on the kinetics of their association with the ribosomal A-site was analyzed. The computed diffusion limited rates of association are of the order of 10(10)[Formula: see text] and they weakly depend on ionic strength. Prior to binding antibiotics often slide along the RNA groove with the time scale of approximately 10 ns per base pair in case of neamine. We observed that upon forming the encounter complex aminoglycosides displace from the binding pocket up to two Mg(2+) ions.
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Affiliation(s)
- Maciej Długosz
- Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University, Żwirki i Wigury 93, Warsaw 02-089, Poland
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Patriciu A, Chirikjian GS, Pappu RV. Analysis of the conformational dependence of mass-metric tensor determinants in serial polymers with constraints. J Chem Phys 2006; 121:12708-20. [PMID: 15606297 DOI: 10.1063/1.1821492] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It is well known that mass-metric tensor determinants det(G(s)) influence the equilibrium statistics and the rates of conformational transitions for polymers with constrained bond lengths and bond angles. It is now standard practice to include a Fixman-style compensating potential of the form U(c)(q(s)) proportional, variant(-k(B)T/2)ln[det(G(s))] as part of algorithms for torsional space molecular dynamics. This elegant strategy helps eliminate unwarranted biases that arise due to the imposition of holonomic constraints. However, the precise nature and extent of variation of det(G(s)) and hence ln[det(G(s))] with chain conformation and chain length has never been quantified. This type of analysis is crucial for understanding the nature of the conformational bias that the introduction of a Fixman potential aims to eliminate. Additionally, a detailed analysis of the conformational dependence of det(G(s)) will help resolve ambiguities regarding suggestions for incorporating terms related to det(G(s)) in the design of move sets in torsional space Monte Carlo simulations. In this work, we present results from a systematic study of the variation of det(G(s)) for a serial polymer with fixed bond lengths and bond angles as a function of chain conformation and chain length. This analysis requires an algorithm designed for rapid computation of det(G(s)) which simultaneously allows for a physical/geometric interpretation of the conformational dependence of det(G(s)). Consequently, we provide a detailed discussion of our adaptation of an O(n) algorithm from the robotics literature, which leads to simple recursion relations for direct evaluation of det(G(s)). Our analysis of the conformational dependence of det(G(s)) yields the following insights. (1) det(G(s)) is maximized for spatial conformers and minimized for planar conformations. (2) Previous work suggests that it is logical to expect that the conformational dependence of det(G(s)) becomes more pronounced with increase in chain length. Confirming this expectation, we provide systematic quantification of the nature of this dependency and show that the difference in det(G(s)) between spatial and planar conformers, i.e., between the maxima and minima of det(G(s)) grows systematically with chain length. Finally, we provide a brief discussion of implications of our analysis for the design of move sets in Monte Carlo simulations.
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Affiliation(s)
- Alexandru Patriciu
- Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
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Troisi A, Wong V, Ratner MA. Self-assembly on multiple length scales: A Monte Carlo algorithm with data augmentation. J Chem Phys 2005; 122:024102. [PMID: 15638567 DOI: 10.1063/1.1831256] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a Monte Carlo algorithm that allows simulations where portions of the system of variable size are moved. The algorithm requires the definition of an augmented space that contains information on the bonding between components of the system and is updated as the simulation proceeds. With this method it is possible to incorporate, within the same simulation, processes involving motion of smaller and larger portions of a given system. The algorithm is presented in general terms and illustrated for a simple one-dimensional lattice model.
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Affiliation(s)
- Alessandro Troisi
- Dipartimento di Chimica G. Ciamician, Università di Bologna, via Selmi 2, 40126 Bologna, Italy.
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Beard DA, Schlick T. Inertial stochastic dynamics. II. Influence of inertia on slow kinetic processes of supercoiled DNA. J Chem Phys 2000. [DOI: 10.1063/1.481371] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Schlick T, Beard D, Jing Huang, Strahs D, Xiaoliang Qian. Computational challenges in simulating large DNA over long times. Comput Sci Eng 2000. [DOI: 10.1109/5992.881706] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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