1
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Lamura A. Excluded volume effects on tangentially driven active ring polymers. Phys Rev E 2024; 109:054611. [PMID: 38907431 DOI: 10.1103/physreve.109.054611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2023] [Accepted: 05/08/2024] [Indexed: 06/24/2024]
Abstract
The conformational and dynamical properties of active ring polymers are studied by numerical simulations. The two-dimensionally confined polymer is modeled as a closed bead-spring chain, driven by tangential forces, put in contact with a heat bath described by the Brownian multiparticle collision dynamics. Both phantom polymers and chains comprising excluded volume interactions are considered for different bending rigidities. The size and shape are found to be dependent on persistence length, driving force, and bead mutual exclusion. The lack of excluded volume interactions is responsible for a shrinkage of active rings when increasing driving force in the flexible limit, while the presence induces a moderate swelling of chains. The internal dynamics of flexible phantom active rings shows activity-enhanced diffusive behavior at large activity values while, in the case of self-avoiding active chains, it is characterized by active ballistic motion not depending on stiffness. The long-time dynamics of active rings is marked by rotational motion whose period scales as the inverse of the applied tangential force, irrespective of persistence length and beads' self-exclusion.
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Affiliation(s)
- A Lamura
- Istituto Applicazioni Calcolo, Consiglio Nazionale delle Ricerche (CNR), Via Amendola 122/D, 70126 Bari, Italy
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2
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Shin S, Shi G, Cho HW, Thirumalai D. Transcription-induced active forces suppress chromatin motion. Proc Natl Acad Sci U S A 2024; 121:e2307309121. [PMID: 38489381 PMCID: PMC10963020 DOI: 10.1073/pnas.2307309121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 02/06/2024] [Indexed: 03/17/2024] Open
Abstract
The organization of interphase chromosomes in a number of species is starting to emerge thanks to advances in a variety of experimental techniques. However, much less is known about the dynamics, especially in the functional states of chromatin. Some experiments have shown that the motility of individual loci in human interphase chromosome decreases during transcription and increases upon inhibiting transcription. This is a counterintuitive finding because it is thought that the active mechanical force (F) on the order of ten piconewtons, generated by RNA polymerase II (RNAPII) that is presumably transmitted to the gene-rich region of the chromatin, would render it more open, thus enhancing the mobility. We developed a minimal active copolymer model for interphase chromosomes to investigate how F affects the dynamical properties of chromatin. The movements of the loci in the gene-rich region are suppressed in an intermediate range of F and are enhanced at small F values, which has also been observed in experiments. In the intermediate F, the bond length between consecutive loci increases, becoming commensurate with the distance at the minimum of the attractive interaction between nonbonded loci. This results in a transient disorder-to-order transition, leading to a decreased mobility during transcription. Strikingly, the F-dependent change in the locus dynamics preserves the organization of the chromosome at [Formula: see text]. Transient ordering of the loci, which is not found in the polymers with random epigenetic profiles, in the gene-rich region might be a plausible mechanism for nucleating a dynamic network involving transcription factors, RNAPII, and chromatin.
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Affiliation(s)
- Sucheol Shin
- Department of Chemistry, The University of Texas at Austin, Austin, TX78712
| | - Guang Shi
- Department of Chemistry, The University of Texas at Austin, Austin, TX78712
- Department of Materials Science, University of Illinois, Urbana, IL61801
| | - Hyun Woo Cho
- Department of Fine Chemistry and Center for Functional Biomaterials, Seoul National University of Science and Technology, Seoul01811, Republic of Korea
| | - D. Thirumalai
- Department of Chemistry, The University of Texas at Austin, Austin, TX78712
- Department of Physics, The University of Texas at Austin, Austin, TX78712
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3
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Miranda JP, Locatelli E, Valeriani C. Self-Organized States from Solutions of Active Ring Polymers in Bulk and under Confinement. J Chem Theory Comput 2024; 20:1636-1645. [PMID: 38153343 DOI: 10.1021/acs.jctc.3c00818] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2023]
Abstract
In the present work, we study, by means of numerical simulations, the structural and dynamical behavior of a suspension of active ring polymers in bulk and under lateral confinement. At high activity, when changing the distance between the confining planes and the polymers' density, we identify the emergence of a self-organized dynamical state, characterized by the coexistence of slowly diffusing clusters of rotating disks and faster rings moving in between them. We further assess that self-organization is robust in a range of polymer sizes, and we identify a critical value of the activity, necessary to trigger cluster formation. This system has distinctive features resembling at the same time polymers, liquid crystals, and active systems, where the interplay between activity, topology, and confinement leads to a spontaneous segregation in an initially one-component solution.
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Affiliation(s)
- Juan Pablo Miranda
- Dep. Est. de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid, 28040 Madrid, Spain
- GISC - Grupo Interdisciplinar de Sistemas Complejos, 28040 Madrid, Spain
| | - Emanuele Locatelli
- Department of Physics and Astronomy, University of Padova, 35131 Padova, Italy
- INFN, Sezione di Padova, via Marzolo 8, I-35131 Padova, Italy
| | - Chantal Valeriani
- Dep. Est. de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid, 28040 Madrid, Spain
- GISC - Grupo Interdisciplinar de Sistemas Complejos, 28040 Madrid, Spain
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4
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Vatin M, Kundu S, Locatelli E. Conformation and dynamics of partially active linear polymers. SOFT MATTER 2024; 20:1892-1904. [PMID: 38323323 DOI: 10.1039/d3sm01162c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2024]
Abstract
We perform numerical simulations of isolated, partially active polymers, driven out-of-equilibrium by a fraction of their monomers. We show that, if the active beads are all gathered in a contiguous block, the position of the section along the chain determines the conformational and dynamical properties of the system. Notably, one can modulate the diffusion coefficient of the polymer from active-like to passive-like just by changing the position of the active block. Further, we show that a slight modification of the self-propulsion rule may give rise to an enhancement of diffusion under certain conditions, despite a decrease of the overall polymer activity. Our findings may help in the modelisation of active biophysical systems, such as filamentous bacteria or worms.
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Affiliation(s)
- Marin Vatin
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy.
- INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Sumanta Kundu
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy.
- INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
- International School for Advanced Studies (SISSA), 34136, Trieste, Italy
| | - Emanuele Locatelli
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy.
- INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
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5
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Tan F, Wang J, Yan R, Zhao N. Forced and spontaneous translocation dynamics of a semiflexible active polymer in two dimensions. SOFT MATTER 2024; 20:1120-1132. [PMID: 38224190 DOI: 10.1039/d3sm01409f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/16/2024]
Abstract
Polymer translocation is a fundamental topic in non-equilibrium physics and is crucially important to many biological processes in life. In the present work, we adopt two-dimensional Langevin dynamics simulations to study the forced and spontaneous translocation dynamics of an active filament. The influence of polymer stiffness on the underlying dynamics is explicitly analyzed. For the forced translocation, the results show a robust stiffness-induced inhibition, and the translocation time exhibits a dual-exponent scaling relationship with the bending modulus. Tension propagation (TP) is also examined, where we find prominent modifications in terms of both activity and stiffness. For spontaneous translocation into a pure solvent, the translocation time is almost independent of the polymer stiffness. However, when the polymer is translocated into a porous medium, an intriguing non-monotonic alteration of translocation time with increasing chain stiffness is demonstrated. The semiflexible chain is beneficial for translocation while the rigid chain is not conducive. Stiffness regulation on the diffusion dynamics of the polymer in porous media shows a consistent scenario. The interplay of activity, stiffness, and porous crowding provides a new mechanism for understanding the non-trivial translocation dynamics of an active filament in complex environments.
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Affiliation(s)
- Fei Tan
- College of Chemistry, Sichuan University, Chengdu 610064, China.
| | - Jingli Wang
- College of Chemistry, Sichuan University, Chengdu 610064, China.
| | - Ran Yan
- College of Chemistry, Sichuan University, Chengdu 610064, China.
| | - Nanrong Zhao
- College of Chemistry, Sichuan University, Chengdu 610064, China.
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6
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Tišma M, Janissen R, Antar H, Martin-Gonzalez A, Barth R, Beekman T, van der Torre J, Michieletto D, Gruber S, Dekker C. Dynamic ParB-DNA interactions initiate and maintain a partition condensate for bacterial chromosome segregation. Nucleic Acids Res 2023; 51:11856-11875. [PMID: 37850647 PMCID: PMC10681803 DOI: 10.1093/nar/gkad868] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Revised: 09/05/2023] [Accepted: 09/26/2023] [Indexed: 10/19/2023] Open
Abstract
In most bacteria, chromosome segregation is driven by the ParABS system where the CTPase protein ParB loads at the parS site to trigger the formation of a large partition complex. Here, we present in vitro studies of the partition complex for Bacillus subtilis ParB, using single-molecule fluorescence microscopy and AFM imaging to show that transient ParB-ParB bridges are essential for forming DNA condensates. Molecular Dynamics simulations confirm that condensation occurs abruptly at a critical concentration of ParB and show that multimerization is a prerequisite for forming the partition complex. Magnetic tweezer force spectroscopy on mutant ParB proteins demonstrates that CTP hydrolysis at the N-terminal domain is essential for DNA condensation. Finally, we show that transcribing RNA polymerases can steadily traverse the ParB-DNA partition complex. These findings uncover how ParB forms a stable yet dynamic partition complex for chromosome segregation that induces DNA condensation and segregation while enabling replication and transcription.
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Affiliation(s)
- Miloš Tišma
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, the Netherlands
| | - Richard Janissen
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, the Netherlands
| | - Hammam Antar
- Department of Fundamental Microbiology, Faculty of Biology and Medicine, University of Lausanne, Lausanne, Switzerland
| | - Alejandro Martin-Gonzalez
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, the Netherlands
| | - Roman Barth
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, the Netherlands
| | - Twan Beekman
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, the Netherlands
| | - Jaco van der Torre
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, the Netherlands
| | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK
- MRC Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh, Edinburgh, UK
| | - Stephan Gruber
- Department of Fundamental Microbiology, Faculty of Biology and Medicine, University of Lausanne, Lausanne, Switzerland
| | - Cees Dekker
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, the Netherlands
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7
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Panda A, Winkler RG, Singh SP. Characteristic features of self-avoiding active Brownian polymers under linear shear flow. SOFT MATTER 2023; 19:8577-8586. [PMID: 37905462 DOI: 10.1039/d3sm01334k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
We present Brownian dynamics simulation results of a flexible linear polymer with excluded-volume interactions under shear flow in the presence of active noise. The active noise strongly affects the polymer's conformational and dynamical properties, such as the stretching in the flow direction and compression in the gradient direction, shear-induced alignment, and shear viscosity. In the asymptotic limit of large activities and shear rates, the power-law scaling exponents of these quantities differ significantly from those of passive polymers. The chain's shear-induced stretching at a given shear rate is reduced by active noise, and it displays a non-monotonic behavior, where an initial polymer compression is followed by its stretching with increasing active force. The compression of the polymer in the gradient direction follows the relation ∼WiPe-3/4 as a function of the activity-dependent Weissenberg number WiPe, which differs from the scaling observed in passive systems ∼WiPe-1/2. The flow-induced alignment at large Péclet numbers Pe ≫ 1, where Pe is the Péclet number, and large shear rates WiPe ≫ 1 displays the scaling behavior WiPe-1/2, with an exponent differing from the passive value -1/3. Furthermore, the polymer's zero-shear viscosity displays a non-monotonic behavior, decreasing in an intermediate activity regime due to excluded-volume interactions and increasing again for large Pe. Shear thinning appears with increasing Weissenberg number with the power-laws WiPe-1/2 and WiPe-3/4 for passive and active polymers, respectively. In addition, our simulation results are compared with the results of an analytical approach, which predicts quantitatively similar behaviors for the various aforementioned physical quantities.
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Affiliation(s)
- Arindam Panda
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India.
| | - Roland G Winkler
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52428 Jülich, Germany.
| | - Sunil P Singh
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India.
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8
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Jain N, Thakur S. Structure and dynamics of chemically active ring polymers: swelling to collapse. SOFT MATTER 2023; 19:7358-7369. [PMID: 37740385 DOI: 10.1039/d3sm00839h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/24/2023]
Abstract
The ring structures are common in many synthetic or natural systems and experience both local and long-range forces by chemical sensing. This work is an effort to investigate the structural and dynamical properties of a chemically active ring in an explicit solvent bath utilizing hybrid molecular dynamics (MD) and multiparticle collision dynamics (MPCD) simulation techniques. We show that by tuning the chemical properties of the ring, it can be converted from a chemo-attractant to a chemo-repellent, thereby changing the steady state to be either collapsed or swelled as compared to its passive limit. We quantify these observations by comparing the scaling laws, local structures and the dynamics of active and passive rings. Furthermore, we show the impact of varying numbers of active sites by calculating the contact probability of the collapse state that highlights diverse structures. We also analyze the dynamics of the ring by finding the relaxation time and the mean square displacement of the centre of mass. A faster relaxation with enhanced diffusion is observed for the active rings.
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Affiliation(s)
- Namita Jain
- Department of Physics, Indian Institute of Science Education and Research Bhopal, Bhopal 462066, India.
| | - Snigdha Thakur
- Department of Physics, Indian Institute of Science Education and Research Bhopal, Bhopal 462066, India.
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9
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Goychuk A, Kannan D, Chakraborty AK, Kardar M. Polymer folding through active processes recreates features of genome organization. Proc Natl Acad Sci U S A 2023; 120:e2221726120. [PMID: 37155885 PMCID: PMC10194017 DOI: 10.1073/pnas.2221726120] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Accepted: 04/02/2023] [Indexed: 05/10/2023] Open
Abstract
From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.
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Affiliation(s)
- Andriy Goychuk
- Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Deepti Kannan
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Arup K. Chakraborty
- Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA02139
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA02139
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA02139
- Ragon Institute of Massachusetts General Hospital, Massachusetts Institute of Technology and Harvard University, Cambridge, MA02139
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA02139
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10
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Yan R, Tan F, Wang J, Zhao N. Conformation and dynamics of an active filament in crowded media. J Chem Phys 2023; 158:114905. [PMID: 36948796 DOI: 10.1063/5.0142559] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/04/2023] Open
Abstract
The structural and dynamical properties of active filamentous objects under macromolecular crowding have a great relevance in biology. By means of Brownian dynamics simulations, we perform a comparative study for the conformational change and diffusion dynamics of an active chain in pure solvents and in crowded media. Our result shows a robust compaction-to-swelling conformational change with the augment of the Péclet number. The presence of crowding facilitates self-trapping of monomers and, thus, reinforces the activity mediated compaction. In addition, the efficient collisions between the self-propelled monomers and crowders induce a coil-to-globulelike transition, indicated by a marked change of the Flory scaling exponent of the gyration radius. Moreover, the diffusion dynamics of the active chain in crowded solutions demonstrates activity-enhanced subdiffusion. The center of mass diffusion manifests rather new scaling relations with respect to both the chain length and Péclet number. The interplay of chain activity and medium crowding provides a new mechanism to understand the non-trivial properties of active filaments in complex environments.
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Affiliation(s)
- Ran Yan
- College of Chemistry, Sichuan University, Chengdu 610064, China
| | - Fei Tan
- College of Chemistry, Sichuan University, Chengdu 610064, China
| | - Jingli Wang
- College of Chemistry, Sichuan University, Chengdu 610064, China
| | - Nanrong Zhao
- College of Chemistry, Sichuan University, Chengdu 610064, China
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11
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Hu HX, Shen YF, Wang C, Luo MB. Dynamics of a two-dimensional active polymer chain with a rotation-restricted active head. SOFT MATTER 2022; 18:8820-8829. [PMID: 36367147 DOI: 10.1039/d2sm01139e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
The dynamics of a two-dimensional active polymer composed of an active Brownian particle (ABP) at the head and a passive polymer chain is investigated using Langevin dynamics simulation. The ABP experiences a self-propulsion force fs and a resistance torque M as the passive polymer chain is bonded to the edge of the ABP. M restricts the rotation of the ABP, and thus the dynamics of the ABP and that of the whole active polymer are influenced significantly. Due to this restriction, the persistence time τr, which characterizes the random rotation of the ABP, is increased significantly and changes non-monotonically with the rotational friction coefficient ηr. Our simulation results show that the effect of M on the dynamics of the active polymer can be characterized mainly by the change of τr. Moreover, the propulsive diffusion coefficient DP of the whole polymer chain originated from the self-propulsion force can be described by a scaling relation DP ∝ fs2τr/N2ηt2 with ηt the translational friction coefficient and N the polymer length. Our results show that the diffusion is promoted by the resistance torque M and τr is a key factor for the diffusion of active polymers.
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Affiliation(s)
- Han-Xian Hu
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China.
| | - Yi-Fan Shen
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China.
| | - Chao Wang
- Department of Physics, Taizhou University, Taizhou 318000, Zhejiang, China.
| | - Meng-Bo Luo
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China.
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12
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Dey R, Kundu A, Das B, Banerjee A. Experimental verification of arcsine laws in mesoscopic nonequilibrium systems. Phys Rev E 2022; 106:054113. [PMID: 36559344 DOI: 10.1103/physreve.106.054113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2022] [Accepted: 10/04/2022] [Indexed: 06/17/2023]
Abstract
A large number of processes in the mesoscopic world occur out of equilibrium, where the time evolution of a system becomes immensely important since it is driven principally by dissipative effects. Nonequilibrium steady states (NESS) represent a crucial category in such systems, where relaxation timescales are comparable to the operational timescales. In this study, we employ a model NESS stochastic system, which is comprised of a colloidal microparticle optically trapped in a viscous fluid, externally driven by a temporally correlated noise, and show that time-integrated observables such as the entropic current, the work done on the system or the work dissipated by it, follow the three Lévy arcsine laws [A. C. Barato et al., Phys. Rev. Lett. 121, 090601 (2018)0031-900710.1103/PhysRevLett.121.090601], in the large time limit. We discover that cumulative distributions converge faster to arcsine distributions when it is near equilibrium and the rate of entropy production is small, because in that case the entropic current has weaker temporal autocorrelation. We study this phenomenon by changing the strength of the added noise as well as by perturbing our system with a flow field produced by a microbubble at close proximity to the trapped particle. We confirm our experimental findings with theoretical simulations of the systems. Our work provides an interesting insight into the NESS statistics of the meso-regime, where stochastic fluctuations play a pivotal role.
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Affiliation(s)
- Raunak Dey
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Mohanpur, West Bengal 741246, India and School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Avijit Kundu
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Mohanpur, West Bengal 741246, India
| | - Biswajit Das
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Mohanpur, West Bengal 741246, India
| | - Ayan Banerjee
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Mohanpur, West Bengal 741246, India
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13
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Mao DJ, Qin CR, Tian WD. Kick effect of enzymes causes filament compression. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:284003. [PMID: 35477158 DOI: 10.1088/1361-648x/ac6b09] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2021] [Accepted: 04/27/2022] [Indexed: 06/14/2023]
Abstract
We investigate the influence of enzymes on the structure and dynamics of a filament by dissipative particle dynamics simulations. Enzyme exerts a kick force on the filament monomer. We pay particular attention to two factors: the magnitude of kick force and enzyme concentration. Large kick force as well as high enzyme concentration prefers a remarkable compression of the filament reminiscent of the effective depletion interaction owing to an effective increase in enzyme size and the reduction of solvent quality. Additionally, the kick effect gives rise to an increase of enzyme density from the center-of-mass of the filament to its periphery. Moreover, the increase of enzyme concentration and kick force also causes a decrease in relaxation time. Our finding is helpful to understand the role of catalytic force in chemo-mechano-biological function and the filament behavior under chemical reaction via kick-induced change of solvent quality.
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Affiliation(s)
- Dan-Jian Mao
- Center for Soft Condensed Matter Physics & Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, People's Republic of China
| | - Chao-Ran Qin
- Center for Soft Condensed Matter Physics & Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, People's Republic of China
| | - Wen-de Tian
- Center for Soft Condensed Matter Physics & Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, People's Republic of China
- Department of Chemical Engineering, Macromolecular Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States of America
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14
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Affiliation(s)
- Namita Jain
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462066, India
| | - Snigdha Thakur
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462066, India
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15
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Paul S, Majumder S, Das SK, Janke W. Effects of alignment activity on the collapse kinetics of a flexible polymer. SOFT MATTER 2022; 18:1978-1990. [PMID: 35023525 DOI: 10.1039/d1sm01055g] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The dynamics of various biological filaments can be understood within the framework of active polymer models. Here we consider a bead-spring model for a flexible polymer chain in which the active interaction among the beads is introduced via an alignment rule adapted from the Vicsek model. Following quenching from the high-temperature coil phase to a low-temperature state point, we study the coarsening kinetics via molecular dynamics (MD) simulations using the Langevin thermostat. For the passive polymer case the low-temperature equilibrium state is a compact globule. The results from our MD simulations reveal that though the globular state is also the typical final state in the active case, the nonequilibrium pathways to arrive at such a state differ from the picture for the passive case due to the alignment interaction among the beads. We notice that deviations from the intermediate "pearl-necklace"-like arrangement, which is observed in the passive case, and the formation of more elongated dumbbell-like structures increase with increasing activity. Furthermore, it appears that while a small active force on the beads certainly makes the coarsening process much faster, there exists a nonmonotonic dependence of the collapse time on the strength of active interaction. We quantify these observations by comparing the scaling laws for the collapse time and growth of pearls with the passive case.
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Affiliation(s)
- Subhajit Paul
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
| | - Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore-560064, India.
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
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16
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Shen C, Qin CR, Xu TL, Chen K, Tian WD. Structure and dynamics of an active polymer adsorbed on the surface of a cylinder. SOFT MATTER 2022; 18:1489-1497. [PMID: 35089305 DOI: 10.1039/d1sm01658j] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The structure and dynamics of an active polymer on a smooth cylindrical surface are studied by Brownian dynamics simulations. The effect of an active force on the polymer adsorption behavior and the combined effect of chain mobility, length N, rigidity κ, and cylinder radius, R, on the phase diagrams are systemically investigated. We find that complete adsorption is replaced by the irregular alternative adsorption/desorption process at a large driving force. Three typical (spiral, helix-like, and rod-like) conformations of the active polymer are observed, dependent on N, κ, and R. Dynamically, the polymer shows rotational motion in the spiral state, snake-like motion in the intermediate state, and straight translational motion without turning back in the rod-like state. In the spiral state, we find that the rotation velocity ω and the chain length follow a power-law relation ω ∼ N-0.42, consistent with the torque-balance theory of general Archimedean spirals. And the polymer shows super-diffusive behavior along the cylinder for a long time in the helix-like and rod-like states. Our results highlight that the mobility, rigidity, and curvature of surface can be used to regulate the polymer behavior.
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Affiliation(s)
- Chen Shen
- Center for Soft Condensed Matter Physics & Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, China.
| | - Chao-Ran Qin
- Center for Soft Condensed Matter Physics & Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, China.
| | - Tian-Liang Xu
- Center for Soft Condensed Matter Physics & Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, China.
| | - Kang Chen
- Center for Soft Condensed Matter Physics & Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, China.
| | - Wen-de Tian
- Center for Soft Condensed Matter Physics & Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, China.
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17
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Spatial organization of chromosomes leads to heterogeneous chromatin motion and drives the liquid- or gel-like dynamical behavior of chromatin. Genome Res 2021; 32:28-43. [PMID: 34963660 PMCID: PMC8744683 DOI: 10.1101/gr.275827.121] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Accepted: 12/02/2021] [Indexed: 11/25/2022]
Abstract
Chromosome organization and dynamics are involved in regulating many fundamental processes such as gene transcription and DNA repair. Experiments unveiled that chromatin motion is highly heterogeneous inside cell nuclei, ranging from a liquid-like, mobile state to a gel-like, rigid regime. Using polymer modeling, we investigate how these different physical states and dynamical heterogeneities may emerge from the same structural mechanisms. We found that the formation of topologically associating domains (TADs) is a key driver of chromatin motion heterogeneity. In particular, we showed that the local degree of compaction of the TAD regulates the transition from a weakly compact, fluid state of chromatin to a more compact, gel state exhibiting anomalous diffusion and coherent motion. Our work provides a comprehensive study of chromosome dynamics and a unified view of chromatin motion enabling interpretation of the wide variety of dynamical behaviors observed experimentally across different biological conditions, suggesting that the "liquid" or "solid" state of chromatin are in fact two sides of the same coin.
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18
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Starkov D, Parfenyev V, Belan S. Conformational statistics of non-equilibrium polymer loops in Rouse model with active loop extrusion. J Chem Phys 2021; 154:164106. [PMID: 33940823 DOI: 10.1063/5.0048942] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Motivated by the recent experimental observations of the DNA loop extrusion by protein motors, in this paper, we investigate the statistical properties of the growing polymer loops within the ideal chain model. The loop conformation is characterized statistically by the mean gyration radius and the pairwise contact probabilities. It turns out that a single dimensionless parameter, which is given by the ratio of the loop relaxation time over the time elapsed since the start of extrusion, controls the crossover between near-equilibrium and highly non-equilibrium asymptotics in the statistics of the extruded loop, regardless of the specific time dependence of the extrusion velocity. In addition, we show that two-sided and one-sided loop extruding motors produce the loops with almost identical properties. Our predictions are based on two rigorous semi-analytical methods accompanied by asymptotic analysis of slow and fast extrusion limits.
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Affiliation(s)
- Dmitry Starkov
- Landau Institute for Theoretical Physics, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia and National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000 Moscow, Russia
| | - Vladimir Parfenyev
- Landau Institute for Theoretical Physics, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia and National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000 Moscow, Russia
| | - Sergey Belan
- Landau Institute for Theoretical Physics, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia and National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000 Moscow, Russia
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19
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Papale A, Smrek J, Rosa A. Nanorheology of active-passive polymer mixtures differentiates between linear and ring polymer topology. SOFT MATTER 2021; 17:7111-7117. [PMID: 34254620 DOI: 10.1039/d1sm00665g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We study the motion of dispersed nanoprobes in entangled active-passive polymer mixtures. By comparing the two architectures of linear vs. unconcatenated and unknotted circular polymers, we demonstrate that novel, rich physics emerge. For both polymer architectures, nanoprobes of size smaller than the entanglement threshold of the solution move faster as activity is increased and more energy is pumped in the system. For larger nanoprobes, a surprising phenomenon occurs: while in linear solutions they move qualitatively as before, in active-passive ring solutions nanoprobes decelerate with respect to the purely passive conditions. We rationalize this effect in terms of the non-equilibrium, topology-dependent association (clustering) of nanoprobes to the cold component of the ring mixture reminiscent of the recently discovered [Weber et al., Phys. Rev. Lett., 2016, 116, 058301] phase separation in scalar active-passive mixtures. We conclude with a potential connection to the microrheology of the chromatin in the nuclei of the cells.
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Affiliation(s)
- Andrea Papale
- SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy.
| | - Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria.
| | - Angelo Rosa
- SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy.
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20
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Locatelli E, Bianco V, Malgaretti P. Activity-Induced Collapse and Arrest of Active Polymer Rings. PHYSICAL REVIEW LETTERS 2021; 126:097801. [PMID: 33750170 DOI: 10.1103/physrevlett.126.097801] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Revised: 01/24/2021] [Accepted: 02/01/2021] [Indexed: 06/12/2023]
Abstract
We investigate, using numerical simulations, the conformations of isolated active ring polymers. We find that their behavior depends crucially on their size: Short rings (N≲100) swell, whereas longer rings (N≳200) collapse, at sufficiently high activity. By investigating the nonequilibrium process leading to the steady state, we find a universal route driving both outcomes; we highlight the central role of steric interactions, at variance with linear chains, and of topology conservation. We further show that the collapsed rings are arrested by looking at different observables, all underlining the presence of an extremely long timescales at the steady state, associated with the internal dynamics of the collapsed section. Finally, we found that in some circumstances the collapsed state spins about its axis.
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Affiliation(s)
| | - Valentino Bianco
- Faculty of Chemistry, Chemical Physics Department, Complutense University of Madrid, Plaza de las Ciencias, Ciudad Universitaria, Madrid 28040, Spain
| | - Paolo Malgaretti
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
- IV Institute for Theoretical Physics, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Helmholtz Institut Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Fürther Strasse 248, 90429 Nürnberg, Germany
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21
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Shee A, Gupta N, Chaudhuri A, Chaudhuri D. A semiflexible polymer in a gliding assay: reentrant transition, role of turnover and activity. SOFT MATTER 2021; 17:2120-2131. [PMID: 33439187 DOI: 10.1039/d0sm01181a] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We consider a model of an extensible semiflexible filament moving in two dimensions on a motility assay of motor proteins represented explicitly as active harmonic linkers. Their heads bind stochastically to polymer segments within a capture radius, and extend along the filament in a directed fashion before detaching. Both the extension and detachment rates are load-dependent and generate an active drive on the filament. The filament undergoes a first order phase transition from the open chain to spiral conformation and shows a reentrant behavior in both the active extension and the turnover, defined as the ratio of attachment-detachment rates. Associated with the phase transition, the size and shape of the polymer change non-monotonically, and the relevant autocorrelation functions display a double-exponential decay. The corresponding correlation times show a maximum signifying the dominance of spirals. The orientational dynamics captures the rotation of spirals, and its correlation time decays with activity as a power law.
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Affiliation(s)
- Amir Shee
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India. and Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
| | - Nisha Gupta
- Department of Physics, Indian Institute of Technology Palakkad, Palakkad 678557, India
| | - Abhishek Chaudhuri
- Indian Institute of Science Education and Research Mohali, Knowledge City, Sector 81, SAS Nagar 140306, Punjab, India
| | - Debasish Chaudhuri
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India. and Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
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22
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Abstract
Chromatin ‘blobs’ were recently identified by live super-resolution imaging of labeled nucleosomes as pervasive but fleeting structural entities. However, the mechanisms leading to the formation of these blobs and their functional implications are unknown. We explore here whether causal relationships exist between parameters that characterize the chromatin blob dynamics and structure, by adapting a framework for spatio-temporal Granger-causality inference. Our analysis reveals that chromatin dynamics is a key determinant for both blob area and local density. Such causality, however, could be demonstrated only in 10–20% of the nucleus, suggesting that chromatin dynamics and structure at the nanometer scale are dominated by stochasticity. We show that the theory of active semiflexible polymers can be invoked to provide potential mechanisms leading to the organization of chromatin into blobs. Our results represent a first step toward elucidating the mechanisms that govern the dynamic and stochastic organization of chromatin in the cell nucleus.
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Affiliation(s)
- Roman Barth
- Department of Bionanoscience, Delft University of Technology , Delft, The Netherlands
| | - Genevieve Fourel
- Laboratory of Biology and Modelling of the Cell, University of Lyon, ENS de Lyon, University of Claude Bernard, CNRS UMR 5239, Inserm U1210 , Lyon, France.,Centre Blaise Pascal, ENS de Lyon , Lyon, France
| | - Haitham A Shaban
- Spectroscopy Department, Physics Division, National Research Centre , Cairo, Egypt.,Center for Advanced Imaging, Faculty of Arts and Sciences, Harvard University , Cambridge, MA, USA
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23
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Michieletto D. Non-Equilibrium Living Polymers. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1130. [PMID: 33286899 PMCID: PMC7597270 DOI: 10.3390/e22101130] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/11/2020] [Revised: 09/28/2020] [Accepted: 09/29/2020] [Indexed: 12/25/2022]
Abstract
Systems of "living" polymers are ubiquitous in industry and are traditionally realised using surfactants. Here I first review the theoretical state-of-the-art of living polymers and then discuss non-equilibrium extensions that may be realised with advanced synthetic chemistry or DNA functionalised by proteins. These systems are not only interesting in order to realise novel "living" soft matter but can also shed insight into how genomes are (topologically) regulated in vivo.
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Affiliation(s)
- Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK;
- MRC Human Genetics Unit, Institute of Genetics and Molecular Medicine, University of Edinburgh, Edinburgh EH4 2XU, UK
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24
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Tortora MMC, Salari H, Jost D. Chromosome dynamics during interphase: a biophysical perspective. Curr Opin Genet Dev 2020; 61:37-43. [DOI: 10.1016/j.gde.2020.03.001] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Revised: 02/24/2020] [Accepted: 03/02/2020] [Indexed: 12/29/2022]
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25
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Natali L, Caprini L, Cecconi F. How a local active force modifies the structural properties of polymers. SOFT MATTER 2020; 16:2594-2604. [PMID: 32091062 DOI: 10.1039/c9sm02258a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study the dynamics of a polymer, described as a variant of a Rouse chain, driven by an active terminal monomer (head). The local active force induces a transition from a globule-like to an elongated state, as revealed by the study of the end-to-end distance, the variance of which is analytically predicted under suitable approximations. The change in the relaxation times of the Rouse-modes produced by the local self-propulsion is consistent with the transition from globule to elongated conformations. Moreover, also the bond-bond spatial correlation for the chain head are affected by the self-propulsion and a gradient of over-stretched bonds along the chain is observed. We compare our numerical results both with the phenomenological stiff-polymer theory and several analytical predictions in the Rouse-chain approximation.
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Affiliation(s)
- Laura Natali
- Dipartimento di Fisica, Università"Sapienza", Piazzale A. Moro 5, I00185 Rome, Italy
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26
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Anand SK, Singh SP. Conformation and dynamics of a self-avoiding active flexible polymer. Phys Rev E 2020; 101:030501. [PMID: 32289970 DOI: 10.1103/physreve.101.030501] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2019] [Accepted: 02/14/2020] [Indexed: 06/11/2023]
Abstract
We investigate conformations and dynamics of a polymer considering its monomers to be active Brownian particles. This active polymer shows very intriguing physical behavior which is absent in an active Rouse chain. The chain initially shrinks with active force, which starts swelling on further increase in force. The shrinkage followed by swelling is attributed purely to excluded-volume interactions among the monomers. In the swelling regime, the chain shows a crossover from the self-avoiding behavior to the Rouse behavior with scaling exponent ν_{a}≈1/2 for end-to-end distance. The nonmonotonicity in the structure is analyzed through various physical quantities; specifically, radial distribution function of monomers, scattering time, as well as various energy calculations. The chain relaxes faster than the Rouse chain in the intermediate force regime, with a crossover in variation of relaxation time at large active force as given by a power law τ_{r}∼Pe^{-4/3} (Pe is Péclet number).
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Affiliation(s)
- Shalabh K Anand
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
| | - Sunil P Singh
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
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