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Janssen M, Liese S, Al-Izzi SC, Carlson A. Stability of a biomembrane tube covered with proteins. Phys Rev E 2024; 109:044403. [PMID: 38755805 DOI: 10.1103/physreve.109.044403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 02/29/2024] [Indexed: 05/18/2024]
Abstract
Membrane tubes are essential structural features in cells that facilitate biomaterial transport and inter- and intracellular signaling. The shape of these tubes can be regulated by the proteins that surround and adhere to them. We study the stability of a biomembrane tube coated with proteins by combining linear stability analysis, out-of-equilibrium hydrodynamic calculations, and numerical solutions of a Helfrich-like membrane model. Our analysis demonstrates that both long- and short-wavelength perturbations can destabilize the tubes. Numerical simulations confirm the derived linear stability criteria and yield the nonlinearly perturbed vesicle shapes. Our study highlights the interplay between membrane shape and protein density, where the shape instability concurs with a redistribution of proteins into a banded pattern.
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Affiliation(s)
- Mathijs Janssen
- Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Oslo, 0315 Oslo, Norway
- Centre for Cancer Cell Reprogramming, Faculty of Medicine, University of Oslo, Montebello, N-0379 Oslo, Norway
- Norwegian University of Life Sciences, Faculty of Science and Technology, 1433 Ås, Norway
| | - Susanne Liese
- Institute of Physics, University of Augsburg, 86159 Augsburg, Germany
| | - Sami C Al-Izzi
- Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Oslo, 0315 Oslo, Norway
| | - Andreas Carlson
- Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Oslo, 0315 Oslo, Norway
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2
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Nolte DD. Coherent light scattering from cellular dynamics in living tissues. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:036601. [PMID: 38433567 DOI: 10.1088/1361-6633/ad2229] [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: 11/01/2022] [Accepted: 01/24/2024] [Indexed: 03/05/2024]
Abstract
This review examines the biological physics of intracellular transport probed by the coherent optics of dynamic light scattering from optically thick living tissues. Cells and their constituents are in constant motion, composed of a broad range of speeds spanning many orders of magnitude that reflect the wide array of functions and mechanisms that maintain cellular health. From the organelle scale of tens of nanometers and upward in size, the motion inside living tissue is actively driven rather than thermal, propelled by the hydrolysis of bioenergetic molecules and the forces of molecular motors. Active transport can mimic the random walks of thermal Brownian motion, but mean-squared displacements are far from thermal equilibrium and can display anomalous diffusion through Lévy or fractional Brownian walks. Despite the average isotropic three-dimensional environment of cells and tissues, active cellular or intracellular transport of single light-scattering objects is often pseudo-one-dimensional, for instance as organelle displacement persists along cytoskeletal tracks or as membranes displace along the normal to cell surfaces, albeit isotropically oriented in three dimensions. Coherent light scattering is a natural tool to characterize such tissue dynamics because persistent directed transport induces Doppler shifts in the scattered light. The many frequency-shifted partial waves from the complex and dynamic media interfere to produce dynamic speckle that reveals tissue-scale processes through speckle contrast imaging and fluctuation spectroscopy. Low-coherence interferometry, dynamic optical coherence tomography, diffusing-wave spectroscopy, diffuse-correlation spectroscopy, differential dynamic microscopy and digital holography offer coherent detection methods that shed light on intracellular processes. In health-care applications, altered states of cellular health and disease display altered cellular motions that imprint on the statistical fluctuations of the scattered light. For instance, the efficacy of medical therapeutics can be monitored by measuring the changes they induce in the Doppler spectra of livingex vivocancer biopsies.
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Affiliation(s)
- David D Nolte
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, United States of America
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3
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Chen T, Karedla N, Enderlein J. Measuring sub-nanometer undulations at microsecond temporal resolution with metal- and graphene-induced energy transfer spectroscopy. Nat Commun 2024; 15:1789. [PMID: 38413608 PMCID: PMC10899616 DOI: 10.1038/s41467-024-45822-x] [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: 06/01/2023] [Accepted: 02/01/2024] [Indexed: 02/29/2024] Open
Abstract
Out-of-plane fluctuations, also known as stochastic displacements, of biological membranes play a crucial role in regulating many essential life processes within cells and organelles. Despite the availability of various methods for quantifying membrane dynamics, accurately quantifying complex membrane systems with rapid and tiny fluctuations, such as mitochondria, remains a challenge. In this work, we present a methodology that combines metal/graphene-induced energy transfer (MIET/GIET) with fluorescence correlation spectroscopy (FCS) to quantify out-of-plane fluctuations of membranes with simultaneous spatiotemporal resolution of approximately one nanometer and one microsecond. To validate the technique and spatiotemporal resolution, we measure bending undulations of model membranes. Furthermore, we demonstrate the versatility and applicability of MIET/GIET-FCS for studying diverse membrane systems, including the widely studied fluctuating membrane system of human red blood cells, as well as two unexplored membrane systems with tiny fluctuations, a pore-spanning membrane, and mitochondrial inner/outer membranes.
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Affiliation(s)
- Tao Chen
- Third Institute of Physics - Biophysics, Georg August University, Friedrich-Hund-Platz 1, Göttingen, 37077, Germany
| | - Narain Karedla
- The Rosalind Franklin Institute, Harwell Campus, Didcot, OX11 OFA, UK
- Kennedy Institute of Rheumatology, University of Oxford, Roosevelt Drive, Oxford, OX3 7LF, UK
| | - Jörg Enderlein
- Third Institute of Physics - Biophysics, Georg August University, Friedrich-Hund-Platz 1, Göttingen, 37077, Germany.
- Cluster of Excellence "Multiscale Bioimaging: from Molecular Machines to Networks of Excitable Cells" (MBExC), Universitätsmedizin Göttingen, Robert-Koch-Str. 40, Göttingen, 37075, Germany.
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4
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Fossati M, Scheibner C, Fruchart M, Vitelli V. Odd elasticity and topological waves in active surfaces. Phys Rev E 2024; 109:024608. [PMID: 38491602 DOI: 10.1103/physreve.109.024608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Accepted: 01/12/2024] [Indexed: 03/18/2024]
Abstract
Odd elasticity describes active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new antisymmetric (odd) components appear in the elastic tensor. In this work we study the odd elasticity and non-Hermitian wave dynamics of active surfaces, specifically plates of moderate thickness. These odd moduli can endow the vibrational modes of the plate with a nonzero topological invariant known as the first Chern number. Within continuum elastic theory, we show that the Chern number is related to the presence of unidirectional shearing waves that are hosted at the plate's boundary. We show that the existence of these chiral edge waves hinges on a distinctive two-step mechanism. Unlike electronic Chern insulators where the magnetic field at the same time gaps the spectrum and imparts chirality, here the finite thickness of the sample gaps the shear modes, and the odd elasticity makes them chiral.
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Affiliation(s)
- Michele Fossati
- SISSA, Trieste 34136, Italy
- INFN Sezione di Trieste, Trieste 34127, Italy
| | - Colin Scheibner
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Michel Fruchart
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Vincenzo Vitelli
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, USA
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5
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Suchanek T, Kroy K, Loos SAM. Irreversible Mesoscale Fluctuations Herald the Emergence of Dynamical Phases. PHYSICAL REVIEW LETTERS 2023; 131:258302. [PMID: 38181332 DOI: 10.1103/physrevlett.131.258302] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 10/30/2023] [Indexed: 01/07/2024]
Abstract
We study fluctuating field models with spontaneously emerging dynamical phases. We consider two typical transition scenarios associated with parity-time symmetry breaking: oscillatory instabilities and critical exceptional points. An analytical investigation of the low-noise regime reveals a drastic increase of the mesoscopic entropy production toward the transitions. For an illustrative model of two nonreciprocally coupled Cahn-Hilliard fields, we find physical interpretations in terms of actively propelled interfaces and a coupling of eigenmodes of the linearized dynamics near the critical exceptional point.
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Affiliation(s)
- Thomas Suchanek
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Klaus Kroy
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Sarah A M Loos
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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6
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Rombouts J, Elliott J, Erzberger A. Forceful patterning: theoretical principles of mechanochemical pattern formation. EMBO Rep 2023; 24:e57739. [PMID: 37916772 DOI: 10.15252/embr.202357739] [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: 06/30/2023] [Revised: 09/21/2023] [Accepted: 09/27/2023] [Indexed: 11/03/2023] Open
Abstract
Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.
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Affiliation(s)
- Jan Rombouts
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Developmental Biology Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
| | - Jenna Elliott
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
| | - Anna Erzberger
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
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7
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Suchanek T, Kroy K, Loos SAM. Time-reversal and parity-time symmetry breaking in non-Hermitian field theories. Phys Rev E 2023; 108:064123. [PMID: 38243548 DOI: 10.1103/physreve.108.064123] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 11/06/2023] [Indexed: 01/21/2024]
Abstract
We study time-reversal symmetry breaking in non-Hermitian fluctuating field theories with conserved dynamics, comprising the mesoscopic descriptions of a wide range of nonequilibrium phenomena. They exhibit continuous parity-time (PT) symmetry-breaking phase transitions to dynamical phases. For two concrete transition scenarios, exclusive to non-Hermitian dynamics, namely, oscillatory instabilities and critical exceptional points, a low-noise expansion exposes a pretransitional surge of the mesoscale (informatic) entropy production rate, inside the static phases. Its scaling in the susceptibility contrasts conventional critical points (such as second-order phase transitions), where the susceptibility also diverges, but the entropy production generally remains finite. The difference can be attributed to active fluctuations in the wavelengths that become unstable. For critical exceptional points, we identify the coupling of eigenmodes as the entropy-generating mechanism, causing a drastic noise amplification in the Goldstone mode.
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Affiliation(s)
- Thomas Suchanek
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Klaus Kroy
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Sarah A M Loos
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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8
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Singha T, Polley A, Barma M. Clustering of lipids driven by integrin. SOFT MATTER 2023; 19:6814-6824. [PMID: 37654180 DOI: 10.1039/d3sm00809f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
Integrin is an important transmembrane receptor protein which remodels the actin network and anchors the cell membrane towards the extracellular matrix via mechanochemical pathways. The clustering of specific lipids and lipid-anchored proteins, which is essential for a certain type of endocytosis process, is facilitated at integrin-mediated active regions. To study this, we propose a minimal exactly solvable model which includes the interplay of stochastic shuttling between integrin on and off states with the intrinsic dynamics of the membrane. We propose a two-step mechanism in which the integrin induces an aster-like arrangement in the actin network, followed by clustering of lipids in that region. We obtain an analytic expression for the deformation and local membrane velocity, and thereby the evolution of clustering mediated by a single integrin. The deformation evolves nonmonotonically and its dependence on the stochastic shuttling timescales and membrane properties is elucidated. Our estimates of the area of the deformed region and the number of lipids in it indicate strong clustering.
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Affiliation(s)
- Tapas Singha
- Institut Curie, Université PSL, Sorbonne Université, CNRS UMR168, Laboratoire Physico Chimie Curie, 75005 Paris, France
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA.
| | - Anirban Polley
- Shanmugha Arts, Science, Technology and Research Academy, Tirumalaisamudram, Thanjavur, Tamilnadu 613401, India
- National Centre for Biological Sciences, UAS-GKVK Campus, Bellary Road, Bangalore 560065, India
| | - Mustansir Barma
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Gopanpally, Hyderabad 500107, India
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9
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Agrawal V, Pandey V, Mitra D. Active buckling of pressurized spherical shells: Monte Carlo simulation. Phys Rev E 2023; 108:L032601. [PMID: 37849090 DOI: 10.1103/physreve.108.l032601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Accepted: 08/06/2023] [Indexed: 10/19/2023]
Abstract
We study the buckling of pressurized spherical shells by Monte Carlo simulations in which the detailed balance is explicitly broken-thereby driving the shell to be active, out of thermal equilibrium. Such a shell typically has either higher (active) or lower (sedate) fluctuations compared to one in thermal equilibrium depending on how the detailed balance is broken. We show that, for the same set of elastic parameters, a shell that is not buckled in thermal equilibrium can be buckled if turned active. Similarly a shell that is buckled in thermal equilibrium can unbuckle if sedated. Based on this result, we suggest that it is possible to experimentally design microscopic elastic shells whose buckling can be optically controlled.
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Affiliation(s)
- Vipin Agrawal
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, 106 91 Stockholm, Sweden
- Department of Physics, Stockholm University, AlbaNova University Centre, Fysikum, 106 91 Stockholm, Sweden
| | - Vikash Pandey
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, 106 91 Stockholm, Sweden
| | - Dhrubaditya Mitra
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, 106 91 Stockholm, Sweden
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10
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Maitra A, Ramaswamy S. Erratum: Oriented Active Solids [Phys. Rev. Lett. 123, 238001 (2019)]. PHYSICAL REVIEW LETTERS 2023; 130:269901. [PMID: 37450834 DOI: 10.1103/physrevlett.130.269901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2023] [Indexed: 07/18/2023]
Abstract
This corrects the article DOI: 10.1103/PhysRevLett.123.238001.
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11
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Sokolova A, Galic M. Modulation of self-organizing circuits at deforming membranes by intracellular and extracellular factors. Biol Chem 2023; 404:417-425. [PMID: 36626681 DOI: 10.1515/hsz-2022-0290] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 12/16/2022] [Indexed: 01/12/2023]
Abstract
Mechanical forces exerted to the plasma membrane induce cell shape changes. These transient shape changes trigger, among others, enrichment of curvature-sensitive molecules at deforming membrane sites. Strikingly, some curvature-sensing molecules not only detect membrane deformation but can also alter the amplitude of forces that caused to shape changes in the first place. This dual ability of sensing and inducing membrane deformation leads to the formation of curvature-dependent self-organizing signaling circuits. How these cell-autonomous circuits are affected by auxiliary parameters from inside and outside of the cell has remained largely elusive. Here, we explore how such factors modulate self-organization at the micro-scale and its emerging properties at the macroscale.
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Affiliation(s)
- Anastasiia Sokolova
- Institute of Medical Physics and Biophysics, University of Münster, Robert-Koch-Straße 31, 48149 Münster, Germany.,CiM-IMRPS Graduate Program, Schlossplatz 5, 48149 Münster, Germany
| | - Milos Galic
- Institute of Medical Physics and Biophysics, University of Münster, Robert-Koch-Straße 31, 48149 Münster, Germany.,'Cells in Motion' Interfaculty Centre, University of Münster, Röntgenstraße 16, 48149 Münster, Germany
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12
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Jülicher F, Prost J, Toner J. Broken living layers: Dislocations in active smectic liquid crystals. Phys Rev E 2022; 106:054607. [PMID: 36559431 DOI: 10.1103/physreve.106.054607] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2022] [Accepted: 10/24/2022] [Indexed: 11/16/2022]
Abstract
We show that dislocations in active two-dimensional (2D) smectic liquid crystals with underlying rotational symmetry are always unbound in the presence of noise, meaning the active smectic phase does not exist for nonzero noise in d=2. The active smectic phase can, like equilibrium smectics in 2D, be stabilized by applying rotational symmetry-breaking fields; however, even in the presence of such fields, active smectics are still much less stable against noise than equilibrium ones, when the symmetry-breaking field(s) are weak.
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Affiliation(s)
- Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany and Cluster of Excellence, Physics of Life, TU Dresden, 01307 Dresden, Germany
| | - Jacques Prost
- Mechanobiology Institute and Department of Biological Sciences, National University of Singapore, Singapore 117411 and Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, CNRS UMR168, 75005 Paris, France
| | - John Toner
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon 97403, USA
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13
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Campi G, Bianconi A. Periodic recurrent waves of Covid-19 epidemics and vaccination campaign. CHAOS, SOLITONS, AND FRACTALS 2022; 160:112216. [PMID: 35601116 PMCID: PMC9114150 DOI: 10.1016/j.chaos.2022.112216] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/18/2022] [Revised: 04/11/2022] [Accepted: 05/12/2022] [Indexed: 06/15/2023]
Abstract
While understanding of periodic recurrent waves of Covid-19 epidemics would aid to combat the pandemics, quantitative analysis of data over a two years period from the outbreak, is lacking. The complexity of Covid-19 recurrent waves is related with the concurrent role of i) the containment measures enforced to mitigate the epidemics spreading ii) the rate of viral gene mutations, and iii) the variable immune response of the host implemented by vaccination. This work focuses on the effect of massive vaccination and gene variants on the recurrent waves in a representative case of countries enforcing mitigation and vaccination strategy. The spreading rate is measured by the ratio between the reproductive number Rt(t) and the doubling time Td(t) called RIC-index and the daily fatalities number. The dynamics of the Covid-19 epidemics have been studied by wavelet analysis and represented by a non-linear helicoid vortex in a 3D space where both RIC-index and fatalities change with time. The onset of periodic recurrent waves has been identified by the transition from convergent to divergent trajectories on the helicoid vortex. We report a main period of recurrent waves of 120 days and the elongation of this period after the vaccination campaign.
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Affiliation(s)
- Gaetano Campi
- Institute of Crystallography, Consiglio Nazionale delle Ricerche CNR, via Salaria Km 29.300, Monterotondo, Roma I-00015, Italy
- Rome International Centre Materials Science Superstripes RICMASS, via dei Sabelli 119A, 00185 Rome, Italy
| | - Antonio Bianconi
- Institute of Crystallography, Consiglio Nazionale delle Ricerche CNR, via Salaria Km 29.300, Monterotondo, Roma I-00015, Italy
- Rome International Centre Materials Science Superstripes RICMASS, via dei Sabelli 119A, 00185 Rome, Italy
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14
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Fournier JB. Field-mediated interactions of passive and conformation-active particles: multibody and retardation effects. SOFT MATTER 2022; 18:2634-2645. [PMID: 35302131 DOI: 10.1039/d1sm01823j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Particles in soft matter interact through the deformation field they create, as in the "cheerios" effect or the curvature-mediated interactions of membrane proteins. Using a simple model for field-mediated interactions between passive particles, or active particles that switch conformation randomly or synchronously, we derive generic results concerning multibody interactions, activity driven patterns, and retardation effects.
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Affiliation(s)
- Jean-Baptiste Fournier
- Université Paris Cité, CNRS, Laboratoire Matière et Systèmes Complexes (MSC), F-75013 Paris, France.
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15
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Baccouch R, Rascol E, Stoklosa K, Alves ID. The role of the lipid environment in the activity of G protein coupled receptors. Biophys Chem 2022; 285:106794. [DOI: 10.1016/j.bpc.2022.106794] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Revised: 02/11/2022] [Accepted: 03/08/2022] [Indexed: 12/21/2022]
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16
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Poncet A, Bartolo D. When Soft Crystals Defy Newton's Third Law: Nonreciprocal Mechanics and Dislocation Motility. PHYSICAL REVIEW LETTERS 2022; 128:048002. [PMID: 35148143 DOI: 10.1103/physrevlett.128.048002] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2021] [Revised: 10/07/2021] [Accepted: 12/23/2021] [Indexed: 06/14/2023]
Abstract
The effective interactions between the constituents of driven soft matter generically defy Newton's third law. Combining theory and numerical simulations, we establish that six classes of mechanics with no counterparts in equilibrium systems emerge in elastic crystals challenged by nonreciprocal interactions. Going beyond linear deformations, we reveal that interactions violating Newton's third law generically turn otherwise quiescent dislocations into motile singularities which steadily glide though periodic lattices.
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Affiliation(s)
- Alexis Poncet
- Université Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Denis Bartolo
- Université Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
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17
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Cagnetta F, Škultéty V, Evans MR, Marenduzzo D. Universal properties of active membranes. Phys Rev E 2022; 105:L012604. [PMID: 35193286 DOI: 10.1103/physreve.105.l012604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Accepted: 11/24/2021] [Indexed: 06/14/2023]
Abstract
We put forward a general field theory for nearly flat fluid membranes with embedded activators and analyze their critical properties using renormalization group techniques. Depending on the membrane-activator coupling, we find a crossover between acoustic and diffusive scaling regimes, with mean-field dynamical critical exponents z=1 and 2, respectively. We argue that the acoustic scaling, which is exact in all spatial dimensions, leads to an early-time behavior, which is representative of the spatiotemporal patterns observed at the leading edge of motile cells, such as oscillations superposed on the growth of the membrane width. In the case of mean-field diffusive scaling, one-loop corrections to the mean-field exponents reveal universal behavior distinct from the Kardar-Parisi-Zhang scaling of passive interfaces and signs of strong-coupling behavior.
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Affiliation(s)
- Francesco Cagnetta
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdom
| | - Viktor Škultéty
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdom
| | - Martin R Evans
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdom
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdom
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18
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Cagnetta F, Škultéty V, Evans MR, Marenduzzo D. Renormalization group study of the dynamics of active membranes: Universality classes and scaling laws. Phys Rev E 2022; 105:014610. [PMID: 35193300 DOI: 10.1103/physreve.105.014610] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2020] [Accepted: 11/24/2021] [Indexed: 06/14/2023]
Abstract
Motivated by experimental observations of patterning at the leading edge of motile eukaryotic cells, we introduce a general model for the dynamics of nearly-flat fluid membranes driven from within by an ensemble of activators. We include, in particular, a kinematic coupling between activator density and membrane slope which generically arises whenever the membrane has a nonvanishing normal speed. We unveil the phase diagram of the model by means of a perturbative field-theoretical renormalization group analysis. Due to the aforementioned kinematic coupling the natural early-time dynamical scaling is acoustic, that is the dynamical critical exponent is 1. However, as soon as the the normal velocity of the membrane is tuned to zero, the system crosses over to diffusive dynamic scaling in mean field. Distinct critical points can be reached depending on how the limit of vanishing velocity is realized: in each of them corrections to scaling due to nonlinear coupling terms must be taken into account. The detailed analysis of these critical points reveals novel scaling regimes which can be accessed with perturbative methods, together with signs of strong coupling behavior, which establishes a promising ground for further nonperturbative calculations. Our results unify several previous studies on the dynamics of active membrane, while also identifying nontrivial scaling regimes which cannot be captured by passive theories of fluctuating interfaces and are relevant for the physics of living membranes.
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Affiliation(s)
- Francesco Cagnetta
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD Scotland, United Kingdom
| | - Viktor Škultéty
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD Scotland, United Kingdom
| | - Martin R Evans
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD Scotland, United Kingdom
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD Scotland, United Kingdom
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Gao J, Hou R, Li L, Hu J. Membrane-Mediated Interactions Between Protein Inclusions. Front Mol Biosci 2021; 8:811711. [PMID: 35004858 PMCID: PMC8727768 DOI: 10.3389/fmolb.2021.811711] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Accepted: 11/30/2021] [Indexed: 11/13/2022] Open
Abstract
Integral or peripheral membrane proteins, or protein oligomers often get close to each other on cell membranes and carry out biological tasks in a collective manner. In addition to electrostatic and van der Waals interactions, those proteins also experience membrane-mediated interactions, which may be necessary for their functionality. The membrane-mediated interactions originate from perturbation of lipid membranes by the presence of protein inclusions, and have been the subject of intensive research in membrane biophysics. Here we review both theoretical and numerical studies of such interactions for membrane proteins and for nanoparticles bound to lipid membranes.
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Affiliation(s)
- Jie Gao
- Kuang Yaming Honors School, Nanjing University, Nanjing, China
| | - Ruihan Hou
- Kuang Yaming Honors School, Nanjing University, Nanjing, China
| | - Long Li
- State Key Laboratory of Nonlinear Mechanics (LNM) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China
| | - Jinglei Hu
- Kuang Yaming Honors School, Nanjing University, Nanjing, China
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20
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Ghosh S, Gutti S, Chaudhuri D. Pattern formation, localized and running pulsation on active spherical membranes. SOFT MATTER 2021; 17:10614-10627. [PMID: 34605510 DOI: 10.1039/d1sm00937k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Active force generation by an actin-myosin cortex coupled to a cell membrane allows the cell to deform, respond to the environment, and mediate cell motility and division. Several membrane-bound activator proteins move along it and couple to the membrane curvature. Besides, they can act as nucleating sites for the growth of filamentous actin. Actin polymerization can generate a local outward push on the membrane. Inward pull from the contractile actomyosin cortex can propagate along the membrane via actin filaments. We use coupled evolution of fields to perform linear stability analysis and numerical calculations. As activity overcomes the stabilizing factors such as surface tension and bending rigidity, the spherical membrane shows instability towards pattern formation, localized pulsation, and running pulsation between poles. We present our results in terms of phase diagrams and evolutions of the coupled fields. They have relevance for living cells and can be verified in experiments on artificial cell-like constructs.
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Affiliation(s)
- Subhadip Ghosh
- Department of Physics, Faculty of Science, University of Zagreb, Bijenička cesta 32, 10000 Zagreb, Croatia.
| | - Sashideep Gutti
- BITS Pilani Hyderabad Campus, Hyderabad 500078, Telengana, India.
| | - Debasish Chaudhuri
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
- Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India.
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21
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Dendrite tapering actuates a self-organizing signaling circuit for stochastic filopodia initiation in neurons. Proc Natl Acad Sci U S A 2021; 118:2106921118. [PMID: 34686599 DOI: 10.1073/pnas.2106921118] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/01/2021] [Indexed: 01/09/2023] Open
Abstract
How signaling units spontaneously arise from a noisy cellular background is not well understood. Here, we show that stochastic membrane deformations can nucleate exploratory dendritic filopodia, dynamic actin-rich structures used by neurons to sample its surroundings for compatible transcellular contacts. A theoretical analysis demonstrates that corecruitment of positive and negative curvature-sensitive proteins to deformed membranes minimizes the free energy of the system, allowing the formation of long-lived curved membrane sections from stochastic membrane fluctuations. Quantitative experiments show that once recruited, curvature-sensitive proteins form a signaling circuit composed of interlinked positive and negative actin-regulatory feedback loops. As the positive but not the negative feedback loop can sense the dendrite diameter, this self-organizing circuit determines filopodia initiation frequency along tapering dendrites. Together, our findings identify a receptor-independent signaling circuit that employs random membrane deformations to simultaneously elicit and limit formation of exploratory filopodia to distal dendritic sites of developing neurons.
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22
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Almendro-Vedia V, Natale P, Valdivieso González D, Lillo MP, Aragones JL, López-Montero I. How rotating ATP synthases can modulate membrane structure. Arch Biochem Biophys 2021; 708:108939. [PMID: 34052190 DOI: 10.1016/j.abb.2021.108939] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Revised: 05/19/2021] [Accepted: 05/20/2021] [Indexed: 01/03/2023]
Abstract
F1Fo-ATP synthase (ATP synthase) is a central membrane protein that synthetizes most of the ATP in the cell through a rotational movement driven by a proton gradient across the hosting membrane. In mitochondria, ATP synthases can form dimers through specific interactions between some subunits of the protein. The dimeric form of ATP synthase provides the protein with a spontaneous curvature that sustain their arrangement at the rim of the high-curvature edges of mitochondrial membrane (cristae). Also, a direct interaction with cardiolipin, a lipid present in the inner mitochondrial membrane, induces the dimerization of ATP synthase molecules along cristae. The deletion of those biochemical interactions abolishes the protein dimerization producing an altered mitochondrial function and morphology. Mechanically, membrane bending is one of the key deformation modes by which mitochondrial membranes can be shaped. In particular, bending rigidity and spontaneous curvature are important physical factors for membrane remodelling. Here, we discuss a complementary mechanism whereby the rotatory movement of the ATP synthase might modify the mechanical properties of lipid bilayers and contribute to the formation and regulation of the membrane invaginations.
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Affiliation(s)
- Víctor Almendro-Vedia
- Departamento Química Física, Universidad Complutense de Madrid, Avda. Complutense s/n, 28040, Madrid, Spain; Instituto de Investigación Hospital Doce de Octubre (imas12), Avenida de Córdoba s/n, 28041, Madrid, Spain
| | - Paolo Natale
- Departamento Química Física, Universidad Complutense de Madrid, Avda. Complutense s/n, 28040, Madrid, Spain; Instituto de Investigación Hospital Doce de Octubre (imas12), Avenida de Córdoba s/n, 28041, Madrid, Spain
| | - David Valdivieso González
- Departamento Química Física, Universidad Complutense de Madrid, Avda. Complutense s/n, 28040, Madrid, Spain; Instituto de Investigación Hospital Doce de Octubre (imas12), Avenida de Córdoba s/n, 28041, Madrid, Spain
| | - M Pilar Lillo
- Departamento Química Física Biológica, Instituto de Química-Física "Rocasolano" (CSIC), Serrano 119, 28006, Madrid, Spain
| | - Juan L Aragones
- Departamento de Física Teórica de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Centre (IFIMAC), Universidad Autónoma de Madrid, E-28049, Madrid, Spain
| | - Iván López-Montero
- Departamento Química Física, Universidad Complutense de Madrid, Avda. Complutense s/n, 28040, Madrid, Spain; Instituto de Investigación Hospital Doce de Octubre (imas12), Avenida de Córdoba s/n, 28041, Madrid, Spain.
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23
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Noguchi H. Vesicle budding induced by binding of curvature-inducing proteins. Phys Rev E 2021; 104:014410. [PMID: 34412221 DOI: 10.1103/physreve.104.014410] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Accepted: 07/13/2021] [Indexed: 12/22/2022]
Abstract
Vesicle budding induced by protein binding that generates an isotropic spontaneous curvature is studied using a mean-field theory. Many spherical buds are formed via protein binding. As the binding chemical potential increases, the proteins first bind to the buds and then to the remainder of the vesicle. For a high spontaneous curvature and/or high bending rigidity of the bound membrane, it is found that a first-order transition occurs between a small number of large buds and a large number of small buds. These two states coexist around the transition point. The proposed scheme is simple and easily applicable to many interaction types, so we investigate the effects of interprotein interactions, the protein-insertion-induced changes in area, the variation of the saddle-splay modulus, and the area-difference-elasticity energy. The differences in the preferred curvatures for curvature sensing and generation are also clarified.
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Affiliation(s)
- Hiroshi Noguchi
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
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24
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Al-Izzi SC, Morris RG. Active flows and deformable surfaces in development. Semin Cell Dev Biol 2021; 120:44-52. [PMID: 34266757 DOI: 10.1016/j.semcdb.2021.07.001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Revised: 06/30/2021] [Accepted: 07/01/2021] [Indexed: 12/15/2022]
Abstract
We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients- active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.
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Affiliation(s)
- Sami C Al-Izzi
- School of Physics and EMBL Australia Node in Single Molecule Science, School of Medical Sciences, University of New South Wales - Sydney, 2052, Australia
| | - Richard G Morris
- School of Physics and EMBL Australia Node in Single Molecule Science, School of Medical Sciences, University of New South Wales - Sydney, 2052, Australia.
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25
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Abstract
We use a theoretical approach to examine the effect of a radial fluid flow or electric current on the growth and homeostasis of a cell spheroid. Such conditions may be generated by a drain of micrometric diameter. To perform this analysis, we describe the tissue as a continuum. We include active mechanical, electric, and hydraulic components in the tissue material properties. We consider a spherical geometry and study the effect of the drain on the dynamics of the cell aggregate. We show that a steady fluid flow or electric current imposed by the drain could be able to significantly change the spheroid long-time state. In particular, our work suggests that a growing spheroid can systematically be driven to a shrinking state if an appropriate external field is applied. Order-of-magnitude estimates suggest that such fields are of the order of the indigenous ones. Similarities and differences with the case of tumors and embryo development are briefly discussed.
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26
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Liu K, Patteson AE, Banigan EJ, Schwarz JM. Dynamic Nuclear Structure Emerges from Chromatin Cross-Links and Motors. PHYSICAL REVIEW LETTERS 2021; 126:158101. [PMID: 33929233 DOI: 10.1103/physrevlett.126.158101] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2020] [Accepted: 02/22/2021] [Indexed: 06/12/2023]
Abstract
The cell nucleus houses the chromosomes, which are linked to a soft shell of lamin protein filaments. Experiments indicate that correlated chromosome dynamics and nuclear shape fluctuations arise from motor activity. To identify the physical mechanisms, we develop a model of an active, cross-linked Rouse chain bound to a polymeric shell. System-sized correlated motions occur but require both motor activity and cross-links. Contractile motors, in particular, enhance chromosome dynamics by driving anomalous density fluctuations. Nuclear shape fluctuations depend on motor strength, cross-linking, and chromosome-lamina binding. Therefore, complex chromosome dynamics and nuclear shape emerge from a minimal, active chromosome-lamina system.
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Affiliation(s)
- Kuang Liu
- Department of Physics and BioInspired Syracuse, Syracuse University, Syracuse, New York 13244, USA
| | - Alison E Patteson
- Department of Physics and BioInspired Syracuse, Syracuse University, Syracuse, New York 13244, USA
| | - Edward J Banigan
- Institute for Medical Engineering and Science and Department of Physics, MIT, Cambridge, Massachusetts 02139, USA
| | - J M Schwarz
- Department of Physics and BioInspired Syracuse, Syracuse University, Syracuse, New York 13244, USA
- Indian Creek Farm, Ithaca, New York 14850, USA
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27
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Frey F, Idema T. More than just a barrier: using physical models to couple membrane shape to cell function. SOFT MATTER 2021; 17:3533-3549. [PMID: 33503097 DOI: 10.1039/d0sm01758b] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.
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Affiliation(s)
- Felix Frey
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands.
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28
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Al-Izzi SC, Sens P, Turner MS, Komura S. Dynamics of passive and active membrane tubes. SOFT MATTER 2020; 16:9319-9330. [PMID: 32935733 DOI: 10.1039/d0sm01290d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Utilising Onsager's variational formulation, we derive dynamical equations for the relaxation of a fluid membrane tube in the limit of small deformation, allowing for a contrast of solvent viscosity across the membrane and variations in surface tension due to membrane incompressibility. We compute the relaxation rates, recovering known results in the case of purely axis-symmetric perturbations and making new predictions for higher order (azimuthal) m-modes. We analyse the long and short wavelength limits of these modes by making use of various asymptotic arguments. We incorporate stochastic terms to our dynamical equations suitable to describe both passive thermal forces and non-equilibrium active forces. We derive expressions for the fluctuation amplitudes, an effective temperature associated with active fluctuations, and the power spectral density for both the thermal and active fluctuations. We discuss an experimental assay that might enable measurement of these fluctuations to infer the properties of the active noise. Finally we discuss our results in the context of active membranes more generally and give an overview of some open questions in the field.
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Affiliation(s)
- Sami C Al-Izzi
- School of Physics & EMBL-Australia node in Single Molecule Science, University of New South Wales, Sydney, Australia and Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK and Institut Curie, PSL Research University, CNRS, Physical Chemistry Curie, F-75005, Paris, France and Sorbonne Université, CNRS, UMR 168, F-75005, Paris, France
| | - Pierre Sens
- Institut Curie, PSL Research University, CNRS, Physical Chemistry Curie, F-75005, Paris, France and Sorbonne Université, CNRS, UMR 168, F-75005, Paris, France
| | - Matthew S Turner
- Department of Physics & Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, UK and Department of Chemical Engineering, University of Kyoto, Kyoto 615-8510, Japan
| | - Shigeyuki Komura
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, Tokyo 192-0397, Japan.
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29
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30
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Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models. Nat Commun 2020; 11:2951. [PMID: 32528158 PMCID: PMC7289815 DOI: 10.1038/s41467-020-16424-0] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2019] [Accepted: 04/28/2020] [Indexed: 12/12/2022] Open
Abstract
Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.
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31
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Loewe B, Serafin F, Shankar S, Bowick MJ, Marchetti MC. Shape and size changes of adherent elastic epithelia. SOFT MATTER 2020; 16:5282-5293. [PMID: 32462170 DOI: 10.1039/d0sm00239a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Epithelial tissues play a fundamental role in various morphogenetic events during development and early embryogenesis. Although epithelial monolayers are often modeled as two-dimensional (2D) elastic surfaces, they distinguish themselves from conventional thin elastic plates in three important ways- the presence of an apical-basal polarity, spatial variability of cellular thickness, and their nonequilibrium active nature. Here, we develop a minimal continuum model of a planar epithelial tissue as an active elastic material that incorporates all these features. We start from a full three-dimensional (3D) description of the tissue and derive an effective 2D model that captures, through the curvature of the apical surface, both the apical-basal asymmetry and the spatial geometry of the tissue. Crucially, variations of active stresses across the apical-basal axis lead to active torques that can drive curvature transitions. By identifying four distinct sources of activity, we find that bulk active stresses arising from actomyosin contractility and growth compete with boundary active tensions due to localized actomyosin cables and lamellipodial activity to generate the various states spanning the morphospace of a planar epithelium. Our treatment hence unifies 3D shape deformations through the coupled mechanics of apical curvature change and in-plane expansion/contraction of substrate-adhered tissues. Finally, we discuss the implications of our results for some biologically relevant processes such as tissue folding at the onset of lumen formation.
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Affiliation(s)
- Benjamin Loewe
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA.
| | - Francesco Serafin
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.
| | - Suraj Shankar
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - Mark J Bowick
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - M Cristina Marchetti
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA.
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32
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Liang CC, Yasuda K, Komura S, Wu KA, Chen HY. Dynamics of a membrane coupled to an active fluid. Phys Rev E 2020; 101:042601. [PMID: 32422731 DOI: 10.1103/physreve.101.042601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2019] [Accepted: 03/11/2020] [Indexed: 11/07/2022]
Abstract
The dynamics of a membrane coupled to an active fluid on top of a substrate is considered theoretically. It is assumed that the director field of the active fluid has rotational symmetry in the membrane plane. This situation is likely to be relevant for in vitro reconstructed actomyosin-membrane system. Different from a membrane coupled to a polar active fluid, this model predicts that only when the viscosity of the fluid above the membrane is sufficiently large, a contractile active fluid is able to slow down the relaxation of the membrane for perturbations with wavelength comparable to the thickness of the active fluid. Hence, our model predicts a finite-wavelength instability in the limit of strong contractility, which is different from a membrane coupled to a polar active fluid. However, a membrane coupled to an extensile active fluid is always unstable against long-wavelength perturbations due to active extensile stress enhanced membrane undulation.
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Affiliation(s)
- Chia-Chun Liang
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Kento Yasuda
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, 192-0397 Tokyo, Japan
| | - Shigeyuki Komura
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, 192-0397 Tokyo, Japan
| | - Kuo-An Wu
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Hsuan-Yi Chen
- Department of Physics, National Central University, Jhongli 32001, Taiwan.,Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
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33
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Takatori SC, Sahu A. Active Contact Forces Drive Nonequilibrium Fluctuations in Membrane Vesicles. PHYSICAL REVIEW LETTERS 2020; 124:158102. [PMID: 32357050 DOI: 10.1103/physrevlett.124.158102] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2019] [Accepted: 03/20/2020] [Indexed: 05/24/2023]
Abstract
We analyze the nonequilibrium shape fluctuations of giant unilamellar vesicles encapsulating motile bacteria. Owing to bacteria-membrane collisions, we experimentally observe a significant increase in the magnitude of membrane fluctuations at low wave numbers, compared to the well-known thermal fluctuation spectrum. We interrogate these results by numerically simulating membrane height fluctuations via a modified Langevin equation, which includes bacteria-membrane contact forces. Taking advantage of the lengthscale and timescale separation of these contact forces and thermal noise, we further corroborate our results with an approximate theoretical solution to the dynamical membrane equations. Our theory and simulations demonstrate excellent agreement with nonequilibrium fluctuations observed in experiments. Moreover, our theory reveals that the fluctuation-dissipation theorem is not broken by the bacteria; rather, membrane fluctuations can be decomposed into thermal and active components.
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Affiliation(s)
- Sho C Takatori
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Amaresh Sahu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
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34
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Abstract
The essential features of many interfaces driven out of equilibrium are described by the same equation—the Kardar-Parisi-Zhang (KPZ) equation. How do living interfaces, such as the cell membrane, fit into this picture? In an endeavour to answer such a question, we proposed in [F. Cagnetta, M. R. Evans, D. Marenduzzo, PRL 120, 258001 (2018)] an idealised model for the membrane of a moving cell. Here we discuss how the addition of simple ingredients inspired by the dynamics of the membrane of moving cells affects common kinetic roughening theories such as the KPZ and Edwards-Wilkinson equations.
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35
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Bisht P, Barma M. Interface growth driven by a single active particle. Phys Rev E 2019; 100:052120. [PMID: 31869981 DOI: 10.1103/physreve.100.052120] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2019] [Indexed: 11/07/2022]
Abstract
We study pattern formation, fluctuations, and scaling induced by a growth-promoting active walker on an otherwise static interface. Active particles on an interface define a simple model for energy-consuming proteins embedded in the plasma membrane, responsible for membrane deformation and cell movement. In our model, the active particle overturns local valleys of the interface into hills, simulating growth, while itself sliding and seeking new valleys. In one dimension, this "overturn-slide-search" dynamics of the active particle causes it to move superdiffusively in the transverse direction while pulling the immobile interface upward. Using Monte Carlo simulations, we find an emerging tentlike mean profile developing with time, despite large fluctuations. The roughness of the interface follows scaling with the growth, dynamic, and roughness exponents, derived using simple arguments as β=2/3, z=3/2, and α=1/2, respectively, implying a breakdown of the usual scaling law β=α/z, due to very local growth of the interface. The transverse displacement of the puller on the interface scales as ∼t^{2/3} and the probability distribution of its displacement is bimodal, with an unusual linear cusp at the origin. Both the mean interface pattern and probability distribution display scaling. A puller on a static two-dimensional interface also displays aspects of scaling in the mean profile and probability distribution. We also show that a pusher on a fluctuating interface moves subdiffusively leading to a separation of timescale in pusher motion and interface response.
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Affiliation(s)
- Prachi Bisht
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Gopanpally, Hyderabad 500107, India.,Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala 695547, India
| | - Mustansir Barma
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Gopanpally, Hyderabad 500107, India
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36
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Maitra A, Ramaswamy S. Oriented Active Solids. PHYSICAL REVIEW LETTERS 2019; 123:238001. [PMID: 31868448 DOI: 10.1103/physrevlett.123.238001] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2019] [Revised: 09/08/2019] [Indexed: 06/10/2023]
Abstract
We present a complete analysis of the linearized dynamics of active solids with uniaxial orientational order, taking into account a hitherto overlooked consequence of rotation invariance. Our predictions include a purely active response of two-dimensional orientationally ordered solids to shear, the possibility of stable active solids with quasi-long-range order in two dimensions and long-range order in three dimensions, generic instability of the solid for one sign of active forcing, and the instability of the uniaxially ordered phase in momentum-conserved systems for large active forcing irrespective of its sign.
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Affiliation(s)
- Ananyo Maitra
- Sorbonne Université and CNRS, Laboratoire Jean Perrin, F-75005 Paris, France
| | - Sriram Ramaswamy
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, 560 012 Bangalore, India
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37
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Li S, Yan Z, Huang F, Zhang X, Yue T. How a lipid bilayer membrane responds to an oscillating nanoparticle: Promoted membrane undulation and directional wave propagation. Colloids Surf B Biointerfaces 2019; 187:110651. [PMID: 31784121 DOI: 10.1016/j.colsurfb.2019.110651] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2019] [Revised: 11/15/2019] [Accepted: 11/16/2019] [Indexed: 01/14/2023]
Abstract
Mechanical forces acting on a plasma membrane are of essential importance to cellular functioning via inducing delicate change of the membrane shape with the underlying mechanism yet to be elucidated. Here, we introduce an oscillating nanoparticle (NP) interaction with a lipid bilayer membrane, using the coarse-grained simulation to investigate the dynamic membrane response to constrained mechanical stimulation, which is ubiquitous in biology. Our results demonstrate that, the membrane responds to an oscillating NP by generating nanoscale undulation waves, which immediately propagate through the membrane. In dynamics, propagation of the generated membrane undulation waves always starts from flattening of the region where the NP locates, thus producing a lateral force to propel the waves away from the point of stimulation. The speed of membrane undulation wave propagation is proportional to that of NP oscillation and accelerated by increasing the integral membrane surface tension, suggesting that both the membrane bending and stretching contribute to the energy driving the unique response of membrane undulation wave propagation.
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Affiliation(s)
- Shixin Li
- State Key Laboratory of Heavy Oil Processing, Center for Bioengineering and Biotechnology, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, 266580, China
| | - Zengshuai Yan
- State Key Laboratory of Heavy Oil Processing, Center for Bioengineering and Biotechnology, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, 266580, China
| | - Fang Huang
- State Key Laboratory of Heavy Oil Processing, Center for Bioengineering and Biotechnology, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, 266580, China
| | - Xianren Zhang
- State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing, 100029, China
| | - Tongtao Yue
- State Key Laboratory of Heavy Oil Processing, Center for Bioengineering and Biotechnology, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, 266580, China.
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38
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Duclut C, Sarkar N, Prost J, Jülicher F. Fluid pumping and active flexoelectricity can promote lumen nucleation in cell assemblies. Proc Natl Acad Sci U S A 2019; 116:19264-19273. [PMID: 31492815 PMCID: PMC6765252 DOI: 10.1073/pnas.1908481116] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We discuss the physical mechanisms that promote or suppress the nucleation of a fluid-filled lumen inside a cell assembly or a tissue. We discuss lumen formation in a continuum theory of tissue material properties in which the tissue is described as a 2-fluid system to account for its permeation by the interstitial fluid, and we include fluid pumping as well as active electric effects. Considering a spherical geometry and a polarized tissue, our work shows that fluid pumping and tissue flexoelectricity play a crucial role in lumen formation. We furthermore explore the large variety of long-time states that are accessible for the cell aggregate and its lumen. Our work reveals a role of the coupling of mechanical, electrical, and hydraulic phenomena in tissue lumen formation.
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Affiliation(s)
- Charlie Duclut
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
| | - Niladri Sarkar
- Laboratoire Physico Chimie Curie, UMR 168, Institut Curie, PSL Research University, CNRS, Sorbonne Université, 75005 Paris, France
- Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, Netherlands
| | - Jacques Prost
- Laboratoire Physico Chimie Curie, UMR 168, Institut Curie, PSL Research University, CNRS, Sorbonne Université, 75005 Paris, France
- Mechanobiology Institute, National University of Singapore, 117411 Singapore
| | - Frank Jülicher
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany;
- Center for Systems Biology Dresden, 01307 Dresden, Germany
- Cluster of Excellence Physics of Life, Technische Universität Dresden, 01062 Dresden, Germany
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39
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Statistical Mechanics of an Elastically Pinned Membrane: Equilibrium Dynamics and Power Spectrum. Biophys J 2019; 117:542-552. [PMID: 31349987 DOI: 10.1016/j.bpj.2019.06.036] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2018] [Revised: 06/22/2019] [Accepted: 06/26/2019] [Indexed: 11/21/2022] Open
Abstract
In biological settings, membranes typically interact locally with other membranes: the extracellular matrix in the exterior or internal cellular structures such as the cytoskeleton, locally pinning the membrane. Characterizing the dynamical properties of such interactions presents a difficult task. Significant progress has been achieved through simulations and experiments, yet analytical progress in modeling pinned membranes has been impeded by the complexity of governing equations. Here, we circumvent these difficulties by calculating analytically the time-dependent Green's function of the operator governing the dynamics of an elastically pinned membrane in a hydrodynamic surrounding and subject to external forces. This enables us to calculate the equilibrium power spectral density for an overdamped membrane pinned by an elastic, permanently attached spring subject to thermal excitations. By considering the effects of the finite experimental resolution on the measured spectra, we show that the elasticity of the pinning can be extracted from the experimentally measured spectrum. Membrane fluctuations can thus be used as a tool to probe mechanical properties of the underlying structures. Such a tool may be particularly relevant in the context of cell mechanics, in which the elasticity of the membrane's attachment to the cytoskeleton could be measured.
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40
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Wang CH, Matin S, George AB, Korolev KS. Pinned, locked, pushed, and pulled traveling waves in structured environments. Theor Popul Biol 2019; 127:102-119. [DOI: 10.1016/j.tpb.2019.04.003] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2015] [Revised: 04/01/2019] [Accepted: 04/03/2019] [Indexed: 11/26/2022]
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41
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Cagnetta F, Evans MR, Marenduzzo D. Statistical mechanics of a single active slider on a fluctuating interface. Phys Rev E 2019; 99:042124. [PMID: 31108715 DOI: 10.1103/physreve.99.042124] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 01/01/2023]
Abstract
We study the statistical mechanics of a single active slider on a fluctuating interface, by means of numerical simulations and theoretical arguments. The slider, which moves by definition towards the interface minima, is active as it also stimulates growth of the interface. Even though such a particle has no counterpart in thermodynamic systems, active sliders may provide a simple model for ATP-dependent membrane proteins that activate cytoskeletal growth. We find a wide range of dynamical regimes according to the ratio between the timescales associated with the slider motion and the interface relaxation. If the interface dynamics is slow, the slider behaves like a random walker in a random environment, which, furthermore, is able to escape environmental troughs by making them grow. This results in different dynamic exponents to the interface and the particle: the former behaves as an Edward-Wilkinson surface with dynamic exponent 2, whereas the latter has dynamic exponent 3/2. When the interface is fast, we get sustained ballistic motion with the particle surfing a membrane wave created by itself. However, if the interface relaxes immediately (i.e., it is infinitely fast), particle motion becomes symmetric and goes back to diffusive. Due to such a rich phenomenology, we propose the active slider as a toy model of fundamental interest in the field of active membranes and, generally, whenever the system constituent can alter the environment by spending energy.
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Affiliation(s)
- F Cagnetta
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - M R Evans
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - D Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
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42
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Kelley EG, Butler PD, Nagao M. Scaling of lipid membrane rigidity with domain area fraction. SOFT MATTER 2019; 15:2762-2767. [PMID: 30789180 PMCID: PMC8220873 DOI: 10.1039/c8sm02362j] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Biological membranes are highly heterogeneous in composition which in turn leads to local variations in the physical properties. Here we quantify how heterogeneity in stiffness determines the effective bending modulus, κeff, of model phase-separated membranes with coexisting soft fluid and rigid gel domains. We find that the temperature- and composition- dependent trends in membrane rigidity collapse onto a single curve, such that κeff directly scales with the area fraction of the rigid gel domains. Using no adjustable parameters, the measurements are found to agree with theoretical predictions for inhomogenous membranes and indicate that κeff is sensitive to the lateral distribution of the rigid phase within the membrane. This key finding confirms that the properties of heterogeneous membranes can be quantitatively predicted if the area fraction and properties of the individual phases are known.
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Affiliation(s)
- Elizabeth G Kelley
- NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD, USA.
| | - Paul D Butler
- NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD, USA. and Department of Chemical and Biomolecular Engineering, University of Delaware, 150 Academy Street, Newark, DE, USA and Department of Chemistry, The University of Tennessee, Knoxville, TN 37996, USA
| | - Michihiro Nagao
- NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD, USA. and Center for Exploration of Energy and Matter, Indiana University, 2401 N. Milo B. Sampson Lane, Bloomington, IN, USA.
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43
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Gov NS. Guided by curvature: shaping cells by coupling curved membrane proteins and cytoskeletal forces. Philos Trans R Soc Lond B Biol Sci 2019; 373:rstb.2017.0115. [PMID: 29632267 DOI: 10.1098/rstb.2017.0115] [Citation(s) in RCA: 58] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/19/2017] [Indexed: 01/11/2023] Open
Abstract
Eukaryote cells have flexible membranes that allow them to have a variety of dynamical shapes. The shapes of the cells serve important biological functions, both for cells within an intact tissue, and during embryogenesis and cellular motility. How cells control their shapes and the structures that they form on their surface has been a subject of intensive biological research, exposing the building blocks that cells use to deform their membranes. These processes have also drawn the interest of theoretical physicists, aiming to develop models based on physics, chemistry and nonlinear dynamics. Such models explore quantitatively different possible mechanisms that the cells can employ to initiate the spontaneous formation of shapes and patterns on their membranes. We review here theoretical work where one such class of mechanisms was investigated: the coupling between curved membrane proteins, and the cytoskeletal forces that they recruit. Theory indicates that this coupling gives rise to a rich variety of membrane shapes and dynamics, while experiments indicate that this mechanism appears to drive many cellular shape changes.This article is part of the theme issue 'Self-organization in cell biology'.
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Affiliation(s)
- N S Gov
- Department of Chemical Physics, Weizmann Institute of Science, PO Box 26, Rehovot 76100, Israel
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44
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Yang Y, Wu M. Rhythmicity and waves in the cortex of single cells. Philos Trans R Soc Lond B Biol Sci 2019; 373:rstb.2017.0116. [PMID: 29632268 PMCID: PMC5904302 DOI: 10.1098/rstb.2017.0116] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 12/30/2017] [Indexed: 12/15/2022] Open
Abstract
Emergence of dynamic patterns in the form of oscillations and waves on the cortex of single cells is a fascinating and enigmatic phenomenon. Here we outline various theoretical frameworks used to model pattern formation with the goal of reducing complex, heterogeneous patterns into key parameters that are biologically tractable. We also review progress made in recent years on the quantitative and molecular definitions of these terms, which we believe have begun to transform single-cell dynamic patterns from a purely observational and descriptive subject to more mechanistic studies. Specifically, we focus on the nature of local excitable and oscillation events, their spatial couplings leading to propagating waves and the role of active membrane. Instead of arguing for their functional importance, we prefer to consider such patterns as basic properties of dynamic systems. We discuss how knowledge of these patterns could be used to dissect the structure of cellular organization and how the network-centric view could help define cellular functions as transitions between different dynamical states. Last, we speculate on how these patterns could encode temporal and spatial information. This article is part of the theme issue ‘Self-organization in cell biology’.
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Affiliation(s)
- Yang Yang
- Department of Biological Sciences, Centre for Bioimaging Sciences, Mechanobiology Institute, National University of Singapore, Singapore
| | - Min Wu
- Department of Biological Sciences, Centre for Bioimaging Sciences, Mechanobiology Institute, National University of Singapore, Singapore
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45
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Knežević M, Jiang H, Wang S. Active Tuning of Synaptic Patterns Enhances Immune Discrimination. PHYSICAL REVIEW LETTERS 2018; 121:238101. [PMID: 30576186 DOI: 10.1103/physrevlett.121.238101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2017] [Revised: 07/07/2018] [Indexed: 06/09/2023]
Abstract
Immune cells learn about their antigenic targets using tactile sense: a self-organized motif named immunological synapse forms between an immune cell and an antigen-presenting cell (APC) during recognition. Via synapses, immune cells apply mechanical pulling forces to selectively extract antigen (Ag) from APCs. Curiously, depending on its stage of development, a B lymphocyte exhibits distinct synaptic patterns and uses force at different strength and timing, which appears to strongly impact its ability to distinguish Ag affinities. We use a statistical-mechanical model to study how the experimentally observed synaptic architectures can originate from normal cytoskeletal forces coupled to the lateral organization of mobile receptors, and show how this active regulation scheme, collective in nature, may enhance the efficiency and capacity of discrimination.
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Affiliation(s)
- Miloš Knežević
- Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California 90095, USA
| | - Hongda Jiang
- Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California 90095, USA
| | - Shenshen Wang
- Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California 90095, USA
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46
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Alimohamadi H, Rangamani P. Modeling Membrane Curvature Generation due to Membrane⁻Protein Interactions. Biomolecules 2018; 8:E120. [PMID: 30360496 PMCID: PMC6316661 DOI: 10.3390/biom8040120] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2018] [Revised: 10/15/2018] [Accepted: 10/16/2018] [Indexed: 01/03/2023] Open
Abstract
To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications.
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Affiliation(s)
- Haleh Alimohamadi
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA.
| | - Padmini Rangamani
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA.
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47
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Zakine R, Fournier JB, van Wijland F. Field-Embedded Particles Driven by Active Flips. PHYSICAL REVIEW LETTERS 2018; 121:028001. [PMID: 30085741 DOI: 10.1103/physrevlett.121.028001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2018] [Revised: 04/06/2018] [Indexed: 06/08/2023]
Abstract
Systems of independent active particles embedded into a fluctuating environment are relevant to many areas of soft-matter science. We use a minimal model of noninteracting spin-carrying Brownian particles in a Gaussian field and show that activity-driven spin dynamics leads to patterned order. We find that the competition between mediated interactions and active noise alone can yield such diverse behaviors as phase transitions and microphase separation, from lamellar up to hexagonal ordering of clusters of opposite magnetization. These rest on complex multibody interactions. We find regimes of stationary patterns, but also dynamical regimes of relentless birth and growth of lumps of magnetization opposite of the surrounding one. Our approach combines Monte Carlo simulations with analytical methods based on dynamical density functional approaches.
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Affiliation(s)
- Ruben Zakine
- Laboratoire Matière et Systèmes Complexes (MSC), Université Paris Diderot, USPC, UMR 7057 CNRS, F-75205 Paris, France
| | - Jean-Baptiste Fournier
- Laboratoire Matière et Systèmes Complexes (MSC), Université Paris Diderot, USPC, UMR 7057 CNRS, F-75205 Paris, France
| | - Frédéric van Wijland
- Laboratoire Matière et Systèmes Complexes (MSC), Université Paris Diderot, USPC, UMR 7057 CNRS, F-75205 Paris, France
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48
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Jülicher F, Grill SW, Salbreux G. Hydrodynamic theory of active matter. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:076601. [PMID: 29542442 DOI: 10.1088/1361-6633/aab6bb] [Citation(s) in RCA: 99] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/11/2024]
Abstract
We review the general hydrodynamic theory of active soft materials that is motivated in particular by biological matter. We present basic concepts of irreversible thermodynamics of spatially extended multicomponent active systems. Starting from the rate of entropy production, we identify conjugate thermodynamic fluxes and forces and present generic constitutive equations of polar active fluids and active gels. We also discuss angular momentum conservation which plays a role in the the physics of active chiral gels. The irreversible thermodynamics of active gels provides a general framework to discuss the physics that underlies a wide variety of biological processes in cells and in multicellular tissues.
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Affiliation(s)
- Frank Jülicher
- Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzerstr. 38, 01187 Dresden, Germany
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49
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Cagnetta F, Evans MR, Marenduzzo D. Active Growth and Pattern Formation in Membrane-Protein Systems. PHYSICAL REVIEW LETTERS 2018; 120:258001. [PMID: 29979071 DOI: 10.1103/physrevlett.120.258001] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2017] [Revised: 02/14/2018] [Indexed: 06/08/2023]
Abstract
Inspired by recent experimental observations of patterning at the membrane of a living cell, we propose a generic model for the dynamics of a fluctuating interface driven by particlelike inclusions which stimulate its growth. We find that the coupling between interfacial and inclusions dynamics yields microphase separation and the self-organization of traveling waves. These patterns are strikingly similar to those detected in experiments on biological membranes. Our results further show that the active growth kinetics do not fall into the Kardar-Parisi-Zhang universality class for growing interfaces, displaying instead a novel superposition of scaling and sustained oscillations.
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Affiliation(s)
- F Cagnetta
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - M R Evans
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - D Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
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50
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Abstract
Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction-diffusion waves that describe a switch from one alternative state to another. Only two types of waves are known: pulled, driven by the leading edge, and pushed, driven by the bulk of the wave. Here, we report a distinct class of semipushed waves for which both the bulk and the leading edge contribute to the dynamics. These hybrid waves have the kinetics of pushed waves, but exhibit giant fluctuations similar to pulled waves. The transitions between pulled, semipushed, and fully pushed waves occur at universal ratios of the wave velocity to the Fisher velocity. We derive these results in the context of a species invading a new habitat by examining front diffusion, rate of diversity loss, and fluctuation-induced corrections to the expansion velocity. All three quantities decrease as a power law of the population density with the same exponent. We analytically calculate this exponent, taking into account the fluctuations in the shape of the wave front. For fully pushed waves, the exponent is -1, consistent with the central limit theorem. In semipushed waves, however, the fluctuations average out much more slowly, and the exponent approaches 0 toward the transition to pulled waves. As a result, a rapid loss of genetic diversity and large fluctuations in the position of the front occur, even for populations with cooperative growth and other forms of an Allee effect. The evolutionary outcome of spatial spreading in such populations could therefore be less predictable than previously thought.
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Affiliation(s)
- Gabriel Birzu
- Department of Physics, Boston University, Boston, MA 02215
| | - Oskar Hallatschek
- Department of Physics, University of California, Berkeley, CA 94720
- Department of Integrative Biology, University of California, Berkeley, CA 94720
| | - Kirill S Korolev
- Department of Physics, Boston University, Boston, MA 02215;
- Graduate Program in Bioinformatics, Boston University, Boston, MA 02215
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