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Bergamaschi G, Taris KKH, Biebricher AS, Seymonson XMR, Witt H, Peterman EJG, Wuite GJL. Viscoelasticity of diverse biological samples quantified by Acoustic Force Microrheology (AFMR). Commun Biol 2024; 7:683. [PMID: 38834871 DOI: 10.1038/s42003-024-06367-3] [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: 12/13/2023] [Accepted: 05/21/2024] [Indexed: 06/06/2024] Open
Abstract
In the context of soft matter and cellular mechanics, microrheology - the use of micron-sized particles to probe the frequency-dependent viscoelastic response of materials - is widely used to shed light onto the mechanics and dynamics of molecular structures. Here we present the implementation of active microrheology in an Acoustic Force Spectroscopy setup (AFMR), which combines multiplexing with the possibility of probing a wide range of forces ( ~ pN to ~nN) and frequencies (0.01-100 Hz). To demonstrate the potential of this approach, we perform active microrheology on biological samples of increasing complexity and stiffness: collagen gels, red blood cells (RBCs), and human fibroblasts, spanning a viscoelastic modulus range of five orders of magnitude. We show that AFMR can successfully quantify viscoelastic properties by probing many beads with high single-particle precision and reproducibility. Finally, we demonstrate that AFMR to map local sample heterogeneities as well as detect cellular responses to drugs.
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Affiliation(s)
- Giulia Bergamaschi
- Department of Physics and Astronomy and LaserLaB Amsterdam, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - Kees-Karel H Taris
- Department of Physics and Astronomy and LaserLaB Amsterdam, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - Andreas S Biebricher
- Department of Physics and Astronomy and LaserLaB Amsterdam, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - Xamanie M R Seymonson
- Department of Physics and Astronomy and LaserLaB Amsterdam, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - Hannes Witt
- Department of Physics and Astronomy and LaserLaB Amsterdam, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - Erwin J G Peterman
- Department of Physics and Astronomy and LaserLaB Amsterdam, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - Gijs J L Wuite
- Department of Physics and Astronomy and LaserLaB Amsterdam, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands.
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2
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Schmitt MS, Colen J, Sala S, Devany J, Seetharaman S, Caillier A, Gardel ML, Oakes PW, Vitelli V. Machine learning interpretable models of cell mechanics from protein images. Cell 2024; 187:481-494.e24. [PMID: 38194965 DOI: 10.1016/j.cell.2023.11.041] [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: 03/21/2023] [Revised: 09/20/2023] [Accepted: 11/29/2023] [Indexed: 01/11/2024]
Abstract
Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. Currently, no systematic strategy exists to infer large-scale physical properties of a cell from its molecular components. This is an obstacle to understanding processes such as cell adhesion and migration. Here, we develop a data-driven modeling pipeline to learn the mechanical behavior of adherent cells. We first train neural networks to predict cellular forces from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion (FA) protein, such as zyxin, are sufficient to predict forces and can generalize to unseen biological regimes. Using this observation, we develop two approaches-one constrained by physics and the other agnostic-to construct data-driven continuum models of cellular forces. Both reveal how cellular forces are encoded by two distinct length scales. Beyond adherent cell mechanics, our work serves as a case study for integrating neural networks into predictive models for cell biology.
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Affiliation(s)
- Matthew S Schmitt
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA; Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637, USA
| | - Jonathan Colen
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA; Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637, USA
| | - Stefano Sala
- Department of Cell & Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL 60153, USA
| | - John Devany
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA
| | - Shailaja Seetharaman
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA
| | - Alexia Caillier
- Department of Cell & Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL 60153, USA
| | - Margaret L Gardel
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA.
| | - Patrick W Oakes
- Department of Cell & Molecular Physiology, Stritch School of Medicine, Loyola University Chicago, Maywood, IL 60153, USA.
| | - Vincenzo Vitelli
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA; Department of Physics, University of Chicago, Chicago, IL 60637, USA; Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637, USA.
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3
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Nakul U, Roy S, Nalupurackal G, Chakraborty S, Siwach P, Goswami J, Edwina P, Bajpai SK, Singh R, Roy B. Studying fluctuating trajectories of optically confined passive tracers inside cells provides familiar active forces. BIOMEDICAL OPTICS EXPRESS 2023; 14:5440. [PMID: 37810271 PMCID: PMC7615170 DOI: 10.1364/boe.499990] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Revised: 08/14/2023] [Accepted: 09/05/2023] [Indexed: 10/10/2023]
Abstract
In recent years, there has been a growing interest in studying the trajectories of microparticles inside living cells. Among other things, such studies are useful in understanding the spatio-temporal properties of a cell. In this work, we study the stochastic trajectories of a passive microparticle inside a cell using experiments and theory. Our theory is based on modeling the microparticle inside a cell as an active particle in a viscoelastic medium. The activity is included in our model from an additional stochastic term with non-zero persistence in the Langevin equation describing the dynamics of the microparticle. Using this model, we are able to predict the power spectral density (PSD) measured in the experiment and compute active forces. This caters to the situation where a tracer particle is optically confined and then yields a PSD for positional fluctuations. The low frequency part of the PSD yields information about the active forces that the particle feels. The fit to the model extracts such active force. Thus, we can conclude that trapping the particle does not affect the values of the forces extracted from the active fits if accounted for appropriately by proper theoretical models. In addition, the fit also provides system properties and optical tweezers trap stiffness.
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Affiliation(s)
- Urvashi Nakul
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Srestha Roy
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Gokul Nalupurackal
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Snigdhadev Chakraborty
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Priyanka Siwach
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Jayesh Goswami
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Privita Edwina
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
- Department of Applied Mechanics, IIT Madras, Chennai 600036, India
| | | | - Rajesh Singh
- Department of Physics, IIT Madras, Chennai 600036, India
| | - Basudev Roy
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
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4
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Baule A, Sollich P. Exponential increase of transition rates in metastable systems driven by non-Gaussian noise. Sci Rep 2023; 13:3853. [PMID: 36890184 PMCID: PMC9995508 DOI: 10.1038/s41598-023-30577-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2022] [Accepted: 02/27/2023] [Indexed: 03/10/2023] Open
Abstract
Noise-induced escape from metastable states governs a plethora of transition phenomena in physics, chemistry, and biology. While the escape problem in the presence of thermal Gaussian noise has been well understood since the seminal works of Arrhenius and Kramers, many systems, in particular living ones, are effectively driven by non-Gaussian noise for which the conventional theory does not apply. Here we present a theoretical framework based on path integrals that allows the calculation of both escape rates and optimal escape paths for a generic class of non-Gaussian noises. We find that non-Gaussian noise always leads to more efficient escape and can enhance escape rates by many orders of magnitude compared with thermal noise, highlighting that away from equilibrium escape rates cannot be reliably modelled based on the traditional Arrhenius-Kramers result. Our analysis also identifies a new universality class of non-Gaussian noises, for which escape paths are dominated by large jumps.
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Affiliation(s)
- Adrian Baule
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK.
| | - Peter Sollich
- Institute for Theoretical Physics, Georg-August-University Göttingen, 37077, Göttingen, Germany.,Department of Mathematics, King's College London, London, WC2R 2LS, UK
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5
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Assante R, Corbett D, Marenduzzo D, Morozov A. Active turbulence and spontaneous phase separation in inhomogeneous extensile active gels. SOFT MATTER 2023; 19:189-198. [PMID: 36503973 DOI: 10.1039/d2sm01188c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
We report numerical results for the hydrodynamics of inhomogeneous lyotropic and extensile active nematic gels. By simulating the coupled Cahn-Hilliard, Navier-Stokes, and Beris-Edwards equation for the evolution of the composition, flow and orientational order of an active nematic, we ask whether composition variations are important to determine its emergent physics. As in active gels of uniform composition, we find that increasing either activity or nematic tendency (e.g., overall active matter concentration) triggers a transition between an isotropic passive phase and an active nematic one. We show that composition inhomogeneities are important in the latter phase, where we find three types of possible dynamical regimes. First, we observe regular patterns with defects and vortices: these exist close to the passive-active transition. Second, for larger activity, or deeper in the nematic phase, we find active turbulence, as in active gels of uniform composition, but with exceedingly large composition variation. In the third regime, which is uniquely associated with inhomogeneity and occurs for large nematic tendency and low activity, we observe spontaneous microphase separation into active and passive domains. The microphase separated regime is notable in view of the absence of an explicit demixing term in the underlying free energy which we use, and we provide a theoretical analysis based on the common tangent construction which explains its existence. We hope this regime can be probed experimentally in the future.
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Affiliation(s)
- Renato Assante
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - Dom Corbett
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - Alexander Morozov
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
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6
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Dwyer ME, Robertson-Anderson RM, Gurmessa BJ. Nonlinear Microscale Mechanics of Actin Networks Governed by Coupling of Filament Crosslinking and Stabilization. Polymers (Basel) 2022; 14:polym14224980. [PMID: 36433106 PMCID: PMC9696012 DOI: 10.3390/polym14224980] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Revised: 11/11/2022] [Accepted: 11/14/2022] [Indexed: 11/19/2022] Open
Abstract
Actin plays a vital role in maintaining the stability and rigidity of biological cells while allowing for cell motility and shape change. The semiflexible nature of actin filaments-along with the myriad actin-binding proteins (ABPs) that serve to crosslink, bundle, and stabilize filaments-are central to this multifunctionality. The effect of ABPs on the structural and mechanical properties of actin networks has been the topic of fervent investigation over the past few decades. Yet, the combined impact of filament stabilization, stiffening and crosslinking via ABPs on the mechanical response of actin networks has yet to be explored. Here, we perform optical tweezers microrheology measurements to characterize the nonlinear force response and relaxation dynamics of actin networks in the presence of varying concentrations of α-actinin, which transiently crosslinks actin filaments, and phalloidin, which stabilizes filamentous actin and increases its persistence length. We show that crosslinking and stabilization can act both synergistically and antagonistically to tune the network resistance to nonlinear straining. For example, phalloidin stabilization leads to enhanced elastic response and reduced dissipation at large strains and timescales, while the initial microscale force response is reduced compared to networks without phalloidin. Moreover, we find that stabilization switches this initial response from that of stress stiffening to softening despite the increased filament stiffness that phalloidin confers. Finally, we show that both crosslinking and stabilization are necessary to elicit these emergent features, while the effect of stabilization on networks without crosslinkers is much more subdued. We suggest that these intriguing mechanical properties arise from the competition and cooperation between filament connectivity, bundling, and rigidification, shedding light on how ABPs with distinct roles can act in concert to mediate diverse mechanical properties of the cytoskeleton and bio-inspired polymeric materials.
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Affiliation(s)
- Mike E. Dwyer
- Department of Physics and Astronomy, Bucknell University, Lewisburg, PA 17837, USA
| | | | - Bekele J. Gurmessa
- Department of Physics and Astronomy, Bucknell University, Lewisburg, PA 17837, USA
- Correspondence:
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7
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Floyd C, Ni H, Gunaratne RS, Erban R, Papoian GA. On Stretching, Bending, Shearing, and Twisting of Actin Filaments I: Variational Models. J Chem Theory Comput 2022; 18:4865-4878. [PMID: 35895330 DOI: 10.1021/acs.jctc.2c00318] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Mechanochemical simulations of actomyosin networks are traditionally based on one-dimensional models of actin filaments having zero width. Here, and in the follow up paper (arXiv, DOI 10.48550/arXiv.2203.01284), approaches are presented for more efficient modeling that incorporates stretching, shearing, and twisting of actin filaments. Our modeling of a semiflexible filament with a small but finite width is based on the Cosserat theory of elastic rods, which allows for six degrees of freedom at every point on the filament's backbone. In the variational models presented in this paper, a small and discrete set of parameters is used to describe a smooth filament shape having all degrees of freedom allowed in the Cosserat theory. Two main approaches are introduced: one where polynomial spline functions describe the filament's configuration, and one in which geodesic curves in the space of the configurational degrees of freedom are used. We find that in the latter representation the strain energy function can be calculated without resorting to a small-angle expansion, so it can describe arbitrarily large filament deformations without systematic error. These approaches are validated by a dynamical model of a Cosserat filament, which can be further extended by using multiresolution methods to allow more detailed monomer-based resolution in certain parts of the actin filament, as introduced in the follow up paper. The presented framework is illustrated by showing how torsional compliance in a finite-width filament can induce broken chiral symmetry in the structure of a cross-linked bundle.
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Affiliation(s)
- Carlos Floyd
- Department of Chemistry & Biochemistry, Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
| | - Haoran Ni
- Department of Chemistry & Biochemistry, Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
| | - Ravinda S Gunaratne
- Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom
| | - Radek Erban
- Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom
| | - Garegin A Papoian
- Department of Chemistry & Biochemistry, Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
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8
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Katuri J, Poehnl R, Sokolov A, Uspal W, Snezhko A. Arrested-motility states in populations of shape-anisotropic active Janus particles. SCIENCE ADVANCES 2022; 8:eabo3604. [PMID: 35776793 PMCID: PMC10883369 DOI: 10.1126/sciadv.abo3604] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The emergence of large-scale collective phenomena from simple interactions between individual units is a hallmark of active matter systems. Active colloids with alignment-dominated interparticle interactions tend to develop orientational order and form motile coherent states, such as flocks and swarms. Alternatively, a combination of self-propulsion and excluded-volume interactions results in self-trapping and active phase separation into dense clusters. Here, we reveal unconventional arrested-motility states in ensembles of active discoidal particles powered by induced-charge electrophoresis. Combining experiments and computational modeling, we demonstrate that the shape asymmetry of the particles promotes the hydrodynamically assisted formation of active particles' bound states in a certain range of excitation parameters, ultimately leading to a spontaneous collective state with arrested motility. Unlike the jammed clusters obtained through self-trapping, the arrested-motility phase remains sparse, dynamic, and reconfigurable. The demonstrated mechanism of phase separation seeded by bound state formation in ensembles of oblate active particles is generic and should be applicable to other active colloidal systems.
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Affiliation(s)
- Jaideep Katuri
- Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, IL 60439, USA
| | - Ruben Poehnl
- Department of Mechanical Engineering, University of Hawai'i at Mānoa, 2540 Dole Street, Holmes Hall 302, Honolulu, HI 96822, USA
| | - Andrey Sokolov
- Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, IL 60439, USA
| | - William Uspal
- Department of Mechanical Engineering, University of Hawai'i at Mānoa, 2540 Dole Street, Holmes Hall 302, Honolulu, HI 96822, USA
| | - Alexey Snezhko
- Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, IL 60439, USA
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9
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Cates ME, Fodor É, Markovich T, Nardini C, Tjhung E. Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production. ENTROPY 2022; 24:e24020254. [PMID: 35205548 PMCID: PMC8870959 DOI: 10.3390/e24020254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Revised: 01/18/2022] [Accepted: 01/27/2022] [Indexed: 12/04/2022]
Abstract
Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself.
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Affiliation(s)
- Michael E. Cates
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK;
| | - Étienne Fodor
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg;
| | - Tomer Markovich
- Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
- Correspondence:
| | - Cesare Nardini
- Service de Physique de l’Etat Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France;
- Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS, 75005 Paris, France
| | - Elsen Tjhung
- Department of Physics, University of Durham, Science Laboratories, South Road, Durham DH1 3LE, UK;
- School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK
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10
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Markovich T, Lubensky TC. Odd Viscosity in Active Matter: Microscopic Origin and 3D Effects. PHYSICAL REVIEW LETTERS 2021; 127:048001. [PMID: 34355935 DOI: 10.1103/physrevlett.127.048001] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Revised: 04/19/2021] [Accepted: 06/03/2021] [Indexed: 06/13/2023]
Abstract
In common fluids, viscosity is associated with dissipation. However, when time-reversal symmetry is broken a new type of nondissipative "viscosity" emerges. Recent theories and experiments on classical 2D systems with active spinning particles have heightened interest in "odd viscosity," but a microscopic theory for it in active materials is still absent. Here, we present such first-principles microscopic Hamiltonian theory, valid for both 2D and 3D, showing that odd viscosity is present in any system, even at zero temperature, with globally or locally aligned spinning components. Our work substantially extends the applicability of odd viscosity into 3D fluids, and specifically to internally driven active materials, such as living matter (e.g., actomyosin gels). We find intriguing 3D effects of odd viscosity such as propagation of anisotropic bulk shear waves and breakdown of Bernoulli's principle.
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Affiliation(s)
- Tomer Markovich
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Tom C Lubensky
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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11
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Lv Z, de-Carvalho J, Telley IA, Großhans J. Cytoskeletal mechanics and dynamics in the Drosophila syncytial embryo. J Cell Sci 2021; 134:134/4/jcs246496. [PMID: 33597155 DOI: 10.1242/jcs.246496] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Abstract
Cell and tissue functions rely on the genetic programmes and cascades of biochemical signals. It has become evident during the past decade that the physical properties of soft material that govern the mechanics of cells and tissues play an important role in cellular function and morphology. The biophysical properties of cells and tissues are determined by the cytoskeleton, consisting of dynamic networks of F-actin and microtubules, molecular motors, crosslinkers and other associated proteins, among other factors such as cell-cell interactions. The Drosophila syncytial embryo represents a simple pseudo-tissue, with its nuclei orderly embedded in a structured cytoskeletal matrix at the embryonic cortex with no physical separation by cellular membranes. Here, we review the stereotypic dynamics and regulation of the cytoskeleton in Drosophila syncytial embryos and how cytoskeletal dynamics underlies biophysical properties and the emergence of collective features. We highlight the specific features and processes of syncytial embryos and discuss the applicability of biophysical approaches.
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Affiliation(s)
- Zhiyi Lv
- Institute of Evolution and Marine Biodiversity, Ocean University of China, Qingdao, 266003, China
| | - Jorge de-Carvalho
- Instituto Gulbenkian de Ciência, Fundação Calouste Gulbenkian, 2780-156 Oeiras, Portugal
| | - Ivo A Telley
- Instituto Gulbenkian de Ciência, Fundação Calouste Gulbenkian, 2780-156 Oeiras, Portugal
| | - Jörg Großhans
- Fachbereich Biologie, Philipps-Universität Marburg, 35043 Marburg, Germany
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12
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Gnesotto FS, Gradziuk G, Ronceray P, Broedersz CP. Learning the non-equilibrium dynamics of Brownian movies. Nat Commun 2020; 11:5378. [PMID: 33097699 PMCID: PMC7585442 DOI: 10.1038/s41467-020-18796-9] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 09/10/2020] [Indexed: 01/30/2023] Open
Abstract
Time-lapse microscopy imaging provides direct access to the dynamics of soft and living systems. At mesoscopic scales, such microscopy experiments reveal intrinsic thermal and non-equilibrium fluctuations. These fluctuations, together with measurement noise, pose a challenge for the dynamical analysis of these Brownian movies. Traditionally, methods to analyze such experimental data rely on tracking embedded or endogenous probes. However, it is in general unclear, especially in complex many-body systems, which degrees of freedom are the most informative about their non-equilibrium nature. Here, we introduce an alternative, tracking-free approach that overcomes these difficulties via an unsupervised analysis of the Brownian movie. We develop a dimensional reduction scheme selecting a basis of modes based on dissipation. Subsequently, we learn the non-equilibrium dynamics, thereby estimating the entropy production rate and time-resolved force maps. After benchmarking our method against a minimal model, we illustrate its broader applicability with an example inspired by active biopolymer gels.
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Affiliation(s)
- Federico S Gnesotto
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333, München, Germany
| | - Grzegorz Gradziuk
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333, München, Germany
| | - Pierre Ronceray
- Center for the Physics of Biological Function, Princeton University, Princeton, NJ, 08544, USA.
| | - Chase P Broedersz
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333, München, Germany.
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, Amsterdam, HV, 1081, The Netherlands.
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13
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Mierke CT. Mechanical Cues Affect Migration and Invasion of Cells From Three Different Directions. Front Cell Dev Biol 2020; 8:583226. [PMID: 33043017 PMCID: PMC7527720 DOI: 10.3389/fcell.2020.583226] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Accepted: 08/24/2020] [Indexed: 12/20/2022] Open
Abstract
Cell migration and invasion is a key driving factor for providing essential cellular functions under physiological conditions or the malignant progression of tumors following downward the metastatic cascade. Although there has been plentiful of molecules identified to support the migration and invasion of cells, the mechanical aspects have not yet been explored in a combined and systematic manner. In addition, the cellular environment has been classically and frequently assumed to be homogeneous for reasons of simplicity. However, motility assays have led to various models for migration covering only some aspects and supporting factors that in some cases also include mechanical factors. Instead of specific models, in this review, a more or less holistic model for cell motility in 3D is envisioned covering all these different aspects with a special emphasis on the mechanical cues from a biophysical perspective. After introducing the mechanical aspects of cell migration and invasion and presenting the heterogeneity of extracellular matrices, the three distinct directions of cell motility focusing on the mechanical aspects are presented. These three different directions are as follows: firstly, the commonly used invasion tests using structural and structure-based mechanical environmental signals; secondly, the mechano-invasion assay, in which cells are studied by mechanical forces to migrate and invade; and thirdly, cell mechanics, including cytoskeletal and nuclear mechanics, to influence cell migration and invasion. Since the interaction between the cell and the microenvironment is bi-directional in these assays, these should be accounted in migration and invasion approaches focusing on the mechanical aspects. Beyond this, there is also the interaction between the cytoskeleton of the cell and its other compartments, such as the cell nucleus. In specific, a three-element approach is presented for addressing the effect of mechanics on cell migration and invasion by including the effect of the mechano-phenotype of the cytoskeleton, nucleus and the cell's microenvironment into the analysis. In precise terms, the combination of these three research approaches including experimental techniques seems to be promising for revealing bi-directional impacts of mechanical alterations of the cellular microenvironment on cells and internal mechanical fluctuations or changes of cells on the surroundings. Finally, different approaches are discussed and thereby a model for the broad impact of mechanics on cell migration and invasion is evolved.
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Affiliation(s)
- Claudia Tanja Mierke
- Faculty of Physics and Earth Science, Peter Debye Institute of Soft Matter Physics, Biological Physics Division, University of Leipzig, Leipzig, Germany
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14
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Nazockdast E, Redemann S. Mechanics of the spindle apparatus. Semin Cell Dev Biol 2020; 107:91-102. [PMID: 32747191 DOI: 10.1016/j.semcdb.2020.06.018] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2020] [Revised: 06/02/2020] [Accepted: 06/30/2020] [Indexed: 12/01/2022]
Abstract
During mitosis microtubules self-organize to form a bipolar mitotic spindle structure, which positions the sister chromatids on the spindle mid-plane and separates them afterwards. Previous studies have identified many spindle associated proteins. Yet, we do not fully understand how these nanoscopic proteins lead to force generation through interactions of individual microtubules, motor proteins and chromosomes, and how a large number of these local interactions ultimately determine the structure and mechanics of the spindle in micron scale. Here we review the current understanding and open questions related to the structure and mechanics of the mitotic spindle. We then discuss how a combination of electron microscopy and computational modeling can be used to tackle some of these open questions.
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Affiliation(s)
- Ehssan Nazockdast
- Department of Applied Physical Sciences, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA.
| | - Stefanie Redemann
- Center for Membrane and Cell Physiology & Department of Molecular Physiology and Biological Physics, University of Virginia, School of Medicine, Charlottesville, VA, USA.
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15
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Cao X, Zhang B, Zhao N. Contrastive factors of activity and crowding on conformational properties of a flexible polymer. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.137213] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
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16
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Banerjee S, Gardel ML, Schwarz US. The Actin Cytoskeleton as an Active Adaptive Material. ANNUAL REVIEW OF CONDENSED MATTER PHYSICS 2020; 11:421-439. [PMID: 33343823 PMCID: PMC7748259 DOI: 10.1146/annurev-conmatphys-031218-013231] [Citation(s) in RCA: 55] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Actin is the main protein used by biological cells to adapt their structure and mechanics to their needs. Cellular adaptation is made possible by molecular processes that strongly depend on mechanics. The actin cytoskeleton is also an active material that continuously consumes energy. This allows for dynamical processes that are possible only out of equilibrium and opens up the possibility for multiple layers of control that have evolved around this single protein.Here we discuss the actin cytoskeleton from the viewpoint of physics as an active adaptive material that can build structures superior to man-made soft matter systems. Not only can actin be used to build different network architectures on demand and in an adaptive manner, but it also exhibits the dynamical properties of feedback systems, like excitability, bistability, or oscillations. Therefore, it is a prime example of how biology couples physical structure and information flow and a role model for biology-inspired metamaterials.
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Affiliation(s)
- Shiladitya Banerjee
- Department of Physics and Astronomy and Institute for the Physics of Living Systems, University College London, London WC1E 6BT, United Kingdom
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Margaret L Gardel
- Department of Physics, James Franck Institute, and Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, USA
| | - Ulrich S Schwarz
- Institute for Theoretical Physics and BioQuant, Heidelberg University, 69120 Heidelberg, Germany
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17
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Cao X, Zhang B, Zhao N. Effective temperature scaled dynamics of a flexible polymer in an active bath. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1730992] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Xiuli Cao
- College of Chemistry, Sichuan University, Chengdu, China
| | - Bingjie Zhang
- College of Chemistry, Sichuan University, Chengdu, China
| | - Nanrong Zhao
- College of Chemistry, Sichuan University, Chengdu, China
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18
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Mura F, Gradziuk G, Broedersz CP. Mesoscopic non-equilibrium measures can reveal intrinsic features of the active driving. SOFT MATTER 2019; 15:8067-8076. [PMID: 31576897 DOI: 10.1039/c9sm01169b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Biological assemblies such as chromosomes, membranes, and the cytoskeleton are driven out of equilibrium at the nanoscale by enzymatic activity and molecular motors. Similar non-equilibrium dynamics can be realized in synthetic systems, such as chemically fueled colloidal particles. Characterizing the stochastic non-equilibrium dynamics of such active soft assemblies still remains a challenge. Recently, new non-invasive approaches have been proposed to determine the non-equilibrium behavior, which are based on detecting broken detailed balance in the stochastic trajectories of several coordinates of the system. Inspired by the method of two-point microrheology, in which the equilibrium fluctuations of a pair of probe particles reveal the viscoelastic response of an equilibrium system, here, we investigate whether we can extend such an approach to non-equilibrium assemblies: can one extract information on the nature of the active driving in a system from the analysis of a two-point non-equilibrium measure? We address this question theoretically in the context of a class of elastic systems, driven out of equilibrium by a spatially heterogeneous stochastic internal driving. We consider several scenarios for the spatial features of the internal driving that may be relevant in biological and synthetic systems, and investigate how such features of the active noise may be reflected in the long-range scaling behavior of two-point non-equilibrium measures.
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Affiliation(s)
- Federica Mura
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany.
| | - Grzegorz Gradziuk
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany.
| | - Chase P Broedersz
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany.
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19
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Force Spectrum Microscopy Using Mitochondrial Fluctuations of Control and ATP-Depleted Cells. Biophys J 2019; 114:2933-2944. [PMID: 29925029 DOI: 10.1016/j.bpj.2018.05.002] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2017] [Revised: 04/15/2018] [Accepted: 05/01/2018] [Indexed: 11/24/2022] Open
Abstract
A single-cell assay of active and passive intracellular mechanical properties of mammalian cells could give significant insight into cellular processes. Force spectrum microscopy (FSM) is one such technique, which combines the spontaneous motion of probe particles and the mechanical properties of the cytoskeleton measured by active microrheology using optical tweezers to determine the force spectrum of the cytoskeleton. A simpler and noninvasive method to perform FSM would be very useful, enabling its widespread adoption. Here, we develop an alternative method of FSM using measurement of the fluctuating motion of mitochondria. Mitochondria of the C3H-10T1/2 cell line were labeled and tracked using confocal microscopy. Mitochondrial probes were selected based on morphological characteristics, and their mean-square displacement, creep compliance, and distributions of directional change were measured. We found that the creep compliance of mitochondria resembles that of particles in viscoelastic media. However, comparisons of creep compliance between controls and cells treated with pharmacological agents showed that perturbations to the actomysoin network had surprisingly small effects on mitochondrial fluctuations, whereas microtubule disruption and ATP depletion led to a significantly decreased creep compliance. We used properties of the distribution of directional change to identify a regime of thermally dominated fluctuations in ATP-depleted cells, allowing us to estimate the viscoelastic parameters for a range of timescales. We then determined the force spectrum by combining these viscoelastic properties with measurements of spontaneous fluctuations tracked in control cells. Comparisons with previous measurements made using FSM revealed an excellent match.
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20
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Andorfer R, Alper JD. From isolated structures to continuous networks: A categorization of cytoskeleton-based motile engineered biological microstructures. WILEY INTERDISCIPLINARY REVIEWS. NANOMEDICINE AND NANOBIOTECHNOLOGY 2019; 11:e1553. [PMID: 30740918 PMCID: PMC6881777 DOI: 10.1002/wnan.1553] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Revised: 12/27/2018] [Accepted: 12/28/2018] [Indexed: 11/06/2022]
Abstract
As technology at the small scale is advancing, motile engineered microstructures are becoming useful in drug delivery, biomedicine, and lab-on-a-chip devices. However, traditional engineering methods and materials can be inefficient or functionally inadequate for small-scale applications. Increasingly, researchers are turning to the biology of the cytoskeleton, including microtubules, actin filaments, kinesins, dyneins, myosins, and associated proteins, for both inspiration and solutions. They are engineering structures with components that range from being entirely biological to being entirely synthetic mimics of biology and on scales that range from isotropic continuous networks to single isolated structures. Motile biological microstructures trace their origins from the development of assays used to study the cytoskeleton to the array of structures currently available today. We define 12 types of motile biological microstructures, based on four categories: entirely biological, modular, hybrid, and synthetic, and three scales: networks, clusters, and isolated structures. We highlight some key examples, the unique functionalities, and the potential applications of each microstructure type, and we summarize the quantitative models that enable engineering them. By categorizing the diversity of motile biological microstructures in this way, we aim to establish a framework to classify these structures, define the gaps in current research, and spur ideas to fill those gaps. This article is categorized under: Nanotechnology Approaches to Biology > Nanoscale Systems in Biology Nanotechnology Approaches to Biology > Cells at the Nanoscale Biology-Inspired Nanomaterials > Protein and Virus-Based Structures Therapeutic Approaches and Drug Discovery > Emerging Technologies.
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Affiliation(s)
- Rachel Andorfer
- Department of Bioengineering, Clemson University, Clemson, South Carolina
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina
| | - Joshua D. Alper
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina
- Department of Biological Sciences, Clemson University, Clemson, South Carolina
- Eukaryotic Pathogen Innovations Center, Clemson University, Clemson, South Carolina
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21
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Gradziuk G, Mura F, Broedersz CP. Scaling behavior of nonequilibrium measures in internally driven elastic assemblies. Phys Rev E 2019; 99:052406. [PMID: 31212437 DOI: 10.1103/physreve.99.052406] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2019] [Indexed: 11/07/2022]
Abstract
Detecting and quantifying nonequilibrium activity is essential for studying internally driven assemblies, including synthetic active matter and complex living systems such as cells or tissue. We discuss a noninvasive approach of measuring nonequilibrium behavior based on the breaking of detailed balance. We focus on "cycling frequencies"-the average frequency with which the trajectories of pairs of degrees of freedom revolve in phase space-and explain their connection with other nonequilibrium measures, including the area enclosing rate and the entropy production rate. We test our approach on simple toy models composed of elastic networks immersed in a viscous fluid with site-dependent internal driving. We prove both numerically and analytically that the cycling frequencies obey a power law as a function of distance between the tracked degrees of freedom. Importantly, the behavior of the cycling frequencies contains information about the dimensionality of the system and the amplitude of active noise. The mapping we use in our analytical approach thus offers a convenient framework for predicting the behavior of two-point nonequilibrium measures for a given activity distribution in the network.
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Affiliation(s)
- Grzegorz Gradziuk
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | - Federica Mura
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | - Chase P Broedersz
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
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22
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Goldstein D, Ramaswamy S, Chakraborty B. Stress fluctuations in transient active networks. SOFT MATTER 2019; 15:3520-3526. [PMID: 30969302 DOI: 10.1039/c9sm00205g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Inspired by experiments on dynamic extensile gels of biofilaments and motors, we propose a model of a network of linear springs with kinetics consisting of growth at a prescribed rate, death after a lifetime drawn from a distribution, and birth at a randomly chosen node. The model captures features such as the build-up of self-stress, that are not easily incorporated into hydrodynamic theories. We study the model numerically and show that our observations can largely be understood through a stochastic effective-medium model. The resulting dynamically extending force-dipole network displays many features of yielded plastic solids, and offers a way to incorporate strongly non-affine effects into theories of active solids. A rather distinctive form for the stress distribution, and a Herschel-Bulkley dependence of stress on activity, are our major predictions.
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Affiliation(s)
- Daniel Goldstein
- Martin Fisher School of Physics, Brandeis University, Waltham, USA.
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23
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Razin N, Voituriez R, Gov NS. Signatures of motor susceptibility to forces in the dynamics of a tracer particle in an active gel. Phys Rev E 2019; 99:022419. [PMID: 30934368 DOI: 10.1103/physreve.99.022419] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2018] [Indexed: 06/09/2023]
Abstract
We study a model for the motion of a tracer particle inside an active gel, exposing the properties of the van Hove distribution of the particle displacements. Active events of a typical force magnitude can give rise to non-Gaussian distributions having exponential tails or side peaks. The side peaks are predicted to appear when the local bulk elasticity of the gel is large enough and few active sources are dominant. We explain the regimes of the different distributions and study the structure of the side peaks for active sources that are susceptible to the elastic stress that they cause inside the gel. We show how the van Hove distribution is altered by both the duty cycle of the active sources and their susceptibility, and suggest it as a sensitive probe to analyze microrheology data in active systems with restoring elastic forces.
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Affiliation(s)
- Nitzan Razin
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Raphael Voituriez
- Laboratoire Jean Perrin and Laboratoire de Physique Théorique de la Matière Condensée, CNRS / Sorbonne Universite, 75005 Paris, France
| | - Nir S Gov
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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24
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Mura F, Gradziuk G, Broedersz CP. Nonequilibrium Scaling Behavior in Driven Soft Biological Assemblies. PHYSICAL REVIEW LETTERS 2018; 121:038002. [PMID: 30085773 DOI: 10.1103/physrevlett.121.038002] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2018] [Revised: 04/13/2018] [Indexed: 06/08/2023]
Abstract
Measuring and quantifying nonequilibrium dynamics in active biological systems is a major challenge because of their intrinsic stochastic nature and the limited number of variables accessible in any real experiment. We investigate what nonequilibrium information can be extracted from noninvasive measurements using a stochastic model of soft elastic networks with a heterogeneous distribution of activities, representing enzymatic force generation. In particular, we use this model to study how the nonequilibrium activity, detected by tracking two probes in the network, scales as a function of the distance between the probes. We quantify the nonequilibrium dynamics through the cycling frequencies, a simple measure of circulating currents in the phase space of the probes. We find that these cycling frequencies exhibit power-law scaling behavior with the distance between probes. In addition, we show that this scaling behavior governs the entropy production rate that can be recovered from the two traced probes. Our results provide insight into how internal enzymatic driving generates nonequilibrium dynamics on different scales in soft biological assemblies.
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Affiliation(s)
- Federica Mura
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | - Grzegorz Gradziuk
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | - Chase P Broedersz
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
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25
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Lo WC, Madrak C, Kiehart DP, Edwards GS. Unified biophysical mechanism for cell-shape oscillations and cell ingression. Phys Rev E 2018; 97:062414. [PMID: 30011599 PMCID: PMC6440536 DOI: 10.1103/physreve.97.062414] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2017] [Indexed: 12/31/2022]
Abstract
We describe a mechanochemical and percolation cascade that augments myosin's regulatory network to tune cytoskeletal forces. Actomyosin forces collectively generate cytoskeletal forces during cell oscillations and ingression, which we quantify by elastic percolation of the internally driven, cross-linked actin network. Contractile units can produce relatively large, oscillatory forces that disrupt crosslinks to reduce cytoskeletal forces. A (reverse) Hopf bifurcation switches contractile units to produce smaller, steady forces that enhance crosslinking and consequently boost cytoskeletal forces to promote ingression. We describe cell-shape changes and cell ingression in terms of intercellular force imbalances along common cell junctions.
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Affiliation(s)
- Wei-Chang Lo
- Physics Department, Duke University, Durham, North Carolina 27708, USA
| | - Craig Madrak
- Physics Department, Duke University, Durham, North Carolina 27708, USA
| | - Daniel P Kiehart
- Biology Department, Duke University, Durham, North Carolina 27708, USA
| | - Glenn S Edwards
- Physics Department, Duke University, Durham, North Carolina 27708, USA
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26
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Gnesotto FS, Mura F, Gladrow J, Broedersz CP. Broken detailed balance and non-equilibrium dynamics in living systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:066601. [PMID: 29504517 DOI: 10.1088/1361-6633/aab3ed] [Citation(s) in RCA: 110] [Impact Index Per Article: 18.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.
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Affiliation(s)
- F S Gnesotto
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
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27
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Pegoraro AF, Janmey P, Weitz DA. Mechanical Properties of the Cytoskeleton and Cells. Cold Spring Harb Perspect Biol 2017; 9:9/11/a022038. [PMID: 29092896 DOI: 10.1101/cshperspect.a022038] [Citation(s) in RCA: 156] [Impact Index Per Article: 22.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
SUMMARYThe cytoskeleton is the major mechanical structure of the cell; it is a complex, dynamic biopolymer network comprising microtubules, actin, and intermediate filaments. Both the individual filaments and the entire network are not simple elastic solids but are instead highly nonlinear structures. Appreciating the mechanics of biopolymer networks is key to understanding the mechanics of cells. Here, we review the mechanical properties of cytoskeletal polymers and discuss the implications for the behavior of cells.
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Affiliation(s)
- Adrian F Pegoraro
- Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
| | - Paul Janmey
- Institute for Medicine and Engineering and Department of Physiology, Perelman School of Medicine, and Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104
| | - David A Weitz
- Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
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28
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Gladrow J, Broedersz CP, Schmidt CF. Nonequilibrium dynamics of probe filaments in actin-myosin networks. Phys Rev E 2017; 96:022408. [PMID: 28950472 DOI: 10.1103/physreve.96.022408] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2017] [Indexed: 06/07/2023]
Abstract
Active dynamic processes of cells are largely driven by the cytoskeleton, a complex and adaptable semiflexible polymer network, motorized by mechanoenzymes. Small dimensions, confined geometries, and hierarchical structures make it challenging to probe dynamics and mechanical response of such networks. Embedded semiflexible probe polymers can serve as nonperturbing multiscale probes to detect force distributions in active polymer networks. We show here that motor-induced forces transmitted to the probe polymers are reflected in nonequilibrium bending dynamics, which we analyze in terms of spatial eigenmodes of an elastic beam under steady-state conditions. We demonstrate how these active forces induce correlations among the mode amplitudes, which furthermore break time-reversal symmetry. This leads to a breaking of detailed balance in this mode space. We derive analytical predictions for the magnitude of resulting probability currents in mode space in the white-noise limit of motor activity. We relate the structure of these currents to the spatial profile of motor-induced forces along the probe polymers and provide a general relation for observable currents on two-dimensional hyperplanes.
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Affiliation(s)
- J Gladrow
- Third Institute of Physics, University of Göttingen, 37077 Göttingen, Germany
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, England, United Kingdom
| | - C P Broedersz
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - C F Schmidt
- Third Institute of Physics, University of Göttingen, 37077 Göttingen, Germany
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
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29
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Cintora P, Arikkath J, Kandel M, Popescu G, Best‐Popescu C. Cell density modulates intracellular mass transport in neural networks. Cytometry A 2017; 91:503-509. [DOI: 10.1002/cyto.a.23111] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2017] [Revised: 03/21/2017] [Accepted: 03/24/2017] [Indexed: 11/06/2022]
Affiliation(s)
- Patricia Cintora
- Cellular Neuroscience and Imaging Laboratory, Department of BioengineeringUniversity of Illinois at Urbana‐Champaign208 North Wright StreetUrbana Illinois61801
| | - Jyothi Arikkath
- Munroe‐Meyer InstituteUniversity of Nebraska Medical Center (UNMC)Omaha Nebraska
| | - Mikhail Kandel
- Quantitative Light Imaging Laboratory, Department of Electrical and Computer Engineering, Beckman Institute for Advanced Science and TechnologyUniversity of Illinois at Urbana‐ChampaignUrbana Illinois61801
| | - Gabriel Popescu
- Quantitative Light Imaging Laboratory, Department of Electrical and Computer Engineering, Beckman Institute for Advanced Science and TechnologyUniversity of Illinois at Urbana‐ChampaignUrbana Illinois61801
| | - Catherine Best‐Popescu
- Cellular Neuroscience and Imaging Laboratory, Department of BioengineeringUniversity of Illinois at Urbana‐Champaign208 North Wright StreetUrbana Illinois61801
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30
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Zhuo Y, Choi JS, Marin T, Yu H, Harley BA, Cunningham BT. Quantitative Imaging of Cell Membrane-associated Effective Mass Density Using Photonic Crystal Enhanced Microscopy (PCEM). PROGRESS IN QUANTUM ELECTRONICS 2016. [PMID: 28649149 PMCID: PMC5479321 DOI: 10.1016/j.pquantelec.2016.10.001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Adhesion is a critical cellular process that contributes to migration, apoptosis, differentiation, and division. It is followed by the redistribution of cellular materials at the cell membrane or at the cell-surface interface for cells interacting with surfaces, such as basement membranes. Dynamic and quantitative tracking of changes in cell adhesion mass redistribution is challenging because cells are rapidly moving, inhomogeneous, and nonequilibrium objects, whose physical and mechanical properties are difficult to measure or predict. Here, we report a novel biosensor based microscopy approach termed Photonic Crystal Enhanced Microscopy (PCEM) that enables the movement of cellular materials at the plasma membrane of individual live cells to be dynamically monitored and quantitatively imaged. PCEM utilizes a photonic crystal biosensor surface, which can be coated with arbitrary extracellular matrix materials to facilitate cellular interactions, within a modified brightfield microscope with a low intensity non-coherent light source. Benefiting from the high sensitivity, narrow resonance peak, and tight spatial confinement of the evanescent field atop the photonic crystal biosensor, PCEM enables label-free live cell imaging with high sensitivity and high lateral and axial spatial-resolution, thereby allowing dynamic adhesion phenotyping of single cells without the use of fluorescent tags or stains. We apply PCEM to investigate adhesion and the early stage migration of different types of stem cells and cancer cells. By applying image processing algorithms to analyze the complex spatiotemporal information generated by PCEM, we offer insight into how the plasma membrane of anchorage dependent cells is dynamically organized during cell adhesion. The imaging and analysis results presented here provide a new tool for biologists to gain a deeper understanding of the fundamental mechanisms involved with cell adhesion and concurrent or subsequent migration events.
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Affiliation(s)
- Yue Zhuo
- Department of Bioengineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Ji Sun Choi
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Thibault Marin
- InstaRecon Inc., 60 Hazelwood Dr, Champaign, IL 61820, USA
| | - Hojeong Yu
- Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Brendan A. Harley
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Brian T. Cunningham
- Department of Bioengineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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31
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Gladrow J, Fakhri N, MacKintosh FC, Schmidt CF, Broedersz CP. Broken Detailed Balance of Filament Dynamics in Active Networks. PHYSICAL REVIEW LETTERS 2016; 116:248301. [PMID: 27367410 DOI: 10.1103/physrevlett.116.248301] [Citation(s) in RCA: 49] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2016] [Indexed: 06/06/2023]
Abstract
Myosin motor proteins drive vigorous steady-state fluctuations in the actin cytoskeleton of cells. Endogenous embedded semiflexible filaments such as microtubules, or added filaments such as single-walled carbon nanotubes are used as novel tools to noninvasively track equilibrium and nonequilibrium fluctuations in such biopolymer networks. Here, we analytically calculate shape fluctuations of semiflexible probe filaments in a viscoelastic environment, driven out of equilibrium by motor activity. Transverse bending fluctuations of the probe filaments can be decomposed into dynamic normal modes. We find that these modes no longer evolve independently under nonequilibrium driving. This effective mode coupling results in nonzero circulatory currents in a conformational phase space, reflecting a violation of detailed balance. We present predictions for the characteristic frequencies associated with these currents and investigate how the temporal signatures of motor activity determine mode correlations, which we find to be consistent with recent experiments on microtubules embedded in cytoskeletal networks.
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Affiliation(s)
- J Gladrow
- Third Institute of Physics, Georg August University, 37077 Göttingen, Germany
| | - N Fakhri
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - F C MacKintosh
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
- Department of Physics and Astronomy, Vrije Universiteit, 1081 HV Amsterdam, Netherlands
| | - C F Schmidt
- Third Institute of Physics, Georg August University, 37077 Göttingen, Germany
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - C P Broedersz
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
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32
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Schlosser F, Rehfeldt F, Schmidt CF. Force fluctuations in three-dimensional suspended fibroblasts. Philos Trans R Soc Lond B Biol Sci 2015; 370:20140028. [PMID: 25533089 PMCID: PMC4275901 DOI: 10.1098/rstb.2014.0028] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Cells are sensitive to mechanical cues from their environment and at the same time generate and transmit forces to their surroundings. To test quantitatively forces generated by cells not attached to a substrate, we used a dual optical trap to suspend 3T3 fibroblasts between two fibronectin-coated beads. In this simple geometry, we measured both the cells' elastic properties and the force fluctuations they generate with high bandwidth. Cell stiffness decreased substantially with both myosin inhibition by blebbistatin and serum-starvation, but not with microtubule depolymerization by nocodazole. We show that cortical forces generated by non-muscle myosin II deform the cell from its rounded shape in the frequency regime from 0.1 to 10 Hz. The amplitudes of these forces were strongly reduced by blebbistatin and serum starvation, but were unaffected by depolymerization of microtubules. Force fluctuations show a spectrum that is characteristic for an elastic network activated by random sustained stresses with abrupt transitions.
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Affiliation(s)
- Florian Schlosser
- Third Institute of Physics-Biophysics, Georg August University, 37077 Göttingen, Germany
| | - Florian Rehfeldt
- Third Institute of Physics-Biophysics, Georg August University, 37077 Göttingen, Germany
| | - Christoph F Schmidt
- Third Institute of Physics-Biophysics, Georg August University, 37077 Göttingen, Germany
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33
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Needleman D. The Material Basis of Life. Trends Cell Biol 2015; 25:713-716. [DOI: 10.1016/j.tcb.2015.08.011] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2015] [Revised: 08/31/2015] [Accepted: 08/31/2015] [Indexed: 11/17/2022]
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34
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Gralka M, Kroy K. Inelastic mechanics: A unifying principle in biomechanics. BIOCHIMICA ET BIOPHYSICA ACTA-MOLECULAR CELL RESEARCH 2015; 1853:3025-37. [PMID: 26151340 DOI: 10.1016/j.bbamcr.2015.06.017] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2015] [Revised: 05/13/2015] [Accepted: 06/26/2015] [Indexed: 01/16/2023]
Abstract
Many soft materials are classified as viscoelastic. They behave mechanically neither quite fluid-like nor quite solid-like - rather a bit of both. Biomaterials are often said to fall into this class. Here, we argue that this misses a crucial aspect, and that biomechanics is essentially damage mechanics, at heart. When deforming an animal cell or tissue, one can hardly avoid inducing the unfolding of protein domains, the unbinding of cytoskeletal crosslinkers, the breaking of weak sacrificial bonds, and the disruption of transient adhesions. We classify these activated structural changes as inelastic. They are often to a large degree reversible and are therefore not plastic in the proper sense, but they dissipate substantial amounts of elastic energy by structural damping. We review recent experiments involving biological materials on all scales, from single biopolymers over cells to model tissues, to illustrate the unifying power of this paradigm. A deliberately minimalistic yet phenomenologically very rich mathematical modeling framework for inelastic biomechanics is proposed. It transcends the conventional viscoelastic paradigm and suggests itself as a promising candidate for a unified description and interpretation of a wide range of experimental data. This article is part of a Special Issue entitled: Mechanobiology.
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Affiliation(s)
- Matti Gralka
- Institute for Theoretical Physics, University of Leipzig, Bruederstr. 16, 04103 Leipzig, Germany.
| | - Klaus Kroy
- Institute for Theoretical Physics, University of Leipzig, Bruederstr. 16, 04103 Leipzig, Germany.
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35
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Abstract
Mechanical force organizes life at all scales, from molecules to cells and tissues. Although we have made remarkable progress unraveling the mechanics of life's individual building blocks, our understanding of how they give rise to the mechanics of larger-scale biological structures is still poor. Unlike the engineered macroscopic structures that we commonly build, biological structures are dynamic and self-organize: they sculpt themselves and change their own architecture, and they have structural building blocks that generate force and constantly come on and off. A description of such structures defies current traditional mechanical frameworks. It requires approaches that account for active force-generating parts and for the formation of spatial and temporal patterns utilizing a diverse array of building blocks. In this Perspective, we term this framework “emergent mechanics.” Through examples at molecular, cellular, and tissue scales, we highlight challenges and opportunities in quantitatively understanding the emergent mechanics of biological structures and the need for new conceptual frameworks and experimental tools on the way ahead.
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Affiliation(s)
- Sophie Dumont
- Department of Cell and Tissue Biology and Department of Cellular and Molecular Pharmacology, University of California, San Francisco, San Francisco, CA 94143-0512
| | - Manu Prakash
- Department of Bioengineering, Stanford University, Stanford, CA 94305-4125
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36
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Mak M, Kim T, Zaman MH, Kamm RD. Multiscale mechanobiology: computational models for integrating molecules to multicellular systems. Integr Biol (Camb) 2015; 7:1093-108. [PMID: 26019013 DOI: 10.1039/c5ib00043b] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Mechanical signals exist throughout the biological landscape. Across all scales, these signals, in the form of force, stiffness, and deformations, are generated and processed, resulting in an active mechanobiological circuit that controls many fundamental aspects of life, from protein unfolding and cytoskeletal remodeling to collective cell motions. The multiple scales and complex feedback involved present a challenge for fully understanding the nature of this circuit, particularly in development and disease in which it has been implicated. Computational models that accurately predict and are based on experimental data enable a means to integrate basic principles and explore fine details of mechanosensing and mechanotransduction in and across all levels of biological systems. Here we review recent advances in these models along with supporting and emerging experimental findings.
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Affiliation(s)
- Michael Mak
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
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37
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Ahmed WW, Fodor É, Betz T. Active cell mechanics: Measurement and theory. BIOCHIMICA ET BIOPHYSICA ACTA-MOLECULAR CELL RESEARCH 2015; 1853:3083-94. [PMID: 26025677 DOI: 10.1016/j.bbamcr.2015.05.022] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2015] [Revised: 05/16/2015] [Accepted: 05/21/2015] [Indexed: 10/25/2022]
Abstract
Living cells are active mechanical systems that are able to generate forces. Their structure and shape are primarily determined by biopolymer filaments and molecular motors that form the cytoskeleton. Active force generation requires constant consumption of energy to maintain the nonequilibrium activity to drive organization and transport processes necessary for their function. To understand this activity it is necessary to develop new approaches to probe the underlying physical processes. Active cell mechanics incorporates active molecular-scale force generation into the traditional framework of mechanics of materials. This review highlights recent experimental and theoretical developments towards understanding active cell mechanics. We focus primarily on intracellular mechanical measurements and theoretical advances utilizing the Langevin framework. These developing approaches allow a quantitative understanding of nonequilibrium mechanical activity in living cells. This article is part of a Special Issue entitled: Mechanobiology.
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Affiliation(s)
- Wylie W Ahmed
- Institut Curie, Centre de recherche, 11, rue Pierre et Marie Curie, 75005 Paris, France; Sorbonne Universités, Université Pierre et Marie Curie, Paris, France; Centre National de la Recherche Scientifique, UMR168, Paris, France.
| | - Étienne Fodor
- Laboratoire Matière et Systèmes Complexes, UMR7057, Université Paris Diderot, 75013 Paris, France
| | - Timo Betz
- Institut Curie, Centre de recherche, 11, rue Pierre et Marie Curie, 75005 Paris, France; Sorbonne Universités, Université Pierre et Marie Curie, Paris, France; Centre National de la Recherche Scientifique, UMR168, Paris, France
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38
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Sonn-Segev A, Bernheim-Groswasser A, Roichman Y. Extracting the dynamic correlation length of actin networks from microrheology experiments. SOFT MATTER 2014; 10:8324-8329. [PMID: 25192175 DOI: 10.1039/c4sm01538j] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The mechanical properties of polymer gels based on cytoskeleton proteins (e.g. actin) have been studied extensively due to their significant role in biological cell motility and in maintaining the cell's structural integrity. Microrheology is the natural method of choice for such studies due to its economy in sample volume, its wide frequency range, and its spatial sensitivity. In microrheology, the thermal motion of tracer particles embedded in a complex fluid is used to extract the fluid's viscoelastic properties. Comparing the motion of a single particle to the correlated motion of particle pairs, it is possible to extract viscoelastic properties at different length scales. In a recent study, a crossover between intermediate and bulk response of complex fluids was discovered in microrheology measurements of reconstituted actin networks. This crossover length was related to structural and mechanical properties of the networks, such as their mesh size and dynamic correlation length. Here we capitalize on this result giving a detailed description of our analysis scheme, and demonstrating how this relation can be used to extract the dynamic correlation length of a polymer network. We further study the relation between the dynamic correlation length and the structure of the network, by introducing a new length scale, the average filament length, without altering the network's mesh size. Contrary to the prevailing assumption, that the dynamic correlation length is equivalent to the mesh size of the network, we find that the dynamic correlation length increases once the filament length is reduced below the crossover distance.
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Affiliation(s)
- Adar Sonn-Segev
- Raymond & Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel.
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39
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Guet D, Mandal K, Pinot M, Hoffmann J, Abidine Y, Sigaut W, Bardin S, Schauer K, Goud B, Manneville JB. Mechanical role of actin dynamics in the rheology of the Golgi complex and in Golgi-associated trafficking events. Curr Biol 2014; 24:1700-11. [PMID: 25042587 DOI: 10.1016/j.cub.2014.06.048] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2013] [Revised: 05/06/2014] [Accepted: 06/18/2014] [Indexed: 01/08/2023]
Abstract
BACKGROUND In vitro studies have shown that physical parameters, such as membrane curvature, tension, and composition, influence the budding and fission of transport intermediates. Endocytosis in living cells also appears to be regulated by the mechanical load experienced by the plasma membrane. In contrast, how these parameters affect intracellular membrane trafficking in living cells is not known. To address this question, we investigate here the impact of a mechanical stress on the organization of the Golgi complex and on the formation of transport intermediates from the Golgi complex. RESULTS Using confocal microscopy, we visualize the deformation of Rab6-positive Golgi membranes applied by an internalized microsphere trapped in optical tweezers and simultaneously measure the corresponding forces. Our results show that the force necessary to deform Golgi membranes drops when actin dynamics is altered and correlates with myosin II activity. We also show that the applied stress has a long-range effect on Golgi membranes, perturbs the dynamics of Golgi-associated actin, and induces a sharp decrease in the formation of Rab6-positive vesicles from the Golgi complex as well as tubulation of Golgi membranes. CONCLUSIONS We suggest that acto-myosin contractility strongly contributes to the local rigidity of the Golgi complex and regulates the mechanics of the Golgi complex to control intracellular membrane trafficking.
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Affiliation(s)
- David Guet
- CNRS-Institut Curie, UMR144, 26 rue d'Ulm, 75248 Paris Cedex 05, France
| | - Kalpana Mandal
- CNRS-Institut Curie, UMR144, 26 rue d'Ulm, 75248 Paris Cedex 05, France
| | - Mathieu Pinot
- CNRS-Institut Curie, UMR144, 26 rue d'Ulm, 75248 Paris Cedex 05, France
| | - Jessica Hoffmann
- CNRS-Institut Curie, UMR144, 26 rue d'Ulm, 75248 Paris Cedex 05, France
| | - Yara Abidine
- CNRS-Institut Curie, UMR144, 26 rue d'Ulm, 75248 Paris Cedex 05, France
| | - Walter Sigaut
- CNRS-Institut Curie, UMR144, 26 rue d'Ulm, 75248 Paris Cedex 05, France
| | - Sabine Bardin
- CNRS-Institut Curie, UMR144, 26 rue d'Ulm, 75248 Paris Cedex 05, France
| | - Kristine Schauer
- CNRS-Institut Curie, UMR144, 26 rue d'Ulm, 75248 Paris Cedex 05, France
| | - Bruno Goud
- CNRS-Institut Curie, UMR144, 26 rue d'Ulm, 75248 Paris Cedex 05, France.
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40
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Hawkins RJ, Liverpool TB. Stress reorganization and response in active solids. PHYSICAL REVIEW LETTERS 2014; 113:028102. [PMID: 25062239 DOI: 10.1103/physrevlett.113.028102] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2014] [Indexed: 06/03/2023]
Abstract
We present a microscopic model of a disordered viscoelastic active solid, i.e., an active material whose long time behavior is elastic as opposed to viscous. It is composed of filaments, passive cross-links, and molecular motors powered by stored chemical energy, e.g., actomyosin powered by adenosine triphosphate. Our model allows us to study the collective behavior of contractile active elements and how their interaction with each other and the passive elastic elements determines the macroscopic mechanical properties of the active material. As a result of the (un)binding dynamics of the active elements, we find that this system provides a highly responsive material with a dynamic mechanical response strongly dependent on the amount of deformation.
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Affiliation(s)
- Rhoda J Hawkins
- Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom and School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
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41
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Jansen KA, Bacabac RG, Piechocka IK, Koenderink GH. Cells actively stiffen fibrin networks by generating contractile stress. Biophys J 2014; 105:2240-51. [PMID: 24268136 DOI: 10.1016/j.bpj.2013.10.008] [Citation(s) in RCA: 104] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2013] [Revised: 09/03/2013] [Accepted: 10/07/2013] [Indexed: 12/13/2022] Open
Abstract
During wound healing and angiogenesis, fibrin serves as a provisional extracellular matrix. We use a model system of fibroblasts embedded in fibrin gels to study how cell-mediated contraction may influence the macroscopic mechanical properties of their extracellular matrix during such processes. We demonstrate by macroscopic shear rheology that the cells increase the elastic modulus of the fibrin gels. Microscopy observations show that this stiffening sets in when the cells spread and apply traction forces on the fibrin fibers. We further show that the stiffening response mimics the effect of an external stress applied by mechanical shear. We propose that stiffening is a consequence of active myosin-driven cell contraction, which provokes a nonlinear elastic response of the fibrin matrix. Cell-induced stiffening is limited to a factor 3 even though fibrin gels can in principle stiffen much more before breaking. We discuss this observation in light of recent models of fibrin gel elasticity, and conclude that the fibroblasts pull out floppy modes, such as thermal bending undulations, from the fibrin network, but do not axially stretch the fibers. Our findings are relevant for understanding the role of matrix contraction by cells during wound healing and cancer development, and may provide design parameters for materials to guide morphogenesis in tissue engineering.
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Affiliation(s)
- Karin A Jansen
- Biological Soft Matter Group, FOM Institute AMOLF, Amsterdam, Netherlands
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42
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Persistent super-diffusive motion of Escherichia coli chromosomal loci. Nat Commun 2014; 5:3854. [DOI: 10.1038/ncomms4854] [Citation(s) in RCA: 63] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2013] [Accepted: 04/10/2014] [Indexed: 01/15/2023] Open
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43
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Label-free characterization of emerging human neuronal networks. Sci Rep 2014; 4:4434. [PMID: 24658536 PMCID: PMC3963031 DOI: 10.1038/srep04434] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2013] [Accepted: 02/19/2014] [Indexed: 11/09/2022] Open
Abstract
The emergent self-organization of a neuronal network in a developing nervous system is the result of a remarkably orchestrated process involving a multitude of chemical, mechanical and electrical signals. Little is known about the dynamic behavior of a developing network (especially in a human model) primarily due to a lack of practical and non-invasive methods to measure and quantify the process. Here we demonstrate that by using a novel optical interferometric technique, we can non-invasively measure several fundamental properties of neural networks from the sub-cellular to the cell population level. We applied this method to quantify network formation in human stem cell derived neurons and show for the first time, correlations between trends in the growth, transport, and spatial organization of such a system. Quantifying the fundamental behavior of such cell lines without compromising their viability may provide an important new tool in future longitudinal studies.
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44
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Colin R, Chevry L, Berret JF, Abou B. Rotational microrheology of Maxwell fluids using micron-sized wires. SOFT MATTER 2014; 10:1167-73. [PMID: 24651977 DOI: 10.1039/c3sm52726c] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We demonstrate a simple method for rotational microrheology in complex fluids using micrometric wires. The three-dimensional rotational Brownian motion of the wires suspended in Maxwell fluids is measured from their projection on the focal plane of a microscope. We analyze the mean-squared angular displacement of the wires of length between 1 and 40 μm. The viscoelastic properties of the suspending fluids are examined from this analysis and found to be in good agreement with macrorheology data. Viscosities of simple and complex fluids between 10(-2) and 30 Pa s could be measured. As for the elastic modulus, values up to ∼5 Pa could be determined. This simple technique, allowing for a broad range of probed length scales, opens new perspectives in microrheology of heterogeneous materials such as gels, glasses and cells.
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Affiliation(s)
- Rémy Colin
- Laboratoire Matière et Systèmes Complexes (MSC), UMR CNRS 7057 & Université Paris Diderot, France.
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45
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Whitfield CA, Marenduzzo D, Voituriez R, Hawkins RJ. Active polar fluid flow in finite droplets. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:8. [PMID: 24532222 DOI: 10.1140/epje/i2014-14008-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2013] [Revised: 12/17/2013] [Accepted: 01/23/2014] [Indexed: 06/03/2023]
Abstract
We present a continuum level analytical model of a droplet of active contractile fluid consisting of filaments and motors. We calculate the steady state flows that result from a splayed polarisation of the filaments. We account for interaction with the external medium by imposing a viscous friction at the fixed droplet boundary. We then show that the droplet has non-zero force dipole and quadrupole moments, the latter of which is essential for self-propelled motion of the droplet at low Reynolds' number. Therefore, this calculation describes a simple mechanism for the motility of a droplet of active contractile fluid embedded in a three-dimensional environment, which is relevant to cell migration in confinement (for example, embedded within a gel or tissue). Our analytical results predict how the system depends on various parameters such as the effective friction coefficient, the phenomenological activity parameter and the splay of the imposed polarisation.
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Affiliation(s)
- Carl A Whitfield
- Department of Physics and Astronomy, University of Sheffield, Hicks Building, Hounsfield Road, S3 7RH, Sheffield, UK,
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46
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Aubertin K, Bonneau S, Silva AKA, Bacri JC, Gallet F, Wilhelm C. Impact of photosensitizers activation on intracellular trafficking and viscosity. PLoS One 2013; 8:e84850. [PMID: 24386423 PMCID: PMC3874004 DOI: 10.1371/journal.pone.0084850] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2013] [Accepted: 11/19/2013] [Indexed: 11/19/2022] Open
Abstract
The intracellular microenvironment is essential for the efficiency of photo-induced therapies, as short-lived reactive oxygen species generated must diffuse through their intracellular surrounding medium to reach their cellular target. Here, by combining measurements of local cytoplasmic dissipation and active trafficking, we found that photosensitizers activation induced small changes in surrounding viscosity but a massive decrease in diffusion. These effects are the signature of a return to thermodynamic equilibrium of the system after photo-activation and correlated with depolymerization of the microtubule network, as shown in a reconstituted system. These mechanical measurements were performed with two intracellular photosensitizing chlorins having similar quantum yield of singlet oxygen production but different intracellular localizations (cytoplasmic for mTHPC, endosomal for TPCS2a). These two agents demonstrated different intracellular impact.
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Affiliation(s)
- Kelly Aubertin
- Laboratoire Matière et Systèmes Complexes (MSC), CNRS and Université Paris Diderot, Paris, France
| | - Stéphanie Bonneau
- Laboratoire Jean Perrin-CNRS, Université Pierre et Marie Curie, Paris 6, Paris, France
| | - Amanda K. A. Silva
- Laboratoire Matière et Systèmes Complexes (MSC), CNRS and Université Paris Diderot, Paris, France
| | - Jean-Claude Bacri
- Laboratoire Matière et Systèmes Complexes (MSC), CNRS and Université Paris Diderot, Paris, France
| | - François Gallet
- Laboratoire Matière et Systèmes Complexes (MSC), CNRS and Université Paris Diderot, Paris, France
| | - Claire Wilhelm
- Laboratoire Matière et Systèmes Complexes (MSC), CNRS and Université Paris Diderot, Paris, France
- * E-mail:
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47
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Bausch AR, Schwarz US. Cellular mechanosensing: Sharing the force. NATURE MATERIALS 2013; 12:948-949. [PMID: 24150409 DOI: 10.1038/nmat3791] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Affiliation(s)
- Andreas R Bausch
- Lehrstuhl für Zellbiophysik E27, Technische Universität München, 85748 Garching, Germany
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48
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Chevry L, Colin R, Abou B, Berret JF. Intracellular micro-rheology probed by micron-sized wires. Biomaterials 2013; 34:6299-305. [DOI: 10.1016/j.biomaterials.2013.05.002] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2013] [Accepted: 05/02/2013] [Indexed: 12/21/2022]
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Short-time movement of E. coli chromosomal loci depends on coordinate and subcellular localization. Nat Commun 2013; 4:3003. [DOI: 10.1038/ncomms3003] [Citation(s) in RCA: 91] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2012] [Accepted: 05/09/2013] [Indexed: 11/08/2022] Open
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Radszuweit M, Alonso S, Engel H, Bär M. Intracellular mechanochemical waves in an active poroelastic model. PHYSICAL REVIEW LETTERS 2013; 110:138102. [PMID: 23581377 DOI: 10.1103/physrevlett.110.138102] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2012] [Indexed: 06/02/2023]
Abstract
Many processes in living cells are controlled by biochemical substances regulating active stresses. The cytoplasm is an active material with both viscoelastic and liquid properties. We incorporate the active stress into a two-phase model of the cytoplasm which accounts for the spatiotemporal dynamics of the cytoskeleton and the cytosol. The cytoskeleton is described as a solid matrix that together with the cytosol as an interstitial fluid constitutes a poroelastic material. We find different forms of mechanochemical waves including traveling, standing, and rotating waves by employing linear stability analysis and numerical simulations in one and two spatial dimensions.
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Affiliation(s)
- Markus Radszuweit
- Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin, Germany
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