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Martín-Martín S, Ramos-Tejada MDM, Rubio-Andrés A, Bonhome-Espinosa AB, Delgado ÁV, Jiménez ML. Electro-optical Study of the Anomalous Rotational Diffusion in Polymer Solutions. Macromolecules 2023; 56:518-527. [PMID: 36711111 PMCID: PMC9879198 DOI: 10.1021/acs.macromol.2c01461] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Revised: 12/22/2022] [Indexed: 01/13/2023]
Abstract
Brownian diffusion of spherical nanoparticles is usually exploited to ascertain the rheological properties of complex media. However, the behavior of the tracer particles is affected by a number of phenomena linked to the interplay between the dynamics of the particles and polymer coils. For this reason, the characteristic lengths of the dispersed entities, depletion phenomena, and the presence of sticking conditions have been observed to affect the translational diffusion of the probes. On the other hand, the retardation effect of the host fluid on the rotational diffusion of nonspherical particles is less understood. We explore the possibility of studying this phenomenon by analyzing the electro-orientation of the particles in different scenarios in which we vary the ratio between the particle and polymer characteristic size, and the geometry of the particles, including both elongated and oblate shapes. We find that the Stokes-Einstein relation only applies if the radius of gyration of the polymer is much shorter than the particle size and when some repulsive interaction between both is present.
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Affiliation(s)
- Sergio Martín-Martín
- Department
of Applied Physics, School of Sciences, University of Granada, 18071Granada, Spain
| | | | - Antonio Rubio-Andrés
- Department
of Applied Physics, School of Sciences, University of Granada, 18071Granada, Spain
| | - Ana B. Bonhome-Espinosa
- Department
of Applied Physics, School of Sciences, University of Granada, 18071Granada, Spain
| | - Ángel V. Delgado
- Department
of Applied Physics, School of Sciences, University of Granada, 18071Granada, Spain
| | - María L. Jiménez
- Department
of Applied Physics, School of Sciences, University of Granada, 18071Granada, Spain,
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Arauz-Lara JL, Ramírez-Saíto Á, Haro-Pérez C. Rotational and translational microrheology from shape-anisotropic particles. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:334002. [PMID: 35671751 DOI: 10.1088/1361-648x/ac768b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2022] [Accepted: 06/07/2022] [Indexed: 06/15/2023]
Abstract
In this work, we report measurements of the mean squared angular and translational displacements of a colloidal dumbbell immersed in a viscoelastic fluid using digital microscopy. From the mean squared displacements, we obtain the mechanical properties of the media. Both angular and translational motions provide the same viscoelastic complex modulus and agree with that obtained from the translational motion of a spherical probe particle.
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Affiliation(s)
- José Luis Arauz-Lara
- Instituto de Física, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 7800 San Luis Potosí, S.L.P., Mexico
| | - Ángeles Ramírez-Saíto
- Instituto de Física, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 7800 San Luis Potosí, S.L.P., Mexico
| | - Catalina Haro-Pérez
- Área de Física de Procesos Irreversibles, Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, 02200 Ciudad de México, Mexico
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3
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Radiom M, Oikonomou EK, Grados A, Receveur M, Berret JF. Probing DNA-Amyloid Interaction and Gel Formation by Active Magnetic Wire Microrheology. Methods Mol Biol 2022; 2538:285-303. [PMID: 35951307 DOI: 10.1007/978-1-0716-2529-3_19] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Recent studies have shown that bacterial nucleoid-associated proteins (NAPs) can bind to DNA and result in altered structural organization and bridging interactions. Under spontaneous self-assembly, NAPs may also form anisotropic amyloid fibers, whose effects are still more significant on DNA dynamics. To test this hypothesis, microrheology experiments on dispersions of DNA associated with the amyloid terminal domain (CTR) of the bacterial protein Hfq were performed using magnetic rotational spectroscopy (MRS). In this chapter, we survey this microrheology technique based on the remote actuation of magnetic wires embedded in a sample. MRS is interesting as it is easy to implement and does not require complex procedures regarding data treatment. Pertaining to the interaction between DNA and amyloid fibers, it is found that DNA and Hfq-CTR protein dispersions behave like a gel, an outcome that suggests the formation of a network of amyloid fibers cross-linked with the DNA strands. In contrast, the pristine DNA and Hfq-CTR dispersions behave as purely viscous liquids. To broaden the scope of the MRS technique, we include theoretical predictions for the rotation of magnetic wires regarding the generic behaviors of basic rheological models from continuum mechanics, and we list the complex fluids studied by this technique over the past 10 years.
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Affiliation(s)
- Milad Radiom
- Université de Paris, CNRS, Paris, France
- Institute for Food, Nutrition and Health, D-HEST, ETH Zürich, Zürich, Switzerland
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Radiom M, Hénault R, Mani S, Iankovski AG, Norel X, Berret JF. Magnetic wire active microrheology of human respiratory mucus. SOFT MATTER 2021; 17:7585-7595. [PMID: 34341819 DOI: 10.1039/d1sm00512j] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Mucus is a viscoelastic gel secreted by the pulmonary epithelium in the tracheobronchial region of the lungs. The coordinated beating of cilia moves mucus upwards towards the pharynx, removing inhaled pathogens and particles from the airways. The efficacy of this clearance mechanism depends primarily on the rheological properties of mucus. Here we use magnetic wire based microrheology to study the viscoelastic properties of human mucus collected from human bronchus tubes. The response of wires between 5 and 80 μm in length to a rotating magnetic field is monitored by optical time-lapse microscopy and analyzed using constitutive equations of rheology, including those of Maxwell and Kelvin-Voigt. The static shear viscosity and elastic modulus can be inferred from low frequency (3 × 10-3-30 rad s-1) measurements, leading to the evaluation of the mucin network relaxation time. This relaxation time is found to be widely distributed, from one to several hundred seconds. Mucus is identified as a viscoelastic liquid with an elastic modulus of 2.5 ± 0.5 Pa and a static viscosity of 100 ± 40 Pa s. Our work shows that beyond the established spatial variations in rheological properties due to microcavities, mucus exhibits secondary inhomogeneities associated with the relaxation time of the mucin network that may be important for its flow properties.
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Affiliation(s)
- Milad Radiom
- Université de Paris, CNRS, Matière et Systèmes Complexes, 75013 Paris, France.
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Giavazzi F, Pal A, Cerbino R. Probing roto-translational diffusion of small anisotropic colloidal particles with a bright-field microscope. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:61. [PMID: 33900479 PMCID: PMC8076158 DOI: 10.1140/epje/s10189-021-00063-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Accepted: 03/29/2021] [Indexed: 05/11/2023]
Abstract
Soft and biological materials are often composed of elementary constituents exhibiting an incessant roto-translational motion at the microscopic scale. Tracking this motion with a bright-field microscope becomes increasingly challenging when the particle size becomes smaller than the microscope resolution, a case which is frequently encountered. Here we demonstrate squared-gradient differential dynamic microscopy (SG-DDM) as a tool to successfully use bright-field microscopy to extract the roto-translational dynamics of small anisotropic colloidal particles, whose rotational motion cannot be tracked accurately in direct space. We provide analytical justification and experimental demonstration of the method by successful application to an aqueous suspension of peanut-shaped particles.
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Affiliation(s)
- Fabio Giavazzi
- Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Università degli Studi di Milano, via F.lli Cervi 93, 20090, Segrate, Italy.
| | - Antara Pal
- Division of Physical Chemistry Department of Chemistry, Lund University, Lund, Sweden
| | - Roberto Cerbino
- Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Università degli Studi di Milano, via F.lli Cervi 93, 20090, Segrate, Italy
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria
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6
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El Hamoui O, Yadav I, Radiom M, Wien F, Berret JF, van der Maarel JRC, Arluison V. Interactions between DNA and the Hfq Amyloid-like Region Trigger a Viscoelastic Response. Biomacromolecules 2020; 21:3668-3677. [PMID: 32786728 DOI: 10.1021/acs.biomac.0c00747] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Molecular transport of biomolecules plays a pivotal role in the machinery of life. Yet, this role is poorly understood due the lack of quantitative information. Here, the role and properties of the C-terminal region of Escherichia coli Hfq is reported, involved in controlling the flow of a DNA solution. A combination of experimental methodologies has been used to probe the interaction of Hfq with DNA and to measure the rheological properties of the complex. A physical gel with a temperature reversible elasticity modulus is formed due to the formation of noncovalent cross-links. The mechanical response of the complexes shows that they are inhomogeneous soft solids. Our experiments indicate that the Hfq C-terminal region could contribute to the genome's mechanical response. The reported viscoelasticity of the DNA-protein complex might have implications for cellular processes involving molecular transport of DNA or segments thereof.
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Affiliation(s)
| | - Indresh Yadav
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
| | - Milad Radiom
- Matière et Systèmes Complexes, UMR 7057 CNRS Université de Paris, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, F-75205 Paris, France
| | - Frank Wien
- Synchrotron SOLEIL, F-91192 Gif-sur-Yvette, France
| | - Jean-Francois Berret
- Matière et Systèmes Complexes, UMR 7057 CNRS Université de Paris, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, F-75205 Paris, France
| | | | - Véronique Arluison
- Laboratoire Léon Brillouin LLB, CEA, CNRS UMR12, Université Paris Saclay, CEA Saclay, F-91191 Gif-sur-Yvette, France.,Université de Paris, F-75006 Paris, France
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7
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Domingos JLC, Peeters FM, Ferreira WP. Self-assembly of rigid magnetic rods consisting of single dipolar beads in two dimensions. Phys Rev E 2018; 96:012603. [PMID: 29347093 DOI: 10.1103/physreve.96.012603] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2016] [Indexed: 11/07/2022]
Abstract
Molecular dynamics simulations are used to investigate the structural properties of a two-dimensional ensemble of magnetic rods, which are modeled as aligned single dipolar beads. The obtained self-assembled configurations can be characterized as (1) clusters, (2) percolated, and (3) ordered structures, and their structural properties are investigated in detail. By increasing the aspect ratio of the magnetic rods, we show that the percolation transition is suppressed due to the reduced mobility of the rods in two dimensions. Such a behavior is opposite to the one observed in three dimensions. A magnetic bulk phase is found with local ferromagnetic order and an unusual nonmonotonic behavior of the nematic order is observed.
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Affiliation(s)
- Jorge L C Domingos
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, 60455-760 Fortaleza, Ceará, Brazil.,Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
| | - François M Peeters
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
| | - W P Ferreira
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, 60455-760 Fortaleza, Ceará, Brazil
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8
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Liu W, Wu C. Rheological Study of Soft Matters: A Review of Microrheology and Microrheometers. MACROMOL CHEM PHYS 2017. [DOI: 10.1002/macp.201700307] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Wei Liu
- Department of Physics; The Chinese University of Hong Kong; Shatin N.T. Hong Kong 999077
| | - Chi Wu
- Department of Chemistry; The Chinese University of Hong Kong; Shatin N.T. Hong Kong 999077
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9
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Gerbal F, Wang Y, Sandre O, Montel F, Bacri JC. Extensive characterization of magnetic microrods observed using optical microscopy. SOFT MATTER 2017; 13:3841-3846. [PMID: 28512659 DOI: 10.1039/c7sm00147a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The usage of micro or nanorods is steadily increasing in various applications from fundamental research to industry. Therefore their geometrical, mechanical and eventually magnetic properties need to be well determined. Here, using an optical microscope equipped with magnetic tweezers, we report an experimental procedure to obtain all those information on a single magnetic rod. In particular, we measure magnetic susceptibility χ by analyzing the deformation of a rod subjected to a uniform magnetic field. To do so, we refine a theoretical model which takes into account the variation of χ with the internal field. We prove experimentally that this model yields consistent measurements, at any value of the field strength and the incidence angle. From the combination of the different measurements, we also deduce the number of iron oxide nanoparticles which are embedded within the polymer matrix of the superparamagnetic rods under study.
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Affiliation(s)
- Fabien Gerbal
- Laboratoire Matière et Systèmes Complexes (MSC) UMR 7057 (CNRS) and Université Denis Diderot - Sorbonne Paris Cité, 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France.
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10
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Gerbal F, Wang Y. Optical detection of nanometric thermal fluctuations to measure the stiffness of rigid superparamagnetic microrods. Proc Natl Acad Sci U S A 2017; 114:2456-2461. [PMID: 28228530 PMCID: PMC5347538 DOI: 10.1073/pnas.1608697114] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The rigidity of numerous biological filaments and crafted microrods has been conveniently deduced from the analysis of their thermal fluctuations. However, the difficulty of measuring nanometric displacements with an optical microscope has so far limited such studies to sufficiently flexible rods, of which the persistence length ([Formula: see text]) rarely exceeds 1 m at room temperature. Here, we demonstrate the possibility to probe 10-fold stiffer rods by a combination of superresolutive optical methods and a statistical analysis of the data based on a recent theoretical model that predicts the amplitude of the fluctuations at any location of the rod [Benetatos P, Frey E (2003) Phys Rev E Stat Nonlin Soft Matter Phys 67(5):051108]. Using this approach, we report measures of [Formula: see text] up to 0.5 km. We obtained these measurements on recently designed superparamagnetic [Formula: see text]40-[Formula: see text]m-long microrods containing iron-oxide nanoparticles connected by a polymer mesh. Using their magnetic properties, we provide an alternative proof of validity of these thermal measurements: For each individual studied rod, we performed a second measure of its rigidity by deflecting it with a uniform magnetic field. The agreement between the thermal and the magnetoelastic measures was realized with more than a decade of values of [Formula: see text] from 5.1 m to 129 m, corresponding to a bending modulus ranging from 2.2 to 54 (×[Formula: see text] Jm). Despite the apparent homogeneity of the analyzed microrods, their Young modulus follows a broad distribution from 1.9 MPa to 59 MPa and up to 200 MPa, depending on the size of the nanoparticles.
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Affiliation(s)
- Fabien Gerbal
- Laboratoire Matière et Systèmes Complexes UMR 7057 (CNRS) and Université Denis Diderot-Sorbonne Paris Cité, 75013 Paris, France;
- Université Pierre et Marie Curie-Paris 6, Sorbonne Universités, 75252 Paris Cedex 05, France
| | - Yuan Wang
- Laboratoire Matière et Systèmes Complexes UMR 7057 (CNRS) and Université Denis Diderot-Sorbonne Paris Cité, 75013 Paris, France
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Gomez-Solano JR, Blokhuis A, Bechinger C. Dynamics of Self-Propelled Janus Particles in Viscoelastic Fluids. PHYSICAL REVIEW LETTERS 2016; 116:138301. [PMID: 27082004 DOI: 10.1103/physrevlett.116.138301] [Citation(s) in RCA: 82] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2016] [Indexed: 06/05/2023]
Abstract
We experimentally investigate active motion of spherical Janus colloidal particles in a viscoelastic fluid. Self-propulsion is achieved by a local concentration gradient of a critical polymer mixture which is imposed by laser illumination. Even in the regime where the fluid's viscosity is independent of the deformation rate induced by the particle, we find a remarkable increase of up to 2 orders of magnitude of the rotational diffusion with increasing particle velocity, which can be phenomenologically described by an effective rotational diffusion coefficient dependent on the Weissenberg number. We show that this effect gives rise to a highly anisotropic response of microswimmers in viscoelastic media to external forces, depending on its orientation.
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Affiliation(s)
- Juan Ruben Gomez-Solano
- 2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Alex Blokhuis
- 2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Clemens Bechinger
- 2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max-Planck-Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
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12
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Berret JF. Local viscoelasticity of living cells measured by rotational magnetic spectroscopy. Nat Commun 2016; 7:10134. [PMID: 26729062 PMCID: PMC4728338 DOI: 10.1038/ncomms10134] [Citation(s) in RCA: 90] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2015] [Accepted: 11/06/2015] [Indexed: 02/08/2023] Open
Abstract
When submitted to a magnetic field, micron-size wires with superparamagnetic properties behave as embedded rheometers and represent interesting sensors for microrheology. Here we use rotational magnetic spectroscopy to measure the shear viscosity of the cytoplasm of living cells. We address the question of whether the cytoplasm is a viscoelastic liquid or an elastic gel. The main result of the study is the observation of a rotational instability between a synchronous and an asynchronous regime of rotation, found for murine fibroblasts and human cancer cells. For wires of susceptibility 3.6, the transition occurs in the range 0.01–1 rad s−1. The determination of the shear viscosity (10–100 Pa s) and elastic modulus (5–20 Pa) confirms the viscoelastic character of the cytoplasm. In contrast to earlier studies, it is concluded that the interior of living cells can be described as a viscoelastic liquid, and not as an elastic gel. Cells are recognized as having viscoelastic properties, but whether the cytoplasm resembles a viscoelastic liquid or an elastic gel is still debated. Here the authors use micron-sized wires rotating at variable speeds to show that the cytoplasm has properties of a viscoelastic liquid.
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Affiliation(s)
- J-F Berret
- Matière et Systèmes Complexes, UMR 7057 CNRS Université Denis Diderot Paris-VII, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75205 Paris, France
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13
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Tierno P. Recent advances in anisotropic magnetic colloids: realization, assembly and applications. Phys Chem Chem Phys 2014; 16:23515-28. [DOI: 10.1039/c4cp03099k] [Citation(s) in RCA: 114] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
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Puertas AM, Voigtmann T. Microrheology of colloidal systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:243101. [PMID: 24848328 DOI: 10.1088/0953-8984/26/24/243101] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.
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Affiliation(s)
- A M Puertas
- Group of Complex Fluids Physics, Department of Applied Physics, University of Almeria, 04120 Almeria, Spain
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