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Duarte LKR, Rizzi LG. Revisiting the strain-induced softening behaviour in hydrogels. SOFT MATTER 2024; 20:5616-5624. [PMID: 38979672 DOI: 10.1039/d4sm00430b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
The strain-induced softening behaviour observed in the differential modulus K(T,γ) of hydrogels is typically attributed to the breakage of internal network structures, such as the cross-links that bind the polymer chains. In this study, however, we consider a stress-strain relationship derived from a coarse-grained model to demonstrate that rupture of the network is not necessary for rubber-like gels to exhibit such behaviour. In particular, we show that, in some cases, the decrease of K(T,γ) as a function of the strain γ can be associated with the energy-related contribution to the elastic modulus that has been experimentally observed, e.g., for tetra-PEG hydrogels. Our findings suggest that the softening behaviour can be also attributed to the effective interaction between polymer chains and their surrounding solvent molecules, rather than the breakage of structural elements. We compare our theoretical expressions with experimental data determined for several hydrogels to illustrate and validate our approach.
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Affiliation(s)
- L K R Duarte
- Departamento de Física, Universidade Federal de Viçosa (UFV), Av. P. H. Rolfs, s/n, 36570-900, Viçosa, Brazil.
- Instituto Federal de Educação, Ciência e Tecnologia de Minas Gerais, Praça José Emiliano Dias, 87, 35430-034, Ponte Nova, Brazil
| | - L G Rizzi
- Departamento de Física, Universidade Federal de Viçosa (UFV), Av. P. H. Rolfs, s/n, 36570-900, Viçosa, Brazil.
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2
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Pinchiaroli J, Saldanha R, Patteson AE, Robertson-Anderson RM, Gurmessa BJ. Switchable microscale stress response of actin-vimentin composites emerges from scale-dependent interactions. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.06.07.597906. [PMID: 38895280 PMCID: PMC11185688 DOI: 10.1101/2024.06.07.597906] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/21/2024]
Abstract
The mechanical properties of the mammalian cell regulate many cellular functions and are largely dictated by the cytoskeleton, a composite network of protein filaments, including actin, microtubules, and intermediate filaments. Interactions between these distinct filaments give rise to emergent mechanical properties that are difficult to generate synthetically, and recent studies have made great strides in advancing our understanding of the mechanical interplay between actin and microtubule filaments. While intermediate filaments play critical roles in the stress response of cells, their effect on the rheological properties of the composite cytoskeleton remains poorly understood. Here, we use optical tweezers microrheology to measure the linear viscoelastic properties and nonlinear stress response of composites of actin and vimentin with varying molar ratios of actin to vimentin. We reveal a surprising, nearly opposite effect of actin-vimentin network mechanics compared to single-component networks in the linear versus nonlinear regimes. Namely, the linear elastic plateau modulus and zero-shear viscosity are markedly reduced in composites compared to single-component networks of actin or vimentin, whereas the initial response force and stiffness are maximized in composites versus single-component networks in the nonlinear regime. While these emergent trends are indicative of distinct interactions between actin and vimentin, nonlinear stiffening and longtime stress response appear to both be dictated primarily by actin, at odds with previous bulk rheology studies. We demonstrate that these complex, scale-dependent effects arise from the varied contributions of network density, filament stiffness, non-specific interactions, and poroelasticity to the mechanical response at different spatiotemporal scales. Cells may harness this complex behavior to facilitate distinct stress responses at different scales and in response to different stimuli to allow for their hallmark multifunctionality.
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3
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Hauke L, Primeßnig A, Eltzner B, Radwitz J, Huckemann SF, Rehfeldt F. FilamentSensor 2.0: An open-source modular toolbox for 2D/3D cytoskeletal filament tracking. PLoS One 2023; 18:e0279336. [PMID: 36745610 PMCID: PMC9901806 DOI: 10.1371/journal.pone.0279336] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2022] [Accepted: 12/05/2022] [Indexed: 02/07/2023] Open
Abstract
Cytoskeletal pattern formation and structural dynamics are key to a variety of biological functions and a detailed and quantitative analysis yields insight into finely tuned and well-balanced homeostasis and potential pathological alterations. High content life cell imaging of fluorescently labeled cytoskeletal elements under physiological conditions is nowadays state-of-the-art and can record time lapse data for detailed experimental studies. However, systematic quantification of structures and in particular the dynamics (i.e. frame-to-frame tracking) are essential. Here, an unbiased, quantitative, and robust analysis workflow that can be highly automatized is needed. For this purpose we upgraded and expanded our fiber detection algorithm FilamentSensor (FS) to the FilamentSensor 2.0 (FS2.0) toolbox, allowing for automatic detection and segmentation of fibrous structures and the extraction of relevant data (center of mass, length, width, orientation, curvature) in real-time as well as tracking of these objects over time and cell event monitoring.
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Affiliation(s)
- Lara Hauke
- Third Institute of Physics—Biophysics, Georg-August-University Göttingen, Göttingen, Germany
- Institute of Pharmacology and Toxicology, University Medical Center, Göttingen, Germany
- CIDAS (Campus Institute Data Science), University of Göttingen, Göttingen, Germany
- * E-mail: (LH); (FR)
| | - Andreas Primeßnig
- Third Institute of Physics—Biophysics, Georg-August-University Göttingen, Göttingen, Germany
- Institute of Pharmacology and Toxicology, University Medical Center, Göttingen, Germany
| | - Benjamin Eltzner
- Research Group Computational Biomolecular Dynamics, Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
- Felix-Bernstein-Institute for Mathematical Statistics in the Biosciences, Georg-August-University Göttingen, Göttingen, Germany
| | - Jennifer Radwitz
- Third Institute of Physics—Biophysics, Georg-August-University Göttingen, Göttingen, Germany
- Department of Molecular Neurogenetics, ZMNH, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
| | - Stefan F. Huckemann
- Felix-Bernstein-Institute for Mathematical Statistics in the Biosciences, Georg-August-University Göttingen, Göttingen, Germany
| | - Florian Rehfeldt
- Third Institute of Physics—Biophysics, Georg-August-University Göttingen, Göttingen, Germany
- Experimental Physics I, University of Bayreuth, Bayreuth, Germany
- * E-mail: (LH); (FR)
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4
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A computational framework for biomaterials containing three-dimensional random fiber networks based on the affine kinematics. Biomech Model Mechanobiol 2022; 21:685-708. [PMID: 35084592 DOI: 10.1007/s10237-022-01557-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2021] [Accepted: 01/06/2022] [Indexed: 11/02/2022]
Abstract
Understanding the structure-function relationship of biomaterials can provide insights into different diseases and advance numerous biomedical applications. This paper presents a finite element-based computational framework to model biomaterials containing a three-dimensional fiber network at the microscopic scale. The fiber network is synthetically generated by a random walk algorithm, which uses several random variables to control the fiber network topology such as fiber orientations and tortuosity. The geometric information of the generated fiber network is stored in an array-like data structure and incorporated into the nonlinear finite element formulation. The proposed computational framework adopts the affine fiber kinematics, based on which the fiber deformation can be expressed by the nodal displacement and the finite element interpolation functions using the isoparametric relationship. A variational approach is developed to linearize the total strain energy function and derive the nodal force residual and the stiffness matrix required by the finite element procedure. Four numerical examples are provided to demonstrate the capabilities of the proposed computational framework, including a numerical investigation about the relationship between the proposed method and a class of anisotropic material models, a set of synthetic examples to explore the influence of fiber locations on material local and global responses, a thorough mesh-sensitivity analysis about the impact of mesh size on various numerical results, and a detailed case study about the influence of material structures on the performance of eggshell-membrane-hydrogel composites. The proposed computational framework provides an efficient approach to investigate the structure-function relationship for biomaterials that follow the affine fiber kinematics.
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5
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Wang X, Zhu H, Lu Y, Wang Z, Kennedy D. The elastic properties and deformation mechanisms of actin filament networks crosslinked by filamins. J Mech Behav Biomed Mater 2020; 112:104075. [PMID: 32942229 DOI: 10.1016/j.jmbbm.2020.104075] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2019] [Revised: 08/17/2020] [Accepted: 08/28/2020] [Indexed: 10/23/2022]
Abstract
As a substructure of cell cytoskeleton, the crosslinked actin filament networks (CAFNs) play a major role in different cell functions, however, the elastic properties and the deformation mechanisms of CAFNs still remain to be understood. In this paper, a novel three-dimensional (3D) finite element (FE) model has been developed to mimic the mechanical properties of actin filament (F-actin) networks crosslinked by filamin A (FLNA). The simulation results indicate that although the Young's modulus of CAFNs varies in different directions for each random model, the statistical mean value is in-plane isotropic. The crosslinking density and the actin filament volume fraction are found to strongly affect the in-plane shear modulus of CAFNs. The simulation results agree well with the relevant experimental results. In addition, an L-shaped cantilever beam model has been developed for dimensional analysis on the shear stiffness of CAFNs and for quantifying the deformation mechanisms. It has been demonstrated that the in-plane shear modulus of CAFNs is mainly dominated by FLNA (i.e., cross-linkers), and that the bending and torsion deformations of FLNA have almost the same contribution to the stiffness of CAFNs. It has also been found that the stiffness of CAFNs is almost insensitive to the variation of the Poisson's ratios of FLNA and actin filament in the range from 0.29 to 0.499.
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Affiliation(s)
- Xiaobo Wang
- School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK
| | - Hanxing Zhu
- School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK.
| | - Yongtao Lu
- State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China
| | - Zuobin Wang
- International Research Centre for Nano Handling and Manufacturing of China, Changchun University of Science and Technology, Changchun, 130022, China
| | - David Kennedy
- School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK
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6
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Agonistic and antagonistic roles of fibroblasts and cardiomyocytes on viscoelastic stiffening of engineered human myocardium. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2019; 144:51-60. [DOI: 10.1016/j.pbiomolbio.2018.11.011] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2018] [Revised: 11/02/2018] [Accepted: 11/27/2018] [Indexed: 01/18/2023]
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7
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Liu W, Zhang L. Mechanisms of the Complex Thermo-Mechanical Behavior of Polymer Glass Across a Wide Range of Temperature Variations. Polymers (Basel) 2018; 10:E1153. [PMID: 30961079 PMCID: PMC6403929 DOI: 10.3390/polym10101153] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2018] [Revised: 10/13/2018] [Accepted: 10/15/2018] [Indexed: 11/25/2022] Open
Abstract
This paper aims to explore the mechanisms of the complex thermo-mechanical behavior of polymer glass across a wide range of temperature variations. To this end, the free vibration frequency spectrum of simply supported poly(methyl methacrylate) (PMMA) beams was thoroughly investigated with the aid of the impulse excitation technique. It was found that the amplitude ratio of the multiple peaks in the frequency spectrum is a strongly dependent on temperature, and that the peaks correspond to the multiple vibrational modes of the molecular network of PMMA. At a low temperature, the vibration is dominated by the overall microstructure of PMMA. With increasing the temperature, however, the contribution of the sub-microstructures is retarded by β relaxation. Above 80 °C, the vibration is fully dominated by the microstructure after relaxation. The relaxation time at the transition temperature is of the same order of the vibration period, confirming the contribution of β relaxation. These findings provide a precise method for establishing reliable physical-based constitutive models of polymer glass.
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Affiliation(s)
- Weidong Liu
- Laboratory for Precision and Nano Processing Technologies, School of Mechanical and Manufacturing Engineering, The University of New South Wales, New South Wales 2052, Australia.
| | - Liangchi Zhang
- Laboratory for Precision and Nano Processing Technologies, School of Mechanical and Manufacturing Engineering, The University of New South Wales, New South Wales 2052, Australia.
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8
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Ricketts SN, Ross JL, Robertson-Anderson RM. Co-Entangled Actin-Microtubule Composites Exhibit Tunable Stiffness and Power-Law Stress Relaxation. Biophys J 2018; 115:1055-1067. [PMID: 30177441 PMCID: PMC6139891 DOI: 10.1016/j.bpj.2018.08.010] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2018] [Revised: 07/19/2018] [Accepted: 08/06/2018] [Indexed: 12/25/2022] Open
Abstract
We use optical tweezers microrheology and fluorescence microscopy to characterize the nonlinear mesoscale mechanics and mobility of in vitro co-entangled actin-microtubule composites. We create a suite of randomly oriented, well-mixed networks of actin and microtubules by co-polymerizing varying ratios of actin and tubulin in situ. To perturb each composite far from equilibrium, we use optical tweezers to displace an embedded microsphere a distance greater than the lengths of the filaments at a speed much faster than their intrinsic relaxation rates. We simultaneously measure the force the filaments exert on the bead and the subsequent force relaxation. We find that the presence of a large fraction of microtubules (>0.7) is needed to substantially increase the measured force, which is accompanied by large heterogeneities in force response. Actin minimizes these heterogeneities by reducing the mesh size of the composites and supporting microtubules against buckling. Composites also undergo a sharp transition from strain softening to stiffening when the fraction of microtubules (ϕT) exceeds 0.5, which we show arises from faster poroelastic relaxation and suppressed actin bending fluctuations. The force after bead displacement relaxes via power-law decay after an initial period of minimal relaxation. The short-time relaxation profiles (t < 0.06 s) arise from poroelastic and bending contributions, whereas the long-time power-law relaxation is indicative of filaments reptating out of deformed entanglement constraints. The scaling exponents for the long-time relaxation exhibit a nonmonotonic dependence on ϕT, reaching a maximum for equimolar composites (ϕT = 0.5), suggesting that reptation is fastest in ϕT = 0.5 composites. Corresponding mobility measurements of steady-state actin and microtubules show that both filaments are indeed the most mobile in ϕT = 0.5 composites. This nonmonotonic dependence of mobility on ϕT demonstrates the important interplay between mesh size and filament rigidity in polymer networks and highlights the surprising emergent properties that can arise in composites.
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Affiliation(s)
- Shea N Ricketts
- Department of Physics and Biophysics, University of San Diego, San Diego, California
| | - Jennifer L Ross
- Department of Physics, University of Massachusetts Amherst, Amherst, Massachusetts
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9
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Hatami-Marbini H. Effect of crosslink torsional stiffness on elastic behavior of semiflexible polymer networks. Phys Rev E 2018; 97:022504. [PMID: 29548117 DOI: 10.1103/physreve.97.022504] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2017] [Indexed: 11/07/2022]
Abstract
Networks of semiflexible filaments are building blocks of different biological and structural materials such as cytoskeleton and extracellular matrix. The mechanical response of these systems when subjected to an applied strain at zero temperature is often investigated numerically using networks composed of filaments, which are either rigidly welded or pinned together at their crosslinks. In the latter, filaments during deformation are free to rotate about their crosslinks while the relative angles between filaments remain constant in the former. The behavior of crosslinks in actual semiflexible networks is different than these idealized models and there exists only partial constraint on torques at crosslinks. The present work develops a numerical model in which two intersecting filaments are connected to each other by torsional springs with arbitrary stiffness. We show that fiber networks composed of rigid and freely rotating crosslinks are the limiting case of the present model. Furthermore, we characterize the effects of stiffness of crosslinks on effective Young's modulus of semiflexible networks as a function of filament flexibility and crosslink density. The effective Young's modulus is determined as a function of the mechanical properties of crosslinks and is found to vanish for networks composed of very weak torsional springs. Independent of the stiffness of crosslinks, it is found that the effective Young's modulus is a function of fiber flexibility and crosslink density. In low density networks, filaments primarily bend and the effective Young's modulus is much lower than the affine estimate. With increasing filament bending stiffness and/or crosslink density, the mechanical behavior of the networks becomes more affine and the stretching of filaments depicts itself as the dominant mode of deformation. The torsional stiffness of the crosslinks significantly affects the effective Young's modulus of the semiflexible random fiber networks.
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Affiliation(s)
- H Hatami-Marbini
- Department of Mechanical & Industrial Engineering, University of Illinois at Chicago, Chicago, Illinois 60607, USA
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10
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Abstract
In contrast to most synthetic hydrogels, biological gels are made of fibrous networks. This architecture gives rise to unique properties, like low concentration, high porosity gels with a high mechanical responsiveness as a result of strain-stiffening. Here, we used a synthetic polymer model system, based on polyisocyanides, that we crosslinked selectively inside the bundles. This approach allows us to lock in the fibrous network present at the crosslinking conditions. At minimum crosslink densities, we are able to freeze in the architecture, as well as the associated mechanical properties. Rheology and X-ray scattering experiments show that we able to accurately tailor network mechanics, not by changing the gel composition or architecture, but rather by tuning its (thermal) history. Selective crosslinking is a crucial step in making biomimetic networks with a controlled architecture. Unlike synthetic hydrogels, biological gels are made of fibrous networks which give rise to unique properties, such as high porosity and mechanical responsiveness. Here the authors use polyisocyanide-based gels and selectively crosslink inside the bundles to lock the fibrous network and thus control the architecture and the mechanics.
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11
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Heidemann KM, Sageman-Furnas AO, Sharma A, Rehfeldt F, Schmidt CF, Wardetzky M. Topology determines force distributions in one-dimensional random spring networks. Phys Rev E 2018; 97:022306. [PMID: 29548075 DOI: 10.1103/physreve.97.022306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Indexed: 11/07/2022]
Abstract
Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N,z). Despite the universal properties of such (N,z) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.
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Affiliation(s)
- Knut M Heidemann
- Institute for Numerical and Applied Mathematics, University of Goettingen, 37083 Goettingen, Germany
| | - Andrew O Sageman-Furnas
- Institute for Numerical and Applied Mathematics, University of Goettingen, 37083 Goettingen, Germany
| | - Abhinav Sharma
- Third Institute of Physics - Biophysics, University of Goettingen, 37077 Goettingen, Germany.,Leibniz Institute of Polymer Research Dresden, 01069 Dresden, Germany
| | - Florian Rehfeldt
- Third Institute of Physics - Biophysics, University of Goettingen, 37077 Goettingen, Germany
| | - Christoph F Schmidt
- Third Institute of Physics - Biophysics, University of Goettingen, 37077 Goettingen, Germany
| | - Max Wardetzky
- Institute for Numerical and Applied Mathematics, University of Goettingen, 37083 Goettingen, Germany
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12
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Heidemann KM, Sageman-Furnas AO, Sharma A, Rehfeldt F, Schmidt CF, Wardetzky M. Topology Counts: Force Distributions in Circular Spring Networks. PHYSICAL REVIEW LETTERS 2018; 120:068001. [PMID: 29481239 DOI: 10.1103/physrevlett.120.068001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Indexed: 06/08/2023]
Abstract
Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous, and, although the importance of force distributions for structural properties is well recognized, they are far from being understood quantitatively. Using a combination of probabilistic and graph-theoretical techniques, we derive force distributions in a model system consisting of ensembles of random linear spring networks on a circle. We show that characteristic quantities, such as the mean and variance of the force supported by individual springs, can be derived explicitly in terms of only two parameters: (i) average connectivity and (ii) number of nodes. Our analysis shows that a classical mean-field approach fails to capture these characteristic quantities correctly. In contrast, we demonstrate that network topology is a crucial determinant of force distributions in an elastic spring network. Our results for 1D linear spring networks readily generalize to arbitrary dimensions.
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Affiliation(s)
- Knut M Heidemann
- Institute for Numerical and Applied Mathematics, University of Goettingen, 37083 Goettingen, Germany
| | - Andrew O Sageman-Furnas
- Institute for Numerical and Applied Mathematics, University of Goettingen, 37083 Goettingen, Germany
| | - Abhinav Sharma
- Third Institute of Physics - Biophysics, University of Goettingen, 37077 Goettingen, Germany
- Leibniz Institute of Polymer Research Dresden, 01069 Dresden, Germany
| | - Florian Rehfeldt
- Third Institute of Physics - Biophysics, University of Goettingen, 37077 Goettingen, Germany
| | - Christoph F Schmidt
- Third Institute of Physics - Biophysics, University of Goettingen, 37077 Goettingen, Germany
| | - Max Wardetzky
- Institute for Numerical and Applied Mathematics, University of Goettingen, 37083 Goettingen, Germany
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13
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Wang W, Christensen R, Curtis B, Martin SW, Kieffer J. A new model linking elastic properties and ionic conductivity of mixed network former glasses. Phys Chem Chem Phys 2018; 20:1629-1641. [DOI: 10.1039/c7cp04534d] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Abstract
A new statistical thermodynamic model has been developed to describe the activated process of cation hopping in mixed network former glasses based on the systematic comparison between the adiabatic elastic moduli measured using Brillouin light scattering and the ionic conductivity measured using dielectric impedance spectroscopy.
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Affiliation(s)
- Weimin Wang
- Materials Science and Engineering
- The University of Michigan
- Ann Arbor
- USA
| | | | - Brittany Curtis
- Materials Science and Engineering
- Iowa State University
- Ames
- USA
| | - Steve W. Martin
- Materials Science and Engineering
- Iowa State University
- Ames
- USA
| | - John Kieffer
- Materials Science and Engineering
- The University of Michigan
- Ann Arbor
- USA
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14
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Alvarado J, Sheinman M, Sharma A, MacKintosh FC, Koenderink GH. Force percolation of contractile active gels. SOFT MATTER 2017; 13:5624-5644. [PMID: 28812094 DOI: 10.1039/c7sm00834a] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Living systems provide a paradigmatic example of active soft matter. Cells and tissues comprise viscoelastic materials that exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, an active gel of semiflexible filaments, crosslinks, and molecular motors inside cells. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (∼nN and greater) on cellular, tissue, and organismal length scales. Here we review experimental and theoretical studies on contractile active gels composed of actin filaments and myosin motors. Unlike other active soft matter systems, which tend to form ordered patterns, actin-myosin systems exhibit a generic tendency to contract. Experimental studies of reconstituted actin-myosin model systems have long suggested that a mechanical interplay between motor activity and the network's connectivity governs this contractile behavior. Recent theoretical models indicate that this interplay can be understood in terms of percolation models, extended to include effects of motor activity on the network connectivity. Based on concepts from percolation theory, we propose a state diagram that unites a large body of experimental observations. This framework provides valuable insights into the mechanisms that drive cellular shape changes and also provides design principles for synthetic active materials.
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Affiliation(s)
- José Alvarado
- Systems Biophysics Department, AMOLF, 1098 XG Amsterdam, The Netherlands.
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15
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Wang W, Christensen R, Curtis B, Hynek D, Keizer S, Wang J, Feller S, Martin SW, Kieffer J. Elastic properties and short-range structural order in mixed network former glasses. Phys Chem Chem Phys 2017; 19:15942-15952. [DOI: 10.1039/c6cp08939a] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
A new statistical thermodynamic model has been developed to describe the speciation of network former elements in ternary oxide glasses, which uses data from NMR spectroscopy and the adiabatic elastic moduli measured using Brillouin light scattering as input.
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Affiliation(s)
- Weimin Wang
- Materials Science and Engineering
- University of Michigan
- Ann Arbor
- USA
| | | | - Brittany Curtis
- Materials Science and Engineering
- Iowa State University
- Ames
- USA
| | | | | | | | | | - Steve W. Martin
- Materials Science and Engineering
- Iowa State University
- Ames
- USA
| | - John Kieffer
- Materials Science and Engineering
- University of Michigan
- Ann Arbor
- USA
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16
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Sharma A, Licup AJ, Rens R, Vahabi M, Jansen KA, Koenderink GH, MacKintosh FC. Strain-driven criticality underlies nonlinear mechanics of fibrous networks. Phys Rev E 2016; 94:042407. [PMID: 27841637 DOI: 10.1103/physreve.94.042407] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2016] [Indexed: 06/06/2023]
Abstract
Networks with only central force interactions are floppy when their average connectivity is below an isostatic threshold. Although such networks are mechanically unstable, they can become rigid when strained. It was recently shown that the transition from floppy to rigid states as a function of simple shear strain is continuous, with hallmark signatures of criticality [Sharma et al., Nature Phys. 12, 584 (2016)1745-247310.1038/nphys3628]. The nonlinear mechanical response of collagen networks was shown to be quantitatively described within the framework of such mechanical critical phenomenon. Here, we provide a more quantitative characterization of critical behavior in subisostatic networks. Using finite-size scaling we demonstrate the divergence of strain fluctuations in the network at well-defined critical strain. We show that the characteristic strain corresponding to the onset of strain stiffening is distinct from but related to this critical strain in a way that depends on critical exponents. We confirm this prediction experimentally for collagen networks. Moreover, we find that the apparent critical exponents are largely independent of the spatial dimensionality. With subisostaticity as the only required condition, strain-driven criticality is expected to be a general feature of biologically relevant fibrous networks.
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Affiliation(s)
- A Sharma
- Department of Physics and Astronomy, VU University, 1081 NL Amsterdam, The Netherlands
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| | - A J Licup
- Department of Physics and Astronomy, VU University, 1081 NL Amsterdam, The Netherlands
| | - R Rens
- Department of Physics and Astronomy, VU University, 1081 NL Amsterdam, The Netherlands
| | - M Vahabi
- Department of Physics and Astronomy, VU University, 1081 NL Amsterdam, The Netherlands
| | - K A Jansen
- FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
- Wellcome Trust Centre for Cell-Matrix Research, Faculty of Biology, Medicine and Health, University of Manchester, Manchester M13 9PT, United Kingdom
| | - G H Koenderink
- FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - F C MacKintosh
- Department of Physics and Astronomy, VU University, 1081 NL Amsterdam, The Netherlands
- Departments of Chemical & Biomolecular Engineering, Chemistry, Physics & Astronomy, Rice University, Houston, Texas 77005, USA
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Sulfo-SMCC Prevents Annealing of Taxol-Stabilized Microtubules In Vitro. PLoS One 2016; 11:e0161623. [PMID: 27561096 PMCID: PMC4999061 DOI: 10.1371/journal.pone.0161623] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2015] [Accepted: 08/09/2016] [Indexed: 11/21/2022] Open
Abstract
Microtubule structure and functions have been widely studied in vitro and in cells. Research has shown that cysteines on tubulin play a crucial role in the polymerization of microtubules. Here, we show that blocking sulfhydryl groups of cysteines in taxol-stabilized polymerized microtubules with a commonly used chemical crosslinker prevents temporal end-to-end annealing of microtubules in vitro. This can dramatically affect the length distribution of the microtubules. The crosslinker sulfosuccinimidyl 4-(N-maleimidomethyl)cyclohexane-1-carboxylate, sulfo-SMCC, consists of a maleimide and an N-hydroxysuccinimide ester group to bind to sulfhydryl groups and primary amines, respectively. Interestingly, addition of a maleimide dye alone does not show the same interference with annealing in stabilized microtubules. This study shows that the sulfhydryl groups of cysteines of tubulin that are vital for the polymerization are also important for the subsequent annealing of microtubules.
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Vahabi M, Sharma A, Licup AJ, van Oosten ASG, Galie PA, Janmey PA, MacKintosh FC. Elasticity of fibrous networks under uniaxial prestress. SOFT MATTER 2016; 12:5050-60. [PMID: 27174568 DOI: 10.1039/c6sm00606j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We present theoretical and experimental studies of the elastic response of fibrous networks subjected to uniaxial strain. Uniaxial compression or extension is applied to extracellular networks of fibrin and collagen using a shear rheometer with free water in/outflow. Both uniaxial stress and the network shear modulus are measured. Prior work [van Oosten, et al., Sci. Rep., 2015, 6, 19270] has shown softening/stiffening of these networks under compression/extension, together with a nonlinear response to shear, but the origin of such behaviour remains poorly understood. Here, we study how uniaxial strain influences the nonlinear mechanics of fibrous networks. Using a computational network model with bendable and stretchable fibres, we show that the softening/stiffening behaviour can be understood for fixed lateral boundaries in 2D and 3D networks with comparable average connectivities to the experimental extracellular networks. Moreover, we show that the onset of stiffening depends strongly on the imposed uniaxial strain. Our study highlights the importance of both uniaxial strain and boundary conditions in determining the mechanical response of hydrogels.
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Affiliation(s)
- Mahsa Vahabi
- Department of Physics and Astronomy, VU University, Amsterdam, The Netherlands.
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Jin T, Stanciulescu I. Computational modeling of the arterial wall based on layer-specific histological data. Biomech Model Mechanobiol 2016; 15:1479-1494. [DOI: 10.1007/s10237-016-0778-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2015] [Accepted: 02/26/2016] [Indexed: 11/29/2022]
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Rens R, Vahabi M, Licup AJ, MacKintosh FC, Sharma A. Nonlinear Mechanics of Athermal Branched Biopolymer Networks. J Phys Chem B 2016; 120:5831-41. [PMID: 26901575 DOI: 10.1021/acs.jpcb.6b00259] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Naturally occurring biopolymers such as collagen and actin form branched fibrous networks. The average connectivity in branched networks is generally below the isostatic threshold at which central force interactions marginally stabilize the network. In the submarginal regime, for connectivity below this threshold, such networks are unstable toward small deformations unless stabilized by additional interactions such as bending. Here we perform a numerical study on the elastic behavior of such networks. We show that the nonlinear mechanics of branched networks is qualitatively similar to that of filamentous networks with freely hinged cross-links. In agreement with a recent theoretical study,1 we find that branched networks also exhibit nonlinear mechanics consistent with athermal critical phenomena controlled by strain. We obtain the critical exponents capturing the nonlinear elastic behavior near the critical point by performing scaling analysis of the stiffening curves. We find that the exponents evolve with the connectivity in the network. We show that the nonlinear mechanics of disordered networks, independent of the detailed microstructure, can be characterized by a strain-driven second-order phase transition, and that the primary quantitative differences among different architectures are in the critical exponents describing the transition.
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Affiliation(s)
- R Rens
- Department of Physics and Astronomy, Vrije Universiteit , Amsterdam 1081 HV, The Netherlands.,Institute of Physics, University of Amsterdam , Amsterdam 1098 XH, The Netherlands
| | - M Vahabi
- Department of Physics and Astronomy, Vrije Universiteit , Amsterdam 1081 HV, The Netherlands
| | - A J Licup
- Department of Physics and Astronomy, Vrije Universiteit , Amsterdam 1081 HV, The Netherlands
| | - F C MacKintosh
- Department of Physics and Astronomy, Vrije Universiteit , Amsterdam 1081 HV, The Netherlands
| | - A Sharma
- Department of Physics and Astronomy, Vrije Universiteit , Amsterdam 1081 HV, The Netherlands
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Licup AJ, Sharma A, MacKintosh FC. Elastic regimes of subisostatic athermal fiber networks. Phys Rev E 2016; 93:012407. [PMID: 26871101 DOI: 10.1103/physreve.93.012407] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2015] [Indexed: 11/07/2022]
Abstract
Athermal models of disordered fibrous networks are highly useful for studying the mechanics of elastic networks composed of stiff biopolymers. The underlying network architecture is a key aspect that can affect the elastic properties of these systems, which include rich linear and nonlinear elasticity. Existing computational approaches have focused on both lattice-based and off-lattice networks obtained from the random placement of rods. It is not obvious, a priori, whether the two architectures have fundamentally similar or different mechanics. If they are different, it is not clear which of these represents a better model for biological networks. Here, we show that both approaches are essentially equivalent for the same network connectivity, provided the networks are subisostatic with respect to central force interactions. Moreover, for a given subisostatic connectivity, we even find that lattice-based networks in both two and three dimensions exhibit nearly identical nonlinear elastic response. We provide a description of the linear mechanics for both architectures in terms of a scaling function. We also show that the nonlinear regime is dominated by fiber bending and that stiffening originates from the stabilization of subisostatic networks by stress. We propose a generalized relation for this regime in terms of the self-generated normal stresses that develop under deformation. Different network architectures have different susceptibilities to the normal stress but essentially exhibit the same nonlinear mechanics. Such a stiffening mechanism has been shown to successfully capture the nonlinear mechanics of collagen networks.
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Affiliation(s)
- A J Licup
- Department of Physics and Astronomy, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - A Sharma
- Department of Physics and Astronomy, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - F C MacKintosh
- Department of Physics and Astronomy, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
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Numerical simulation of fibrous biomaterials with randomly distributed fiber network structure. Biomech Model Mechanobiol 2015; 15:817-30. [DOI: 10.1007/s10237-015-0725-6] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2015] [Accepted: 08/28/2015] [Indexed: 10/23/2022]
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