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Provided for Non-Commercial Research and Educational Use Only. Not for Reproduction, Distribution Or Commercial Use Provided for non-commercial research and educational use only. Not for reproduction, distribution or commercial use. This chapter was originally published in the Comprehensive Biophysics, the copy attached is provided by Elsevier for the author’s benefit and for the benefit of the author’s institution, for non-commercial research and educational use. This includes without limitation use in instruction at your institution, distribution to specific colleagues, and providing a copy to your institution’s administrator. All other uses, reproduction and distribution, including without limitation commercial reprints, selling or licensing copies or access, or posting on open internet sites, your personal or institution’s website or repository, are prohibited. For exceptions, permission may be sought for such use through Elsevier’s permissions site at: http://www.elsevier.com/locate/permissionusematerial From D. Wirtz, Biophysics of Molecular Cell Mechanics. In: Edward H. Egelman, editor: Comprehensive Biophysics, Vol 7, Cell Biophysics, Denis Wirtz. Oxford: Academic Press, 2012. pp. 104-121. ISBN: 978-0-12-374920-8 © Copyright 2012 Elsevier B.V. Academic Press. Author's personal copy 7.8 Biophysics of Molecular Cell Mechanics D Wirtz, Johns Hopkins University, Baltimore, MD, USA r 2012 Elsevier B.V. All rights reserved. 7.8.1 Introduction and Motivation 104 7.8.2 Basic Concepts of Molecular and Cellular Mechanics 105 7.8.2.1 Definitions of Stress, Strain, Viscosity, Elasticity, and Compliance 105 7.8.2.2 A Model System: A Solution of Actin Filaments 109 7.8.3 Particle Tracking Microrheology 110 7.8.3.1 Particle Tracking Microrheology of a Viscous Liquid 110 7.8.3.2 Particle Tracking Microrheology of an Elastic Solid 112 7.8.3.3 Particle Tracking Microrheology of a Viscoelastic Material 112 7.8.3.4 Dynamic Viscosity versus Shear Viscosity 113 7.8.3.5 Creep Compliance from Particle Tracking Microrheology 114 7.8.4 Microrheology of Live Cells 114 7.8.4.1 Applications of Particle Tracking Microrheology in Cell Biology 114 7.8.4.2 Interstitial Viscosity versus Mesoscale Viscoelasticity of the Cytoplasm 116 7.8.4.3 Active versus Passive Microrheology of Cells 116 7.8.4.4 Advantages of Particle Tracking Microrheology 117 Acknowledgments 118 References 118 Abbreviations LINC linkers of nucleus and cytoskeleton 3-D three-dimensional MSD mean squared displacement AFM atomic force microscopy VEGF vascular endothelial growth factor GFP green fluorescence protein Glossary Strain The shear deformation experienced by a material; it Creep compliance The time-dependent deformation is either externally applied or induced in the material by an induced by continuously applied stress. Compliance is applied mechanical stress. Strain is dimensionless. proportional to time and inversely proportional to viscosity Stress The force per unit area to which a material may be for a viscous liquid. Compliance is independent of time for subjected; it is either externally applied or induced in the an elastic solid. Time-dependence of creep compliance of material by an applied mechanical strain. Stress is cytoplasm and nucleus is hybrid between those of a liquid proportional to strain for an elastic solid, and is and a solid. Creep compliance is dimensionless. proportional to the rate of strain for a viscous liquid. Stress Elasticity Quantity that measures the propensity of a is expressed in units of Pa. material to rebound after a deformation is eliminated. It is Viscosity Quantity that measures the propensity of a also called storage, stiffness, or elastic modulus. The material to flow. It is the ratio of the stress over the rate of elasticity of a material typically depends on both the deformation. Viscosity is expressed in units of Pa  s. See amplitude and the rate of the applied deformation. typical values in Tables 1 and 2. Elasticity is expressed in units of Pa ¼ NmÀ2 or dyn cmÀ2. See typical values in Tables 1 and 2. 7.8.1 Introduction and Motivation cellular edge.1,2 In migrating cells, the regulated movements of the nucleus, which is very stiff, within the cytoplasm, which is A multitude of cellular functions in both normal and patho- much softer, is partly controlled by the local viscosity of logical conditions depend critically on the dynamic changes in the cytoplasm.3–6 The organization of chromosomes depend the mechanical compliance of the cytoplasm and nucleus, and on the local micromechanical properties of the intranuclear the cell as a whole. For example, migrating epithelial cells at space, which mechanically softens in laminopathies and fol- the wound edge significantly increase the elasticity of their lowing oncogenic transformation. Cells derived from mouse cytoplasm so to produce net forces by actin filament as- models of progeria (premature aging) or muscular dystrophy sembling against the plasma membrane at the protruding display significantly softer (i.e., less elastic) cytoplasm than 104 Comprehensive Biophysics, Volume 7 doi:10.1016/B978-0-12-374920-8.00708-6 Author's personal copy Biophysics of Molecular Cell Mechanics 105 their wild-type controls,3 which in turn affects these cells’ micromechanical properties are often altered in the context of ability to resist shear forces and migrate during wound healing disease, including cancer, muscular dystrophy, and progeria. processes.7 This chapter describes the basic concepts of mechanics and The method of particle tracking microrheology, which was polymer physics that form the foundations of particle tracking introduced more than 15 years ago,8 allows for rapid meas- microrheology. We also describe the key advantages of particle urements (B30 s) of the local viscoelastic properties of the tracking microrheology over traditional cell-mechanics meth- cytoplasm and nucleus in live cells in vitro and in vivo.9 In this ods in a wide range of applications. This review then shows method, the spontaneous movements of submicron fluor- how particle tracking microrheology can readily reveal the lost escent beads dispersed throughout the cytoplasm and/or the ability of a wide range of diseased cells to deform and resist nucleus of live cells (Figure 1) are monitored by time-lapsed shear forces. fluorescence microscopy.8 Movements of multiple beads are recorded simultaneously with a spatial resolution o10 nm by tracking the beads’ centroids. The recorded movements of the 7.8.2 Basic Concepts of Molecular and Cellular beads are transformed into mean squared displacements, Mechanics which can subsequently be analyzed in terms of local, fre- quency-dependent, viscous and elastic moduli of the cyto- 7.8.2.1 Definitions of Stress, Strain, Viscosity, Elasticity, plasm and nucleus. Particle tracking microrheology has and Compliance been successfully used to probe the viscoelastic properties of various types of cells in a wide range of normal and Because different experimental methods measure different disease conditions.7,10–21 These measurements have revealed rheological parameters, the intracellular mechanics of a living important new mechanistic insights into the biophysical cell is best characterized by multiple, and often related, mechanisms by which the micromechanical properties of the rheological quantities, including viscosity, elasticity, and creep cytoplasm and nucleus adapt to various chemical and physical compliance. These rheological parameters describe in different stimuli, how they can control key cell functions – such as cell ways the mechanical response of a material (such as the cell’s division, cell migration, and cell polarization; and how these cytoplasm or the intranuclear network) subjected to a force or ) 2 t Γ(t) ~ 〈Δr (t)〉 ( Γ ~t ~t 3/4 Creep compliance e R ) 2 Time lag m ~t μ ~t 3/4 Mean squared displacement ( e R (a) (b) (c) Time lag (s) Slow longitudinal back-and-forth fluctuations ( > e) Fast lateral fluctuations ( < e) Cytoskeleton polymer Figure 1 Particle tracking microrheology. (a) Submicron fluorescent beads are dialyzed and placed inside a ballistic injection machine. After ballistic injection, the beads disperse rapidly within the cytoplasm. The cells are placed under a high-magnification fluorescence microscope. Ballistically injected beads are lodged within the cytoskeleton. The size of the beads is chosen to be larger than the average mesh size of the cytoskeleton network, B50 nm in fibroblasts. (b) The spontaneous movements of the cytoskeleton filaments that surround each bead induce displacements of the beads. At short timescales, the displacements of the beads are predominantly induced by the fast lateral bending fluctuations of the cytoskeleton filaments (white arrows). At long times, the displacements of the beads are predominantly induced by the slow longitudinal back-and-forth lateral fluctuations of the cytoskeleton filaments (red arrows). Finally, filaments move sufficiently to allow beads to escape the cage to move to the next cage. (c) Accordingly, the mean squared displacements of the beads show a t3/4 power-law dependence at short timescales, a quasi-plateau value at intermediate timescales between te and tR, and a linear dependence at long times caused by the slow viscous diffusion of the beads. Inset: The time lag-dependent mean squared displacements of the beads are subsequently transformed into local values of the creep compliance, G(t), of the cytoplasm. Taken from Panorchan, P.; Lee, J. S.; Daniels, B. R.; Kole, T. P.; Tseng, Y.; Wirtz, D. Probing cellular mechanical responses to stimuli using ballistic intracellular nanorheology. Methods Cell Biol. 2007, 83,
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