## Experimental findings in living cells

To study the rheology of cytoskeletal polymers requires a probe whose operative frequency range spans, insofar as possible, the internal molecular time scales of the rate processes in question. The expectation from such measurements is that the rheological behavior changes at characteristic relaxation frequencies, which in turn can be interpreted as the signature of underlying molecular interactions that dominate the response (Hill, 1965 Kawai and Brandt, 1980). Much of what follows in this...

## Frequency dependence of g and g

The relationship of G' and G vs. frequency for human airway smooth muscle (HASM) cells under control conditions is shown in Fig. 3-4, where each data point represents the median value of 256 cells. Throughout the frequency range studied, G' increased with increasing frequency, f, according to a power law, f x-1 (as explained below, the formula is written in this way because the parameter x takes on a special meaning, namely, that of an effective temperature). Because the axes in Fig. 3-4 are...

## The cytoskeleton as a soft glassy material

ABSTRACT Using a novel method that was both quantitative and reproducible, Francis Crick and Arthur Hughes (Crick and Hughes, 1950) were the first to measure the mechanical properties inside single, living cells. They concluded their groundbreaking work with the words If we were compelled to suggest a model (of cell mechanics) we would propose Mother's Work Basket - a jumble of beads and buttons of all shapes and sizes, with pins and threads for good measure, all jostling about and held...

## Micropipette aspiration Cells

The micropipette aspiration technique has been used extensively to study the mechanical properties of both fluid-like and solid-like cells (Hochmuth, 2000), including circulating cells such as red blood cells (Evans, 1989) and neutrophils (Sung et al., 1982 Dong etal., 1991 Ting-Beallet al., 1993), or adhesion-dependent cells such as fibroblasts (Thoumine and Ott, 1997), endothelial cells (Theret et al., 1988 Sato et al., 1990), or chondrocytes (Jones et al., 1999 Trickey et al., 2000 Guilak et...

## Roger D Kamm

Massachusetts Institute of Technology Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title www.cambridge.org 9780521846370 Cambridge University Press 2006 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any...

## Principles of continuum models

A continuum cell model provides the displacement, strain, and stress fields induced in the cell, given its initial geometry and material properties, and the boundary conditions it is subjected to (such as displacements or forces applied on the cell surface). Laws of continuum mechanics are used to solve for the distribution of mechanical stress and deformation in the cell. Continuum cell models of interest lead to equations that are generally not tractable analytically. In practice, the...

## O

Oosawa and colleagues found that actin polymerizes in two phases (a) an unfavorable nucleation phase involving an actin trimer and (b) a rapid assembly phase in which actin monomers add to both barbed and pointed ends. In the presence of excess ATP, actin does not polymerize to equilibrium but to a 'treadmilling' steady-state in which monomers continuously add to the barbed end and fall off of the pointed end. reactions. Oozawa also assumed that spontaneous...

## N J Z u2

Where Z is the frequency variable to integrate over and P denotes a principal value integral, one can then calculate the real part of the compliance. Knowing both real and imaginary parts of the compliance, one then finds the complex shear modulus via where R is the probe bead radius. This procedure is explained in detail in Schnurr etal. (1997). The shear modulus can also be derived from position fluctuation data in a different way. After first calculating the mean square displacement as a...

## Measurements of cell mechanics

The mechanical torque of the bead is proportional to the external magnetic field (which was generated using an electromagnet), the bead's magnetic moment (which was calibrated by measuring the speed of bead rotation in a viscous medium), and the cosine between the bead's magnetization direction with the direction of the twisting field. Consider the specific torque of a bead, T, which is the mechanical torque per bead volume, and has dimensions of stress (Pa). The ratio of the complex-specific...

## James L McGrath and C Forbes Dewey Jr

ABSTRACT This chapter focuses on the mechanical structure of the cell and how it is affected by the dynamic events that shape the cytoskeleton. We pay particular attention to actin because the actin structure turns over rapidly (on the order of tens of seconds to tens of minutes) and is strongly correlated with dynamic events such as cell crawling. The chapter discusses the way in which actin and its associated binding proteins provide the dominant structure within the cell, and how the actin...

## Info

The elastic properties of actin filaments and microtubules are approximately consistent with a prediction based on the force of van der Waals attraction between two surfaces (J. Howard, 2001). Persistence length (lp) and bending stiffness (Kb ) are related through the expression lp Kb kB T. Bending stiffness and Young's modulus (E) are related through the expression Kb EI 4 a4 E for a solid rod of circular cross-section with radius a, and I 4 (a J a4) for a hollow cylinder with inside and...

## Biphasic solidfluid models of cell mechanics

Viscoelastic behavior in cells can arise from both flow-dependent (fluid-solid interactions and fluid viscosity) and flow-independent mechanisms (for example, intrinsic viscoelasticity of the cytoskeleton). Previous studies have described the cytoplasm of solid-like cells as a gel or as a porous-permeable, fluid-saturated meshwork (Oster, 1984 Oster, 1989 Pollack, 2001) such that the forces within the cell exhibit a balance of stresses arising from hydrostatic and osmotic pressures and the...

## FC Mac Kintosh

ABSTRACT Most plant and animal cells possess a complex structure of filamentous proteins and associated proteins and enzymes for bundling, cross-linking, and active force generation. This cytoskeleton is largely responsible for cell elasticity and mechanical stability. It can also play a key role in cell locomotion. Over the last few years, the single-molecule micromechanics of many of the important constituents of the cytoskeleton have been studied in great detail by biophysical techniques...

## Experimental measurements of intracellular mechanics

ABSTRACT Novel methods to measure the viscoelasticity of soft materials and new theories relating these measurements to the underlying molecular structures have the potential to revolutionize our understanding of complex viscoelastic materials like cytoplasm. Much of the progress in this field has been in methods to apply piconewton forces and to detect motions over distances of nanometers, thus performing mechanical manipulations on the scale of single macromolecules and measuring the...

## Do microtubules carry compression

Microscopic visualization of green fluorescent protein-labeled microtubules of living cells see Fig. 6-2 shows that microtubules buckle as they oppose contraction of the actin network Waterman-Storer and Salmon, 1997 Wang et al., 2001 . It was not known, however, whether the compression that causes this buckling could balance a substantial fraction of the contractile prestress. To investigate this possibility, an energetic analysis of buckling of microtubules was carried out Stamenovic et al.,...