Power-law creep behavior of a semiflexible chain

Physical review letters, 2006

Advances in Structural Biology, 1999

2011

Living cells cytoskeleton is made of polymers which are constantly being re-modelled by polymerisation and depolymerisation, and which are bound to one another (crosslinked) through even more unstable molecules, lasting for about one second. With such a dynamic structure, one may wonder how cells can maintain a given shape over time ranges several orders of magnitude larger than the turn-over time of their constituents. We propose a rheological model which features crosslink turn-over, polymerisation and molecular motor-generated contractile forces, and provides answers to these questions.

Journal of Theoretical Biology, 2002

This study describes the viscoelastic properties of a refined cellular-tensegrity model composed of six rigid bars connected to a continuous network of 24 viscoelastic pre-stretched cables (Voigt bodies) in order to analyse the role of the cytoskeleton spatial rearrangement on the viscoelastic response of living adherent cells. This structural contribution was determined from the relationships between the global viscoelastic properties of the tensegrity model, i.e., normalized viscosity modulus (Z n), normalized elasticity modulus (E n), and the physical properties of the constitutive elements, i.e., their normalized length (L n) and normalized initial internal tension (T n). We used a numerical method to simulate the deformation of the structure in response to different types of loading, while varying by several orders of magnitude L n and T n : The numerical results obtained reveal that Z n remains almost independent of changes in T n (Z n pT nþ0:1), whereas E n increases with approximately the square root of the internal tension T n (from E n pT nþ0:3 to E n pT nþ0:7). Moreover, structural viscosity Z n and elasticity E n are both inversely proportional to the square of the size of the structure (Z n pL nÀ2 and E n pL nÀ2). These structural properties appear consistent with cytoskeleton (CSK) mechanical properties measured experimentally by various methods which are specific to the CSK micromanipulation in living adherent cells. Present results suggest, for the first time, that the effect of structural rearrangement of CSK elements on global CSK behavior is characterized by a faster cellular mechanical response relatively to the CSK element response, which thus contributes to the solidification process observed in adherent cells. In extending to the viscoelastic properties the analysis of the mechanical response of the cellular 30-element tensegrity model, the present study contributes to the understanding of recent results on the cellular-dynamic response and allows to reunify the scattered data reported for the viscoelastic properties of living adherent cells.

2003

Semiflexible polymers such as filamentous actin play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominately affine and the filaments stretch and compress; and a second in which bending modes dominate. We identify a dimensionless scalar quantity, being a combination of the material length scales, that specifies to which regime a given network belongs. A scaling argument is presented that approximately agrees with this crossover variable. By a direct geometric measure, we also confirm that the degree of affinity under strain correlates with the distinct elastic regimes. We discuss the implications of our findings and suggest possible directions for future investigations.

Biophysical Journal, 2008

A living cell deforms or flows in response to mechanical stresses. A recent report shows that dynamic mechanics of living cells depends on the timescale of mechanical loading, in contrast to the prevailing view of some authors that cell rheology is timescale-free. Yet the molecular basis that governs this timescale-dependent behavior is elusive. Using molecular dynamics simulations of protein-protein noncovalent interactions, we show that multipower laws originate from a nonequilibrium-to-equilibrium transition: when the loading rate is faster than the transition rate, the power-law exponent a 1 is weak; when the loading rate is slower than the transition rate, the exponent a 2 is strong. The model predictions are confirmed in both embryonic stem cells and differentiated cells. Embryonic stem cells are less stiff, more fluidlike, and exhibit greater a 1 than their differentiated counterparts. By introducing a near-equilibrium frequency f eq , we show that all data collapse into two power laws separated by f/f eq , which is unity. These findings suggest that the timescale-dependent rheology in living cells originates from the nonequilibrium-to-equilibrium transition of the dynamic response of distinct, force-driven molecular processes.

Scientific Reports, 2020

Living cells are constantly exchanging momentum with their surroundings. So far, there is no consensus regarding how cells respond to such external stimuli, although it reveals much about their internal structures, motility as well as the emergence of disorders. Here, we report that twelve cell lines, ranging from healthy fibroblasts to cancer cells, hold a ubiquitous double power-law viscoelastic relaxation compatible with the fractional Kelvin-Voigt viscoelastic model. Atomic Force Microscopy measurements in time domain were employed to determine the mechanical parameters, namely, the fast and slow relaxation exponents, the crossover timescale between power law regimes, and the cell stiffness. These cell-dependent quantities show strong correlation with their collective migration and invasiveness properties. Beyond that, the crossover timescale sets the fastest timescale for cells to perform their biological functions.

Annals of Biomedical Engineering, 2000

Rheological properties of living cells play a key role in the control of cell shape, growth, movement, and contractility, yet little is known about how these properties are governed. Past approaches to understanding cell mechanics focused on the contributions of membranes, the viscous cytoplasm, and the individual filamentous biopolymers that are found within the cytoskeleton. In contrast, recent work has revealed that the dynamic mechanical behavior of cells depends on generic system properties, rather than on a single molecular property of the cell. In this paper, we show that a mathematical model of cell mechanics that depicts the intracellular cytoskeleton as a tensegrity structure composed of a prestressed network of interconnected microfilaments, microtubules, and intermediate filaments, and that has previously explained static cellular properties, also can predict fundamental dynamic behaviors of living cells.

Annual Review of Fluid Mechanics, 2009

The cytoskeleton is the primary internal structure of the cell, providing its structural integrity. The rheology and mechanics of the cytoskeleton, therefore, are key to the cell's ability to accomplish its diverse functions in health and disease. Although the importance of the cytoskeleton is well established, the relationship between the microstructural details and the macroscopic rheological behavior of the cytoskeleton remains elusive. A wide range of computational and phenomenological models as well as experimental techniques have been proposed over the past two decades to describe the cytoskeleton, giving rise to several, often contradictory, theories for describing its rheology. This concise review attempts to bring together the key experimental methods and theoretical and computational models regarding cytoskeletal rheology and mechanics.

New Journal of Physics, 2007

We report a systematic investigation of the mechanical properties of fibroblast cells using a novel cell monolayer rheology (CMR) technique.