Cell mechanics: principles, practices, and prospects

Abstract

Cells generate and sustain mechanical forces within their environment as part of their normal physiology. They are active materials that can detect mechanical stimulation by the activation of mechanosensitive signaling pathways, and respond to physical cues through cytoskeletal re-organization and force generation. Genetic mutations and pathogens that disrupt the cytoskeletal architecture can result in changes to cell mechanical properties such as elasticity, adhesiveness, and viscosity. On the other hand, perturbations to the mechanical environment can affect cell behavior. These transformations are often a hallmark and symptom of a variety of pathologies. Consequently, there are now a myriad of experimental techniques and theoretical models adapted from soft matter physics and mechanical engineering to characterize cell mechanical properties. Interdisciplinary research combining modern molecular biology with advanced cell mechanical characterization techniques now paves the way for furthering our fundamental understanding of cell mechanics and its role in development, physiology, and disease. We describe a generalized outline for measuring cell mechanical properties including loading protocols, tools, and data interpretation.We summarize recent advances in the field and explain how cell biomechanics research can be adopted by physicists, engineers, biologists, and clinicians alike.

Figure 1

Fundamental quantities involved in mechanical characterization of a material. (a) Stress and strain defined as force per unit area and deformation per unit length respectively, are basic quantities that allow characterization of the mechanical response of materials. Materials deform differently under compressive, tensile, and shear forces. (b) The relationship between the stress and strain defines the material static mechanical properties. For simple elastic and purely viscous materials a simple linear relationship between the stress and strain/strain rate governs the mechanical properties. The elastic and shear moduli are measures of material rigidity and describe the tendency of a material to deform under normal and shear forces respectively. The viscosity is a measure of material resistance to flow under applied force and defined as the ratio of shear stress to shear strain rate. (c) For soft materials including cells, typically the stress is proportional to the strain under small deformations. However under larger deformations the stress–strain relationship is non-linear and the stress increases more rapidly under application of large strains.

Figure 2

Main parameters involved in choosing the mechanical measurement tool. The choice of experimental tool requires consideration of (a) the lengthscale, (b) the timescale of the measurement and (c) the level of forces (or elasticity of the sample). A reasonable estimate of these three factors indicates which characterization tool is the most appropriate technique for mechanical study of a particular sample.

Figure 3

Common loading conditions for measuring time-dependent mechanical properties. (a) Typical rheological characterization incorporates measuring the temporal evolution of strain under application of a constant stress (creep) or the temporal evolution of stress under application of a constant strain (stress-relaxation). (b) Oscillatory techniques are another method of characterizing the viscoelastic properties of materials where normally a sinusoidal strain is applied and the cyclic stress response is monitored. In this approach the timescale of the test is defined by the frequency of oscillation ω. By observing material response at a range of frequencies the relative contribution of elastic (indicated by storage modulus G′) and viscous (indicated by loss modulus G″) responses can be characterized at different timescales. The dynamic modulus G* is the indicator of overall viscoelastic behavior. Oscillatory tests can reveal a set of material viscoelastic responses over specific span of frequencies (timescales).

Figure 4

Four cell mechanical measurement techniques. (a) AFM: A laser beam is reflected off the back of the cantilever and collected by photodiodes. Interactions between the tip and the sample change the bending of the cantilever and consequently the reflection path of the laser beam which is precisely measured by the photodiodes. The bending of the cantilever is converted to force using its spring constant. A piezo-electric ceramic in a feedback loop is used to move the cantilever up and down to adjust bending of the cantilever and the applied force. (a-I) A confocal microscopy image shows the HeLa cell profile as the cell (green) is indented by a spherical bead (blue) attached to AFM cantilever. (a-II) A typical AFM force-indentation curve on cell. This curve can be fitted with an indentation model to estimate the cell elasticity. (Reprinted with permission from Ref . Copyright 2013 Nature Publishing Group.) (b) Optical tweezers: A small particle is stably trapped by a highly focused laser beam. The position of the optically trapped particle can be controlled by the movement of trap and small forces can be estimated from the changes in the displacement of the particle from the center of trap. (b-I, II) A tether extraction experiment involves pulling of an optically trapped bead attached to a cell membrane away from the cell. (b-II) The force-distance curve of tether extraction experiments on microglial cell. (Reprinted with permission from Ref . Copyright 2013 Public Library of Science.) (c) PTM: The micron or submicron beads disperse within the cytoplasm following injection into live cells. Using a high magnification objective the random spontaneous motions of the beads are captured with high spatial and temporal resolution. (c-I) 100 nm fluorescent beads injected into the cytoplasm of 3T3 fibroblasts. (c-II, III) The recorded time-dependent trajectories (c-II) of the beads are used to calculate their mean squared displacements (c-III) by which the nature of intracellular diffusion and microscopic viscoelastic properties of cellular environment can be studied. (Reprinted with permission from Ref . Copyright 2009 Public Library of Science.) (d) TFM: The cell is cultured onto (or within) a bead-embedded polymeric gel. Cellular contractions deform the gel and for a known gel elastic modulus the cellular traction forces can be calculated from the bead displacements. (d-I, II) Deformation vectors and traction stress field of fibroblast cultured on polyacrylamide gel were calculated by monitoring the displacement of fluorescent beads embedded in the gel. (Reprinted with permission from Ref . Copyright 2001 Cell Press.)

Figure 5

Cell universal behaviors. (a) The frequency response of cells measured with several mechanical measurement techniques (such as AFM, PTM, and magnetic twisting cytometry) collapses into two master curves after rescaling the experimental data from different rheological measurements (see Ref for details). The frequency dependent dynamic modulus follow two distinct regimes in these master curves that can be fitted by a power law function: |G * (ω)| : ∼ω^β, where ω is frequency and β is power law exponent. At high frequencies both curves show β = 3/4 but at low frequencies they exhibit lower range of power-law exponents, β₁ ∼ 0.25 and β₂ ∼ 0.15 (see Ref for further details). (b) Spontaneous retraction of a single actin stress fiber upon severing with a laser nanoscissor shows existence of prestress in the cytosketal bundles. Scale bar = 2 µm. (Reprinted with permission from Ref . Copyright 2006 Cell Press.) (c) Anomalous diffusion and response of the cell to stretch. (c-I, II) Spontaneous movements of beads attached firmly to the cell show intermittent dynamics. Scale bars = 10 µm. (Reprinted with permission from Ref . Copyright 2005 Nature Publishing Group.) (c-III) The mean square displacement (MSD) of a bead anchored to the cytoskeleton exhibits anomalous diffusion dynamics < r² > ∼ t^α (subdiffusive α < 1 at short time intervals and superdiffusive α > 1 at longer time intervals). Red curve indicates the MSD of the bead for a non-stretched cell and other curves show the MSD of the bead in response to a global stretch measured at different waiting times (t_ω) after stretch cessation. (Reprinted with permission from Ref . Copyright 2007 Nature Publishing Group.)

Figure 6

Models of cell rheology. (a) Spring and dashpot representation of Standard Linear Solid viscoelastic model and the functional form of its stress relaxation in response to sudden constant strain. (b) The power law type of relaxation in log–log scale is a line with the slope β which is the power law exponent. For purely elastic and viscos materials the power law exponents are β = 0 and β = 1 respectively. When 0 < β < 1 combination of elastic and viscous mechanisms contribute to relaxation response. (c) Schematic representation of soft glassy rheology: A rheological model that explains glassy and weak power-law behavior of soft disordered materials such as foams and colloids. (d) Dynamic network of cytoskeletal filaments such as actin network determine the cell rheology. (d-I) Image of actin filaments in a COS-7 cell taken by dual stochastic optical reconstruction microscopy (STORM) (Reprinted with permission from Ref 100. Copyright 2012 Nature Publishing Group). The height is color coded with respect to the scaling shown in the color scale bar. Scale bars = 2 µm. (d-II) In reconstituted gel models of cytoskeletal filaments, interaction of binding proteins with different properties (such as type, organization, and concentration) with filaments significantly influence the network rheology.