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- Mechanics of living cells: nonlinear viscoelasticity of single fibroblasts and shape instabilities in axons (2006)
- Biomechanics is a field of major biological relevance. In spite of the vast complexity of biological matter, a number of generic features are found to hold in the mechanics of soft tissues throughout all of its length scales. A major goal in biomechanics is to reduce its general features to those of the cytoskeleton, the filamentous scaffold which provides cells with mechanical integrity, architecture and contractility. The first part of this report describes single-cell uniaxial stretching experiments performed on fibroblasts. When placed between fibronectin coated microplates, fibroblasts adopt a regular, symmetrical shape and generate forces. When a constant cell length is imposed, an increase with time of the pulling force can be observed. This active behaviour can be probed in more detail by superimposing small-amplitude oscillations at frequencies in the range 0.1--1 Hz. The response to the superimposed oscillations is then characterised by the viscoelastic moduli. These are seen to be a function of the average force acting on the cell. This master-relation holds for all cells. At low forces, both moduli are constant; beyond a crossover force, power-law stress stiffening is observed, where as a function of the average force both moduli go as a power-law with exponents in the range 1-1.8. The loss factor depends only weakly on the average force. Remarkably, the moduli are a function of the average force but are independent of the cell length. Therefore this mechanical behaviour is not strain stiffening; rather, it is an example of active, intrinsic stress stiffening. The precise way of sweeping force-space is seen to be irrelevant. The stiffening relation shows a striking similarity to rheological measurements performed on purified actin gels, in an unprecedented example of quantitative agreement between living and dead matter. This mechanical response originates in the semiflexible behaviour of biopolymers. The precise mechanism is however at present not fully understood. Here, a simple explanation is proposed. It is shown that stress stiffening in fibroblasts bears a strong resemblance to the nonlinear mechanics of Euler-Bernoulli beams, which also show a linear regime at low forces and a crossover to power-law stiffening. Systematic analysis of the response of fibroblasts to large amplitude deformations reveals a striking similarity to plasticity in metals. Fibroblasts can be described as showing kinematic (or directional) hardening, a hallmark of composite materials. The second part of this report addresses experiments performed on neurites. These comprise axons --the processes extended by neurons-- as well as PC12 neurites, a model system for axons. After a sudden increase in the external osmotic pressure, axons swell and a cylindrical-peristaltic shape transformation sets in. We interprete this transition as a Rayleigh-Plateau-like instability triggered by elastic membrane tension, similar to the pearling instability known in membrane tubes. Microtubuli disruption by nocodazol strongly increases the maximum amplitude of the instability, as well as slightly increases the wavenumber of the fastest mode, showing microtubuli to be the most important cytoskeletal component in stabilising neurites. After a hypoosmotic shock the neurite volume increases, reaches a maximum, and relaxes back close to its initial value. These experiments were performed at different temperatures and initial osmotic pressure differences. The relaxation time as a function of the temperature closely follows an Arrhenius dependence, suggesting the rate-limiting factor of the relaxation to be the movement of ions through channels. Similar experiments were also performed under drug-induced perturbation of actin, myosin and microtubuli. Cytoskeleton perturbation does not have any significant effect on volume relaxation, indicating that it takes place solely by changes in osmolarity, without a significant role for hydrostatic pressures. A clear effect of drugs is seen in the initial swelling phase, especially after microtubuli disruption by nocodazol. The rate and extent of swelling are significantly higher. Taking the effect of drugs on the evolution of neurite volume together with that on the pearling instability, we suggest that hydrostatic pressure is present in the initial swelling phase and determines the swelling rate. In conclusion, reproducible, quantitative experiments at the single-cell level have been developed which address biologically relevant phenomena. Following a time-honoured tradition in physics, both the cell-pulling experiments and the shape transformations in axons address highly symmetric systems, where the geometry does not preclude the understanding. First interpretations of the observed phenomena have been found, in terms of generic behaviours common to all objects under tension.