Under physiological and pathological conditions, cells experience large forces and deformations that often exceed the linear viscoelastic regime. Here we drive CD34 + cells isolated from healthy and leukemic bone marrows in the highly nonlinear elasto-plastic regime, by poking their perinuclear region with a sharp AFM cantilever tip. We use the wavelet transform mathematical microscope to identify singular events in the force-indentation curves induced by local rupture events in the cytoskeleton (CSK). We distinguish two types of rupture events, brittle failures likely corresponding to irreversible ruptures in a stiff and highly cross-linked CSK and ductile failures resulting from dynamic cross-linker unbindings during plastic deformation without loss of CSK integrity. We propose a stochastic multiplicative cascade model of mechanical ruptures that reproduces quantitatively the experimental distributions of the energy released during these events, and provides some mathematical and mechanistic understanding of the robustness of the log-normal statistics observed in both brittle and ductile situations. We also show that brittle failures are relatively more prominent in leukemia than in healthy cells suggesting their greater fragility.

Actin is the major cytoskeletal protein of mammal cells that forms microfilaments organized into higher-order structures by a dynamic assembly-disassembly mechanism with cross-linkers. These networks provide the cells with mechanical support, and allow cells to change their shape, migrate, divide and develop a mechanical communication with their environment. The quick adaptation of these networks upon stretch or compression is important for cell survival in real situations. Using atomic force microscopy to poke living cells with sharp tips, we revealed that they respond to a local and quick shear through a cascade of random and abrupt ruptures of their cytoskeleton, suggesting that they behave as a quasi-rigid random network of intertwined filaments. Surprisingly, the distribution of the strength and the size of these rupture events did not follow power-law statistics but log-normal statistics, suggesting that the mechanics of living cells would not fit into self-organized critical systems. We propose a random Gilbert network to model a cell cytoskeleton, identifying the network nodes as the actin filaments, and its links as the actin cross-linkers. We study mainly two versions of avalanches. First, we do not include the fractional visco-elasticity of living cells, assuming that the ruptures are instantaneous, and we observe three avalanche regimes, 1) a regime where avalanches are rapidly interrupted, and their size follows a distribution decaying faster than a power-law; 2) an explosive regime with avalanches of large size where the whole network is damaged and 3) an intermediate regime where the avalanche distribution goes from a power-law, at the critical point, to a distribution containing both 1) and (ii). Then, we introduce a time varying breaking probability, to include the fractional visco-elasticity of living cells, and recover an approximated log-normal distribution of avalanche sizes, similar to those observed in experiments. Our simulations show that the log-normal statistics requires two simple ingredients: a random network without characteristic length scale, and a breaking rule capturing the broadly observed visco-elasticity of living cells. This work paves the way for future applications to large populations of non-linear individual elements (brain, heart, epidemics, … ) where similar log-normal statistics have also been observed.

We study the avalanche statistics observed in a minimal random growth model. The growth is governed by a reproduction rate obeying a probability distribution with finite mean ā and variance v a . These two control parameters determine if the avalanche size tends to a stationary distribution (finite scale statistics with finite mean and variance, or power-law tailed statistics with exponent ∈ (1, 3]), or instead to a nonstationary regime with log-normal statistics. Numerical results and their statistical analysis are presented for a uniformly distributed growth rate, which are corroborated and generalized by mathematical results. The latter show that the numerically observed avalanche regimes exist for a wide family of growth rate distributions, and they provide a precise definition of the boundaries between the three regimes.