A minimal rupture cascade model for living cell plasticity

Abstract

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.

Emergence of Log-Normal Type Distributions in Avalanche Processes in Living Systems: A Network Model

“…The ability of cells to switch quickly from fluid-like responses to more brittle solid-like responses [2] is directly linked to the interplay between stability/rigidity and flexibility, in a way similar to what happens in neural networks [63]. This fast switch is likely driven by avalanche processes, which allow fast transfer of information.…”

“…Recently, some doubts about the ubiquity of power-law distributions have been advanced [15], pointing out that many real system's data are actually better fitted by other skewed, fat-tailed distributions, such as the log-normal. This is true for network degree distributions, in social, biological or technological networks [15], but also for avalanche statistics, in neural networks [16,17] or living cells cytoskeleton [2]. Indeed, the growth of a network can be seen itself as an avalanche process, thinking for example of the preferential attachment rule [18].…”

“…Avalanche processes are very common in living systems, such as firing rates in brain [1], fractures in living cells cytoskeleton (CSK) [2], but also in amorphous [3] and random media [4], or earthquakes. Actually, all the systems that can be considered as composed by elementary threshold units, which are connected and can transfer information to each other, are subject to avalanches.…”

“…Originally motivated by the experimental observation of log-normal statistics in avalanches of fractures of the CSK of living cells [2,29], we focus in this paper on the modeling of log-normal avalanches on random networks. Our model is inspired by our previous 1-D model [2] and by works on epidemics spreading on networks [30,31], in our case the population is represented by actin filaments, being in two possible states: cross-linked or not. The network structure models the CSK structure and the avalanche is a model for rupture mechanics in living cells, when plastic deformations are considered.…”

Clonal pattern dynamics in tumor: the concept of cancer stem cells

“…Nevertheless it explains several biological evidences such as the relapse of tumor post-surgery and treatments 9 or the ability to generate tumors in xenotransplantation 10 . Nowadays, surface biomarkers, in charge of identification and detection of these cells, are more and more evaluated for different classes of cancer which allows new therapeutics in clinical 11 but also experimental measurements of their physical properties 12 .…”