Glass-like dynamics in the cell and in cellular collectives

Abstract

Prominent fluctuations, heterogeneity, and cooperativity dominate the dynamics of the cytoskeleton as well as the dynamics of the cellular collective. Such systems are out of equilibrium, disordered, and remain poorly understood. To explain these findings, we consider a unifying mechanistic rubric that imagines these systems as comprising phases of soft condensed matter in proximity to a glass or jamming transition, with associated transitions between solid-like versus liquid-like phases. At the scale of the cytoskeleton, data suggest that intermittent dynamics, kinetic arrest, and dynamic heterogeneity represent mesoscale features of glassy protein-protein interactions that link underlying biochemical events to integrative cellular behaviors such as crawling, contraction, and remodeling. At the scale of the multicellular collective, jamming has the potential to unify diverse biological factors that previously had been considered mostly as acting separately and independently. Although a quantitative relationship between intra- and intercellular dynamics is still lacking, glassy dynamics and jamming offer insights linking the mechanobiology of cell to human physiology and pathophysiology.

Figure 1. Aging and rejuvenation

a) In Optical Magnetic Twisting Cytometry (OMTC), to measure the cytoskeleton properties, a torque induced by a magnetic field rotates and displaces beads which are tightly bound on cell surface, b) HASM cell with a series of biological perturbations shows power law responses, c) creep behavior indicates stiffening and of the cytoskeleton with increasing t_w, d) Behavior of τ with waiting time t_w. Solid lines are best fits by a power law, the exponent of which gives the aging exponent μ = 0.4 for t_w ≤ 1600 s. Grey symbols (data) and dashed lines (best fits) correspond to time controls (no shear applied). Inset, J(t, t_w) (for t_w = 1600 s) collapsed onto a master curve using the rescaled time with μ = 0.4. e) Rejuvenation was quantified as the per cent change between J(t, t_w) at t = 1 s, t_w = 10 s after shear, and the creep before shear, at t = 1 s. f) The MSD of the spontaneous bead motions exhibited subdiffusive behavior for small Δt (β < 1) and superdiffusive behavior for large Δt (β > 1) and non-Gaussian probability distribution. Adapted with permission from Fabry et al. and Bursac et al.

Figure 2. Cells behave as strong colloidal glass formers

a) Evolution of relative stiffness, G′_n (stiffness after stretch relative to stiffness immediately before) of HASM cells after different magnitude of a single transient stretch. b) Evolution of the phase angle (δ = tan^-1(G″/G′)) after stretch. c) Phase angle changes between 0 and π/2 for a Newtonian fluid and a Hookean solid, respectively. This places cells closer to the solid like state. In response to the transient stretch of similar magnitude, cells show a fluidization response comparable to but to the left of hard sphere colloids. d) Estimation of the viscosity of the colloidal phase of cells. The exponential growth of viscosity for cells is sharply contrasted by the stronger increase in viscosity for hard spheres, which greatly accelerates as the volume fraction increased toward the glass transition (pluses). In the x axis the volume fraction has been normalized by that at the glass transition, defined as the point at which viscosity reaches an arbitrarily chosen high value, 40,000 Pa.s. Data for the hard spheres are fitted with Mooney's equation for hard-sphere viscosity (the black curve), and the red line is the Arrhenius equation with 1/T replaced by ϕ. e) The fragility as m = dlog₁₀ (η)/d(ϕ/ϕ _g)|_ϕ=ϕg, was quantified and plotted against the isotonic stiffness. This stiffness for hard spheres was estimated at the volume fraction of 0.3. The fragility of the hard spheres is >1 order of magnitude higher, whereas their “isotonic stiffness” is a few orders of magnitude lower, than the corresponding values for cells. Data points with error bars represent median values and interquartile ranges. (In panels d and e, symbol shape represents cell type: square, diamond, triangle and star correspond to HASM cells, lung fibroblasts, MDCK cells, and neurons, respectively; different colors stand for different treatments: no treatment (black), ATP depletion (green), cytochalasin D (cyan), and latrunculin A (red). Adapted with permission from Trepat et al. and Zhou et al.

Figure 3

Intercellular stress forms a rugged landscape (colored topography denotes local tensile stress) and cell migrations (red arrows) follow stress orientation (blue ellipses). Reprinted with permission from Tambe et al.

Figure 4

Hypothetical jamming phase diagram for the cellular monolayer in the inverse density, adhesion and external stress space. The jammed region is the one close to the origin, bounded by the hypothetical jamming surface. Arrow-heads depict the migration speed and migration direction of individual cells. Colors depict cell clusters (packs) that move collectively. As cell density increases, MCF10A cells in the controlled state move from outside the jamming transition towards the jammed region while their motion becomes more cooperative and slower. Cell migration follows the local orientation of maximal principal stress, the phenomenon called plithotaxis. As cells proliferate and crowd more due to overexpression of oncogene ErbB2, cell packs become progressively larger and slower, and plithotaxis becomes amplified. However, overexpression of oncogene 14-3-3ζ disrupts cell-cell junctions, therefore the monolayer becomes unjammed and fluidized, collectivity is lost and plithotaxis is ablated. Reprinted with permission from Sadati et al.