Scaling-law variance and invariance of cell plasticity

Scaling-laws are ubiquitous as universal physical principles in physics, biological systems, and human behavior. The scaling-law rheological responses of viscoelastic and plastic deformations and rate-dependent softening and stiffening during dynamic loading are remarkable characteristics of living cells and cell-like materials; however, the underlying mechanisms remain poorly understood. Here, we first propose a cellular structural model with 3-dimensional anisotropic discrete and plastic cytoskeletal networks to study the scaling-law rheological responses of cells. Besides the scaling-law invariance observed in cellular plastic deformation and viscoelastic deformation under large force ranges, there is evidence of scaling-law variance under relatively small force ranges. We develop a minimal mechanical model to elucidate the origins of scaling-law variance and invariance of cellular viscoelastic and plastic deformations. Interestingly, we find that cell materials can transition from fluid to solid over time and from elasticity to plasticity with increasing force. Furthermore, it is shown that the heterogeneity of three-dimensional cytoskeletal network dominates the anisotropic viscoplastic behavior of cells. We show that the stress-strain curves of cells with plastic cytoskeletons can be collapsed onto a single master curve of cells with elastic cytoskeletons. Moreover, we discover and derive a novel scaling-law ΔF∼v₀^α wherein the extent of force relaxation on cells during cyclical mechanical stimuli follows the same power-law dependence on the loading rate, as creep compliance on time. Our findings provide evidence that structure-based simulation and theoretical models can naturally capture the scaling-law invariance and variance of cellular deformations, in agreement with many experimental findings.