A unified rheological model for cells and cellularised materials

Abstract

The mechanical response of single cells and tissues exhibits a broad distribution of time scales that gives often rise to a distinctive power-law regime. Such complex behaviour cannot be easily captured by traditional rheological approaches, making material characterisation and predictive modelling very challenging. Here, we present a novel model combining conventional viscoelastic elements with fractional calculus that successfully captures the macroscopic relaxation response of epithelial monolayers. The parameters extracted from the fitting of the relaxation modulus allow prediction of the response of the same material to slow stretch and creep, indicating that the model captured intrinsic material properties. Two characteristic times can be derived from the model parameters, and together these explain different qualitative behaviours observed in creep after genetic and chemical treatments. We compared the response of tissues with the behaviour of single cells as well as intra and extra-cellular components, and linked the power-law behaviour of the epithelium to the dynamics of the cell cortex. Such a unified model for the mechanical response of biological materials provides a novel and robust mathematical approach for diagnostic methods based on mechanical traits as well as more accurate computational models of tissues mechanics.As part of their physiological function, single cells and tissues are continuously exposed to mechanical stress. For example, leukocytes circulating in the blood must squeeze through small capillaries, and the epidermis must deform in response to movements of our limbs. During development, mechanical forces initiate morphogenetic processes involving epithelial growth, elongation or bending, acting as cues to coordinate morphogenetic events [1]. Epithelial cell sheets are also continuously subjected to deformation as part of normal physiology. For instance, lung epithelial cells are exposed to fast cyclical mechanical stress during respiration [2], while epithelia lining the intestinal wall or those in the skin can experience long lasting strain [3]. Failure to withstand physiological forces results in fracture of monolayers which may lead to severe clinical conditions, such as hemorrhage or pressure ulcers [3]- [6]. Despite significant progress with the experimental characterization of cell and tissue mechanics, understanding the role of mechanical forces in development and pathology is hampered by the lack of a unified quantitative approach to capture, compare and predict the complex mechanical behaviours of tissues, cells, and sub-cellular components across all physiologically relevant time-scales. Such a framework would also enable us to assess the effects of pharmacological treatments on tissue mechanical response without necessitating experimental characterization of the tissue response to all loading conditions, something important for tissue engineering and the design of palliative treatment strategies.In recent years, experimental characterization of the mechanical behaviour o...

Mechanosensitive Junction Remodeling Promotes Robust Epithelial Morphogenesis

“…Despite the growing evidence for active remodeling of junction mechanical properties (12,13), most theoretical models for epithelial mechanics, such as the vertex model (14)(15)(16), cellular Potts model (17,18), or continuum models (19)(20)(21), assume constant interfacial tensions and cell contractility. Although some recent models attempt to model junctional mechanics (9,(22)(23)(24)(25), these have not been directly tested in experiments at the scale of individual cell junctions.…”

All-in-one rheology of multicellular aggregates

“…Observed non-linearities may therefore be mainly associated with the cellular contribution. One caveat concerns the threshold stress values above which stress stiening is observed, of the order of 1Pa here, vs. 10 − 1000 Pa in single cells [47,53] and several hundreds Pa in monolayers [33,34]. However, the magnetic rheometer allows to exert comparatively small stresses, while most other techniques involve larger stresses.…”

“…However the link between cellular and junctional contributions is not straightforward. The response of suspended epithelial cell monolayers has been characterized by combining conventional viscoelastic and fractional elements with an exponent close to 0.3 [33,34]. Plus power-law rheology has been observed at the organ scale in a shear rheometer [35,36] with an exponent close to 0.2.…”

m‐Parameter Mittag–Leffler function, its various properties, and relation with fractional calculus operators

“…The Mittag–Leffler function with one parameter has found its applications in the AB Model and in relaxation models that involves interpolation between exponential and power‐law behavior 50 . The data received from experimenting with models for cells and tissues is linked to the Wiman function 51 . Prabhakar function is associated with Havriliak–Negami relaxation 52 .…”