A low-dimensional deformation model for cancer cells in flow

Abstract

A low-dimensional parametric deformation model of a cancer cell under shear flow is developed. The model is built around an experiment in which MDA-MB-231 adherent cells are subjected to flow with increasing shear. The cell surface deformation is imaged using differential interference contrast microscopy imaging techniques until the cell releases into the flow. We post-process the time sequence of images using an active shape model from which we obtain the principal components of deformation. These principal components are then used to obtain the parameters in an empirical constitutive equation determining the cell deformations as a function of the fluid normal and shear forces imparted. The cell surface is modeled as a 2D Gaussian interface which can be deformed with three active parameters: H (height), σ(x) (x-width), and σ(y) (y-width). Fluid forces are calculated on the cell surface by discretizing the surface with regularized Stokeslets, and the flow is driven by a stochastically fluctuating pressure gradient. The Stokeslet strengths are obtained so that viscous boundary conditions are enforced on the surface of the cell and the surrounding plate. We show that the low-dimensional model is able to capture the principal deformations of the cell reasonably well and argue that active shape models can be exploited further as a useful tool to bridge the gap between experiments, models, and numerical simulations in this biological setting.

The Cytoskeleton Regulates Cell Attachment Strength

“…7). Instead, we observed that they leave behind a significant portion of their FAs, including Paxillin, Vinculin, and FAK, but not actin, which is consistent with other observations made without further quantification (5,15,16). These data are similar to the trailing edge of cell migration in two-dimensional, where cells also leave pieces of their FAs behind (26).…”

“…(10)(11)(12). Although some quantitative assessments of cell adhesion are in agreement with this paradigm (13,14) others have detected cell components, i.e., integrins and other FA proteins, that remain on the substrate after cell detachment (5,15,16). Although these recent data would suggest that detaching cells break their connection to the ECM higher up than at the integrin-ECM interface, i.e., somewhere between the FA-cytoskeleton, the frequency of occurrence of this detachment mechanism and its functional impact on detachment strength has yet to be determined.…”

Modeling viscoelastic networks in Stokes flow

“…This method has been widely used to investigate low Reynolds number hydrodynamics in applications such as microorganism motility, 15, 21-24 biofilm dynamics, 25,26 cancer cells in flow, 27 microfiltration as a method for removing particulate matter, 28 and to study hydrodynamic interactions that cause synchronization between rotating paddles in a viscous fluid. 29 The inclusion of a rigid wall where the fluid velocity must satisfy the zero-flow boundary condition can be accomplished by using a method of images.…”

A general system of images for regularized Stokeslets and other elements near a plane wall

“…It turned out that some of those element had to be derived from a "companion" blob in order to achieve the necessary cancellation of terms. While the regularized image system has been useful in many applications of microorganism motility, nano motors, sperm motility, cilia dynamics, and more [34,10,9,21,20,35,24,33], it is clear that a more general theory is needed to allow the use of specialized blobs in the regularized Stokeslet. For example, higher accuracy in computing the Stokeslet flow due to a moving object may be achieved if the blobs used to regularize the surface forces satisfy certain moment conditions of the form ∞ 0 r m+2 φ δ (r)dr = 0 for integers m ≥ 1 (see [4,28]).…”