Investigating dynamical deformations of tumor cells in circulation: predictions from a theoretical model

Abstract

It is inevitable for tumor cells to deal with various mechanical forces in order to move from primary to metastatic sites. In particular, the circulating tumor cells that have detached from the primary tumor and entered into the bloodstream need to survive in a completely new microenvironment. They must withstand hemodynamic forces and overcome the effects of fluid shear before they can leave the vascular system (extravasate) to establish new metastatic foci. One of the hypotheses of the tumor cell extravasation process is based on the so called "adhesion cascade" that was formulated and observed in the context of leukocytes circulating in the vascular system. During this process, the cell needs to switch between various locomotion strategies, from floating with the blood stream, to rolling on the endothelial wall, to tumor cell arrest and crawling, and finally tumor cell transmigration through the endothelial layer. The goal of this project is to use computational mechanical modeling to investigate the fundamental biophysical parameters of tumor cells in circulation. As a first step to build a robust in silico model, we consider a single cell exposed to the blood flow. We examine parameters related to structure of the actin network, cell nucleus and adhesion links between the tumor and endothelial cells that allow for successful transition between different transport modes of the adhesion cascade.

Keywords: cell deformation; circulating tumor cells; computational modeling; immersed boundary method; metastatic cascade.

FIGURE 1

Model schematics and equations. A schematic representation of the 2D model of the tumor cell in circulation. The blood vessel (red walls, E) is interpenetrated by a laminar flow (gray arrows representing blood velocity field) that interacts with a circulating tumor cell (CTC). The cell nucleus (gray, N) is surrounded by the cell cortex (blue, C) that both define cell shape and stiffness. The cell near the endothelial wall (EW) develops CTC–EW adhesive connections (green links, A). Insets show the magnification of a meshwork defining the nucleus and the cortex (top), and the network defining the EW and CTC–EW adhesive springs (bottom). Representative springs of the cortex, nucleus, endothelium, and adhesive CTC–EW links (X_C–X_C*, X_N–X_N*, X_A–X_A*, X_E–X_E*) are indicated by thick lines. Equations 1–5 define the mathematical frameworks of the Immersed Boundary method.

FIGURE 2

Circulating tumor cell stiffness relationship. Circulating tumor cell deformation under steady blood flow in relation to the cell cortex versus cell nuclear envelope stiffness. Final configurations of two separately simulated cells that vary only by their location within the vessel (red) are overexposed on one picture. The cell cortex stiffness (blue) and cell nuclear envelope stiffness (gray) were varied by sixfold each.

FIGURE 3

Circulating tumor cell rolling on the endothelium. Each of the four cases (A–D) is characterized by a different cortex C and nucleus N stiffness value, however the strength of all adhesive bonds is fixed. The values are reported similarly as in Figure 2. (A) both the cortex and nucleus stiffness are 3-fold higher than the baseline; (B) the nucleus stiffness is 3-fold and cortex stiffness is 6-fold higher than the baseline; (C) nucleus 6-fold and cortex 3-fold; (D) both the nucleus and cortex stiffness is 6-fold higher than the baseline. For each case, four time snapshots (taken at time t, 2t, 3t, and 4t) are overexposed on the same picture for comparison of cell deformation and translocation in each case. A fixed small part of the cell cortex is stained for illustration of the rolling effect.

FIGURE 4

Circulating tumor cell migrating on the endothelium. Four time snapshots (taken at time t, 2t, 5t, and 10t) are overexposed on the same picture for comparison of cell deformation and translocation. (A) The cell cortex is stained differently depending on its local stiffness: soft (cyan) close to cell focal adhesion with EW, and stiff (blue) far from EW contacts. (B) A fixed small part of the cell cortex is stained for illustration of the rolling effect.

FIGURE 5

Dynamical changes in the cell cytoskeleton during CTC intravenous transport. Each of the steps of the adhesive cascade requires different cytoskeletal properties of the CTC actin cortex stiffness (blue), cortex stiffness near the adhesion sites (cyan), stiffness of the CTC nuclear envelope (gray), and strength of the CTC–EW adhesion bonds (green). A typical cell configuration for each of the steps of the adhesive cascade is shown in the top row together with a color-coded cell stiffness signature. Lines represent the best continuous fit of the computational data.

FIGURE 6

Three-dimensional model schematics and equations. A schematic representation of the structure of the 3D cell (left, top), the microvessel with a single attached cell (left, bottom), and model equations in three dimensions (right).