On the mechanism of long-range orientational order of fibroblasts

Abstract

Long-range alignment ordering of fibroblasts have been observed in the vicinity of cancerous tumors and can be recapitulated with in vitro experiments. However, the mechanisms driving their ordering are not understood. Here, we show that local collision-driven nematic alignment interactions among fibroblasts are insufficient to explain observed long-range alignment. One possibility is that there exists another orientation field coevolving with the cells and reinforcing their alignment. We propose that this field reflects the mechanical cross-talk between the fibroblasts and the underlying fibrous material on which they move. We show that this long-range interaction can give rise to high nematic order and to the observed patterning of the cancer microenvironment.

Keywords: alignment; collagen fibers; extracellular matrix; fibroblasts; long-range order.

Fig. 1.

Illustration of the modeling approaches used in this study. Both simulation frameworks describe the effective steric interactions and can result in the local alignment of fibroblasts. (A) In the Monte Carlo simulation framework, fibroblasts are treated as hard elliptic particles. Each fibroblast moves along its long (major) axis with a constant velocity and can reverse its direction. If fibroblasts overlap with neighbors, they rotate by a randomly selected angle within a fixed range. (B) In the Newtonian dynamic simulation framework, a fibroblast is represented by a spherocylinder. It moves along its long axis driven by a constant self-driving force with direction that can also reverse. A constant collisional force is applied after each contact, and the consequent torques drive the rotations of fibroblasts. Detailed descriptions of both simulations are presented in Materials and Methods.

Fig. 2.

(A and B) Snapshots of the simulation at step 2,000 for (A) ellipses or (B) spherocylinders. Color code for the orientation of particles is displayed. (C) Nematic order parameter $Q$ in a channel. Values of nematic order parameter are shown as circles for elliptic particles or as triangles for spherocylinders. In these simulations, channels are set as 60 cells across the horizontal axis. Periodic boundary conditions are applied along the vertical axis. Two hard walls are implemented on the left and right boundaries. The parameters and detailed simulation procedures can be found in Materials and Methods.

Fig. 3.

Numerical simulations generating long-range alignment order in a channel-like geometry. The number of particles gradually increases from 300 (packing fraction 0.12) to over 1,500 (packing fraction 0.58) in the simulations. The aspect ratio of particles in these examples is five; $\alpha$ (Materials and Methods) is chosen as 0.1 in those simulations. (A) Snapshots of the particle configuration of one simulation at steps 10, 600, and 1,200. (B) Evolution of perfect nematic alignment of fibroblasts in a 2D channel in vitro. Width of channel is 0.5 mm. Adapted from ref. , with permission of The Royal Society of Chemistry; dx.doi.org/10.1039/c3sm52323c. (C) Different realizations of our Monte Carlo simulation carried out in a channel-like structure. Black lines are different realizations of the system with only collision interactions, and the parameters are the same as those in Fig. 2. Red lines represent the evolution of nematic order with multialignment interactions between fibroblasts and fibers applied ($R_c=15b$, $\alpha =0.1$).

Fig. 4.

(A and B) Numerical simulations with mutual alignment of fibroblasts and fibers. Hard elliptic obstacles were assigned beforehand; 400 particles were first randomly assigned. New particles are added only within a range close to large obstacles (i.e., half-length of a fibroblast) Color-coding of elliptic particles is the same as that in Fig. 3A. Configurations of fibroblasts are shown in A. Orientation field is shown in B by the direction of each black line on each grid point. We reduce the number of grid points to make the plot clear. Qualitatively, the simulation results are comparable with experimental result shown in C and D. (C) A breast cancer specimen from a patient. Regions with cancer cells are labeled in blue, and background color is set as red for clearer presentation. One particular protein, alpha smooth muscle actin, which is expressed by cancer-associated fibroblasts (23) in cancerous tissue, is labeled in yellow. These fibroblasts are found mostly in the space between cancer cell clusters and orient azimuthally around the clusters. (Scale bar: 100 $\mu$m.) (D) The same field of view as in C. Collagen fibers captured by a Second Harmonic Generation microscope (24) are labeled in white. They surround regions of breast cancer cells clusters (blue) and are parallel to the boundary of the cancer cell clusters. Detailed experimental methods on immunohistochemical labeling of the specimens and image acquisition can be found in SI Appendix. (Scale bar: 100 $\mu$m.)

Fig. 5.

Illustration of our proposed mechanism. A cyan dot emphasizes a specific grid point on which we consider the orientation field. Elliptic particles falling within the dashed circle (radius $R_c$) will affect the orientation field at that grid point. The cyan arrow at the center of the circle indicates the current direction of that orientation field. Each particle’s current orientation is denoted by a red arrow from its center, and it will bias the orientation field toward its direction; this is described quantitatively by Eq. 3.