Realizations of highly heterogeneous collagen networks via stochastic reconstruction for micromechanical analysis of tumor cell invasion

Abstract

Three-dimensional (3D) collective cell migration in a collagen-based extracellular matrix (ECM) is among one of the most significant topics in developmental biology, cancer progression, tissue regeneration, and immune response. Recent studies have suggested that collagen-fiber mediated force transmission in cellularized ECM plays an important role in stress homeostasis and regulation of collective cellular behaviors. Motivated by the recent in vitro observation that oriented collagen can significantly enhance the penetration of migrating breast cancer cells into dense Matrigel which mimics the intravasation process in vivo [Han et al. Proc. Natl. Acad. Sci. USA 113, 11208 (2016)PNASA60027-842410.1073/pnas.1610347113], we devise a procedure for generating realizations of highly heterogeneous 3D collagen networks with prescribed microstructural statistics via stochastic optimization. Specifically, a collagen network is represented via the graph (node-bond) model and the microstructural statistics considered include the cross-link (node) density, valence distribution, fiber (bond) length distribution, as well as fiber orientation distribution. An optimization problem is formulated in which the objective function is defined as the squared difference between a set of target microstructural statistics and the corresponding statistics for the simulated network. Simulated annealing is employed to solve the optimization problem by evolving an initial network via random perturbations to generate realizations of homogeneous networks with randomly oriented fibers, homogeneous networks with aligned fibers, heterogeneous networks with a continuous variation of fiber orientation along a prescribed direction, as well as a binary system containing a collagen region with aligned fibers and a dense Matrigel region with randomly oriented fibers. The generation and propagation of active forces in the simulated networks due to polarized contraction of an embedded ellipsoidal cell and a small group of cells are analyzed by considering a nonlinear fiber model incorporating strain hardening upon large stretching and buckling upon compression. Our analysis shows that oriented fibers can significantly enhance long-range force transmission in the network. Moreover, in the oriented-collagen-Matrigel system, the forces generated by a polarized cell in collagen can penetrate deeply into the Matrigel region. The stressed Matrigel fibers could provide contact guidance for the migrating cell cells, and thus enhance their penetration into Matrigel. This suggests a possible mechanism for the observed enhanced intravasation by oriented collagen.

Tumor-associated collagen signatures: pushing tumor boundaries

“…Importantly, the outermost layer (TACS3) is defined by linear branches of collagen growing perpendicularly away from invasive breast tumors [1]. Within breast cancer literature, words like "aligned," "oriented," "organized," and "linear" can be found referring to a specific extracellular matrix (ECM) pattern of the invasive breast tumors [2][3][4]. Clinically, there is a well-established link between the collagen architecture of the primary tumor and prognosis.…”

Dynamically Re‐Organized Collagen Fiber Bundles Transmit Mechanical Signals and Induce Strongly Correlated Cell Migration and Self‐Organization

“…In particular, as the cell contracts isotopically, the fibers attached to the cell surface are pulled towards the cell center. The pulling forces result in re‐orientation and alignment of successive fiber segments to form linear chain‐like structures (see Figure 2 e), whose extent (≈20 to 40 μm) is much larger than the average length of the fiber segment (≈2 to 5 μm), [14a,b, 17] representing the experimentally observed fiber bundles. It is found that such chain‐like structures (i.e., fiber bundles) carry the majority of the tensile forces generated by the cell, and the force on the fiber bundles decays much slower, with a scaling ≈1/ r β (with β≈0.68), than that in a continuous elastic medium (with ≈1/ r ) (see Figure 2 f).…”

Geometric Dependence of 3D Collective Cancer Invasion

“…To further test our hypothesis in explaining the observed contrast between circular and triangular tumors, we devise a multiscale computational model that takes into account the fibrous microstructure of the ECM (11,12) and nonlinear ECM mechanics (13)(14)(15), as well as cell motility directed by ECM mechanical cues (16)(17)(18)(19). In particular, in our simulations, the tumor diskoid is modeled as a 3D packing of (spherical) cells within a flat cylinder with a thickness of 100 mm (i.e., $4-5 cell lengths) (see Fig.…”