Computational modeling reveals a vital role for proximity-driven additive and synergistic cell-cell interactions in increasing cancer invasiveness

A key process in metastasis, the typically lethal spread of cancer [1] to local or distant body-sites, is migration and invasion of cancer cells that have detached from the primary tumor. Cell migration and invasion are regulated by various cell-cell and cell-extracellular matrix interactions [2]. Existence of strong cell-cell bonds can determine whether cancer cells will invade in attached cohorts or as single cells. Relying on cell-cell junctions, solid tumors, such as breast cancers, predominantly exhibit collective invasion with cells migrating in connected groups, and disruption of integrin- or protease-function typically leads to single cell migration [3]. Without cell-cell bonds, e.g. due to cadherin deficiency as in the widely studied, metastatic, MDA-MB-231 breast cancer cell line [4], cells may still mechanically interact through the substrate, which may increase their invasiveness. Aptly, MDA-MB-231 cells are more invasive in vitro and in vivo when in close proximity, as compared to single, well-spaced cells [5], [6], [7]. Therefore, cancer cell interactions through their substrate may promote collective invasion even when direct cell-cell connections are lacking and thus potentially increase the risk for metastasis.

Invasiveness of cancer cells arises from their dynamic mechanobiology. Invasive cancer cells are more pliable than non-invasive or benign cells [8,9] likely due to their sparse and highly dynamic intracellular mechanostructure [10,11]. The dynamic cytoskeleton also facilitates application of stronger adhesive and invasive forces by cancer cells [12], [13], [14], [15], [16]. Aptly, cells from various invasive cancers have demonstrated higher contractility and stronger, more directionally applied traction forces, as well as a stiffness response, on two- and three-dimensional gels, as compared to non-invasive cells [12,15,17]. Consequently, we have shown that invasive cancer-cell subpopulations can forcefully push into and indent impenetrable, physiological stiffness, elastic, polyacrylamide gels [13,18] by utilizing their dynamic cytoskeletons [6,16,19]; the invasive cancer-cell subpopulations also exhibit higher migratory capacity through in vitro Boyden chambers [18,20]. In contrast, non-invasive, benign, or normal cells primarily apply adhesive tractions and can migrate across the substrate surface [15,21,22]. Invasive cells indent gels by combining adhesive, in-plane traction forces with pushing- and pulling-forces, normal to the gel-substrate [13,23]. The percentage of indenting cells and their attained indentation depths, together a measure of the sample's mechanical invasiveness, agree with the clinically determined, in vivo invasiveness and metastatic risk in different cancer types [18,24]. Thus, cell interactions with their substrate have been shown to indicate and may also facilitate invasiveness.

Cell proximity on a substrate may enable mechanisms for synergistic increase of forceful invasiveness. We have observed that single, closely adjacent, metastatic MDA-MB-231 breast cancer cells indented to depths of 18 µm, while well-spaced cells only indented up to 10 µm [5]. Invasive cell indentations rely on cytoskeletal dynamics and especially the actin machinery [6,16], which is likely affected by mechano-sensing and mechanobiological response mechanisms [25]. Hence, the increased cell-indentations may result, for example, from mechanical deformations and tensions applied by closely situated cells [26] or due to changes in gel stiffness. Substrate stiffness gradients can induce durotaxis and have, for example, increased motility and migration of fibroblasts and vascular smooth muscle cells towards stiffer substrate regions [27,28]. Increase in substrate stiffness has also promoted malignant cell phenotypes [29] and stimulated metastatic cancer cells to apply stronger adhesive and invasive forces [12,13,15]. Chemical and mechanostructural matrix remodeling changes the force and tension landscape, which affects cell communication via mechano-sensing. Matrix remodeling, for example, allows adjacent cancer cells to communicate with each other as well as with neighboring stromal cells, potentially facilitating cancer progression [2]. As a result, tension forces transmitted through a substrate can induce cell migration, or tensotaxis [30,31]. Similarly, mechanical strains transmitted through the substrate can induce motion, and e.g. fibroblasts have been observed to migrate towards higher strain regions [32]. Moreover, mechanical strains applied on a matrix with MDA-MB-231 breast cancer cells encapsulated in low- or high-density, caused cells to migrate, respectively, in or against the direction of the mechanical strains [33], again highlighting potential effects of cell proximity. Thus, we propose that substrate deformations, tensions, or forces induced by adjacent cancer cells can synergistically increase each cell's capacity for forceful invasiveness or its metastatic potential.

Here, we evaluate additive and synergistic mechanisms that may increase invasiveness of closely adjacent cells that do not directly interact, using computational modeling. As single cell interactions with a gel include complex time evolution [26] and effects of cell mechanostructure [14], individual mechanisms are difficult to regulate experimentally, while in silico experiments, or computational modeling allow modulation and controlled application of predefined configurations. We have thus developed finite element models to identify conditions facilitating cell-proximity-induced increase in invasiveness, as defined by experimentally attained indentation depths. The developed models are based on experimental gel mechanics, cell morphologies, and force magnitudes. We show that inclusion of the nucleus mechanics, being the stiffest element in the cell, increases strains and cell-attained indentation depths in single, invasive cells, yet has a minor effect on non-invasive cells. We then evaluate effects of cell proximity, comparing additive and synergistic contributions to indentation depths when 2 and 3 cells are closely adjacent. We show that additive and synergistic, proximity-triggered responses, such as changes in cell mechanostructure or increased force-magnitudes, can facilitate the deep indentations experimentally observed in closely adjacent cells.

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