Early stages of collective cell invasion: Biomechanics

The early stages of the collective invasion may occur by single mesenchymal cells or hybrid epithelial-mesenchymal cell groups that detach from cancerous tissue. Tumors may also emit invading protrusions of epithelial cells, which could be led (or not) by a basal cell. Here we devise a fractional step cellular Potts model comprising passive and active cells able to describe these different types of collective invasion before cells start proliferating. Durotaxis and active forces have different symmetry properties and are included in different half steps of the fractional step method. Compared with a single step method, fractional step produces more realistic cellular invasion scenarios with little extra computational effort. Biochemical mechanisms that determine how cells acquire their different phenotypes and cellular proliferation will be incorporated to the model in future publications.

💡 Research Summary

This paper addresses the physical mechanisms underlying the earliest phases of collective cancer cell invasion, a stage that precedes proliferation and can involve single mesenchymal cells, hybrid epithelial‑mesenchymal clusters, or protruding epithelial sheets sometimes led by a basal cell. To capture these diverse scenarios, the authors develop a Cellular Potts Model (CPM) that distinguishes between passive and active cells and implements a fractional‑step integration scheme. In the first half‑step, a durotactic force—derived from gradients in substrate stiffness and possessing symmetric scalar properties—is applied to passive cells. In the second half‑step, active cells experience non‑symmetric vectorial forces that model contractile or protrusive activity. By separating these forces into distinct sub‑steps, the method respects their differing symmetry characteristics and avoids the numerical instability that arises when they are combined in a single update.

Compared with a conventional single‑step CPM, the fractional‑step approach yields invasion patterns that are qualitatively more realistic: single cells can detach and follow stiffness gradients, epithelial sheets can extend with or without a leader cell, and hybrid clusters display mixed migration modes. Importantly, the computational overhead is modest; the extra half‑step does not significantly increase total run time, and the algorithm remains amenable to parallelization.

The authors acknowledge current limitations: the model does not yet incorporate cell proliferation, apoptosis, or biochemical signaling such as growth‑factor gradients and cytokine communication. Future work will embed these processes, allowing the framework to span from early invasion through later tumor expansion. Validation against experimental data and systematic parameter calibration are also planned.

Overall, the study demonstrates that a fractional‑step Cellular Potts Model can faithfully reproduce the biomechanics of early collective invasion while maintaining computational efficiency. By explicitly treating durotaxis and active forces in separate sub‑steps, the model provides a versatile platform for investigating not only cancer metastasis but also other biological phenomena involving coordinated cell movement, such as wound healing and tissue morphogenesis.