Bridging the Gap in Cancer Cell Behavior Against Matrix Stiffening: Insights from a Trizonal Model

Reviewer #1 (Public review):

The manuscript presents a novel nonlinear mathematical model that addresses a critical gap in our understanding of how cell shape transitions in response to ECM stiffness. The focus on the interplay between actomyosin contractility and ECM stiffening is highly relevant, especially in the context of cancer invasion and tissue morphogenesis. The originality of the proposed trizonal model is commendable, as it offers a comprehensive framework that could significantly advance the field.

More specifically, the paper makes a significant contribution by providing a model that can predict multimodal cell shapes based on motility levels, which is a substantial improvement over current constitutive models. The potential to calibrate the model against experimental cell shape data is a strong point, as it ensures that the model's predictions are grounded in empirical evidence. The methodology appears to be rigorous and should provide reliable results when applied. This advancement could lead to a better understanding of the complex dynamics involved in cell-matrix interactions, particularly at intermediate ranges of collagen density. The potential applications of this research are vast and span across various medical and biological fields. The ability to predict cancer-induced tissue impairment, cachexia, and muscle injury, as well as to assess therapeutic methods, is particularly noteworthy. The mention of specific treatments like Blebbistatin and HAPLN1 treatments further adds depth to the discussion and highlights the practical relevance of the model.

I'm curious if the authors could further elaborate on the use of this model to examine cellular unjamming transition or the cell shape changes during cancer invasion in various scenarios. Some discussions on that aspect will be helpful. It will also be useful to provide some perspectives on how this model could be integrated with others in a multi-scale modeling framework for understanding cell shape transitions during collective cell migration in various physiologically relevant scenarios.

I recommend some minor revisions but overall, this is a very nice paper.

Reviewer #2 (Public review):

In this work the authors develop a mathematical model that incorporates three contributions to cellular force generation in 3D matrices: (1) actively generated contractile forces via myosin motors and consumption of ATP; (2) the energy stored in the extracellular matrix as it is deformed by the contractile cell; and (3), the energy associated with the interactions at the interface between the matrix and the cell, e.g. at focal adhesions. The authors make predictions about the dependence of cell shape on these three contributions.

The authors succeed in making a number of predictions of how cell shapes will depend on these contributions to force generation. However, these predictions seem to be largely buried in the supplemental material and come in a form that will be accessible to a certain type of physicist and modeler but will likely not be accessible to many experimentalists who may want to test the predictions of the model. The authors show a comparison between their expected cell shape distributions and those predicted by the model, under multiple regimes: cells in two different concentrations of collagen (Figure 4c), cells with inhibited myosin and therefore reduced contractility (Figure 4d), cells with impaired interactions with the ECM (Figure 4e), and for cells with both contractility and ECM interactions impaired. They find a strong agreement between the experiments and their predictions. However, it should be noted that there are multiple "tuning parameters" in their model, so the ability to match experiment and theory may not be ultimately so surprising.

While the authors do achieve their aim of building this modeling and testing it in comparison to experimental data, the text is frequently unclear and doesn't seem to have the right information at the right place and time to allow the reader to most clearly understand the motivation, the approach, or the results. A number of elements of this manuscript were confusing to this reviewer, and I discuss these below in the hopes that raising these points here can bring more clarity in future revisions, and/or that readers will be able to provide additional insight or attention to these questions.

There are certain elements of the writing that obscure, rather than clarify, the model and the results. For example, the authors frequently refer to "matrix stiffening" and "strain stiffening", which are typically used in the literature to describe the phenomenon whereby an applied force changes the mechanical properties of the substrate; here, for example in regard to the discussion of Figure 4C, these terms instead seem to be simply referring to the experimental intervention of exposing different cells to different concentrations of the collagen matrix. While there may be some element of classically understood strain stiffening, incorporated into the model as the function f(λ_i), this doesn't seem to match the experimental validation - which, as described above, is not about strain stiffening but instead simply uses softer vs. stiffer gels. Therefore, it is unclear what exactly is meant throughout the manuscript by strain stiffening - does it mean "difference in stiffness between two conditions" or does it mean "change in substrate stiffness upon application of force"?

Furthermore, while the introductory text emphasizes collective migration, the model itself focuses on the interactions between single cells and their environments. The emphasis on collective migration and cell shape in the introduction invokes previous literature focusing on collective phase transitions, but that is misleading. This paper is all about individual cell mechanics, not about collective migration or unjamming.

The experimental validation seems to have a significant flaw. The mechanics and interactions of the cellular extensions seem to be completely ignored. We see, in Figure 4, that cell bodies are outlined to determine cell shape, but that the extremely long extensions are simply ignored. We know from previous studies that these extensions are generating quite a bit of traction and are contractile, and yet they've been excluded from the analysis. This doesn't make physical sense or fit with previous literature, and would seem to indicate that the regimes predicted by the model are missing an essential component of force generation and cell-matrix interaction.