Contact guidance as a consequence of coupled morphological evolution and motility of adherent cells

Tumor proliferation and invasion are intrinsically coupled and unraveled through tunable spheroid and physics-based models

Proliferation and invasion are two key drivers of tumor growth that are traditionally considered independent multicellular processes. However, these processes are intrinsically coupled through a maximum carrying capacity, i.e., the maximum spatial cell concentration supported by the tumor volume, total cell count, nutrient access, and mechanical properties of the tissue stroma. We explored this coupling of proliferation and invasion through in vitro and in silico methods where we modulated the mechanical properties of the tumor and the surrounding extracellular matrix. E-cadherin expression and stromal collagen concentration were manipulated in a tunable breast cancer spheroid to determine the overall impacts of these tumor variables on net tumor proliferation and continuum invasion. We integrated these results into a mixed-constitutive formulation to computationally delineate the influences of cellular and extracellular adhesion, stiffness, and mechanical properties of the extracellular matrix on net proliferation and continuum invasion. This framework integrates biological in vitro data into concise computational models of invasion and proliferation to provide more detailed physical insights into the coupling of these key tumor processes and tumor growth. STATEMENT OF SIGNIFICANCE: Tumor growth involves expansion into the collagen-rich stroma through intrinsic coupling of proliferation and invasion within the tumor continuum. These processes are regulated by a maximum carrying capacity that is determined by the total cell count, tumor volume, nutrient access, and mechanical properties of the surrounding stroma. The influences of biomechanical parameters (i.e., stiffness, cell elongation, net proliferation rate and cell-ECM friction) on tumor proliferation or invasion cannot be unraveled using experimental methods alone. By pairing a tunable spheroid system with computational modeling, we delineated the interdependencies of each system parameter on tumor proliferation and continuum invasion, and established a concise computational framework for studying tumor mechanobiology.

A continuum mechanical model of cell motion driven by a biphasic traction stress

The aim of this paper is to place the cell locomotion problem within the general framework of classical continuum mechanics, and while doing so, to account for the deformation of the actin network in the cytoskeleton; the myosin activity on the lamellum including its effect on depolymerization at the trailing edge; model the stress-dependent driving forces and kinetic laws controlling polymerization at the leading edge, depolymerization at the trailing edge and ATP hydrolysis consistently with the dissipation inequality; and, based on the observations in Gardel et al. (Gardel et al. 2008 J. Cell Biol. 183, 999-1005 (doi:10.1083/jcb.200810060)), include a biphasic velocity-dependent traction stress acting on the actin network. While we chose certain specific models for each of these, in part to allow for an analytical solution, the generality of the framework allows one to readily introduce different constitutive laws to describe these phenomena as might be needed, for example, to study some different type of cells. As described in §5, the predictions of the model compare well with observations such as the magnitude of the very different actin retrograde speeds in the lamellum and lamellipodium including their jump at the interface, the magnitude of the cell speed, and the relative lengths of the lamellipodium and lamellum.

The influence of entropic crowding in cell monolayers

Cell-cell interaction dictates cell morphology and organization, which play a crucial role in the micro-architecture of tissues that guides their biological and mechanical functioning. Here, we investigate the effect of cell density on the responses of cells seeded on flat substrates using a novel statistical thermodynamics framework. The framework recognizes the existence of nonthermal fluctuations in cellular response and thereby naturally captures entropic interactions between cells in monolayers. In line with observations, the model predicts that cell area and elongation decrease with increasing cell seeding density-both are a direct outcome of the fluctuating nature of the cellular response that gives rise to enhanced cell-cell interactions with increasing cell crowding. The modeling framework also predicts the increase in cell alignment with increasing cell density: this cellular ordering is also due to enhanced entropic interactions and is akin to nematic ordering in liquid crystals. Our simulations provide physical insights that suggest that entropic cell-cell interactions play a crucial role in governing the responses of cell monolayers.

Cell reorientation on a cyclically strained substrate

Cyclic strain avoidance, the phenomenon of cell and cytoskeleton alignment perpendicular to the direction of cyclic strain of the underlying 2D substrate, is an important characteristic of the adherent cell organization. This alignment has typically been attributed to the stress-fiber reorganization although observations clearly show that stress-fiber reorganization under cyclic loading is closely coupled to cell morphology and reorientation of the cells. Here, we develop a statistical mechanics framework that couples the cytoskeletal stress-fiber organization with cell morphology under imposed cyclic straining and make quantitative comparisons with observations. The framework accurately predicts that cyclic strain avoidance stems primarily from cell reorientation away from the cyclic straining rather than cytoskeletal reorganization within the cell. The reorientation of the cell is a consequence of the cell lowering its free energy by largely avoiding the imposed cyclic straining. Furthermore, we investigate the kinetics of the cyclic strain avoidance mechanism and demonstrate that it emerges primarily due to the rigid body rotation of the cell rather than via a trajectory involving cell straining. Our results provide clear physical insights into the coupled dynamics of cell morphology and stress-fibers, which ultimately leads to cellular organization in cyclically strained tissues.

Thermodynamically-motivated chemo-mechanical models and multicellular simulation to provide new insight into active cell and tumour remodelling

Computational models can shape our understanding of cell and tissue remodelling, from cell spreading, to active force generation, adhesion, and growth. In this mini-review, we discuss recent progress in modelling of chemo-mechanical cell behaviour and the evolution of multicellular systems. In particular, we highlight recent advances in (i) free-energy based single cell models that can provide new fundamental insight into cell spreading, cancer cell invasion, stem cell differentiation, and remodelling in disease, and (ii) mechanical agent-based models to simulate large numbers of discrete interacting cells in proliferative tumours. We describe how new biological understanding has emerged from such theoretical models, and the trade-offs and constraints associated with current approaches. Ultimately, we aim to make a case for why theory should be integrated with an experimental workflow to optimise new in-vitro studies, to predict feedback between cells and their microenvironment, and to deepen understanding of active cell behaviour.