Cell crawling migration is vital in various biological processes, including development, wound healing, immune response, and cancer metastasis. Understanding the minimal components for cell motility is crucial, particularly the symmetry break between the cell's front and back. In mesenchymal cells, the front utilizes actin polymerization for forward membrane protrusion, while the back employs myosin II contractility for retrograde flow and rearward movement. These processes are often coordinated by biochemical gradients, such as the antagonistic Rac/Cdc42 and RhoA pathways. A key feature of cell motility is bistability: sessile cells can be induced to migrate by sufficiently strong stimuli that polarize the cytoskeleton. While bistability can arise from cell shape changes on 2D substrates, in one-dimensional environments like microchannels, it's mediated by internal polarization. Recent optogenetic studies, activating or inhibiting contractility, have demonstrated that contractile cells operate at intermediate tension, allowing for up- and down-regulation, providing insights into cell migration control. However, the extent of optogenetic control and the relative roles of local versus global myosin recruitment remain open questions. Active gel theory provides a framework for understanding cytoskeletal flow and the role of contraction in cell migration. While previous active gel models have assumed saturated contractile active stress, recent experimental findings show that further contractility can be achieved optogenetically, necessitating a refined model.

Existing literature highlights the importance of actin polymerization and myosin contractility in cell migration, often coordinated by antagonistic signaling pathways like Rac/Cdc42 and RhoA. Studies have shown the bistable nature of cell motility, where sessile cells can be triggered to migrate by external stimuli. Optogenetic manipulation of contractility has revealed that cells operate at intermediate tension levels, enabling both up- and down-regulation of contractility. Active gel theory has been utilized to model cell migration, but previous models often assumed saturated contractile stress, inconsistent with recent experimental observations. This study addresses the limitations of previous models by incorporating the observation that myosin II molecules assemble into larger minifilaments, leading to a nonlinear concentration-dependent diffusion coefficient.

The researchers developed a one-dimensional active gel model to simulate cell migration in microchannels. The model incorporates the constitutive relation of an infinitely compressible active gel with active stress linearly dependent on myosin concentration. Viscous drag with the substrate is considered. The cell's length is variable, reflecting volume homeostasis through elastic boundary conditions. The model includes a microscopic model for myosin binding kinetics, considering binding, unbinding, and cooperative binding of myosin II motors to actin filaments, accounting for excluded volume effects and minifilament formation. This microscopic model leads to a nonlinear concentration-dependent diffusion coefficient, which is shown to be consistent with the linear irreversible thermodynamics of a van der Waals fluid. The full model combines the active gel equation for velocity, the advection-diffusion equation for myosin concentration with the nonlinear diffusion coefficient, and the elastic boundary conditions. The model is non-dimensionalized, resulting in three dimensionless parameters: length ratio L, Péclet number Pe (representing the importance of advection versus diffusion), and myosin contractility P. The study uses numerical continuation methods (AUTO07p) to analyze the steady states and bifurcations of the system, as well as discontinuous Galerkin finite element methods (FEniCS) for time-dependent simulations. Optogenetic effects are simulated by introducing an optogenetic contribution to the contractility, allowing for both activation and inhibition of myosin II contractility. The effects of local contractility changes and global myosin recruitment are investigated separately. Actin polymerization is incorporated through boundary conditions.

The model predicts bistability between sessile and motile states when cell adhesion and contractility are sufficiently large and balanced. Optogenetic activation of contractility at the front or inhibition at the back can reverse cell migration direction, consistent with experimental observations. The model predicts the required activation strengths and initiation times for motility. Local, reversible contractility increases provide full controllability of migration, while global myosin recruitment is less versatile but effectively initiates motility. Actin polymerization alone significantly impacts motility reversal only at very high strengths, highlighting the central role of contractility. The model accurately reproduces experimental observations of motility perturbation, arrest, and reorientation as functions of contractility. The model explains the experimentally observed variability in response to optogenetic inhibition by showing a strong dependence on inhibition strength and duration. Global myosin recruitment robustly initiates motility but offers limited control over direction. Finally, while actin polymerization can contribute to reorientation, the model suggests that the optogenetic effect on myosin contractility is the dominant factor in experimentally observed reorientation.

The findings address the research question of how optogenetics can be used to control cell migration in contractile cells. The model's successful prediction of experimental results validates its ability to capture the essential physics of the system. The results highlight the importance of nonlinear myosin diffusion arising from minifilament formation and excluded volume effects in determining motility behavior and its response to optogenetic perturbations. The model's ability to predict both the qualitative and quantitative aspects of optogenetic control of cell migration provides a valuable tool for understanding and manipulating cell behavior. The identification of local contractility increase as the primary mechanism for direction control and global myosin recruitment as a means for robust motility initiation offers significant insights into cellular regulatory mechanisms. The model's predictions can be tested experimentally by varying activation strengths, durations, and spatial patterns of optogenetic stimulation.

This study demonstrates that an active gel model incorporating nonlinear myosin diffusion, stemming from minifilament formation and excluded volume effects, successfully explains bistability and optogenetic switching in cell migration. The model accurately predicts experimental observations, highlighting the central role of contractility in cell motility control. Future work could focus on integrating detailed biochemical signaling networks and the role of cell adhesion into the model for a more comprehensive understanding of cell migration regulation.

The model is one-dimensional, simplifying the complex three-dimensional reality of cell migration. The model simplifies the biochemical signaling pathways, focusing primarily on myosin contractility. Adhesion effects are not fully incorporated, although the model is designed to focus on cells in microchannels where adhesion effects are less prominent. Parameter estimations rely on approximations and may benefit from more precise experimental measurements.