Diversity in emergent cell locomotion from the coupling cytosolic and cortical Marangoni flows with reaction-diffusion dynamics

TL;DR

A cross-scale mean-field framework that integrates RD signalling with cytosolic and cortical hydrodynamics to capture emergent cellular locomotion is developed, revealing that coupling to both cytosolic flow and spatially varying surface tension is essential to recover the full spectrum of motility modes.

Abstract

Cell migration is a fundamental process underlying the survival and function of both unicellular and multicellular organisms. Crawling motility in eukaryotic cells arises from cyclic protrusion and retraction driven by the cytoskeleton, whose organization is regulated by reaction-diffusion (RD) dynamics of Rho GTPases between the cytosol and the cortex. These dynamics generate spatial membrane patterning and establish front-rear polarity through the coupling of biochemical signalling and mechanical feedback. We develop a cross-scale mean-field framework that integrates RD signalling with cytosolic and cortical hydrodynamics to capture emergent cellular locomotion. Our model reproduces diverse experimentally observed shape and motility phenotypes with small parameter changes, indicating that these behaviours correspond to self-organized limit cycles. Phase-space analysis reveals that coupling to both cytosolic flow and spatially varying surface tension is essential to recover the full spectrum of motility modes, providing a theoretical foundation for understanding amoeboid migration.

Figures (6)

• Figure 1: Diagram of the components of the model. To fully capture complex biological process of cell motility one needs to couple membrane patterning by reaction--diffusion--advection network to forces which induce cytosolic and membrane flows as well as facilitate shape change and motility in general. The coupling loop is closed by allowing the generated flows and geometry of the cell to influence reaction--diffusion--advection system.
• Figure 2: Schematic representation of the reactions of the model. Arrows indicate the direction of the reaction with governing constants for that reaction annotated beside them. Cytosolic substrate binds to the membrane becoming the activator. Membrane bound activator can form a complex with the cytosolic inhibitor. The cycle ends when the complex dissociates, releasing substrate and inhibitor back into the cytosol.
• Figure 3: Flow induced by protrusive coupling. Cytosolic and cortex flows, in the centre-of-mass reference frame of the cell, during movement under the influence of only protrusive coupling for $k_\mathrm{C}=0.04$ and $k_\sigma=0$. The black arrow marks the polarity direction (and, consequently, the direction of motion as well as the position of the patch of activator). Red lines represent streamlines inside the cytosol. The colour scale for both plots is shown in the middle. Left panel shows cytosolic flow and right panel presents cortex flow induced by protrusive coupling.
• Figure 4: Constrictive and dispersive flow. The flow induced in the cell without protrusion force ($k_\mathrm{C}=0$) A: for a positive surface tension coupling $k_\sigma=0.03$, and B: for a negative coupling $k_\sigma=-0.03$. On both panels the patch of activator is located on the right side of cell and the snapshot has been taken in the initial phase of the simulation, where the effect of Marangoni flow is the best visible. In both panels the flow field is presented with arrows and streamlines are denoted with red lines. The magnitude of velocity is also shown with the colour code as presented on the scale bar in the middle of panels. Top and bottom graphs show the cytosolic and the cortex flows, respectively. C: The effect of Marangoni flow on the profile of activator concentration along the cortex. Purple arrows refer to positive surface tension coupling while orange ones represent negative surface tension coupling. D: Mean period of the rotation or oscillation RD dynamics as a function of surface tension coupling. Colour marks the type of initial concentration profile for each simulation. Markers represent the observed limit cycle RD pattern obtained after 1300s of simulation time. Mean period was averaged over 9001300 of simulation time. Higher values of surface tension coupling speed up the RD dynamics and favour oscillation pattern. After the threshold of $0.03$ is passed limit cycle solution of simulations initiated with rotation pattern becomes oscillation.
• Figure 5: Characteristic motility phenotypes.A: stationary cells, B: persistent runner cells, C: alternating runner cells, D: circular runner cells, and E: run-and-turn cells. In each panel snapshots of cells are presented with the colour code denoting the concentration of activator in the cortex (as shown by scale bars), and a trajectory of the centre of mass of the cell is plotted with red colour. In panel C we present the dependence of elongation and polarity on simulation time for the illustrated cell. Vertical black lines denote moments in which the plotted snapshots were taken. In panel D we plot velocity autocorrelation functions of presented cells. In panel E the trajectory is plotted separately on the right side and four circles mark the points in which snapshots plotted on the left side were taken. For the videos showing the time evolution of presented cells, see the \ref{['supporting_information']} Section.