Cell Size, Mechanical Tension, and GTPase Signaling in the Single Cell

Geometry-induced patterns through mechanochemical coupling

Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic cell-shape changes. These changes in cell shape may in turn affect the dynamics of pattern-forming proteins, hence leading to an intricate feedback loop between cell shape and chemical dynamics. While several computational studies have examined the rich resulting dynamics, the underlying mechanisms are not yet fully understood. To elucidate some of these mechanisms, we explore a conceptual model for cell polarity on a dynamic one-dimensional manifold. Using concepts from differential geometry, we derive the equations governing mass-conserving reaction-diffusion systems on time-evolving manifolds. Analyzing these equations mathematically, we show that dynamic shape changes of the membrane can induce pattern-forming instabilities in parts of the membrane, which we refer to as regional instabilities. Deformations of the local membrane geometry can also (regionally) suppress pattern formation and spatially shift already existing patterns. We explain our findings by applying and generalizing the local equilibria theory of mass-conserving reaction-diffusion systems. This allows us to determine a simple onset criterion for geometry-induced pattern-forming instabilities, which is linked to the phase-space structure of the reaction-diffusion system. The feedback loop between membrane shape deformations and reaction-diffusion dynamics then leads to a surprisingly rich phenomenology of patterns, including oscillations, traveling waves, and standing waves, even if these patterns do not occur in systems with a fixed membrane shape. Our paper reveals that the local conformation of the membrane geometry acts as an important dynamical control parameter for pattern formation in mass-conserving reaction-diffusion systems.

Cell Repolarization: A Bifurcation Study of Spatio-Temporal Perturbations of Polar Cells

The intrinsic polarity of migrating cells is regulated by spatial distributions of protein activity. Those proteins (Rho-family GTPases, such as Rac and Rho) redistribute in response to stimuli, determining the cell front and back. Reaction-diffusion equations with mass conservation and positive feedback have been used to explain initial polarization of a cell. However, the sensitivity of a polar cell to a reversal stimulus has not yet been fully understood. We carry out a PDE bifurcation analysis of two polarity models to investigate routes to repolarization: (1) a single-GTPase ("wave-pinning") model and (2) a mutually antagonistic Rac-Rho model. We find distinct routes to reversal in (1) vs. (2). We show numerical simulations of full PDE solutions for the RD equations, demonstrating agreement with predictions of the bifurcation results. Finally, we show that simulations of the polarity models in deforming 1D model cells are consistent with biological experiments.

Pulsatile contractions and pattern formation in excitable actomyosin cortex

The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense, generate, and transmit mechanical forces. The cortex exhibits a wide range of dynamic behaviours, from generating pulsatory contractions and travelling waves to forming organised structures. Despite the progress in characterising the biochemical and mechanical components of the actin cortex, the emergent dynamics of this mechanochemical system is poorly understood. Here we develop a reaction-diffusion model for the RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an active actomyosin gel, to investigate how the interplay between chemical signalling and mechanical forces regulates stresses and patterns in the cortex. We demonstrate that mechanochemical feedback in the cortex acts to destabilise homogeneous states and robustly generate pulsatile contractions. By tuning active stress in the system, we show that the cortex can generate propagating contraction pulses, form network structures, or exhibit topological turbulence.

The cellular actin cortex is a dynamic sub-membranous network of filamentous actin, myosin motors, and other accessory proteins that regulates the ability of cells to maintain or change shapes. While the key molecular components and mechanical properties of the actin cortex have been characterized, the ways in which biochemical signalling and mechanical forces interact to regulate cortex behaviours remain poorly understood. In this article, we develop a mathematical model for the actomyosin cortex that combines the reaction-diffusion dynamics of signalling proteins with active force generation by actomyosin networks. Using this model, we investigate how the feedback between mechanics and biochemical signalling regulates the propagation of actomyosin flows, mechanical stresses, and pattern formation in the cortex. Our work reveals a variety of ways in which the cortex can tune the dynamic coupling between biochemical activity, force production, and advective transport to control mechanical behaviours.

Proteomic and phosphorylated proteomic landscape of injured lung in juvenile septic rats with therapeutic application of umbilical cord mesenchymal stem cells

Acute lung injury (ALI) is the most common complication of sepsis. Intravenous injection of HUMSCs can regulate the level of circulating endothelial cytokines and alleviate lung injury in juvenile septic rats. In this study, we performed proteomic and phosphorylated proteomic analysis of lung tissue of juvenile septic rats after Human Umbilical Cord Mesenchymal Stem Cells (HUMSCs) intervention for the first time, and screened the potential proteins and pathways of HUMSCs for therapeutic effect. The 4D proteome quantitative technique was used to quantitatively analyze the lung tissues of septic rats 24 hours (3 biological samples) and 24 hours after HUMSCs intervention (3 biological samples). A total of 213 proteins were identified as differentially expressed proteins, and 971 phosphorylation sites changed significantly. Based on the public database, we analyzed the functional enrichment of these proteins and phosphorylated proteins. In addition, Tenascin-C may be the key differential protein and ECM receptor interaction pathway may be the main signal pathway by using various algorithms to analyze the protein-protein interaction network. Phosphorylation analysis showed that tight junction pathway was closely related to immune inflammatory reaction, and EGFR interacted most, which may be the key differential phosphorylated protein. Finally, 123 conserved motifs of serine phosphorylation site (pS) and 17 conserved motifs of threonine (pT) phosphorylation sites were identified by motif analysis of phosphorylation sites. Results from proteomics and phosphorylated proteomics, the potential new therapeutic targets of HUMSCs in alleviating lung injury in juvenile septic rats were revealed.

Modern perspectives on near-equilibrium analysis of Turing systems

In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction-diffusion theory. Some of these developments were nascent in Turing's paper, and others have been due to new insights from modern mathematical techniques, advances in numerical simulations and extensive biological experiments. Despite such progress, there are still important gaps between theory and experiment, with many examples of biological patterning where the underlying mechanisms are still unclear. Here, we review modern developments in the mathematical theory pioneered by Turing, showing how his approach has been generalized to a range of settings beyond the classical two-species reaction-diffusion framework, including evolving and complex manifolds, systems heterogeneous in space and time, and more general reaction-transport equations. While substantial progress has been made in understanding these more complicated models, there are many remaining challenges that we highlight throughout. We focus on the mathematical theory, and in particular linear stability analysis of 'trivial' base states. We emphasize important open questions in developing this theory further, and discuss obstacles in using these techniques to understand biological reality. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Cellular Tango: how extracellular matrix adhesion choreographs Rac-Rho signaling and cell movement

The small GTPases Rac and Rho are known to regulate eukaryotic cell shape, promoting front protrusion (Rac) or rear retraction (Rho) of the cell edge. Such cell deformation changes the contact and adhesion of cell to the extracellular matrix (ECM), while ECM signaling through integrin receptors also affects GTPase activity. We develop and investigate a model for this three-way feedback loop in 1D and 2D spatial domains, as well as in a fully deforming 2D cell shapes with detailed adhesion-bond biophysics. The model consists of reaction-diffusion equations solved numerically with open-source software, Morpheus, and with custom-built cellular Potts model simulations. We find a variety of patterns and cell behaviors, including persistent polarity, flipped front-back cell polarity oscillations, spiral waves, and random protrusion-retraction. We show that the observed spatial patterns depend on the cell shape, and vice versa.

Spots, stripes, and spiral waves in models for static and motile cells : GTPase patterns in cells

The polarization and motility of eukaryotic cells depends on assembly and contraction of the actin cytoskeleton and its regulation by proteins called GTPases. The activity of GTPases causes assembly of filamentous actin (by GTPases Cdc42, Rac), resulting in protrusion of the cell edge. Mathematical models for GTPase dynamics address the spontaneous formation of patterns and nonuniform spatial distributions of such proteins in the cell. Here we revisit the wave-pinning model for GTPase-induced cell polarization, together with a number of extensions proposed in the literature. These include introduction of sources and sinks of active and inactive GTPase (by the group of A. Champneys), and negative feedback from F-actin to GTPase activity. We discuss these extensions singly and in combination, in 1D, and 2D static domains. We then show how the patterns that form (spots, waves, and spirals) interact with cell boundaries to create a variety of interesting and dynamic cell shapes and motion.

Membrane Tension Can Enhance Adaptation to Maintain Polarity of Migrating Cells

Migratory cells are known to adapt to environments that contain wide-ranging levels of chemoattractant. Although biochemical models of adaptation have been previously proposed, here, we discuss a different mechanism based on mechanosensing, in which the interaction between biochemical signaling and cell tension facilitates adaptation. We describe and analyze a model of mechanochemical-based adaptation coupling a mechanics-based physical model of cell tension coupled with the wave-pinning reaction-diffusion model for Rac GTPase activity. The mathematical analysis of this model, simulations of a simplified one-dimensional cell geometry, and two-dimensional finite element simulations of deforming cells reveal that as a cell protrudes under the influence of high stimulation levels, tension-mediated inhibition of Rac signaling causes the cell to polarize even when initially overstimulated. Specifically, tension-mediated inhibition of Rac activation, which has been experimentally observed in recent years, facilitates this adaptation by countering the high levels of environmental stimulation. These results demonstrate how tension-related mechanosensing may provide an alternative (and potentially complementary) mechanism for cell adaptation.