Three-Dimensional Cell Geometry Controls Excitable Membrane Signaling in Dictyostelium Cells

Self-organization of PIP3 waves is controlled by the topology and curvature of cell membranes

Phosphatidylinositol (3,4,5)-trisphosphate (PIP3) is a signaling lipid on the plasma membrane that plays a fundamental role in cell signaling with a strong impact on cell physiology and diseases. It is responsible for the protruding edge formation, cell polarization, macropinocytosis, and other membrane remodeling dynamics in cells. It has been shown that the membrane confinement and curvature affects the wave formation of PIP3 and F-actin. But, even in the absence of F-actin, a complex self-organization of the spatiotemporal PIP3 waves is observed. In recent findings, we have shown that these waves can be guided and pinned on strongly bended Dictyostelium membranes caused by molecular crowding and curvature-limited diffusion. Based on these experimental findings, we investigate the spatiotemporal PIP3 wave dynamics on realistic three-dimensional cell-like membranes to explore the effect of curvature-limited diffusion, as observed experimentally. We use an established stochastic reaction-diffusion model with enzymatic Michaelis-Menten-type reactions that mimics the dynamics of Dictyostelium cells. As these cells mimic the three-dimensional shape and size observed experimentally, we found that the PIP3 wave directionality can be explained by a Hopf-like and a reverse periodic-doubling bifurcation for uniform diffusion and curvature-limited diffusion properties. Finally, we compare the results with recent experimental findings and discuss the discrepancy between the biological and numerical results.

Cargo Size Limits and Forces of Cell-Driven Microtransport

The integration of motile cells into biohybrid microrobots offers unique properties such as sensitive responses to external stimuli, resilience, and intrinsic energy supply. Here, biohybrid cell-cargo systems that are driven by amoeboid Dictyostelium discoideum cells are studied and how the cargo speed and the resulting viscous drag force scales with increasing radius of the spherical cargo particle are explored. Using a simplified geometrical model of the cell-cargo interaction, the findings toward larger cargo sizes, which are not accessible with the experimental setup, are extrapolated and a maximal cargo size is predicted beyond which active cell-driven movements will stall. The active forces exerted by the cells to move a cargo show mechanoresponsive adaptation and increase dramatically when challenged by an external pulling force, a mechanism that may become relevant when navigating cargo through complex heterogeneous environments.

From actin waves to mechanism and back: How theory aids biological understanding

Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.

Cell-Size Space Regulates the Behavior of Confined Polymers: From Nano- and Micromaterials Science to Biology

Polymer micromaterials in a liquid or gel phase covered with a surfactant membrane are widely used materials in pharmaceuticals, cosmetics, and foods. In particular, cell-sized micromaterials of biopolymer solutions covered with a lipid membrane have been studied as artificial cells to understand cells from a physicochemical perspective. The characteristics and phase transitions of polymers confined to a microscopic space often differ from those in bulk systems. The effect that causes this difference is referred to as the cell-size space effect (CSE), but the specific physicochemical factors remain unclear. This study introduces the analysis of CSE on molecular diffusion, nanostructure transition, and phase separation and presents their main factors, i.e., short- and long-range interactions with the membrane surface and small volume (finite element nature). This serves as a guide for determining the dominant factors of CSE. Furthermore, we also introduce other factors of CSE such as spatial closure and the relationships among space size, the characteristic length of periodicity, the structure size, and many others produced by biomolecular assemblies through the analysis of protein reaction-diffusion systems and biochemical reactions.

Versatile Patterns in the Actin Cortex of Motile Cells: Self-Organized Pulses Can Coexist with Macropinocytic Ring-Shaped Waves

Self-organized patterns in the actin cytoskeleton are essential for eukaryotic cellular life. They are the building blocks of many functional structures that often operate simultaneously to facilitate, for example, nutrient uptake and movement of cells. However, identifying how qualitatively distinct actin patterns can coexist remains a challenge. Using bifurcation theory of a mass conserved activator-inhibitor system, we uncover a generic mechanism of how different actin waves-traveling waves and excitable pulses-organize and simultaneously emerge. Live-cell imaging experiments indeed reveal that narrow, planar, and fast-moving excitable pulses may coexist with ring-shaped macropinocytic actin waves in the cortex of motile amoeboid cells.

Computational framework for single-cell spatiotemporal dynamics of optogenetic membrane recruitment

We describe a modular computational framework for analyzing cell-wide spatiotemporal signaling dynamics in single-cell microscopy experiments that accounts for the experiment-specific geometric and diffractive complexities that arise from heterogeneous cell morphologies and optical instrumentation. Inputs are unique cell geometries and protein concentrations derived from confocal stacks and spatiotemporally varying environmental stimuli. After simulating the system with a model of choice, the output is convolved with the microscope point-spread function for direct comparison with the observable image. We experimentally validate this approach in single cells with BcLOV4, an optogenetic membrane recruitment system for versatile control over cell signaling, using a three-dimensional non-linear finite element model with all parameters experimentally derived. The simulations recapitulate observed subcellular and cell-to-cell variability in BcLOV4 signaling, allowing for inter-experimental differences of cellular and instrumentation origins to be elucidated and resolved for improved interpretive robustness. This single-cell approach will enhance optogenetics and spatiotemporally resolved signaling studies.

Local Membrane Curvature Pins and Guides Excitable Membrane Waves in Chemotactic and Macropinocytic Cells - Biomedical Insights From an Innovative Simple Model

PIP3 dynamics observed in membranes are responsible for the protruding edge formation in cancer and amoeboid cells. The mechanisms that maintain those PIP3 domains in three-dimensional space remain elusive, due to limitations in observation and analysis techniques. Recently, a strong relation between the cell geometry, the spatial confinement of the membrane, and the excitable signal transduction system has been revealed by Hörning and Shibata (2019) using a novel 3D spatiotemporal analysis methodology that enables the study of membrane signaling on the entire membrane (Hörning and Shibata, 2019). Here, using 3D spatial fluctuation and phase map analysis on actin polymerization inhibited Dictyostelium cells, we reveal a spatial asymmetry of PIP3 signaling on the membrane that is mediated by the contact perimeter of the plasma membrane — the spatial boundary around the cell-substrate adhered area on the plasma membrane. We show that the contact perimeter guides PIP3 waves and acts as a pinning site of PIP3 phase singularities, that is, the center point of spiral waves. The contact perimeter serves as a diffusion influencing boundary that is regulated by a cell size- and shape-dependent curvature. Our findings suggest an underlying mechanism that explains how local curvature can favor actin polymerization when PIP3 domains get pinned at the curved protrusive membrane edges in amoeboid cells.

Mechanobiology in cortical waves and oscillations

Cortical actin waves have emerged as a widely prevalent phenomena and brought pattern formation to many fields of cell biology. Cortical excitabilities, reminiscent of the electric excitability in neurons, are likely fundamental property of the cell cortex. Although they have been mostly considered to be biochemical in nature, accumulating evidence support the role of mechanics in the pattern formation process. Both pattern formation and mechanobiology approach biological phenomena at the collective level, either by looking at the mesoscale dynamical behavior of molecular networks or by using collective physical properties to characterize biological systems. As such they are very different from the traditional reductionist, bottom-up view of biology, which brings new challenges and potential opportunities. In this essay, we aim to provide our perspectives on what the proposed mechanochemical feedbacks are and open questions regarding their role in cortical excitable and oscillatory dynamics.

How cortical waves drive fission of motile cells

Cytokinesis-the division of a cell into two daughter cells-is a key step in cell growth and proliferation. It typically occurs in synchrony with the cell cycle to ensure that a complete copy of the genetic information is passed on to the next generation of daughter cells. In animal cells, cytokinesis commonly relies on an actomyosin contractile ring that drives equatorial furrowing and separation into the two daughter cells. However, also contractile ring-independent forms of cell division are known that depend on substrate-mediated traction forces. Here, we report evidence of an as yet unknown type of contractile ring-independent cytokinesis that we termed wave-mediated cytofission. It is driven by self-organized cortical actin waves that travel across the ventral membrane of oversized, multinucleated Dictyostelium discoideum cells. Upon collision with the cell border, waves may initiate the formation of protrusions that elongate and eventually pinch off to form separate daughter cells. They are composed of a stable elongated wave segment that is enclosed by a cell membrane and moves in a highly persistent fashion. We rationalize our observations based on a noisy excitable reaction-diffusion model in combination with a dynamic phase field to account for the cell shape and demonstrate that daughter cells emerging from wave-mediated cytofission exhibit a well-controlled size.

A minimal computational model for three-dimensional cell migration

During migration, eukaryotic cells can continuously change their three-dimensional morphology, resulting in a highly dynamic and complex process. Further complicating this process is the observation that the same cell type can rapidly switch between different modes of migration. Modelling this complexity necessitates models that are able to track deforming membranes and that can capture the intracellular dynamics responsible for changes in migration modes. Here we develop an efficient three-dimensional computational model for cell migration, which couples cell mechanics to a simple intracellular activator-inhibitor signalling system. We compare the computational results to quantitative experiments using the social amoeba Dictyostelium discoideum. The model can reproduce the observed migration modes generated by varying either mechanical or biochemical model parameters and suggests a coupling between the substrate and the biomechanics of the cell.

Curved surface geometry-induced topological change of an excitable planar wavefront

On the curved surfaces of living and nonliving materials, planar excitable wavefronts frequently exhibit a directional change and subsequently undergo a discontinuous (topological) change; i.e., a series of wavefront dynamics from collision, annihilation to splitting. Theoretical studies have shown that excitable planar stable waves change their topology significantly depending on the initial conditions on flat surfaces, whereas the directional change of the waves occurs based on the geometry of curved surfaces. However, it is not clear if the geometry of curved surfaces induces this topological change. In this study, we first demonstrated that the curved surface geometry induces bending, collision, and splitting of a planar stable wavefront by numerically solving an excitable reaction-diffusion equation on a bell-shaped surface. We determined two necessary conditions for inducing the topological change: the characteristic length of the curved surface (i.e., the height of the bell-shaped structure) should be greater than the width of the wave, and the ratio of the height to the width of the bell shape should be greater than a threshold. As for the geometrical mechanism of the latter, we found that a bifurcation of the geodesics on the curved surface provides the alternative minimal paths of the wavefront, which circumvent the surface region with a high local curvature, thereby resulting in the topological change. These conditions imply that the topological change of the wavefront can be predicted on the basis of the curved surfaces, whose structures are larger than the wave width.