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Cell migration is a pervasive process in many biology systems and involves protrusive forces generated by actin polymerization, myosin dependent contractile forces, and force transmission between the cell and the substrate through adhesion sites. Here we develop a computational model for cell motion that uses the phase-field method to solve for the moving boundary with physical membrane properties. It includes a reaction-diffusion model for the actin-myosin machinery and discrete adhesion sites which can be in a \"gripping\" or \"slipping\" mode and integrates the adhesion dynamics with the dynamics of the actin filaments, modeled as a viscous network. To test this model, we apply it to fish keratocytes, fast moving cells that maintain their morphology, and show that we are able to reproduce recent experimental results on actin flow and stress patterns. Furthermore, we explore the phase diagram of cell motility by varying myosin II activity and adhesion strength. Our model suggests that the pattern of the actin flow inside the cell, the cell velocity, and the cell morphology are determined by the integration of actin polymerization, myosin contraction, adhesion forces, and membrane forces.

Cells organized in tissues exert forces on their neighbors and their environment. Those cellular forces determine tissue homeostasis as well as reorganization during embryonic development and wound healing. To understand how cellular forces are generated and how they can influence the tissue state, we develop a particle-based simulation model for adhesive cell clusters and monolayers. Cells are contractile, exert forces on their substrate and on each other, and interact through contact inhibition of locomotion (CIL), meaning that cell–cell contacts suppress force transduction to the substrate and propulsion forces align away from neighbors. Our model captures the traction force patterns of small clusters of nonmotile cells and larger sheets of motile Madin–Darby canine kidney (MDCK) cells. In agreement with observations in a spreading MDCK colony, the cell density in the center increases as cells divide and the tissue grows. A feedback between cell density, CIL, and cell–cell adhesion gives rise to a linear relationship between cell density and intercellular tensile stress and forces the tissue into a nonmotile state characterized by a broad distribution of traction forces. Our model also captures the experimentally observed tissue flow around circular obstacles, and CIL accounts for traction forces at the edge.

Recent experiments have shown that spreading epithelial sheets exhibit a long-range coordination of motility forces that leads to a buildup of tension in the tissue, which may enhance cell division and the speed of wound healing. Furthermore, the edges of these epithelial sheets commonly show finger-like protrusions whereas the bulk often displays spontaneous swirls of motile cells. To explain these experimental observations, we propose a simple flocking-type mechanism, in which cells tend to align their motility forces with their velocity. Implementing this idea in a mechanical tissue simulation, the proposed model gives rise to efficient spreading and can explain the experimentally observed long-range alignment of motility forces in highly disordered patterns, as well as the buildup of tensile stress throughout the tissue. Our model also qualitatively reproduces the dependence of swirl size and swirl velocity on cell density reported in experiments and exhibits an undulation instability at the edge of the spreading tissue commonly observed in vivo. Finally, we study the dependence of colony spreading speed on important physical and biological parameters and derive simple scaling relations that show that coordination of motility forces leads to an improvement of the wound healing process for realistic tissue parameters.

Diverse interactions among species within bacterial colonies lead to intricate spatiotemporal dynamics, which can affect their growth and survival. Here, we describe the emergence of complex structures in a colony grown from mixtures of motile and non-motile bacterial species on a soft agar surface. Time-lapse imaging shows that non-motile bacteria 'hitchhike' on the motile bacteria as the latter migrate outward. The non-motile bacteria accumulate at the boundary of the colony and trigger an instability that leaves behind striking flower-like patterns. The mechanism of the front instability governing this pattern formation is elucidated by a mathematical model for the frictional motion of the colony interface, with friction depending on the local concentration of the non-motile species. A more elaborate two-dimensional phase-field model that explicitly accounts for the interplay between growth, mechanical stress from the motile species, and friction provided by the non-motile species, fully reproduces the observed flower-like patterns. Communities of bacteria and other microbes live in every ecosystem on Earth, including in soil, in hydrothermal vents, on the surface of plants and in the human gut. They often attach to solid surfaces and form dense colonies called biofilms. Most biofilms found in nature are comprised of many different species of bacteria. How the bacteria interact shapes the internal structures of these communities. Many previous studies have focused on the molecules that bacteria use to relate to each other, for example, some bacteria exchange nutrients or release toxins that are harmful to their neighbors. However, it is less clear how direct physical contacts between bacteria affect the whole community. Escherichia coli is a rod-shaped bacterium that is a good swimmer, but has a hard time moving on solid surfaces. Therefore, when a droplet of liquid containing these bacteria is placed in a Petri dish containing a jelly-like substance called agar, the droplet barely expands over a 24-hour period. On the other hand, a droplet containing another rod-shaped bacterium known as Acinetobacter baylyi expands rapidly on agar because these bacteria are able to crawl using microscopic “legs” called pili. Here, Xiong et al. set out to investigate how a colony containing both E. coli and A. baylyi developed on a solid surface. The experiments showed that when a droplet of liquid containing both species was placed on agar, both species grew and spread rapidly, as if the E. coli hitchhiked on the highly motile A. baylyi cells. Furthermore, the growing colony developed a complex flower-like shape. Xiong et al. developed mathematical models that took into account how quickly each species generally grows, their ability to move, the friction between cells and the agar, and other physical properties. The models predicted that the E. coli cells that accumulate at the expanding boundary of the colony make the boundary unstable, leading to the flower-like patterns. Further analysis suggested that similar patterns may form in other situations when motile and non-motile species of bacteria are together. These findings may help us understand the origins of the complex structures observed in many naturally occurring communities of bacteria.

Eukaryotic cells can migrate using different modes, ranging from amoeboid-like, during which actin filled protrusions come and go, to keratocyte-like, characterized by a stable morphology and persistent motion. How cells can switch between these modes is not well understood but waves of signaling events are thought to play an important role in these transitions. Here we present a simple two-component biochemical reaction-diffusion model based on relaxation oscillators and couple this to a model for the mechanics of cell deformations. Different migration modes, including amoeboid-like and keratocyte-like, naturally emerge through transitions determined by interactions between biochemical traveling waves, cell mechanics and morphology. The model predictions are explicitly verified by systematically reducing the protrusive force of the actin network in experiments using Dictyostelium discoideum cells. Our results indicate the importance of coupling signaling events to cell mechanics and morphology and may be applicable in a wide variety of cell motility systems.

Motile cells can use and switch between different modes of migration. Here, we use traction force microscopy and fluorescent labeling of actin and myosin to quantify and correlate traction force patterns and cytoskeletal distributions in Dictyostelium discoideum cells that move and switch between keratocyte‐like fan‐shaped, oscillatory, and amoeboid modes. We find that the wave dynamics of the cytoskeletal components critically determine the traction force pattern, cell morphology, and migration mode. Furthermore, we find that fan‐shaped cells can exhibit two different propulsion mechanisms, each with a distinct traction force pattern. Finally, the traction force patterns can be recapitulated using a computational model, which uses the experimentally determined spatiotemporal distributions of actin and myosin forces and a viscous cytoskeletal network. Our results suggest that cell motion can be generated by friction between the flow of this network and the substrate. SYNOPSIS A combination of imaging and computational modeling is used to investigate the traction force patterns and the distribution of actin and myosin in three different modes of migration in Dictyostelium discoideum cells. The wave dynamics of actin and myosin critically determine the traction force patterns, cell morphology, and migration modes. Two types of keratocyte‐like motion are observed, consistent with two different propulsion mechanisms. A computational model reveals that cell motion can be generated by friction between the flow of the cytoskeletal network and the substrate. Graphical Abstract A combination of imaging and computational modeling is used to investigate the traction force patterns and the distribution of actin and myosin in three different modes of migration in Dictyostelium discoideum cells.

Significance During the growth of an embryo or the spreading of a tumor, cells may travel collectively. We study a computational model of a simple example of collective migration: two cells confined to a square adhesive pattern. In this confinement, some cell types rotate, whereas others do not. We model these crawling cells, the forces between them, and several possible ways that the cells could choose what direction they will crawl—their “polarity mechanism.” We show that the cell polarity mechanism can control whether the pairs of cells rotate or remain fixed. This suggests that we can learn about how large groups of cells choose their direction by studying the rotation of pairs. Pairs of endothelial cells on adhesive micropatterns rotate persistently, but pairs of fibroblasts do not; coherent rotation is present in normal mammary acini and kidney cells but absent in cancerous cells. Why? To answer this question, we develop a computational model of pairs of mammalian cells on adhesive micropatterns using a phase field method and study the conditions under which persistent rotational motion (PRM) emerges. Our model couples the shape of the cell, the cell’s internal chemical polarity, and interactions between cells such as volume exclusion and adhesion. We show that PRM can emerge from this minimal model and that the cell-cell interface may be influenced by the nucleus. We study the effect of various cell polarity mechanisms on rotational motion, including contact inhibition of locomotion, neighbor alignment, and velocity alignment, where cells align their polarity to their velocity. These polarity mechanisms strongly regulate PRM: Small differences in polarity mechanisms can create significant differences in collective rotation. We argue that the existence or absence of rotation under confinement may lead to insight into the cell’s methods for coordinating collective cell motility.

Dark respiration causes an increase in leaf CO2 concentration (Ci), and the continuing increases in atmospheric [CO2] further increases Ci. Elevated leaf CO2 concentration causes stomatal pores to close. Here, we demonstrate that high intracellular CO2/HCO3 − enhances currents mediated by the Arabidopsis thaliana guard cell S-type anion channel SLAC1 upon coexpression of any one of the Arabidopsis protein kinases OST1, CPK6, or CPK23 in Xenopus laevis oocytes. Split-ubiquitin screening identified the PIP2;1 aquaporin as an interactor of the βCA4 carbonic anhydrase, which was confirmed in split luciferase, bimolecular fluorescence complementation, and coimmunoprecipitation experiments. PIP2;1 exhibited CO2 permeability. Mutation of PIP2;1 in planta alone was insufficient to impair CO2- and abscisic acid-induced stomatal closing, likely due to redundancy. Interestingly, coexpression of βCA4 and PIP2;1 with OST1-SLAC1 or CPK6/23-SLAC1 in oocytes enabled extracellular CO2 enhancement of SLAC1 anion channel activity. An inactive PIP2;1 point mutation was identified that abrogated water and CO2 permeability and extracellular CO2 regulation of SLAC1 activity. These findings identify the CO2-permeable PIP2;1 as key interactor of βCA4 and demonstrate functional reconstitution of extracellular CO2 signaling to ion channel regulation upon coexpression of PIP2;1, βCA4, SLAC1, and protein kinases. These data further implicate SLAC1 as a bicarbonate-responsive protein contributing to CO2 regulation of S-type anion channels.

Increases in CO₂ concentration in plant leaves due to respiration in the dark and the continuing atmospheric [CO₂] rise cause closing of stomatal pores, thus affecting plant–water relations globally. However, the underlying CO₂/bicarbonate (CO₂/HCO₃⁻) sensing mechanisms remain unknown. [CO₂] elevation in leaves triggers stomatal closure by anion efflux mediated via the SLAC1 anion channel localized in the plasma membrane of guard cells. Previous reconstitution analysis has suggested that intracellular bicarbonate ions might directly up-regulate SLAC1 channel activity. However, whether such a CO₂/HCO₃⁻ regulation of SLAC1 is relevant for CO₂ control of stomatal movements in planta remains unknown. Here, we computationally probe for candidate bicarbonate-interacting sites within the SLAC1 anion channel via long-timescale Gaussian accelerated molecular dynamics (GaMD) simulations. Mutations of two putative bicarbonate-interacting residues, R256 and R321, impaired the enhancement of the SLAC1 anion channel activity by CO₂/HCO₃⁻ in Xenopus oocytes. Mutations of the neighboring charged amino acid K255 and residue R432 and the predicted gate residue F450 did not affect HCO₃⁻ regulation of SLAC1. Notably, gas-exchange experiments with slac1-transformed plants expressing mutated SLAC1 proteins revealed that the SLAC1 residue R256 is required for CO₂ regulation of stomatal movements in planta, but not for abscisic acid (ABA)-induced stomatal closing. Patch clamp analyses of guard cells show that activation of S-type anion channels by CO₂/HCO₃⁻, but not by ABA, was impaired, indicating the relevance of R256 for CO₂ signal transduction. Together, these analyses suggest that the SLAC1 anion channel is one of the physiologically relevant CO₂/HCO₃⁻ sensors in guard cells.

Natural chemical gradients to which cells respond chemotactically are often dynamic, with both spatial and temporal components. A primary example is the social amoeba Dictyostelium, which migrates to the source of traveling waves of chemoattractant as part of a self-organized aggregation process. Despite its physiological importance, little is known about how cells migrate directionally in response to traveling waves. The classic back-of-the-wave problem is how cells chemotax toward the wave source, even though the spatial gradient reverses direction in the back of the wave. Here, we address this problem by using microfluidics to expose cells to traveling waves of chemoattractant with varying periods. We find that cells exhibit memory and maintain directed motion toward the wave source in the back of the wave for the natural period of 6 min, but increasingly reverse direction for longer wave periods. Further insights into cellular memory are provided by experiments quantifying cell motion and localization of a directional-sensing marker after rapid gradient switches. The results can be explained by a model that couples adaptive directional sensing to bistable cellular memory. Our study shows how spatiotemporal cues can guide cell migration over large distances.