Pulsatile contractions and pattern formation in excitable actomyosin cortex

Actomyosin clusters as active units shaping living matter

Stress generation by the actin cytoskeleton shapes cells and tissues. Despite impressive progress in live imaging and quantitative physical descriptions of cytoskeletal network dynamics, the connection between processes at molecular scales and spatiotemporal patterns at the cellular scale is still unclear. Here, we review studies reporting actomyosin clusters of micrometre size and with lifetimes of several minutes in a large number of organisms, ranging from fission yeast to humans. Such structures have also been found in reconstituted systems in vitro and in theoretical analyses of cytoskeletal dynamics. We propose that tracking these clusters could provide a simple readout for characterising living matter. Spatiotemporal patterns of clusters could serve as determinants of morphogenetic processes that have similar roles in diverse organisms.

Actomyosin cortex: Inherently oscillatory?

A new analysis of cytokinetic furrow ingression in the Caenorhabditis elegans zygote at high spatiotemporal resolution demonstrates that, rather than being a process of steady, spatially uniform constriction, furrow ingression is modulated by complex contractile oscillations that move around the furrow, possibly in the form of propagating waves.

Mechanical and biochemical feedback combine to generate complex contractile oscillations in cytokinesis

The actomyosin cortex is an active material that generates force to drive shape changes via cytoskeletal remodeling. Cytokinesis is the essential cell division event during which a cortical actomyosin ring closes to separate two daughter cells. Our active gel theory predicted that actomyosin systems controlled by a biochemical oscillator and experiencing mechanical strain would exhibit complex spatiotemporal behavior. To test whether active materials in vivo exhibit spatiotemporally complex kinetics, we imaged the C. elegans embryo with unprecedented temporal resolution and discovered that sections of the cytokinetic cortex undergo periodic phases of acceleration and deceleration. Contractile oscillations exhibited a range of periodicities, including those much longer periods than the timescale of RhoA pulses, which was shorter in cytokinesis than in any other biological context. Modifying mechanical feedback in vivo or in silico revealed that the period of contractile oscillation is prolonged as a function of the intensity of mechanical feedback. Fast local ring ingression occurs where speed oscillations have long periods, likely due to increased local stresses and, therefore, mechanical feedback. Fast ingression also occurs where material turnover is high, in vivo and in silico. We propose that downstream of initiation by pulsed RhoA activity, mechanical feedback, including but not limited to material advection, extends the timescale of contractility beyond that of biochemical input and, therefore, makes it robust to fluctuations in activation. Circumferential propagation of contractility likely allows for sustained contractility despite cytoskeletal remodeling necessary to recover from compaction. Thus, like biochemical feedback, mechanical feedback affords active materials responsiveness and robustness.

Change in RhoGAP and RhoGEF availability drives transitions in cortical patterning and excitability in Drosophila

Actin cortex patterning and dynamics are critical for cell shape changes. These dynamics undergo transitions during development, often accompanying changes in collective cell behavior. Although mechanisms have been established for individual cells' dynamic behaviors, the mechanisms and specific molecules that result in developmental transitions in vivo are still poorly understood. Here, we took advantage of two developmental systems in Drosophila melanogaster to identify conditions that altered cortical patterning and dynamics. We identified a Rho guanine nucleotide exchange factor (RhoGEF) and Rho GTPase activating protein (RhoGAP) pair required for actomyosin waves in egg chambers. Specifically, depletion of the RhoGEF, Ect2, or the RhoGAP, RhoGAP15B, disrupted actomyosin wave induction, and both proteins relocalized from the nucleus to the cortex preceding wave formation. Furthermore, we found that overexpression of a different RhoGEF and RhoGAP pair, RhoGEF2 and Cumberland GAP (C-GAP), resulted in actomyosin waves in the early embryo, during which RhoA activation precedes actomyosin assembly by ∼4 s. We found that C-GAP was recruited to actomyosin waves, and disrupting F-actin polymerization altered the spatial organization of both RhoA signaling and the cytoskeleton in waves. In addition, disrupting F-actin dynamics increased wave period and width, consistent with a possible role for F-actin in promoting delayed negative feedback. Overall, we showed a mechanism involved in inducing actomyosin waves that is essential for oocyte development and is general to other cell types, such as epithelial and syncytial cells.

Spiking at the edge: Excitability at interfaces in reaction-diffusion systems

Excitable media, ranging from bioelectric tissues and chemical oscillators to forest fires and competing populations, are nonlinear, spatially extended systems capable of spiking. Most investigations of excitable media consider situations where the amplifying and suppressing forces necessary for spiking coexist at every point in space. In this case, spikes arise due to local bistabilities, which require a fine-tuned ratio between local amplification and suppression strengths. But, in nature and engineered systems, these forces can be segregated in space, forming structures like interfaces and boundaries. Here, we show how boundaries can generate and protect spiking when the reacting components can spread out: Even arbitrarily weak diffusion can cause spiking at the edge between two non-excitable media. This edge spiking arises due to a global bistability, which can occur even if amplification and suppression strengths do not allow spiking when mixed. We analytically derive a spiking phase diagram that depends on two parameters: i) the ratio between the system size and the characteristic diffusive length-scale and ii) the ratio between the amplification and suppression strengths. Our analysis explains recent experimental observations of action potentials at the interface between two non-excitable bioelectric tissues. Beyond electrophysiology, we highlight how edge spiking emerges in predator-prey dynamics and in oscillating chemical reactions. Our findings provide a theoretical blueprint for a class of interfacial excitations in reaction-diffusion systems, with potential implications for spatially controlled chemical reactions, nonlinear waveguides and neuromorphic computation, as well as spiking instabilities, such as cardiac arrhythmias, that naturally occur in heterogeneous biological media.

The dynamics and biophysics of shape formation: Common themes in plant and animal morphogenesis

The emergence of tissue form in multicellular organisms results from the complex interplay between genetics and physics. In both plants and animals, cells must act in concert to pattern their behaviors. Our understanding of the factors sculpting multicellular form has increased dramatically in the past few decades. From this work, common themes have emerged that connect plant and animal morphogenesis-an exciting connection that solidifies our understanding of the developmental basis of multicellular life. In this review, we will discuss the themes and the underlying principles that connect plant and animal morphogenesis, including the coordination of gene expression, signaling, growth, contraction, and mechanical and geometric feedback.

Localized States in Active Fluids

Biological active matter is typically tightly coupled to chemical reaction networks affecting its assembly-disassembly dynamics and stress generation. We show that localized states can emerge spontaneously if assembly of active matter is regulated by chemical species that are advected with flows resulting from gradients in the active stress. The mechanochemical localized patterns form via a subcritical bifurcation and for parameter values for which patterns do not exist in absence of the advective coupling. Our work identifies a generic mechanism underlying localized cellular patterns.

Mechanical positive feedback and biochemical negative feedback combine to generate complex contractile oscillations in cytokinesis

Contractile force generation by the cortical actomyosin cytoskeleton is essential for a multitude of biological processes. The actomyosin cortex behaves as an active material that drives local and large-scale shape changes via cytoskeletal remodeling in response to biochemical cues and feedback loops. Cytokinesis is the essential cell division event during which a cortical actomyosin ring generates contractile force to change cell shape and separate two daughter cells. Our recent work with active gel theory predicts that actomyosin systems under the control of a biochemical oscillator and experiencing mechanical strain will exhibit complex spatiotemporal behavior, but cytokinetic contractility was thought to be kinetically simple. To test whether active materials in vivo exhibit spatiotemporally complex kinetics, we used 4-dimensional imaging with unprecedented temporal resolution and discovered sections of the cytokinetic cortex undergo periodic phases of acceleration and deceleration. Quantification of ingression speed oscillations revealed wide ranges of oscillation period and amplitude. In the cytokinetic ring, activity of the master regulator RhoA pulsed with a timescale of approximately 20 seconds, shorter than that reported for any other biological context. Contractility oscillated with 20-second periodicity and with much longer periods. A combination of in vivo and in silico approaches to modify mechanical feedback revealed that the period of contractile oscillation is prolonged as a function of the intensity of mechanical feedback. Effective local ring ingression is characterized by slower speed oscillations, likely due to increased local stresses and therefore mechanical feedback. Fast ingression also occurs where material turnover is high, in vivo and in silico . We propose that downstream of initiation by pulsed RhoA activity, mechanical positive feedback, including but not limited to material advection, extends the timescale of contractility beyond that of biochemical input and therefore makes it robust to fluctuations in activation. Circumferential propagation of contractility likely allows sustained contractility despite cytoskeletal remodeling necessary to recover from compaction. Our work demonstrates that while biochemical feedback loops afford systems responsiveness and robustness, mechanical feedback must also be considered to describe and understand the behaviors of active materials in vivo .

Change in RhoGAP and RhoGEF availability drives transitions in cortical patterning and excitability in Drosophila

Actin cortex patterning and dynamics are critical for cell shape changes. These dynamics undergo transitions during development, often accompanying changes in collective cell behavior. While mechanisms have been established for individual cells' dynamic behaviors, mechanisms and specific molecules that result in developmental transitions in vivo are still poorly understood. Here, we took advantage of two developmental systems in Drosophila melanogaster to identify conditions that altered cortical patterning and dynamics. We identified a RhoGEF and RhoGAP pair whose relocalization from nucleus to cortex results in actomyosin waves in egg chambers. Furthermore, we found that overexpression of a different RhoGEF and RhoGAP pair resulted in actomyosin waves in the early embryo, during which RhoA activation precedes actomyosin assembly and RhoGAP recruitment by ~4 seconds. Overall, we showed a mechanism involved in inducing actomyosin waves that is essential for oocyte development and is general to other cell types.

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.

A multiscale whole-cell theory for mechanosensitive migration on viscoelastic substrates

Increasing experimental evidence validates that both the elastic stiffness and viscosity of the extracellular matrix regulate mesenchymal cell behavior, such as the rational switch between durotaxis (cell migration to stiffer regions), anti-durotaxis (migration to softer regions), and adurotaxis (stiffness-insensitive migration). To reveal the mechanisms underlying the crossover between these motility regimes, we have developed a multiscale chemomechanical whole-cell theory for mesenchymal migration. Our framework couples the subcellular focal adhesion dynamics at the cell-substrate interface with the cellular cytoskeletal mechanics and the chemical signaling pathways involving Rho GTPase proteins. Upon polarization by the Rho GTPase gradients, our simulated cell migrates by concerted peripheral protrusions and contractions, a hallmark of the mesenchymal mode. The resulting cell dynamics quantitatively reproduces the experimental migration speed as a function of the uniform substrate stiffness and explains the influence of viscosity on the migration efficiency. In the presence of stiffness gradients and absence of chemical polarization, our simulated cell can exhibit durotaxis, anti-durotaxis, and adurotaxis respectively with increasing substrate stiffness or viscosity. The cell moves toward an optimally stiff region from softer regions during durotaxis and from stiffer regions during anti-durotaxis. We show that cell polarization through steep Rho GTPase gradients can reverse the migration direction dictated by the mechanical cues. Overall, our theory demonstrates that opposing durotactic behaviors emerge via the interplay between intracellular signaling and cell-medium mechanical interactions in agreement with experiments, thereby elucidating complex mechanosensing at the single-cell level.