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.

Oligomerization of peripheral membrane proteins provides tunable control of cell surface polarity.

Asymmetric distributions of peripheral membrane proteins define cell polarity across all kingdoms of life. Non-linear positive feedback on membrane binding is essential to amplify and stabilize these asymmetries, but how specific molecular sources of non-linearity shape polarization dynamics remains poorly understood. Here we show that the ability to oligomerize, which is common to many peripheral membrane proteins, can play a profound role in shaping polarization dynamics in simple feedback circuits. We show that size-dependent binding avidity and mobility of membrane-bound oligomers endow polarity circuits with several key properties. Size-dependent membrane binding avidity confers a form of positive feedback on the accumulation of oligomer subunits. Although insufficient by itself, this sharply reduces the amount of additional feedback required for spontaneous emergence and stable maintenance of polarized states. Size-dependent oligomer mobility makes symmetry breaking and stable polarity more robust with respect to variation in subunit diffusivities and cell sizes, and slows the approach to a final stable spatial distribution, allowing cells to "remember" polarity boundaries imposed by transient external cues. Together, these findings reveal how oligomerization of peripheral membrane proteins can provide powerful and highly tunable sources of non-linear feedback in biochemical circuits that govern cell surface polarity. Given its prevalence and widespread involvement in cell polarity, we speculate that self-oligomerization may have provided an accessible path to evolving simple polarity circuits.

Mechanosensitive Junction Remodeling Promotes Robust Epithelial Morphogenesis.

Morphogenesis of epithelial tissues requires tight spatiotemporal coordination of cell shape changes. In vivo, many tissue-scale shape changes are driven by pulsatile contractions of intercellular junctions, which are rectified to produce irreversible deformations. The functional role of this pulsatory ratchet and its mechanistic basis remain unknown. Here we combine theory and biophysical experiments to show that mechanosensitive tension remodeling of epithelial cell junctions promotes robust epithelial shape changes via ratcheting. Using optogenetic control of actomyosin contractility, we find that epithelial junctions show elastic behavior under low contractile stress, returning to their original lengths after contraction, but undergo irreversible deformation under higher magnitudes of contractile stress. Existing vertex-based models for the epithelium are unable to capture these results, with cell junctions displaying purely elastic or fluid-like behaviors, depending on the choice of model parameters. To describe the experimental results, we propose a modified vertex model with two essential ingredients for junction mechanics: thresholded tension remodeling and continuous strain relaxation. First, junctions must overcome a critical strain threshold to trigger tension remodeling, resulting in irreversible junction length changes. Second, there is a continuous relaxation of junctional strain that removes mechanical memory from the system. This enables pulsatile contractions to further remodel cell shape via mechanical ratcheting. Taken together, the combination of mechanosensitive tension remodeling and junctional strain relaxation provides a robust mechanism for large-scale morphogenesis.

Filament turnover tunes both force generation and dissipation to control long-range flows in a model actomyosin cortex.

Actomyosin-based cortical flow is a fundamental engine for cellular morphogenesis. Cortical flows are generated by cross-linked networks of actin filaments and myosin motors, in which active stress produced by motor activity is opposed by passive resistance to network deformation. Continuous flow requires local remodeling through crosslink unbinding and and/or filament disassembly. But how local remodeling tunes stress production and dissipation, and how this in turn shapes long range flow, remains poorly understood. Here, we study a computational model for a cross-linked network with active motors based on minimal requirements for production and dissipation of contractile stress: Asymmetric filament compliance, spatial heterogeneity of motor activity, reversible cross-links and filament turnover. We characterize how the production and dissipation of network stress depend, individually, on cross-link dynamics and filament turnover, and how these dependencies combine to determine overall rates of cortical flow. Our analysis predicts that filament turnover is required to maintain active stress against external resistance and steady state flow in response to external stress. Steady state stress increases with filament lifetime up to a characteristic time τm, then decreases with lifetime above τm. Effective viscosity increases with filament lifetime up to a characteristic time τc, and then becomes independent of filament lifetime and sharply dependent on crosslink dynamics. These individual dependencies of active stress and effective viscosity define multiple regimes of steady state flow. In particular our model predicts that when filament lifetimes are shorter than both τc and τm, the dependencies of effective viscosity and steady state stress on filament turnover cancel one another, such that flow speed is insensitive to filament turnover, and shows a simple dependence on motor activity and crosslink dynamics. These results provide a framework for understanding how animal cells tune cortical flow through local control of network remodeling.

Single-molecule analysis of cell surface dynamics in Caenorhabditis elegans embryos.

We describe a general, versatile and minimally invasive method to image single molecules near the cell surface that can be applied to any GFP-tagged protein in Caenorhabditis elegans embryos. We exploited tunable expression via RNAi and a dynamically exchanging monomer pool to achieve fast, continuous single-molecule imaging at optimal densities with signal-to-noise ratios adequate for robust single-particle tracking (SPT). We introduce a method called smPReSS, single-molecule photobleaching relaxation to steady state, that infers exchange rates from quantitative analysis of single-molecule photobleaching kinetics without using SPT. Combining SPT and smPReSS allowed for spatially and temporally resolved measurements of protein mobility and exchange kinetics. We used these methods to (i) resolve distinct mobility states and spatial variation in exchange rates of the polarity protein PAR-6 and (ii) measure spatiotemporal modulation of actin filament assembly and disassembly. These methods offer a promising avenue to investigate dynamic mechanisms that pattern the embryonic cell surface.

PAR proteins and the cytoskeleton: a marriage of equals.

The PAR proteins are a group of widely conserved regulators of polarity, many of which are asymmetrically localized in polarized cells. Recent work shows that distinct modes of actomyosin- and microtubule-based transport contribute to the establishment of PAR asymmetries in different cell types. Cross-regulatory interactions among PAR proteins and with other conserved polarity complexes stabilize asymmetries once they form, and shape the evolution of PAR protein distributions in response to cytoskeletal transport or other polarizing inputs. The PAR proteins in turn modulate the actomyosin and microtubule cytoskeletons. In some cases, this is a form of feedback control, central to the establishment and maintenance of PAR asymmetries. In others, it underlies the elaboration of functional cell polarity.

PAR-3 oligomerization may provide an actin-independent mechanism to maintain distinct par protein domains in the early Caenorhabditis elegans embryo.

Par proteins establish discrete intracellular spatial domains to polarize many different cell types. In the single-cell embryo of the nematode worm Caenorhabditis elegans, the segregation of Par proteins is crucial for proper division and cell fate specification. Actomyosin-based cortical flows drive the initial formation of anterior and posterior Par domains, but cortical actin is not required for the maintenance of these domains. Here we develop a model of interactions between the Par proteins that includes both mutual inhibition and PAR-3 oligomerization. We show that this model gives rise to a bistable switch mechanism, allowing the Par proteins to occupy distinct anterior and posterior domains seen in the early C. elegans embryo, independent of dynamics or asymmetries in the actin cortex. The model predicts a sharp loss of cortical Par protein asymmetries during gradual depletion of the Par protein PAR-6, and we confirm this prediction experimentally. Together, these results suggest both mutual inhibition and PAR-3 oligomerization are sufficient to maintain distinct Par protein domains in the early C. elegans embryo.

Ascidian prickle regulates both mediolateral and anterior-posterior cell polarity of notochord cells.

The ascidian notochord follows a morphogenetic program that includes convergent extension (C/E), followed by anterior-posterior (A/P) elongation [1-4]. As described here, developing notochord cells show polarity first in the mediolateral (M/L) axis during C/E, and subsequently in the A/P axis during elongation. Previous embryological studies [3] have shown that contact with neighboring tissues is essential for directing M/L polarity of ascidian notochord cells. During C/E, the planar cell polarity (PCP) gene products prickle (pk) and dishevelled (dsh) show M/L polarization. pk and dsh colocalize at the notochord cell membranes, with the exception of those in contact with neighboring muscle cells. In the mutant aimless (aim), which carries a deletion in pk, notochord morphogenesis is disrupted, and cell polarization is lost. After C/E, there is a dynamic relocalization of PCP proteins in the notochord cells with dsh localized to the lateral edges of the membrane, and pk and strabismus (stbm) at the anterior edges. An A/P polarity is present in the extending notochord cells and is evident by the position of the nuclei, which in normal embryos are invariably found at the posterior edge of each cell. In the aim mutant, all appearances of A/P polarity in the notochord are lost.

Excitable RhoA dynamics drive pulsed contractions in the early C. elegans embryo.

Pulsed actomyosin contractility underlies diverse modes of tissue morphogenesis, but the underlying mechanisms remain poorly understood. Here, we combined quantitative imaging with genetic perturbations to identify a core mechanism for pulsed contractility in early Caenorhabditis elegans embryos. We show that pulsed accumulation of actomyosin is governed by local control of assembly and disassembly downstream of RhoA. Pulsed activation and inactivation of RhoA precede, respectively, the accumulation and disappearance of actomyosin and persist in the absence of Myosin II. We find that fast (likely indirect) autoactivation of RhoA drives pulse initiation, while delayed, F-actin-dependent accumulation of the RhoA GTPase-activating proteins RGA-3/4 provides negative feedback to terminate each pulse. A mathematical model, constrained by our data, suggests that this combination of feedbacks is tuned to generate locally excitable RhoA dynamics. We propose that excitable RhoA dynamics are a common driver for pulsed contractility that can be tuned or coupled differently to actomyosin dynamics to produce a diversity of morphogenetic outcomes.

Sequential contraction and exchange of apical junctions drives zippering and neural tube closure in a simple chordate.

Unidirectional zippering is a key step in neural tube closure that remains poorly understood. Here, we combine experimental and computational approaches to identify the mechanism for zippering in a basal chordate, Ciona intestinalis. We show that myosin II is activated sequentially from posterior to anterior along the neural/epidermal (Ne/Epi) boundary just ahead of the advancing zipper. This promotes rapid shortening of Ne/Epi junctions, driving the zipper forward and drawing the neural folds together. Cell contact rearrangements (Ne/Epi + Ne/Epi → Ne/Ne + Epi/Epi) just behind the zipper lower tissue resistance to zipper progression by allowing transiently stretched cells to detach and relax toward isodiametric shapes. Computer simulations show that measured differences in junction tension, timing of primary contractions, and delay before cell detachment are sufficient to explain the speed and direction of zipper progression and highlight key advantages of a sequential contraction mechanism for robust efficient zippering.

Cytokinetic furrowing in toroidal, binucleate and anucleate cells in C. elegans embryos.

Classical experimental studies on echinoderm zygotes concluded that the juxtaposition of two astral microtubule arrays localizes the stimulus for cytokinetic furrowing. However, recent experimental and genetic studies in Caenorhabditis elegans, Drosophila and mammalian cultured cells implicate microtubules of the central spindle, and regulatory proteins associated with this structure, suggesting that the essential conditions for furrow induction may differ from one animal cell to another. We used micromanipulation and laser microsurgery to create, in three ways, the juxtaposition of astral microtubules in C. elegans embryonic cells. In toroidal cells we observe that furrows initiate both where astral microtubule arrays are juxtaposed, and where the cortex most closely approaches the central spindle. We find that binucleate cells successfully furrow not only across the spindles, but also between unconnected spindle poles. Finally, we find that anucleate cells containing only a pair of centrosomes nevertheless attempt to cleave. Therefore, in C. elegans embryonic cells, as in echinoderms, juxtaposition of two asters suffices to induce furrowing, and neither the chromatin nor the physical structure of the central spindle are indispensable for furrow initiation. However, furrows that cross a central spindle are more likely to complete than those that do not.

Morphogenetic pattern formation during ascidian notochord formation is regulative and highly robust.

The ascidian notochord forms through simultaneous invagination and convergent extension of a monolayer epithelial plate. Here we combine micromanipulation with time lapse and confocal microscopy to examine how notochord-intrinsic morphogenetic behaviors and interactions with surrounding tissues, determine these global patterns of movement. We show that notochord rudiments isolated at the 64-cell stage divide and become motile with normal timing; but, in the absence of interactions with non-notochordal tissues, they neither invaginate nor converge and extend. We find that notochord formation is robust in the sense that no particular neighboring tissue is required for notochord formation. Basal contact with either neural plate or anterior endoderm/lateral mesenchyme or posterior mesoderm are each alone sufficient to ensure that the notochord plate forms and extends a cylindrical rod. Surprisingly, the axis of convergent extension depends on the specific tissues that contact the notochord, as do other patterns of cell shape change, movement and tissue deformation that accompany notochord formation. We characterize one case in detail, namely, embryos lacking neural plates, in which a normal notochord forms but by an entirely different trajectory. Our results show ascidian notochord formation to be regulative in a fashion and to a degree never before appreciated. They suggest this regulative behavior depends on a complex interplay between morphogenetic tendencies intrinsic to the notochord plate and instructive and permissive interactions with surrounding tissues. We discuss mechanisms that could account for these data and what they imply about notochord morphogenesis and its evolution within the chordate phylum.

Polarized basolateral cell motility underlies invagination and convergent extension of the ascidian notochord.

We use 3D time-lapse analysis of living embryos and laser scanning confocal reconstructions of fixed, staged, whole-mounted embryos to describe three-dimensional patterns of cell motility, cell shape change, cell rearrangement and tissue deformation that accompany formation of the ascidian notochord. We show that notochord formation involves two simultaneous processes occurring within an initially monolayer epithelial plate: The first is invagination of the notochord plate about the axial midline to form a solid cylindrical rod. The second is mediolaterally directed intercalation of cells within the plane of the epithelial plate, and then later about the circumference of the cylindrical rod, that accompanies its extension along the anterior/posterior (AP) axis. We provide evidence that these shape changes and rearrangements are driven by active extension of interior basolateral notochord cell edges directly across the faces of their adjacent notochord neighbors in a manner analogous to leading edge extension of lamellapodia by motile cells in culture. We show further that local edge extension is polarized with respect to both the AP axis of the embryo and the apicobasal axis of the notochord plate. Our observations suggest a novel view of how active basolateral motility could drive both invagination and convergent extension of a monolayer epithelium. They further reveal deep similarities between modes of notochord morphogenesis exhibited by ascidians and other chordate embryos, suggesting that cellular mechanisms of ascidian notochord formation may operate across the chordate phylum.

C. elegans PAR-3 and PAR-6 are required for apicobasal asymmetries associated with cell adhesion and gastrulation.

PAR proteins distribute asymmetrically across the anterior-posterior axis of the 1-cell-stage C. elegans embryo, and function to establish subsequent anterior-posterior asymmetries. By the end of the 4-cell stage, anteriorly localized PAR proteins, such as PAR-3 and PAR-6, redistribute to the outer, apical surfaces of cells, whereas posteriorly localized PAR proteins, such as PAR-1 and PAR-2, redistribute to the inner, basolateral surfaces. Because PAR proteins are provided maternally, distinguishing apicobasal from earlier anterior-posterior functions requires a method that selectively prevents PAR activity after the 1-cell stage. In the present study we generated hybrid PAR proteins that are targeted for degradation after the 1-cell stage. Embryos containing the hybrid PAR proteins had normal anterior-posterior polarity, but showed defects in apicobasal asymmetries associated with gastrulation. Ectopic separations appeared between lateral surfaces of cells that are normally tightly adherent, cells that ingress during gastrulation failed to accumulate nonmuscle myosin at their apical surfaces and ingression was slowed. Thus, PAR proteins function in both apicobasal and anterior-posterior asymmetry during the first few cell cycles of embryogenesis.

Ingeneue: a versatile tool for reconstituting genetic networks, with examples from the segment polarity network.

Here we describe a software tool for synthesizing molecular genetic data into models of genetic networks. Our software program Ingeneue, written in Java, lets the user quickly turn a map of a genetic network into a dynamical model consisting of a set of ordinary differential equations. We developed Ingeneue as part of an ongoing effort to explore the design and evolvability of genetic networks. Ingeneue has three principal advantages over other available mathematical software: it automates instantiation of the same network model in each cell in a 2-D sheet of cells; it constructs model equations from pre-made building blocks corresponding to common biochemical processes; and it automates searches through parameter space, sensitivity analyses, and other common tasks. Here we discuss the structure of the software and some of the issues we have dealt with. We conclude with some examples of results we have achieved with Ingeneue for the Drosophila segment polarity network.