Genetic induction and mechanochemical propagation of a morphogenetic wave.

Tissue morphogenesis arises from coordinated changes in cell shape driven by actomyosin contractions. Patterns of gene expression regionalize cell behaviours by controlling actomyosin contractility. Here we report two modes of control over Rho1 and myosin II (MyoII) activation in the Drosophila endoderm. First, Rho1-MyoII are induced in a spatially restricted primordium via localized transcription of the G-protein-coupled receptor ligand Fog. Second, a tissue-scale wave of Rho1-MyoII activation and cell invagination progresses anteriorly away from the primordium. The wave does not require sustained gene transcription, and is not governed by regulated Fog delivery. Instead, MyoII inhibition blocks Rho1 activation and propagation, revealing a mechanical feedback driven by MyoII. We find that MyoII activation and invagination in each row of cells drives adhesion to the vitelline membrane mediated by integrins, apical spreading, MyoII activation and invagination in the next row. Endoderm morphogenesis thus emerges from local transcriptional initiation and a mechanically driven cycle of cell deformation.

Force generation, transmission, and integration during cell and tissue morphogenesis.

Cell shape changes underlie a large set of biological processes ranging from cell division to cell motility. Stereotyped patterns of cell shape changes also determine tissue remodeling events such as extension or invagination. In vitro and cell culture systems have been essential to understanding the fundamental physical principles of subcellular mechanics. These are now complemented by studies in developing organisms that emphasize how cell and tissue morphogenesis emerge from the interplay between force-generating machines, such as actomyosin networks, and adhesive clusters that transmit tensile forces at the cell cortex and stabilize cell-cell and cell-substrate interfaces. Both force production and transmission are self-organizing phenomena whose adaptive features are essential during tissue morphogenesis. A new era is opening that emphasizes the similarities of and allows comparisons between distant dynamic biological phenomena because they rely on core machineries that control universal features of cytomechanics.

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.

Actin bundle architecture and mechanics regulate myosin II force generation.

The actin cytoskeleton is a soft, structural material that underlies biological processes such as cell division, motility, and cargo transport. The cross-linked actin filaments self-organize into a myriad of architectures, from disordered meshworks to ordered bundles, which are hypothesized to control the actomyosin force generation that regulates cell migration, shape, and adhesion. Here, we use fluorescence microscopy and simulations to investigate how actin bundle architectures with varying polarity, spacing, and rigidity impact myosin II dynamics and force generation. Microscopy reveals that mixed-polarity bundles formed by rigid cross-linkers support slow, bidirectional myosin II filament motion, punctuated by periods of stalled motion. Simulations reveal that these locations of stalled myosin motion correspond to sustained, high forces in regions of balanced actin filament polarity. By contrast, mixed-polarity bundles formed by compliant, large cross-linkers support fast, bidirectional motion with no traps. Simulations indicate that trap duration is directly related to force magnitude and that the observed increased velocity corresponds to lower forces resulting from both the increased bundle compliance and filament spacing. Our results indicate that the microstructures of actin assemblies regulate the dynamics and magnitude of myosin II forces, highlighting the importance of architecture and mechanics in regulating forces in biological materials.

Roadmap for the multiscale coupling of biochemical and mechanical signals during development.

The way in which interactions between mechanics and biochemistry lead to the emergence of complex cell and tissue organization is an old question that has recently attracted renewed interest from biologists, physicists, mathematicians and computer scientists. Rapid advances in optical physics, microscopy and computational image analysis have greatly enhanced our ability to observe and quantify spatiotemporal patterns of signalling, force generation, deformation, and flow in living cells and tissues. Powerful new tools for genetic, biophysical and optogenetic manipulation are allowing us to perturb the underlying machinery that generates these patterns in increasingly sophisticated ways. Rapid advances in theory and computing have made it possible to construct predictive models that describe how cell and tissue organization and dynamics emerge from the local coupling of biochemistry and mechanics. Together, these advances have opened up a wealth of new opportunities to explore how mechanochemical patterning shapes organismal development. In this roadmap, we present a series of forward-looking case studies on mechanochemical patterning in development, written by scientists working at the interface between the physical and biological sciences, and covering a wide range of spatial and temporal scales, organisms, and modes of development. Together, these contributions highlight the many ways in which the dynamic coupling of mechanics and biochemistry shapes biological dynamics: from mechanoenzymes that sense force to tune their activity and motor output, to collectives of cells in tissues that flow and redistribute biochemical signals during development.

A self-organized biomechanical network drives shape changes during tissue morphogenesis.

Tissue morphogenesis is orchestrated by cell shape changes. Forces required to power these changes are generated by non-muscle myosin II (MyoII) motor proteins pulling filamentous actin (F-actin). Actomyosin networks undergo cycles of assembly and disassembly (pulses) to cause cell deformations alternating with steps of stabilization to result in irreversible shape changes. Although this ratchet-like behaviour operates in a variety of contexts, the underlying mechanisms remain unclear. Here we investigate the role of MyoII regulation through the conserved Rho1-Rok pathway during Drosophila melanogaster germband extension. This morphogenetic process is powered by cell intercalation, which involves the shrinkage of junctions in the dorsal-ventral axis (vertical junctions) followed by junction extension in the anterior-posterior axis. While polarized flows of medial-apical MyoII pulses deform vertical junctions, MyoII enrichment on these junctions (planar polarity) stabilizes them. We identify two critical properties of MyoII dynamics that underlie stability and pulsatility: exchange kinetics governed by phosphorylation-dephosphorylation cycles of the MyoII regulatory light chain; and advection due to contraction of the motors on F-actin networks. Spatial control over MyoII exchange kinetics establishes two stable regimes of high and low dissociation rates, resulting in MyoII planar polarity. Pulsatility emerges at intermediate dissociation rates, enabling convergent advection of MyoII and its upstream regulators Rho1 GTP, Rok and MyoII phosphatase. Notably, pulsatility is not an outcome of an upstream Rho1 pacemaker. Rather, it is a self-organized system that involves positive and negative biomechanical feedback between MyoII advection and dissociation rates.

Rapid diffusion-state switching underlies stable cytoplasmic gradients in the Caenorhabditis elegans zygote.

Protein concentration gradients organize cells and tissues and commonly form through diffusion away from a local source of protein. Interestingly, during the asymmetric division of the Caenorhabditis elegans zygote, the RNA-binding proteins MEX-5 and PIE-1 form opposing concentration gradients in the absence of a local source. In this study, we use near-total internal reflection fluorescence (TIRF) imaging and single-particle tracking to characterize the reaction/diffusion dynamics that maintain the MEX-5 and PIE-1 gradients. Our findings suggest that both proteins interconvert between fast-diffusing and slow-diffusing states on timescales that are much shorter (seconds) than the timescale of gradient formation (minutes). The kinetics of diffusion-state switching are strongly polarized along the anterior/posterior (A/P) axis by the PAR polarity system such that fast-diffusing MEX-5 and PIE-1 particles are approximately symmetrically distributed, whereas slow-diffusing particles are highly enriched in the anterior and posterior cytoplasm, respectively. Using mathematical modeling, we show that local differences in the kinetics of diffusion-state switching can rapidly generate stable concentration gradients over a broad range of spatial and temporal scales.

The PAR proteins: from molecular circuits to dynamic self-stabilizing cell polarity.

PAR proteins constitute a highly conserved network of scaffolding proteins, adaptors and enzymes that form and stabilize cortical asymmetries in response to diverse inputs. They function throughout development and across the metazoa to regulate cell polarity. In recent years, traditional approaches to identifying and characterizing molecular players and interactions in the PAR network have begun to merge with biophysical, theoretical and computational efforts to understand the network as a pattern-forming biochemical circuit. Here, we summarize recent progress in the field, focusing on recent studies that have characterized the core molecular circuitry, circuit design and spatiotemporal dynamics. We also consider some of the ways in which the PAR network has evolved to polarize cells in different contexts and in response to different cues and functional constraints.

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.

Isoforms Confer Characteristic Force Generation and Mechanosensation by Myosin II Filaments.

Myosin II isoforms with varying mechanochemistry and filament size interact with filamentous actin (F-actin) arrays to generate contractile forces in muscle and nonmuscle cells. How myosin II force production is shaped by isoform-specific motor properties and environmental stiffness remains poorly understood. Here, we used computer simulations to analyze force production by an ensemble of myosin motors against an elastically tethered actin filament. We found that force output depends on two timescales: the duration of F-actin attachment, which varies sharply with the ensemble size, motor duty ratio, and external load; and the time to build force, which scales with the ensemble stall force, gliding speed, and environmental stiffness. Although force-dependent kinetics were not required to sense changes in stiffness, the myosin catch bond produced positive feedback between the attachment time and force to trigger switch-like transitions from transient attachments, generating small forces, to high-force-generating runs. Using parameters representative of skeletal muscle myosin, nonmuscle myosin IIB, and nonmuscle myosin IIA revealed three distinct regimes of behavior, respectively: 1) large assemblies of fast, low-duty ratio motors rapidly build stable forces over a large range of environmental stiffness; 2) ensembles of slow, high-duty ratio motors serve as high-affinity cross-links with force buildup times that exceed physiological timescales; and 3) small assemblies of low-duty ratio motors operating at intermediate speeds are poised to respond sharply to changes in mechanical context-at low force or stiffness, they serve as low-affinity cross-links, but they can transition to force production via the positive-feedback mechanism described above. Together, these results reveal how myosin isoform properties may be tuned to produce force and respond to mechanical cues in their environment.

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.

Bond flexibility and low valence promote finite clusters of self-aggregating particles.

Systems of complex particles such as proteins or colloidal particles have a widely observed tendency to form nonconnected nanometer-size clusters at steady state, but the underlying mechanisms remain poorly understood. We report here a numerical study on the self-aggregation of low-valence particles with flexible bonds (i.e., free bond orientations) in two dimensions and predict the formation of a stable cluster phase for average valences ranging from 2 to 3.6. For the intermediate case of trivalent particles, we show that a cluster phase is present over a wide range of concentrations and interaction energies. The clusters are polydisperse in size, have a fractal dimension of 1.5, and tend to fully saturate their bonds at high interaction energies. The number of unformed bonds scales linearly with the number of particles in a cluster, which implies the absence of phase transition in the explored region of interaction energies and concentrations. We discuss possible implications of our model for membrane protein clustering.

Modulating RhoA effectors induces transitions to oscillatory and more wavelike RhoA dynamics in Caenorhabditis elegans zygotes.

Pulsatile RhoA dynamics underlie a wide range of cell and tissue behaviors. The circuits that produce these dynamics in different cells share common architectures based on fast positive and delayed negative feedback through F-actin, but they can produce very different spatiotemporal patterns of RhoA activity. However, the underlying causes of this variation remain poorly understood. Here we asked how this variation could arise through modulation of actin network dynamics downstream of active RhoA in early Caenorhabditis elegans embryos. We find that perturbing two RhoA effectors-formin and anillin-induce transitions from nonrecurrent focal pulses to either large noisy oscillatory pulses (formin depletion) or noisy oscillatory waves (anillin depletion). In both cases these transitions could be explained by changes in local F-actin levels and depletion dynamics, leading to changes in spatial and temporal patterns of RhoA inhibition. However, the underlying mechanisms for F-actin depletion are distinct, with different dependencies on myosin II activity. Thus, modulating actomyosin network dynamics could shape the spatiotemporal dynamics of RhoA activity for different physiological or morphogenetic functions.

Fat2 polarizes the WAVE complex in trans to align cell protrusions for collective migration.

For a group of cells to migrate together, each cell must couple the polarity of its migratory machinery with that of the other cells in the cohort. Although collective cell migrations are common in animal development, little is known about how protrusions are coherently polarized among groups of migrating epithelial cells. We address this problem in the collective migration of the follicular epithelial cells in Drosophila melanogaster. In this epithelium, the cadherin Fat2 localizes to the trailing edge of each cell and promotes the formation of F-actin-rich protrusions at the leading edge of the cell behind. We show that Fat2 performs this function by acting in trans to concentrate the activity of the WASP family verprolin homolog regulatory complex (WAVE complex) at one long-lived region along each cell's leading edge. Without Fat2, the WAVE complex distribution expands around the cell perimeter and fluctuates over time, and protrusive activity is reduced and unpolarized. We further show that Fat2's influence is very local, with sub-micron-scale puncta of Fat2 enriching the WAVE complex in corresponding puncta just across the leading-trailing cell-cell interface. These findings demonstrate that a trans interaction between Fat2 and the WAVE complex creates stable regions of protrusive activity in each cell and aligns the cells' protrusions across the epithelium for directionally persistent collective migration.

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.

Filament-guided filament assembly provides structural memory of filament alignment during cytokinesis.

During cytokinesis, animal cells rapidly remodel the equatorial cortex to build an aligned array of actin filaments called the contractile ring. Local reorientation of filaments by active equatorial compression is thought to underlie the emergence of filament alignment during ring assembly. Here, combining single molecule analysis and modeling in one-cell C. elegans embryos, we show that filaments turnover is far too fast for reorientation of individual filaments by equatorial compression to explain the observed alignment, even if favorably oriented filaments are selectively stabilized. By tracking single formin/CYK-1::GFP particles to monitor local filament assembly, we identify a mechanism that we call filament-guided filament assembly (FGFA), in which existing filaments serve as templates to orient the growth of new filaments. FGFA sharply increases the effective lifetime of filament orientation, providing structural memory that allows cells to build highly aligned filament arrays in response to equatorial compression, despite rapid turnover of individual filaments.

Asymmetric cell division: a CAB driver for spindle movements.

To divide asymmetrically, a cell must position the mitotic spindle relative to localized cell fate determinants. Recent work in the early ascidian embryo reveals the function of a single factor that coordinates this act to control cleavage pattern and cell fate determination.