How to Grow a Flat Leaf.

Growing a flat lamina such as a leaf is almost impossible without some feedback to stabilize long wavelength modes that are easy to trigger since they are energetically cheap. Here we combine the physics of thin elastic plates with feedback control theory to explore how a leaf can remain flat while growing. We investigate both in-plane (metric) and out-of-plane (curvature) growth variation and account for both local and nonlocal feedback laws. We show that a linearized feedback theory that accounts for both spatially nonlocal and temporally delayed effects suffices to suppress long wavelength fluctuations effectively and explains recently observed statistical features of growth in tobacco leaves. Our work provides a framework for understanding the regulation of the shape of leaves and other leaflike laminar objects.

Matrix viscoelasticity controls spatiotemporal tissue organization.

Biomolecular and physical cues of the extracellular matrix environment regulate collective cell dynamics and tissue patterning. Nonetheless, how the viscoelastic properties of the matrix regulate collective cell spatial and temporal organization is not fully understood. Here we show that the passive viscoelastic properties of the matrix encapsulating a spheroidal tissue of breast epithelial cells guide tissue proliferation in space and in time. Matrix viscoelasticity prompts symmetry breaking of the spheroid, leading to the formation of invading finger-like protrusions, YAP nuclear translocation and epithelial-to-mesenchymal transition both in vitro and in vivo in a Arp2/3-complex-dependent manner. Computational modelling of these observations allows us to establish a phase diagram relating morphological stability with matrix viscoelasticity, tissue viscosity, cell motility and cell division rate, which is experimentally validated by biochemical assays and in vitro experiments with an intestinal organoid. Altogether, this work highlights the role of stress relaxation mechanisms in tissue growth dynamics, a fundamental process in morphogenesis and oncogenesis.

Muscular hydraulics drive larva-polyp morphogenesis.

Development is a highly dynamic process in which organisms often experience changes in both form and behavior, which are typically coupled to each other. However, little is known about how organismal-scale behaviors such as body contractility and motility impact morphogenesis. Here, we use the cnidarian Nematostella vectensis as a developmental model to uncover a mechanistic link between organismal size, shape, and behavior. Using quantitative live imaging in a large population of developing animals, combined with molecular and biophysical experiments, we demonstrate that the muscular-hydraulic machinery that controls body movement also drives larva-polyp morphogenesis. We show that organismal size largely depends on cavity inflation through fluid uptake, whereas body shape is constrained by the organization of the muscular system. The generation of ethograms identifies different trajectories of size and shape development in sessile and motile animals, which display distinct patterns of body contractions. With a simple theoretical model, we conceptualize how pressures generated by muscular hydraulics can act as a global mechanical regulator that coordinates tissue remodeling. Altogether, our findings illustrate how organismal contractility and motility behaviors can influence morphogenesis.

Photosynthetic artificial organelles sustain and control ATP-dependent reactions in a protocellular system.

Inside cells, complex metabolic reactions are distributed across the modular compartments of organelles. Reactions in organelles have been recapitulated in vitro by reconstituting functional protein machineries into membrane systems. However, maintaining and controlling these reactions is challenging. Here we designed, built, and tested a switchable, light-harvesting organelle that provides both a sustainable energy source and a means of directing intravesicular reactions. An ATP (ATP) synthase and two photoconverters (plant-derived photosystem II and bacteria-derived proteorhodopsin) enable ATP synthesis. Independent optical activation of the two photoconverters allows dynamic control of ATP synthesis: red light facilitates and green light impedes ATP synthesis. We encapsulated the photosynthetic organelles in a giant vesicle to form a protocellular system and demonstrated optical control of two ATP-dependent reactions, carbon fixation and actin polymerization, with the latter altering outer vesicle morphology. Switchable photosynthetic organelles may enable the development of biomimetic vesicle systems with regulatory networks that exhibit homeostasis and complex cellular behaviors.

Organ size control via hydraulically gated oscillations.

Hollow vesicular tissues of various sizes and shapes arise in biological organs such as ears, guts, hearts, brains and even entire organisms. Regulating their size and shape is crucial for their function. Although chemical signaling has been thought to play a role in the regulation of cellular processes that feed into larger scales, it is increasingly recognized that mechanical forces are involved in the modulation of size and shape at larger length scales. Motivated by a variety of examples of tissue cyst formation and size control that show simultaneous growth and size oscillations, we create a minimal theoretical framework for the growth and dynamics of a soft, fluid-permeable, spherical shell. We show that these shells can relieve internal pressure by bursting intermittently, shrinking and re-growing, providing a simple mechanism by which hydraulically gated oscillations can regulate size. To test our theory, we develop an in vitro experimental set-up to monitor the growth and oscillations of a hollow tissue spheroid growing freely or when confined. A simple generalization of our theory to account for irreversible deformations allows us to explain the time scales and the amplitudes of oscillations in terms of the geometry and mechanical properties of the tissue shells. Taken together, our theory and experimental observations show how soft hydraulics can regulate the size of growing tissue shells.

BMP signaling controls buckling forces to modulate looping morphogenesis of the gut.

Looping of the initially straight embryonic gut tube is an essential aspect of intestinal morphogenesis, permitting proper placement of the lengthy small intestine within the confines of the body cavity. The formation of intestinal loops is highly stereotyped within a given species and results from differential-growth-driven mechanical buckling of the gut tube as it elongates against the constraint of a thin, elastic membranous tissue, the dorsal mesentery. Although the physics of this process has been studied, the underlying biology has not. Here, we show that BMP signaling plays a critical role in looping morphogenesis of the avian small intestine. We first exploited differences between chicken and zebra finch gut morphology to identify the BMP pathway as a promising candidate to regulate differential growth in the gut. Next, focusing on the developing chick small intestine, we determined that Bmp2 expressed in the dorsal mesentery establishes differential elongation rates between the gut tube and mesentery, thereby regulating the compressive forces that buckle the gut tube into loops. Consequently, the number and tightness of loops in the chick small intestine can be increased or decreased directly by modulation of BMP activity in the small intestine. In addition to providing insight into the molecular mechanisms underlying intestinal development, our findings provide an example of how biochemical signals act on tissue-level mechanics to drive organogenesis, and suggest a possible mechanism by which they can be modulated to achieve distinct morphologies through evolution.

Biased migration of confined neutrophil-like cells in asymmetric hydraulic environments.

Cells integrate multiple measurement modalities to navigate their environment. Soluble and substrate-bound chemical gradients and physical cues have all been shown to influence cell orientation and migration. Here we investigate the role of asymmetric hydraulic pressure in directional sensing. Cells confined in microchannels identified and chose a path of lower hydraulic resistance in the absence of chemical cues. In a bifurcating channel with asymmetric hydraulic resistances, this choice was preceded by the elaboration of two leading edges with a faster extension rate along the lower resistance channel. Retraction of the "losing" edge appeared to precipitate a final choice of direction. The pressure differences altering leading edge protrusion rates were small, suggesting weak force generation by leading edges. The response to the physical asymmetry was able to override a dynamically generated chemical cue. Motile cells may use this bias as a result of hydraulic resistance, or "barotaxis," in concert with chemotaxis to navigate complex environments.

Structural dynamics of an actin spring.

Actin-based motility in cells is usually associated with either polymerization/depolymerization in the presence of cross-linkers or contractility in the presence of myosin motors. Here, we focus on a third distinct mechanism involving actin in motility, seen in the dynamics of an active actin spring that powers the acrosomal reaction of the horseshoe crab (Limulus polyphemus) sperm. During this process, a 60-µm bent and twisted bundle of cross-linked actin uncoils and becomes straight in a few seconds in the presence of Ca(2+). This straightening, which occurs at a constant velocity, allows the acrosome to forcefully penetrate the egg. Synthesizing ultrastructural information with the kinetics, energetics, and imaging of calcium binding allows us to construct a dynamical theory for this mechanochemical engine consistent with our experimental observations. It also illuminates the general mechanism by which energy may be stored in conformational changes and released cooperatively in ordered macromolecular assemblies.

Animal cell hydraulics.

Water is the dominant ingredient of cells and its dynamics are crucial to life. We and others have suggested a physical picture of the cell as a soft, fluid-infiltrated sponge, surrounded by a water-permeable barrier. To understand water movements in an animal cell, we imposed an external, inhomogeneous osmotic stress on cultured cancer cells. This forced water through the membrane on one side, and out on the other. Inside the cell, it created a gradient in hydration, that we visualized by tracking cellular responses using natural organelles and artificially introduced quantum dots. The dynamics of these markers at short times were the same for normal and metabolically poisoned cells, indicating that the cellular responses are primarily physical rather than chemical. Our finding of an internal gradient in hydration is inconsistent with a continuum model for cytoplasm, but consistent with the sponge model, and implies that the effective pore size of the sponge is small enough to retard water flow significantly on time scales ( approximately 10-100 seconds) relevant to cell physiology. We interpret these data in terms of a theoretical framework that combines mechanics and hydraulics in a multiphase poroelastic description of the cytoplasm and explains the experimentally observed dynamics quantitatively in terms of a few coarse-grained parameters that are based on microscopically measurable structural, hydraulic and mechanical properties. Our fluid-filled sponge model could provide a unified framework to understand a number of disparate observations in cell morphology and motility.

Calcium regulation of an actin spring.

Calcium is essential for many biological processes involved in cellular motility. However, the pathway by which calcium influences motility, in processes such as muscle contraction and neuronal growth, is often indirect and complex. We establish a simple and direct mechanochemical link that shows how calcium quantitatively regulates the dynamics of a primitive motile system, the actin-based acrosomal bundle of horseshoe crab sperm. The extension of this bundle requires the continuous presence of external calcium. Furthermore, the extension rate increases with calcium concentration, but at a given concentration, we find that the volumetric rate of extension is constant. Our experiments and theory suggest that calcium sequentially binds to calmodulin molecules decorating the actin filaments. This binding leads to a collective wave of untwisting of the actin filaments that drives bundle extension.

Dynamics of chromatin decondensation reveals the structural integrity of a mechanically prestressed nucleus.

Genome organization within the cell nucleus is a result of chromatin condensation achieved by histone tail-tail interactions and other nuclear proteins that counter the outward entropic pressure of the polymeric DNA. We probed the entropic swelling of chromatin driven by enzymatic disruption of these interactions in isolated mammalian cell nuclei. The large-scale decondensation of chromatin and the eventual rupture of the nuclear membrane and lamin network due to this entropic pressure were observed by fluorescence imaging. This swelling was accompanied by nuclear softening, an effect that we quantified by measuring the fluctuations of an optically trapped bead adhered onto the nucleus. We also measured the pressure at which the nuclear scaffold ruptured using an atomic force microscope cantilever. A simple theory based on a balance of forces in a swelling porous gel quantitatively explains the diffusive dynamics of swelling. Our experiments on decondensation of chromatin in nuclei suggest that its compaction is a critical parameter in controlling nuclear stability.

Force of an actin spring.

Cellular movements are produced by forces. Typically, cytoskeletal proteins such as microtubules and actin filaments generate forces via polymerization or in conjunction with molecular motors. However, the fertilization of a Limulus polyphemus egg involves a third type of actin-based cellular engine--a biological spring. During the acrosome reaction, a 60-microm long coiled and twisted bundle of actin filaments straightens and extends from a sperm cell, penetrating the vitelline layer surrounding the egg. A subtle overtwist of 0.2 degrees /subunit underlies the mechanochemical basis for the extension of this actin spring. Upon calcium activation, this conformational strain energy is converted to mechanical work, generating the force required to extend the bundle through the vitelline layer. In this article, we stall the extension of the acrosome bundle in agarose gels of different concentrations. From the stall forces, we estimate a maximum force of 2 nN and a puncturing pressure of 1.6 MPa. We show the maximum force of extension is three times larger than the force required to puncture the vitelline layer. Thus, the elastic strain energy stored in the acrosome bundle is more than sufficient to power the acrosome reaction through the egg envelope.

The universal dynamics of cell spreading.

Cell adhesion and motility depend strongly on the interactions between cells and extracellular matrix (ECM) substrates. When plated onto artificial adhesive surfaces, cells first flatten and deform extensively as they spread. At the molecular level, the interaction of membrane-based integrins with the ECM has been shown to initiate a complex cascade of signaling events [1], which subsequently triggers cellular morphological changes and results in the generation of contractile forces [2]. Here, we focus on the early stages of cell spreading and probe their dynamics by quantitative visualization and biochemical manipulation with a variety of cell types and adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. We find that the dynamics of adhesion follows a universal power-law behavior. This is in sharp contrast with the common belief that spreading is regulated by either the diffusion of adhesion receptors toward the growing adhesive patch [3-5] or by actin polymerization [6-8]. To explain this, we propose a simple quantitative and predictive theory that models cells as viscous adhesive cortical shells enclosing a less viscous interior. Thus, although cell spreading is driven by well-identified biomolecular interactions, it is dynamically limited by its mesoscopic structure and material properties.

Relating microstructure to rheology of a bundled and cross-linked F-actin network in vitro.

The organization of individual actin filaments into higher-order structures is controlled by actin-binding proteins (ABPs). Although the biological significance of the ABPs is well documented, little is known about how bundling and cross-linking quantitatively affect the microstructure and mechanical properties of actin networks. Here we quantify the effect of the ABP scruin on actin networks by using imaging techniques, cosedimentation assays, multiparticle tracking, and bulk rheology. We show how the structure of the actin network is modified as the scruin concentration is varied, and we correlate these structural changes to variations in the resultant network elasticity.

Bending stiffness of a crystalline actin bundle.

The acrosomal process of the sperm of the horseshoe crab (Limulus polyphemus) is a unique crystalline actin bundle, consisting of multiple actin filaments cross-linked by the actin-bundling protein, scruin. For successful fertilization, the acrosomal bundle must penetrate through a 30 microm thick jelly coat surrounding the egg and thus it must be sufficiently stiff. Here, we present two measurements of the bending stiffness of a single crystalline bundle of actin. Results from these measurements indicate that the actin:scruin composite bundle has an average elastic modulus of 2 GPa, which is similar to that of a single actin filament, and a bending stiffness that is more than two orders of magnitude larger than that of a bundle of uncross-linked actin filaments due to stiffening by the scruin matrix.

Crack street: the cycloidal wake of a cylinder tearing through a thin sheet.

When a cylindrical tool cuts through a thin sheet of a relatively brittle material, it leaves behind a visually arresting crack street in its wake, reminiscent of a vortex street in the wake of a cylinder moving through a fluid. We show that simple geometrical arguments based on the interplay of in-plane stretching and out-of-plane bending suffice to explain the cycloidal morphology of the curved crack. The coupling between geometry and dynamics also allows us to explain the "stick-slip"-like behavior of tearing and suggests that these oscillations should occur generically in the brittle fracture of thin solid films.

Stored elastic energy powers the 60-microm extension of the Limulus polyphemus sperm actin bundle.

During the 5 s of the acrosome reaction of Limulus polyphemus sperm, a 60-microm-long bundle of scruin-decorated actin filaments straightens from a coiled conformation and extends from the cell. To identify the motive force for this movement, we examined the possible sources of chemical and mechanical energy and show that the coil releases approximately 10-13 J of stored mechanical strain energy, whereas chemical energy derived from calcium binding is approximately 10-15 J. These measurements indicate that the coiled actin bundle extends by a spring-based mechanism, which is distinctly different from the better known polymerization or myosin-driven processes, and that calcium initiates but does not power the reaction.

How aphids lose their marbles.

Insects provide examples of many cunning stratagems to cope with the challenges of living in a world dominated by surface forces. Despite being the current masters of the land environment, they are at constant risk of being entrapped in liquids, which they prevent by having waxy and hairy surfaces. The problem is particularly acute in an enclosed space, such as a plant gall. Using secreted wax to efficiently parcel and transport their own excrement, aphids were able to solve this problem 200 Myr ago. Here, we report on the physical and physiological significance of this ingenious solution. The secreted powdery wax has three distinct roles: (i) it is hydrophobic, (ii) it creates a microscopically rough inner gall surface made of weakly compacted wax needles making the gall ultra-hydrophobic, and (iii) it coats the honeydew droplets converting them into liquid marbles, that can be rapidly and efficiently moved.

Acetyllysine-binding and function of bromodomain-containing proteins in chromatin.

Acetylated histones are generally associated with active chromatin. The bromodomain has recently been identified as a protein module capable of binding to acetylated lysine residues, and hence is able to mediate the recruitment of factors to acetylated chromatin. Functional studies of bromodomain-containing proteins indicate how this domain contributes to the activity of a number of nuclear factors including histone acetyltransferases and chromatin remodelling complexes. Here, we review the characteristics of acetyllysine-binding by bromodomains, discuss associated domains found in these proteins, and address the function of the bromodomain in the context of chromatin. Finally, the modulation of bromodomain binding by neighbouring post-translational modifications within histone tails might provide a mechanism through which combinations of covalent marks could exert control on chromatin function.