Myosin waves and a mechanical asymmetry guide the oscillatory migration of Drosophila cardiac progenitors.

Heart development begins with the formation of a tube as cardiac progenitors migrate from opposite sides of the embryo. Abnormal cardiac progenitor movements cause congenital heart defects. However, the mechanisms of cell migration during early heart development remain poorly understood. Using quantitative microscopy, we found that in Drosophila embryos, cardiac progenitors (cardioblasts) migrated through a sequence of forward and backward steps. Cardioblast steps were associated with oscillatory non-muscle myosin II waves that induced periodic shape changes and were necessary for timely heart tube formation. Mathematical modeling predicted that forward cardioblast migration required a stiff boundary at the trailing edge. Consistent with this, we found a supracellular actin cable at the trailing edge of the cardioblasts that limited the amplitude of the backward steps, thus biasing the direction of cell movement. Our results indicate that periodic shape changes coupled with a polarized actin cable produce asymmetrical forces that promote cardioblast migration.

PyJAMAS: open-source, multimodal segmentation and analysis of microscopy images.

SUMMARY: Our increasing ability to resolve fine details using light microscopy is matched by an increasing need to quantify images in order to detect and measure phenotypes. Despite their central role in cell biology, many image analysis tools require a financial investment, are released as proprietary software, or are implemented in languages not friendly for beginners, and thus are used as black boxes. To overcome these limitations, we have developed PyJAMAS, an open-source tool for image processing and analysis written in Python. PyJAMAS provides a variety of segmentation tools, including watershed and machine learning-based methods; takes advantage of Jupyter notebooks for the display and reproducibility of data analyses; and can be used through a cross-platform graphical user interface or as part of Python scripts via a comprehensive application programming interface. AVAILABILITY AND IMPLEMENTATION: PyJAMAS is open-source and available at https://bitbucket.org/rfg_lab/pyjamas. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

3D viscoelastic drag forces contribute to cell shape changes during organogenesis in the zebrafish embryo.

The left-right organizer in zebrafish embryos, Kupffer's Vesicle (KV), is a simple organ that undergoes programmed asymmetric cell shape changes that are necessary to establish the left-right axis of the embryo. We use simulations and experiments to investigate whether 3D mechanical drag forces generated by the posteriorly-directed motion of the KV through the tailbud tissue are sufficient to drive such shape changes. We develop a fully 3D vertex-like (Voronoi) model for the tissue architecture, and demonstrate that the tissue can generate drag forces and drive cell shape changes. Furthermore, we find that tailbud tissue presents a shear-thinning, viscoelastic behavior consistent with those observed in published experiments. We then perform live imaging experiments and particle image velocimetry analysis to quantify the precise tissue velocity gradients around KV as a function of developmental time. We observe robust velocity gradients around the KV, indicating that mechanical drag forces must be exerted on the KV by the tailbud tissue. We demonstrate that experimentally observed velocity fields are consistent with the viscoelastic response seen in simulations. This work also suggests that 3D viscoelastic drag forces could be a generic mechanism for cell shape change in other biological processes.

Myosin cables control the timing of tissue internalization in the Drosophila embryo.

Compartment boundaries prevent cell mixing during animal development. In the early Drosophila embryo, the mesectoderm is a group of glial precursors that separate ectoderm and mesoderm, forming the ventral midline. Mesectoderm cells undergo one round of oriented divisions during axis elongation and are eventually internalized 6 h later. Using spinning disk confocal microscopy and image analysis, we found that after dividing, mesectoderm cells reversed their planar polarity. The polarity factor Bazooka was redistributed to mesectoderm-mesectoderm cell interfaces, and the molecular motor non-muscle Myosin II and its upstream activator Rho-kinase (Rok) accumulated at mesectoderm-ectoderm (ME) interfaces, forming supracellular cables flanking the mesectoderm on either side of the tissue. Laser ablation revealed the presence of increased tension at ME cables, where Myosin was stabilized, as shown by fluorescence recovery after photobleaching. We used laser nanosurgery to reduce tension at the ME boundary, and we found that Myosin fluorescence decreased rapidly, suggesting a role for tension in ME boundary maintenance. Mathematical modelling predicted that increased tension at the ME boundary was necessary to prevent the premature establishment of contacts between the two ectodermal sheets on opposite sides of the mesectoderm, thus controlling the timing of mesectoderm internalization. We validated the model in vivo: Myosin inhibition disrupted the linearity of the ME boundary and resulted in early internalization of the mesectoderm. Our results suggest that the redistribution of Rok polarizes Myosin and Bazooka within the mesectoderm to establish tissue boundaries, and that ME boundaries control the timely internalization of the mesectoderm as embryos develop.

Effect of cellular rearrangement time delays on the rheology of vertex models for confluent tissues.

Large-scale tissue deformation during biological processes such as morphogenesis requires cellular rearrangements. The simplest rearrangement in confluent cellular monolayers involves neighbor exchanges among four cells, called a T1 transition, in analogy to foams. But unlike foams, cells must execute a sequence of molecular processes, such as endocytosis of adhesion molecules, to complete a T1 transition. Such processes could take a long time compared to other timescales in the tissue. In this work, we incorporate this idea by augmenting vertex models to require a fixed, finite time for T1 transitions, which we call the "T1 delay time". We study how variations in T1 delay time affect tissue mechanics, by quantifying the relaxation time of tissues in the presence of T1 delays and comparing that to the cell-shape based timescale that characterizes fluidity in the absence of any T1 delays. We show that the molecular-scale T1 delay timescale dominates over the cell shape-scale collective response timescale when the T1 delay time is the larger of the two. We extend this analysis to tissues that become anisotropic under convergent extension, finding similar results. Moreover, we find that increasing the T1 delay time increases the percentage of higher-fold coordinated vertices and rosettes, and decreases the overall number of successful T1s, contributing to a more elastic-like-and less fluid-like-tissue response. Our work suggests that molecular mechanisms that act as a brake on T1 transitions could stiffen global tissue mechanics and enhance rosette formation during morphogenesis.

The Cell Adaptation Time Sets a Minimum Length Scale for Patterned Substrates.

The structure and dynamics of tissue cultures depend strongly on the physical and chemical properties of the underlying substrate. Inspired by previous advances in the context of inorganic materials, the use of patterned culture surfaces has been proposed as an effective way to induce space-dependent properties in cell tissues. However, cells move and diffuse, and the transduction of external stimuli to biological signals is not instantaneous. Here, we show that the fidelity of patterns to demix tissue cells depends on the relation between the diffusion (τD) and adaptation (τ) times. Numerical results for the self-propelled Voronoi model reveal that the fidelity decreases with τ/τD, a result that is reproduced by a continuum reaction-diffusion model. Based on recent experimental results for single cells, we derive a minimal length scale for the patterns in the substrate that depends on τ/τD and can be much larger than the cell size.

Anisotropy links cell shapes to tissue flow during convergent extension.

Within developing embryos, tissues flow and reorganize dramatically on timescales as short as minutes. This includes epithelial tissues, which often narrow and elongate in convergent extension movements due to anisotropies in external forces or in internal cell-generated forces. However, the mechanisms that allow or prevent tissue reorganization, especially in the presence of strongly anisotropic forces, remain unclear. We study this question in the converging and extending Drosophila germband epithelium, which displays planar-polarized myosin II and experiences anisotropic forces from neighboring tissues. We show that, in contrast to isotropic tissues, cell shape alone is not sufficient to predict the onset of rapid cell rearrangement. From theoretical considerations and vertex model simulations, we predict that in anisotropic tissues, two experimentally accessible metrics of cell patterns-the cell shape index and a cell alignment index-are required to determine whether an anisotropic tissue is in a solid-like or fluid-like state. We show that changes in cell shape and alignment over time in the Drosophila germband predict the onset of rapid cell rearrangement in both wild-type and snail twist mutant embryos, where our theoretical prediction is further improved when we also account for cell packing disorder. These findings suggest that convergent extension is associated with a transition to more fluid-like tissue behavior, which may help accommodate tissue-shape changes during rapid developmental events.

Linear and nonlinear mechanical responses can be quite different in models for biological tissues.

The fluidity of biological tissues - whether cells can change neighbors and rearrange - is important for their function. In traditional materials, researchers have used linear response functions, such as the shear modulus, to accurately predict whether a material will behave as a fluid. Similarly, in disordered 2D vertex models for confluent biological tissues, the shear modulus becomes zero precisely when the cells can change neighbors and the tissue fluidizes, at a critical value of control parameter s0* = 3.81. However, the ordered ground states of 2D vertex models become linearly unstable at a lower value of control parameter (3.72), suggesting that there may be a decoupling between linear and nonlinear response. We demonstrate that the linear response does not correctly predict the nonlinear behavior in these systems: when the control parameter is between 3.72 and 3.81, cells cannot freely change neighbors even though the shear modulus is zero. These results highlight that the linear response of vertex models should not be expected to generically predict their rheology. We develop a simple geometric ansatz that correctly predicts the nonlinear response, which may serve as a framework for making nonlinear predictions in other vertex-like models.

Tissue Flow Induces Cell Shape Changes During Organogenesis.

In embryonic development, cell shape changes are essential for building functional organs, but in many cases, the mechanisms that precisely regulate these changes remain unknown. We propose that fluid-like drag forces generated by the motion of an organ through surrounding tissue could generate changes to its structure that are important for its function. To test this hypothesis, we study the zebrafish left-right organizer, Kupffer's vesicle (KV), using experiments and mathematical modeling. During development, monociliated cells that comprise KV undergo region-specific shape changes along the anterior-posterior axis that are critical for KV function: anterior cells become long and thin, whereas posterior cells become short and squat. Here, we develop a mathematical vertex-like model for cell shapes that incorporates both tissue rheology and cell motility and constrain the model parameters using previously published rheological data for the zebrafish tailbud as well as our own measurements of the KV speed. We find that drag forces due to dynamics of cells surrounding KV could be sufficient or work in concert with previously identified mechanisms to drive KV cell shape changes during KV development. More broadly, these results suggest that cell shape changes during embryonic development and beyond could be driven by dynamic forces not typically considered in models or experiments.

The effect of RNA stiffness on the self-assembly of virus particles.

Under many in vitro conditions, some small viruses spontaneously encapsidate a single stranded (ss) RNA into a protein shell called the capsid. While viral RNAs are found to be compact and highly branched because of long distance base-pairing between nucleotides, recent experiments reveal that in a head-to-head competition between an ssRNA with no secondary or higher order structure and a viral RNA, the capsid proteins preferentially encapsulate the linear polymer! In this paper, we study the impact of genome stiffness on the encapsidation free energy of the complex of RNA and capsid proteins. We show that an increase in effective chain stiffness because of base-pairing could be the reason why under certain conditions linear chains have an advantage over branched chains when it comes to encapsidation efficiency. While branching makes the genome more compact, RNA base-pairing increases the effective Kuhn length of the RNA molecule, which could result in an increase of the free energy of RNA confinement, that is, the work required to encapsidate RNA, and thus less efficient packaging.

RNA Base Pairing Determines the Conformations of RNA Inside Spherical Viruses.

Many simple RNA viruses enclose their genetic material by a protein shell called the capsid. While the capsid structures are well characterized for most viruses, the structure of RNA inside the shells and the factors contributing to it remain poorly understood. We study the impact of base pairing on the conformations of RNA and find that it undergoes a swollen coil to globule continuous transition as a function of the strength of the pairing interaction. We also observe a first order transition and kink profile as a function of RNA length. All these transitions could explain the different RNA profiles observed inside viral shells.

Impact of a nonuniform charge distribution on virus assembly.

Many spherical viruses encapsulate their genomes in protein shells with icosahedral symmetry. This process is spontaneous and driven by electrostatic interactions between positive domains on the virus coat proteins and the negative genomes. We model the effect of the nonuniform icosahedral charge distribution from the protein shell instead using a mean-field theory. We find that this nonuniform charge distribution strongly affects the optimal genome length and that it can explain the experimentally observed phenomenon of overcharging of virus and viruslike particles.

In vitro protease cleavage and computer simulations reveal the HIV-1 capsid maturation pathway.

HIV-1 virions assemble as immature particles containing Gag polyproteins that are processed by the viral protease into individual components, resulting in the formation of mature infectious particles. There are two competing models for the process of forming the mature HIV-1 core: the disassembly and de novo reassembly model and the non-diffusional displacive model. To study the maturation pathway, we simulate HIV-1 maturation in vitro by digesting immature particles and assembled virus-like particles with recombinant HIV-1 protease and monitor the process with biochemical assays and cryoEM structural analysis in parallel. Processing of Gag in vitro is accurate and efficient and results in both soluble capsid protein and conical or tubular capsid assemblies, seemingly converted from immature Gag particles. Computer simulations further reveal probable assembly pathways of HIV-1 capsid formation. Combining the experimental data and computer simulations, our results suggest a sequential combination of both displacive and disassembly/reassembly processes for HIV-1 maturation.

Effects of RNA branching on the electrostatic stabilization of viruses.

Many single-stranded (ss) ribonucleic acid (RNA) viruses self-assemble from capsid protein subunits and the nucleic acid to form an infectious virion. It is believed that the electrostatic interactions between the negatively charged RNA and the positively charged viral capsid proteins drive the encapsidation, although there is growing evidence that the sequence of the viral RNA also plays a role in packaging. In particular, the sequence will determine the possible secondary structures that the ssRNA will take in solution. In this work, we use a mean-field theory to investigate how the secondary structure of the RNA combined with electrostatic interactions affects the efficiency of assembly and stability of the assembled virions. We show that the secondary structure of RNA may result in negative osmotic pressures while a linear polymer causes positive osmotic pressures for the same conditions. This may suggest that the branched structure makes the RNA more effectively packaged and the virion more stable.

Functional analysis of the N-terminal basic motif of a eukaryotic satellite RNA virus capsid protein in replication and packaging.

Efficient replication and assembly of virus particles are integral to the establishment of infection. In addition to the primary role of the capsid protein (CP) in encapsidating the RNA progeny, experimental evidence on positive sense single-stranded RNA viruses suggests that the CP also regulates RNA synthesis. Here, we demonstrate that replication of Satellite tobacco mosaic virus (STMV) is controlled by the cooperative interaction between STMV CP and the helper virus (HV) Tobacco mosaic virus (TMV) replicase. We identified that the STMV CP-HV replicase interaction requires a positively charged residue at the third position (3R) in the N-terminal 13 amino acid (aa) motif. Far-Northwestern blotting showed that STMV CP promotes binding between HV-replicase and STMV RNA. An STMV CP variant having an arginine to alanine substitution at position 3 in the N-terminal 13aa motif abolished replicase-CP binding. The N-terminal 13aa motif of the CP bearing alanine substitutions for positively charged residues located at positions 5, 7, 10 and 11 are defective in packaging full-length STMV, but can package a truncated STMV RNA lacking the 3' terminal 150 nt region. These findings provide insights into the mechanism underlying the regulation of STMV replication and packaging.

Role of Genome in the Formation of Conical Retroviral Shells.

Human immunodeficiency virus (HIV) capsid proteins spontaneously assemble around the genome into a protective protein shell called the capsid, which can take on a variety of shapes broadly classified as conical, cylindrical, and irregular. The majority of capsids seen in in vivo studies are conical in shape, while in vitro experiments have shown a preference for cylindrical capsids. The factors involved in the selection of the unique shape of HIV capsids are not well understood, and in particular the impact of RNA on the formation of the capsid is not known. In this work, we study the role of the genome and its interaction with the capsid protein by modeling the genomic RNA through a mean-field theory. Our results show that the confinement free energy for a homopolymeric model genome confined in a conical capsid is lower than that in a cylindrical capsid, at least when the genome does not interact with the capsid, which seems to be the case in in vivo experiments. Conversely, the confinement free energy for the cylinder is lower than that for a conical capsid if the genome is attracted to the capsid proteins as the in vitro experiments. Understanding the factors that contribute to the formation of conical capsids may shed light on the infectivity of HIV particles.

Adsorption of annealed branched polymers on curved surfaces.

The behavior of annealed branched polymers near adsorbing surfaces plays a fundamental role in many biological and industrial processes. Most importantly single stranded RNA in solution tends to fold up and self-bind to form a highly branched structure. Using a mean field theory, we both perturbatively and numerically examine the adsorption of branched polymers on surfaces of several different geometries in a good solvent. Independent of the geometry of the wall, we observe that as branching density increases, surface tension decreases. However, we find a coupling between the branching density and curvature in that a further lowering of surface tension occurs when the wall curves towards the polymer, but the amount of lowering of surface tension decreases when the wall curves away from the polymer. We find that for branched polymers confined into spherical cavities, most of branch-points are located in the vicinity of the interior wall and the surface tension is minimized for a critical cavity radius. For branch polymers next to sinusoidal surfaces, we find that branch-points accumulate at the valleys while end-points on the peaks.

RNA topology remolds electrostatic stabilization of viruses.

Simple RNA viruses efficiently encapsulate their genome into a nano-sized protein shell: the capsid. Spontaneous coassembly of the genome and the capsid proteins is driven predominantly by electrostatic interactions between the negatively charged RNA and the positively charged inner capsid wall. Using field theoretic formulation we show that the inherently branched RNA secondary structure allows viruses to maximize the amount of encapsulated genome and make assembly more efficient, allowing viral RNAs to out-compete cellular RNAs during replication in infected host cells.