Interplay of mechanical deformation and patterned gene expression in developing embryos

Phyllotaxis as an example of the symbiosis of mechanical forces and biochemical processes in living tissue

Phyllotaxis, the arrangement of a plant's phylla (flowers, bracts, stickers) near its shoot apical meristem (SAM), has intrigued natural scientists for centuries. Even today, the reasons for the observed patterns and their special properties, the physical and chemical mechanisms which give rise to strikingly similar configurations in a wide variety of plants, the almost-constant golden divergence angle, the almost constant plastichrone ratio, the choices of parastichy numbers and the prevalence of Fibonacci sequences to which these numbers belong, are at best only partially understood. Our goals in this Addendum are: To give a brief overview of current thinking on possible mechanisms for primordia (the bumps on the plant surface which eventually mature into fully developed structures such as leaves or florets) formation and give a descriptive narrative of the mathematical models which encode various hypotheses.To emphasize the point that patterns, whether they be phyllotactic configurations on plant surfaces or convection cells on the sun's surface, are macroscopic objects whose behaviors are determined more by symmetries of the proposed model and less by microscopic details. Because of this, the identification of observations with the predications of a particular model can only be made with confidence when the match coincides over a range of circumstances and parameters.To discuss some of the key results of the proposed models and, in particular, introduce the prediction of a new and, in principle, measurable invariant in plant phyllotaxis.To introduce a new model of primordia formation which is more in keeping with the pictures and paradigms of Hofmeister,1 Snow & Snow,2 and Douady and Couder3,4 which see primordia as forming in a fairly narrow annular zone surrounding the plant's SAM separating a region of undifferentiated cells from a fully developed patterned state.To consider the challenge of phyllotaxis in the broader context of pattern formation in biological tissue which responds to both mechanical and biochemical processes.

Morphogenic machines evolve more rapidly than the signals that pattern them: lessons from amphibians

The induction of mesoderm and the patterning of its dorsal-ventral and anterior-posterior axes seems to be relatively conserved throughout the chordates, as do the morphogenic movements that produce a phylotypic stage embryo. What is not conserved is the initial embryonic architecture of the fertilized egg, and the specific cell behaviors used to drive mesoderm morphogenesis. How then do conserved patterning pathways adapt to diverse architectures and where do they diverge to direct the different cell behaviors used to shape the phylotypic body plan? Amphibians in particular, probably because of their broad range of reproductive strategies, show diverse embryonic architectures across their class and use diverse cell behaviors during their early morphogenesis, making them an interesting comparative group. We examine three examples from our work on amphibians that show variations in the use of cell behaviors to drive the morphogenesis of the same tissues. We also consider possible points where the conserved patterning pathways might diverge to produce different cell behaviors.

[Genes, forces and forms: mechanical aspects of prenatal craniofacial development]

Current knowledge of molecular signaling during craniofacial development is advancing rapidly. We know that cells can respond to mechanical stimuli by biochemical signaling. Thus, the link between mechanical stimuli and gene expression has become a new and important area of the morphological sciences. This field of research seems to be a revival of the old approach of developmental mechanics, which goes back to the embryologists His [36], Carey [13, 14], and Blechschmidt [5]. These researchers argued that forces play a fundamental role in tissue differentiation and morphogenesis. They understood morphogenesis as a closed system with living cells as the active part and biological, chemical, and physical laws as the rules. This review reports on linking mechanical aspects of developmental biology with the contemporary knowledge of tissue differentiation. We focus on the formation of cartilage (in relation to pressure), bone (in relation to shearing forces), and muscles (in relation to dilation forces). The cascade of molecules may be triggered by forces, which arise during physical cell and tissue interaction. Detailed morphological knowledge is mandatory to elucidate the exact location and timing of the regions where forces are exerted. Because this finding also holds true for the exact timing and location of signals, more 3D images of the developmental processes are required. Further research is also required to create methods for measuring forces within a tissue. The molecules whose presence and indispensability we are investigating appear to be mediators rather than creators of form.

Phyllotaxis: cooperation and competition between mechanical and biochemical processes

Current theories and models of the formation of phyllotactic patterns at plant apical meristems center on either transport of the growth hormone auxin or the mechanical buckling of the plant tunica. By deriving a continuum approximation of an existing discrete biochemical model and comparing it with a mechanical model, we show that the model partial differential equations are similar in form. The implications of this universality in the form of the equations on interpreting the results of simulations are discussed. We develop a combined model that incorporates the coupling of biochemistry and mechanics. The combined model is accessible to analysis by reduction to a set of ordinary differential equations for the amplitudes of shapes associated with both the auxin concentration field and plant surface deformation. Analysis of these amplitude equations reveals the parameter choices under which the two mechanisms may cooperate in determining the pattern, or under which one or the other mechanism may dominate.

Upregulation of forces and morphogenic asymmetries in dorsal closure during Drosophila development

Tissue dynamics during dorsal closure, a stage of Drosophila development, provide a model system for cell sheet morphogenesis and wound healing. Dorsal closure is characterized by complex cell sheet movements, driven by multiple tissue specific forces, which are coordinated in space, synchronized in time, and resilient to UV-laser perturbations. The mechanisms responsible for these attributes are not fully understood. We measured spatial, kinematic, and dynamic antero-posterior asymmetries to biophysically characterize both resiliency to laser perturbations and failure of closure in mutant embryos and compared them to natural asymmetries in unperturbed, wild-type closure. We quantified and mathematically modeled two processes that are upregulated to provide resiliency--contractility of the amnioserosa and formation of a seam between advancing epidermal sheets, i.e., zipping. Both processes are spatially removed from the laser-targeted site, indicating they are not a local response to laser-induced wounding and suggesting mechanosensitive and/or chemosensitive mechanisms for upregulation. In mutant embryos, tissue junctions initially fail at the anterior end indicating inhomogeneous mechanical stresses attributable to head involution, another developmental process that occurs concomitant with the end stages of closure. Asymmetries in these mutants are reversed compared to wild-type, and inhomogeneous stresses may cause asymmetries in wild-type closure.

Genes, forces, and forms: mechanical aspects of prenatal craniofacial development

Current knowledge of molecular signaling during craniofacial development is advancing rapidly. We know that cells can respond to mechanical stimuli by biochemical signaling. Thus, the link between mechanical stimuli and gene expression has become a new and important area of the morphological sciences. This field of research seems to be a revival of the old approach of developmental mechanics, which goes back to the embryologists His (1874), Carey (1920), and Blechschmidt (1948). These researchers argued that forces play a fundamental role in tissue differentiation and morphogenesis. They understood morphogenesis as a closed system with living cells as the active part and biological, chemical, and physical laws as the rules. This review reports on linking mechanical aspects of developmental biology with the contemporary knowledge of tissue differentiation. We focus on the formation of cartilage (in relation to pressure), bone (in relation to shearing forces), and muscles (in relation to dilation forces). The cascade of molecules may be triggered by forces, which arise during physical cell and tissue interaction. Detailed morphological knowledge is mandatory to elucidate the exact location and timing of the regions where forces are exerted. Because this finding also holds true for the exact timing and location of signals, more 3D images of the developmental processes are required. Further research is also required to create methods for measuring forces within a tissue. The molecules whose presence and indispensability we are investigating appear to be mediators rather than creators of form.

Morphogenetic adaptation of the looping embryonic heart to altered mechanical loads

The biophysical mechanisms that drive and regulate cardiac looping are not well understood, but mechanical forces likely play a central role. Previous studies have shown that cardiac torsion, which defines left-right directionality, is caused largely by forces exerted on the heart tube by a membrane called the splanchnopleure (SPL). Here we show that, when the SPL is removed from the embryonic chick heart, torsion is initially suppressed. Several hours later, however, normal torsion is restored. This delayed torsion coincides with increased myocardial stiffness, especially on the right side of the heart. Exposure to the myosin inhibitor Y-27632 suppressed both responses, suggesting that the delayed torsion is caused by an abnormal cytoskeletal contraction. This hypothesis is supported further by computational modeling. These results suggest that the looping embryonic heart has the ability to adapt to changes in the mechanical environment, which may play a regulatory role during morphogenesis.

Buckling of swelling gels

The patterns arising from the differential swelling of gels are investigated experimentally and theoretically as a model for the differential growth of living tissues. Two geometries are considered: a thin strip of soft gel clamped to a stiff gel, and a thin corona of soft gel clamped to a disk of stiff gel. When the structure is immersed in water, the soft gel swells and bends out of plane leading to a wavy periodic pattern whose wavelength is measured. The linear stability of the flat state is studied in the framework of linear elasticity using the equations for thin plates. The flat state is shown to become unstable to oscillations above a critical swelling rate and the computed wavelengths are in quantitative agreement with the experiment.

Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling

Vasculogenesis, the de novo growth of the primary vascular network from initially dispersed endothelial cells, is the first step in the development of the circulatory system in vertebrates. In the first stages of vasculogenesis, endothelial cells elongate and form a network-like structure, called the primary capillary plexus, which subsequently remodels, with the size of the vacancies between ribbons of endothelial cells coarsening over time. To isolate such intrinsic morphogenetic ability of endothelial cells from its regulation by long-range guidance cues and additional cell types, we use an in vitro model of human umbilical vein endothelial cells (HUVEC) in Matrigel. This quasi-two-dimensional endothelial cell culture model would most closely correspond to vasculogenesis in flat areas of the embryo like the yolk sac. Several studies have used continuum mathematical models to explore in vitro vasculogenesis: such models describe cell ensembles but ignore the endothelial cells' shapes and active surface fluctuations. While these models initially reproduce vascular-like morphologies, they eventually stabilize into a disconnected pattern of vascular "islands." Also, they fail to reproduce temporally correct network coarsening. Using a cell-centered computational model, we show that the endothelial cells' elongated shape is key to correct spatiotemporal in silico replication of stable vascular network growth. We validate our simulation results against HUVEC cultures using time-resolved image analysis and find that our simulations quantitatively reproduce in vitro vasculogenesis and subsequent in vitro remodeling.

A common biomechanical model for the formation of stationary cell domains and propagating waves in the developing organisms

Many important morphogenetic processes that take place in the development of an animal start from the segregation of a homogeneous layer of cells into a different number of the domains of columnar and flattened cells. In many cases, waves of cell shape transformation travel throughout embryonic tissues. A biomechanical model is presented which embraces both kinds of event. The model is based on the idea of interplay between short- and long-range factors. While the former promote the spreading of a given cell state along a cell row in the recalculation direction, long-range factors are associated with self-generated tensions which, after exceeding a certain threshold, induce active cell extension and hence the rise of tangential pressure. Different kinds of biologically realistic stationary structures, as well as various kinds of the running waves, can be modelled under different parameter values. Moreover, the current model can be coupled with the previous one (Beloussov and Grabovsky, Comput. Methods Biomech. Biomed. Eng., 6: 53-63 (2003)) permitting a common causal chain to be created, moving from the state of an initial homogeneous cell layer towards the complicated shapes of embryonic rudiments.

In vivo modulation of morphogenetic movements in Drosophila embryos with femtosecond laser pulses

The complex biomechanical events associated with embryo development are investigated in vivo, by using femtosecond laser pulse-induced ablation combined with multimodal nonlinear microscopy. We demonstrate controlled intravital ablations preserving local cytoskeleton dynamics and resulting in the modulation of specific morphogenetic movements in nonmutant Drosophila embryos. A quantitative description of complex movements is obtained both in GFP-expressing systems by using whole-embryo two-photon microscopy and in unlabeled nontransgenic embryos by using third harmonic generation microscopy. This methodology provides insight into the issue of mechano-sensitive gene expression by revealing the correlation of in vivo tissue deformation patterns with Twist protein expression in stomodeal cells at gastrulation.