Cytoskeletal mechanics of neurulation: insights obtained from computer simulations

Contraction and stress-dependent growth shape the forebrain of the early chicken embryo

During early vertebrate development, local constrictions, or sulci, form to divide the forebrain into the diencephalon, telencephalon, and optic vesicles. These partitions are maintained and exaggerated as the brain tube inflates, grows, and bends. Combining quantitative experiments on chick embryos with computational modeling, we investigated the biophysical mechanisms that drive these changes in brain shape. Chemical perturbations of contractility indicated that actomyosin contraction plays a major role in the creation of initial constrictions (Hamburger-Hamilton stages HH11-12), and fluorescent staining revealed that F-actin is circumferentially aligned at all constrictions. A finite element model based on these findings shows that the observed shape changes are consistent with circumferential contraction in these regions. To explain why sulci continue to deepen as the forebrain expands (HH12-20), we speculate that growth depends on wall stress. This idea was examined by including stress-dependent growth in a model with cerebrospinal fluid pressure and bending (cephalic flexure). The results given by the model agree with observed morphological changes that occur in the brain tube under normal and reduced eCSF pressure, quantitative measurements of relative sulcal depth versus time, and previously published patterns of cell proliferation. Taken together, our results support a biphasic mechanism for forebrain morphogenesis consisting of differential contractility (early) and stress-dependent growth (late).

Computational models for mechanics of morphogenesis

In the developing embryo, tissues differentiate, deform, and move in an orchestrated manner to generate various biological shapes driven by the complex interplay between genetic, epigenetic, and environmental factors. Mechanics plays a key role in regulating and controlling morphogenesis, and quantitative models help us understand how various mechanical forces combine to shape the embryo. Models allow for the quantitative, unbiased testing of physical mechanisms, and when used appropriately, can motivate new experimentaldirections. This knowledge benefits biomedical researchers who aim to prevent and treat congenital malformations, as well as engineers working to create replacement tissues in the laboratory. In this review, we first give an overview of fundamental mechanical theories for morphogenesis, and then focus on models for specific processes, including pattern formation, gastrulation, neurulation, organogenesis, and wound healing. The role of mechanical feedback in development is also discussed. Finally, some perspectives aregiven on the emerging challenges in morphomechanics and mechanobiology.

Unit operations of tissue development: epithelial folding

The development of multicellular organisms relies on a small set of construction techniques-assembly, sculpting, and folding-that are spatially and temporally regulated in a combinatorial manner to produce the diversity of tissues within the body. These basic processes are well conserved across tissue types and species at the level of both genes and mechanisms. Here we review the signaling, patterning, and biomechanical transformations that occur in two well-studied model systems of epithelial folding to illustrate both the complexity and modularity of tissue development. In particular, we discuss the possibility of a spatial code specifying morphogenesis. To decipher this code, engineers and scientists need to establish quantitative experimental systems and to develop models that address mechanisms at multiple levels of organization, from gene sequence to tissue biomechanics. In turn, quantitative models of embryogenesis can inspire novel methods for creating synthetic organs and treating degenerative tissue diseases.

From genes to neural tube defects (NTDs): insights from multiscale computational modeling

The morphogenetic movements, and the embryonic phenotypes they ultimately produce, are the consequence of a series of events that involve signaling pathways, cytoskeletal components, and cell- and tissue-level mechanical interactions. In order to better understand how these events work together in the context of amphibian neurulation, an existing multiscale computational model was augmented. Geometric data for this finite element-based mechanical model were obtained from 3D surface reconstructions of live axolotl embryos and serial sections of fixed specimens. Tissue mechanical properties were modeled using cell-based constitutive equations that include internal force generation and cell rearrangement, and equation parameters were adjusted manually to reflect biochemical changes including alterations in Shroom or the planar-cell-polarity pathway. The model indicates that neural tube defects can arise when convergent extension of the neural plate is reduced by as little as 20%, when it is eliminated on one side of the embryo, when neural ridge elevation is disrupted, when tension in the non-neural ectoderm is increased, or when the ectoderm thickness is increased. Where comparable conditions could be induced in Xenopus embryos, good agreement was found, an important step in model validation. The model reveals the neurulating embryo to be a finely tuned biomechanical system.

Theoretical study of Beloussov's hyper-restoration hypothesis for mechanical regulation of morphogenesis

Computational models were used to explore the idea that morphogenesis is regulated, in part, by feedback from mechanical stress according to Beloussov's hyper-restoration (HR) hypothesis. According to this hypothesis, active tissue responses to stress perturbations tend to restore, but overshoot, the original (target) stress. To capture this behavior, the rate of growth or contraction is assumed to depend on the difference between the current and target stresses. Stress overshoot is obtained by letting the target stress change at a rate proportional to the same stress difference. The feasibility of the HR hypothesis is illustrated by models for stretching of epithelia, cylindrical bending of plates, invagination of cylindrical and spherical shells, and early amphibian development. In each case, an initial perturbation leads to an active mechanical response that changes the form of the tissue. The results show that some morphogenetic processes can be entirely self-driven by HR responses once they are initiated (possibly by genetic activity). Other processes, however, may require secondary mechanisms or perturbations to proceed to completion.

Multiview Robotic Microscope Reveals the In-plane Kinematics of Amphibian Neurulation

A new robotic microscope system, called the Frogatron 3000, was developed to collect time-lapse images from arbitrary viewing angles over the surface of live embryos. Embryos are mounted at the center of a horizontal, fluid-filled, cylindrical glass chamber around which a camera with special optics traverses. To hold them at the center of the chamber and revolve them about a vertical axis, the embryos are placed on the end of a small vertical glass tube that is rotated under computer control. To demonstrate operation of the system, it was used to capture time-lapse images of developing axolotl (amphibian) embryos from 63 viewing angles during the process of neurulation and the in-plane kinematics of the epithelia visible at the center of each view was calculated. The motions of points on the surface of the embryo were determined by digital tracking of their natural surface texture, and a least-squares algorithm was developed to calculate the deformation-rate tensor from the motions of these surface points. Principal strain rates and directions were extracted from this tensor using decomposition and eigenvector techniques. The highest observed principal true strain rate was 28 +/- 5% per hour, along the midline of the neural plate during developmental stage 14, while the greatest contractile true strain rate was--35 +/- 5% per hour, normal to the embryo midline during stage 15.

Cell-level finite element studies of viscous cells in planar aggregates

A new cell-level finite element formulation is presented and used to investigate how epithelia and other planar collections of viscous cells might deform during events such as embryo morphogenesis and wound healing. Forces arising from cytoskeletal components, cytoplasm viscosity, and cell-cell adhesions are included. Individual cells are modeled using multiple finite elements, and cell rearrangements can occur. Simulations of cell-sheet stretching indicate that the initial stages of sheet stretching are characterized by changes in cell shape, while subsequent stages are governed by cell rearrangement. Inferences can be made from the simulations about the forces that act in real cell sheets when suitable experimental data are available.

Three-dimensional reconstruction of live embryos using robotic macroscope images

To determine the three-dimensional (3-D) shape of a live embryo is a technically challenging task. We show that reconstructions of live embryos can be done by collecting images from different viewing angles using a robotic macroscope, establishing point correspondences between these views by block matching, and using a new 3-D reconstruction algorithm that accommodates camera positioning errors. The algorithm assumes that the images are orthographic projections of the object and that the camera scaling factors are known. Point positions and camera errors are found simultaneously. Reconstructions of test objects and embryos show that meaningful reconstructions are possible only when camera positioning and alignment errors are accommodated since these errors can be substantial. Reconstructions of early-stage axolotl embryos were made from sets of 33 images. In a typical reconstruction, 781 points, each visible in at least three different views, were used to form 1511 triangles to represent the embryo surface. The resulting reconstruction had a mean radius of error of 0.27 pixels (1.1 microns). Mathematical properties of the reconstruction algorithm are identified and discussed.