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Biomedical subjects

G W Brodland

Publications and source records attributed to G W Brodland.

13 recordsLinked to original sources

Lamellipodium-driven tissue reshaping: a parametric study.

We recently showed that lamellipodia are able to generate forces of the right type to drive convergent extension (CE), an important class of tissue reshaping, in early stage embryos. The purpose of the present work is to quantify the mechanics of this process using parametric analyses. We use finite elements to implement a gamma-mu model in which a net interfacial tension gamma acts along each cell boundary and the cytoplasm exhibits an effective viscosity mu. The stress-strain characteristics of a rectangular patch of model tissue are investigated in terms of the rate r at which lamellipodia form and the relative strength q of their contractions. In tissues that are not constrained in-plane by adjacent tissues, the rate of tissue reshaping is proportional to r the rate of lamellipodium formation and its dependence on q is nonlinear and, near its expected value of 2 highly sensitive to q. Cell elongation, a central characteristic of CE, and stress is found to vary linearly with e the degree of kinematic restraint. Relevant "mechanical pathways" are also identified.

Animals↗

Do lamellipodia have the mechanical capacity to drive convergent extension?

Convergent extension (CE), a kinematic motif associated with several important morphogenetic movements in embryos, entails narrowing of a tissue in one in-plane direction and elongation in the other. Although the cell elongation and intercalation which accompany this process have been investigated and relevant genes and biochemical pathways have been studied in multiple organisms, a fundamental question that has not yet been answered is "Do the lamellipodia thought to drive these motions actually have the mechanical capacity to do so?" Here, we address this and a number of related issues using a state-of-the-art computational model which can replicate cell motions, changes in cell shape and tissue deformations. The model is based on the cell-level finite element approach of Chen and Brodland, but has additional features which allow it to model lamellipodium formation and contraction. In studying CE, computational models provide an important complement to molecular approaches because they reveal the "mechanical pathways" through which gene products must ultimately act in order to produce physical movements. The model shows that lamellipodia can drive CE, that they do so through cell intercalations and that the elongated cells characteristic of CE arise only when adjacent tissues resist convergence, a result which we confirm experimentally.

Ambystoma mexicanum↗

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.

Biomechanical Phenomena↗

The mechanics of heterotypic cell aggregates: insights from computer simulations.

Finite element-based computer simulations are used to investigate a number of phenomena, including tissue engulfment, cell sorting, and checkerboard-pattern formation, exhibited by heterotypic cell aggregates. The simulations show that these phenomena can be driven by a single equivalent force, namely a surface (or interfacial) tension, that results from cytoskeletal components and cell-cell adhesions. They also reveal that tissue engulfment, cell sorting, and checkerboard-pattern formation involve several discernible mechanical features or stages. With the aid of analytical arguments, we identify the conditions necessary for each of these phenomena. These findings are consistent with previous experimental investigations and computer simulations, but pose significant challenges to current theories of cell sorting and tissue engulfment.

Biomechanical Phenomena↗

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.

Algorithms↗

Furrowing surface contraction wave coincident with primary neural induction in amphibian embryos.

We predicted, and have now observed, a surface contraction wave in axolotl (Ambystoma mexicanum) embryos that appears to coincide temporally and spatially with primary neural induction and homoiogenetic induction, and with involution of the chordomesoderm. The wave starts from a focus anterior to the dorsal lip of the blastopore and spreads as an ellipse, until part of it encounters the rim of the blastopore and vanishes there. The remaining arc then continues over the dorsal hemisphere until it reforms an ellipse that decreases in size. About 9 to 12 hours after it begins, the wave vanishes at a focus diametrically opposite its point of origin. The wave involves both local contraction and furrowing in the monolayer ectoderm. To a good approximation, the hemispherical portion of the ectoderm traversed by the wave becomes neuroepithelium, while the ectoderm not traversed by the wave becomes epidermis. The wave might provide a mechanism to determine the time and location at which neuroepithelial differentiation occurs.

Ambystoma mexicanum↗

Embryonic tissue morphogenesis modeled by FEM.

A three-dimensional, large-strain finite element formulation for the simulation of morphogenetic behaviors in embryonic tissues is presented. It is used to investigate aspects of invagination, neural tube morphogenesis, contraction wave propagation and mechanical pattern formation. The simulations show that the spacing of patterns and the shapes produced by certain morphogenetic movements in epithelial sheets depend only slightly on the properties of the materials which underlie these sheets. Simulations of neural tube closure show that numerous, experimentally-observed features can be produced by contraction of apical microfilament bundles alone. That certain systems of forces are mechanically equivalent and that certain patterns of deformations are equivalent set practical limits on what can be inferred from the simulations.

Cell Differentiation↗

The cytoskeletal mechanics of brain morphogenesis. Cell state splitters cause primary neural induction.

There is a functional device in embryonic ectodermal cells that we propose causes them to differentiate into either neuroepithelial or epidermal tissue during the process called primary neural induction. We call this apparatus the "cell state splitter." Its main components are the apical microfilament ring and the coplanar apical mat of microtubules, which exert forces in opposite radial directions. We analyze the mechanical interaction between these cytoskeletal components and show that they are in an unstable mechanical equilibrium. The role of the cell state splitter is thus to create a mechanical instability corresponding to the embryonic state of "competence" in an otherwise mechanically stable cell. When the equilibrium of the cell state splitter is disturbed so as to produce a slight contraction of the apical end, apical contraction continues and the distinctive columnar neuroepithelial cells are produced. A slight expansion from the equilibrium state, on the other hand, results in flattened epidermal cells. The calculated forces are consistent with the known constitutive and force-generating properties and morphology of microfilaments and microtubules, and with free tubulin concentrations. There are no free parameters in the analysis. The first cells to assume the neuroepithelial state lie over the notochord. Propagation of the neuroepithelial state (homoiogenetic induction) then proceeds via stretch-induced constriction of the apical microfilament rings, until a hemisphere is covered, at which point the high rate of change of the meridional stress component necessary for further propagation vanishes. The remaining cells are stretched somewhat by this process and become epidermis. A sharp boundary between the tissues is thus formed (explaining "compartmentalization" and the binary nature of differentiation in general). Normal induction apparently involves setup of the cell state splitters in all of the ectoderm cells, perhaps synchronously timed by global embryo tension. The initial transition of cells from the ectodermal to the neuroepithelial state begins at the notoplate, where cell attachments to the notochord may both cause basal actin deposition and significantly reduce the stress induced in the ectoderm by the global tension, biasing the notoplate cell state splitters toward the neuroepithelial state. Introduction of an organizer or other solid substrate (artificial inducer) elsewhere, to which ectodermal cells can adhere, may likewise have both of these effects. Differentiation to either epidermis or neuroepithelium is thus a mechanical event followed by the synthesis of specific proteins.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

Gait reaction reconstruction and a heel strike algorithm.

A mathematical model of gait ground loading is presented. The model allows the ground reactions produced by any particular single- or multiple-footfall pattern to be constructed, given a sufficient variety of other measured ground reactions. An algorithm which uses center of vertical pressure data only to determine the instants of successive heel strikes on a large force plate is then presented. Experiments show the high accuracy of the heel strike algorithm and show that reconstructions of the vertical component of ground reactions are typically within 3% of corresponding measured reactions. The techniques presented allow certain problems associated with small force plates and other problems associated with large force plates to be largely overcome.

Algorithms↗

Cytoskeletal mechanics of neurulation: insights obtained from computer simulations.

The morphogenetic movements associated with the process of neurulation have been the subject of much investigation during the last one hundred years. A plethora of experimental evidence has been generated regarding the forces that drive this seemingly simple process, and many theories about the mechanics of the process have been proposed. Recent computer simulations have proved useful for evaluating these theories from a mechanical perspective. In this work, computer simulations are used to investigate several theories about the forces that drive neurulation. A simplified version of a formulation previously presented by the authors provides the mathematical foundation for these simulations. The simulations confirm that forces generated by circumferential microfilament bundles (CMB's) in conjunction with notochord forces can produce the rolling motions characteristic of amphibian neurulation. They also support the notion that redundancies exist in the systems of forces available to drive neurulation shape changes. The shape changes that occur following a variety of surgical and teratogenic interventions are also simulated. These simulations corroborate the role of circumferential microfilament bundles as a primary force generator.

Computer Simulation↗