Benjamen A. Filas

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.

Optical coherence tomography as a tool for measuring morphogenetic deformation of the looping heart

Optical coherence tomography (OCT) was used to investigate morphogenesis of the embryonic chick heart during the first phase of looping (c‐looping), as the heart bends and twists into a c‐shaped tube. The present study focuses on the morphomechanical effects of the splanchnopleure (SPL), a membrane that has been shown to play a major role in cardiac torsion by pressing against the ventral surface of the heart. Without the SPL, rightward torsion (rotation) is delayed. The images show that compressive forces exerted by the SPL alter the shapes of the heart tube and primitive atria, as well as their spatial relationships. The SPL normally holds the heart in the plane of the embryo and forces cardiac jelly (CJ) out of adjacent regions in the atria. When the SPL is removed, cross‐sections become more circular, CJ is more uniformly distributed, and the heart displaces ventrally. In addition, OCT‐based morphogenetic strain maps were measured during looping by tracking the three‐dimensional motions of microspheres placed on the myocardium. The spatial–temporal patterns of the strains correlated well with the observed behavior of the heart, including delayed torsion that occurs in SPL‐lacking embryos. These results illustrate the potential of OCT as a tool in studies of morphogenesis, as well as provide a better understanding of the mechanical forces that drive cardiac looping. Anat Rec, 290:1057–1068, 2007.

On Modeling Morphogenesis of the Looping Heart Following Mechanical Perturbations

Looping is a crucial early phase during heart development, as the initially straight heart tube (HT) deforms into a curved tube to lay out the basic plan of the mature heart. This paper focuses on the first phase of looping, called c-looping, when the HT bends ventrally and twists dextrally (rightward) to create a c-shaped tube. Previous research has shown that bending is an intrinsic process, while dextral torsion is likely caused by external forces acting on the heart. However, the specific mechanisms that drive and regulate looping are not yet completely understood. Here, we present new experimental data and finite element models to help define these mechanisms for the torsional component of c-looping. First, with regions of growth and contraction specified according to experiments on chick embryos, a three-dimensional model exhibits morphogenetic deformation consistent with observations for normal looping. Next, the model is tested further using experiments in which looping is perturbed by removing structures that exert forces on the heart--a membrane (splanchnopleure (SPL)) that presses against the ventral surface of the heart and the left and right primitive atria. In all cases, the model predicts the correct qualitative behavior. Finally, a two-dimensional model of the HT cross section is used to study a feedback mechanism for stress-based regulation of looping. The model is tested using experiments in which the SPL is removed before, during, and after c-looping. In each simulation, the model predicts the correct response. Hence, these models provide new insight into the mechanical mechanisms that drive and regulate cardiac looping.

A New Method for Measuring Deformation of Folding Surfaces During Morphogenesis

During morphogenesis, epithelia (cell sheets) undergo complex deformations as they stretch, bend, and twist to form the embryo. Often these changes in shape create multivalued surfaces that can be problematic for strain measurements. This paper presents a method for quantifying deformation of such surfaces. The method requires four-dimensional spatiotemporal coordinates of a finite number of surface markers, acquired using standard imaging techniques. From the coordinates of the markers, various deformation measures are computed as functions of time and space using straightforward matrix algebra. This method accommodates sparse randomly scattered marker arrays, with reasonable errors in marker locations. The accuracy of the method is examined for some sample problems with exact solutions. Then, the utility of the method is illustrated by using it to measure surface stretch ratios and shear in the looping heart and developing brain of the early chick embryo. In these examples, microspheres are tracked using optical coherence tomography. This technique provides a new tool that can be used in studies of the mechanics of morphogenesis.

Enzymatic degradation identifies components responsible for the structural properties of the vitreous body.

PURPOSE Vitreous degeneration contributes to several age-related eye diseases, including retinal detachment, macular hole, macular traction syndrome, and nuclear cataracts. Remarkably little is understood about the molecular interactions responsible for maintaining vitreous structure. The purpose of this study was to measure the structural properties of the vitreous body after enzymatic degradation of selected macromolecules. METHODS Mechanical properties of plugs of bovine and porcine vitreous were analyzed using a rheometer. Oscillatory and extensional tests measured vitreous stiffness and adhesivity, respectively. Major structural components of the vitreous were degraded by incubation overnight in collagenase, trypsin, or hyaluronidase, singly or in combination. Vitreous bodies were also incubated in hyper- or hypotonic saline. Effects of these treatments on the mechanical properties of the vitreous were measured by rheometry. RESULTS Enzymatic digestion of each class of macromolecules decreased the stiffness of bovine vitreous by approximately half (P < 0.05). Differential effects were observed on the damping capacity of the vitreous (P < 0.05), which was shown to correlate with material behavior in extension (P < 0.01). Digestion of hyaluronan significantly decreased the damping capacity of the vitreous and increased adhesivity. Collagen degradation resulted in the opposite effect, whereas digestion of proteins and proteoglycans with trypsin did not alter behavior relative to controls. Osmotic perturbations and double-enzyme treatments further implicated hyaluronan and hyaluronan-associated water as a primary regulator of adhesivity and material behavior in extension. CONCLUSIONS Collagen, hyaluronan, and proteoglycans act synergistically to maintain vitreous stiffness. Hyaluronan is a key mediator of vitreous adhesivity, and mechanical damping is an important factor influencing dynamic vitreous behavior.

Regional differences in actomyosin contraction shape the primary vesicles in the embryonic chicken brain

In the early embryo, the brain initially forms as a relatively straight, cylindrical epithelial tube composed of neural stem cells. The brain tube then divides into three primary vesicles (forebrain, midbrain, hindbrain), as well as a series of bulges (rhombomeres) in the hindbrain. The boundaries between these subdivisions have been well studied as regions of differential gene expression, but the morphogenetic mechanisms that generate these constrictions are not well understood. Here, we show that regional variations in actomyosin-based contractility play a major role in vesicle formation in the embryonic chicken brain. In particular, boundaries did not form in brains exposed to the nonmuscle myosin II inhibitor blebbistatin, whereas increasing contractile force using calyculin or ATP deepened boundaries considerably. Tissue staining showed that contraction likely occurs at the inner part of the wall, as F-actin and phosphorylated myosin are concentrated at the apical side. However, relatively little actin and myosin was found in rhombomere boundaries. To determine the specific physical mechanisms that drive vesicle formation, we developed a finite-element model for the brain tube. Regional apical contraction was simulated in the model, with contractile anisotropy and strength estimated from contractile protein distributions and measurements of cell shapes. The model shows that a combination of circumferential contraction in the boundary regions and relatively isotropic contraction between boundaries can generate realistic morphologies for the primary vesicles. In contrast, rhombomere formation likely involves longitudinal contraction between boundaries. Further simulations suggest that these different mechanisms are dictated by regional differences in initial morphology and the need to withstand cerebrospinal fluid pressure. This study provides a new understanding of early brain morphogenesis.

Mechanical Stress as a Regulator of Cytoskeletal Contractility and Nuclear Shape in Embryonic Epithelia

The mechano-sensitive responses of the heart and brain were examined in the chick embryo during Hamburger and Hamilton stages 10–12. During these early stages of development, cells in these structures are organized into epithelia. Isolated hearts and brains were compressed by controlled amounts of surface tension (ST) at the surface of the sample, and microindentation was used to measure tissue stiffness following several hours of culture. The response of both organs was qualitatively similar, as they stiffened under reduced loading. With increased loading, however, the brain softened while heart stiffness was similar to controls. In the brain, changes in nuclear shape and morphology correlated with these responses, as nuclei became more elliptical with decreased loading and rounder with increased loading. Exposure to the myosin inhibitor blebbistatin indicated that these changes in stiffness and nuclear shape are likely caused by altered cytoskeletal contraction. Computational modeling suggests that this behavior tends to return peak tissue stress back toward the levels it has in the intact heart and brain. These results suggest that developing cardiac and neural epithelia respond similarly to changes in applied loads by altering contractility in ways that tend to restore the original mechanical stress state. Hence, this study supports the view that stress-based mechanical feedback plays a role in regulating epithelial development.

Computational Model for Oxygen Transport and Consumption in Human Vitreous

PURPOSE Previous studies that measured liquefaction and oxygen content in human vitreous suggested that exposure of the lens to excess oxygen causes nuclear cataracts. Here, we developed a computational model that reproduced available experimental oxygen distributions for intact and degraded human vitreous in physiologic and environmentally perturbed conditions. After validation, the model was used to estimate how age-related changes in vitreous physiology and structure alter oxygen levels at the lens. METHODS A finite-element model for oxygen transport and consumption in the human vitreous was created. Major inputs included ascorbate-mediated oxygen consumption in the vitreous, consumption at the posterior lens surface, and inflow from the retinal vasculature. Concentration-dependent relations were determined from experimental human data or estimated from animal studies, with the impact of all assumptions explored via parameter studies. RESULTS The model reproduced experimental data in humans, including oxygen partial pressure (Po2) gradients (≈15 mm Hg) across the anterior-posterior extent of the vitreous body, higher oxygen levels at the pars plana relative to the vitreous core, increases in Po2 near the lens after cataract surgery, and equilibration in the vitreous chamber following vitrectomy. Loss of the antioxidative capacity of ascorbate increases oxygen levels 3-fold at the lens surface. Homogeneous vitreous degeneration (liquefaction), but not partial posterior vitreous detachment, greatly increases oxygen exposure to the lens. CONCLUSIONS Ascorbate content and the structure of the vitreous gel are critical determinants of lens oxygen exposure. Minimally invasive surgery and restoration of vitreous structure warrant further attention as strategies for preventing nuclear cataracts.

A potential role for differential contractility in early brain development and evolution

Differences in brain structure between species have long fascinated evolutionary biologists. Understanding how these differences arise requires knowing how they are generated in the embryo. Growing evidence in the field of evolutionary developmental biology (evo-devo) suggests that morphological differences between species result largely from changes in the spatiotemporal regulation of gene expression during development. Corresponding changes in functional cellular behaviors (morphogenetic mechanisms) are only beginning to be explored, however. Here we show that spatiotemporal patterns of tissue contractility are sufficient to explain differences in morphology of the early embryonic brain between disparate species. We found that enhancing cytoskeletal contraction in the embryonic chick brain with calyculin A alters the distribution of contractile proteins on the apical side of the neuroepithelium and changes relatively round cross-sections of the tubular brain into shapes resembling triangles, diamonds, and narrow slits. These perturbed shapes, as well as overall brain morphology, are remarkably similar to those of corresponding sections normally found in species such as zebrafish and Xenopus laevis (frog). Tissue staining revealed relatively strong concentration of F-actin at vertices of hyper-contracted cross-sections, and a finite element model shows that local contraction in these regions can convert circular sections into the observed shapes. Another model suggests that these variations in contractility depend on the initial geometry of the brain tube, as localized contraction may be needed to open the initially closed lumen in normal zebrafish and Xenopus brains, whereas this contractile machinery is not necessary in chick brains, which are already open when first created. We conclude that interspecies differences in cytoskeletal contraction may play a larger role in generating differences in morphology, and at much earlier developmental stages, in the brain than previously appreciated. This study is a step toward uncovering the underlying morphomechanical mechanisms that regulate how neural phenotypic differences arise between species.

Negative and positive auto-regulation of BMP expression in early eye development

Previous results have shown that Bone Morphogenetic Protein (BMP) signaling is essential for lens specification and differentiation. How BMP signals are regulated in the prospective lens ectoderm is not well defined. To address this issue we have modulated BMP activity in a chicken embryo pre-lens ectoderm explant assay, and also studied transgenic mice, in which the type I BMP receptors, Bmpr1a and Acvr1, are deleted from the prospective lens ectoderm. Our results show that chicken embryo pre-lens ectoderm cells express BMPs and require BMP signaling for lens specification in vitro, and that in vivo inhibition of BMP signals in the mouse prospective lens ectoderm interrupts lens placode formation and prevents lens invagination. Furthermore, our results provide evidence that BMP expression is negatively auto-regulated in the lens-forming ectoderm, decreasing when the tissue is exposed to exogenous BMPs and increasing when BMP signaling is prevented. In addition, eyes lacking BMP receptors in the prospective lens placode develop coloboma in the adjacent wild type optic cup. In these eyes, Bmp7 expression increases in the ventral optic cup and the normal dorsal-ventral gradient of BMP signaling in the optic cup is disrupted. Pax2 becomes undetectable and expression of Sfrp2 increases in the ventral optic cup, suggesting that increased BMP signaling alter their expression, resulting in failure to close the optic fissure. In summary, our results suggest that negative and positive auto-regulation of BMP expression is important to regulate early eye development.