Chapter

The Interplay of Active Forces and Passive Mechanical Stresses in Animal Morphogenesis

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Abstract

Both for an experienced and for a naive observer the development of a living sample, be it plant or animal, looks, first of all, as a regular succession of complicated changes in the shapes and mutual arrangement of its parts; such a succession is usually defined as a morphogenesis while its components as morphogenetic processes. Invaginations, evaginations and the bending of epithelial layers, condensations of freely moving mesenchymal cells, as well as the changes in shapes and overall proportions of the large masses of almost immobile plant cells may serve as the examples of morphogenetic processes. As was shown by the molecular biology within several last decades, all of these processes are based upon a highly regulated motile activity of the molecular and supramolecular components of the living cells. In the first approximation, all of these processes may be considered as mechanical, what means that they are associated with the production of mechanical forces and changes in space positions of the material constituents.

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... This structure is also known as the cortical actin layer [19]. It is composed of series of antiparallel, mutually sliding actin filaments, connected by myosin bridges [4]. In embryonic epithelial cells of some species -including the Drosophila melanogaster -actin is also present in a bundle surrounding the apical end of the cell [4,65]. ...
... It is composed of series of antiparallel, mutually sliding actin filaments, connected by myosin bridges [4]. In embryonic epithelial cells of some species -including the Drosophila melanogaster -actin is also present in a bundle surrounding the apical end of the cell [4,65]. Actin is also present in bundles criss-crossing the cell, which reinforce the cortical actin [19]. ...
... The microfilaments contract, generating tensile forces along and in the vicinity of the cellular membrane. Apical bundles of microfilaments in a group of neighbouring cells can act in concert to create contractions over large distances along a tissue [4]. ...
... Many seminal experiments highlighting the crucial role of chemo-mechanical cue in morphogenesis have been performed in the last decades by the research group lead by Lev Beloussov. In particular, these works have reported that the active responses of living matter may overshoot the passive mechanical stimuli, proposing a hyper-restoration principle for homeostasis [8]. Another open area of investigation concerns the identification of the local regulation mechanisms, mainly signalling pathways that spatially and temporally control cell behaviour, which allow the global orchestration of a macroscopic shape [76]. ...
... Using the divergence theorem in Eq. (8) and the properties of the cross product, the first term in the r.h.s of Eq.(18) transforms into the volume integral: ...
Chapter
From a mathematical viewpoint, the study of morphogenesis focuses on the description of all geometric and structural changes which locally orchestrate the underlying biological processes directing the formation of a macroscopic shape in living matter. In this chapter, we introduce a continuous chemo-mechanical approach of morphogenesis, deriving the balance principles and evolution laws for both volumetric and interfacial processes. The proposed theory is applied to the study of pattern formation for either a fluid-like or a solid-like biological system model, using both theoretical methods and simulation tools.
... Time-lapse imaging of tissue movement is very important in embryology, as it allows observation of important transient features of a developing embryo, such as problastopores and propagation of differentiation waves . If we could measure the forces generated by the cells and how cells react to those forces, it would allow us to distinguish cause and effect for cell sheet movements and cell differentiation (Beloussov and Harris, 2006;Beloussov, 1994;Beloussov et al., 2015;Gordon, 1999). How cells react to the forces placed on them plays a major part in how an embryo develops (Ambrosi et al., 2017;Fleury and Gordon, 2012 (Brodland et al., 2010b(Brodland et al., , 2014Cranston et al., 2010) based on a method initiated by Stein and Gordon (1982). ...
Research
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Full-text available
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Chapter
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Article
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Book
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Chapter
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Chapter
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A finite elements model imitating the morphogenesis of smoothly curved tubular epithelial rudiments is suggested. It is based upon the experimentally proved assumption of the lateral (tangential) pressure between adjacent epithelial cells. The main idea of the model is that under a non-zero local curvature the lateral cell-cell pressure acquires the radial components which are absent under zero curvature. In the framework of the model we investigate the roles of initial geometry, the different coefficients relating the local curvatures and radial cell shifts, and of visco-elastical cell-cell linkages in the shaping process. We also employ the different temporal regimes (both periodical and constant) of the lateral pressure exerted and the different overall durations of the modelling. As a result, we get a set of biologically realistical shapes, almost all of them belonging to the same basical "trefoiled" archetype. Among the variables explored, shaping was most affected by the changes in visco-elastical coefficients, in the temporal regimes and in the overall duration of the modelling. The model shows that rather complicated and realistical shapes of epithelial rudiments can be obtained without assuming any initial regional differences inside cell layers. The model may be useful for understanding the principles underlying both genetical and epigenetical regulation of the morphogenesis.
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We recognize organisms first and foremost by their forms, but how they grow and shape themselves still largely passes understanding. The objective of this article is to survey what has been learned of morphogenesis of walled eucaryotic microorganisms as a set of problems in cellular heredity, biochemistry, physiology, and organization. Despite the diversity of microbial forms and habits, some common principles can be discerned. (i) That the form of each organism represents the expression of a genetic program is almost universally taken for granted. However, reflection on the findings with morphologically aberrant mutants suggests that the metaphor of a genetic program is misleading. Cellular form is generated by a web of interacting chemical and physical processes, whose every strand is woven of multiple gene products. The relationship between genes and form is indirect and cumulative; therefore, morphogenesis must be addressed as a problem not of molecular genetics but of cellular physiology. (ii) The shape of walled cells is determined by the manner in which the wall is laid down during growth and development. Turgor pressure commonly, perhaps always, supplies the driving force for surface enlargement. Cells yield to this scalar force by localized, controlled wall synthesis; their forms represent variations on the theme of local compliance with global force. (iii) Growth and division in bacteria display most immediately the interplay of hydrostatic pressure, localized wall synthesis, and structural constraints. Koch's surface stress theory provides a comprehensive and quantitative framework for understanding bacterial shapes. (iv) In the larger and more versatile eucaryotic cells, expansion is mediated by the secretion of vesicles. Secretion and ancillary processes, such as cytoplasmic transport, are spatially organized on the micrometer scale. The diversity of vectorial physiology and of the forms it generates is illustrated by examples: apical growth of fungal hyphae, bud formation in yeasts, germination of fucoid zygotes, and development of cells of Nitella, Closterium, and other unicellular algae. (v) Unicellular organisms, no less than embryos, have a remarkable capacity to impose spatial order upon themselves with or without the help of directional cues. Self-organization is reviewed here from two perspectives: the theoretical exploration of morphogens, gradients, and fields, and experimental study of polarization in Fucus cells, extension of hyphal tips, and pattern formation in ciliates. Here is the heart of the matter, yet self-organization remains nearly as mysterious as it was a century ago, a subject in search of a paradigm.
Article
Animal cells cleave by the progressive constriction of an equatorial region. The plane of the constricting equator is orthogonal to the mitotic spindle axis and is positioned so that the spindle is bisected, thus ensuring equipartitioning of the chromosomes. Constriction is achieved by the active contraction of a circumferential band of actomyosin-containing filaments. The mitotic apparatus is necessary for the formation of the contractile ring and specifies its position and orientation; however, it takes no active part in furrowing. One of the central questions that has to be answered to understand cytokinesis is: how does the mitotic apparatus act to organize the contractile ring? It has been suggested that the mitotic apparatus acts to modulate locally the force generated by the cortical contractile filaments. The resultant gradients of cortical tension cause filaments to be pulled into regions of higher tension. The geometry of the stimulus from the mitotic apparatus is such that the highest levels of tension occur in the equatorial regions. The geometric distortions that take place when contractile filaments are pulled into this region cause them to become partially oriented circumferentially. When furrowing commences, mechanical forces act to align the filaments further and concentrate them in a narrow band. The furrow therefore becomes self-sharpening. Similar lateral flows of contractile filaments may occur during cell locomotion and growth cone extension.
Article
The aim of this study was to examine the reorganization of the microfilamentous cortical layer (MC) accompanying ooplasmic segregation in loach eggs. Using scanning (SEM) and transmission electron microscopy (TEM), we found that the MC is thicker in folded areas. Prior to fertilization, surface microvilli are distributed more or less uniformly throughout the egg. A similar, more or less uniform, distribution of endocytotic events was observed in the eggs 5-15 min after insemination using fluorescence microscopy of Lucifer yellow CH uptake. During ooplasmic segregation, the surface is progressively polarized so that before the first cleavage onset (50-60 min after insemination) only the blastodisc surface is folded and undergoes endocytosis, whereas the vegetal surface is smooth and does not show internalization. In two-cell embryos, the blastomeric surface is also regionalized according to its relief and endocytosis. When surface tension was lowered by sucking most yolk granules out of the egg, we observed contractile responses only in the animal folded surface. These data suggest that a polar distribution of contractile structures is established in the loach egg undergoing ooplasmic segregation.
Article
Morphometric data from scanning electron micrographs (SEM) of cells in intact embryos and high-resolution time-lapse recordings of cell behavior in cultured explants were used to analyze the cellular events underlying the morphogenesis of the notochord during gastrulation and neurulation of Xenopus laevis. The notochord becomes longer, narrower, and thicker as it changes its shape and arrangement and as more cells are added at the posterior end. The events of notochord development fall into three phases. In the first phase, occurring in the late gastrula, the cells of the notochord become distinct from those of the somitic mesoderm on either side. Boundaries form between the two tissues, as motile activity at the boundary is replaced by stabilizing lamelliform protrusions in the plane of the boundary. In the second phase, spanning the late gastrula and early neurula, cell intercalation causes the notochord to narrow, thicken, and lengthen. Its cells elongate and align mediolaterally as they rearrange. Both protrusive activity and its effectiveness are biased: the anterioposterior (AP) margins of the cells advance and retract but produce much less translocation than the more active left and right ends. The cell surfaces composing the lateral boundaries of the notochord remain inactive. In the last phase, lasting from the mid- to late neurula stage, the increasingly flattened cells spread at all their interior margins, transforming the notochord into a cylindrical structure resembling a stack of pizza slices. The notochord is also lengthened by the addition of cells to its posterior end from the circumblastoporal ring of mesoderm. Our results show that directional cell movements underlie cell intercalation and raise specific questions about the cell polarity, contact behavior, and mechanics underlying these movements. They also demonstrate that the notochord is built by several distinct but carefully coordinated processes, each working within a well-defined geometric and mechanical environment.
Article
We make use of a novel system of explant culture and high resolution video-film recording to analyse for the first time the cell behaviour underlying convergent extension and segmentation in the somitic mesoderm of Xenopus. We find that a sequence of activities sweeps through the somitic mesoderm from anterior to posterior during gastrulation and neurulation, beginning with radial cell intercalation or thinning, continuing with mediolateral intercalation and cell elongation, and culminating in segmentation and somite rotation. Radial intercalation at the posterior tip lengthens the tissue, while mediolateral intercalation farther anterior converges it toward the midline. This extension of the somitic mesoderm helps to elongate the dorsal side of intact neurulae. By separating tissues, we demonstrate that cell rearrangement is independent of the notochord, but radial intercalation - and thus the bulk of extension - requires the presence of an epithelium, either endodermal or ectodermal. Segmentation, on the other hand, can proceed in somitic mesoderm isolated at the end of gastrulation. Finally, we discuss the relationship between cell rearrangement and segmentation.
Article
We show with time-lapse micrography that narrowing in the circumblastoporal dimension (convergence) and lengthening in the animal-vegetal dimension (extension) of the involuting marginal zone (IMZ) and the noninvoluting marginal zone (NIMZ) are the major tissue movements driving blastopore closure and involution of the IMZ during gastrulation in the South African clawed frog, Xenopus laevis. Analysis of blastopore closure shows that the degree of convergence is uniform from dorsal to ventral sides, whereas the degree of extension is greater on the dorsal side of the gastrula. Explants of the gastrula show simultaneous convergence and extension in the dorsal IMZ and NIMZ. In both regions, convergence and extension are most pronounced at their common boundary, and decrease in both animal and vegetal directions. Convergent extension is autonomous to the IMZ and begins at stage 10.5, after the IMZ has involuted. In contrast, expression of convergent extension in the NIMZ appears to be dependent on basal contact with chordamesoderm or with itself. The degree of extension decreases progressively in lateral and ventral sectors. Isolated ventral sectors show convergence without a corresponding degree of extension, perhaps reflecting the transient convergence and thickening that occurs in this region of the intact embryo. We present a detailed mechanism of how these processes are integrated with others to produce gastrulation. The significance of the regional expression of convergence and extension in Xenopus is discussed and compared to gastrulation in other amphibians.
Article
Explants extirpated from Xenopus laevis embryos at the early gastrula stage were placed on pieces of hydrophilized latex film which were then either stretched or remained intact. In explants cultivated on the intact films most cells emigrated out of the explants and remained undifferentiated, whereas the explants on the films stretched for 10 min or more developed a normal set of rudiments. In the explants of suprablastoporal zone stretched perpendicularly to the cranio-caudal direction, the axial organs were oriented in the direction of stretching. In the stretched explants, unlike the intact ones, a system of microfilament-associated intercellular contacts was formed within a few minutes.
Article
One of the most universal events in morphogenesis is the formation of domains of morphologically polarized cells in the initially homogeneous epithelial sheets. We investigate the possibility of considering this process as a phenomenon of self-organization which is based upon the following experimentally proven mechanochemical cell properties: (1) a capacity of individual cells for morphological polarization considered as a bistable "all-or-none" transition of a cell from a non-polarized to a polarized state; (2) transmission of this capacity from one cell to another on their contacts; (3) feedback relations between co-operative cell polarization and tangential elastic tensions in a cell sheet: cell polarization increases tangential tensions whereas the latter inhibit further cell polarization. We have constructed a phenomenological model which formally expresses the above properties. Its mathematical description includes but few macroscopic parameters available to experimental investigation and controlled changes. The analysis of the collective dynamic regimes of cell polarization demonstrates that variations of some non-specific parameters leads to spontaneous transition in the morphology of cell layers accompanied by symmetry breaking (Turing's instability). Under these conditions either long-range ordered patterns of cell polarization (including hexagonal cell nets) or non-regular spotted structures can emerge. In the particular case of a sheet having fixed complete dimensions and lacking any external elastic bonds a stable macrostate is created; it corresponds to the sheet's binary subdivision into polarized and non-polarized cell domains of size-invariant proportions. The model conclusions are compared with the morphogenetical processes in sea-urchin development, the morphogenesis of skin derivates and artificially induced budding in hydrozoa.
Article
The pieces of dorsal ectoderm of the Rana temporaria embryos at the early and midgastrula stages were transplated onto the dorsal surface of the X. laevis embryos of the same age and the movements and changes in the form and area of the transplants were followed from early gastrula to neurula. During the first period (early--midgastrula) all movements of the transplants were directed towards the blastopore and related ma- In the beginning of the second period the transplants moved toward the blastopore only in the most caudal region, whereas in all other regions the material was markedly displaced craniad. Until the early neurula stage these movements were related to the longitudinal expansion of the material in the dorsal area and later, during neurulation, to its transverse compression. The head region material was first markedly expanded in the transverse direction and then also contracted. Alternation of active contractions and expansion of the suprablastopore material has been revealed and mediocaudal (gastrulation) vs. craniopetal (neurulation) cell movements were distinctly shown.
Article
1. The sensitivity of the membrane potential of cells of early embryos of Xenopus laevis to variations in the extracellular concentrations of sodium and potassium has been determined. 2. Alterations in the extracellular sodium concentration have little effect on the membrane potential at all pregastrular stages tested. 3. Up to the 32 cell stage an increase in the concentration of potassium in the bathing medium causes a fall in cell membrane potential only when membrane newly synthesized in the furrow during cleavage is exposed at the embryo surface, during the second half of the cell division cycle. 4. Beyond the morula stage (48 cells) a fall in membrane potential on raising external potassium can only be demonstrated when the seal which isolates the intercellular fluid from the bathing medium is broken so that cells lining the inner face of the embryo come into contact with the high potassium solution. 5. The results suggest that the egg membrane has little selective permeability whereas membrane synthesized after fertilization is highly potassium permeable. 6. No evidence could be obtained for any potential difference between the intercellular fluid and the external bathing medium. 7. Dinitrophenol, sodium azide and cyanide prevented normal development only if they were injected into the intercellular cavity. Embryos reared in solutions containing these poisons turned into normal tadpoles. 8. The formation of the intercellular cavity could be halted by injecting ouabain into the cavity while it was still small. Embryos reared in ouabain turned into normal tadpoles. 9. The results suggest that the active transfer of sodium ions from the cells to the intercellular spaces is an integral part of the formation of the intercellular fluid. A hypothesis for the mechanism of formation of the cavity is put forward along these lines.
Article
The roles of microfilaments and microtubules as causative organelles in the cell shape changes required forin vitro morphogenesis of embryonic mouse salivary epithelium have been explored by use of the drugs cytochalasin B and colchicine. Cytochalasin inhibits morphogenesis, causes flattening of the epithelium and loss of the clefts that were present at the time of drug application. These effects correlate with a specific disruption of cytoplasmic microfilaments when viewed with the electron microscope. Removal of cytochalasin results in reappearance of ordered microfilaments and resumption of morphogenesis. Colchicine disrupts microtubules and halts morphogenesis, but does not cause flattening of the epithelium or loss of clefts. Treatment with cytochalasin followed by recovery in the presence of colchicine demonstrates that recovery clefts can form in the absence of microtubules. It is proposed that normal salivary gland morphogenesis includes microfilament participation via contractile activity, in addition to mitosis and to extracellular stabilization processes.
Article
During urodele neurulation, presumptive neural cells elongate to form the neural plate and then constrict apically as the plate rolls up to form the neural tube. During the same period, epidermal cells gradually flatten. Electron microscopy of these cells has been carried out in an attempt to understand the mechanism of morphogenetic cell shape changes. In elongating neural plate cells, microtubules are oriented parallel to the long axis. Counts of numbers of these “paraxial” microtubules per cell do not differ significantly at three apicobasal levels of the cells; therefore, it is practical to consider the paraxial microtubules as a single population of full-cell-length microtubules. The number of paraxial microtubules per cell decreases significantly as the cell elongates, but the degree of elongation of a cell at a given stage is not closely related to the number of paraxial microtubules it contains. Several observations suggest that microtubules contribute to cell elongation by some form of transport mechanism. During the apical constriction of neural ectoderm cells, there is marked increase in thickness of a circumferential bundle of microfilaments which encircles the cell apex. The inverse relationship between increase in bundle thickness and decrease in circumference of the cell apex suggests that these processes result from increased overlap and interdigitation of the original complement of apical filaments. Flattening epidermal cells display randomly oriented microtubules and bundles of thicker filaments (70–100 Å in diameter) which are reminiscent of “tonofibrils” and appear to span the cell from desmosome to desmosome.
Article
Despite the large amount of knowledge which continues to accumulate about early developmental events, very little is known about the processes which control them. Part of the problem may lie in that workers applying different approaches and techniques have different points of view and appear to be reluctant to read each others' literature. My aim in this paper is not to give a generative, formal model for early development, but rather to suggest several connecting strands between the physiological, biochemical, cell biological and experimental embryological approaches which may stimulate new research in fields between those already exploited.
Article
We present a mechanical model for the morphogenetic folding of embryonic epithelia based on hypothesized mechanical properties of the cellular cytoskeleton. In our model we consider a simple cuboidal epithelium whose cells are joined at their apices by circumferential junctions; to these junctions are attached circumferential arrays of microfilament bundles assembled into a “purse string” around the cell apex. We assume that this purse string has the following property: if its circumference is increased beyond a certain threshold, an active contraction is initiated which “draws the purse-string” and reduces the apical circumference of the cell to a new, shorter, resting length. The remainder of the cell is modeled as a visoelastic body of constant volume. Clearly contraction in one cell could stretch the apical circumferences of neighboring cells and, if the threshold is exceeded, cause them “to fire” and contract. The objective of this paper is to demonstrate that our model, based on the local behavior of individual cells, generates a propagating contraction wave which is sufficient to explain the globally coherent morphogenetic infolding of a wide variety of embryonic epithelia. Representative computer simulations, based on the model, are presented for the initial gastrulation movements of echinoderms, neural tube formation in urodele amphibians, and ventral furrow formation in Drosophila.