Mechanical feedback in morphogenesis and cell differentiation

Studies of mechanical stresses and mechanical feedback at the cell level are reviewed. It is shown that cells and embryonic tissues respond to external mechanical stresses and can generate such stresses themselves. Regular feedback loops between external (passive) and internal (active) mechanical stresses have been established. They are essential for cell survival, determination of the direction of their differentiation, and selforganization of morphogenetic processes. Relevant experimental data are presented, and models of mechanical feedback loops are discussed.     

Morphomechanics: goals, basic experiments and models

Morphomechanics is a branch of developmental biology, studying the generation, space-time patterns and morphogenetic role of mechanical stresses (MS) which reside in embryonic tissues. All the morphogenetically active embryonic tissues studied in this respect have been shown to bear substantial mechanical stresses of tension or pressure. MS are indispensable for organized cell movements, expression of a number of developmentally important genes and the very viability of cells. Even a temporary relaxation of MS leads to an increase in the morphological variability and asymmetry of embryonic rudiments. Moreover, MS may be among the decisive links of morphogenetic feedback required for driving forth embryonic development and providing its regular space-time patterns. We hypothesize that one such feedback is based upon the tendency of cells and tissues to hyperrestore (restore with an overshoot) their MS values after any deviations, either artificial or produced by neighboring morphogenetically active tissues. This idea is supported by a number of observations and experiments performed on the tissue and individual cell levels. We describe also the models demonstrating that a number of biologically realistic stationary shapes and propagating waves can be generated by varying the parameters of the hyperrestoration feedback loop. Morphomechanics is an important and rapidly developing branch of developmental and cell biology, being complementary to other approaches.     

Patterns of mechanical stress at the successive stages of early development of frog]

The immediate relaxation deformations have been studied in the embryonic frog tissues from the late blastula stage till the early tail bud stage. As a result, the maps of mechanical stresses were constructed which were characterized by the existence of distinct tension-lines dissecting the embryonic tissues (cross-lines). A few discrete moments of development were established when new cross-lines formed or the previous ones disappeared; they are separated by the topologically invariant periods of development. The cross-lines play an important role in morphogenesis in that they determine the ways of active cell migration and trace the boundaries between different anlages. The orientation of the cross-lines coincides, as a rule, with the direction of predominant tension of tissues during the preceding topologically invariant period of development.     

Cytomechanical control of morphogenesis

The role of mechanically strained state of cells and multicellular structures in morphogenesis regulating in vertebrate embryos is discussed. Regular changes in patterns of mechanical strain during embryonic development are described. Artificial relaxation of mechanical strain performed on definite developmental stages and retension of embryonic tissues in arbitrary directions considerably affects morphogenesis and cell differentiation patterns. Cytomechanical models of morphogenesis are reviewed and a concept of hyperrestoration of mechanical strain as a possible driving force of morphogeneiss is suggested.     

Rate of dehydration and cumulative desiccation stress interacted to modulate desiccation tolerance of recalcitrant cocoa and ginkgo embryonic tissues

Rate of dehydration greatly affects desiccation tolerance of recalcitrant seeds. This effect is presumably related to two different stress vectors: direct mechanical or physical stress because of the loss of water and physicochemical damage of tissues as a result of metabolic alterations during drying. The present study proposed a new theoretic approach to represent these two types of stresses and investigated how seed tissues responded differently to two stress vectors, using the models of isolated cocoa (Theobroma cacao) and ginkgo (Ginkgo biloba) embryonic tissues dehydrated under various drying conditions. This approach used the differential change in axis water potential (DeltaPsi/Deltat) to quantify rate of dehydration and the intensity of direct physical stress experienced by embryonic tissues during desiccation. Physicochemical effect of drying was expressed by cumulative desiccation stress [integralf(psi,t)], a function of both the rate and time of dehydration. Rapid dehydration increased the sensitivity of embryonic tissues to desiccation as indicated by high critical water contents, below which desiccation damage occurred. Cumulative desiccation stress increased sharply under slow drying conditions, which was also detrimental to embryonic tissues. This quantitative analysis of the stress-time-response relationship helps to understand the physiological basis for the existence of an optimal dehydration rate, with which maximum desiccation tolerance could be achieved. The established numerical analysis model will prove valuable for the design of experiments that aim to elucidate biochemical and physiological mechanisms of desiccation tolerance.     

A simple model for estimating the active reactions of embryonic tissues to a deforming mechanical force

Active reactions of embryonic tissues to mechanical forces play an important role in morphogenesis. To study these reactions, experimental models that enable to evaluate the applied forces and the deformations of the tissues are required. A model based upon the active intrusion of a living early gastrula Xenopus embryo into a tube half the embryo in diameter is described. The intrusion is initially triggered by a suction force of several dozen Pa but then continues in the absence of external driving force, stopping immediately after the entire embryo has penetrated into the tube. The process can be stopped by cytoskeletal drugs or by the damage of the part of the embryo still non-aspirated and is associated with the transversal contraction and meridional elongation of the non-aspirated part of the embryo surface and quasi-periodic longitudinal contractions/extensions of the cells within the part already aspirated. We suggest that this reaction is an active response to the embryo deformation and discuss its morphogenetic role. The problem of estimating the elastic modules of embryonic tissues is also discussed.     

Mechanical stresses as factors in the autoregulation of morphogenesis

Since morphogenetic processes are nonlinear, feedback must be essential for their regulation. Two concepts of feedback in morphogenesis are developed: 1) inhibition by diffusing morphogenetic substances and 2) action of mechanical strain resulting from morphogenetic movements. The data on the role of mechanical strain in formation of integral structure of embryonic tissues, primary demarcation of embryonic epithelia and mesenchymal rudiments and bending of epithelial layers are presented. Evolutionary aspects of morphogenetic role of mechanical strain and its possible use in applied biotechnology are discussed.     

Mechanical effects of cell anisotropy on epithelia

Theoretical, numerical and experimental methods are used to develop a comprehensive understanding of how cell shape affects the mechanical characteristics of two-dimensional aggregates such as epithelia. This is an important step in relating the mechanical properties of tissues to those of the cells of which they are composed. Statistical mechanics is used to derive formulas for the in-plane stresses generated by tensions gamma along cell-cell interfaces in sheets with anisotropic cellular fabric characterized by average cell aspect ratio kappa. These formulas are then used to investigate self-deformation (strain relaxation) of an anisotropic sheet composed of cells of thickness h and having effective viscosity mu. Finite element simulations of epithelia and of isolated cells and novel relaxation studies of specimens of embryonic epithelia reported herein are consistent with the predictions of the theory. In all cases, geometric factors cause the relaxation responses to be more complex than a single decaying exponential.     

Surprisingly simple mechanical behavior of a complex embryonic tissue

Background

Previous studies suggest that mechanical feedback could coordinate morphogenetic events in embryos. Furthermore, embryonic tissues have complex structure and composition and undergo large deformations during morphogenesis. Hence we expect highly non-linear and loading-rate dependent tissue mechanical properties in embryos.

Methodology/Principal Findings

We used micro-aspiration to test whether a simple linear viscoelastic model was sufficient to describe the mechanical behavior of gastrula stage Xenopus laevis embryonic tissue in vivo. We tested whether these embryonic tissues change their mechanical properties in response to mechanical stimuli but found no evidence of changes in the viscoelastic properties of the tissue in response to stress or stress application rate. We used this model to test hypotheses about the pattern of force generation during electrically induced tissue contractions. The dependence of contractions on suction pressure was most consistent with apical tension, and was inconsistent with isotropic contraction. Finally, stiffer clutches generated stronger contractions, suggesting that force generation and stiffness may be coupled in the embryo.

Conclusions/Significance

The mechanical behavior of a complex, active embryonic tissue can be surprisingly well described by a simple linear viscoelastic model with power law creep compliance, even at high deformations. We found no evidence of mechanical feedback in this system. Together these results show that very simple mechanical models can be useful in describing embryo mechanics.     

Stress amplification during development of the tendon-to-bone attachment

Mechanical stress is necessary to sustain the mineral content of bone in adults. However, in a developing neonatal mouse, the mineralization of soft tissues progresses despite greatly reduced average mechanical stresses. In adults, these reduced loads would likely lead to bone loss. Although biochemical factors may partly explain these different responses, it is unclear how mineralization is initiated in low load environments. We present here the effect of morphometric data and initial modeling supporting a hypothesis that mechanical factors across several length scales amplify stresses, and we suggest that these stresses are of a level adequate to contribute to mechanical signaling for initiation of mineralization at the developing tendon-to-bone enthesis. A mineral gradient is evident across the insertion from the onset of mineralization. This grading maintains a constant size from early postnatal time points to adulthood. At the tissue level, this grading contributes to reduced stresses in an adult animal and to a minor elevation of stresses in a neonatal animal. At the cellular level, stress concentrations around mineralizing chondrocytes are enhanced in neonatal animals compared with adult animals. The enhancement of stresses around cells at early time points may serve to amplify and transduce low loads in order to initiate mineralization.     

Impact orientation can significantly affect the outcome of a blunt impact to the rabbit patellofemoral joint

This laboratory has developed a subfracture, joint trauma model in rabbits. Using a dropped impact mass directed onto a slightly abducted joint, chronic softening of retropatellar cartilage and thickening of underlying subchondral bone are documented in studies to 1 year post-insult. It has been hypothesized that these tissue changes are initiated by stresses developed during impact loading. A previous analytical study by this laboratory suggests that tensile strains in retropatellar cartilage can be significantly lowered, without significantly changing the intensity of stresses in the underlying subchondral bone, by reorientation of patellar impact more centrally on the joint. In the current study comparative experiments were performed on groups of animals after either an impact directed on the slightly abducted limb or a more central impact. One-year post-trauma in animals subjected to the central-oriented impact no degradation of the shear modulus for the retropatellar cartilage was documented, but the thickness of the underlying subchondral bone was significantly increased. In contrast, alterations in cartilage and underlying bone following impact on the slightly abducted limb were consistent with previous studies. The current experimental investigation showed the sensitivity of post-trauma alterations in joint tissues to slight changes in the orientation of impact load on the joint. Interestingly, for this trauma model thickening of the underlying subchondral plate occurred without mechanical degradation of the overlying articular cartilage. This supports the current laboratory hypothesis that alterations in the subchondral bone and overlying cartilage occur independently in this animal model.     

Mathematical modeling of the stretching-induced elongation of the embryonic epithelium layer in the absence of an external load

The problem of deformation of a planar embryonic epithelium layer that is unloaded after a short period of uniaxial stretching with subsequent fixation in the stretched state for different periods of time is solved. The initial conditions for solving this problem are derived from the previously discussed problem of the uniform stretching of a tissue fragment (explant) with subsequent fixation of the obtained length. In this study we used the previously developed continuum model that describes the stress–strain state of epithelial tissue taking the parameters that characterize the shape of the cells and their stress state into account, as well as the active stresses they exert when they interact with each other. The experimentally observed continuation of the deformation of a stretched tissue after the external force has ceased to act is described theoretically as a result of active cell reactions to mechanical stress. The duration of explant fixation is shown to have a strong effect on its further elongation and on the pattern of cell activity.     

Evaluating the viscoelastic properties of biological tissues in a new way

In this paper, a new method for evaluating the viscoelastic properties of biological tissues such as tendons and ligaments is presented. This method obtains the complex modulus of these tissues to characterize their viscoelastic properties. With this method, the stresses and strains measured in time are first transformed (using FFT), and the complex modulus is then obtained. The complex modulus contains sufficient information about the viscoelastic characteristics of the biological tissues. With this method, the mechanical properties of biological tissues can be measured without making apriori assumptions regarding their structures, and the measurements can be made in real time.     

The Mechanochemical Basis of Cell and Tissue Regulation

This article is a summary of a lecture presented at a symposium on "Mechanics and Chemistry of Biosystems' in honor of Professor Y.C. Fung that convened at the University of California, Irvine in February 2004. The article reviews work from our laboratory that focuses on the mechanism by which mechanical and chemical signals interplay to control how individual cells decide whether to grow, differentiate, move, or die, and thereby promote pattern formation during tissue morphogenesis. Pursuit of this challenge has required development and application of new microtechnologies, theoretical formulations, computational models and bioinformatics tools. These approaches have been used to apply controlled mechanical stresses to specific cell surface molecules and to measure mechanical and biochemical responses; to control cell shape independently of chemical factors; and to handle the structural, hierarchical and informational complexity of living cells. Results of these studies have changed our view of how cells and tissues control their shape and mechanical properties, and have led to the discovery that integrins and the cytoskeleton play a central role in cellular mechanotransduction. Recognition of these critical links between mechanics and cellular biochemistry should lead to novel strategies for the development of new drugs and engineered tissues, as well as biomimetic microdevices and nanotechnologies that more effectively function within the context of living tissues.     

Regional passive ventricular stress-strain relations during development of altered loads in chick embryo

Mechanical load influences embryonic ventricular growth, morphogenesis, and function. However, little is known about changes in regional passive ventricular properties during the development of altered mechanical loading conditions in the embryo. We tested the hypothesis that regional mechanical loads are a critical determinant of embryonic ventricular passive properties. We measured biaxial passive right and left ventricular (RV and LV, respectively) stress-strain relations in chick embryos at Hamburger-Hamilton stages 21 and 27 after conotruncal banding (CTB) to increase biventricular pressure load or left atrial ligation (LAL) to reduce LV volume load and increase RV volume load. In the RV, wall strains at end-diastolic (ED) pressure normalized whereas ED stresses increased after either CTB or LAL during development. In the left ventricle, both ED strain and stress normalized after CTB, whereas both remained reduced with significantly increased myocardial stiffness after LAL. These results suggest that the embryonic ventricle adapts to chronically altered mechanical loading conditions by changing specific RV and LV passive properties. Thus regional mechanical load has a critical role during cardiogenesis.     

Simulation of the aging face

A three-dimensional finite element program is described which attempts to simulate the nonlinear mechanical behavior of an aging human face with specific reference to progressive gravimetric soft tissue descent. A cross section of the facial structure is considered to consist of a multilayered composite of tissues with differing mechanical behavior. Relatively short time (elastic-viscoplastic) behavior is governed by equations previously developed which are consistent with mechanical tests. The long time response is controlled by the aging elastic components of the tissues. An aging function is introduced which, in a simplified manner, models the observed loss of stiffness of these aging elastic components due to the history of straining as well as other physiological and environmental influences. Calculations have been performed for 30 years of exposure to gravitational forces. The deformations and stress distributions in the layers of the soft tissues are described. Overall, the feasibility of using constitutive relations which reflect the highly nonlinear elastic-viscoplastic behavior of facial soft tissues in finite element based three-dimensional mechanical analyses of the human face is demonstrated. Further developments of the program are discussed in relation to possible clinical applications. Although the proposed aging function produces physically reasonable long-term response, experimental data are not yet available for more quantitative validation.     

An inverse approach for the mechanical characterisation of vascular tissues via a generalised rule of mixtures

Mechanical factors such as stresses and strains play a major role in the growth and remodelling of soft biological tissues. The main constituents of tissue undergo different processes reacting to mechanical stimulus. Thereby, the characterisation of growth and remodelling requires an accurate estimation of the stresses and strains of their main components. Many soft tissues can be considered as composite materials and can be analysed using an appropriate rule of mixtures. Particularly, arterial tissue can be modelled as an isotropic soft matrix reinforced with preferentially oriented collagen fibres. An inverse approach to obtain the mechanical characterisation of each main component is proposed in this work. The procedure is based on a rule of mixtures raised in a finite deformation framework and generalised to include kinematics and compatibility equations for serial–parallel behaviour. This methodology allows obtaining the stress–strain relationship of the components fitting experimental data.     

Development and Experimental Validation of a Fluid/Structure-Interaction Finite Element Model of a Vacuum-Driven Cell Culture Mechanostimulus System

A new fluid/structure-interaction finite element formulation is reported, by means of which reactive fluid stresses can be determined for what is currently the most widely used laboratory apparatus (the Flexercell Strain Unit) for delivering controlled in vitro mechanical stimuli to cultured cells. The apparatus functions by means of cyclic vacuum application to the undersurface of a membrane-like circular rubber substrate. When operated in its original embodiment (i.e., without axial constraint to substrate motion), the pulsatile vacuum causes appreciable pulsatile excursions (often several millimeters) of the substrate. The mechanical stimuli experienced by cells attached atop the substrate include not only substrate distention, but also potentially confounding reactive fluid stresses due to coupled motions of the overlying liquid culture nutrient medium. Since it is impractical to directly measure reactive fluid stress in such environments, a corresponding mathematical model has been developed. The formulation involves transient continuum finite element solutions for the nutrient medium flow field and for the deformation of the substrate, coupled at their mutual interface (the substrate culture surface). Besides the nonlinearities inherent in the flow field and substrate treatments per se, the numerical problem is complicated by the presence of moving boundaries at the nutrient free surface and at the nutrient/substrate interface, as well as by the need to enforce fluid/structure interaction throughout the duty cycle. Algorithmic considerations appropriate to achieving physically realistic numerical performance are reported, and a confirmatory laboratory validation experiment is described.     

Molecular assembly and mechanical properties of the extracellular matrix: A fibrous protein perspective

The extracellular matrix is an integral and dynamic component of all tissues. Macromolecular compositions and structural architectures of the matrix are tissue-specific and typically are strongly influenced by the magnitude and direction of biomechanical forces experienced as part of normal tissue function. Fibrous extracellular networks of collagen and elastin provide the dominant response to tissue mechanical forces. These matrix proteins enable tissues to withstand high tensile and repetitive stresses without plastic deformation or rupture. Here we provide an overview of the hierarchical molecular and supramolecular assembly of collagens and elastic fibers, and review their capacity for mechanical behavior in response to force. This article is part of a Special Issue entitled: Fibrosis: Translation of basic research to human disease.     

Contributions to the Biomechanics of Plants. I. Stabilities of Plant Stems with Strengthening Elements of Different Cross-Sections Against Weight and Wind Forces*

Biophysical considerations allow estimates of the mechanical stresses on self-bearing vertical stems of plants. Even at moderate wind velocities the stresses induced by aerodynamic forces dominate over those induced by the own weight. Using polar coordinates, analytical expressions of cross-sectional area and axial second moment of area for centrisymmetric structures with symmetries threefold or higher are derived. Calculating the relative section modulus for various (centrisymmetric) arrangements of stabilizing structures leads to an estimate of the “mechanical effectivity” of these structures. If for plant stems, seen as composite materials, the second moments of area and the elastic moduli are known, the contribution of the different tissues to mechanical stability can be determined quantitatively. The mechanical design of early “vascular” land plants and of stems of (fossil) trees and lianas in different ontogenetic stages can be assessed.