Cytomechanics of axonal development

Mechanical tension is a robust regulator of axonal development of cultured neurons. We review work from our laboratory, using calibrated glass needles to measure or apply tension to chick sensory neurons, chick forebrain neurons, and rat PC12 cells. We survey direct evidence for two different regimes of tension effects on neurons, a fluid-like growth regime, and a nongrowth, elastic regime. Above a minimum tension threshold, we observe growth effects of tension regulating four phases of axonal development:

1. Initiation of process outgrowth from the cell body;
2. Growth cone-mediated elongation of the axon;
3. Elongation of the axon after synaptogenesis, which normally accommodates the skeletal growth of vertebrates; and
4. Axonal elimination by retraction.

Significantly, the quantitative relationship between the force and the growth response is suprisingly similar to the simple relationship characteristic of Newtonian fluid mechanical elements: elongation rate is directly proportional to tension (above the threshold), and this robust linear relationship extends from physiological growth rates to far-above-physiological rates. Thus, tension apparently integrates the complex biochemistry of axonal elongation, including cytoskeletal and membrane dynamics, to produce a simple “force input/growth output” relationship. In addition to this fluid-like growth response, peripheral neurons show elastic behaviors at low tensions (below the threshold tension for growth), as do most cell types. Thus, neurites could exert small static forces without diminution for long periods. In addition, axons of peripheral neurons can actively generate modest tensions, presumably similar to muscle contraction, at tensions near zero. The elastic and force-generating capability of neural axons has recently been proposed to play a major role in the morphogenesis of the brain.     

The cytomechanics of axonal elongation and retraction

Neurites of PC12 and chick dorsal root ganglion neurons behave as viscoelastic solids in response to applied forces. This passive behavior can be modeled with three mechanical elements; a relatively stiff, undamped spring in series with a Voight element composed of a less stiff spring in parallel with a dashpot. In response to applied tensions greater than 100 microdynes, PC12 cells show lengthening behavior distinct from and in addition to the passive viscoelastic response. We interpret this as "towed growth" (Bray, D. 1984. Dev. Biol. 102:379-389) because the neurites can become twice as long without obvious thinning of the neurite and because in two cases neurite tensions fell below original rest tensions, a result that cannot be obtained with passive viscoelastic elements. The rate of towed growth showed a linear dependence of growth rate with applied tensions in 8 of 12 PC12 neurites exposed to applied tension greater than 100 microdynes. Both PC12 and chick sensory neurons showed evidence of retraction when neurite tensions were suddenly diminished. This response was measured as tension recovery after slackening in chick sensory neurites. In 62% of the cases, tension recovery exceeded and sometimes doubled the preexperimental steady-state tension. Our data indicate that this response is active tension generation by the neurite shaft. We conclude that neurite length is regulated by axial tension in both elongation and retraction. Our data suggest a three-way controller: above some tension set point, the neurite is stimulated to elongate. Below some different, lower tension threshold the neurite is stimulated to retract. Between these two tension thresholds, the neurite responds passively as a viscoelastic solid.     

A cytomechanical investigation of neurite growth on different culture surfaces

We have examined the relationship between tension, an intrinsic stimulator of axonal elongation, and the culture substrate, an extrinsic regulator of axonal elongation. Chick sensory neurons were cultured on three substrata: (a) plain tissue culture plastic; (b) plastic treated with collagen type IV; and (c) plastic treated with laminin. Calibrated glass needles were used to increase the tension loads on growing neurites. We found that growth cones on all substrata failed to detach when subjected to two to threefold and in some cases 5-10-fold greater tensions than their self-imposed rest tension. We conclude that adhesion to the substrate does not limit the tension exerted by growth cones. These data argue against a "tug-of-war" model for substrate-mediated guidance of growth cones. Neurite elongation was experimentally induced by towing neurites with a force-calibrated glass needle. On all substrata, towed elongation rate was proportional to applied tension above a threshold tension. The proportionality between elongation rate and tension can be regarded as the growth sensitivity of the neurite to tension, i.e., its growth rate per unit tension. On this basis, towed growth on all substrata can be described by the simple linear equation: elongation rate = sensitivity x (applied tension - tension threshold) The numerical values of tension thresholds and neurite sensitivities varied widely among different neurites. On all substrata, thresholds varied from near zero to greater than 200 mudynes, with some tendency for thresholds to cluster between 100 and 150 mudynes. Similarly, the tension sensitivity of neurites varied between 0.5 and 5.0 microns/h/mudyne. The lack of significant differences among sensitivity or threshold values on the various substrata suggest to use that the substratum does not affect the internal "set points" of the neurite for its response to tension. The growth cone of chick sensory neurons is known to pull on its neurite. The simplest cytomechanical model would assume that both growth cone-mediated elongation and towed growth are identical as far as tension input and elongation rate are concerned. We used the equation above and mean values for thresholds and sensitivity from towing experiments to predict the mean growth cone-mediated elongation rate based on mean rest tensions. These predictions are consistent with the observed mean values.     

植物根系和叶片生长对水分亏缺的原初反应

细胞扩张生长是植物受水分亏缺影响最敏感的生理过程之一。主要在对细胞水分导性、细胞壁特性和延伸组织中溶质传输结果分析的基础上 ,从细胞、组织和器官水平上对细胞扩展生长进行了探讨。根系和叶片细胞主要通过以下 2个过程来补偿水分胁迫的作用 :调节扩展生长需要的细胞临界膨压 ;溶质在延伸组织中的运移。此外 ,还探讨了植物根系和叶片生长对水分亏缺的生理适应机制     

Regulating tension in three-dimensional culture environments

The processes of development, repair, and remodeling of virtually all tissues and organs, are dependent upon mechanical signals including external loading, cell-generated tension, and tissue stiffness. Over the past few decades, much has been learned about mechanotransduction pathways in specialized two-dimensional culture systems; however, it has also become clear that cells behave very differently in two- and three-dimensional (3D) environments. Three-dimensional in vitro models bring the ability to simulate the in vivo matrix environment and the complexity of cell–matrix interactions together. In this review, we describe the role of tension in regulating cell behavior in three-dimensional collagen and fibrin matrices with a focus on the effective use of global boundary conditions to modulate the tension generated by populations of cells acting in concert. The ability to control and measure the tension in these 3D culture systems has the potential to increase our understanding of mechanobiology and facilitate development of new ways to treat diseased tissues and to direct cell fate in regenerative medicine and tissue engineering applications.     

Tensile forces govern germ-layer organization in zebrafish

Understanding the factors that direct tissue organization during development is one of the most fundamental goals in developmental biology. Various hypotheses explain cell sorting and tissue organization on the basis of the adhesive and mechanical properties of the constituent cells. However, validating these hypotheses has been difficult due to the lack of appropriate tools to measure these parameters. Here we use atomic force microscopy (AFM) to quantify the adhesive and mechanical properties of individual ectoderm, mesoderm and endoderm progenitor cells from gastrulating zebrafish embryos. Combining these data with tissue self-assembly in vitro and the sorting behaviour of progenitors in vivo, we have shown that differential actomyosin-dependent cell-cortex tension, regulated by Nodal/TGFbeta-signalling (transforming growth factor beta), constitutes a key factor that directs progenitor-cell sorting. These results demonstrate a previously unrecognized role for Nodal-controlled cell-cortex tension in germ-layer organization during gastrulation.     

Experimental research on mechanical stresses in the neuroepithelial layers of the brain

The embryonic brain was dissected in urodele amphibians at the early postneurulation stages. Tangential mechanical tensions were shown to exist in the embryonic brain. The reaction of neuroepithelial cells characterizing the topology of tensions was found by the use of dissections in two interperpendicular directions. The cells were oriented along the acting force in the case of unidirectional tension. In the case of two interbalanced tensions the cells were inclined along the lines of force of greater tension. Three types of tangential tensions were revealed which differ in force, direction, range of action and life time. The life times of tangential tensions were shown to depend on their force and range of action. The strongest tensions were short-lived and, besides, limited in space. Weak tensions were long-lived and spread all over the brain. In all cases of dissections the cells inducing tangential tensions reacted in the same way: by elongation of cell bodies along the normals to the brain layer. It is suggested that the tendency of cell elongation can cause the tangential tension of the layer. It was found that the partial removal of tensions enhances the curvatures of brain layers. The cells reacted to the tension removal in accordance with their position in the layer. If the cells are located in the grooves, they are shortened. If the cells are outside the grooves, they are elongated. It was found that after the tension was removed the nuclei migrated along the cell bodies. The migration of the nuclei depends on the direction of the layer flexure. The nuclei always migrated to the external surface of evagination or to the internal surface of flexure. It is suggested that the tangential tensions stabilize the changes in the brain shape.     

Assessing the mechanical energy costs of various tissue reshaping mechanisms

Early-stage embryos must reshape the tissues of which they are made into organs and other life-sustaining structures; and if non-mammalian embryos fail to complete these tasks before the energy provided by their yolk runs out, they die. The aim of this study is to use a cell-level computational model to investigate the energetic cost of a variety of mechanisms that can drive an in-plane reshaping pattern known as convergent extension—a motif in which a tissue narrows in one in-plane direction and expands in another. Mechanisms considered include oriented lamellipodia, directed mitosis, stress fibers, and anisotropic external tension. Both isolated patches of tissue and actively contracting tissues that deform adjacent passive areas are considered. The cell-level finite element model used here assumes that the cell membrane and its associated proteins generate a net tension γ along each cell–cell interface and that the cytoplasm and its embedded networks and structures have an effective viscosity?μ. Work costs are based exclusively on mechanical considerations such as edge lengths and tensions, and because a traditional mechanical efficiency cannot be calculated, mechanisms are compared on the basis of the work they must do to the tissue to cause a specified rate of in-plane reshaping. Although the model contains a number of simplifications compared to real embryonic tissues, it is able to show that the work requirements for tissue reshaping by mitoses and by lamellipodia are of the same order. Lamellipodia are energetically most effective when their tensions are approximately twice as large as the interfacial tensions in the surrounding cells. The model also shows that stress fibers or other direct stretch or compression mechanisms are at least five times more efficient for tissue reshaping than are mitoses or lamellipodia and that the work needed to deform a typical cellular tissue is more than thirty times greater than if it did not contain cell boundaries. Collectively, these findings indicate that common tissue reshaping mechanisms have mechanical efficiencies of less than one percent and that mechanical efficiency is not the primary determinant of which mechanism(s) an embryo uses to reshape its tissues.     

Mathematical treatment of water movement in plant cells and tissue: a review

Abstract. Over the past three decades, many contributions have been made to the development of a mathematical basis for describing water transport in plant cells and tissue. This review paper attempts to summarize the more significant contributions and to outline the concepts upon which the various mathematical analyses are founded.
The paper itself is divided into three major sections. Section I deals with the quantitative water relations of single plant cells. Basic equations are developed which describe the water statics and water dynamics of such cells. Included is a discussion of the theory and methods for measuring the various parameters (permeabilities, cell wall elastic moduli, etc.) which enter into the development. The section closes with a presentation of circuit analog models for single plant cells.
Section II is devoted to a review and development of the water relations of plant tissues which contain numerous cells in series. Following a historical overview, various existing models are derived and physical tissue properties which enter the derivation are identified. The concept of 'local equilibrium' is discussed and circuit analog models for single cells are generalized and applied to several cells in series.
The final section contains two example applications of water transport theory as it applies to plant tissue. One application involves radial water movement in a soybean hypocotyl while the other deals with water transport in a growing root tip. A summary at the end of the section is largely devoted to a discussion of the limitations of mathematical models dial are presently available.     

Determination of mechanical stress distribution in Drosophila wing discs using photoelasticity

Morphogenesis, the process by which all complex biological structures are formed, is driven by an intricate interplay between genes, growth, as well as intra- and intercellular forces. While the expression of different genes changes the mechanical properties and shapes of cells, growth exerts forces in response to which tissues, organs and more complex structures are shaped. This is exemplified by a number of recent findings for instance in meristem formation in Arabidopsis and tracheal tube formation in Drosophila. However, growth not only generates forces, mechanical forces can also have an effect on growth rates, as is seen in mammalian tissues or bone growth. In fact, mechanical forces can influence the expression levels of patterning genes, allowing control of morphogenesis via mechanical feedback. In order to study the connections between mechanical stress, growth control and morphogenesis, information about the distribution of stress in a tissue is invaluable. Here, we applied stress-birefringence to the wing imaginal disc of Drosophila melanogaster, a commonly used model system for organ growth and patterning, in order to assess the stress distribution present in this tissue. For this purpose, stress-related differences in retardance are measured using a custom-built optical set-up. Applying this method, we found that the stresses are inhomogeneously distributed in the wing disc, with maximum compression in the centre of the wing pouch. This compression increases with wing disc size, showing that mechanical forces vary with the age of the tissue. These results are discussed in light of recent models proposing mechanical regulation of wing disc growth.     

Mechanical forces shaping the development of the inner ear

The inner ear is one of the most complex structures in the mammalian body. Embedded within it are the hearing and balance sensory organs that contain arrays of hair cells that serve as sensors of sound and acceleration. Within the sensory organs, these hair cells are prototypically arranged in regular mosaic patterns. The development of such complex, yet precise, patterns require the coordination of differentiation, growth, and morphogenesis, both at the tissue and cellular scales. In recent years, there is accumulating evidence that mechanical forces at the tissue, the cellular, and the subcellular scales coordinate the development and organization of this remarkable organ. Here, we review recent works that reveal how such mechanical forces shape the inner ear, control its size, and establish regular cellular patterns. The insights learned from studying how mechanical forces drive the inner ear development are relevant for many other developmental systems in which precise cellular patterns are essential for their function.     

RELATIVE GROWTH RATES OF VINES AND SHRUBS OF WESTERN POISON OAK,TOXICODENDRON DIVERSILOBUM (ANACARDIACEAE)

Because of the different mechanical constraints on vines and self-supporting plants, vines are thought to differ from trees and shrubs in a variety of their growth characteristics. I tested the hypotheses that vines grow faster than shrubs and that supported shoots have delayed leaf expansion relative to stem elongation, using western poison oak, Toxicodendron diversilobum (T. & G.) Greene, a plant that grows as a vine when externally supported but otherwise as a shrub. In the field, supported shoots (vines) had significantly higher aboveground biomass and relative growth rates than did their paired unsupported shoots (shrubs) growing nearby. This was not due to differences in leaf phenology, but may have resulted from vines growing into more favorable habitats for growth. In contrast, whereas 2-yr-old cloned plants in a common garden differed in their stem and internode lengths, they had the same aboveground dry weight, proportion of dry weight that was leaf, and relative rate of increase in primary stem length whether grown with stakes (vines) or without stakes (shrubs). These results suggest that there is no inherent requirement of vines to grow faster than shrubs. As hypothesized, leaf elongation was more delayed relative to stem elongation in staked than unstaked individuals in 19 paired plants (each pair cloned from a different source plant). Thus, physical cues resulting from the presence of support can alter the plant's spatial and temporal patterns of development, but do not necessarily dictate the quantity of biomass that will be produced.     

Spatial-specific regulation of root development by phytochromes in Arabidopsis thaliana

Distinct tissues and organs of plants exhibit dissimilar responses to light exposure – cotyledon growth is promoted by light, whereas hypocotyl growth is inhibited by light. Light can have different impacts on root development, including impacting root elongation, morphology, lateral root proliferation and root tropisms. In many cases, light inhibits root elongation. There has been much attention given to whether roots themselves are the sites of photoperception for light that impacts light-dependent growth and development of roots. A number of approaches including photoreceptor localization in planta, localized irradiation and exposure of dissected roots to light have been used to explore the site(s) of light perception for the photoregulation of root development. Such approaches have led to the observation that photoreceptors are localized to roots in many plant species, and that roots are capable of light absorption that can alter morphology and/or gene expression. Our recent results show that localized depletion of phytochrome photoreceptors in Arabidopsis thaliana disrupts root development and root responsiveness to the plant hormone jasmonic acid. Thus, root-localized light perception appears central to organ-specific, photoregulation of growth and development in roots.     

Biomechanical study of the effect of a controlled bending on tomato stem elongation: local strain sensing and spatial integration of the signal

In a previous paper it has been demonstrated that tomato stems, submitted to a controlled basal bending, had a reduced terminal primary elongation, indicating mechanosensing and intra plant signalling. The 'intensity' of the growth response, as measured by the time to recover an elongation rate similar to the control, varied hugely between plants. However, no relation was found between the intensity of this response and the mechanical variables characterizing the global mechanical state of the stem. In this paper, a local analysis of mechanical state of each bent stem is performed in the context of beam theory. The spatial distributions of local variables all along the stem (curvature, bending moment, strains and stresses) are established. The validity of hypotheses underlying the mechanical analysis is demonstrated. To investigate the relationships between the mechanical stimulus and the growth response, a novel biomechanical analysis based on spatial integration of the mechanical stimulus is presented. It revealed that the mechanosensing is local and scattered through the stem and that the variability of the growth response is only explained by the integrals of the longitudinal strain field.     

The cellular basis of cell sorting kinetics

Cell sorting is a dynamical cooperative phenomenon that is fundamental for tissue morphogenesis and tissue homeostasis. According to Steinberg's differential adhesion hypothesis, the structure of sorted cell aggregates is determined by physical characteristics of the respective tissues, the tissue surface tensions. Steinberg postulated that tissue surface tensions result from quantitative differences in intercellular adhesion. Several experiments in cell cultures as well as in developing organisms support this hypothesis.The question of how tissue surface tension might result from differential adhesion was addressed in some theoretical models. These models describe the cellular interdependence structure once the temporal evolution has stabilized. In general, these models are capable of reproducing sorted patterns. However, the model dynamics at the cellular scale are defined implicitly and are not well-justified. The precise mechanism describing how differential adhesion generates the observed sorting kinetics at the tissue level is still unclear.It is necessary to formulate the concepts of cell level kinetics explicitly. Only then it is possible to understand the temporal development at the cellular and tissue scales. Here we argue that individual cell mobility is reduced the more the cells stick to their neighbors. We translate this assumption into a precise mathematical model which belongs to the class of stochastic interacting particle systems. Analyzing this model, we are able to predict the emergent sorting behavior at the population level. We describe qualitatively the geometry of cell segregation depending on the intercellular adhesion parameters. Furthermore, we derive a functional relationship between intercellular adhesion and surface tension and highlight the role of cell mobility in the process of sorting. We show that the interaction between the cells and the boundary of a confining vessel has a major impact on the sorting geometry.     

Root pressurization affects growth-induced water potentials and growth in dehydrated maize leaves

Profiles of water potential (Psi w) were measured from the soil to the tips of growing leaves of maize (Zea mays L.) when pressure (P) was applied to the soil/root system. At moderately low soil Psi w, leaf elongation was somewhat inhibited, large tensions existed in the xylem, and Psi w were slightly lower in the elongating leaf tissues than in the xylem, i.e. a growth-induced Psi w was present but small. With P, the tension was relieved, enlarging the difference in Psi w between the xylem and the elongating tissues, i.e. enlarging the growth-induced Psi w, which is critical for growth. Guttation occurred, confirming the high Psi w of the xylem, and the mature leaf tissue rehydrated. Water uptake increased and met the requirements of transpiration. Leaf elongation recovered to control rates. Under more severe conditions at lower soil Psi w, P induced only a brief elongation and the growth-induced Psi w responded only slightly. Guttation did not occur, water flow did not meet the requirements of transpiration, and the mature leaf tissues did not rehydrate. A rewatering experiment indicated that a low conductance existed in the severely dehydrated soil, which limited water delivery to the root and shoot. Therefore, the initial growth inhibition appeared to be hydraulic because the enlargement of the growth-induced Psi w by P together with rehydration of the mature leaf tissue were essential for growth recovery. In more severe conditions, P was ineffective because the soil could not supply water at the required rate, and metabolic factors began to contribute to the inhibition.     

Plant nutrition and growth: Basic principles

Soil compaction may restrict shoot growth of sugar beet plants. Roots, however, are the plant organs directly exposed to soil compaction and should therefore be primarily affected. The aim of this study was to determine the influence of mechanical resistance and aeration of compacted soil on root and shoot growth and on phosphorus supply of sugar beet. For this purpose, a silt loam soil was adjusted to bulk densities of 1.30, 1.50 and 1.65 g cm^–3 and water tensions of 300 and 60 hPa. Sugar beet was grown in a growth chamber under constant climatic conditions for 4 weeks. Both, decrease of water tension and increase of bulk density impeded root and shoot growth. In contrast, the P supply of the plants was differently affected. At the same air-filled pore volume, the P concentration of the shoots was reduced by a decrease of soil water tension, but not by an increase of bulk density. Both factors also reduced root length and root hair formation, however, in compacted soil the plants partly substituted for the reduction of root size by increasing the P uptake efficiency per unit of root. Shoot growth decreased when root growth was restricted. Both characteristics were closely related irrespective of the cause of root growth limitation by either compaction or water saturation. It is therefore concluded that shoot growth in both the compacted and the wet soil was regulated by root growth. The main factor impeding root growth in compacted soil was penetration resistance, not soil aeration.FAX no corresponding author: +49551 5056299