Kinematics of surface growth

 In this paper a general mathematical framework is developed to describe cases of fixed and moving growth surfaces. This formulation has the mathematical structure suggested by Skalak (1981), but is extended herein to include discussion of possible singularities, incompatibilities, residual stresses and moving growth surfaces. Further, the general theoretical equations necessary for the computation of the final form of a structure from the distribution of growth velocities on a growth surface are presented and applied in a number of examples. It is shown that although assuming growth is always in a direction normal to the current growth surface is generally sufficient, growth at an angle to the growth surface may represent the biological reality more fully in some respects. From a theoretical viewpoint, growth at an angle to a growth surface is necessary in some situations to avoid postulating singularities in the growth velocity field. Examples of growth on fixed and moving surfaces are developed to simulate the generation of horns, seashells, antlers, teeth and similar biological structures. Received 20 February 1996; received in revised form 15 October 1996     

Heterogeneous growth of plant tissues

KORN, R., 1993. Heterogeneous growth of plant tissues. Heterogeneous growth is defined as different rates or patterns of growth in adjacent tissue regions, in contrast to homogeneous growth where a region expresses a uniform rate or pattern of growth. Heterogeneous growth is inspected in a variety of plant tissues and the pattern of expansion is characterized for each. In the case of epidermal cell proliferation, different growth rates for cell plates and old walls lead to the feature of coordinated growth in which slow growth of the former is compensated for by a faster rate of the latter. Examples include leaf epidermal cells above veins growing differently from those above areole regions, and pairs of guard cells of stomata ceasing to expand before other epidermal cells. In the alga Coleochaete only marginal walls grow, and at different rates around the colony, to generate a fractal, stochastic type of coordinated growth. In the fern gametophyte there are complex gradients of differential growth rates. Epidermal cells of apices are often of mixed growth, as cells at the summit undergo two dimensional expansion while cells along the flanks express one dimensional expansion. Coordinated growth requires matched rates where the constraining effect of the slower growing region is compensated for by a faster rate in an encircling region compared to the average rate of the overall tissue. Mixed and differential growth patterns do not necessarily create constraints and so lead to smooth tissue expansion. Emergence of some constraints leads to breaking of symmetry and disruptive growth as in the appearance of new axes found in organs and epidermal derivatives. In planar development heterogeneous growth appears to be the rule, and homogeneous growth the exception.     

Model for the regulation of size in the wing imaginal disc of Drosophila

For animal development it is necessary that organs stop growing after they reach a certain size. However, it is still largely unknown how this termination of growth is regulated. The wing imaginal disc of Drosophila serves as a commonly used model system to study the regulation of growth. Paradoxically, it has been observed that growth occurs uniformly throughout the disc, even though Decapentaplegic (Dpp), a key inducer of growth, forms a gradient. Here, we present a model for the control of growth in the wing imaginal disc, which can account for the uniform occurrence and termination of growth. A central feature of the model is that net growth is not only regulated by growth factors, but by mechanical forces as well. According to the model, growth factors like Dpp induce growth in the center of the disc, which subsequently causes a tangential stretching of surrounding peripheral regions. Above a certain threshold, this stretching stimulates growth in these peripheral regions. Since the stretching is not completely compensated for by the induced growth, the peripheral regions will compress the center of the disc, leading to an inhibition of growth in the center. The larger the disc, the stronger this compression becomes and hence the stronger the inhibiting effect. Growth ceases when the growth factors can no longer overcome this inhibition. With numerical simulations we show that the model indeed yields uniform growth. Furthermore, the model can also account for other experimental data on growth in the wing disc.     

Role of microtubules in tip growth of fungi

Polarized cell growth is observed ubiquitously in all living organisms. Tip growth of filamentous fungi serves as a typical model for polar growth. It is well known that the actin cytoskeleton plays a central role in cellular growth. In contrast, the role of microtubules in polar growth of fungal tip cells has not been critically addressed. Our recent study, using a green fluorescent protein (GFP)-labeled tubulin-expressing strain of the filamentous fungus Aspergillus nidulans and treatment with an anti-microtubule reagent, revealed that microtubules are essential for rapid hyphal growth. Our results indicated that microtubule organization contributes to continuous tip growth throughout the cell cycle, which in turn enables the maintenance of an appropriate mass of cytoplasm for the multinucleate system. In filamentous fungi, the microtubule is an essential component of the tip growth machinery that enables continuous and rapid growth. Recent research developments are starting to elucidate the components of the tip growth machinery and their functions in many organisms. This recent knowledge, in turn, is starting to enhance the importance of fungal systems as simple model systems to understand the polar growth of cells.     

Temporal analysis of rat growth plates: cessation of growth with age despite presence of a physis.

Despite the continued presence of growth plates in aged rats, longitudinal growth no longer occurs. The aims of this study were to understand the reasons for the cessation of growth. We studied the growth plates of femurs and tibiae in Wistar rats aged 62-80 weeks and compared these with the corresponding growth plates from rats aged 2-16 weeks. During skeletal growth, the heights of the plates, especially that of the hypertrophic zone, reflected the rate of bone growth. During the period of decelerating growth, it was the loss of large hydrated chondrocytes that contributed most to the overall decrease in the heights of the growth plates. In the old rats we identified four categories of growth plate morphology that were not present in the growth plates of younger rats: (a). formation of a bone band parallel to the metaphyseal edge of the growth plate, which effectively sealed that edge; (b). extensive areas of acellularity, which were resistant to resorption and/or remodeling; (c). extensive remodeling and bone formation within cellular regions of the growth plate; and (d). direct bone formation by former growth plate chondrocytes. These processes, together with a loss of synchrony across the plate, would prevent further longitudinal expansion of the growth plate despite continued sporadic proliferation of chondrocytes.     

杉木不同生长类型对养分供应的持续效应

应用“正态分布标准差分类法”把杉木(Cunninghamia lanceolata)试验林分树高生长划分为5个生长类型，按不同生长类型进行施肥试验。结果表明，不同生长类型杉木施肥后2年生长期的树高年生长量表现为，生长类型好的群体对施肥有更好的持续促进高生长效应；生长类型差的群体，在施肥量相对少时高生长持续效应不明显，当施肥量较大时能有较好的树高年生长量持续生长效应。不同生长类型杉木胸径年生长量对施肥量的响应表现为，相同条件下，好的生长类型比差的生长类型有更好的胸径年生长量效果，施肥量相对不足时，差的生长类型群体胸径年生长持续效应逐渐衰退，好的生长类型对施肥有更好的持续促进生长效果，施肥量大对胸径年生长有更好的持续促进作用，与树高生长表现基本一致。研究表明，遗传品质好的杉木群体对立地适应能力越强，有更好的耐瘠薄能力和更好的年生长量。施肥措施对不同遗传品质生长类型杉木树高与胸径年生长量都有较好的促进效应，能有效恢复与提高杉木低产林分生长，为杉木低产与小老林林分改良提供理论指导。     

Simulation of biological growth

Researchers concerned with the growth of biological tissue often use models that predict the growth as a function of a mechanical stimulus such as stress, strain or elastic energy. However, a general theory for bulk growth should consider that the mechanical stimulus may only be one of many factors contributing to growth. Another important factor could be time, as living tissues can be assumed to have a pre-programmed directional biological growth that is independent of mechanical stimuli. This paper has two objectives: the first is to introduce the concept of directional biological growth within a well developed growth theory, the second is to present the computational methods by which three-dimensional growth that encompasses time and stress effects can be simulated using commercially available finite element analysis software.     

Acute Regulation of the Epidermal Growth Factor Receptor in Response to Nerve Growth Factor

PC12 cells possess specific receptors for both nerve growth factor and epidermal growth factor, and by an unknown mechanism, nerve growth factor is able to attenuate the propagation of a mitogenic response to epidermal growth factor. The differentiation response of PC12 cells to nerve growth factor, therefore, predominates over the proliferative response to epidermal growth factor. We have observed that the addition of nerve growth factor to PC12 cells rapidly produces a decrease in surface 125I-epidermal growth factor binding capacity. Unlike previously described nerve growth factor effects on 125I-epidermal growth factor binding capacity, which required several days of nerve growth factor exposure, the decreases we report occur within minutes of nerve growth factor addition: A 50% decrease in 125I-epidermal growth factor binding capacity is evident at 10 min. This rapid nerve growth factor response is concentration dependent; inhibition of 125I-epidermal growth factor binding is detectable at nerve growth factor levels as low as 0.2 ng/ml and is maximal at approximately 50 ng/ml, consistent with known ranges of biological activity. No demonstrable differences in the rate of epidermal growth factor receptor synthesis or degradation were observed in cells acutely exposed to nerve growth factor. Scatchard analysis revealed that acute nerve growth factor treatment decreased the number of both high- and low-affinity 125I-epidermal growth factor binding sites, while the receptor affinity remained unchanged. We have also investigated the involvement of various potential intracellular mediators of nerve growth factor action and of known intracellular modulatory systems of the epidermal growth factor receptor for their capacity to participate in this nerve growth factor activity.     

The tensor-based model of plant growth applied to leaves of Arabidopsis thaliana: A two-dimensional computer model

Plant organs grow in coordinated and continuous way. Such growth is of a tensor nature, hence there is an infinite number of different directions of growth rate in each point of the growing organ. Three mutually orthogonal directions of growth can be recognized in which growth achieves extreme values (principal directions of growth [PDGs]). Models based on the growth tensor have already been successfully applied to the root and shoot apex. This paper presents the 2D model of growth applied to the arabidopsis leaf. The model employs the growth tensor method with a non-stationary velocity field. The postulated velocity functions are confirmed by growth measurements with the aid of the replica method.     

Evolution of human growth spurts

This study investigates subadult growth spurts in a large sample of anthropoid primates, including humans. Analyses of body mass growth curves show that humans are not unique in the expression of female and male body mass growth spurts. Subadult growth spurts are observed in both New World and Old World anthropoid primates and are more common in males than in females. Allometric analyses of growth spurts indicate that many aspects of primate growth spurts are strongly correlated with species size. Small species tend not to exhibit growth spurts. Although male and female scaling patterns for velocity and size measures are comparable, scaling relations of variables that measure the timing of growth spurts differ by sex. These patterns can he related to sexual differences in life histories. Scaling analyses further show that humans do not depart substantially from patterns that describe other anthropoid primates. Thus, in relative terms, human growth spurts are not exceptional compared to this sample of primates. The long absolute delay in the initiation of the human growth spurt may be of substantial evolutionary importance and serves to distinguish humans from other primates. In essence, humans exhibit growth spurts that are comparable to other primates in many respects. However, human growth spurts are shifted to very late absolute ages. © 1996 Wiley-Liss, Inc.     

Inferring temperature adaptation from thermal performance curves of somatic growth rate: The importance of growth measurements and mortality

When comparing somatic growth thermal performance curves (TPCs), higher somatic growth across experimental temperatures is often observed for populations originating from colder environments. Such countergradient variation has been suggested to represent adaptation to seasonality, or shorter favourable seasons in colder climates. Alternatively, populations from cold climates may outgrow those from warmer climates at low temperature, and vice versa at high temperature, representing adaptation to temperature. Using modelling, we show that distinguishing between these two types of adaptation based on TPCs requires knowledge about (i) the relationship between somatic growth rate and population growth rate, which in turn depends on the scale of somatic growth (absolute or proportional), and (ii) the relationship between somatic growth rate and mortality rate in the wild. We illustrate this by quantifying somatic growth rate TPCs for three populations of Daphnia magna where population growth scales linearly with proportional somatic growth. For absolute somatic growth, the northern population outperformed the two more southern populations across temperatures, and more so at higher temperatures, consistent with adaptation to seasonality. In contrast, for the proportional somatic growth TPCs, and hence population growth rate, TPCs tended to converge towards the highest temperatures. Thus, if the northern population pays an ecological mortality cost of rapid growth in the wild, this may create crossing population growth TPCs consistent with adaptation to temperature. Future studies within this field should be more explicit in how they extrapolate from somatic growth in the lab to fitness in the wild.     

Autocrine mechanism of growth of neonatal rat hepatocytes in primary culture

Hepatocytes from neonatal rats of 0 to 3 days old grew actively in primary culture without added serum or growth factors. In these culture conditions, growth of hepatocytes decreased progressively with increase in age of the rats from which they were isolated, and hepatocytes from rats of 2 weeks old showed scarcely any growth. Actively growing hepatocytes were found to secrete a growth factor that promoted their growth and that of Swiss 3T3 cells, but not that of adult hepatocytes. This growth factor in conditioned medium of growing hepatocytes was heat- and acid-stable, but sensitive to trypsin, and had a molecular weight of over 10,000. It did not inhibit the binding of [125I]epidermal growth factor to its receptor, and its growth promoting activity was not inhibited by monoclonal antibody against insulin-like growth factor II. Therefore, it seems to be a new growth factor. These results, together with previous findings (Nakamura, T., Nagao, M., & Ichihara, A. (1987) Exp. Cell Res. 169, 1-14) demonstrated a reciprocal relation between growth and maturation of neonatal hepatocytes during development, like that of adult cells, but indicated that unlike growth of the latter, growth of neonatal cells is induced by an autocrine mechanism.     

遮荫对峦大杉1年生苗木生长的影响及动态优化

以当年播种的峦大杉(Cunninghamia konishii)幼苗为材料,采用单因素试验设计3个遮荫处理(50%、75%、100%光照),每隔7 d监测地径、苗高等生长进程;应用Logistic方程拟合苗高、地径生长过程并分析其生长节律。结果表明,遮荫显著促进峦大杉幼苗全生长季的苗高、地径生长,以50%光照表现最好;不同生长阶段遮荫对峦大杉苗高、地径生长量的影响有所不同,进行动态优化十分必要。Logistic方程能较好地拟合峦大杉苗木生长动态。50%光照处理显著提高峦大杉苗高、地径的线性生长速率、最大线性生长速率和线性生长量,显著提前苗高线性生长终期、缩短线性生长持续时间,显著推迟地径线性生长始期。峦大杉苗期光照强度动态优化方案：在t≤133 d前阶段宜采用50%光照,在t＞133 d期间宜采用100%光照。     

Constant and continuous growth reduction as a possible cause of ageing

Post-embryonic growth is characterized by a constant reduction of some growth parameters in relation to other growth parameters. Comparison of growth in chickens, rats and nematodes reveals an identical growth pattern, so a theory about the growth process in general is presented. It is presumed that the same growth promoting and growth inhibiting substances regulate not only growth but also ageing and that it is the equilibrium between growth promoters and growth inhibitors which is constantly changed.     

Immunochemical comparison of peptide angiogenic factors

A panel of 40 monoclonal antibodies was constructed in response to cationic endothelial cell growth factor (c-ECGF), the cationic peptide mitogen isolated from endothelial mitogen. The monoclonal antibodies were assayed by dot blot for immunoreactivity to various other peptide angiogenic factors. The panel of monoclonal antibodies to c-ECGF exhibited complete cross-reactivity with pituitary fibroblast growth factor and sarcoma-derived growth factor. A group of 28 monoclonal antibodies was found to exhibit reactivity to anionic endothelial mitogen (a-ECGF), brain fibroblast growth factor, endothelial cell growth factor, and retina-derived growth factor. None of the monoclonal antibodies was found to react with epidermal growth factor or platelet-derived growth factor. These data provide an immunological basis for grouping heparin-binding endothelial cell growth factors into anionic and cationic groups.     

The Dynamics of Size-at-Age Variability

In this paper, we propose a theoretical framework within which a unified treatment of the key sources of size-at-age variability—size dependence of growth rate, stochastic growth rate variations and individual-to-individual variability in growth performance—is possible. We use this framework to develop a general criterion for growth depensation in cohorts, which we define as the increase of the coefficient of variation of size-at-age, with increasing age. We use this criterion to show that size dependence of growth rate, acting alone, is depensatory only if the growth rate increases faster than linearly with size (that is, if growth is faster than exponential), while stochastic growth rate variation is invariably depensatory. Many species exhibit growth rates that scale less than linearly with size; indeed the commonly used von Bertalanffy model shows growth rates which actually decrease with size. In such a species, the size dependence of growth rate acts compensatorily, while stochastic growth rate variability is depensatory. We show that the tension between these two mechanisms leads to quasi-stationary size-at-age variability, which we can calculate analytically in some special cases and obtain by a simple numerical procedure where analysis is impractical.     

Expression of growth hormone and insulin-like growth factor in the immune system of children.

Our objective was to study the effect of the growth hormone--insulin-like growth factor axis on the development of the immune system in children. We used radio receptor analysis, dot blot, in situ hybridization, and immunohistochemical techniques to determine the expression and distribution of growth hormone and growth hormone receptors, insulin-like growth factors, receptors and binding proteins in the thymus, lymph nodes and peripheral blood lymphocytes of children and adults. Our results showed that almost all components of the growth hormone-insulin-like growth factor axis were expressed in immune organs and cells, but the levels of expression varied. Growth hormone, insulin-like growth factor I, and insulin-like growth factor-binding proteins 1-6 were produced by immune cells in autocrine or paracrine ways. The expression of growth hormone receptors on peripheral blood lymphocytes was to be age-related. The growth hormone-insulin-like growth factor axis may help regulate the development and function of the immune system in children.     

营巢类型、巢捕食和窝卵数对高寒草甸雀形目雏鸟生长期的影响

根据1998—2001年高寒草甸10种雀形目鸟类的窝卵数、雏期和巢捕食数据,以Logistic方程拟合雏鸟生长过程,并计算出有关生长率参数;根据营巢类型将10种雀形目鸟划分为开放或半开放类群(GOB)和全封闭穴居类群(HCB)两类,将把雏鸟的生长过程划分为3个生长期(缓增期、快增期和渐增期)。3个生长期占雏期的比例因营巢类型而异,GOB类群快增期>渐增期>缓增期;HCB类群渐增期>快增期>缓增期。分析营巢类型、巢捕食和窝卵数与各生长期之间的关系,结果表明3个生长期的体重积累占离巢时体重的比例因巢型不同而有显著差异;营巢类型和巢捕食显著影响各生长期占雏期的比例和体重积累占离巢时体重的比例;窝卵数影响快增期和渐增期长度,而不影响缓增期长度。快增期体重积累与渐增期的生长率不相关,但与渐增期长度显著相关。因此,前期的能量积累不影响后期生长率,而影响后期生长的长度。该结果进一步印证在晚成鸟中不存在补偿性生长。     

The role of polypeptide growth factors in phenotypic transformation of normal rat kidney cells

A serum-free assay has been established for studying the role of polypeptide growth factors in inducing loss of density-dependent inhibition of growth of normal rat kidney (NRK) cells. The process has been characterized by measuring the time course of [3H]thymidine incorporation into confluent, quiescent NRK cultures stimulated by defined polypeptide growth factors, in combination with cell counting studies, increases in DNA content, and cell cycle analysis by means of a fluorescence-activated cell sorter. It is shown that none of the growth factors tested (epidermal growth factor, platelet-derived growth factor, transforming growth factor-beta, and retinoic acid) is able to induce loss of density-dependent inhibition of growth by itself, but strong synergism was observed when combinations of growth factors were tested. None of the above factors was found to be essential, however, since any combination of three of the above four growth factors strongly induced the process. Strong parallels were observed between the growth factor requirements for inducing loss of density-dependent inhibition of growth under serum-free conditions and the requirements for induction of anchorage-independent proliferation under growth factor-defined assay conditions. This indicates that most likely the same cellular processes underlie these two aspects of phenotypic transformation, although data indicate that anchorage-independent proliferation may be a more restricted property of phenotypic transformation than loss of density dependence of proliferation. It is concluded that phenotypic transformation of NRK cells does not require specific polypeptide growth factors, but reflects the ability of these cells to respond to multiple growth factors.