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.     

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.     

Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach

Scientific formalizations of the notion of growth and measurement of the rate of growth in living organisms are age-old problems. The most frequently used metric, “Average Relative Growth Rate” is invariant under the choice of the underlying growth model. Theoretically, the estimated rate parameter and relative growth rate remain constant for all mutually exclusive and exhaustive time intervals if the underlying law is exponential but not for other common growth laws (e.g., logistic, Gompertz, power, general logistic). We propose a new growth metric specific to a particular growth law and show that it is capable of identifying the underlying growth model. The metric remains constant over different time intervals if the underlying law is true, while the extent of its variation reflects the departure of the assumed model from the true one. We propose a new estimator of the relative growth rate, which is more sensitive to the true underlying model than the existing one. The advantage of using this is that it can detect crucial intervals where the growth process is erratic and unusual. It may help experimental scientists to study more closely the effect of the parameters responsible for the growth of the organism/population under study.     

A flexible sigmoid function of determinate growth

A new empirical equation for the sigmoid pattern of determinate growth, 'the beta growth function', is presented. It calculates weight (w) in dependence of time, using the following three parameters: t(m), the time at which the maximum growth rate is obtained; t(e), the time at the end of growth; and w(max), the maximal value for w, which is achieved at t(e). The beta growth function was compared with four classical (logistic, Richards, Gompertz and Weibull) growth equations, and two expolinear equations. All equations described successfully the sigmoid dynamics of seed filling, plant growth and crop biomass production. However, differences were found in estimating w(max). Features of the beta function are: (1) like the Richards equation it is flexible in describing various asymmetrical sigmoid patterns (its symmetrical form is a cubic polynomial); (2) like the logistic and the Gompertz equations its parameters are numerically stable in statistical estimation; (3) like the Weibull function it predicts zero mass at time zero, but its extension to deal with various initial conditions can be easily obtained; (4) relative to the truncated expolinear equation it provides more reasonable estimates of final quantity and duration of a growth process. In addition, the new function predicts a zero growth rate at both the start and end of a precisely defined growth period. Therefore, it is unique for dealing with determinate growth, and is more suitable than other functions for embedding in process-based crop simulation models to describe the dynamics of organs as sinks to absorb assimilates. Because its parameters correspond to growth traits of interest to crop scientists, the beta growth function is suitable for characterization of environmental and genotypic influences on growth processes. However, it is not suitable for estimating maximum relative growth rate to characterize early growth that is expected to be close to exponential.     

Control of gluconeogenic growth by pps and pck in Escherichia coli.

It is well-known that Escherichia coli grows more slowly on gluconeogenic carbon sources than on glucose. This phenomenon has been attributed to either energy or monomer limitation. To investigate this problem further, we varied the expression levels of pck, encoding phosphoenolpyruvate carboxykinase (Pck), and pps, encoding phosphoenolpyruvate synthase (Pps). We found that the growth rates of E. coli in minimal medium supplemented with succinate and with pyruvate are limited by the levels of Pck and Pps, respectively. Optimal overexpression of pck or pps increases the unrestricted growth rates on succinate and on pyruvate, respectively, to the same level attained by the wild-type growth rate on glycerol. Since Pps is needed to supply precursors for biosyntheses, we conclude that E. coli growing on pyruvate is limited by monomer supply. However, because pck is required both for biosyntheses and catabolism for cells growing on succinate, it is possible that growth on succinate is limited by both monomer and energy supplies. The growth yield with respect to oxygen remains approximately constant, even though the overproduction of these enzymes enhances gluconeogenic growth. It appears that the constant yield for oxygen is characteristic of efficient growth on a particular substrate and that the yield is already optimal for wild-type strains. Further increases in either Pck or Pps above the optimal levels become growth inhibitory, and the growth yield for oxygen is reduced, indicating less efficient growth.     

The estimation of algal yield parameters associated with mixotrophic and photoheterotrophic growth under batch cultivation

The true growth yield and maintenance coefficient for algal growth under batch cultivation are estimated by employing a modified yield model used for continuous systems. The data of aerobic and anaerobic growth are utilized for mixotrophic and photoheterotrophic growth. Chlorella species show the highest bioenergetic yield of 0·6802 for aerobic and mixotrophic growth. Yeast extract proved to be a good nutrient with a high growth yield of 0·7838. Aerobic and mixotrophic growth required less maintenance energy than anaerobic and photoheterotrophic growth: 0·0057 (1/h) and 0·0494 (1/h) for aerobic and anaerobic growth, respectively. It is concluded that mixotrophic growth utilizing glucose is the most efficient process for producing photosynthetic biomass.     

Computational modeling of volumetric soft tissue growth: application to the cardiac left ventricle

As an initial step to investigate stimulus–response relations in growth and remodeling (G&R) of cardiac tissue, this study aims to develop a method to simulate 3D-inhomogeneous volumetric growth. Growth is regarded as a deformation that is decomposed into a plastic component which describes unconstrained growth and an elastic component to satisfy continuity of the tissue after growth. In current growth models, a single reference configuration is used that remains fixed throughout the entire growth process. However, considering continuous turnover to occur together with growth, such a fixed reference is unlikely to exist in reality. Therefore, we investigated the effect of tissue turnover on growth by incrementally updating the reference configuration. With both a fixed reference and an updated reference, strain-induced cardiac growth in magnitude of 30% could be simulated. However, with an updated reference, the amplitude of the stimulus for growth decreased over time, whereas with a fixed reference this amplitude increased. We conclude that, when modeling volumetric growth, the choice of the reference configuration is of great importance for the computed growth.     

Functional mapping of quantitative trait loci underlying growth trajectories using a transform-both-sides logistic model

The incorporation of developmental control mechanisms of growth has proven to be a powerful tool in mapping quantitative trait loci (QTL) underlying growth trajectories. A theoretical framework for implementing a QTL mapping strategy with growth laws has been established. This framework can be generalized to an arbitrary number of time points, where growth is measured, and becomes computationally more tractable, when the assumption of variance stationarity is made. In practice, however, this assumption is likely to be violated for age-specific growth traits due to a scale effect. In this article, we present a new statistical model for mapping growth QTL, which also addresses the problem of variance stationarity, by using a transform-both-sides (TBS) model advocated by Carroll and Ruppert (1984, Journal of the American Statistical Association 79, 321-328). The TBS-based model for mapping growth QTL cannot only maintain the original biological properties of a growth model, but also can increase the accuracy and precision of parameter estimation and the power to detect a QTL responsible for growth differentiation. Using the TBS-based model, we successfully map a QTL governing growth trajectories to a linkage group in an example of forest trees. The statistical and biological properties of the estimates of this growth QTL position and effect are investigated using Monte Carlo simulation studies. The implications of our model for understanding the genetic architecture of growth are discussed.     

Nonlinear growth cost in Menidia menidia: theory and empirical evidence

Juvenile growth is submaximal in many species, suggesting that a trade-off with juvenile growth must exist. In support of this, recent studies have demonstrated that rapid growth early in life results in decreased physiological performance. Theory clearly shows that for submaximal growth in juveniles to be optimal, the cost of growth must be nonlinear. However, nearly all of the empirical evidence for costs of growth comes from linear comparisons between fast- and slow-growing groups. It is consequently unclear whether any known cost can account for the evolution of submaximal juvenile growth. To test whether the cost of growth exhibits the logically necessary nonlinearity, we measured critical swimming speed (Ucrit), the maximum speed sustained in incremental velocity trials, in Atlantic silversides, a species for which the costs and benefits of growth are well studied. To increase our ability to detect a nonlinear relationship between Ucrit, a proxy for juvenile fitness, and growth, we manipulated ration levels to produce a broad range of growth rates (0.16 mm/day(-1) to 1.20 mm/day(-1)). Controlling for size and age, we found that Ucrit decreased precipitously as growth approached the physiological maximum. Using Akaike's information criterion, we show that swimming performance decreases with the square of growth rate, providing the first demonstration of a nonlinear cost of growth.     

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.     

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.     

Spatio-temporal leaf growth patterns of Arabidopsis thaliana and evidence for sugar control of the diel leaf growth cycle

Leaf growth dynamics are driven by diel rhythms. The analysis of spatio-temporal leaf growth patterns in Arabidopsis thaliana wild type and mutants of interest is a promising approach to elucidate molecular mechanisms controlling growth. The diel availability of carbohydrates is thought to affect diel growth. A digital image sequence processing (DISP)-based noninvasive technique for visualizing and quantifying highly resolved spatio-temporal leaf growth was adapted for the model plant A. thaliana. Diel growth patterns were analysed for the wild type and for a mutant with altered diel carbohydrate metabolism. A. thaliana leaves showed highest relative growth rates (RGRs) at dawn and lowest RGRs at the beginning of the night. Along the lamina, a clear basipetal gradient of growth rate distribution was found, similar to that in many other dicotyledonous species. The starch-free 1 (stf1) mutant revealed changed temporal growth patterns with reduced nocturnal, and increased afternoon, growth activity. The established DISP technique is presented as a valuable tool to detect altered temporal growth patterns in A. thaliana mutants. Endogenous changes in the diel carbohydrate availability of the starch-free mutant clearly affected its diel growth rhythms.     

Growth distribution during first positive phototropic curvature of maize coleoptiles*

Abastract Measurements of growth increments on the shaded and the irradiated sides of phototropically stimulated maize (Zea mays L.) coleoptiles, obtained over the entire fluence range of the first positive curvature, indicate that the curvature is induced by growth stimulation on the shaded side and compensating inhibition on the irradiated side (length increments on the coleoptile flanks were determined 100 min after 30 s phototropic induction with blue light). At high fluences of blue light, overall stimulation of growth takes place, but this tendency is largely eliminated when only the tip of the coleoptile is irradiated. Time courses for growth increments obtained for the maximum first positive response show that the growth stimulation on the shaded side and the growth inhibition on the irradiated side commence almost simultaneously 20-30 min after the phototropic induction. The growth on the irradiated side almost ceases, but the growth rate on the shaded side is doubled, relative to the control rate. The onset of differential growth migrates basipetally from the tip at a velocity similar to that for polar auxin transport. The first positive phototropic response of the coleoptile is concluded to be the consequence of lateral redistribution of growth, which is not necessarily accompanied by changes in the net growth. The results are consonant with the Cholodny-Went theory of tropisms, in which lateral redistribution of auxin is considered to be the cause of tropic responses.     

Neonatal and post-natal growth

Growth velocity is higher in late intra-uterine and early post-natal life than at any time thereafter, and accurate measurements are essential for appropriate monitoring. The accuracy with which such measurements are made and recorded is frequently questionable, however, and short- and medium-term changes in growth may be difficult to interpret in the light of normal variations in the pattern of growth. Infants who are small at birth must be accurately classified because intra-uterine growth retardation and small for gestational age have different implications for both causation and outcome. Prediction of expected growth on the basis of mid-parental height is essential but frequently omitted. Post-natal growth impairment is common in pre-term infants and is often rapid in onset. Poor growth may continue for many months, and catch-up may be incomplete. Early growth failure may have a significant influence on subsequent morbidity and mortality.     

Optimal growth pattern of defensive organs: the diversity of shell growth among mollusks

Mollusks show a diversity of shell growth patterns. We develop a model for the dynamic resource allocation to defense organs and analyze it with the Pontryagin maximum principle. A typical optimal growth schedule is composed of the initial phase of soft-body growth without shell followed by a simultaneous growth of shell and soft body and finally the reproductive phase without growth (simultaneous shell growth). If the defensible predation risk is low or if the cost of defense is high, the optimal strategy is to have no shell (shell-less growth). If defensible predation pressure or general mortality differs before and after maturation, an additional three strategies, characteristic of the exclusive growth of shell or soft body, can be optimal (sequential shell growth, additional body-expansion growth, and additional callus-building growth). These optimal strategies are in accord with the patterns observed for mollusks. In particular, the growth strategies with exclusive growth phase of external shells are preferred when durophagous predation pressure after maturation is higher than that before maturation. This result explains the observation that many tropical gastropods with thickened shell lips spend their vulnerable juvenile phase in sheltered habitats.     

Dynamic regulation of growing domains for elongating and branching morphogenesis in plants

With their continuous growth, understanding how plant shapes form is fundamentally linked to understanding how growth rates are controlled across different regions of the plant. Much of a plant's architecture is generated in shoots and roots, where fast growth in tips contrasts with slow growth in supporting stalks. Shapes can be determined by where the boundaries between fast- and slow-growing regions are positioned, determining whether tips elongate, branch, or cease to grow. Across plants, there is a diversity in the cell wall chemistry through which growth operates. However, prototypical morphologies, such as tip growth and branching, suggest there are common dynamic constraints in localizing chemical growth catalysts. We have used Turing-type reaction-diffusion mechanisms to model this spatial localization and the resulting growth trajectories, characterizing the chemistry-growth feedback necessary for maintaining tip growth and for inducing branching. The mechanism defining the boundaries between fast- and slow-growing regions not only affects tip shape, it must be able to form new boundaries when the pattern-forming dynamics break symmetry, for instance in the branching of a tip. In previous work, we used an arbitrary concentration threshold to switch between two dynamic regimes of the growth catalyst in order to define growth boundaries. Here, we present a chemical dynamic basis for this threshold, in which feedback between two pattern-forming mechanisms controls the extent of the regions in which fast growth occurs. This provides a general self-contained mechanism for growth control in plant morphogenesis (not relying on external cues) which can account for both simple tip extension and symmetry-breaking branching phenomena.     

COLONY FORM AND THE EXPLOITATION OF SPATIAL REFUGES BY ENCRUSTING BRYOZOA

The sheet-runner continuum model of unilaminar encrusting colony growth is reassessed for cheilostome Bryozoa. It is concluded that the model does not adequately account for the existence of spatially predictable refuges from mortality, which can be selected by the larva at the time of settlement.
A third end-point category of colony form, named the spot colony, is recognized for species settling in small spatially predictable refuges and growing to small, early maturing colonies of determinate or semi-determinate size. Similar colonies are reported from spatially restrictive substrates such as flexible algal fronds and single sediment grains on particulate seabeds.
Runner growth is also reappraised. In some cases, uniserial growth may be regarded as a primary adaptation for growth in linear refuges, or on maze-like or strongly three-dimensional surfaces where multiserial growth is impossible, rather than as a general fugitive strategy adopted by competitively inferior forms.
A revised classificatory model for encrusting growth is proposed. This consists of two continua, sheet-ribbon-runner and sheet-patch-spot. It is suggested that an improved ecological classification of encrusting growth might be framed as a series of coupled settlement/growth strategies.     

Fission yeast cells grow approximately exponentially

How the rate of cell growth is influenced by cell size is a fundamental question of cell biology. The simple model that cell growth is proportional to cell size, based on the proposition that larger cells have proportionally greater synthetic capacity than smaller cells, leads to the prediction that the rate of cell growth increases exponentially with cell size. However, other modes of cell growth, including bilinear growth, have been reported. The distinction between exponential and bilinear growth has been explored in particular detail in the fission yeast Schizosaccharomyces pombe. We have revisited the mode of fission yeast cell growth using high-resolution time-lapse microscopy and find, as previously reported, that these two growth models are difficult to distinguish both because of the similarity in shapes between exponential and bilinear curves over the two-fold change in length of a normal cell cycle and because of the substantial biological and experimental noise inherent to these experiments. Therefore, we contrived to have cells grow more than twofold, by holding them in G2 for up to 8 h. Over this extended growth period, in which cells grow up to 5.5-fold, the two growth models diverge to the point that we can confidently exclude bilinear growth as a general model for fission yeast growth. Although the growth we observe is clearly more complicated than predicted by simple exponential growth, we find that exponential growth is a robust approximation of fission yeast growth, both during an unperturbed cell cycle and during extended periods of growth.