A new computational growth model for sea urchin skeletons

A new computational model has been developed to simulate growth of regular sea urchin skeletons. The model incorporates the processes of plate addition and individual plate growth into a composite model of whole-body (somatic) growth. A simple developmental model based on hypothetical morphogens underlies the assumptions used to define the simulated growth processes. The data model is based on a Delaunay triangulation of plate growth center points, using the dual Voronoi polygons to define plate topologies. A spherical frame of reference is used for growth calculations, with affine deformation of the sphere (based on a Young-Laplace membrane model) to result in an urchin-like three-dimensional form. The model verifies that the patterns of coronal plates in general meet the criteria of Voronoi polygonalization, that a morphogen/threshold inhibition model for plate addition results in the alternating plate addition pattern characteristic of sea urchins, and that application of the Bertalanffy growth model to individual plates results in simulated somatic growth that approximates that seen in living urchins. The model suggests avenues of research that could explain some of the distinctions between modern sea urchins and the much more disparate groups of forms that characterized the Paleozoic Era.     

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.     

Theoretical Study of Stress-Modulated Growth in the Aorta

A theoretical model is presented for stress-modulated growth in the aorta. The model consists of a pseudoelastic tube composed of two layers representing the intima/media and the adventitia. Finite volumetric growth is included by letting the time-rate of change of the zero-stress dimensions of each volume element depends linearly on the local stresses. After analyzing the model, we examine its fundamental growth response under changes in loads, material properties, and growth parameters. The behaviour of the model is quite sensitive to changes in material nonlinearity and in the coefficients of the growth law. Next, growth of the aorta is simulated during development and maturity. For an appropriate choice of the parameters, the model exhibits patterns of growth that agree qualitatively with known characteristics of aortic growth. Comparison of model results with published experimental data during hypertension in the rat shows good agreement in the time course of the vessel radii and residual strain. Finally, the implications of the results are discussed in the context of deducing a general mechanical growth law for soft tissues. The proposed model should be useful in studies to determine the biomechanical factor that regulates growth.     

黄土丘陵半干旱区柠条林株高生长过程新模型

黄土丘陵半干旱区柠条林的株高生长不随时间单调增加,在生长末期因生长动力小于生长阻力,株高随时间小幅度减小。采用宁夏固原上黄生态站柠条林的生长观测资料,以经典Logistic方程为基础,添加了生长阻力因素,建立了柠条林生长的改进模型,使得生长速率在生长末期出现负值;并以高密度柠条成林多年生长观测数据为依据,建立了连年生长模型。用数学建模和统计检验的方法对数据进行处理,其结果表明,改进模型较Logistic方程具有更高的拟合度和相关系数。建立的模型与传统生长方程不同,由于微分方程中引入了阻力因子,故生长曲线中存在极值坐标且不具有严格单调性。将多年的株高生长曲线综合到一个坐标系内后,新模型中位置参数a与内禀生长率b的比值随着生长呈现逐渐增大的趋势。改进模型的生长顶点出现在8月,与柠条林株高的实际生长过程吻合;计算了新模型的生长顶点与生长期结束时的株高的差值,并将该值记为生长损失。由于柠条林的灌丛较为矮小,在越冬时干梢现象对株高的影响不可忽略,该过程导致生长方程中第二年初始点小于第一年最末点;在考虑了该现象后所建立的连年生长模型中,2002年和2003年干稍现象的终止点位于2月,与植物生长的节律吻合。本研究为描述半干旱区灌木林生长过程提供了依据。     

Modeling surface growth of Escherichia coli on agar plates

Surface growth of Escherichia coli cells on a membrane filter placed on a nutrient agar plate under various conditions was studied with a mathematical model. The surface growth of bacterial cells showed a sigmoidal curve with time on a semilogarithmic plot. To describe it, a new logistic model that we presented earlier (H. Fujikawa et al., Food Microbiol. 21:501-509, 2004) was modified. Growth curves at various constant temperatures (10 to 34 degrees C) were successfully described with the modified model (model III). Model III gave better predictions of the rate constant of growth and the lag period than a modified Gompertz model and the Baranyi model. Using the parameter values of model III at the constant temperatures, surface growth at various temperatures was successfully predicted. Surface growth curves at various initial cell numbers were also sigmoidal and converged to the same maximum cell numbers at the stationary phase. Surface growth curves at various nutrient levels were also sigmoidal. The maximum cell number and the rate of growth were lower as the nutrient level decreased. The surface growth curve was the same as that in a liquid, except for the large curvature at the deceleration period. These curves were also well described with model III. The pattern of increase in the ATP content of cells grown on a surface was sigmoidal, similar to that for cell growth. We discovered several characteristics of the surface growth of bacterial cells under various growth conditions and examined the applicability of our model to describe these growth curves.     

A model for energy-sufficient culture growth

Pirt's maintenance model has been widely accepted for the effects of growth rate and maintenance on growth yield. However, the interpretation of parameters in Pirt's model as biological constants is difficult for energy-sufficient culture growth. In this study, a mechanistic model for the growth energetics of energy-sufficient chemostat cultures is proposed and verified with literature data. In the model, the overutilization of the energy substrate in energy-sufficient culture growth is attributed to the defective regulation of the energy substrate metabolism and energy uncoupling. The model also uses an "energy surplus" concept to collectively represent the effects of energy excessiveness. The proposed model provides a better quantitative understanding of the maximum growth yield and maintenance of energy-sufficient cultures. It also explains the glucose concentration effect reported in the literature.     

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.     

A Model of Grass Growth

A model of grass growth is constructed and applied to above-grounddry-weight data on a well-fertilized and irrigated grass cropgrown at Hurley. The processes of light interception, photosynthesis,respiration, growth and senescence are represented in the model.Temperature, daily light receipt and daylength are the environmentinput variables required. The model is able to simulate thetwo limiting cases of exponential growth, and a steady-statecrop which is in dynamic equilibrium without net growth. Themodel fits the data well, and provides a simple framework forthe analysis of the growth of grass. Lolium perenne L., perennial ryegrass, light interception, photosynthesis, growth, respiration, senescence, mathematical model     

Modeling the growth of individuals in crowded plant populations

Aims We present an improved model for the growth of individuals in plant populations experiencing competition.Methods Individuals grow sigmoidally according to the Birch model, which is similar to the more commonly used Richards model, but has the advantage that initial plant growth is always exponential. The individual plant growth models are coupled so that there is a maximum total biomass for the population. The effects of size-asymmetric competition are modeled with a parameter that reflects the size advantage that larger individual have over smaller individuals. We fit the model to data on individual growth in crowded populations of Chenopodium album .Important findings When individual plant growth curves were not coupled, there was a negative or no correlation between initial growth rate and final size, suggesting that competitive interactions were more important in determining final plant size than were plants' initial growth rates. The coupled growth equations fit the data better than individual, uncoupled growth models, even though the number of estimated parameters in the coupled competitive growth model was far fewer, indicating the importance of modeling competition and the degree of size-asymmetric growth explicitly. A quantitative understanding of stand development in terms of the growth of individuals, as altered by competition, is within reach.     

A prototype model structure for mixed microbial populations in homogeneous food products

An important factor which has not been included in many models in the field of predictive microbiology is the influence of a background of microflora in a food product. It is however generally known that the growth of a microorganism as a pure culture can be substantially different from its growth in a mixed culture, due to microbial interactions. Because of the importance of these interactions and the lack of suitable modeling techniques in the field of predictive microbiology to describe them, the potential of models in other research fields-namely ecology-to deal with interactions is explored in previous work of the authors. However, a model structure for microbial growth in food products cannot simply be copied from those elaborated in ecology. The structure of a predictive growth model is indeed typical, primarily due to the explicit modeling of a lag phase. The current paper proposes a prototype model structure for growth of mixed microbial populations in homogeneous food products. The model is able to describe a lag phase and reduces to a classical predictive growth model in the special case of single-species growth.     

Temperature dependence of vegetative growth and dark respiration: a mathematical model

A mathematical model of the processes involved in carbon metabolism is described that predicts the influence of temperature on the growth of plants. The model assumes that the rate of production of dry matter depends both on the temperature and the level of nonstructural carbohydrate. The level of nonstructural carbohydrate is determined by the rates of photosynthesis, growth, and maintenance respiration. The model describes the rate of growth and dark respiration, and the levels of carbohydrate seen in vegetative growth of carnation and tomato. The model suggests that the growth of plants at low temperatures is limited by a shortage of respiratory energy, whereas at high temperatures growth is limited by the shortage of carbohydrate. Thermoperiodism, wherein a warm day and cool night results in faster growth than does constant temperature, is explained by the model as an increase in the level of nonstructural carbohydrate which promotes the rate of growth relative to the rate of maintenance respiration.     

A Population-Based Morphologically Structured Model for Hyphal Growth and Product Formation in Streptomycin Fermentation

Summary A population model discriminating the hyphae according to the hyphal length and a morphologically structured model considering the specific function of different morphological forms of a hypha are combined together to describe mycelial growth, substrate consumption and secondary metabolite formation in streptomycin fermentation. In the population model, the growth modes of hyphae with different age or length are considered, while in the morphologically structured model, the morphological forms of hyphae and their functions in growth and metabolism are described. The population model and the morphologically structured model are interrelated by a branching function and a differentiation function. In the model, the growth rate of immature apical compartment is distinguished from those of matured ones, branching is proposed to occur only in the subapical region, and the hyphal compartment is assumed to synthesize secondary metabolites. The model is successfully applied to simulate the batch fermentation process of streptomycin production. The growth characteristics of filamentous microorganisms are also discussed using the model predictions.     

Modeling Surface Growth of Escherichia coli on Agar Plates

Surface growth of Escherichia coli cells on a membrane filter placed on a nutrient agar plate under various conditions was studied with a mathematical model. The surface growth of bacterial cells showed a sigmoidal curve with time on a semilogarithmic plot. To describe it, a new logistic model that we presented earlier (H.Fujikawa et al., Food Microbiol. 21:501-509, 2004) was modified. Growth curves at various constant temperatures (10 to 34°C) were successfully described with the modified model (model III). Model III gave better predictions of the rate constant of growth and the lag period than a modified Gompertz model and the Baranyi model. Using the parameter values of model III at the constant temperatures, surface growth at various temperatures was successfully predicted. Surface growth curves at various initial cell numbers were also sigmoidal and converged to the same maximum cell numbers at the stationary phase. Surface growth curves at various nutrient levels were also sigmoidal. The maximum cell number and the rate of growth were lower as the nutrient level decreased. The surface growth curve was the same as that in a liquid, except for the large curvature at the deceleration period. These curves were also well described with model III. The pattern of increase in the ATP content of cells grown on a surface was sigmoidal, similar to that for cell growth. We discovered several characteristics of the surface growth of bacterial cells under various growth conditions and examined the applicability of our model to describe these growth curves.     

Description of growth by simple versus complex models for Baltic Sea spring spawning herring

The objective was to find a length–growth model to help differentiate between herring stocks (Clupea harengus l.) when their length–growth shows systematically different patterns. The most essential model restriction was that it should react robustly against variations in the underlying age range which varies not only over time but also between the different herring stocks. Because of the limited age range, significance tests as well as confidence intervals of the model parameters should allow a small sample restriction. Thus, parameter estimation should be of an analytical rather than asymptotic nature and the model should contain a minimum set of parameters. The article studies the comparative characteristics of a simple non‐asymptotic two‐parameter growth model (allometric length–growth function, abbreviated as ALG model) in contrast to higher parametric and more complex growth models (logistic and von‐Bertalanffy growth functions, abbreviated as LGF and VBG models). An advantage of the ALG model is that it can be easily linearized and the growth coefficients can be directly derived as regression parameters. The intrinsic ALG model linearity makes it easy to test restrictions (normality, homoscedasticity and serial uncorrelation of the error term) and to formulate analytic confidence intervals. The ALG model features were exemplified and validated by a 1995 Baltic spring spawning herring (BSSH) data set that included a 12‐year age range. The model performance was compared with that of the logistic and the von‐Bertalanffy length–growth curves for different age ranges and by means of various parameter estimation techniques. In all cases the ALG model performed better and all ALG model restrictions (no autocorrelation, homoscedasticity, and normality of the error term) were fulfilled. Furthermore, all findings seemed to indicate a pseudo‐asymptotic growth for BSSH. The proposed model was explicitly derived for of herring length‐growth; the results thus should not be generalized interspecifically without additional proof.     

Identification of quantitative trait nucleotides that regulate cancer growth: a simulation approach

A general growth model derived from basic cellular properties can be used to describe the dynamic process of cancer growth with mathematical equations. It has been recognized that cancer growth is under genetic control, with a multitude of interacting genes each segregating in a Mendelian fashion and displaying environmental sensitivity. In this article, we integrate the mathematical aspects of the pervasive growth model into a statistical framework for the identification of quantitative trait nucleotides that underlie cancer growth. This integrative framework is constructed with a single nucleotide polymorphism-based haplotype blocking analysis. Simulation studies have been performed to demonstrate the usefulness of the model. The proposed model provides a generic platform model for testing and detecting specific DNA sequence variants that regulates the timing of cancer emergence, growth and differentiation.     

Scale-Up of flat plate photobioreactors considering diffuse and direct light characteristics

This study investigates the scaling of photobioreactor productivity based on the growth of Nannochloropsis salina incorporating the effects of direct and diffuse light. The scaling and optimization of photobioreactor geometry was analyzed by determining the growth response of a small-scale system designed to represent a core sample of a large-scale photobioreactor. The small-scale test apparatus was operated at a variety of light intensities on a batch time scale to generate a photosynthetic irradiance (PI) growth dataset, ultimately used to inform a PI growth model. The validation of the scalability of the PI growth model to predict productivity in large-scale systems was done by comparison with experimental growth data collected from two geometrically different large-scale photobioreactors operated at a variety of light intensities. For direct comparison, the small-scale and large-scale experimental systems presented were operated similarly and in such a way to incorporate cultivation relevant time scales, light intensities, mixing, and nutrient loads. Validation of the scalability of the PI growth model enables the critical evaluation of different photobioreactor geometries and design optimization incorporating growth effects from diffuse and direct light. Discussion focuses on the application of the PI growth model to assess the effect of diffuse light growth compared to direct light growth for the evaluation of photobioreactors followed by the use of the model for photobioreactor geometry optimization on the metric of areal productivity.     

Kinetic study of hybridoma cell growth in continuous culture: II. Behavior of producers and comparison to nonproducers

A hybridoma cell line, AFP-27-P, was cultivated in continuous culture under glucose-limited conditions. The viable cell concentration, dead-cell concentration, and cell volume all varied with the dilution rate. A model previously developed for a nonproducing clone of the same cell line, AFP-27-NP, was extended to describe the behavior of the cells. The relationship between the specific growth rate and glucose concentration is described by a function similar to the Monod model. A threshold glucose concentration and a minimum specific growth rate are incorporated; the model is meaningful only at glucose concentration and a minimum specific growth rate are incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. The relationship between the death rate and the glucose concentration is described by an inverted Monod-type function. Furthermore, the yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper range of specific growth rates. No maintenance term for glucose consumption is used; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepts the specific growth rate at a value close to the minimum growth rate. The productivity of antibody as a function of the specific growth rate is described by a mixed type model with a noon-growth-associated term and a negative-growth-associated term. The values for the model parameters were determined from regression analysis of the steady state data.