A comparative analysis of leaf shape of wheat, barley and maize using an empirical shape model

Background and Aims

The phenotypes of grasses show differences depending on growth conditions and ontogenetic stage. Understanding these responses and finding suitable mathematical formalizations are an essential part of the development of plant and crop models. Usually, a marked change in architecture between juvenile and adult plants is observed, where dimension and shape of leaves are likely to change. In this paper, the plasticity of leaf shape is analysed according to growth conditions and ontogeny.

Methods

Leaf shape of Triticum aestivum, Hordeum vulgare and Zea mays cultivars grown under varying conditions was measured using digital image processing. An empirical leaf shape model was fitted to measured shape data of single leaves. Obtained values of model parameters were used to analyse the patterns in leaf shape.

Key Results

The model was able to delineate leaf shape of all studied species. The model error was small. Differences in leaf shape between juvenile and adult leaves in T. aestivum and H. vulgare were observed. Varying growth conditions impacted leaf dimensions but did not impact leaf shape of the respective species.

Conclusions

Leaf shape of the studied T. aestivum and H. vulgare cultivars was remarkably stable for a comparable ontogenetic stage (leaf rank), but differed between stages. Along with other aspects of grass architecture, leaf shape changed during the transition from juvenile to adult growth phase. Model-based analysis of leaf shape is a method to investigate these differences. Presented results can be integrated into architectural models of plant development to delineate leaf shape for different species, cultivars and environmental conditions.     

Global evaluation of growth in a rural population: comparative analysis of shape and size

In this work the analogies and differences in shape and size between a rural school population (6–14 aged) of the Lozoya-Somosierra region (Madrid) and several recent and past Spanish populations from different environments have been studied. The results show the growth trend as well as the influences of ecological and socioeconomical factors. Paper presented at the 4^th congress of the European Anthropology Association (Florence, Sept. 1984).     

A new mathematical evaluation of smoking problem based of algebraic statistical method

Smoking problem is considered as one of the hot topics for many years. In spite of overpowering facts about the dangers, smoking is still a bad habit widely spread and socially accepted. Many people start smoking during their gymnasium period. The discovery of the dangers of smoking gave a warning sign of danger for individuals. There are different statistical methods used to analyze the dangers of smoking. In this study, we apply an algebraic statistical method to analyze and classify real data using Markov basis for the independent model on the contingency table. Results show that the Markov basis based classification is able to distinguish different date elements. Moreover, we check our proposed method via information theory by utilizing the Shannon formula to illustrate which one of these alternative tables is the best in term of independent.     

A new way of tracking motion, shape, and divisions

The process of detecting and tracking biological features such as bacteria and nuclei is complicated by the fact that they constantly change their shape. Shape changes happen both continuously as the biological features grow and discontinuously as they divide or die. In this paper I present a new method of tracking such features for the case that they can be reasonably approximated by a relatively simple mathematical shape such as a cylinder or an ellipse. Using contour plots with multiple levels to detect the features and their shapes, rather than the commonly used single contour detection technique, this method can efficiently detect multiple features even if they have large differences in brightness, as well as reliably track divisions when both brightness and size drop dramatically.     

A comparative evaluation of Cephalosporin C production using various immobilization modes

The production of Cephalosporin C was investigated in a lab-scale 1.4 l air-lift reactor (ALR), using various immobilization modes. Bioparticles were developed by forming biofilm of growing hyphae around an inorganic siran particle which contained spores of the organism. Silk sachet was the other immobilization matrix. The maximum specific growth rate of the Cephalosporium acremonium, free cells, pellets, siran carrier and silk sachets were 0.037, 0.003, 0.047, and 0.035 h(-1), and specific antibiotic productivities (as compared to 100% for free cells) were 180, 150, and 125% for siran carrier, silk sachets and pellets, respectively. Immobilization modes exhibited enhanced volumetric oxygen transfer coefficient and well-controlled, three-phase hydrodynamics.     

A comparative evaluation of oxygen mass transfer and broth viscosity using Cephalosporin-C production as a case strategy

The production of Cephalosporin-C (CPC) a secondary metabolite, using a mold Acremonium chrysogenum was studied in a lab scale Internal loop air lift reactor. Cephalosporin-C production process is a highly aerobic fermentation process. Volumetric gas–liquid mass transfer coefficient (k_La) and viscosity (η) were evaluated, during the growth and production phases of the microbial physiology. An attempt has been made to correlate the broth viscosity, η and volumetric oxygen transfer coefficient, k_La during the Cephalosporin-C production in an air lift reactor. The impact of biomass concentration and mycelial morphology on broth viscosity has been also evaluated. The broth exhibits a typical non-Newtonian fermentation broth. Rheology parameters like consistency index and fluidity index are also studied.     

The observed form of coated vesicles and a mathematical covering problem

A connection is made between (1) the observed structures of clathrin cages and (2) the mathematical problem of determination of the smallest diameter of n equal circles by which the surface of a sphere can be covered without gaps. For different numbers n of circles, it is found that the various clathrin polyhedra identified so far provide topologically the same configurations as the proven solutions of the sphere-covering problem for some n or improve on the currently best conjectured solutions for other n. Thus a study of some biological structures has, in this case, given additional insight into a mathematical problem.     

A mathematical model of a crocodilian population using delay-differential equations

The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong age-dependence. We develop delay-differential equation (DDE) models describing the evolution of a crocodilian population. In using the delay formulation, we are able to account for both the TSD and the age-dependence of the life parameters while maintaining some analytical tractability. In our single-delay model we also find an equilibrium point and prove its local asymptotic stability. We numerically solve the different models and investigate the effects of multiple delays on the age structure of the population as well as the sex ratio of the population. For all models we obtain very strong agreement with the age structure of crocodilian population data as reported in Smith and Webb (Aust. Wild. Res. 12, 541-554, 1985). We also obtain reasonable values for the sex ratio of the simulated population.     

A mathematical model for cell sorting,migration and shape in the slug stage ofDictyostelium discoideum

A mathematical model for cell sorting and migration in the slug stage of cellular slime moldsDictyostelium discoideum is proposed. Assuming that a slug is a “mixed fluid” of prespore and prestalk cells, a set of equations which describe the dynamics of cell distribution, internal pressure and velocity of hte slug are derived from the balance formula of individual cell movement. These equations are analyzed to obtain the spatial patterns of the two types of cells at dynamical equilibrium and the relationship between the migration velocity and the slug size. The body shape of the elongated slug at the migrating stage is also investigated, taking account of the law of surface tension. The stable shapes of slugs with different volumes are explicity obtaained and the existence of critical size of a slug is suggested.     

A new mathematical approach predicts individual cell growth behavior using bacterial population information

A theoretical methodology has been developed for studying the growth kinetics of bacterial cells. It utilizes the steady-state cell length distribution in a bacterial population to predict the dependency of growth and division rates on cell length and age. The mathematical model has been applied to the analysis of two bacterial populations, a wild-type strain of Bacillus subtilis, and a minicell-producing strain that carries the divIVB1 mutation. The results show that our model describes the wild-type population very well and that the assumptions typically used in traditional methods are unrealistic. In the case of the minicell-producing mutant we find evidence that the rate of cell division must be a function not only of cell size but also of cell age.     

七种蒿属植物种子重量形状及萌发特性的比较研究

在实验室条件下 ,对 7种蒿属植物种子 (差巴嘎蒿、乌丹蒿、万年蒿、大籽蒿、黄蒿、野艾蒿和冷蒿 )进行重量、形状及萌发特性的比较研究。沙生先锋植物乌丹蒿和差巴嘎蒿的种子重量较大、形状扁平 ,这些特征是植物对流沙环境进化的适应机制之一。黄蒿种子小且呈圆形 ,具有持久土壤种子库 ,因此黄蒿抗干扰能力较强。 7种蒿属植物有 3种萌发格局 :大籽蒿、万年蒿、差巴嘎蒿和冷蒿的萌发前期快 ,后期平缓 ;野艾蒿和黄蒿整个萌发过程平缓 ;乌丹蒿早期和后期萌发平缓 ,中间快。乌丹蒿推迟萌发高峰是它比差巴嘎蒿更适应流沙环境的机制之一。从种子萌发格局分析 ,黄蒿种子具有生理后熟或休眠机制 ,大籽蒿种子萌发是典型的机会主义。黄蒿、野艾蒿和冷蒿种子具有风险分摊的萌发机制。种子重量和形状与发芽率之间无相关性 ,重量和形状则显著相关。     

A new model for the quantitative analysis of cell movements in vitro: definition of a shape change factor

Changes in shape, in addition to translocations, are an important aspect of cell motility. We propose a simple geometrical model for the quantitative analysis of shape changes undergone by cultured cells. The extent to which images of a given cell do not overlap at the beginning and end of a time interval is used as a measure of motility, and a translation step included to eliminate translocation effects. Initial findings suggest that the method is widely applicable.     

Comparison of DNA ploidy and nuclear size, shape and chromatin irregularity in tissue sections and smears of prostatic carcinoma

Image analysis measurements of nuclear size, shape, texture and DNA ploidy were compared in smears versus the corresponding 4-microns tissue sections, both prepared from radical prostatectomy specimens obtained from resections for prostatic cancer. Thirty-nine cases (78%) showed concordant DNA histograms between the smear and the tissue section. In six cases (12%), both preparations were nondiploid, but a tetraploid population was also present in one, but not both, of the preparations. In five cases (10%), there was a major discordance between the smear and the tissue section, with one preparation diploid and the other nondiploid. One source of discrepancy between the smear and tissue histograms was the overlapping of larger nuclei in tissue sections, which often precluded the analysis of the most atypical cells. Some tissue histograms were difficult to interpret due to wide coefficients of variation, irregular peaks and some shift from 2n in the diploid peaks. The best morphometric correlation (0.78) between the smears and the tissue sections was for the modal nuclear shape. Nuclear size and texture measurements showed poorer correlations. These findings suggest that cytologic preparations of prostatic carcinoma should be preferred for image analysis.