Representation of Germination Curves with the Logistic Function

The fitting of the logistic function to germination progressdata by simple linear regression is demonstrated. Acceptablegoodness of fit is obtained for both fast and slowly-germinatingseed populations. The rate and final percentage of germinationare positively correlated in these experiments, although mathematicallyindependent. The rate appears to be more sensitive to environmentalconditions during germination than is the final percentage.The limitations of the logistic function and the desirabilityof a standard means of expressing germination rates are discussed.     

猴面包树种子萌发及苗期生长规律研究

在3种处理条件下对猴面包树Adansonia digitata种子进行播种育苗,观察记录种子萌发特性、苗高和地径,以及连续观察两年物候。结果表明：(1)70 ℃热水浸种发芽率和发芽势最高,分别为18.72%、6.20%。(2)苗高和地径增长呈“S”型,苗木生长分为缓慢期、速生期和停滞期;苗高和地径的速生期起点均为7月上旬,一直持续至9月上旬,在8月中旬出现苗高和地径速生点。1年生猴面包树苗高和地径可达81.9 cm和12.6 mm,苗木整齐度较好,苗木质量较高,苗木移栽成活率高达90%以上。(3)在云南元阳县干热河谷地区,2年内猴面包树苗期的物候无显著差异,生长发育正常,证明该地区是猴面包树理想的引种栽培区域之一。     

A Mathematical Model Coupling Tumor Growth and Angiogenesis

We present a mathematical model for vascular tumor growth. We use phase fields to model cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and nutrients. The model naturally predicts the shift from avascular to vascular growth at realistic scales. Our computations indicate that the negative regulation of the Delta-like ligand 4 signaling pathway slows down tumor growth by producing a larger density of non-functional capillaries. Our results show good quantitative agreement with experiments.     

浑善达克沙地黄柳种子发芽和幼苗生长特性的研究

在实验室通过模拟野外自然条件,研究了土壤水分、沙埋厚度和温度对黄柳种子发芽与幼苗生长的影响。结果表明:(1)黄柳种子对水分条件很敏感,发芽的适宜土壤含水量为3%~20%,低于3%或高于20%发芽都会受到抑制;(2)种子萌发需要沙土覆盖,适宜覆沙厚度为0.1~0.4 cm,此条件下第5天种子发芽率达80%以上;但当沙埋厚度超过0.6 cm时,种子出苗就会受到抑制;当沙埋厚度超过1.2 cm时,将不能出苗;(3)种子发芽的适宜温度为15~35℃,当温度高于45℃时种子将不能萌发并最终死亡;(4)幼苗的耐热性较强,40℃处理下幼苗出现热害症状,并且热害症状发展缓慢,60℃处理下90 min后幼苗干枯死亡;(5)种子的寿命为120 d左右。     

Seed Germination and Seedling Growth in Sopubia delphinifolia - a Hemi-root Parasite: Germination Requirements

Requirements for seed germination (emergence of radicle) andseedling formation (emergence of both radicle and cotyledons)of a hemi-root parasite Sopubia delphinifolia were studied inthe absence of any host stimulus, in Petri dish and asepticcultures. Both water washing in trickling tap water as wellas cold treatment were effective in inducing/stimulating germinationand seedling formation in the light. Although ethrel, an ethylenereleasing compound, stimulated radicle emergence it inhibitedthe emergence of the cotyledons. Light was found to be essentialfor germination; none of the growth substances could replacethe light requirement. Light responses seem to be mediated throughthe phytochrome system. The results indicate that the emergenceof the radicle, its further growth into the root and the emergenceof cotyledons are controlled by different factors. Sopubia delphinifolia, hemi-root parasite, seed germination requirements, pretreatment, seedling formation     

Influence of Ultraviolet Radiation on Germination and Early Seedling Growth

The influence of UV-B radiation (280–320 nm) from filtered and unfiltered FS-40 fluorescent sunlamps on germination and early seedling growth was examined for a range of vegetables (tomato, radish, cucumber, lettuce, and bean) and field crops (wheat, cotton, soybean, and millet). Continuous exposure of seeds for 3 days to 26.9 × 10⁻² W × m⁻² UV-B radiation (280–320 nm) at 25°C, had a slight effect on fresh weight of seedlings but no appreciable influence on germination percentage, or dry weight of seedlings. Extending the time of exposure to 6 days, however, resulted in abnormal seedling growth in all species but wheat. Typical responses were short, stubby roots, bronzing of the cotyledons, increased pigmentation, and abnormal curvature of the shoots.     

农杆菌对大麦种子萌发及幼苗生长发育的影响

以大麦品种(系)为主区('云引大麦Ⅰ'、'云引大麦Ⅱ'和'U008'),农杆菌浸种时间为副区(0.5、1.5和2.5 h),农杆菌菌液浓度为副副区(0.5、1.5和2.5 OD),采用再裂区试验研究了农杆菌浸种处理对大麦种子萌发和幼苗生长发育的影响.结果表明:品种、农杆菌菌液浓度、浸种时间对大麦的种子发芽率、幼苗高度、幼苗鲜重、叶绿素含量、丙二醛(MDA)含量影响无显著的互作效应,而对幼苗POD活性的影响存在显著互作效应;随着浸种时间的延长和菌液浓度的增加,各大麦品种(系)的种子发芽率、幼苗高度、幼苗鲜重、叶绿素含量均呈逐渐降低趋势,幼苗MDA含量则逐渐增加,并以'U008'变化幅度最大;在菌液浓度为0～1.5 OD、浸种时间为0～1.5 h范围内,幼苗POD活性随着菌液浓度的增加和浸种时间的延长而增强,超过该范围则均呈下降趋势,并以'U008'下降最为明显.可见,农杆菌处理对大麦种子萌发和幼苗生长发育有抑制作用,并在菌液浓度超过1.5 OD、浸种时间大于1.5 h时达极显著水平,且大麦品种间存在一定差异.     

火焰兰的种子培养和试管育苗

1植物名称火焰兰(Renanthera CoCCinea). 2材料类别种子. 3培养条件种子萌发培养基:(1)VW;(2)VW 100 mL·L-1椰子乳;(3)KC;(4)KC 100 mL·L-1椰子乳(5)1/2MS;(6)MS.生根育苗培养基:(7)3 g·L-1花宝1号(美国Haponex公司产品,N:P:K=7:6:19) 2 g·L-1蛋白胨 2 g·L-1活性炭 0.5 mg·L-1NAA 0.2 mg·L-16-BA;(8)1 g·L-1花宝1号 1 g·L-1花宝2号(N:P:K=20:20:20) 2 g·L-1蛋白胨 2 g·L-1活性炭 0.5 mg·L-1NAA 0.2 mg·L-16-BA.以上培养基均附加1.5%蔗糖、0.6%琼脂,pH 5.2～5.4.培养温度为(25±2)℃,光照度1 500～2000lx,光照时间12 h·d-1.     

盐碱胁迫对两种高粱种子萌发及幼苗生长的影响

以纤维高粱和普通高粱种子为材料,将NaCl、Na2SO4和NaHCO3按不同比例混合,模拟15种盐度和碱度各不相同的复杂盐碱条件,采用培养皿纸上发芽法研究了混合盐碱胁迫对两种高粱种子萌发及幼苗生长的影响,以探讨两种高粱种子和幼苗的耐盐碱能力及在盐碱胁迫下的变化规律。结果表明,低盐低碱环境促进了两种高粱种子的萌发;随着盐碱胁迫的增强,高粱种子的萌发率、萌发指数与对照相比均显著下降,而纤维高粱的累积萌发率下降幅度较普通高粱小,表明纤维高粱对盐渍环境的适应性略高于普通高粱。在高粱幼苗生长过程中,随着盐碱胁迫的增强,两种高粱的幼根和幼芽长均显著下降,且与对照均具有显著性差异。盐度对两种高粱的萌发率、萌发指数、幼苗长均有极显著影响,盐度与pH相互作用对两种高粱的幼根长有极显著影响。     

Analysis of Variation in the Rates of Germination and Early Seedling Growth in Tomato

Studies have been made on the time to germination and earlyseedling growth of the tomato Lycopersicon esculentum var. Potentateand Lycopersicon pimpinellifolium var. Red Currant, as wellas on derivative generations from their hybridization. Althoughtime to germination showed a genetic component, the relationshipsbetween different genotypes was much influenced by environmentalfactors. A marked maternal effect on time to germination dueto the varying seed sizes was noted while variation betweendifferent genotypes of similar seeds size was ascribed to anendospermic effect. The F¹ hybrid embryo with L. Pimpinellifoliumas maternal parent contained more cells than that of the parentbut the hybrid cmbryo with L. esculentum as maternal parentcontained a similar number of cells to that of the parent itself.It is suggested that the results for embryo size both supportAshby‘s assertion that embryo size may be important indetermining heterosis, and also Hatcher’s findings in1940, that heterosis for hypocotyl extension is found in hybridsfrom parcnts of different sized seeds provided the small seededvariety is the maternal parent.     

A Multiscale Mathematical Model of Tumour Invasive Growth

Known as one of the hallmarks of cancer (Hanahan and Weinberg in Cell 100:57–70, 2000) cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Through the secretion of various proteolytic enzymes such as matrix metalloproteinases or the urokinase plasminogen activator (uPA), the cancer cell population alters the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue. The active interplay between the tissue-scale tumour dynamics and the molecular mechanics of the involved proteolytic enzymes at the cell scale underlines the biologically multiscale character of invasion and raises the challenge of modelling this process with an appropriate multiscale approach. In this paper, we present a new two-scale moving boundary model of cancer invasion that explores the tissue-scale tumour dynamics in conjunction with the molecular dynamics of the urokinase plasminogen activation system. Building on the multiscale moving boundary method proposed in Trucu et al. (Multiscale Model Simul 11(1):309–335, 2013), the modelling that we propose here allows us to study the changes in tissue-scale tumour morphology caused by the cell-scale uPA microdynamics occurring along the invasive edge of the tumour. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as the tumour infiltrative growth patterns discussed in Ito et al. (J Gastroenterol 47:1279–1289, 2012).     

Quantification of the Effect of Environmental Factors on Seed Germination and Seedling Growth of Eruca (Eruca sativa) Using Mathematical Models

Eruca (Eruca sativa; Brassicaceae) is an important industrial crop due to its ability to grow under a wide range of climatic conditions and in poor fertility lands and also for the quality of seed oil and protein. Seed germination (SG) is an important event in plant’s life history which can significantly be influenced by several environmental factors such as temperature (T), water potential (ψ), salinity, pH, and burial depth. Therefore, this study aimed (i) to investigate the effects of these environmental factors on SG behavior of Eruca using several mathematical models, (ii) to determine the cardinal Ts and tolerance threshold value for each trait (i.e., 50% reduction than its maximum value) affected by the environmental factor, and (iii) to quantify the response of Eruca seedling growth to each environmental factor. The results indicated that Eruca SG and seedling growth were significantly influenced by these factors (P < 0.05). The estimated cardinal Ts were 1 °C for the base T, 30 °C for the optimum T, and 40.8 °C for the ceiling T. The salt and drought tolerance threshold values were 257 mM NaCl and − 1.2 MPa for SG and 247 mM NaCl and − 1 MPa for the seedling growth, respectively, suggesting that the seedling growth was more sensitive than SG under both salt and drought stresses in Eruca. In addition, the maximum SG and seedling growth were observed at pH 7 and burial depth 1.9 cm. In general, the models used in this study could describe well the response of Eruca SG under different levels of environmental factors and also their parameters could easily be used in Eruca SG simulation models. This information also could help us to better manage the production of this plant under stressful conditions and/or to determine its geographic range expansion in the world.

     

NaCl胁迫对超大甜椒种子萌发及幼苗生长的影响

以超大甜椒种子和幼苗为材料,采用水培法研究低、中、高浓度(50、150、250 mmol·L-1)NaCl胁迫对其种子萌发和幼苗生长的影响.结果显示:(1)低浓度NaCl处理促进种子萌发,而中、高浓度NaCl处理抑制种子萌发;NaCl处理第18天时,高浓度NaCl处理植株全部死亡,其余各处理植株苗高、叶面积、地上部鲜重和干重均随处理浓度升高而下降,但低浓度NaCl能刺激超大甜椒的根系生长.(2)低、中浓度NaCl处理时,植株叶绿素含量未受到大的影响,类胡萝卜素含量却随胁迫时间延长微量升高;在盐胁迫7 d的周期内,低、中浓度NaCl处理植株MDA含量、SOD活性和可溶性糖含量均随浓度升高及时间延长显著增加,脯氨酸含量在低浓度下变化不明显而中浓度下显著升高;在高浓度NaCl处理3 d中,MDA含量急剧升高,SOD活性先升高后下降,脯氨酸和可溶性糖含量显著增加.研究发现,NaCl胁迫浓度越高对超大甜椒种子萌发和幼苗生长的抑制效应越明显;低中浓度NaCl处理幼苗能通过自身的抗氧化酶清除系统和渗透调节物质来抵抗胁迫引起伤害,类胡萝卜素可能也有一定的抗胁迫作用,而高浓度NaCl处理增加了膜脂过氧化程度,严重影响了活性氧和渗透调节物质的正常代谢.     

A Simple Mathematical Model of Growth Pattern in Tree Stems

Stem formation process is analysed by examining annual ringsfor coniferous and broadleaved trees. Cutting a tree stem intoseveral segments of a constant length, the weight of each segmentis denoted as the stem density (S). In addition the verticallyaccumulated current increment of the stem densities is definedas the cumulative stem increment (CSI). Examining the relationshipsbetween CSI and S for tree stems, it is shown that most of themdepict straight lines. Redefining S as a function with two independentvariables, time t and vertical position z along the stem, thelinear partial differential equation     

An Extension of the Logistic Model of Plant Growth

The kinetics of growth of Dactylis glomerata L. were studiedunder controlled temperature and nutritional conditions at threelevels of irradiance (35·55 and 85 W m^–s). Thedry weights of the root and shoot parts of the plants were measuredeach week between the fourth and eleventh weeks after sowing. The growth kinetics were found to be dependent on the levelof irradiance, but no significant differences in the root: totaldry weight ratio were observed. To characterize the effect of illuminance, the experimentalgrowth curves were analysed initially using the logistic model,the adequacy of which is discussed. An extension of the logisticmodel is proposed, represented by the kinetic equation dM/dt= kM, with < 1 and where M is the dry weight of the plant.It is shown that this relationship allows a distinction to bemade between two kinds of plant material according to theirfunctions in the growth process. Dactylis glomerata L., illuminance, growth curves, kinetic analyses, logistic model, shoot:root ratio, partition of assimilates     

氯化钠胁迫对罗布麻种子萌发及幼苗生长的影响

用不同浓度的氯化钠溶液处理罗布麻种子,试验结果表明,氯化钠浓度低于0.8%时,可促进罗布麻种子萌芽,高于0.8%小于2.0%时抑制萌芽,超过2.0%时极显著抑制种子萌芽。氯化钠浓度高低均对罗布麻幼苗生长有抑制作用,当浓度大于0.4%时,出叶速度减慢,植株矮化、相对抑制率超过60%,鲜重与对照相比降低了50%以上。     

A Mathematical Model for Vegetative Growth of Bacillus Thuringiensis

A structured but unsegregated model was developed for the vegetative growth of Bacillus thuringiensis (Bt) cells. This model included cell growth, limiting‐substrate consumption, production and consumption of acetic acid, and production of poly‐β‐hydroxy butyric acid. The parameter estimation and model validation were conducted using data from carbon‐limited batch experiments. The model successfully predicted batch behavior of biomass and glucose concentrations.     

Oxygen-Driven Tumour Growth Model: A Pathology-Relevant Mathematical Approach

Xenografts -as simplified animal models of cancer- differ substantially in vasculature and stromal architecture when compared to clinical tumours. This makes mathematical model-based predictions of clinical outcome challenging. Our objective is to further understand differences in tumour progression and physiology between animal models and the clinic.To achieve that, we propose a mathematical model based upon tumour pathophysiology, where oxygen -as a surrogate for endocrine delivery- is our main focus. The Oxygen-Driven Model (ODM), using oxygen diffusion equations, describes tumour growth, hypoxia and necrosis. The ODM describes two key physiological parameters. Apparent oxygen uptake rate (kR′) represents the amount of oxygen cells seem to need to proliferate. The more oxygen they appear to need, the more the oxygen transport. kR′ gathers variability from the vasculature, stroma and tumour morphology. Proliferating rate (k _p) deals with cell line specific factors to promote growth. The K _H,K _N describe the switch of hypoxia and necrosis. Retrospectively, using archived data, we looked at longitudinal tumour volume datasets for 38 xenografted cell lines and 5 patient-derived xenograft-like models.Exploration of the parameter space allows us to distinguish 2 groups of parameters. Group 1 of cell lines shows a spread in values of kR′ and lower k _p, indicating that tumours are poorly perfused and slow growing. Group 2 share the value of the oxygen uptake rate (kR′) and vary greatly in k _p, which we interpret as having similar oxygen transport, but more tumour intrinsic variability in growth.However, the ODM has some limitations when tested in explant-like animal models, whose complex tumour-stromal morphology may not be captured in the current version of the model. Incorporation of stroma in the ODM will help explain these discrepancies. We have provided an example. The ODM is a very simple -and versatile- model suitable for the design of preclinical experiments, which can be modified and enhanced whilst maintaining confidence in its predictions.