Richards方程的数学属性及其在兽类生长过程中的应用

通过对Richards方程数学属性的分析表明 ,该方程具有变动的拐点值 ,因而在描绘兽类多种多样的生长过程时具有良好的可塑性。依据其方程参数n取值的不同 ,Richards方程包含了Spillman ,Logistic,Gompertz以及Bertalanffy方程。为了评估Richards方程对兽类生长过程的拟合优度 ,作者引用 1 0组哺乳动物兽类生长数据 ,将它与一些经典的生长模型如Spillman ,Logistic,Gompertz以及Bertalanffy方程共同进行了拟合比较。结果表明 ,Richards方程具有良好的拟合优度 ,适于描绘多种多样的兽类生长模式。     

广义Schumacher模型的改进及其应用

通过对前人提出的生长方程的具体分析,提出了一种改进的Schumacher生长方程．该模型包含了Gompenz函数、Schumacher方程及广义Schumacher方程,具有很强的自适应性和实用性．采用遗传算法。利用该模型对珍稀植物长苞铁杉和侧柏生长资料分别进行了拟合．结果表明,改进的Schumacher方程的拟合精度明显优于Schumache,方程和广义Schumacher方程,也优于经典的Logistic模型和李新运等自适应模型。可以在林木生长动态模拟及种群增长动态研究中广泛应用．     

中华乌塘鳢的生长、生长模型和生活史类型

采用胸鳍第三支鳍骨作为研究湛江沿海中华乌塘鳢的年龄鉴定材料。胸鳍第三支鳍骨（远侧部）的关径（R）与体长（L）的关系为L＝6.1145 51.1288R。用特殊von Bertalanffy生长方程、一般von Bertalanffy生长方程、逻辑斯谛生长方程、Gompertz生长方程和灰色动态生长模型等5种生长模型拟合了中华乌塘鳢的生长,根据各模型拟合残差平方和大小判断,灰色动态生长模型对中华乌塘鳢生长的拟合效果最好,其次是一般von Bertalanffy生长方程。根据r-选择和κ－选择的典型行征以及渐近体长（L∞）、渐近体重（W∞）、生长系数（κ）、初次生殖年龄（Tm）、最大年龄（Tmax）、瞬时自然死亡率（M）和性腺指数（GI）等7个生态学参数值,可以判断中华乌塘鳢偏向r-选择。应用单位补充量产量模型计算改变起捕年龄（Tc）和瞬时捕捞死亡率（F）的产量,分析产量变化曲线同样证实中华乌塘鳢生活史偏向r-选择。作为渔业管理对策,中华乌塘鳢的起捕年龄应定为2龄。     

大肠杆菌群体的生理异质性对药敏实验的影响

E. coli CVCC249分批培养的过程根据菌群瞬时生长速率的变化分为加速生长期、恒速生长期、减速生长期和衰亡期4个阶段. 各阶段分别取样, 测定抗生素浓度-杀菌曲线(concentration- killing curve, CKC), 结果表明菌群的生理异质性导致菌群个体间的药物敏感性不同, 总体呈现正态分布. 检测表明各阶段中菌群的核酸、蛋白质含量和脱氢酶活力都有明显差别, 这种生理异质性导致各阶段菌群对药物敏感性的差异. 以加速生长期菌群的CKC曲线为参照, 对于庆大霉 素, 恒速生长期和衰亡期菌群敏感性增强; 对于恩诺沙星恒速生长期反而减弱, 其他阶段差别不大. 这是常规药敏实验方法难以显示的, 表明对不同生理状态菌群的药敏实验测定结果可深入反映出药物的杀菌机理. 这有助于常规药敏实验方法的改进, 并可为抗菌药物的合理使用提供理论支持.     

杨树生长模型的选择

本文选用常用生长模型和4类灰色模型,分别对6个新品系杨树生长动态规律进行模拟;结果表明：在常用的生长模型中,Richards方程模拟效果最好,而不是通常认为的Logistic方程;在灰色模型中．以GM（1,1）模拟效果最好,也可作为杨树生长模型．     

甘肃鼠兔幼子生长的初步研究

根据3 窝14只甘肃鼠兔幼子56 天的生长发育资料初步分析了甘肃鼠兔的生长发育规律。依据逻辑斯蒂曲线的拐点,甘肃鼠兔的体重生长可划分为加速增长相（0～0.5日龄）和减速增长相（20.5日龄以后）。按照瞬时生长率曲线的拐点,体重增长过程可分为3个时期,即缓慢生长期（0～6.5 日龄）、快速生长期（6.5～34.5 日龄）和渐进生长期（34.5 日龄以后）。文章对使用逻辑斯蒂方程和其它“S”形曲线描述动物生长过程存在的一些问题进行了讨论,认为：如果只用1条“S”形曲线描述动物的整个生长过程,就有可能会因为成年期动物生长规律的变化而破坏模型参数的生物学意义,同时引起模型拟合精度的降低。为克服这一问题,作者建议：在使用“S”形曲线拟合动物生长模型时,生长过程的资料最好不要覆盖体重波动较大的成年阶段。     

中华鳖幼鳖的生长模式及身体各部分生化组成

在实验条件下,模拟了中华鳖幼鳖背甲宽随年龄变化的生长曲线,观测了幼鳖身体总干重及内脏,脂肪块,骨骼和其它（肌肉和皮脍）各部分干重与背甲宽的相关关系,并测定了上述身体各部分的生化组成,结果发现幼鳖生长曲线呈Ｓ型,用逻辑斯缔生长方程可进行很好的拟合,该方程为：Ｃｗ＝９．７５６３／（１＋５．８００８ｅｘｐ（－０．２３０１ｔ）（ｒ＝０．８９,ｎ＝４２０,Ｐ〈０．００１）,幼鳖身体总干重及内脏,脂肪块,骨骼     

生物生长的Richrds模型

生物的生长过程若用图形来描述将是一条S曲线,随生物物种、生态环境等因素不同,这一曲线是多样性变化．Richards生长方程当其参数m在数轴上滑动取值时,不仅包含了Mitscherlich,Brody,Bertalanffy,Gompertz,Logistic等生长方程,而且包含了它们的中间过渡类型和更为广义的形状,因而对众多生物物种的多样性生长过程,在细胞、器官、个体与群体等不同层次上具有广泛的适用性．本文中以变形虫、水稻、新疆乌伦古河鲈鱼、福建黄牛与海南坡鹿的Richards生长模型,图示了它的可塑性．     

应加强对单细胞生物分批培养生长曲线中减速期的认识和教学

根据单细胞生物分批培养过程中比生长速率(μ)的变化,其生长曲线分为延滞期、加速期、对数期、减速期、稳定期和衰亡期6个时期.与其他生长时期相比,在减速期生物的生长、基质的利用、产物的合成和基因表达谱等方面有显著的不同,并对发酵生产有着重要作用.然而,长期以来,对减速期的认识和教学相当薄弱,亟需加强对减速期的认识和教学.     

蛋黄液中沙门氏菌温度预测模型的建立

为探究温度对沙门氏菌在蛋液中生长规律的影响,测定了在4、10、15、20、25、30、37和42℃等不同温度下沙门氏菌的生长曲线,利用Origin 8.0软件中非线性最小二乘法的原理进行修正Gompertz方程、修正Logistic方程的拟合以及DMFit软件进行Baranyi模型的拟合,研究结果表明修正Gompertz模型、修正Logistic模型和Baranyi模型均能得到较高的决定系数(0.99),选取决定系数相对较高的修正Logistic模型进行一级模型的建立。通过参数估计后利用Ratkowsky模型对最大比生长速率以及迟滞期进行二级模型的拟合,通过Baranyi模型得到的生长参数建立的二级模型拟合度高于其他模型,最大比生长速率以及迟滞期二级模型决定系数分别为0.978和0.866。经检验,研究建立的模型可用于10~42℃温度范围内蛋黄液中沙门氏菌的生长预测。     

两种测定固氮菌NT06菌株生长曲线方法的比较

通过分光光度法和活菌计数法分别对固氮菌NT06的生长曲线进行测定,结果表明对数期以前两种方法所测结果基本一致,而在稳定期和衰亡期,活菌计数法能更真实地反映细菌的生长情况、同时还发现固氮菌NT06培养液的0D600和活菌数之间,在对数生长期有很好的相关性,并确定了两者的函数关系。     

Environmental factors influencing the relationship between optical density and cell count for Listeria monocytogenes

AIMS: The effect of temperature (2-30 degrees C), pH (4.8-7.4) and water activity (0.946-0.995) on the relationship between optical density (OD) at 600 nm and the plate count (CFU ml(-1)) was investigated for Listeria monocytogenes. METHODS AND RESULTS: Calibration curves, relating OD with plate counts, were collected by measuring the OD of consecutive one-half dilution series, before determining the cell density by classic plate count methods. The calibration curves were observed to be shifting in a parallel way, with increasing stress levels. Especially pH influenced the curve in a great extent, while the other variables were showing more synergetic effects. The reason for the shift was investigated by a microscopic viability test, showing a viability decrease with increasing stress levels, causing the shift of the calibration curve. In a last step a model was made describing the effect of environmental factors on the calibration curve, with different data transformations being tested. A polynomial equation was fitted to the data, taking into account a set of constraints to incorporate microbiological knowledge in the black box model. Hence, illogical interpolation results and overfitting of the data could be avoided. CONCLUSIONS: Different stress factors are affecting the relationship between the OD and the cell count of L. monocytogenes by lowering the cell viability. These effects could be modelled using a constrained polynomial model. SIGNIFICANCE AND IMPACT OF THE STUDY: The observed phenomena are important when calculating growth parameters, like growth rate and lag phase, based on OD data.     

A novel approach for estimating growth phases and parameters of bacterial population in batch culture

Using mathematical analysis, a new method has been developed for studying the growth kinetics of bacterial populations in batch culture. First, sampling data were smoothed with the spline interpolation method. Second, the instantaneous rates were derived by numerical differential techniques and finally, the derived data were fitted with the Gaussian function to obtain growth parameters. We named this the Spline-Numerical-Gaussian or SNG method. This method yielded more accurate estimates of the growth rates of bacterial populations and new parameters. It was possible to divide the growth curve into four different but continuous phases based on changes in the instantaneous rates. The four phases are the accelerating growth phase, the constant growth phase, the decelerating growth phase and the declining phase. Total DNA content was measured by flow cytometry and varied depending on the growth phase. The SNG system provides a very powerful tool for describing the kinetics of bacterial population growth. The SNG method avoids the unrealistic assumptions generally used in the traditional growth equations.     

A novel approach for estimating growth phases and parameters of bacterial population in batch culture

Traditionally, microbiologists divided bacterial growth in batch cultures into lag, exponential, station-ary and death phases[1], following the Logistic equa-tion that has been applied to the growth of human populations. The growth curves can always be ch…     

Propagation and Growth Cycle of Rickettsia quintana in a New Liquid Medium

The growth cycle of Rickettsia quintana was studied for the first time in liquid culture. Growth of the microorganism in a transparent broth medium was made possible by the finding that fetal calf serum (FCS), but not calf serum (CS), satisfied the requirement of R. quintana (Fuller strain) for red blood cell lysate. The three constituents of the medium, other than FCS, were autoclavable. The growth cycle was characterized by a lag phase of approximately 24 hr, an exponential growth phase of 72 hr, and a doubling time of approximately 4.5 hr. In FCS medium, titers increased 10(5)-fold over starting titers and reached a peak after 5 days of greater than 10(8) colony-forming-units (CFU)/ml. Optical density readings at 520 nm (OD(520)) served as useful estimates of the titers only during the last 30 hr of exponential growth. Before this time, titers were below 3 x 10(7) CFU/ml and could not be detected at OD(520). The growth-promoting activity of FCS appeared to be a normal serum component widely distributed among fetal calves. FCS from five commercial suppliers supported growth of R. quintana. The active factor(s) was: (i) non-dialyzable, (ii) resistant to heating at 56 C for 30 min, and (iii) partially inactivated at 100 C in 2 min and completely lost at 100 C in 10 min. The results emphasize the presence of erythrocyte and serum factors other than hemoglobin which stimulate the growth of R. quintana.     

Flow cytometry of the differentiation of Physarum polycephalum myxamoebae to cysts

Myxamoebae of Physarum polycephalum, strain Cld, were grown on agar lawns on live bacteria. Myxamoebae were harvested, fixed and stained with propidium iodide. Flow cytometry showed that, as in the case of Physarum plasmodia, there is no G1 phase during rapid exponential growth. However, an apparent G1 phase was observed at the end of exponential growth when the culture arrested with the G1 DNA content for about a day between growth and differentiation. Most myxamoebae differentiated into cysts, but some formed microplasmodia and others appeared to lose DNA. The cysts possessed the G2 phase DNA content and there was an S phase connecting the G1-arrested state with the encysted state. Encystment was blocked by hydroxyurea (HU) suggesting that DNA synthesis is essential for encystment. The natural temporary synchronization in G1 phase may provide the basis of a method for selecting mutants with a conditional block in G2 or M phases.     

Optimization of a cultivation process for recombinant protein production by Escherichia coli.

A single-stage fed-batch bioprocess for the production of a recombinant protein beta-galactosidase, by E. coli has been developed. The XL1-blue strain of E. coli which harbors a multi-number foreign plasmid PT was cultured in a reformulated medium. Critical medium components were selected and their respective concentrations were optimized with the Orthogonal Table method. An exponential substrate feeding schedule was used to maintain optimum conditions. Inhibition of growth and protein expression caused by excessive concentrations of glucose and acetate was investigated and subsequently minimized with an incremental nutrient feeding schedule which limited the specific growth rate of a culture. The program necessary to facilitate the control of substrate addition is fully described. This program has been used with a 2.5 l bioreactor and a commercially available software package for optimization without on-line or off-line measurement of optical density (OD), CO2, glucose or acetate. The optimized fed-batch process limited the acetate concentration to less than 20 mM; maintained an exponential growth phase for 50 h; and produced a cell density of 51 g l-1 dry cell weight (DCW) or 154 OD600 with a beta-galactosidase activity of 990 U ml-1.     

Population analysis of a commercial Saccharomyces cerevisiae wine yeast in a batch culture by electric particle analysis, light diffraction and flow cytometry

Data from electric particle analysis, light diffraction and flow cytometry analysis provide information on changes in cell morphology. Here, we report analyses of Saccharomyces cerevisiae populations growing in a batch culture using these techniques. The size distributions were determined by electric particle analysis and by light diffraction in order to compare their outcomes. Flow cytometry parameters forward (related to cell size) and side (related to cell granularity) scatter were also determined to complement this information. These distributions of yeast properties were analysed statistically and by a complexity index. The cell size of Saccharomyces at the lag phase was smaller than that at the beginning of the exponential phase, whereas during the stationary phase, the cell size converged with the values observed during the lag phase. These experimental techniques, when used together, allow us to distinguish among and characterize the cell size, cell granularity and the structure of the yeast population through the three growth phases. Flow cytometry patterns are better than light diffraction and electric particle analysis in showing the existence of subpopulations during the different phases, especially during the stationary phase. The use of a complexity index in this context helped to differentiate these phases and confirmed the yeast cell heterogeneity.     

Effect of physiological heterogeneity of <Emphasis Type="Italic">E. coli</Emphasis> population on antibiotic susceptivity test

According to the instantaneous growth rate (dN/dt) of E. coli CVCC249 growing in batch culture, the entire growth progress was distinguished into four phases: accelerating growth phase, constant growth phase, decelerating growth phase and declining phase, in each of which obvious variation in physiological and biochemical properties was detected, including total DNA, total protein, and MTT-dehydrogenase activity, etc., that led to difference in their antibiotic susceptivity. Antibiotic susceptivity of the population sampled from each phase was tested by Concentration-killing Curve (CKC) approach following the formula N=N ₀/{1+exp[r·(x-BC ₅₀)]}, showing as normal distribution at the individual cell level for an internal population, in which the median bactericidal concentration BC ₅₀ represents the mean level of susceptivity, while the bactericidal span BC ₁₋₉₉=(2lnN ₀)/r indicates the variation degree of the antibiotic susceptivity. Furthermore, tested by CKC approach, the antibiotic susceptivity of E. coli CVCC249 population in each physiological phase to gentamicin or enoxacin was various: susceptivity of the population in the constant growth phase and declining phase all increased compared with that in the accelerating growth phase for gentamicin but declined for enoxacin. The primary investigations revealed that the physiological phase should be taken into account in the context of antibiotic susceptivity and research into antimicrobial mechanism. However there are few reports concerned with this study. Further research using different kinds of antibiotics with synchronized continuous culture of different bacterial strains is required.