Modeling bacterial growth responses

Summary The main steps of modeling bacterial growth responses are summarized and a new model for growth curves is shown. Its advantages are analyzed from some theoretical and practical points of view. The new model fits better and has more advantageous statistical properties than the Gompertz curve.     

Effects of repeated cultivation of transgenic Bt cotton on functional bacterial populations in rhizosphere soil

The impact of multiple-year (0–5 years) cultivation of transgenic Bacillus thuringiensis (Bt) cotton on the functional bacterial populations in rhizosphere soil was investigated. The transgenic Bt + CpTI cotton line SGK321 and a non-Bt cotton line Shiyuan321 were planted in four fields in which Bt cotton had been continuously cultivated for 0, 1, 3, and 5 years. Rhizosphere soil samples were collected at the seedling, squaring, flower and boll, and boll-opening stages of cotton. Numbers of bacteria involved in nitrogen-fixing, organic phosphate-dissolving, inorganic phosphate-dissolving, and potassium-dissolving were measured with cultivation-dependent approaches. The data presented here showed no consistent statistically significant differences in the numbers of different groups of functional bacteria between rhizosphere soil of Bt and non-Bt cotton in the same field, and no obvious trends in the numbers of the various group of functional bacteria with the increasing duration of Bt cotton cultivation. These studies suggest that multiple-year cultivation of transgenic Bt cotton may not affect the functional bacterial populations in rhizosphere soil.     

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.     

Modeling Spruce Budworm Population Revisited: Impact of Physiological Structure on Outbreak Control

Understanding the dynamics of spruce budworm population is very important for the protection of spruce and balsam fir trees of North American forests, and a full understanding of the dynamics requires careful consideration of the individual physiological structures that is essential for outbreak control. A model as a delay differential equation is derived from structured population system, and is validated by comparing simulation results with real data from the Green River area of New Brunswick (Canada) and with the periodic outbreaks widely observed. Analysis of the equilibrium stability and examination of the amplitudes and frequencies of periodic oscillations are conducted, and the effect of budworm control strategies such as mature population control, immature population control and predation by birds are assessed. Analysis and simulation results suggest that killing only budworm larvae might not be enough for the long-term control of the budworm population. Since the time required for development during the inactive stage (from egg to second instar caterpillar) causes periodic outbreak, a strategy of reducing budworms in the inactive stage, such as removing egg biomass, should also be implemented for successful control.     

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.     

The effect of time delays on Caribbean coral-algal interactions

The analysis of ecological models often focuses on their asymptotic behavior, but there is increasing recognition that it is important to understand the role of transient behavior. By introducing a time delay into a model of coral-algal interactions in Caribbean coral reefs that exhibits alternative stable states (a favorable coral rich state and a degraded coral-depleted state), we demonstrate the criticality of understanding the basins of attraction for stable equilibria in addition to the systems' asymptotic behavior. Specifically, we show that although the introduction of a time delay into the model does not change the asymptotic stability of the stable equilibria, there are significant changes to their basins of attraction. An understanding of these effects is necessary when determining appropriate reef management options. We then demonstrate that this is a general phenomenon by considering similar behavior underlying the changes in the basins of attraction in a simple Lotka-Volterra model of competition.     

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…     

Modeling relapse in infectious diseases

An integro-differential equation is proposed to model a general relapse phenomenon in infectious diseases including herpes. The basic reproduction number R(0) for the model is identified and the threshold property of R(0) established. For the case of a constant relapse period (giving a delay differential equation), this is achieved by conducting a linear stability analysis of the model, and employing the Lyapunov-Razumikhin technique and monotone dynamical systems theory for global results. Numerical simulations, with parameters relevant for herpes, are presented to complement the theoretical results, and no evidence of sustained oscillatory solutions is found.     

Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays

In the glucose-insulin regulatory system, ultradian insulin secretory oscillations are observed to have a period of 50-150 min. After pioneering work traced back to the 1960s, several mathematical models have been proposed during the last decade to model these ultradian oscillations as well as the metabolic system producing them. These currently existing models still lack some of the key physiological aspects of the glucose-insulin system. Applying the mass conservation law, we introduce two explicit time delays and propose a more robust alternative model for better understanding the glucose-insulin endocrine metabolic regulatory system and the ultradian insulin secretory oscillations for the cases of continuous enteral nutrition and constant glucose infusion. We compare the simulation profiles obtained from this two time delay model with those from the other existing models. As a result, we notice many unique features of this two delay model. Based on our intensive simulations, we suspect that one of the possibly many causes of ultradian insulin secretion oscillations is the time delay of the insulin secretion stimulated by the elevated glucose concentration.     

刺芹侧耳生长条件和栽培特性的研究

对刺芹侧耳[Pleurotus eryngii(DC.ex Fr.)Quel]生长条件与栽培特性进行了分析.结果表明:刺芹侧耳菌丝生长的适宜pH值为pH 5～pH 7,最适pH值为pH 6;黑暗环境有利于菌丝生长,光照对菌丝生长具有抑制作用;菌丝生长适宜的碳源为可溶性淀粉、葡萄糖和蔗糖,适宜的氮源为蛋白胨和钼酸铵,葡萄糖和蛋白胨的适宜浓度分别为50和1 g·L-1;在马铃薯黄豆粉培养基、黄豆粉玉米粉培养基和马铃薯蛋白胨培养基中可较好地形成菌丝球.采用液体菌种栽培,菌丝的生长速度比使用玉米固体菌种快,其中用马铃薯黄豆粉液体菌种栽培,菌丝生长最快;使用马铃薯蛋白胨液体菌种在木屑棉籽壳混合培养料中栽培,可获得菌柄长菌盖大的子实体,而且产量高.     

The effect of integral conditions in certain equations modelling epidemics and population growth

Summary Models of epidemics that lead to delay differential equations often have subsidiary integral conditions that are imposed by the interpretation of these models. The neglect of these conditions may lead to solutions that behave in a radically different manner from solutions restricted to obey them. Examples are given of such behavior, including cases where periodic solutions may occur off the natural set defined by these conditions but not on it. A complete stability analysis is also given of a new model of a disease propagated by a vector where these integral conditions play an important role.This work was partially supported by N.S.F. Grant MCS 7903497     

Multistability in an age-structured model of hematopoiesis: Cyclical neutropenia

Cyclical neutropenia (CN) is a rare hematopoietic disorder in which the patient's neutrophil level drops to extremely low levels for a few days approximately every three weeks. CN is effectively treated with granulocyte colony stimulating factor (G-CSF), which is known to interfere with apoptosis in neutrophil precursors and to consequently increase the circulating neutrophil level. However, G-CSF treatment usually fails to eliminate the oscillation. In this study, we establish an age-structured model of hematopoiesis, which reduces to a set of four delay differential equations with specific forms of initial functions. We numerically investigate the possible stable solutions of the model equations with respect to changes in the parameters as well as the initial conditions. The results show that the hematopoietic system possesses multistability for parameters typical of the normal healthy state. From our numerical results, decreasing the proliferation rate of neutrophil precursors or increasing the stem cell death rate are two possible mechanisms to induce cyclical neutropenia, and the periods of the resulting oscillations are independent of the changing parameters. We also discuss the dependence of the model solution on the initial condition at normal parameter values corresponding to a healthy state. Using insight from our results we design a hybrid treatment method that is able to abolish the oscillations in CN.     

Synchronous germination of Streptomyces antibioticus spores: Tool for the analysis of hyphal growth in liquid cultures

Abstract We have devised a method for obtaining synchronous and dispersed growth of Streptomyces antibioticus in liquid cultures. After ultrasonic treatment, most of the spores germinated at the same time, yielding hyphae very similar in length. Dispersed growth was achieved in media without Ca²⁺ and in which the levels of Fe²⁺ and Mg²⁺ were carefully controlled. Studies on the kinetics of growth carried out with synchronous cultures of young hyphae revealed a multiphasic pattern of hyphal elongation, with successive periods of linear growth and changes in growth rate at defined intervals.     

A current approach to the control of filamentous fungal growth in media: microparticle enhanced cultivation technique

Various strategies have been carried out to date in order to overcome the problem of the adverse effects of bulk fungal growth in bioreactors. Nevertheless, previous conventional methods such as modifying the cultivation temperature or pH resulted in limited biomass production and consequently lower yields. In recent years microparticle enhanced cultivation (MPEC) techniques are one of the most remarkable and novel methods employed for submerged fungal production to overcome bulk microbial growth. In addition to low cost advantages, MPEC also provides benefits such as not interfering with fungal metabolism, enhancing final product concentration and improving homogeneity in the fermentation broth. In this review, a comparison of conventional and novel methods to control fungal morphology has been discussed. Additionally, the application of microparticles in fungal fermentations, their benefits to the process in terms of fungal morphology, biomass accumulation, substrate consumption, and product formation also effect mechanisms of microparticle function are discussed in detail.     

番茄基质通气栽培模式的效果

针对雾培模式在提高作物产量同时增加无土栽培成本的问题,研制了一种新型的珍珠岩通气栽培模式,探讨了其对番茄的栽培效果.试验设计3种栽培方式:全珍珠岩栽培(CK),珍珠岩通气栽培(T1)和气雾培(T2).结果表明:T1可显著改善番茄根际通气环境,其中根际CO2浓度仅为CK的1/5,O2浓度则为CK的1.17倍;显著增加了番茄的株高和茎粗,在定植后60d时,株高和茎粗分别比CK增加了5.1%和8.4%;植株净光合速率显著高于CK,在净光合速率达到最大值(定植后45d)时,比CK提高了13%;显著提高了植株根系活力和吸收能力,在定植后45d时,其根系活力为CK的1.23倍,在定植后60d时,根系钾、钙、镁含量分别比CK增加了31%、37%和27%,番茄产量为CK的1.16倍.且T1上述指标均与T2无显著差异;而CK、T1和T2在果实的可溶性糖、有机酸、糖酸比方面无显著差异.表明以珍珠岩为基质的通气栽培模式简便易行且可显著提高番茄产量.     

一类具有时滞的传染病模型的稳定性分析

研究了一类具有时滞的传染病生物模型．首先研究了该模型的线性稳定性,并给出了一列Hopf分支值,然后利用中心流形定理和正规型方法,给出了确定分支周期解的分支方向与稳定性的计算公式．     

大白口蘑菌丝的培养优化

从大白口蘑子实体中分离得到菌种,并进行不同营养条件对大白口蘑菌丝生长的影响实验。结果表明,最佳氮源为酵母粉;最佳碳源为果糖;能明显促进菌丝生长的矿质元素为磷酸二氢钾;最佳生长调节因子为吲哚乙酸;最适温度为28－32℃;最适pH4.0－5.0。     

Tank cultivation of the red alga Palmaria palmata: Effects of intermittent light on growth rate, yield and growth kinetics

Tank cultivation of marine macroalgaeinvolves air-agitation of the algal biomassand intermittent light conditions,i.e.periodic, short light exposure of thethalli in the range of 10 s at the watersurface followed by plunging to low lightor darkness at the tank bottom andrecirculation back to the surface in therange of 1–2 min. Open questions relate toeffects of surface irradiance on growthrate and yield in such tumble cultures andthe possibility of chronic photoinhibitionin full sunlight. A specially constructedshallow-depth tank combined with a darktank allowed fast circulation times ofapproximately 5 s, at a density of 4.2 kgfresh weight (FW) m^-2s^-1. Growthrate and yield of the red alga Palmaria palmata increased over a widerange of irradiances, with no signs ofchronic photoinhibition, up to agrowth-saturating irradiance ofapproximately 1600 mol m^-2s^-1 in yellowish light supplied by asodium high pressure lamp at 16 h light perday. Maximum growth rate ranged at 12% FWd^-1, and maximum yield at 609 gFW m^-2 d^-1. This shows that highgrowth rates of individual thalli may bereached in a dense tumble culture, if highsurface irradiances and short circulationtimes are supplied. Another aspect ofintermittent light relates to possiblechanges of basic growth kinetics, ascompared to continuous light. For thispurpose on-line measurements of growth ratewere performed with a daily light reductionby 50% in light-dark cycles of 1, 2 or 3min duration during the daily light period.Growth rates at 10 °C and 50 molphoton m^-2 s^-1 dropped in allthree intermittent light regimes duringboth the main light and dark periods andreached with all three periodicitiesapproximately 50% of the control , with noapparent changes in basic growth kinetics,as compared to continuous light.     

Translocation of assimilates in Undaria and its cultivation in China

Undaria cultivation on a commercial scale began in China only in the last decade. Today, Undaria pinnatifida is the main species under cultivation concentrated in two provinces, Liaoning and Shandong. The annual production in the early nineties was 8000-13 000 tons dry weight, which is two or three times the pre-1980 figures. The raft cultivation method maintaining the alga at the desired depths generally ensures the light saturated rate of photosynthesis on clear days, and enhances production. Under the cultivated condition, the calculated annual primary productivity of this alga is 160 gC m⁻² y⁻¹. Translocation of ¹⁴C-labelled photoassimilates in rapidly growing sporophyte of Undaria pinnatifida was studied in the open sea. Samples from different parts of the blade with counterparts exposed to tracer (NaH¹⁴CO₃) showed that the translocation that occurred mainly from the tip of the blade to the growing region had obvious source-sink relationship. It took 20 minutes to translocate the labelled photoassimilates from the epidermis, via cortex, to the medulla of the midrib, where rates of translocation averaging 42–48 cm h⁻¹ were observed in the open sea. Production experiments of tip-cutting of the blades showed an increased production of 9%. This revised version was published online in August 2006 with corrections to the Cover Date.