嗜酸氧化亚铁硫杆菌生长动力学

在确定二价铁离子为A.f生长过程中惟一限制性底物条件下,通过考察初始亚铁离子浓度、初始pH值两种影响亚铁离子氧化代谢的主要因素来研究细菌的生长特性,得到以限制性底物亚铁离子浓度为表征的细菌生长曲线。利用基于Monod方程建立的细菌生长动力学方程模型,采用Matlab软件中的Gauss-Newton算法确定了在不同条件下细菌生长动力学参数,包括最大比生长速率μm、Monod常数K及Ro,推导出了不同条件下A.f对数期以底物Fe(Ⅱ)浓度为表征的生长动力学方程。     

Analytical solution for a hybrid Logistic-Monod cell growth model in batch and continuous stirred tank reactor culture

Monod and Logistic growth models have been widely used as basic equations to describe cell growth in bioprocess engineering. In the case of the Monod equation, the specific growth rate is governed by a limiting nutrient, with the mathematical form similar to the Michaelis–Menten equation. In the case of the Logistic equation, the specific growth rate is determined by the carrying capacity of the system, which could be growth-inhibiting factors (i.e., toxic chemical accumulation) other than the nutrient level. Both equations have been found valuable to guide us build unstructured kinetic models to analyze the fermentation process and understand cell physiology. In this work, we present a hybrid Logistic-Monod growth model, which accounts for multiple growth-dependent factors including both the limiting nutrient and the carrying capacity of the system. Coupled with substrate consumption and yield coefficient, we present the analytical solutions for this hybrid Logistic-Monod model in both batch and continuous stirred tank reactor (CSTR) culture. Under high biomass yield (Y_x/s) conditions, the analytical solution for this hybrid model is approaching to the Logistic equation; under low biomass yield condition, the analytical solution for this hybrid model converges to the Monod equation. This hybrid Logistic-Monod equation represents the cell growth transition from substrate-limiting condition to growth-inhibiting condition, which could be adopted to accurately describe the multi-phases of cell growth and may facilitate kinetic model construction, bioprocess optimization, and scale-up in industrial biotechnology.     

Modelling the growth of Trichoderma virens with limited sampling of digital images

AIMS: Using limited digital image sampling, a model of fungal growth in soil that considers both hyphal production and lysis was constructed for two strains of Trichoderma virens over a range of four temperatures. MATERIALS AND METHODS: A growth model was developed by fitting the radial cross sectional data with a modified form of the Ratkowsky equation to determine maximum growth rate and a modified Arrhenius equation to determine maximal rate of decrease in area covered by mycelia. The parameters obtained from a combined equation were then verified by using the data obtained from the whole colony to determine the appropriateness of the model. CONCLUSIONS: Using a limited data set and a combination of the Ratkowsky and Arrhenius equations, the mycelial coverage of the T. virens colony was determined, relating microscopic hyphal growth to macroscopic colony growth. This model was sufficiently robust to predict growth across four temperatures for a genetically modified and wild-type strain of T. virens. SIGNIFICANCE AND IMPACT OF STUDY: By using simple assumptions for the increase and eventual decline in fungal growth on a resource-limited medium, this model constructs an initial framework onto which additional parameters such as nutrient consumption could be incorporated for prediction of fungal growth.     

Fractional Reproduction-Dispersal Equations and Heavy Tail Dispersal Kernels

Reproduction-Dispersal equations, called reaction-diffusion equations in the physics literature, model the growth and spreading of biological species. Integro-Difference equations were introduced to address the shortcomings of this model, since the dispersal of invasive species is often more widespread than what the classical RD model predicts. In this paper, we extend the RD model, replacing the classical second derivative dispersal term by a fractional derivative of order 1相似文献   

On the dynamics of a toxicant-individual system

The dynamics of a toxicant-individual model where the individual is represented by von Bertalanffy dynamics and the uptake model component is one developed by Barber, Suarez & Lassiter is discussed. A sufficient condition for the death of an individual subjected to chemical stress is found. Another possible behavior of the system is an oscillatory mode of individual size and internal chemical concentration determined by a limit cycle. These fluctuations are a consequence of formulations of growth, maintenance, and the dose-response functions in the model system.     

Cell cycles and growth laws: the CCC model

In the cell-cycle-with-control model (CCC model), cells have to satisfy a condition before they are allowed to pass a control point during G1. Different cycle durations within a cell population are explained by individual time spans needed to satisfy the passing condition. If the distribution of cycle durations is time invariant, the population will grow exponentially. However, if the average cycle duration becomes longer, while the population grows, non-exponential population growth results. Simple functions for the lengthening of the average cycle duration, like linear or exponential ones, yield the well-known growth laws found in the biological literature. The same functions can be represented by an "S-system" differential equation that was derived earlier as an approximation for biochemical systems with many fast reactions (metabolism) and one slow process (e.g. ageing).     

Non-equilibrium theory of the allele frequency spectrum

A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection and varying population size, the boundary condition is lim(x downward arrow0)xf(x,t)=thetarho(t), where f(.,t) is the frequency spectrum of derived alleles at independent loci at time t and rho(t) is the relative population size at time t. When population size and selection intensity are independent of time, the forward equation is equivalent to the backwards diffusion usually used to derive the frequency spectrum, but this approach allows computation of the time dependence of the spectrum both before an equilibrium is attained and when population size and selection intensity vary with time. From the diffusion equation, a set of ordinary differential equations for the moments of f(.,t) is derived and the expected spectrum of a finite sample is expressed in terms of those moments. The use of the forward equation is illustrated by considering neutral and selected alleles in a highly simplified model of human history. For example, it is shown that approximately 30% of the expected total heterozygosity of neutral loci is attributable to mutations that arose since the onset of population growth in roughly the last 150,000 years.     

Increasing model structural complexity inhibits the growth of initial condition errors

One source of inaccuracy in non-linear deterministic ecological models is the growth of initial condition errors. A size-resolved pelagic ecosystem model is used to investigate the effects of changing model structural complexity on the growth rate of initial condition errors. Structural complexity is altered by (1) changing the number of biological size-classes; and (2) changing prey size-ranges which changes the number of linkages for the same number of size-classes. Ensembles of model runs with tiny variations in initial conditions are undertaken and member divergence used to estimate ensemble spread (a measure of the growth of initial condition errors). Increasing prey ranges and therefore the number of linkages greatly reduced the rate of growth of initial condition errors, but ecosystem behaviour is also altered, restricting the generality of the result. At more than 123 size-classes, increasing the number of size-classes while not changing either the model equations or parameters does not alter ecosystem behaviour for over 200 days. In this case, increasing structural complexity through increasing the number of size-classes did not alter the growth of initial condition errors for the first 30 days of the simulations, but afterwards reduced error growth. There are many advantages of parsimonious ecological models with small numbers of classes and linkages, but they are more likely to suffer from the growth of initial condition errors than structurally complex models.     

Daisyworld inhabited with daisies incorporating a seed size/number trade-off: the mechanism of negative feedback on selection from a standpoint of the competition theory

We reexamined a Daisyworld model from the traditional view of competition theory. Unlike the original model, white and black daisies in our model incorporate a seeding/germination trade-off against bare ground area without assuming the local temperature reward. As a result, the planetary temperature is automatically regulated by two species if the following conditions are met: (i) the species react equally to an environmental condition, but one can alter the environmental condition in the opposite direction to the other. (ii) that one of the two cannot have both a higher maximal growth rate (mu(max)) and lower half-saturation constant (K) than those of the other. In other words, a pair of phenotypes incorporates a trade-off between quality and number of seeds. We found that the homeostatic regulation can also be reconciled with the adaptive evolution of optimal temperature. The results of simulation imply that biotic environmental feedback can also be maintained when the emergence of polymorphisms (black and white daisies) is closely linked to such a trade-off.     

Molecular feature of the nerve growth factor in human serum

High molecular weight binding components which bind [¹²⁵I] mouse β nerve growth factor exist in human serum. The binding of β nerve growth factor to the serum components was inhibited at alkaline condition. After gel filtration of human serum on a Sephadex G-150 column at neutral condition, the nerve growth factor-like immunoreactivity was observed in only one peak, differing from the high molecular weight serum components. However, at alkaline condition two peaks with nerve growth factor-like immunoreactivity appeared; one was almost at the position observed at neutral pH, and the other was a new peak eluted approximately to the column volume. these results suggest that there are at least two nerve growth factor-like molecules in human serum and most of the nerve growth factor in the serum exists in a complex form associated with serum components with high molecular weight.     

The size and scar distributions of the yeast Saccharomyces cerevisiae

A model for the growth of populations of Saccharomyces cerevisiae is formulated and analysed. The probability of bud emergence is assumed to depend on the size of the cell. Under certain conditions on birth size the model can be reduced to a single renewal equation. Using Laplace transform techniques and renewal theory we establish the existence of a stable scar and size distribution under certain conditions on the growth rate of individual cells. The steady state values for the relative frequencies of unbudded and budded cells in the various scar classes are given.     

螺旋藻批式与连续培养及其生长动力学

在内循环气升式光生物反应器中,分别研究了螺旋藻细胞在批式和连续培养条件下的生长特性,结果表明：Richards模型和指数衰减模型可较好地描述批式培养时细胞和碳源底物浓度与培养时间的关系;批式培养时最大细胞生长速率为0371g/d/L,细胞对碳的得率系数为3.439g/gC;连续培养时随着稀释率的增大,细胞和底物浓度分别呈下降和上升趋势;连续培养时最大细胞产率为0.362g/L/d,最佳稀释率为0.45/d,细胞对碳的得率系数为2.050g/gC;所提出的连续培养动力学模型可较好地拟合实验数据。     

A mathematical model for the design of fibrin microcapsules with skin cells

The use of fibrin in tissue engineering has greatly increased over the last 10 years. The aim of this research was to develop a mathematical model to relate the microcapsule-size and cell-load to growth and oxygen depletion. Keratinocytes were isolated from rat skins and microencapsulated dropping fibrinogen and thrombin solutions. The cell growth was measured with MTT-assay and confirmed using histochemical technique. The oxygen was evaluated using a Clark sensor. It was found that Fick–Monod model explained the cell growth for the first 48 h, but overestimated the same thereafter. It was necessary to add a logistic equation to reach valid results. In relation to the preferred implant alternative, when considering large initial cell loads, the possibility to implant small loads of fast-growing cells arises from the simulations. In relation to the microcapsule size, it was found that a critical diameter could be established from which cell growth velocity is about the same.     

马尾松人工林Sloboda多形地位指数模型的研究

将德国生物统计学家Sloboda B的树高生长模型应用于马尾松人工林优势高生长模型模拟中。结果表明,用Sloboda树高生长方程拟合马尾松人工林多形地位指数曲线能获得良好效果,且优于Richards多形地位指数曲线。     

基于营养供需动态平衡考虑的种群生物量增长模型

本文在种群实际增长是限制性营养供需动态平衡所导致的结果这一假定下,推导出了一个单种群生物量增长数学模型。该模型在形式上与崔-Lawson模型相一致。但其3个参数的生物学意义与崔-Lawson模型有不同的内涵。该模型概括了崔-Lawson模型所不能概括的一类单种群物量增长方式,并给出了不同类型生物量增长方式与种群自身特征和营养再循环的分解条件的关系。本模型的建立和解释具有直观性。     

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。     

Theoretical considerations on the C-D effect in self-thinning plant populations

A model for describing the competition–density (C-D) effect in self-thinning populations was developed on the basis of the following three basic assumptions: (1) the growth of mean phytomass follows a general logistic equation; (2) final yield is independent of initial population density; and (3) there exists a functional relationship between actual and initial population densities at any given time. The resultant equation takes the same reciprocal form as the reciprocal equation of the C-D effect derived from Shinozaki–Kira's theory (i.e., the logistic theory of the C-D effect), which deals with the density effect in nonself-thinning populations. However, one of the two time-dependent coefficients is quite different in mathematical interpretation between the two reciprocal equations. The reciprocal equation for self-thinning populations is essentially the same as the reciprocal equation assumed in the derivation of the functional relationship between actual and initial population densities. The establishment of the reciprocal equation is supported by the empirical facts that the reciprocal relationship between mean phytomass and population density is discernible in not only nonself-thinning populations but also in self-thinning populations. The present model is expected to systematically interpret underlying mechanisms between the C-D effect, which is observed at a time constant among populations with various initial densities, and self-thinning, which is observed along a time continuum in a given population. Received: August 5, 1998 / Accepted: January 7, 1999     

The shade avoidance syndrome: A non-Markovian stochastic growth model

Plants at high population density compete for light, showing a series of physiological responses known as the shade avoidance syndrome. These responses are controlled by the synthesis of the hormone auxin, which is regulated by two signals, an environmental one and an internal one. Considering that the auxin signal induces plant growth after a time lag, this work shows that plant growth can be modelled in terms of an energy-like function extremization, provided that the Markov property is not applied. The simulated height distributions are bimodal and right skewed, as in real community of plants. In the case of isolated plants, theoretical growth dynamics and speed correctly fit Arabidopsis thaliana experimental data reported in literature. Moreover, the growth dynamics of this model is shown to be consistent with the biomass production function of an independent model. These results suggest that memory effects play a non-negligible role in plant growth processes.     

A simple model for periodic cyclostat growth of algae

Summary This paper provides a simple model of nutrient limited periodic cyclostat growth for algae.The basic growth function is assumed to be a time dependent variation of the empirical growth equation developed by Droop (1968). The authors also present the relations for n species' cyclostat coexistence and a stability analysis for the model growth equation.The model, although limited in some respects, agrees very well with available experimental data on Euglena gracilis. The significance of the time dependent amplitude functions developed in this study is also discussed.The term used to describe this system is the cyclostat (see Chisholm et al., 1975).     

A preliminary study of the age and growth of the Cyprinid fish Barilius moorii Blgr. from Lake Kivu

The age and growth of the Cyprinid fish Barilius moorii from Lake Kivu is studied by means of the growth rings occurring in the scales. Although the moment of ring formation and the duration of one growth season were not known, both overall length growth in a population as well as individual length growth could be calculated. Increase of weight was obtained from length growth on the basis of a length-weight relationship. By comparing the growth parameters of the von Bertallanfy equation and data from the literature, a hypothesis is formulated that ring formation should occur at the transition from a dry to a rainy season, and that two rings a year should be formed. Ring formation on the scales might be due to gonad maturation, but this could not be demonstrated.