Effect of Nutrient Concentration on the Growth of Escherichia coli

The relationship between specific growth rate of Escherichia coli and the concentration of limiting nutrient (glucose or phosphate or tryptophan) has been determined for populations in a steady state. At high concentrations the specific growth rate is independent of the concentration of nutrient, but at low concentrations the specific growth rate is a strong function of the nutrient concentration. Such a relationship was predicted by Monod; however, Monod's equation does not predict the relationship over the entire range of nutrient concentration. If parameters of the equation are estimated from the results obtained at low concentrations, then at high concentrations of nutrient, the specific growth rate is significantly higher than that predicted by Monod's equation. These results were interpreted on the basis that the rate of growth is controlled by at least two parallel reactions and that the affinities of the enzymes catalyzing these reactions are different. The relationship between specific growth rate and mean cell volume was also measured, and the results indicate that mean cell volume depends not only on the specific growth rate but also on the nature of the limiting nutrient. There are different mean cell volumes at the same specific growth rate established by different limiting nutrients. Therefore, the mean cell volume is not uniquely determined by the specific growth rate.     

Kinetics of phosphate limited algal growth

The kinetics of phosphate limited growth of two green algae Chorella pyrenoidosa and Selenastrum capricornutum have been studied in chemostats. Several kinetic models which express the specific growth rate as a function of the intracellular phosphours content have been examined, and one of the models was found to be significantly better than the other models. The principles of this model were described in a recent paper by Nyholm. The kinetics of phosphate uptake have been investigated by adding pulses of phosphate to the chemostats. The uptake by phosphours deficient cells could be described by Michaelis–Menten kinetics for phosphate concentrations below approximately 500 μg P/liter. Further, with the assumption of a discontinuous adjustment of the uptake rate at the onset of phosphours deficiency, a complete kinetic model for growth and phosphate removal is proposed. The mean cell size and the contents of chlorophyll and RNA per unit dry weight have been measured for C. pyrenoidosa as a function of the dilution rate.     

A MODEL APPROACH FOR SIZE-SELECTIVE COMPETITION OF MARINE PHYTOPLANKTON FOR FLUCTUATING NITRATE AND AMMONIUM1

Phytoplankton size-selective competition for fluctuating nutrients was studied with the use of a numerical model, which describes nitrate and ammonium uptake, nitrate reduction to ammonium, and growth as a function of cell she under fluctuating nitrogen limitation. The only size-dependent parameter in the model was the cell nutrient quota. Related to this, the cell surface area per biomass was negatively correlated to cell volume, and the vacuole volume per biomass ratio was positively correlated to cell volume. Simulations showed an inverse correlation between the maximum specific growth rate and cell size under steady-state conditions. With nitrate as the limiting nitrogen source, nitrogen quotas were always higher than with ammonium at the same specific growth rate. Net passive transport of ammonium due to unspecific diffusion of ammonia across the plasma membrane decreased the affinity for ammonium, whereas the affinity for nitrate was not influenced. Transient state-specific ammonium uptake was not dependent on cell size. However, small algae always have the highest specific growth rate in ammonium-controlled systems according to our model. Transient state nitrate uptake rate was positively correlated to cell size because larger algae have a higher vacuole volume per biomass, in which nitrate can be stored. Despite their lower maximum growth rate, larger algae became dominant during simulations under fluctuating nitrate supply when amplitude of and the period between nitrate pulses were high enough. Results from model simulations were qualitatively validated by earlier observations that large diatoms become dominant under fluctuating conditions when nitrate is the main nitrogen source.     

Nutrient-limited microbial growth kinetics: overview and recent advances

Traditional concepts of nutrient uptake and growth kinetics as linked by cell yield are presented. Phenomena affecting the kinetics are examined along with a discussion of those which lead to ambiguity. Concepts of flux control are presented to help understand the distribution of material along metabolic pathways. Specific affinity is described to relate nutrient accumulation rates to transporter density. It is shown to be a primary kinetic constant and the best available index of nutrient collection ability. As an aid to understanding, specific affinity is reexpressed in terms of membrane permeability. Formulations of nutrient transport rate as a function of cellular composition, particularly transporter and enzyme content and known as janusian kinetics, are described as an improvement to specific affinity theory. Procedures for quantified unidirectional fluxes are reviewed to identify the difference between gross and net transport rates of substrate. Collision frequency theory is used to show that in addition to total biomass, cell size and transporter density should also be included in rate equations describing microbial growth. Theory diversity suggests that one reason for microbial metabolic is that the likelihood of additional collisions of substrate molecules with a cell surface, after an initial collision, requires only a sparse distribution of transporter sites for maximal rate, leaving room for additional transporters able to collect other substrate types.     

The unsteady continuous culture of phosphate-limited Monochrysis lutheri droop: Experimental and theoretical analysis

A three-state variable model for phosphate-limited phytoplankton growth in a continuously lit continuous culture is proposed. In the model, the phosphate uptake rate per cell is a Michaelis-Mententype hyperbolic function of ambient nutrient concentration and the growth rate is a Droop-type hyperbolic function of cell quota. Steady-state and short-term uptake experiments with unialgal cultures of Monochrysis lutheri Droop, a marine chrysophyte, were used to calibrate the proposed model. For the long-term unsteady experiments, the model predicts well the culture's dynamic response in terms of cell density to steps down and up in influent concentration of limiting nutrient. For step changes in dilution rate, the model predicts well the culture's response to a step down but predicts poorly the culture's response to a step up. The long-term responses of the cultures to impulses in influent concentration show that the model fails to predict, even qualitatively, the behavior of the phytoplankton. Not unexpectedly, the model fails most dramatically in those experiments involving a rapid increase in cell quota, thereby demonstrating both the inherent flaws in the concept of the instantaneous growth rate as a function of instantaneous cell quota and the need for further dynamic characterization of phytoplankton behavior.     

SOME THOUGHTS ON NUTRIENT LIMITATION IN ALGAE1

An empirical relation relating specific growth, rate in steady state systems to nutrient status with respect to more than one nutrient simultaneously is proposed, based on 3 experimentally verifiable postulates: (1) that uptake depends on the external substrate concentration; (2) that growth depends on the interval substrate concentration; and (3) in a steady state system specific rate of uptake (in the absence of significant, excretion) is necessarily the product of the specific growth rate and internal substrate concentration. The implications of this model are discussed in particular in respect to the concept of luxury consumption and Liebig's law of minimum. Some aspects of uptake in transient situations are also discussed.     

A theoretical explanation of the Piper-Steenbjerg effect

The relation between plant yield and plant nutrient concentration is sometimes found to be negative, a phenomenon called the Piper-Steenbjerg (PS) effect. A model was used to examine the underlying causes of the PS effect, and the conditions under which it is most likely to occur. The model uses the nutrient productivity concept for plant growth and a nutrient uptake equation in which root growth rate and external nutrient concentration determine the uptake rate. The study suggests that the PS effect occurs when the fast growth of plants grown in an initially higher nutrient medium eventually leads to a more rapid depletion of external nutrients than the slow growth of plants grown in an initially lower nutrient medium. The fast growth of plants combined with a rapid decrease of nutrient uptake leads to a fall in plant nutrient concentration. When these large plants with very low nutrient concentrations are compared with the smaller, slow-growing plants, a PS effect may be found depending on the time at which the plants are harvested, and on the range of initial values of the external nutrient content. When it occurs, the effect is greatest when the depletion volume per unit new root (V_d) is lowest, and when the mobility of nutrients in the medium is highest (α=1). The results are sufficiently general to apply to a variety of nutrients, plant species and growth media.     

A Definition of Optimum Nutrient Requirements in Birch Seedlings

Birch seedlings (Betula verrucosa Enrh.) were grown in nutrient solutions with pH varied in the range 2.5 to 6.8 or temperature varied in the range 2.5 to 35°C. The criteria for maximum growth previously established for birch seedlings were used and maintained by means of automatic pH and conductivity titrations with stock solutions containing the optimum nutrient proportions. Both nitrogen sources, NH₄ and NO₃, were present in the solutions. Growth rate was maximum or close to maximum between pH 4.0 and 6.8, whether kept at a specific level or allowed to vary between the extremes. At pH 3.5 and lower, the calcium uptake was decreased and root damage was observed. The seedlings has also a high dry matter content and obviously an unsatisfactory water balance. pH 2.5 was rapidly lethal. Growth rate was linearly correlated with solution temperature up to 20°C. Temperatures above 30°C, especially in the range 32.5 to 35°C, resulted in rapid decrease in growth rate. The nutrient contents in the seedlings were strongly affected by solution temperature in the low as well as in the high range when expressed on a dry weight basis. However, this effect was almost entirely attributable to changes in dry matter content. When expressed on a fresh weight basis, nutrient uptake and nutrient status of the seedlings appeared to be optimum throughout, although a variation remained since the varying dry matter content is included in the fresh weight basis. The results indicate, in agreement with the literature, that disturbed water uptake and water balance is the way in which growth is affected by root medium temperature. Similarly, extremely low pH levels in the nutrient solution meant root damage, although birch seedlings appear comparatively insensitive to pH variations. Thus, the growth technique used supplied the seedlings with adequate nutrients, so that the criteria used in the definition of nutrient requirements in birch seedlings are valid within wide ranges of solution pH and temperature; and other factors than nutrition determine growth.     

Linear Cell Growth in Escherichia coli

Growth was studied in synchronous cultures of Escherichia coli, using three strains and several rates of cell division. Synchrony was obtained by the Mitchison-Vincent technique. Controls gave no discernible perturbation in growth or rate of cell division. In all cases, mean cell volumes increased linearly (rather than exponentially) during the cycle except possibly for a small period near the end of the cycle. Linear volume growth occurred in synchronous cultures established from cells of different sizes, and also for the first volume doubling of cells prevented from division by a shift up to a more rapid growth rate. As a model for linear kinetics, it is suggested that linear growth represents constant uptake of all major nutrient factors during the cycle, and that constant uptake in turn is established by the presence of a constant number of functional binding or accumulation sites for each growth factor during linear growth of the cell.     

A model of physiological adaptation in unicellular algae

A simple growth model for unicellular algae is used to show that environmentally induced changes in cellular composition can be explained in terms of controlled adjustments acting to maximize the specific growth rate. The model is based on a division of cellular carbon into four distinct compartments: carbon associated with the photosynthetic apparatus, carbon associated with those components engaged in macromolecular synthesis, carbon associated with structural components and stored carbon. Flows of material between compartments, and between cells and their environment, are defined in terms of the environmental conditions and the distribution of carbon amongst compartments. Given that growth is balanced under a specific set of environmental conditions, there exists a unique, optimal allocation of carbon for which the rate of growth is maximal. Changes in this optimal allocation of material induced by changes in light intensity, nutrient availability or temperature are qualitatively similar to compositional changes observed in a wide variety of algal species. Empirical estimates for each of the model parameters are derived and used to show that reasonable quantitative agreement between observed and predicted behaviour is attainable. The model and parameter set are also used to illustrate the influence of cell size on growth rate. Under a given set of environmental conditions, the function relating cell size to growth rate has a single maximum. The size at which growth rate is maximal varies inversely with light intensity and directly with nutrient availability and temperature. Such behaviour is consistent with some empirical observations on the influence of environmental factors on the size distribution of natural phytoplankton communities.     

氮磷施肥对拟南芥叶片碳氮磷化学计量特征的影响

研究植物碳(C)氮(N)磷(P)化学计量特征, 有助于了解C、N、P元素的分配规律和确定限制植物生长的元素类型, 理解生长速率调控的内在机制。该研究基于盆栽施肥试验, 测定不同N、P供应水平下拟南芥(Arabidopsis thaliana)叶片的生物量和C、N、P含量, 分析拟南芥的限制元素类型、验证生长速率假说、探讨N、P的内稳性差异和C、N、P元素间的异速生长关系。主要结果如下: 盆栽试验基质中限制元素是P, 施N过多可能引起毒害作用; 拟南芥的生长符合生长速率假说, 即随着叶片N:P和C:P的增加, 比生长速率显著减小; 叶片P含量存在显著的调整系数(3.5), 但叶片N含量与基质N含量之间无显著相关; 叶片N和P含量具有显著的异速生长关系, 但不符合N-P^3/4关系, 施P肥导致表征N、P异速生长关系的幂指数(0.209)显著低于施N肥处理(0.466)。该研究首次基于温室培养实验分析了拟南芥C、N、P的化学计量特征及其对N、P添加的响应, 研究结果将为野外研究不同物种、群落或生态系统的化学计量特征提供参考。     

Modelling zinc uptake by rice crop using a Barber-Cushman approach

The Barber-Cushman mechanistic nutrient uptake model which has been utilized extensively to describe and predict nutrient uptake by crop plants at different stages of crop growth was evaluated for its ability to predict the Zn uptake by rice seedlings. Uptake of the nutrient is, therefore, determined by the rate of nutrient supply to the root surface by mass flow and diffusion. Inter root competition and time dependent root density are accounted for by soil volume that delivers nutrients. The radii of these cylinders decline with increasing density. Since mass flow and diffusion each supply zinc to the root, the process can be described mathematically using the model of Barber-Cushman (1984). The 11 parameters of the model for the uptake by rice cultivars were measured by established experimental techniques. Zinc uptake at different growth stages predicted by the model was compared to measured zinc uptake by rice cultivars grown on sandy loam soil in a green house. Predicted zinc uptake was significantly correlated with observed uptake r ²=0.99^**. Sensitivity analysis was also used to investigate the impact of changes in soil nutrient supply, root morphological and root uptake kinetic parameters on simulated nutrient uptake. Overall results of sensitivity analysis indicate that the half distance between root axes, rate of root growth and water flux affect the uptake of zinc particularly at their higher values rather than at lower values and DaZn is the most sensitive parameter for zinc uptake at its lower values.     

Predicting microbial growth dynamics in response to nutrient availability

Developing mathematical models to accurately predict microbial growth dynamics remains a key challenge in ecology, evolution, biotechnology, and public health. To reproduce and grow, microbes need to take up essential nutrients from the environment, and mathematical models classically assume that the nutrient uptake rate is a saturating function of the nutrient concentration. In nature, microbes experience different levels of nutrient availability at all environmental scales, yet parameters shaping the nutrient uptake function are commonly estimated for a single initial nutrient concentration. This hampers the models from accurately capturing microbial dynamics when the environmental conditions change. To address this problem, we conduct growth experiments for a range of micro-organisms, including human fungal pathogens, baker’s yeast, and common coliform bacteria, and uncover the following patterns. We observed that the maximal nutrient uptake rate and biomass yield were both decreasing functions of initial nutrient concentration. While a functional form for the relationship between biomass yield and initial nutrient concentration has been previously derived from first metabolic principles, here we also derive the form of the relationship between maximal nutrient uptake rate and initial nutrient concentration. Incorporating these two functions into a model of microbial growth allows for variable growth parameters and enables us to substantially improve predictions for microbial dynamics in a range of initial nutrient concentrations, compared to keeping growth parameters fixed.     

Positive feedbacks between bottom-up and top-down controls promote the formation and toxicity of ecosystem disruptive algal blooms: A modeling study

Harmful algal blooms that disrupt and degrade ecosystems (ecosystem disruptive algal blooms, EDABs) are occurring with greater frequency and severity with eutrophication and other adverse anthropogenic alterations of coastal systems. EDAB events have been hypothesized to be caused by positive feedback interactions involving differential growth of competing algal species, low grazing mortality rates on EDAB species, and resulting decreases in nutrient inputs from grazer-mediated nutrient cycling as the EDAB event progresses. Here we develop a stoichiometric nutrient–phytoplankton–zooplankton (NPZ) model to test a conceptual positive feedback mechanism linked to increased cell toxicity and resultant decreases in grazing mortality rates in EDAB species under nutrient limitation of growth rate. As our model EDAB alga, we chose the slow-growing, toxic dinoflagellate Karenia brevis, whose toxin levels have been shown to increase with nutrient (nitrogen) limitation of specific growth rate. This species was competed with two high-nutrient adapted, faster-growing diatoms (Thalassiosira pseudonana and Thalassiosira weissflogii) using recently published data for relationships among nutrient (ammonium) concentration, carbon normalized ammonium uptake rates, cellular nitrogen:carbon (N:C) ratios, and specific growth rate. The model results support the proposed positive feedback mechanism for EDAB formation and toxicity. In all cases the toxic bloom was preceded by one or more pre-blooms of fast-growing diatoms, which drew dissolved nutrients to low growth rate-limiting levels, and stimulated the population growth of zooplankton grazers. Low specific grazing rates on the toxic, nutrient-limited EDAB species then promoted the population growth of this species, which further decreased grazing rates, grazing-linked nutrient recycling, nutrient concentrations, and algal specific growth rates. The nutrient limitation of growth rate further increased toxin concentrations in the EDAB algae, which further decreased grazing-linked nutrient recycling rates and nutrient concentrations, and caused an even greater nutrient limitation of growth rate and even higher toxin levels in the EDAB algae. This chain of interactions represented a positive feedback that resulted in the formation of a high-biomass toxic bloom, with low, nutrient-limited specific growth rates and associated high cellular C:N and toxin:C ratios. Together the elevated C:N and toxin:C ratios in the EDAB algae resulted in very high bloom toxicity. The positive feedbacks and resulting bloom formation and toxicity were increased by long water residence times, which increased the relative importance of grazing-linked nutrient recycling to the overall supply of limiting nutrient (N).     

Nutrient uptake and allocation at steady-state nutrition

Ingestad, T. and Ågren, G. I. 1988. Nutrient uptake and allocation at steady-state nutrition. - Physiol. Plant. 72: 450–459. Net nutrient uptake and translocation rates are discussed for conditions of steady-state nutrition and growth. Under these conditions, the relative uptake rate is equal to the relative growth rate, for whole plants as well as for plant parts, since the root/shoot ratio and internal concentrations remain stable. The nutrient productivity and the minimum internal concentration are parameters characteristic for the plant and the nutrient. A conceptual, mathematical model, based on these two fundamental parameters is used for calculation and prediction of the net nutrient uptake rate, which is required to maintain steady-state nutrition at a specified internal nutrient concentration or relative growth rate. When uptake rate is expressed on the basis of the root growth rate, there is, up to optimum, a strong linear relationship between uptake rate and the internal concentration of the limiting nutrient. More complicated and less consistent relationships are obtained when uptake rate is related to root biomass. The limiting factor for suboptimum uptake is the amount of nutrients becoming available at the root surface. When replenishment is efficient, e.g. with vigorous stirring, the concentration requirement at the root surface appears to be extremely low, even at optimum. In the suboptimum range of nutrition, the effect of nutrient status on root growth rate is a critical factor with a strong feed-back on nutrition, growth and allocation. At supraoptimum conditions, the uptake mechanism is interpreted as a protection against too high uptake rates and internal concentrations at high external concentration. In birch (Betula pendula Roth.), the allocation of nitrogen to the shoots is high compared to that of potassium and also to that of phosphorus at low nitrogen or phosphorus status. With decreasing stress, phosphorus allocation becomes more and more similar to nitrogen allocation. The formulation of a mathematical model for calculation of allocation of biomass and nutrients requires more exact information on the quantitative dependence of the growth-regulating processes on nutrition.     

Kinetics of phenol oxidation by Candida tropicalis: effects of oxygen supply rate and nutrients on phenol inhibition

The kinetics of phenol degradation was estimated in a fed-batch reactor system. Effects of oxygen and nutrient excess or limitation as well as the presence of several essential ions on the phenol- and oxygen-specific uptake rates achieved simultaneously in a bioreactor were shown.Candida tropicalis was grown on phenol as the only carbon and energy source. Applying the best fit of polynomial function, the maximum specific uptake rates of phenol and oxygen, the critical concentrations of phenol, the half-saturation constants and inhibition constants were determined. Linear relationship between specific phenol uptake rate and the exogenous respiration rate was found regardless of the kind and presence of essential nutrients. At oxygen limitation both the phenol uptake rate and the cell affinity to phenol decreased more strongly compared with those under nutrient limitation. Oxygen in excess resulted in a significant increase of cell tolerance toward phenol. The presence of essential nutrients increased the specific phenol degradation rate and led to complete phenol oxidation.     

On periodic algal cyclostat populations

A number of useful relations for population growth rate, uptake of limiting nutrient, amount of intracellular growth limiting nutrient and extracellular limiting nutrient concentration are presented in terms of their period averaged functions. These period averages may provide “species specific” information. The period length is shown to be unique for a given dilution rate and amount of intracellular growth limiting nutrient. A plot of residual limiting nutrient concentration versus cell density describes a closed trajectory (or “phase” loop). The area of this loop may be evaluated in terms of certain period averages of the parameters of the cyclostat population. This area is characteristic for a species at any given dilution rate and growth limiting nutrient concentration entering the cyclostat vessel. Equations for describing multispecies cyclostats are presented. Also, some necessary conditions for stable coexistence in such a system are described.     

Influence of nutrient limitation and growth rate on the outer membrane proteins of Klebsiella aerogenes NCTC 418

Four major proteins with molecular weights of 78 000, 37 000, 34 000 and 20 000 were present in the envelope of Klebsiella aerogenes when cultured at a high specific growth rate. However, at lower growth rates, the protein content and composition of the envelope depended on the imposed nutrient limitation. Under potassium-, carbon-, sulphur- and phosphorus-limited conditions, derepression of synthesis of limitation-specific proteins was observed, their apparent molecular weights being 90 000, 48 000, 41 000 and 36 000, respectively. Nitrogen-limited cells had no additional proteins. For a particular limiting nutrient, expression of the limitation-specific proteins was independent of the chemical or physical form in which the nutrient was supplied. Under potassium or sulphur limitation the specific proteins were present maximally at the lowest imposed growth rate, whereas under carbon limitation a maximum expression of these proteins was found at moderate growth rates. It is concluded that limitation-specific proteins which are associated with the outer membrane function in the uptake of limiting nutrients or, possibly, limitation-releasing compounds.     

Kinetic study of hybridoma cell growth in continuous culture: II. Behavior of producers and comparison to nonproducers

A hybridoma cell line, AFP-27-P, was cultivated in continuous culture under glucose-limited conditions. The viable cell concentration, dead-cell concentration, and cell volume all varied with the dilution rate. A model previously developed for a nonproducing clone of the same cell line, AFP-27-NP, was extended to describe the behavior of the cells. The relationship between the specific growth rate and glucose concentration is described by a function similar to the Monod model. A threshold glucose concentration and a minimum specific growth rate are incorporated; the model is meaningful only at glucose concentration and a minimum specific growth rate are incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. The relationship between the death rate and the glucose concentration is described by an inverted Monod-type function. Furthermore, the yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper range of specific growth rates. No maintenance term for glucose consumption is used; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepts the specific growth rate at a value close to the minimum growth rate. The productivity of antibody as a function of the specific growth rate is described by a mixed type model with a noon-growth-associated term and a negative-growth-associated term. The values for the model parameters were determined from regression analysis of the steady state data.