Growth of microbial populations in nonminimal media: some considerations for modeling

Ramkrishna and his co-workers have developed so-called cybernetic models which purport to describe, among other things, how microorganisms make choices when presented with two or more functionally equivalent, or substitutable, nutrients that are sources of carbon and available energy. In general, however, organisms are presented with choices not just between nutrients that are substitutable for one another, but also between sets of nutrients some of which are by no means substitutable for one another. It is postulated herein that the main ideas of cybernetic modeling apply to these more general choices as they seem to apply to the choices considered by Ramkrishna and his co-workers. Some consequences of the postulate are worked out for steady-state growth situations where two, or in one case three, nutrients limit or potentially limit growth rate. If predicted phenomena are observed experimentally so as to verify the postulate, a significantly improved basis for understanding growth of microorganisms in practical fermentation media as well as in natural situations will be provided by this application of cybernetic modeling ideas.     

Double Cell Bulk Acoustic Wave Sensor for Ion Chromatographic Study of the Relation Between Magnesium and Growth of Organisms

An ion chromatography (IC) method with a double cell bulk acoustic wave (DCBAW) detector was used for the detection of magnesium concentration decrease during the culture of whole cells. The detector parameters were optimized according to its theoretical equation, including the cell constants and the background conductance of the adjusting cell. A low temperature coefficient and thus high sensitivity were obtained by this method. The detection limit is 0.01 ppm, and the linear range is 0.05–50 ppm. A new mathematical model was developed to describe the growth of the cell. The baseline for this model is the concept that a noninteractive growth process occurs among perfectly substitutable nutrients if the locus of points of the substrate concentrations producing equal growth rate is linear. The monitoring results agreed well with the calculated results. Received: 17 July 1999 / Accepted: 23 August 1999     

Predicting stability of mixed microbial cultures from single species experiments: 1. Phenomenological model

The growth of mixed microbial cultures on mixtures of substrates is a fundamental problem of both theoretical and practical interest. On the one hand, the literature is abundant with experimental studies of mixed-substrate phenomena [T. Egli, The ecological and physiological significance of the growth of heterotrophic microorganisms with mixtures of substrates, Adv. Microbiol. Ecol. 14 (1995) 305-386]. On the other hand, a number of mathematical models of mixed-substrate growth have been analyzed in the last three decades. These models typically assume specific kinetic expressions for substrate uptake and biomass growth rates and their predictions are formulated in terms of parameters of the model. In this work, we formulate and analyze a general mathematical model of mixed microbial growth on mixtures of substitutable substrates. Using this model, we study the effect of mutual inhibition of substrate uptake rates on the stability of the equilibria of the model. Specifically, we address the following question: How much of the dynamics exhibited by two competing species can be inferred from single species data? We provide geometric criteria for stability of various types of equilibria corresponding to non-competitive exclusion, competitive exclusion, and coexistence of two competing species in terms of growth isoclines and consumption curves. A growth isocline is a curve in the plane of substrate concentrations corresponding to the zero net growth of a given species. In [G.T. Reeves, A. Narang, S.S. Pilyugin, Growth of mixed cultures on mixtures of substitutable substrates: The operating diagram for a structured model, J. Theor. Biol. 226 (2004) 143-157], we introduced consumption curves as sets of all possible combinations of substrate concentrations corresponding to balanced growth of a single microbial species. Both types of curves can be obtained in single species experiments.     

Predicting stability of mixed microbial cultures from single species experiments: 2. Physiological model

In this paper, we study the equilibria of a physiological model describing the continuous culture in which two microbial populations compete for two substitutable resources. This work is an extension of the stability analysis of the phenomenological model of mixed microbial growth [M.M. Ballyk, G.S.K. Wolkowicz, Exploitative competition in the chemostat for two perfectly substitutable resources, Math. Biosci. 118 (1993) 127-180; S.S. Pilyugin, G.T. Reeves, A. Narang, Predicting stability of mixed microbial cultures from single species experiments: 2. Phenomenological model]. Here, we investigate the influence of the peripheral enzymes that catabolize the substrate uptake on the stability of the mixed culture. We show that, under steady state conditions, an increase in the concentration of one substrate inhibits the uptake of the other substrate(s). We present the criteria for existence, uniqueness, and stability of various types of equilibria. We formulate these criteria in terms of growth isoclines and consumption curves for each of the competing species. Since both types of curves can be obtained from a single species experiment, our approach provides a direct connection between theory and experiment and allows one to infer the dynamics of mixed cultures from the dynamics of single species cultures. By expressing the stability criteria in terms of intracellular properties, the model establishes a link between ecology and molecular biology.     

Growth of Zostera marina L. Seedlings under laboratory conditions of nutrient enrichment

The effect of increased nutrients on growth of Zostera marina L. seedlings was tested in the laboratory by adding 2 different formulations (18:6:12 and 14:14:14 Nitrogen: Phosphorus:Potassium (N:P:K), respectively) of a slow release fertilizer, Osmocote®. Three different application rates were used with the 2 formulations by placing appropriate amounts in peat pots containing 1 seedling each.

The addition of fertilizer to the substrate markedly stimulated the growth of seedlings. Nutrient enrichment promoted growth both in terms of increased leaf length and vegetative production of shoots. The nitrogen rich formulation (18:6:12) produced less growth than the equal balance formulation (14:14:14). For both formulations, the highest concentrations produced greater growth than other concentrations of the same formulation. At equal application rates with respect to nitrogen, less growth occurred in the treatments receiving less phosphorus. Results of this experiment corroborate results from previous work suggesting that addition of nutrients to the sediment can stimulate Z. marina growth.     

Structured kinetic model to represent the utilization of multiple substrates in complex media during rifamycin B fermentation

Industrial fermentations typically use media that are balanced with multiple substitutable substrates including complex carbon and nitrogen source. Yet, much of the modeling effort to date has mainly focused on defined media. Here, we present a structured model that accounts for growth and product formation kinetics of rifamycin B fermentation in a multi-substrate complex medium. The phenomenological model considers the organism to be an optimal strategist with an in-built mechanism that regulates the sequential and simultaneous uptake of the substrate combinations. This regulatory process is modeled by assuming that the uptake of a substrate depends on the level of a key enzyme or a set of enzymes, which may be inducible. Further, the fraction of flux through a given metabolic branch is estimated using a simple multi-variable constrained optimization. The model has the typical form of Monod equation with terms incorporating multiple limiting substrates and substrate inhibition. Several batch runs were set up with varying initial substrate concentrations to estimate the kinetic parameters for the rifamycin overproducer strain Amycolatopsis mediterranei S699. Glucose and ammonium sulfate (AMS) demonstrated significant substrate inhibition toward growth as well as product formation. The model correctly predicts the experimentally observed regulated simultaneous uptake of the substitutable substrate combinations under different fermentation conditions. The modeling results may have applications in the optimization and control of rifamycin B fermentation while the modeling strategy presented here would be applicable to other industrially important fermentations.     

Cybernetic modeling and regulation of metabolic pathways in multiple steady states of hybridoma cells

Hybridoma cells utilize a pair of complementary and partially substitutable substrates, glucose and glutamine, for growth. It has been shown that cellular metabolism shifts under different culture conditions. When those cultures at different metabolic states are switched to a continuous mode, they reach different steady states under the same operating conditions. A cybernetic model was constructed to describe the complementary and partial substitutable nature of substrate utilization. The model successfully predicted the metabolic shift and multiple steady-state behavior. The results are consistent with the experimental observation that the history of the culture affects the resulting steady state.     

Optimal metabolic regulation along resource stoichiometry gradients

Most heterotrophic organisms feed on substrates that are poor in nutrients compared to their demand, leading to elemental imbalances that may constrain their growth and function. Flexible carbon (C)‐use efficiency (CUE, C used for growth over C taken up) can represent a strategy to reduce elemental imbalances. Here, we argue that metabolic regulation has evolved to maximise the organism growth rate along gradients of nutrient availability and translated this assumption into an optimality model that links CUE to substrate and organism stoichiometry. The optimal CUE is predicted to decrease with increasing substrate C‐to‐nutrient ratio, and increase with nutrient amendment. These predictions are generally confirmed by empirical evidence from a new database of c. 2200 CUE estimates, lending support to the hypothesis that CUE is optimised across levels of organisation (microorganisms and animals), in aquatic and terrestrial systems, and when considering nitrogen or phosphorus as limiting nutrients.     

Unveiling steady-state multiplicity in hybridoma cultures: the cybernetic approach

Mammalian cells grown in suspension produce waste metabolites such as lactate, alanine, and ammonia, which reduce the yield of cell mass and the desired product on the nutrients supplied. Previous studies (Cruz et al., 1999; Europa et al., 2000; Follstad et al., 1999) have shown that the cells can be made to alter their metabolism by starving them on their nutrients in continuous cultures at low dilution rates or starting the culture as a fed-batch. This leads to multiple steady states in continuous reactors, with some states being more favorable than others. Mathematical models that take into account the metabolic regulation that leads to these multiple steady states are invaluable tools for bioreactor control. In this article we present a cybernetic modeling strategy in which Metabolic Flux Analysis (MFA) is used to guide the cybernetic formulation. The hybridoma model presented as a result of this strategy considers the partially substitutable, partially complementary nature of glucose and glutamine. The choice of competitions within the network is guided by MFA and the model is successful in explaining the three multiple steady states observed. The cybernetic model though identified for the hybridoma experiments of Hu and others (Europa et al., 2000) seem generally applicable to mammalian systems as it captures the pathways that are common to mammalian cells grown in suspension. The model presented here could be used for start-up strategies for continuous reactors and model-based feedback control for maintaining high productivity of the reactor.     

Cybernetic modeling of growth in mixed, substitutable substrate environments: Preferential and simultaneous utilization

Growth of microorganisms on substitutable substrate mixtures display diverse growth dynamics characterized by simultaneous or preferential uptake of carbon sources. This article shows that cybernetic modeling concepts which were successful in predicting diauxic growth patterns can be extended to describe simultaneous consumption of substrates. Thus the growth of Escherichia coli on mixtures of glucose and organic acids such as pyruvate, fumarate, and succinate has been described successfully by the cybernetic model presented here showing both diauxic and simultaneous uptake when observed. The model also describes the changes in utilization patterns that occur under changing dilution rates, substrate concentrations, and models of preculturing. The model recognizes the importance of the synthesis of biosynthetic precursors in cell growth through a kinetic structure that is quite general for any mixture of carbon-energy sources. (c) 1996 John Wiley & Sons, Inc.     

Ideal nutrient productivities and nutrient proportions in plant growth

Abstract I propose that one single formulation can be applied to relate growth and content of several nutrients, including the most important macronutrients, of most plant species. The plant growth rate is proportional to the nutrient content minus a given minimal concentration of the nutrient in minimum. The proportionality factor, the nutrient productivity, and the minimum concentration are species specific properties. The nutrient productivity formulation is shown to apply for very different plant species and for different nutrients.     

The concentrations of hexadecane and inorganic nutrients modulate the production of extracellular membrane-bound vesicles, soluble protein, and bioemulsifier by Acinetobacter venetianus RAG-1 and Acinetobacter sp. strain HO1-N

In the present study, we addressed the possibility that the production of both bioemulsifiers and membrane-bound vesicles may be a common feature of the growth of Acinetobacter spp. on alkanes, and we determined the extent to which the release of extracellular products by these organisms is regulated by the concentrations of the alkane substrate and inorganic nutrients. To accomplish this objective, we grew Acinetobacter venetianus RAG-1 and Acinetobacter sp. strain HO1-N with different concentrations of nutrients and assayed for extracellular products. The results indicated that the release of vesicles, soluble protein, and bioemulsifier was promoted in various degrees by higher concentrations of hexadecane and inorganic nutrients, while the specific activities of the bioemulsifiers were enhanced with lower nutrient concentrations. Based on our findings, we propose that under conditions of nutrient excess, these strains produce membrane-bound vesicles to function in "luxury uptake" of the alkane substrate for delivery and storage in the form of inclusions. Under the same conditions, soluble bioemulsifier and protein may perform auxiliary roles in cell desorption and (or) alkane uptake. With low concentrations of nutrients, the decreased production of vesicles, protein, and bioemulsifier and the increased activity of the emulsifier may represent a mechanism for reducing biosynthetic demands and conserving cellular material.     

Simple model for the energetics of growth on substrates with different degrees of reduction

A simple model is developed for the energy transformation in growing microbial systems. The model is based on a linear equation for ATP consumption in the processes of growth and maintenance. A combination of this equation with macroscopic balances for the various components, the systems exchanges with the environment, and application of the concepts of the elementary balance allow the derivation of linear equations for the exchange of substrate, oxygen, and carbon dioxide with the environment. For growth on one sole carbon and energy source the model allows the definition of a critical substrate yield are expected and below which is decreasing substrate yield and energy supply growth limitation are expected. This restriction can be interpreted in a variety of other ways. It supplies a rationale for non-energy-production-coupled transfer of hydrogen to oxygen or wasteful expenditure of ATP in growth on highly reduced substrates. It also allows the formulation of a limit to the maximum yield on oxygen that can never be exceeded in growth on highly reduced substrates.     

pH influence on enzymic activity: the involvement of two active ionized forms of either substrate or enzyme in the reaction.

The interpretation of graphs of pKm as a function of pH by the theory of Dixon (Dixon, 1953) is based on the assumption that each component of the reaction system is active in a particular ionic state and completely inactive in other ionic states. In this paper we analyse the case in which two ionic forms of either the substrate or the enzyme are active to different degrees. After definition of reaction system of this type, a generalized equation is derived connecting the reaction rate to the total substrate concentration. The pH dependence of Km deduced from this equation is discussed and compared with that deriving from the theory of Dixon. The present model predicts that the pKm dependence on pH has the form of a “wave” with two inflexion points, thus providing an alternative interpretation of such behaviour to that afforded by Dixon's formulation.     

A Model to Describe the Partitioning of Photosynthate during Vegetative Plant Growth

An approach is described to the problem of modelling quantitativelythe partitioning of photosynthate during vegetative plant growth.Two plant processes are important in the scheme: the first ofthese is the utilization of substrate for growth and how thisutilization depends upon substrate concentration, the secondconcerns the transport of substrate between different plantparts and how this depends upon the substrate concentrationsin the plant parts. In both cases simple phenomenological relationshave been assumed which seem to be in reasonable accord withexperimental data and with more basic theoretical considerations.The model is able to describe some of the features of steady-statevegetative plant growth in a natural manner. The limitationsof the present formulation are considered, and the implicationsof this type of approach for whole-plant models are discussed.     

Flux balancing of light and nutrients in a biofilm photobioreactor for maximizing photosynthetic productivity

This article reports a combined experimental and numerical study on the efficient operation of Porous Substrate Bioreactors. A comprehensive model integrating light transport, mass transport, and algal growth kinetics was used to understand the productivity of photosynthetic biofilms in response to delivery rates of photons and nutrients. The reactor under consideration was an evaporation driven Porous Substrate Bioreactor (PSBR) cultivating the cyanobacteria Anabaena variabilis as a biofilm on a porous substrate which delivers water and nutrients to the cells. In an unoptimized experimental case, this reactor was operated with a photosynthetic efficiency of 2.3%, competitive with conventional photobioreactors. Moreover, through a scaling analysis, the location at which the phosphate delivery rate decreased the growth rate to half of its uninhibited value was predicted as a function of microorganism and bioreactor properties. The numerical model along with the flux balancing techniques presented herein can serve as tools for designing and selecting operating parameters of biofilm based cultivation systems for maximum productivity. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 30:348–359, 2014     

Microbial Metabolism of a Parathion-Xylene Pesticide Formulation

A mixed bacterial culture was adapted to growth on a mixed carbon substrate consisting of the pesticide parathion and its xylene-based formulation. The environmental growth parameters of temperature, pH, and dissolved oxygen concentration were optimized to obtain complete metabolism of parathion from this mixed carbon substrate. This adapted culture grew rapidly (mu = 0.7 per h) on the pesticide formulation at high parathion suspensions (3,000 mg/liter). Carbon utilization from this mixed substrate was strongly dependent on pH. At slightly acidic pH, xylene was preferentially metabolized, whereas at slightly alkaline pH, parathion was preferentially metabolized. Diethylthiophosphoric acid, a metabolite from parathion, and toluic acid, a metabolite from xylene, also influenced the selection of the primary carbon source.     

Role of PRAS40 in Akt and mTOR signaling in health and disease

The proline-rich Akt substrate of 40 kDa (PRAS40) acts at the intersection of the Akt- and mammalian target of rapamycin (mTOR)-mediated signaling pathways. The protein kinase mTOR is the catalytic subunit of two distinct signaling complexes, mTOR complex 1 (mTORC1) and mTORC2, that link energy and nutrients to the regulation of cellular growth and energy metabolism. Activation of mTOR in response to nutrients and growth factors results in the phosphorylation of numerous substrates, including the phosphorylations of S6 kinase by mTORC1 and Akt by mTORC2. Alterations in Akt and mTOR activity have been linked to the progression of multiple diseases such as cancer and type 2 diabetes. Although PRAS40 was first reported as substrate for Akt, investigations toward mTOR-binding partners subsequently identified PRAS40 as both component and substrate of mTORC1. Phosphorylation of PRAS40 by Akt and by mTORC1 itself results in dissociation of PRAS40 from mTORC1 and may relieve an inhibitory constraint on mTORC1 activity. Adding to the complexity is that gene silencing studies indicate that PRAS40 is also necessary for the activity of the mTORC1 complex. This review summarizes the regulation and potential function(s) of PRAS40 in the complex Akt- and mTOR-signaling network in health and disease.     

The species composition of Antarctic phytoplankton interpreted in terms of Tilman's competition theory

Summary An attempt was made, to test for the impact of resource competition on Antarctic marine phytoplankton. According to theory, species composition near competitive equilibrium should be determined by the ratios of limiting resources. Enrichment bioassays identified silicon and nitrogen as limiting nutrients for some of the most important phytoplankton species during early austral summer in the region near the Antarctic Peninsula. Together with the generally acknowledged limiting resource light, this gave three meaningful ratios of essential resources (Si:N, Si:light, N:light) and one ratio of substitutable resources (NO₃:NH₄). Phytoplankton species assemblages were found to be well separated by the ratios of the essential resources and by mixing depth. Nine out of 12 individual species were found to be separated along at least one of the gradients of resource ratios. Where comparison with competition experiments was available, predicted and realized distributions of species were compatible.     

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。