Theoretical studies on extinction in the gradostat

A multistage continuous culture system in which nutrients (or substrate) are supplied in the form of gradients has been studied in the laboratory. Called a gradostat, it consists of several chemostats with adjacent vessels connected. Two mathematical models based on Michaelis-Menten kinetics in a gradostat with two culture vessels and two competing species of microorganisms for the cases where there is a gradient of one limiting substrate and there are opposing gradients of two limiting complementary substrates are investigated. Given the parameters of the system, we can answer the basic question as to which species survive and which do not and determine the limiting values.     

Competition in the gradostat: the role of the communication rate

In this paper we study a mathematical model of competition between two species of microorganisms for a single limiting nutrient in a laboratory device called a gradostat. A gradostat consists of several (we consider only two) chemostats (CSTR's) connected together so that material can flow between the vessels in such a way that a nutrient gradient is established. Our model is a slightly modified version of one considered recently by Jäger et al. [3], in that the rate of exchange of material between the two vessels (the communication rate) is allowed to differ from the dilution rate. The outcome of competition turns out to be surprisingly sensitive to variation of the communication rate. We identify several coexistence regimes in parameter space and describe a method for obtaining operating diagrams for given pairs of competing microorganisms.Research supported in part by NSF Grant DMS 8521605     

Equilibrium distribution of species among vessels of a gradostat

The distribution of concentrations of two competing microbial species among the vessels of an n-vessel gradostat at equilibrium is studied for the standard mathematical model of the gradostat. As the equilibrium concentrations cannot be explicitly computed, a continuum limit, as the number of vessels becomes large, is considered which yields a singularly perturbed boundary value problem. Standard singular perturbation techniques yield information on equilibrium species concentration distributions which agree well with numerical calculations for even moderate values of n.Research supported by NSF Grant DMS 8922654     

Models for the continuous culture of microorganisms under both oxygen and carbon limiting conditions

Two models for predicting the behavior of cultures of microorganisms under both oxygen and carbon limiting conditions have been evlauated on a chemostat growing Candida utilis on a glycolysis suppressing glycerol medium. The work indicated that parameter values obtained under wholly oxygen limiting or wholly carbon limiting conditions successfully predict the behavior of the chemostat under the wide range of flow and substrate concentration conditions tested. Both models are satisfactory and hence it is deduced that the simpler one may be used with confidence. It was found that Monod kinetics were applicable to the growth rate dependence on oxygen concentration but that Contois kinetics were superior for the corresponding dependence on carbon substrate concentration.     

On describing microbial growth kinetics from continuous culture data: Some general considerations,observations, and concepts

Analysis of continuous culture methodology suggests that this potentially powerful tool for kinetic analysis can be improved by minimizing several inherent shortcomings. Medium background substrates — organic carbon, phosphate, and manganese — were shown to dominate kinetic observations at concentrations below chemical detection methods. Reactor wall growth, culture size distribution changes, sample removal-induced steady state perturbations, and limiting substrate leakage from organisms are treated in terms of kinetic measurement errors. Large variations in maximal growth rates and substrate uptake rates found are attributed to experimental protocol-induced transient states. Relationships are presented for correcting limiting substrate concentrations for lability during sampling, contamination with unreacted medium, and background substrate effects. Analytical procedures are discussed for improved measurement of limiting substrate kinetics involving enzymes, isotopes, and material balance manipulation. Relaxation methods as applied to continuous culture are introduced as a means for isolating separate rate constants describing net substrate transport and for evaluating cellular metabolite leakage. Low velocity growth, multiple substrate metabolism, and endogenous metabolism are discussed along with measurements showing that 1-month generation times for aquatic microorganisms can be quite normal and that the kinetics are compatible withμg/liter limiting substrate concentrations. The concept of regarding growth kinetics as the sum of several net accumulation processes is suggested.     

A novel directly coupled gradostat

The original bidirectional compound chemostat (gradostat) described by Lovitt and Wimpenny has been simplified by making a more compact apparatus in which chemical gradients are established by diffusion between adjacent culture chambers. The experimental model (diffusion coupled (DC) gradostat) consisted of five chambers whose contents could be agitated by turbines rotating in the horizontal plane on a common shaft. Two biological experiments were designed to reveal the value of the DC gradostat. A methylotroph (Methylophilus methylotrophus) grown in a methanol gradient showed expected changes in cell viability as a function of position in the five vessel array. Cells of two species of photosynthetic bacteria (Rhodobacter capsulata and Rhodopseudomonas marina/agilis) with different salt sensitivities could be mixed and subsequently separated by the DC gradostat operating with a NaCl gradient of 0-3% w/v.     

Modeling and simulation of competition between two microorganisms for a single inhibitory substrate in a biofilm reactor

A simple biofilm model was developed to simulate the competition between two microorganisms for a common inhibitory substrate. The following assumptions were made for the simulations: (1) the biofilm has a uniform thickness and is composed of 5 segments, (2) growth of two microorganisms A and B which utilize the common substrate is expressed by the Haldane kinetics with a spatial limitation term and is independent of the other microorganism in the biofilm reactor, and (3) diffusion of the substrate, movement of the microorganisms, and continuous loss of the biomass by shearing are expressed by Fick's Law-type equations. The qualitative behavior of the biofilm reactor is characterized by five regions, I-V, depending on the operation conditions, the substrate concentration in feed, and the dilution rate. In region I, both microorganisms are washed out of the biofilm reactor. In region II, microorganism B is washed out, and in region III, microorganism A is washed out of the biofilm. In region IV, both microorganisms coexist with one another. In region V, both microorganisms coexist with a sustained oscillatory behavior. Convergence to regions I-V depends on the initial conditions. In regions II-V, washout of either or both microorganisms is also observed with initial conditions too far away.     

Der substratlimitierte pH-Auxostat – Eine neue Methode zur kontinuierlichen Kultur

A method for continuous cultivation of microorganisms is demonstrated, the substrate limited pH-auxostat. The limiting substrate only is added with constant velocity. In this culture the cells grow with high utilization of the limiting substrate and with the highest specific growth rate possible at the given conditions. Yield coefficients and dilution rates of stable K⁺-limited steady states in yeast cultures with different pH-values and biomass concentrations were measured.     

Productivity and Equilibrium in Simple Biofilm Models

Biofilms are dense, sessile collections of microorganisms with complicated internal structures. However, in many applications internal details are less important, rather basic, averaged information such as overall community productivity are of most interest. This paper studies averaged community functions in the context of one dimensional, single species, single limiting substrate biofilm models. In particular, using a derived formula for flux of substrate into the biofilm as a function of biofilm height and substrate loading, overall community production can be calculated and system equilibria can be characterized. Consequences for equilibria dependence on a number of mechanisms for balancing growth are considered.     

A new combined differential-discrete cellular automaton approach for biofilm modeling: application for growth in gel beads

The theoretical basis and quantitative evaluation of a new approach for modeling biofilm growth are presented here. Soluble components (e.g., substrates) are represented in a continuous field, whereas discrete mapping is used for solid components (e.g., biomass). The spatial distribution of substrate is calculated by applying relaxation methods to the reaction-diffusion mass balance. A biomass density map is determined from direct integration in each grid cell of a substrate-limited growth equation. Spreading and distribution of biomass is modeled by a discrete cellular automaton algorithm. The ability of this model to represent diffusion-reaction-microbial growth systems was tested for a well-characterized system: immobilized cells growing in spherical gel beads. Good quantitative agreement with data for global oxygen consumption rate was found. The calculated concentration profiles of substrate and biomass in gel beads corresponded to those measured. Moreover, it was possible, using the discrete spreading algorithm, to predict the spatial two- and three-dimensional distribution of microorganisms in relation to, for example, substrate flux and inoculation density. The new technique looks promising for modeling diffusion-reaction-microbial growth processes in heterogeneous systems as they occur in biofilms.     

模拟油藏条件下内源微生物群落空间分布规律

【背景】油藏内源微生物群落是开展内源微生物驱油技术的物质基础,由于油藏多孔介质取样技术难度大、成本高,实施内源微生物驱油后从注入端到产出端多孔介质中的内源微生物空间分布规律尚不明确。【目的】通过室内长岩心连续驱替实验模拟油藏内源微生物驱油过程,分析实施后不同空间位点油砂上吸附的内源微生物群落结构,揭示从注入端到产出端内源微生物群落的空间分布规律。【方法】借助高通量测序技术及荧光定量PCR技术解析不同空间位点油砂原位微生物群落信息。【结果】注入端到产出端不同空间位点生态环境的差异及菌属间的相互作用造成油藏内源微生物群落空间分布差异,存在明显的好氧、厌氧空间演替变化规律。岩心前端主要存在一些好氧类的产生物表面活性剂类微生物如假单胞菌属,岩心中部主要存在兼性和厌氧类的微生物如地芽孢杆菌、厌氧杆菌属,岩心末端主要分布严格厌氧类细菌和产甲烷古菌,厌氧类微生物代谢产生的H2、CO2和乙酸分子可以为产甲烷古菌提供代谢底物。【结论】通过室内物模油砂研究,首次明确了内源微生物群落在多孔介质中从注入端到产出端的空间分布规律,证实油藏内源微生物的好氧、厌氧空间接替分布规律,深化了对油藏内源微生物的认识。     

The gradostat: A model of competition along a nutrient gradient

The general mathematical theory of the gradostat is presented for two competitors. The gradostat provides a mechanism for studying competition along a nutrient gradient. In the two vessel case, the results are complete and the conditions are testable. In then-vessel case, the relevant conditions are stated in terms of the stability modulii of certain matrices and are testable for any specific case.     

The influence of high substrate concentrations on microbial kinetics

High substrate concentrations inhibit growth and may distort the metabolism of microorganisms. Mechanisms causing substrate inhibition are discussed and used to derive several mathematical models representative of the entire concentration range, including stimulation of growth by low substrate concentrations. These kinetic models are tested with a variety of batch culture measurements of specific growth rate and respiration rate at widely-ranging substrate concentrations. Using one of the kinetic models, equations are developed for batch, continuous, and exponential-feed reactors. Comparison of results obtained in continuous culture with results from exponential-feed culture systems is shown to offer a novel experimental method for evaluating the effect of the cell age distribution on the properties and metabolic activity of a culture.     

``BACWAVE,' a Spatial–Temporal Model for Traveling Waves of Bacterial Populations in Response to a Moving Carbon Source in Soil

Abstract Previously, we discovered the phenomenon of wavelike spatial distributions of bacterial populations and total organic carbon (TOC) along wheat roots. We hypothesized that the principal mechanism underlying this phenomenon is a cycle of growth, death, autolysis, and regrowth of bacteria in response to a moving substrate source (root tip). The aims of this research were (i) to create a simulation model describing wavelike patterns of microbial populations in the rhizosphere, and (ii) to investigate by simulation the conditions leading to these patterns. After transformation of observed spatial data to presumed temporal data based on root growth rates, a simulation model was constructed with the Runge–Kutta integration method to simulate the dynamics of colony-forming bacterial biomass, with growth and death rates depending on substrate content so that the rate curves crossed over at a substrate concentration within the range of substrate availability in the model. This model was named ``BACWAVE,' standing for ``bacterial waves.' Cyclic dynamics of bacteria were generated by the model that were translated into traveling spatial waves along a moving nutrient source. Parameter values were estimated from calculated initial substrate concentrations and observed microbial distributions along wheat roots by an iterative optimization method. The kinetic parameter estimates fell in the range of values reported in the literature. Calculated microbial biomass values produced spatial fluctuations similar to those obtained for experimental biomass data derived from colony forming units. Concentrations of readily utilizable substrate calculated from biomass dynamics did not mimic measured concentrations of TOC, which consist not only of substrate but also various polymers and humic acids. In conclusion, a moving pulse of nutrients resulting in cycles of growth and death of microorganisms can indeed explain the observed phenomenon of moving microbial waves along roots. This is the first report of wavelike dynamics of microorganisms in soil along a root resulting from the interaction of a single organism group with its substrate. Received: 2 October 1999; Accepted: 9 March 2000; Online Publication: 28 August 2000     

Effect of biofilm growth on steady-state biofilm models

The results of numerical simulations for a growing biological film are presented to justify the use of steady-state biofilm models for approximating the behavior of both unlimited and shear-limited biofilms. For an unlimited biofilm we show that although the total biofilm thickness may continue to increase over time, the active biofilm volume will reach a constant value. We also show that the profile of active microorganisms within the biofilm will become constant with respect to the biofilm/fluid interface and simply move outward as the biofilm thickness increases. For a shear-limited biofilm we similarly show that once a "limiting" thickness has been reached the active biofilm volume, substrate consumption, and profile of active microorganisms within the biofilm will also be independent of the biofilm thickness.     

Microbial metabolic activity in soil as measured by dehydrogenase determinations.

The dehydrogenase technique for measuring the metabolic activity of microorganisms in soil was modified to use a 6-h, 37 degrees C incubation with either glucose of yeast extract as the electron-donating substrate. The rate of formazan production remained constant during this time interval, and cellular multiplication apparently did not occur. The technique was used to follow changes in the overall metabolic activities of microorganisms in soil undergoing incubation with a limiting concentration of added nutrient. The sequence of events was similar to that obtained by using the Warburg respirometer to measure O2 consumption. However, the major peaks of activity occurred earlier with the respirometer. This possibly is due to the lack of atmospheric CO2 during the O2 consumption measurements.     

Microbial metabolic activity in soil as measured by dehydrogenase determinations.

The dehydrogenase technique for measuring the metabolic activity of microorganisms in soil was modified to use a 6-h, 37 degrees C incubation with either glucose of yeast extract as the electron-donating substrate. The rate of formazan production remained constant during this time interval, and cellular multiplication apparently did not occur. The technique was used to follow changes in the overall metabolic activities of microorganisms in soil undergoing incubation with a limiting concentration of added nutrient. The sequence of events was similar to that obtained by using the Warburg respirometer to measure O2 consumption. However, the major peaks of activity occurred earlier with the respirometer. This possibly is due to the lack of atmospheric CO2 during the O2 consumption measurements.     

氮添加促进丛枝菌根真菌和根系协作维持土壤磷有效性

磷是亚热带地区植物生长的主要限制营养元素, 而氮沉降量的增加会降低土壤磷的有效性。该研究以微生物和植物细根为重点探究土壤磷转化, 揭示氮沉降背景下低磷有效性土壤的磷供应及生产力维持。通过在福州长安山模拟氮沉降实验, 设置对照(0 kg·hm^-2·a^-1)、低氮(40 kg·hm^-2·a^-1)和高氮(80 kg·hm^-2·a^-1) 3个处理, 收集杉木(Cunninghamia lanceolata)幼苗的土壤和根系样本, 综合分析土壤磷组分和养分含量、土壤微生物特征和植物根系特征。结果显示, 与对照处理相比, 低氮处理显著增加土壤易分解态有机磷、中等易分解态无机磷和闭蓄态磷含量, 但是显著降低原生矿物态磷和中等易分解态有机磷含量; 而高氮处理对土壤磷组分无显著影响。冗余分析表明, 土壤酸性磷酸酶活性、丛枝菌根真菌的相对丰度、土壤微生物生物量磷含量和根系生物量是解释土壤磷组分变化的重要微生物和植物因子。方差分解分析发现植物根系特征-土壤微生物特征共同解释了土壤磷组分变化的57%, 并且通过相关分析发现丛枝菌根真菌的相对丰度和根系生物量呈显著正相关关系。综上所述, 低水平的氮输入促进土壤丛枝菌根真菌的定殖, 丛枝菌根真菌和杉木根系通过协作促进中等易分解态有机磷和原生矿物态磷向易分解态磷的转换, 维持了杉木幼苗的生长。     

Glycerol fermentation by (open) mixed cultures: a chemostat study

Glycerol is an important byproduct of bioethanol and biodiesel production processes. This study aims to evaluate its potential application in mixed culture fermentation processes to produce bulk chemicals. Two chemostat reactors were operated in parallel, one fed with glycerol and the other with glucose. Both reactors operated at a pH of 8 and a dilution rate of 0.1 h(-1). Glycerol was mainly converted into ethanol and formate. When operated under substrate limiting conditions, 60% of the substrate carbon was converted into ethanol and formate in a 1:1 ratio. This product spectrum showed sensitivity to the substrate concentration, which partly shifted towards 1,3-propanediol and acetate in a 2:1 ratio at increasing substrate concentrations. Glucose fermentation mainly generated acetate, ethanol and butyrate. At higher substrate concentrations, acetate and ethanol were the dominant products. Co-fermentations of glucose-glycerol were performed with both mixed cultures, previously cultivated on glucose and on glycerol. The product spectrum of the two experiments was very similar: the main products were ethanol and butyrate (38% and 34% of the COD converted, respectively). The product spectrum obtained for glucose and glycerol fermentation could be explained based on the general metabolic pathways found for fermentative microorganisms and on the metabolic constraints: maximization of the ATP production rate and balancing the reducing equivalents involved.