Bioenergetics and end-product regulation of Clostridium thermosaccharolyticum in response to nutrient limitation

Fermentation of xylose by Clostridium thermosaccharolyticum was studied in batch and continuous culture in which the limiting nutrient was either xylose, phosphate, or ammonia. Transient results obtained in continuous cultures with batch grown inoculum and progressively higher feed substrate concentrations exhibited ethanol selectivities (moles ethanol/moles other products) in excess of 11. The hypothesis that this high ethanol selectivity was a general response to mineral nutrient limitation was tested but could not be supported. Growth and substrate consumption were related by the equation q(s)(1 - Y(x) (c))G(ATP) = (mu/Y(ATP) (max)) + m, with q(s) the specific rate of xylose consumption (moles xylose/hour . g cells), Y(x) (c) the carbon based cell yield (g cell carbon/g substrate carbon), G(ATP) the ATP gain (moles ATP produces/mol substrate catabolized), mu the specific growth rate (1/h), Y(ATP) (max) the ATP-based cell yield (g cells/mol ATP), and m the maintenance coefficient (moles ATP/hour . g cells). Y(ATP) (max) was found to be 11.6 g cells/mol ATP, and m 9.3 mol ATP/hour . g cells for growth on defined medium. Different responses to nutrient limitation were observed depending on the mode of cultivation. Batch and immobilized cell continuous cultures decreased G(ATP) by initiating production of the secondary metabolites, propanediol, and in some cases, D-lactate; in addition, batch cultures increased the fractional allocation of ATP to maintenance and/or wastage. Nitrogen-limited continuous free-cell cultures maintained a constant cell yield, whereas phosphate-limited continuous free-cell cultures did not. In the case of phosphate limitation, the decreased ATP demand associated with the lowered cell yield was accompanied by an increased rate of ATP consumption for maintenance and/or wastage. Neither nitrogen or phosphorus-limited continuous free-cell cultures exhibited an altered G(ATP) in response to mineral nutrient limitation, and neither produced secondary metabolites. (c) 1993 John Wiley & Sons, Inc.     

Estimation of growth yield and maintenance coefficient of plant cell suspensions

Methodology is presented for the determination of growth yield (Y(g)) and maintenance coefficient (m) for carbon utilization of plant cells grown in suspension culture. Estimation of Y(g) and m requires measurements of specific growth rate (micro) and specific rate of substrate uptake (q) at different growth limiting substrate concentrations. Batch culture of tobacco cells did not permit evaluation of Y(g) and m because micro is constant and maximal during most of the growth cycle. In batch culture, the period of declining specific growth rate is extremely brief because of the rapid transition from logarithmic growth to stationary phase. This occurs because the K(m) for growth is relatively small compared to the initial sucrose concentration. Thus, when the substrate level reaches the K(m), the large mass of cells rapidly depletes the remaining substrate. In contrast, semicontinuous culture facilitates the determination of Y(g) and m because various steady-state growth rates can be achieved. Mathematical expressions were developed to determine the effective values of micro and q over the semicontinuous replacement interval. The validity of this approach was verified by conducting simulations using experimentally determined parameters.     

Relationship between substrate inhibition and maintenance energy ofChlamydomonas reinhardtii in heterotrophic culture

The relationship between substrate inhibition and maintenance energy ofChlamydomonas reinhardtii grown heterotrophically on acetate was investigated. At low acetate concentrations (<0.4 g l^–1), where no inhibition of cell growth was observed, the cell growth yield and specific growth rate could be represented by the Pirt model, 1/Y=1/Y _g +m/ with a constant value of maintenance energy coefficient m. However, at high acetate concentrations (>0.4 g l^–1), inhibition of cell growth occurred, in which m became variable and dependent on the acetate concentration. A simple mathematical model was proposed to predict the actual maintenance energy coefficient m in the inhibited cultures and experimentally validated.Author for correspondence     

Quantitative comparison of lactose and glucose utilization in Bifidobacterium longum cultures

In batch cultures, Bifidobacterium longum SH2 has a higher final cell concentration and greater substrate consumption when grown on lactose versus glucose. Continuous cultures were used to compare lactose and glucose utilization by B. longum quantitatively. In the continuous culture, the estimated maintenance coefficients (m) were similar when on lactose and glucose; the maximum cell yield coefficient (Y(X/S)(max)) was higher on lactose; and the specific consumption rate of lactose (q(S)) was lower than that of glucose. Assuming that cell growth followed the Monod model, the maximum specific growth rates (mu(max)) and saturation constants (K(S)) in lactose and glucose media were determined using the Hanes-Woolf plots. The respective values were 0.40 h(-)(1) and 78 mg/L for lactose and 0.46 h(-)(1) and 697 mg/L for glucose. The kinetic parameters of the continuous cultures showed that B. longum preferred lactose to glucose, although the specific consumption rate of glucose was higher than that of lactose.     

Intensification of high cell-density cultivations of rE. coli for production of S. pneumoniae antigenic surface protein, PspA3, using model-based adaptive control

This work proposes an innovative methodology to control high density fed-batch cultures of E. coli, based on measurements of the concentration of dissolved oxygen and on estimations of the cellular specific growth rate (μ), of the yield of biomass/limiting substrate (Y (xs)) and of the maintenance coefficient (m). The underlying idea is to allow cells to grow according to their metabolic capacity, without the constraints inherent to pre-set growth rates. Cellular concentration was assessed on-line through a capacitance probe. Three configurations of the control system were compared: (1) pre-set value for the three control parameters; (2) continuously updating μ; (3) updating μ, Y (xs) and m. Implementation of an efficient noise filter for the signal of the capacitance probe was essential for a good performance of the control system. The third control strategy, within the framework of an adaptive model-based control, led to the best results, with biomass productivity reaching 9.2?g(DCW)/L/h.     

Effects of growth temperature on yield and maintenance during glucose-limited continuous culture of Escherichia coli.

The effects of growth temperature on the aerobic growth yield with respect to oxygen consumption (Y0-grams [dry weight] per gram-atom of O) and the rate of maintenance respiration (m0-milligram-atoms of O/gram [dry weight] per hour) are reported for Escherichia coli B cultivated continuously in the presence of oxygen with limiting glucose. During anaerobic continuous culture, YATP(max) (grams [dry weight] per mole of ATP corrected for maintenance) increases from 10.3 to 12.7 as the growth temperature is lowered from 37 to 25 C. Over this same range, Y0(max) (Y0 corrected for maintenance respiration) rises from 12.5 to 28.8 and remains at the higher value down to 17.5 C. From 37 to 32 C, m0 increases from 0.9 to 4.4 but then falls to 1.5 as the temperature is lowered to 17.5 C. The value of m0 sharply rises some 13-fold as the temperature is raised to 42 C without a significant change in the value of Y0(max). Changes of Y0(max) are consistent with a temperature-sensitive doubling of the efficiency of oxidative phosphorylation, but the reasons for the changes of the rate of maintenance respiration are not known.     

Comments on the “Maintenance coefficient” changes during alcohol fermentation

Summary The concept of maintenance is discussed in terms of the biological meaning and the applicability of the maintenance coefficient, m, in bioengineering for optimization of yields in fermentation. A method of calculation is proposed for the evaluation of m in the course of fermentation in the case of a metabolite (e.g, ethanol). During alcoholic fermentation m is not constant and decreases with the growth rate.The phenomena involved in maintenance are numerous and complex and there is a semantic problem in its definition which can be generalized by the apparently non-finalized substrate consumption.Nomenclature a specific maintenance rate (defined by eq. (9)) - m maintenance coefficient - X cell mass concentration (as a dry weight) - S substrate concentration - P product concentration - r rate of reaction - r_x,r_s,r_p rate of reaction related to biomass, substrate and product - r_sm,r_sg,r_spi rate of reaction related only to the consumption by maintenance, growth and the synthesis of the ith product - r_xe maintenance rate defined by eq. (10) - q_s,q_Pi specific rate of substrate consumption and i^th product production - Y yield coefficient - Y^o, Y^o apparent yield coefficient related to the cell and i^th product - Y _xs ^xs , Y _Pis ^Pis maximum theoretical yield coefficient related to the cell and i^th - specific growth rate produce 420     

Hopf bifurcation for a family of two-state microbial growth models

We describe a family of two-state microbial growth models, in which growth and maintenance are assigned to two different cell states. The way of splitting periodic solutions for low dilution rates of a continuous fermentation is shown. The existence of these periodie solutions is mainly influenced by the properties of substrate consumption, which the maintenance rate in the second cell state amounts to.     

On maintenance models in severely and long-term limited membrane bioreactor cultivations

Membrane bioreactors (MBRs) are combinations of common bioreactors and membrane separation units for biomass retention. Through increased biomass concentration, they allow increased productivity (or smaller reactor volume, respectively). Besides high biomass concentrations, operation at very low growth rates is typical for MBRs. In this regime, maintenance metabolism where substrate uptake only yields energy for cell survival becomes of higher importance than in processes run at higher growth rates. While thermodynamically based correlations for the prediction of maintenance coefficients are available for chemostat or other medium growth rate processes, some authors have mentioned a change in energy demand in MBRs and a dependence of maintenance parameters on operating conditions. Due to the fact that often mixed cultures are used and resulting from the different evaluation methods used by different authors, views on the possible influences on maintenance parameters differ. However, it is accepted that common models describing microbial growth and production of metabolites or degradation of pollutants do not consider the effects caused by severe limitations and therefore cannot sufficiently be applied to MBRs. In this study, maintenance parameters were determined for a model organism (Ustilago maydis) and results from different evaluation methods were compared. A continuous fit of respiration data gave more consistent results than the traditional method of plotting specific uptake versus growth rate. They suggest that below micro = 10% micro(max) the maintenance coefficient drops to a third of the value in short-term limited cultures.     

On the coexistence of competing microbial species in a chemostat under cycling

If a microorganism has a growth coupled production or consumption of acid or alkali, it is possible to use the pH-auxostat as a means of control in continuous fermentation. In using the pH-auxostat, it is possible to separate the inlet substrate flow in two different streams. These will both be pH controlled, with one main flow, consisting of nutrients and a second minor but concentrated flow, of acid or alkali. Hereby, it is possible to vary the difference in pH between the fermentor and the inlet medium. This pH difference is proportional to the steady-state cell mass concentration.(1,2) It is shown that by separating the inlet flow in two different streams and cultivating without any substrate limitation, the maximum growth rate may be obtained while the cell mass concentration will be controlled. This will also give the possibility to reach high cell mass concentrations at mu(max) without the risk of wash-out. A modified expression, based on hydrogen, of the steady-state bio-mass concentration, X, is developed as \documentclass{article}\pagestyle{empty}\begin{document}$$ X = Y_{X/H} \cdot [F_{{\rm Hin}} /(F_{{\rm Hin}} + F_{{\rm Min}} )] \cdot (C_{{\rm Hin}} - C_{{\rm HFERM}} ) $$\end{document} where Y(X/H) is the yield coefficient of cell mass per acid produced. The indexes Hin and Min refer to the inflows of alkali and medium, respectively; C(Hin) is the inlet concentration of hydrogen ions. The boundary condition for the cell mass shows that S(in) > X/Y(X/S), where S(in) is the medium substrate concentration and Y(X/S) is the yield of biomass per consumed substrate. It is shown that when the cell mass concentration exceeds this value, the flow stops. The applicability of the pH-auxostat method is then verified from different experiments. It is hereby used to detect a deviation from the maximal growth rate showing effects on the microbial physiology. With Escherichia coli used as the model organism, the effect on the growth rate of temperature and high concentration of ammonia were investigated.     

Effect of Growth Rate and Nutrient Limitation on the Composition and Biomass Yield of Acinetobacter calcoaceticus

Acinetobacter calcoaceticus was grown on ethanol in a chemostat as a model system for single-cell protein production. The substrate yield coefficient (Y(s), grams of biomass/gram of ethanol), protein yield coefficient (Y(p), grams of protein/gram of ethanol), and biomass composition were measured as a function of the specific growth rate. Nucleic acid, protein, Y(p), and Y(s) all increased at higher growth rates. Although protein content increased only 14% (from 53 to 67%), Y(p) almost doubled over the same range of growth rates. The increase in Y(p) was due to the higher protein content of the biomass and to higher values of Y(s). The higher values of Y(s) were attributed to maintenance metabolism, and the value of the maintenance coefficient was found to be 0.11 g of ethanol per g of cell per h. When A. calcoaceticus was cultivated under a phosphorus limitation protein content, Y(p) and Y(s) were lower than in carbon-limited cultures. It was concluded that a single-cell protein fermentation using A. calcoaceticus should be operated at a high growth rate under ethanol-limiting conditions in order to maximize both the protein content of the biomass and the amount of biomass and/or protein made from the substrate.     

The effect of pyrogenically modified substrates on mineralizing activity and growth strategies of microorganisms of grey forest soil

The rates of the mineralization processes initiated by the input of plant residues and pyrogenically modified plant material into gray forest soil under forests and meadows were assayed. While meadow plant residues was mineralized more rapidly than the forest floor, decomposition of the pyrogenic material resulted in disproportional changes in CO₂ emission from soils. Statistical treatment showed that the respiratory activity of CO₂ emission by heterotrophic microorganisms, which is a physiological characteristic of microbial communities, is 89% determined by the substrate quality. The maximal specific growth rate, which reflects the functional changes in microbial communities, was affected by the cenosis (36%) and the substrate (30%). Most of the carbon of the original plant material (up to 90%) was removed during the burning of plant substrates. The remaining compounds in the pyrogenically transformed material changed the process of mineralization in soil compared both to the control variant and to soil enriched with plant residues. Input of plant residues and ash into the soil resulted in increased total and active biomass, while the maximal specific growth rate decreased and the generation time for the active biomass increased. In the case of soils with plant residues, these changes in the state of microbial communities were brief and occurred during the period of intense mineralization (0–5 days), while, in soils with plant ash, stable changes were revealed after more prolonged incubation. Experimental determination of the microbial biomass turnover time (MTT) by means of two methods (from the ratio between the microbial biomass and respiration and from microbial specific growth rates) made it possible to determine the economical coefficient Y for microbial communities metabolizing the substrates of different availability. Depending on the experimental variant, the Y values varied from 0.22 to 0.51. Decreased maximal specific growth rate and increased values of Y (the coefficient of efficiency of substrate utilization) showed the predominant contribution of K-strategists in the mineralization of low available substrates in soil. The balance calculations and physiological characteristics of the microbial community suggested that the priming effect was most probable in soils enriched with plant ash.     

Unstable steady state operations of substrate inhibited cultures by dissolved oxygen control

Microorganism kinetic growth characterized by substrate inhibition was investigated by means of a continuous stirred tank reactor equipped with a feedback controller of the medium feeding flow rate. The aerobic growth of Pseudomonas sp. OX1 with phenol as carbon/energy source was adopted as a case study to test a new control strategy using dissolved oxygen concentration as a state variable. The controller was successful in steadily operating bioconversion under intrinsically unstable conditions. A simple model of the controlled system was proposed to set the feedback controller. The specific growth rate of Pseudomonas sp. OX1 was successfully described by means of the Haldane model. The regression of the experimental data yielded μ(M)=0.26 h(-1), K(Ph)=5×10(-3)g/L and K(I)=0.2g/L. The biomass-to-substrate fractional yield as a function of the specific growth rate did not change moving from substrate-inhibited to substrate-deficient state. The data was modelled according to the Pirt model: m=1.7×10(-2)g/(gh), Y(X/Ph)(Th)=1.3g/g. The specific growth rates calculated for batch and continuous growth were compared.     

Multiple substrate growth kinetics of Leptothrix discophora SP-6

The growth parameters of Leptothrix discophora SP-6 were quantified on the basis of the steady-state concentrations and utilization rates of pyruvate, dissolved oxygen, and concentration of microorganisms in a chemostat operated at 25 degrees C, pH 7.2, and an agitation rate of 350 rpm. The results showed that the microbial growth was limited by both pyruvate and dissolved oxygen. A combined growth kinetics model using Monod growth kinetics for pyruvate and Tessier growth kinetics for oxygen showed the best correlation with the experimental data when analyzed using an interactive multiple substrate model. The growth kinetics parameters and the respective confidence limits, estimated using the Monte Carlo simulation, were mu(max) = 0.576 +/- 0.021 h(-1), K(sMp) = 38.81 +/- 4.24 mg L(-1), K(sTo) = 0.39 +/- 0.04 mg L(-1), Y(X/p) = 0.150 (mg microorganism mg(-1) pyruvate), Y(X/o) = 1.24 (mg microorganism mg(-1) oxygen), the maintenance factors for pyruvate and oxygen were m(p) = 0.129 (mg pyruvate consumed mg(-1) microorganism h(-1)) and m(o) = 0.076 (mg oxygen consumed mg(-1) microorganism h(-1)), respectively.     

Maintenance and growth requirements in the metabolism of Debaryomyces hansenii performing xylose-to-xylitol bioconversion in corncob hemicellulose hydrolyzate

In order to improve the biotechnological production of xylitol, the metabolism of Debaryomyces hansenii NRRL Y-7426 in corncob hemicellulose hydrolyzate has been investigated under different conditions, where either maintenance or growth requirements predominated. For this purpose, the experimental results of two sets of batch bioconversions carried out alternatively varying the starting xylose concentration in the hydrolyzate (65.6 < or = S(0) < or = 154.7 g L(-1)) or the initial biomass level (3.0 < or = X(0) < or = 54.6 g(DM) L(-1)) were used to fit a metabolic model consisting of carbon material and ATP balances based on five main activities, namely fermentative assimilation of pentoses, semi-aerobic pentose-to-pentitol bioconversion, biomass growth on pentoses, catabolic oxidation of pentoses, and acetic acid and NADH regeneration by the electron transport system. Such an approach allowed separately evaluating the main bioenergetic constants of this microbial system, that is, the specific rates of ATP and xylose consumption due to maintenance (m(ATP) = 21.0 mmol(ATP) C-mol(DM) (-1)h(-1); m(Xyl) = 6.5 C-mmol(Xyl) C-mol(DM) (-1)h(-1)) and the true yields of biomass on ATP (Y(ATP) (max) = 0.83 C-mol(DM) mol(ATP) (-1)) and on xylose (Y(Xyl) (max) = 0.93 C-mol(DM) C-mol(Xyl) (-1)). The results of this study highlighted that the system, at very high S(0) and X(0) values, dramatically increased its energy requirements for cell maintenance, owing to the occurrence of stressing conditions. In particular, for S(0) > 130 g L(-1), these activities required an ATP consumption of about 2.1 mol(ATP) L(-1), that is, a value about seven- to eightfold that observed at low substrate concentration. Such a condition led to an increase in the fraction of ATP addressed to cell maintenance from 47% to 81%. On the other hand, the very high percentage of ATP addressed to maintenance (> 96%) at very high cell concentration (X(0) > or = 25 g(DM) L(-1)) was likely due to the insufficient substrate to sustain the growth.     

Linear growth in microbial cultures limited by accumulated substrate

Summary The linear growth phase in cultures limited by intracellular (conservative) substrate is represented by a flat exponential curve. Within the range of experimental errors, the presented model fits well the data from both batch and continuous cultures ofEscherichia coli, whose growth is limited in that way.List of symbols D dilution rate, h^–1 - K_S saturation constant, g.L^–1 - S concentration of the limiting substrate, g.L^–1 - S_i concentration of the limiting substrate accumulated in the cells, g.g^–1 - S_o initial concentration of the limiting substrate, g.L^–1 - t time of cultivation, h - t₁ time of exhaustion of the limiting substrate from medium, h - t_o beginning of exponential phase, h - X biomass concentration, g.L^–1 - X₁ biomass concentration at the time of exhaustion of the limiting substrate from the medium, g.L^–1 - X_o biomass concn. at the beginning of exponential phase, g.L^–1 - biomass concn. at steady-state, g.L^–1 - Y growth yield coefficient (biomass/substrate) - specific growth rate, h^–1 - _m maximum specific growth rate, h^–1     

Stoichiometric and kinetic characterisation of Nitrobacter in mixed culture by decoupling the growth and energy generation processes

The growth, maintenance and lysis processes of Nitrobacter were characterised. A Nitrobacter culture was enriched in a sequencing batch reactor (SBR). Fluorescent in situ hybridisation showed that Nitrobacter constituted 73% of the bacterial population. Batch tests were carried out to measure the oxygen uptake rate and/or nitrite consumption rate when both nitrite and CO2 were in excess, and in the absence of either of these two substrates. The results obtained, along with the SBR performance data, allowed the determination of the maintenance coefficient and in situ cell lysis rate of Nitrobacter. Nitrobacter spends a significant amount of energy for maintenance, which varies considerably with the specific growth rate. At maximum growth, Nitrobacter consume nitrite at a rate of 0.042 mgN/mgCOD(biomass) . h for maintenance purposes, which increases more than threefold to 0.143 mgN/mgCOD(biomass) . h in the absence of growth. In the SBR, where Nitrobacter grew at 40% of its maximum growth rate, a maintenance coefficient of 0.113 mgN/mgCOD . h was found, resulting in 42% of the total amount of nitrite being consumed for maintenance. The above three maintenance coefficient values obtained at different growth rates appear to support the maintenance model proposed in Pirt (1982). The in situ lysis rate of Nitrobacter was determined to be 0.07/day under aerobic conditions at 22 degrees C and pH 7.3. Further, the maximum specific growth rate of Nitrobacter was estimated to be 0.02/h (0.48/day). The affinity constant of Nitrobacter with respect to nitrite was determined to be 1.50 mgNO2(-)-N/L, independent of the presence or absence of CO2.     

9,10-环甲基十七烷酸干预下灵芝深层发酵合成三萜酸的动力学特征

利用Sigmoid模型对比研究了添加9,10-环甲基十七烷酸（9,10-CMA）前后灵芝深层发酵产三萜酸的动态变化特征。研究显示,灵芝对照组中三萜酸在4-9d大量合成,并于第9天达到最大值（268.62mg/L）;添加9,10-CMA组中三萜酸的合成量于第8天时达到最大值（343.52mg/L）。添加9,10-CMA后,灵芝菌丝体细胞对底物葡萄糖的利用速度加快,细胞比生长速率在3.2天达到最大值（Μ_max）,为0.94d ^-1,显著高于对照组的0.88d ^-1（在第3.4天获得）;葡萄糖比消耗速率在第1.7天达到最大值（Q_{S, max}）,为8.34d ^-1,显著高于对照组的6.80d ^-1（在第2.1天获得）。胞内三萜酸比合成速率显著提高,在第6.2天达到最大值（Q_{ITA, max}）13.76d ^-1,是对照组9.66d ^-1的1.42倍。两组中灵芝三萜酸的合成与细胞生长均呈现部分偶联关系,添加9,10-CMA后,没有改变细胞生长和三萜酸合成在发酵过程中的相互关系。     

Growth kinetics of Escherichia coli with galactose and several other sugars in carbon-limited chemostat culture

Kinetic models for microbial growth describe the specific growth rate (mu) as a function of the concentration of the growth-limiting nutrient (s) and a set of parameters. A typical example is the model proposed by Monod, where mu is related to s using substrate affinity (Ks) and the maximum specific growth rate (mu max). The preferred method to determine such parameters is to grow microorganisms in continuous culture and to measure the concentration of the growth-limiting substrate as a function of the dilution rate. However, owing to the lack of analytical methods to quantify sugars in the microgram per litre range, it has not been possible to investigate the growth kinetics of Escherichia coli in chemostat culture. Using an HPLC method able to determine steady-state concentrations of reducing sugars, we previously have shown that the Monod model adequately describes glucose-limited growth of E. coli ML30. This has not been confirmed for any other sugar. Therefore, we carried out a similar study with galactose and found steady-state concentrations between 18 and 840 micrograms.L-1 for dilution rates between 0.2 and 0.8.h-1, respectively. With these data the parameters of several models giving the specific growth rate as a function of the substrate concentration were estimated by nonlinear parameter estimation, and subsequently, the models were evaluated statistically. From all equations tested, the Monod model described the data best. The parameters for galactose utilisation were mu max = 0.75.h-1 and Ks = 67 micrograms.L-1. The results indicated that accurate Ks values can be estimated from a limited set of steady-state data when employing mu max measured during balanced growth in batch culture. This simplified procedure was applied for maltose, ribose, and fructose. For growth of E. coli with these sugars, mu max and Ks were for maltose 0.87.h-1, 100 micrograms.L-1; for ribose 0.57.h-1, 132 micrograms.L-1, and for fructose 0.70.h-1, 125 micrograms.L-1.     

Statistical analysis of nonlinear parameter estimation for Monod biodegradation kinetics using bivariate data

A nonlinear regression technique for estimating the Monod parameters describing biodegradation kinetics is presented and analyzed. Two model data sets were taken from a study of aerobic biodegradation of the polycyclic aromatic hydrocarbons (PAHs), naphthalene and 2-methylnaphthalene, as the growth-limiting substrates, where substrate and biomass concentrations were measured with time. For each PAH, the parameters estimated were: q(max), the maximum substrate utilization rate per unit biomass; K(S), the half-saturation coefficient; and Y, the stoichiometric yield coefficient. Estimating parameters when measurements have been made for two variables with different error structures requires a technique more rigorous than least squares regression. An optimization function is derived from the maximumlikelihood equation assuming an unknown, nondiagonal covariance matrix for the measured variables. Because the derivation is based on an assumption of normally distributed errors in the observations, the error structures of the regression variables were examined. Through residual analysis, the errors in the substrate concentration data were found to be distributed log-normally, demonstrating a need for log transformation of this variable. The covariance between ln C and X was found to be small but significantly nonzero at the 67% confidence level for NPH and at the 94% confidence level for 2MN. The nonlinear parameter estimation yielded unique values for q(max), K(S), and Y for naphthalene. Thus, despite the low concentrations of this sparingly soluble compound, the data contained sufficient information for parameter estimation. For 2-methylnaphthalene, the values of q(max) and K(S) could not be estimated uniquely; however, q(max)/K(S) was estimated. To assess the value of including the relatively imprecise biomass concentration data, the results from the bivariate method were compared with a univariate method using only the substrate concentration data. The results demonstrated that the bivariate data yielded a better confidence in the estimates and provided additional information about the model fit and model adequacy. The combination of the value of the bivariate data set and their nonzero covariance justifies the need for maximum likelihood estimation over the simpler nonlinear least squares regression.