Monod Kinetics Research Articles

ЧУВСТВИТЕЛЬНОСТЬ BIPOLARIS SOROKINIANA К ФУНГИЦИДАМ «ИНШУР ПЕРФОРМ» И «ВИАЛ ТРИО»

The purpose of research is to study the sensitivity of B. sorokiniana to the fungicides “Inshur Perform” and “Vial Trio” for using the example of a strain isolated from the roots of wheat affected by common root rot in the educational and scientific complex Borsky (Sukhobuzimo District of the Krasnoyarsk Region). It was found that when exposed for 24 hours in the presence of a working solution of the drug “Inshur Perform”, the germination of conidia does not differ from germination in the control, although the length of the seedling hyphae formed during this time is statistically significantly (p < 0.001) lower than the control. In the concentration range from the working solution to the working solution diluted 32 times, the effect of the drug “Inshur Perform” against B. sorokiniana does not depend on the concentration, either in terms of the effect on the germination of conidia, or in terms of the effect on the length of seedling hyphae. In contrast to the drug “Inshur Perform”, the drug “Vial Trio” has pronounced fungicidal activity against the regional isolate of B. sorokiniana. With a 24-hour exposure in the “Vial Trio” working solution, as well as in a working solution diluted 2 times, conidia do not germinate. When the working solution is diluted 4–64 times, germination of some conidia is observed, but over the entire range of dilutions it is statistically (p < 0.001) significantly lower than in the control variant. The same applies to the length of seedling hyphae. The dependence of the effect of the drug “Vial Trio” on concentration in the range of dilutions of the working solution by 4–64 times is nonlinear. For conidial germination it is described by an exponential function (R2 = 0.9997, p < 0.001), for mycelial growth – by the modified Monod equation (R2 = 0.9763, statistical significance of the equation p < 0.001).

An alternative approach to biokinetic modelling for phenol pollutant degradation and microbial growth using Genetic Programming

ABSTRACT Biokinetic models can optimise pollutant degradation and enhance microbial growth processes, aiding to protect ecosystem protection. Traditional biokinetic approaches (such as Monod, Haldane, etc.) can be challenging, as they require detailed knowledge of the organism's metabolism and the ability to solve numerous kinetic differential equations based on the principles of micro, molecular biology and biochemistry (first engineering principles) which can lead to discrepancies between predicted and actual degradation rates. More recently, data-driven machine-learning techniques have emerged as a promising alternative for modelling microbial systems. A few machine learning models (such as ANN, SVM, RF, DT, XG BOOST, etc.) have been used recently for modelling phenol degradation, but they lack the robustness of generating mathematical models. This gap is addressed in this study using Genetic Programming (GP) as the modelling approach for modelling the phenol degradation. This study utilises the microalgae Acutodesmus Obliquus, finding that phenol degradation of 98% required 216 hours. Both the traditional kinetic approach and the Genetic Programming (GP) approach were used to determine the specific growth rate (µ max) and saturation constant (Ks ). It is noted that without any a priori information on the form of the mathematical mode, GP can evolve a model which closely fits the Monod kinetics, thus demonstrating that data-driven models can bring out the first engineering principles on which biokinetic models are dependent or framed in a most swift and effective way. Performance was assessed using root mean square error (RMSE) and correlation coefficient (R), with the GP model showing superior predictive accuracy.

Modelling Temperature Profiles in Food Waste Composting: Monod Kinetics Under Varied Aeration Conditions

Modelling Temperature Profiles in Food Waste Composting: Monod Kinetics Under Varied Aeration Conditions

Biodegradation Study of Used Engine Oil by Free and Immobilized Cells of the Pseudomonas oleovorans Strain NMA and Their Growth Kinetics.

Used engine oil is considered to be one of the high-risk pollutants, and if introduced untreated in the environment, it threatens the whole ecosystem. Therefore, there is a need to find some rapid and efficient methods for the remediation of used engine oil. The present study aimed to isolate indigenous bacterial strains having the capability to degrade used engine oil. The enrichment technique was employed for the isolation of bacterial strains, which were identified by the 16S rRNA technique. As biosurfactants play a vital role in the degradation process, the activity was determined by standard protocols. The bacterial strain was isolated by the enrichment technique and identified as the Pseudomonas oleovorans strain NMA. The bacterial isolate has the ability to utilize used engine oil as the sole source of energy. The biodegradation experiment revealed that both free and immobilized cells degrade used engine oil, but immobilized cells showed the best biodegradation result, with 98-99% degradation efficiency in 7 days of incubation irrespective of all oil concentrations. For the analysis of degraded products, gas chromatography-mass spectrometry (GC-MS) was performed, which indicates that the treated samples do not carry the major engine components, i.e., methyl hexane, pyrene, and phytane, which confirmed that these were transformed by the bacterial activity. Monod kinetics further confirmed that the isolated bacterium utilizes used engine oil as the sole source of energy. These findings clearly indicate the potential of the bacterium NMA to degrade used engine oil with high kinetics, converting it into nontoxic products, and thus be a potential candidate for remediation at contaminated sites.

H2 Consumption by Various Acetogenic Bacteria Follows First-Order Kinetics up to H2 Saturation.

Acetogenic bacteria play an important role in various biotechnological processes, because of their chemolithoautotrophic metabolism converting carbon dioxide with molecular hydrogen (H2) as electron donor into acetate. As the main factor limiting acetogenesis is often H2, insights into the H2 consumption kinetics of acetogens are required to assess their potential in biotechnological processes. In this study, initial H2 consumption rates at a range of different initial H2 concentrations were measured for three different acetogens. Interestingly, for all three strains, H2 consumption was found to follow first-order kinetics, i.e. the H2 consumption rate increased linearly with the dissolved H2 concentration, up to almost saturated H2 levels (600 µM). This is in contrast with Monod kinetics and low half-saturation concentrations, which have commonly been assumed for acetogens. The obtained biomass specific first-order rate coefficients (k1 X) were further validated by comparison with values obtained by fitting first-order kinetics on previous time-course experimental results. The latter method was also used to determine the k1 X value of five additional acetogens strains. Biomass specific first-order rate coefficients were found to vary up to six-fold, with the highest k1 X for Acetobacterium wieringae and the lowest for Sporomusa sphaeroides. Overall, our results demonstrate the importance of the dissolved H2 concentration to understand the rate of acetogenesis in biotechnological systems.

Advancing dental biofilm models: the integral role of pH in predicting S. mutans colonization.

Mathematical models can provide insights into complex interactions and dynamics within microbial communities to complement and extend experimental laboratory approaches. For dental biofilms, they can give a basis for evaluating biofilm growth or the transition from health to disease. We have developed mathematical models to simulate the transition toward a cariogenic microbial biofilm, modeled as the overgrowth of Streptococcus mutans within a five-species dental community. This work builds on experimental data from a continuous flow reactor with hydroxyapatite coupons for biofilm growth, in a chemically defined medium with varying concentrations of glucose and lactic acid. The biofilms formed on the coupons were simulated using individual-based models (IbMs), with bacterial growth modeled using experimentally measured kinetic parameters. The IbM assumes that the maximum theoretical growth yield for biomass is dependent on the local concentration of reactants and products, while the growth rates were described using traditional Monod equations. We have simulated all the conditions studied experimentally, considering different initial relative abundance of the five species, and also different initial clustering in the biofilm. The simulation results only reproduced the experimental dominance of S. mutans at high glucose concentration after we considered the species-specific effect of pH on growth rates. This highlights the significance of the aciduric property of S. mutans in the development of caries. Our study demonstrates the potential of combining in vitro and in silico studies to gain a new understanding of the factors that influence dental biofilm dynamics.IMPORTANCEWe have developed in silico models able to reproduce the relative abundance measured in vitro in the synthetic dental biofilm communities growing in a chemically defined medium. The advantage of this combination of in vitro and in silico models is that we can study the influence of one parameter at a time and aim for direct validation. Our work demonstrates the utility of individual-based models for simulating diverse conditions affecting dental biofilm scenarios, such as the frequency of glucose intake, sucrose pulsing, or integration of pathogenic or probiotic species. Although in silico models are reductionist approaches, they have the advantage of not being limited in the scenarios they can test by the ethical consideration of an in vivo system, thus significantly contributing to dental biofilm research.

Mathematical model of dissolved microbial products in sewage treatment system

Water is the source of life, but all kinds of water resources in the world are suffering from different degrees of pollution. Water pollution leads to a serious shortage of available fresh water resources, and sewage treatment is the main way to solve water pollution. For the sewage after biological treatment of activated sludge, the organic matter contained in the effluent is mainly the dissolved microbial products (SMPs) produced in the process of microbial metabolism. The composition of SMPs is complex, mainly including macromolecular substances such as protein, polysaccharide, humic acid and DNA and cell fragments. The mathematical model of activated sludge is a quantitative description of the mathematical relationship between substrate degradation parameters and microbial growth. Starting from the Monod equation representing the relationship between substrate consumption and microbial growth, it combines the reactor theory and microbiology theory in the chemical field. Based on the principle of conservation of materials and Monod equation, the mathematical expression of organic degradation model was determined according to the collected data and empirical values of parameters. The general idea of activated sludge model No.1 (ASM1) for activated sludge process simulation was introduced, and the influence of sludge concentration on SBR process water treatment was explored. It was found that the removal rate of COD, ammonia nitrogen, total nitrogen and total phosphorus increases with the increase of sludge concentration. When C/N=8, the removal rate of ammonia nitrogen increased from 62% to 81%, and the removal rate of total nitrogen increased from 64% to 82%, with the most obvious effect.

Co-substrate model development and validation on pure sugars and corncob hemicellulosic hydrolysate for xylitol production

A co-substrate model of Candida tropicalis TISTR 5306 cultivated in 10 - 100 g/L xylose and 1 - 10 g/L glucose at the ratio of 10:1 was developed based in part on modified Monod equation. The kinetic parameters include substrate limitation as well as substrate and product inhibitions with inclusion of threshold values. A general good fitting with average RSStotal, R2, and MStotal values of 162, 0.979, and 10.8, respectively, was achieved between ten simulated profiles and experimental kinetics data. The implementation of developed model on xylitol production from non-detoxified corncob hemicellulosic hydrolysate resulted in relatively good agreement with RSStotal, R2, and MStotal values of 368, 0.988, and 24.5, respectively. The developed model can be applied to predict microbial behavior in batch xylitol production system using hemicellulosic hydrolysate over a xylose range of 10 - 100 g/L and provide useful information for subsequent design of fed-batch and continuous systems to achieve the efficient sustainable resource management of this agricultural and agro-industrial waste.

Isolation and degradation characterization of a 1, 4-dioxane-degrading bacterial strain

To address the potential pollution caused by the carcinogen 1, 4-dioxane in aquatic environments, we isolated a highly efficient 1, 4-dioxane-degrading bacterial strain, designated as DXTK-010, from the groundwater contaminated by 1, 4-dioxane. According to the morphological characteristics, the phylogenetic tree established based on the 16S rRNA gene sequence, and the whole genome sequence, we identified DXTK-010 as Aminobacter aminovorans. This strain demonstrated robust degradation capacity within a temperature range of 20 ℃ to 37 ℃ and a pH range of 5.0 to 8.0. Furthermore, single-factor experiments indicated the optimal degradation conditions at 30 ℃ and pH 7.5. Under the optimal conditions, the strain completely degraded 200 mg/L of 1, 4-dioxane within 24 h, achieving a maximum degradation rate of 9.367 mg/(L·h). The Monod equation was adopted to fit the degradation kinetics of 1, 4-dioxane at different initial concentrations, which revealed a maximum specific degradation rate of 0.224 mg 1, 4-dioxane/(mg protein·h), a half-saturation constant (Ks) of 41.350 mg/L, and a cell yield of 0.130 mg protein/(mg 1, 4-dioxane). Whole genome sequencing revealed a circular chromosome and three plasmids within DXTK-010. Functional gene annotation and analysis underscored the significance of the propane monooxygenase gene cluster and alcohol dehydrogenase gene in facilitating the efficient degradation of 1, 4-dioxane by this strain. DXTK-010 outperformed the existing degraders for 1, 4-dioxane, expanding the strain resources for the bioremediation of 1, 4-dioxane pollution. This study provides a theoretical basis for the practical application of DXTK-010 in the remediation of 1, 4-dioxane pollution.

Integration of mathematical and experimental modeling for sustainable phycobiliprotein production via fed-batch cultures

The production of phycobiliproteins, such as cyanobacterial phycocyanins, is a growing interest due to their diverse industrial and biotechnological applications. This study focuses on optimizing phycocyanin production using the strain Potamosiphon sp. through experimental techniques and mathematical modeling in fed-batch cultures. The methodology applied includes determining the kinetic constants by linearizing the Monod equation evaluating the concentrations of biomass, C-phycocyanin (C-PC), nitrates (NO3), and phosphates (PO4). A mathematical model of periodic fed-batch feeding was subsequently established, applying mass conservation principles and evaluating the accuracy of the Monod, Contois, Moser, and Tessier models. The results indicate that phycocyanin production is highly dependent on phosphorus and nitrogen concentrations, with optimal conversion observed at specific levels of these elements (0.832 for phosphorus and 0.805 for nitrogen in terms of C-PC and biomass, respectively). The Tessier model demonstrated the highest accuracy in predicting production and optimizing operational conditions, with a Mean Squared Error (MSE) of 0.005000 for biomass production, 0.200000 for C-PC production, and 0.000010 for substrate consumption. It also achieved high R² values of 0.980 for biomass, 0.999 for C-PC production, and 0.997 for substrate consumption. It presented the lowest Akaike Information Criterion (AIC) scores, indicating its robustness and reliability in modeling these processes and manipulating cultivation conditions and providing adequate nutrition allowed for achieving growth rates of 1.23 g/L and a C-PC concentration of 37 mg/L, which are essential for industrial applications such as natural colorants and antioxidants, among others.

Towards maximization of parameters identifiability: Development of the CalOpt tool and its application to the anaerobic digestion model

This work addresses the need for robust approaches to estimate kinetic parameters in continuous anaerobic co-digestion plants. Specifically, it outlines a procedure for including data from batch activity tests on digestate samples, in addition to the poorly informative dataset from conventional monitoring of biogas facilities. To profitably make use of activity tests, the estimation of the biomass composition in digestate samples is required to improve parameter identifiability. To this purpose, an open-source tool (CalOpt) was developed and tested on a pilot-scale co-digester, simultaneously using data from both conventional monitoring and lab-scale activity tests. Targeting the prediction of volatile fatty acids (VFAs) concentrations in the digestate of the continuous co-digester, the kinetic parameters of different microbial groups were selected for calibration based on parameters importance ranking and collinearity index. The results demonstrate that the CalOpt tool significantly improved the fitting of acetic, propionic, and butyric acid concentrations in digestate as well as the methane flowrate from the digester. Furthermore, the study assessed the necessity of modifying the Monod kinetics to account for substrate inhibition by incorporating the Haldane term in the VFAs uptake kinetic model, which proved to be essential for better interpreting batch activity tests.

Comprehensive model for predicting toxic equivalents (TEQ) reduction due to dechlorination of polychlorinated dibenzo-p-dioxin and dibenzofurans (PCDD/F congeners)

Remediation-focused predictive tools for polychlorinated dibenzo-p-dioxins (PCDD) and polychlorinated dibenzofurans (PCDF) rely on transformation models to evaluate the reduction in total contaminant load and toxic equivalency (TEQ). In this study, a comprehensive model predicting the profiles of PCDD/F congeners and the associated TEQs was developed. The model employs first-order kinetics to describe the transformation of 256 reactions for 75 PCDD congeners and 421 reactions for 135 PCDF congeners. It integrates the growth of anaerobic microbial guilds using Monod kinetics on hydrogen release compounds and stoichiometric growth for Dehalococcoides sp. The effects of temperature, salinity, pH, and availability of vitamin B12 (a cofactor) were also integrated. The PCDD/F congeners model was used to extract the first-order dechlorination rate constants from a number of pure culture and mixed microbial microcosm studies. Simulations for the transformation of PCDD/F congeners at concentrations representative of the Tittabawassee or Saginaw Rivers and watershed in MI, USA were carried out. For a starting TEQ of 5000 ng per kg dry sediment (ppt), the model predicted a decrease in the overall TEQ to below 2000 ppt after 2.6 years and below 250 ppt after ∼21 years. The developed model may be used for extracting rates from microcosm studies and to evaluate the effect of engineering interventions on TEQ reduction.

Contrasting Dynamics of Intracellular and Extracellular Antibiotic Resistance Genes in Response to Nutrient Variations in Aquatic Environments.

The propagation of antibiotic resistance in environments, particularly aquatic environments that serve as primary pathways for antibiotic resistance genes (ARGs), poses significant health risks. The impact of nutrients, as key determinants of bacterial growth and metabolism, on the propagation of ARGs, particularly extracellular ARGs (eARGs), remains poorly understood. In this study, we collected microorganisms from the Yangtze River and established a series of microcosms to investigate how variations in nutrient levels and delivery frequency affect the relative abundance of intracellular ARGs (iARGs) and eARGs in bacterial communities. Our results show that the relative abundance of 7 out of 11 representative eARGs in water exceeds that of iARGs, while 8 iARGs dominate in biofilms. Notably, iARGs and eARGs consistently exhibited opposite responses to nutrient variation. When nutrient levels increased, iARGs in the water also increased, with the polluted group (COD = 333.3 mg/L, COD:N:P = 100:3:0.6, m/m) and the eutrophic group (COD = 100 mg/L, COD:N:P = 100:25:5, m/m) showing 1.2 and 3.2 times higher levels than the normal group (COD = 100 mg/L, COD:N:P = 100:10:2, m/m), respectively. In contrast, eARGs decreased by 6.7% and 8.4% in these groups. On the other hand, in biofilms, higher nutrient levels led to an increase in eARGs by 1.5 and 1.7 times, while iARGs decreased by 17.5% and 50.1% in the polluted and eutrophic groups compared to the normal group. Moreover, while increasing the frequency of nutrient delivery (from 1 time/10 d to 20 times/10 d) generally did not favor iARGs in either water or biofilm, it selectively enhanced eARGs in both. To further understand these dynamics, we developed an ARGs-nutrient model by integrating the Lotka-Volterra and Monod equations. The results highlight the complex interplay of bacterial growth, nutrient availability, and mechanisms such as horizontal gene transfer and secretion influencing ARGs' propagation, driving the opposite trend between these two forms of ARGs. This contrasting response between iARGs and eARGs contributes to a dynamic balance that stabilizes bacterial resistance levels amid nutrient fluctuations. This study offers helpful implications regarding the persistence of bacterial resistance in the environment.

COMPETITION BETWEEN PLASMID-BEARING AND PLASMID-FREE ORGANISMS IN A CHEMOSTAT WITH DISTINCT REMOVAL RATES AND AN EXTERNAL INHIBITOR

A mathematical model of competition between plasmid-bearing and plasmid-free organisms for a single limiting resource in a chemostat with distinct removal rates and in the presence of an external inhibitor is analyzed. This model was previously introduced in the special case where the growth rate functions and the absorption rate of the inhibitor follow the Monod kinetics and the removal rates are the same as the dilution rate. Here, we consider the general case of monotonic growth and absorption functions, and distinct removal rates. Through the three operating parameters of the model, represented by the dilution rate, the input concentrations of the substrate and the inhibitor, we give necessary and sufficient conditions for existence and stability of all equilibria. To better understand the richness of the model’s behavior with respect to those operating parameters, we determine the operating diagram theoretically and numerically. This diagram is very useful to understand the model from both the mathematical and biological points of view.

Advanced temperature control in ethanol fermentation using a PSO-PID controller with split-range control strategy

Global energy demand is experiencing a notable surge due to growing energy security. Renewable energy sources, like ethanol, are becoming more viable. In the present study, the application of a PSO-PID (Particle Swarm Optimization – Proportional Integral Derivative) controller with a split-range control strategy was suggested for the regulation of temperature within the fermentation system. To optimize performance, a POS-PID controller with a split-range arrangement utilizing two control valves for hot and cold utilities was constructed. The study began by examining the open-loop dynamic response of the system to inlet temperature and concentration disturbances during ethanol production fermentation. Subsequently, a transfer function model was developed through linearization at the steady-state operating point. The split-range controller structure, implemented by optimizing the PSO-PID controller parameters using PSO, effectively demonstrated temperature control in simulations of a nonlinear model. In this investigation, the ethanol fermentation system was modeled as a CSTR using a modified Monod equation for microbial growth kinetics. Various dynamic behavioral disturbances were explored and verified in the model with plant data in this study. The simulation model results were validated through plant data. The proposed method showed superior closed-loop performance with respect to errors, with the actuators proving to be effective than other reported methods for temperature control.

Robust, fully quantifiable and scalable bioprocess utilizing spent sulfite liquor with Corynebacterium glutamicum

In this study, a bioprocessing strategy was designed to valorize ultra-filtered spent sulfite liquor (UF-SSL) without prior detoxification steps as well as using it purely as a carbon source supplement to defined or complex media. Hence, a minimal medium for the bioconversion of UF-SSL with Corynebacterium glutamicum was developed and process robustness and reproducibility were validated. Process quantifiability was ensured by development of a biomass measurement technique for matrices with high water-insoluble solids and verified using elemental balancing. Mechanistic modeling based on Monod equations was used to identify batch kinetics. In a final step, scale-up of the developed process was performed to showcase process maturity towards commercialisation.

Dividing active and passive particles in nonuniform nutrient environments

To explore the coupling between a growing population of microorganisms such as E. coli and a nonuniform nutrient distribution, we formulate a minimalistic model. It consists of active Brownian particles that divide and grow at a nutrient-dependent rate following the Monod equation. The nutrient concentration obeys a diffusion equation with a consumption term and a point source. In this setting the heterogeneity in the nutrient distribution can be tuned by the diffusion coefficient. In particle-based simulations, we demonstrate that passive and weakly active particles form proliferation-induced clusters when the nutrient is localized, without relying on further mechanisms such as chemotaxis or adhesion. In contrast, strongly active particles disperse in the whole system during their lifetime and no clustering is present. The steady population is unaffected by activity or nonuniform nutrient distribution and only determined by the ratio of nutrient influx and bacterial death. However, the transient dynamics strongly depends on the nutrient distribution and activity. Passive particles in almost uniform nutrient profiles display a strong population overshoot, with clusters forming all over the system. In contrast, when slowly diffusing nutrients remain centred around the source, the bacterial population quickly approaches the steady state due to its strong coupling to the nutrient. Conversely, the population overshoot of highly active particles becomes stronger when the nutrient localisation increases. We successfully map the transient population dynamics onto a uniform model where the effect of the nonuniform nutrient and bacterial distributions are rationalized by two effective areas.

Simulation of microbial growth based on Euler’s method

Microorganisms such as bacteria, fungi and yeast produce valuable metabolites when they are grown in suitable culture conditions. The cultivation condition affects the cell growth, metabolism, and product production in a sophisticated and nonlinear way. Therefore, in this research, the growth of Lactococcus lactis NZ9000 in response to the growth conditions was simulated using different growth models. The objective was to simulate the effect of temperature, agitation speed, carbon and nitrogen sources, on the cell growth using the exponential model, logistic and Monod equations. All equations were solved according to the Euler’s method using MATLAB R2021a for simulation. The experimental data used for the simulation were from literature. The accuracy of the model was expressed as percentage relative error between the maximum value of experimental and simulated data. Simulation results shows that the optimum conditions for cell growth was achieved at temperature 27°C, agitation speed of 100 rpm with glucose and peptone as the carbon and nitrogen sources respectively equation. The maximum cell concentration by logistic equation gives the lowest percentage error of 6.40% and 0.33% for the effect of temperature and agitation respectively. While Monod equation give the closest accuracy of 1.84% and 7.11% for carbon and nitrogen sources respectively. Thus, it was shown that the complexity of the microorganism growth was able to be simulated using suitable model such as logistic equation with the lowest relative error.

BioReactPy: An open-source software for simulation of microbial-mediated reactive processes in porous media

This paper provides a new open-source software, named BioReactPy, for simulation of microbial-mediated coupled processes of flow and reactive transport in porous media. The software is based on the micro-continuum approach, and geochemistry is handled in a fully coupled manner with biomass-nutrient growth treated with Monod equation in a single integrated framework, without dependencies on third party packages. The distinguishing features of the software, its design principles, and formulation of multiphysics problems and discretizations are discussed. Validation of the Python implementation using several established benchmarks for flow, reactive transport, and biomass growth is presented. The flexibility of the framework is then illustrated by simulations of highly non-linearly coupled flow and microbial reactive transport at conditions relevant to carbon mineralization for CO2 storage. All results can be reproduced by openly available simulation scripts.

Comparison of the bioaccumulation and biosorption of copper ions by Rhizopus delemar and Candida lipolytica

In this study, the bioaccumulation of Cu(II) ion by Rhizopus delemar and Candida lipolytica was investigated and the bioaccumulation and biosorption of Cu(II) ions by Candida lipolytica compared. The specific growth rate and the maximum microorganism concentration of both microorganisms increased with increasing initial molasses concentration whereas decreased with increasing initial Cu(II) ion concentrations up to 250 mg/L. Accoding to Monod equation, the maximum specific growth rate and saturation constant for C. lipolytica and R. delemar were determined as 0.335 h−1-32.330 g/L and 0.406 h−1-24.182 g/L, respectively. The bioaccumulation efficiencies of R. delemar and C. lipolytica were determined as 74.18% and 67.30% in the presence of 50 mg/L Cu(II), respectively. At pH 4.0, the maximum biosorption rate (4.72 mg/g min) and the biosorbed Cu(II) ion concentration (49.0 mg/L) were obtained for C. lipolytica and these values increased with increasing Cu(II) concentration. Cu(II) biosorption by C. lipolytica fitted well to the Langmuir isotherm model and pseudo-second-order kinetic model and maximum adsorption capacity was found as 114.942 mg/g. The bioaccumulated Cu(II) was found to be 21.5 mg/g whereas the amounts of biosorbed Cu(II) were calculated as 53 mg/g by C. lipolytica at a concentration of 100 mg/L of Cu(II).