Primary Growth Models Investigation of Pseudomonas nitroreducens Growth on Octylphenol Polyethoxylates

This study evaluated the degradation of octylphenol polyethoxylates by Pseudomonas nitrore-ducens TX1 using secondary kinetics analysis. Nonlinear kinetic regression was employed through the utilization of curve-fitting software in order to fit the digitized growth degradation data. A comprehensive analysis was conducted using various statistical metrics including root-mean-square error (RMSE), adjusted coefficient of determination ( adjR 2 ), bias factor (BF), accuracy factor (AF), corrected AICc (Akaike Information Criterion), Bayesian Information Criterion (BIC), and Hannan-Quinn information criterion (HQC). The accuracy and statistical analysis of the kinetic models used showed that only the Huang, Baranyi Roborts, modified Gompertz, Buchanan-3-phase, modified Richards and Von Bertalanffy model fit the data, with modified Logistics having the best model with low RMSE and AICc values, highest adjusted R 2 values, and Bias Factor and Accuracy Factor values closest to unity. The calculated values for the modified Logistics constant maximum growth rate ( µ m ), maximum growth value ( A ) and lag period ( l ), were 0.179 (h -1 ), 2.199 and 13.015 h, respectively. Growth curve of the bacterium on varying concentrations of this compound can then be modelled using this model and the maximum growth rate value can be utilized for secondary modelling works further revealing important parameters.


INTRODUCTION
Octylphenol polyethoxylates (OPEs) are a class of non-ionic surfactants extensively used in various industrial applications.However, concerns have been raised about the potential environmental and human health impacts of OPEs due to their widespread use and persistence in aquatic environments [1].OPEs are known to exert toxic effects on aquatic organisms, including fish, algae, and invertebrates.The surfactant properties of OPEs can disrupt cell membranes and impact the normal functioning of aquatic organisms.Studies have shown that OPEs can accumulate in sediments and bioaccumulate in aquatic species, leading to long-term exposure and potential ecological consequences [2].One of the primary concerns associated with OPEs is their potential to act as endocrine disruptors.OPEs have been shown to exhibit estrogenic activity, interfering with the endocrine system of aquatic organisms.This disruption can lead to reproductive abnormalities, altered behavior, and compromised reproductive success in exposed organisms.
While environmental impacts are well-documented, research has also highlighted potential human health risks associated with OPE exposure.OPEs can enter the human body through various pathways, including ingestion, inhalation, and dermal contact.Once inside the body, these compounds may interfere with hormone regulation, raising concerns about their potential role in the development of certain health conditions.In one study, the risk of human exposure to nonylphenol (NP) by reviewing environmental monitoring and biomonitoring data.Estimates, based on source-specific Margins of Exposure (MOEs) calculated from environmental monitoring, and MOEs derived from biomonitoring studies in exposed individuals, indicate reasonable certainty of no harm for both source-specific and aggregate exposures to NP.The MOEs ranged from 2863 to 8.4 × 10 7 , well above 1000 [3].
One study found that nonylphenol polyethoxylate (NPPG) at 5.0 mg/liter inhibits testosterone elimination in Daphnia magna, resembling the effects of its degradation product 4nonylphenol.However, unlike 4-nonylphenol, NPPG did not induce significant chronic toxicity, suggesting environmental concentrations of NPPG may not pose a risk to invertebrates [2].In another study, three phenolic compounds-nonylphenol (NP), nonylphenol monoethoxylate (NP1EO), and nonylphenol diethoxylate (NP2EO)-were assessed for toxicity to Pimephales promelas and Ceriodaphnia dubia.Binary and tertiary mixtures, common in surface waters due to wastewater discharges, were tested.LC50 values for fathead minnows were 136, 218, and 323 µg/L for NP, NP1EO, and NP2EO, respectively.The study indicates additive or synergistic effects in mixtures [4].
Bacteria are also impacted by alkylphenol polyethoxylated.In a study, the researchers investigated the impact of five alkylphenol polyethoxylate nonionic surfactants on the microbial degradation of glucose and pentachlorophenol (PCP) by Sphingomonas chlorophenolicum RA2.Surfactants with mid-range hydrophile-lipophile balance (HLB) values (13.5-15) were most compatible with substrate degradation.The lowest HLB surfactant inhibited RA2 growth, while the highest HLB surfactant was inhibitory only at a concentration well above its critical micelle concentration (CMC).Surfactants were more inhibitory to RA2's PCP biodegradation than glucose, likely due to interactions with membrane-associated PCP-degrading enzymes.These findings have implications for selecting surfactants in remedial applications involving biodegradation or oil dispersion [5].Primary growth kinetic models on alkylphenol polyethoxylated-degrading bacteria can reveal inhibitory parameters useful for further modeling exercise.At this point, very few such modelling exercises have been carried out.In this paper, we propose a kinetic modeling on the growth of Pseudomonas nitroreducens TX1 that biodegrades octylphenol polyethoxylates [6].

Acquisition of Data
To process the data, the graphs were scanned and electronically processed using WebPlotDigitizer [7], which enables to digitize scanned plots into tables of data with sufficient precision [8][9][10][11][12].Data were obtained from the works of Chen et al. (2006), specifically from Fig. 5, which depicts the bacterial growth curves and the corresponding OPEOn disappearance by P. nitroreducens TX1 was measured over many hours and then replotted.

Fitting of the data
CurveExpert Professional software (Version 2.6.5) was employed to fit the growth data through nonlinear regression using a Marquardt algorithm.This strategy aims to minimize the sum of the squares of anticipated and measured values.The software automatically generates starting values by identifying the steepest climb of the curve between four datum points (estimation of µmax), crossing this line with the x-axis (estimation of λ), and using the final datum point as an estimate for the asymptote (A).

Statistical analysis
The aim is to assess the statistical significance of the quality of fit among models with varying parameters using metrics like root-mean-square error (RMSE), adjusted coefficient of determination (R 2 ), bias factor (BF), accuracy factor (AF), and corrected AICc (Akaike Information Criterion).The RMSE calculation (Eq. 1) involves predicted values (Pdi), experimental data (Obi), the number of experimental data (n), and the parameters in the model (p).The expectation is that models with fewer parameters will yield lower RMSE values.
( ) The Akaike information criterion (AIC) measures the relative quality of a particular statistical model for a given set of experimental data to aid in model selection.The equation includes a penalty for the number of parameters; the more parameters, the less desired the result or the higher the AIC score.As a result, AIC not only rewards quality of fit, but also discourages adopting more sophisticated models (overfitting) to fit experimental data.Because the data in this study is tiny in comparison to the number of parameters employed, a corrected version of the Akaike information criterion (AIC) was used.
Where n is the number of data points and p is the number of parameters of the model.The method takes into account the change in goodness-of-fit and the difference in number of parameters between two models.For each data set, the model with the smallest AICc value is highly likely correct.
To assess the goodness-of-fit of the models, the Accuracy Factor (AF) and Bias Factor (BF) are used.A Bias Factor of 1 indicates that the anticipated and observed values are perfectly matched.A bias factor of 1 implies a fail-dangerous model for microbial growth curves or degradation studies, whereas a bias factor of > 1 indicates a fail-safe model.The Accuracy Factor is always one, and larger AF values suggest a less accurate forecast.The accuracy and statistical analysis of the kinetic models used shows that the Huang, Baranyi Roberts, modified Gompertz, Buchanan-3-phase, modified Richards, Modified Logistics and Von Bertalanffy models fitted the data, with modified Logistics having the best fit model because of it lower RMSE and AICc values, highest adjusted R 2 values, and Bias Factor and Accuracy Factor values closest to unity (1.0) (Table 3).Von Bertalanffy model gave the poorest fit due to high value of RMSE and lowest value of adjusted R 2 .The calculated values for the modified Logistics constant maximum growth rate (µm), maximum growth value (A) and lag period (λ), were 0.179 (h -1 ), 2.199 and 13.015 h, respectively (Table 4).
The modified Logistic model has been frequently used to simulate biodegradation processes including primary kinetic models to the biodegradation of phenol from industrial effluents by immobilized Pseudomonas putida [13].In the study, they present different kinetics models such as Von Bertalanffy, Baranyi-Roberts, modified Schnute, modified Richards, modified Gompertz, Huang and modified Logistics.
Nearly all of the models best fit the curves, indicating that Pseudomonas putida growth on phenol can be described mathematically.All the curves fittings present the best models with highest adjusted R 2 value, low RMSE and AICc value.The Accuracy and Bias Factors values were close to unity (1.0).The modelling parameters obtained can be utilized for predicting bioremediation and perhaps in the future will be valuable in modelling growth and degradation of many contaminants.
Moreso, [14] published a similar work on mathematical modeling of the growth of Burkholderia sp. on Glyphosate.Growth models such as Logistic, Gompertz, Richards, Schnute, Baranyi-Roberts, Von Bertalanffy, Buchanan three-phase, and Huang were used.Based on statistical tests such as root-meansquare error (RMSE), adjusted coefficient of determination (adjR 2 ), bias factor (BF), accuracy factor (AF), and corrected AICc (Akaike Information Criterion), they concluded that the modified Gompertz model was the best model.The modified Logistic model is widely used as a general-purpose model for understanding substrate inhibition and degradation kinetics, and it has been used to describe numerous bacterial growths on xenobiotics or hazardous chemicals in its pure and modified forms (Table 5).Studies in marine biology and bioremediation in saline environments. [19] The breakdown of harmful chemicals is one of the many important environmental processes in which microbes participate.For efficient environmental management, it is crucial to comprehend the microbial growth dynamics on these toxins.To represent the growth of microbes on harmful compounds, the modified logistics model has been more common in recent years.An expansion of the standard logistic growth model, the modified logistics model explains how populations of organisms in a restricted setting can increase over time.When investigating microbial growth on harmful compounds, this updated version takes into account other variables that are important.Toxin inhibitory effects on microbial growth are taken into account in the modified logistics model, as opposed to the classic logistics model [20][21][22].
When it comes to measuring how harmful compounds affect microbial development, the model incorporates toxicity characteristics, one of which is the lag period, of which the more toxic the substance the longer the lag period.We can then make an educated guess as to what concentration has a noticeable impact on the growth rate.Toxic chemicals can trigger the development of adaptive mechanisms in microorganisms.These changes are accounted for in the updated logistics model, which better depicts the time-dependent dynamics of microbial development.The model takes into account environmental variables that can affect the development of microbes on harmful compounds, including temperature, pH, and the availability of nutrients.The capacity of the modified logistics model to represent the intricate dynamics of microbial development in the presence of harmful substances has contributed to its rising popularity [23][24][25][26][27][28][29].To optimize bioremediation procedures, forecast microbial growth kinetics, and evaluate pollution impacts, researchers and environmental scientists utilize this model.

CONCLUSION
The work successfully presents the effective primary kinetics analysis of octylphenol polyethoxylates degradation by Pseudomonas nitroreducens TX1.Nonlinear kinetic regression was employed through the utilization of curve-fitting software in order to fit the digitized growth degradation data.Various kinetic models, including Huang, Baranyi Roberts, modified Gompertz, Buchanan-3-phase, modified Richards, Modified Logistics, and Von Bertalanffy, were evaluated for data fitting.The modified Logistics model exhibited the best fit, with lower RMSE, AICc, and highest adjusted R2 values, Bias Factor, and Accuracy Factor close to unity (1.0).Von Bertalanffy model had the poorest fit.Calculated values for the modified Logistics model parameters were presented.The model, frequently used in simulating biodegradation, proved effective for predicting the growth of Pseudomonas nitroreducens on octylphenol polyethoxylates.This study's modeling parameters hold promise for predicting bioremediation and may be valuable for modeling the growth and degradation of various contaminants in the future.These models contribute to the scientific foundation of bioremediation research.They help researchers analyze and interpret experimental data, facilitating the development of new insights and innovations in microbial ecology, physiology, and biotechnology for environmental cleanup.

Fig. 6 .
Fig. 6.Fitting experimental data with the modified Logistics model.

Table .
Widely-utilized primary growth kinetic models.

Table 3 .
Statistical analysis of kinetic models.

Table 4 .
Growth coefficients as modelled using the modified logistics model.

Table 5 .
Some applications of the modified Logistics model and its modified form in modelling growth of bacterium.