Artificial Neural Network-Genetic Algorithm Approach to Optimize Media Constituents for Enhancing Lipase Production by a Soil Microorganism

Synergistic effects of ternary mixture formulation and process parameters optimization in a sequential approach for enhanced L-asparaginase production using agro-industrial wastes

A novel ternary mixture of inexpensive and nutrient-rich agro-substrates comprising groundnut de-oiled cake, corn gluten meal, and soybean meal has been explored to enhance the L-asparaginase production in solid-state fermentation. To achieve the aim, a hybrid strategy was implemented by utilizing a combination of a mixture design and artificial neural networks. The study initiated with the judicious selection of the agro-substrates based on their low C/N content in comparison to the control using the CHNS elemental analysis. The mixture composition of soybean meal (49.0%), groundnut de-oiled cake (31.5%), and corn gluten meal (19.5%) were found optimum using the simplex lattice mixture design. The agro-industrial substrates mix revealed synergistic effects on the L-asparaginase production than either of the substrates alone. The maximum L-asparaginase activity of 141.45 ± 5.24 IU/gds was observed under the physical process conditions of 70% moisture content, autoclaving period of 30 min and 6.0 pH by adopting the machine learning-derived artificial neural network (ANN) methodology. The ANN modeling showed excellent prediction ability with a low mean squared error of 0.7, a low root mean squared error of 0.84, and a high value of 0.99 for regression coefficient. Moisture content (%) was assessed to be the most sensitive process parameter in the global sensitivity analysis. The net outcome from the two sequential optimization designs is the selection of the ideal mixture composition followed by the optimum physical process parameters. The application of the enzyme demonstrated significant cytotoxicity against leukemia cell line and therefore exhibited an anti-cancer effect. The present study reports a novel mixture combination and methodology that can be used to lower the cost and enhance the production of L-asparaginase using an agro-industrial substrate mixture.

Mapping the Bibliometrics Landscape of AI in Medicine: Methodological Study

BACKGROUND

Artificial intelligence (AI), conceived in the 1950s, has permeated numerous industries, intensifying in tandem with advancements in computing power. Despite the widespread adoption of AI, its integration into medicine trails other sectors. However, medical AI research has experienced substantial growth, attracting considerable attention from researchers and practitioners.

OBJECTIVE

In the absence of an existing framework, this study aims to outline the current landscape of medical AI research and provide insights into its future developments by examining all AI-related studies within PubMed over the past 2 decades. We also propose potential data acquisition and analysis methods, developed using Python (version 3.11) and to be executed in Spyder IDE (version 5.4.3), for future analogous research.

METHODS

Our dual-pronged approach involved (1) retrieving publication metadata related to AI from PubMed (spanning 2000-2022) via Python, including titles, abstracts, authors, journals, country, and publishing years, followed by keyword frequency analysis and (2) classifying relevant topics using latent Dirichlet allocation, an unsupervised machine learning approach, and defining the research scope of AI in medicine. In the absence of a universal medical AI taxonomy, we used an AI dictionary based on the European Commission Joint Research Centre AI Watch report, which emphasizes 8 domains: reasoning, planning, learning, perception, communication, integration and interaction, service, and AI ethics and philosophy.

RESULTS

From 2000 to 2022, a comprehensive analysis of 307,701 AI-related publications from PubMed highlighted a 36-fold increase. The United States emerged as a clear frontrunner, producing 68,502 of these articles. Despite its substantial contribution in terms of volume, China lagged in terms of citation impact. Diving into specific AI domains, as the Joint Research Centre AI Watch report categorized, the learning domain emerged dominant. Our classification analysis meticulously traced the nuanced research trajectories across each domain, revealing the multifaceted and evolving nature of AI's application in the realm of medicine.

CONCLUSIONS

The research topics have evolved as the volume of AI studies increases annually. Machine learning remains central to medical AI research, with deep learning expected to maintain its fundamental role. Empowered by predictive algorithms, pattern recognition, and imaging analysis capabilities, the future of AI research in medicine is anticipated to concentrate on medical diagnosis, robotic intervention, and disease management. Our topic modeling outcomes provide a clear insight into the focus of AI research in medicine over the past decades and lay the groundwork for predicting future directions. The domains that have attracted considerable research attention, primarily the learning domain, will continue to shape the trajectory of AI in medicine. Given the observed growing interest, the domain of AI ethics and philosophy also stands out as a prospective area of increased focus.

Artificial Intelligence Aided Lipase Production and Engineering for Enzymatic Performance Improvement

With the development of artificial intelligence (AI), tailoring methods for enzyme engineering have been widely expanded. Additional protocols based on optimized network models have been used to predict and optimize lipase production as well as properties, namely, catalytic activity, stability, and substrate specificity. Here, different network models and algorithms for the prediction and reforming of lipase, focusing on its modification methods and cases based on AI, are reviewed in terms of both their advantages and disadvantages. Different neural networks coupled with various algorithms are usually applied to predict the maximum yield of lipase by optimizing the external cultivations for lipase production, while one part is used to predict the molecule variations affecting the properties of lipase. However, few studies have directly utilized AI to engineer lipase by affecting the structure of the enzyme, and a set of research gaps needs to be explored. Additionally, future perspectives of AI application in enzymes, including lipase engineering, are deduced to help the redesign of enzymes and the reform of new functional biocatalysts. This review provides a new horizon for developing effective and innovative AI tools for lipase production and engineering and facilitating lipase applications in the food industry and biomass conversion.

A review of algorithmic approaches for cell culture media optimization

Cell culture media composition and culture conditions play a crucial role in product yield, quality and cost of production. Culture media optimization is the technique of improving media composition and culture conditions to achieve desired product outcomes. To achieve this, there have been many algorithmic methods proposed and used for culture media optimization in the literature. To help readers evaluate and decide on a method that best suits their specific application, we carried out a systematic review of the different methods from an algorithmic perspective that classifies, explains and compares the available methods. We also examine the trends and new developments in the area. This review provides recommendations to researchers regarding the suitable media optimization algorithm for their applications and we hope to also promote the development of new cell culture media optimization methods that are better suited to existing and upcoming challenges in this biotechnology field, which will be essential for more efficient production of various cell culture products.

L-asparaginase production in solid-state fermentation using Aspergillus niger: process modeling by artificial neural network approach

L-asparaginase has proven itself as a potential anti-cancer drug and in the mitigation of acrylamide formation in the food industry. In the present investigation, a novel utilization of niger (Guizotia abyssinica) de-oiled cake as the sole source for the cost-effective production of L-asparaginase was evaluated and compared with different agro-substrates in solid-state fermentation. The substrate provided a favorable C/N content for the L-asparaginase production as evident from the chemical composition (CHNS analysis) of the substrate. The influential process parameters viz; autoclaving time, moisture content, temperature and pH were optimized and modeled using machine-learning based artificial neural network (ANN) and statistical-based response surface methodology (RSM). The maximum enzyme activity of 34.65 ± 2.18 IU/gds was observed at 30.3 min of autoclaving time, 62% moisture content, 30 °C temperature and 6.2 pH in 96 h. A 1.36 fold improvement in enzyme activity was observed on utilizing optimized parameters. In comparison with RSM, the ANN model showed superior prediction with a low mean squared error of 0.072, low root mean squared error of 0.268 and 0.99 value of regression coefficient. The present study demonstrates the novel utilization of inexpensive and readily available agro-industrial waste for the development of cost-effective L-asparaginase production process.

Energy Modeling of a Refiner in Thermo-Mechanical Pulping Process Using ANFIS Method

In the pulping industry, thermo-mechanical pulping (TMP) as a subdivision of the refiner-based mechanical pulping is one of the most energy-intensive processes where the core of the process is attributed to the refining process. In this study, to simulate the refining unit of the TMP process under different operational states, the idea of machine learning algorithms is employed. Complicated processes and prediction problems could be simulated and solved by utilizing artificial intelligence methods inspired by the pattern of brain learning. In this research, six evolutionary optimization algorithms are employed to be joined with the adaptive neuro-fuzzy inference system (ANFIS) to increase the refining simulation accuracy. The applied optimization algorithms are particle swarm optimization algorithm (PSO), differential evolution (DE), biogeography-based optimization algorithm (BBO), genetic algorithm (GA), ant colony (ACO), and teaching learning-based optimization algorithm (TLBO). The simulation predictor variables are site ambient temperature, refining dilution water, refining plate gap, and chip transfer screw speed, while the model outputs are refining motor load and generated steam. Findings confirm the superiority of the PSO algorithm concerning model performance comparing to the other evolutionary algorithms for optimizing ANFIS method parameters, which are utilized for simulating a refiner unit in the TMP process.

Optimization of process parameters for improved chitinase activity from Thermomyces sp. by using artificial neural network and genetic algorithm

Chitinase is responsible for the breaking down of chitin to N-acetyl-glucosamine units linked through (1-4)-glycosidic bond. The chitinases find several applications in waste management and pest control. The high yield with characteristics thermal stability of chitinase is the key to their industrial application. Therefore, the present work focuses on parameter optimization for chitinase production using fungus Thermomyces lanuginosus MTCC 9331. Three different optimization approaches, namely, response surface methodology (RSM), artificial neural network (ANN) and genetic algorithm (GA) were used. The parameters under study were incubation time, pH and inoculum size. The central composite design with RSM was used for the optimization of the process parameters. Further, results were validated with GA and ANN. A multilayer feed-forward algorithm was performed for ANN, i.e., Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient. The ANN predicted values gave higher chitinase activity, i.e., 102.24 U/L as compared to RSM-predicted values, i.e., 88.38 U/L. The predicted chitinase activity was also closer to the observed data at these levels. The validation study suggested that the highest activity of chitinase as predicted by ANN is in line with experimental analysis. The comparison of three different statistical approaches suggested that ANN gives better optimization results compared to the GA and RSM study.

Improved Pullulan Production and Process Optimization Using Novel GA-ANN and GA-ANFIS Hybrid Statistical Tools

Pullulan production from Aureobasidiumpullulans was explored to increase yield. Non-linear hybrid mathematical tools for optimization of process variables as well as the pullulan yield were analyzed. The one variable at a time (OVAT) approach was used to optimize the maximum pullulan yield of 35.16 ± 0.29 g/L. The tools predicted maximum pullulan yields of 39.4918 g/L (genetic algorithm coupled with artificial neural network (GA-ANN)) and 36.0788 g/L (GA coupled with adaptive network based fuzzy inference system (GA-ANFIS)). The best regression value (0.94799) of the Levenberg-Marquardt (LM) algorithm for ANN and the epoch error (6.1055 × 10-5) for GA-ANFIS point towards prediction precision and potentiality of data training models. The process parameters provided by both the tools corresponding to their predicted yield were revalidated by experiments. Among the two of them GA-ANFIS results were replicated with 98.82% accuracy. Thus GA-ANFIS predicted an optimum pullulan yield of 36.0788 g/L with a substrate concentration of 49.94 g/L, incubation period of 182.39 h, temperature of 27.41 °C, pH of 6.99, and agitation speed of 190.08 rpm.

Phytoremediation of palm oil mill secondary effluent (POMSE) by Chrysopogon zizanioides (L.) using artificial neural networks

Artificial neural networks (ANNs) have been widely used to solve the problems because of their reliable, robust, and salient characteristics in capturing the nonlinear relationships between variables in complex systems. In this study, ANN was applied for modeling of Chemical Oxygen Demand (COD) and biodegradable organic matter (BOD) removal from palm oil mill secondary effluent (POMSE) by vetiver system. The independent variable, including POMSE concentration, vetiver slips density, and removal time, has been considered as input parameters to optimize the network, while the removal percentage of COD and BOD were selected as output. To determine the number of hidden layer nodes, the root mean squared error of testing set was minimized, and the topologies of the algorithms were compared by coefficient of determination and absolute average deviation. The comparison indicated that the quick propagation (QP) algorithm had minimum root mean squared error and absolute average deviation, and maximum coefficient of determination. The importance values of the variables was included vetiver slips density with 42.41%, time with 29.8%, and the POMSE concentration with 27.79%, which showed none of them, is negligible. Results show that the ANN has great potential ability in prediction of COD and BOD removal from POMSE with residual standard error (RSE) of less than 0.45%.

Artificial Intelligence vs. Statistical Modeling and Optimization of Continuous Bead Milling Process for Bacterial Cell Lysis

For a commercially viable recombinant intracellular protein production process, efficient cell lysis and protein release is a major bottleneck. The recovery of recombinant protein, cholesterol oxidase (COD) was studied in a continuous bead milling process. A full factorial response surface methodology (RSM) design was employed and compared to artificial neural networks coupled with genetic algorithm (ANN-GA). Significant process variables, cell slurry feed rate (A), bead load (B), cell load (C), and run time (D), were investigated and optimized for maximizing COD recovery. RSM predicted an optimum of feed rate of 310.73 mL/h, bead loading of 79.9% (v/v), cell loading OD600nm of 74, and run time of 29.9 min with a recovery of ~3.2 g/L. ANN-GA predicted a maximum COD recovery of ~3.5 g/L at an optimum feed rate (mL/h): 258.08, bead loading (%, v/v): 80%, cell loading (OD600nm): 73.99, and run time of 32 min. An overall 3.7-fold increase in productivity is obtained when compared to a batch process. Optimization and comparison of statistical vs. artificial intelligence techniques in continuous bead milling process has been attempted for the very first time in our study. We were able to successfully represent the complex non-linear multivariable dependence of enzyme recovery on bead milling parameters. The quadratic second order response functions are not flexible enough to represent such complex non-linear dependence. ANN being a summation function of multiple layers are capable to represent complex non-linear dependence of variables in this case; enzyme recovery as a function of bead milling parameters. Since GA can even optimize discontinuous functions present study cites a perfect example of using machine learning (ANN) in combination with evolutionary optimization (GA) for representing undefined biological functions which is the case for common industrial processes involving biological moieties.

Constrained azeotropic optimization of extraction system components for the safe and efficient recovery of a desired metabolite (e.g., 3-demethylated colchicine)

Constrained azeotropic optimization of extraction system components for the safe and efficient recovery of a desired metabolite (e.g., 3-DMC) using artificial learning and evolutionary optimization techniques.

Optimization, kinetics, and modeling of inulinase production by K. marxianus var. marxianus

Pressmud, a by-product from the sugarcane industry, was used as a carbon source for the production of inulinase in solid-state fermentation (SSF). Statistical experimental designs were employed to screen the nutrients and optimize the media composition for the production of inulinase by Kluyveromyces marxianus var. marxianus. Eighteen various nutrients were selected for preliminary screening of production medium component by Plackett-Burman design (PBD) technique. Five nutrients were found to be significant for inulinase production and they were optimized by central composite design (CCD). The optimal media components for solid-state fermentation of inulinase using pressmud were (g/gds): corn steep liquor, 0.06072; urea, 0.01916; beef extract, 0.00957; FeSO4 · 7H2O, 0.00013; K2HPO4, 0.00441. The effect of moisture content and substrate concentration was also studied. From the results it was found that a maximum inulinase activity of 288 U/gds occurs at the moisture content of 65% and substrate concentration of 10 g. The constants in the Michaelis-Menten equation were evaluated and a high R (2) value implied the fitness of the model. Artificial neural network (ANN) modeling was also employed to predict the inulinase production.

Back propagation neural network model for predicting the performance of immobilized cell biofilters handling gas-phase hydrogen sulphide and ammonia

Lab scale studies were conducted to evaluate the performance of two simultaneously operated immobilized cell biofilters (ICBs) for removing hydrogen sulphide (H₂S) and ammonia (NH₃) from gas phase. The removal efficiencies (REs) of the biofilter treating H₂S varied from 50 to 100% at inlet loading rates (ILRs) varying up to 13 g H₂S/m³·h, while the NH₃ biofilter showed REs ranging from 60 to 100% at ILRs varying between 0.5 and 5.5 g NH₃/m³·h. An application of the back propagation neural network (BPNN) to predict the performance parameter, namely, RE (%) using this experimental data is presented in this paper. The input parameters to the network were unit flow (per min) and inlet concentrations (ppmv), respectively. The accuracy of BPNN-based model predictions were evaluated by providing the trained network topology with a test dataset and also by calculating the regression coefficient (R²) values. The results from this predictive modeling work showed that BPNNs were able to predict the RE of both the ICBs efficiently.

Efficiency of neural network-based combinatorial model predicting optimal culture conditions for maximum biomass yields in hairy root cultures

KEY MESSAGE : ANN-based combinatorial model is proposed and its efficiency is assessed for the prediction of optimal culture conditions to achieve maximum productivity in a bioprocess in terms of high biomass. A neural network approach is utilized in combination with Hidden Markov concept to assess the optimal values of different environmental factors that result in maximum biomass productivity of cultured tissues after definite culture duration. Five hidden Markov models (HMMs) were derived for five test culture conditions, i.e. pH of liquid growth medium, volume of medium per culture vessel, sucrose concentration (%w/v) in growth medium, nitrate concentration (g/l) in the medium and finally the density of initial inoculum (g fresh weight) per culture vessel and their corresponding fresh weight biomass. The artificial neural network (ANN) model was represented as the function of these five Markov models, and the overall simulation of fresh weight biomass was done with this combinatorial ANN-HMM. The empirical results of Rauwolfia serpentina hairy roots were taken as model and compared with simulated results obtained from pure ANN and ANN-HMMs. The stochastic testing and Cronbach's α-value of pure and combinatorial model revealed more internal consistency and skewed character (0.4635) in histogram of ANN-HMM compared to pure ANN (0.3804). The simulated results for optimal conditions of maximum fresh weight production obtained from ANN-HMM and ANN model closely resemble the experimentally optimized culture conditions based on which highest fresh weight was obtained. However, only 2.99 % deviation from the experimental values could be observed in the values obtained from combinatorial model when compared to the pure ANN model (5.44 %). This comparison showed 45 % better potential of combinatorial model for the prediction of optimal culture conditions for the best growth of hairy root cultures.

Optimization of auto-induction medium for G-CSF production by Escherichia coli using artificial neural networks coupled with genetic algorithm

Granulocyte colony-stimulating factor (G-CSF) is a cytokine widely used in cancer patients receiving high doses of chemotherapeutic drugs to prevent the chemotherapy-induced suppression of white blood cells. The production of recombinant G-CSF should be increased to meet the increasing market demand. This study aims to model and optimize the carbon source of auto-induction medium to enhance G-CSF production using artificial neural networks coupled with genetic algorithm. In this approach, artificial neural networks served as bioprocess modeling tools, and genetic algorithm (GA) was applied to optimize the established artificial neural network models. Two artificial neural network models were constructed: the back-propagation (BP) network and the radial basis function (RBF) network. The root mean square error, coefficient of determination, and standard error of prediction of the BP model were 0.0375, 0.959, and 8.49 %, respectively, whereas those of the RBF model were 0.0257, 0.980, and 5.82 %, respectively. These values indicated that the RBF model possessed higher fitness and prediction accuracy than the BP model. Under the optimized auto-induction medium, the predicted maximum G-CSF yield by the BP-GA approach was 71.66 %, whereas that by the RBF-GA approach was 75.17 %. These predicted values are in agreement with the experimental results, with 72.4 and 76.014 % for the BP-GA and RBF-GA models, respectively. These results suggest that RBF-GA is superior to BP-GA. The developed approach in this study may be helpful in modeling and optimizing other multivariable, non-linear, and time-variant bioprocesses.

Comparison of the estimation capabilities of response surface methodology and artificial neural network for the optimization of recombinant lipase production by E. coli BL21

Response surface methodology (RSM) and artificial neural network (ANN) were used to optimize the effect of four independent variables, viz. glucose, sodium chloride (NaCl), temperature and induction time, on lipase production by a recombinant Escherichia coli BL21. The optimization and prediction capabilities of RSM and ANN were then compared. RSM predicted the dependent variable with a good coefficient of correlation determination (R2) and adjusted R2 values for the model. Although the R2 value showed a good fit, absolute average deviation (AAD) and root mean square error (RMSE) values did not support the accuracy of the model and this was due to the inferiority in predicting the values towards the edges of the design points. On the other hand, ANN-predicted values were closer to the observed values with better R2, adjusted R2, AAD and RMSE values and this was due to the capability of predicting the values throughout the selected range of the design points. Similar to RSM, ANN could also be used to rank the effect of variables. However, ANN could not predict the interactive effect between the variables as performed by RSM. The optimum levels for glucose, NaCl, temperature and induction time predicted by RSM are 32 g/L, 5 g/L, 32°C and 2.12 h, and those by ANN are 25 g/L, 3 g/L, 30°C and 2 h, respectively. The ANN-predicted optimal levels gave higher lipase activity (55.8 IU/mL) as compared to RSM-predicted levels (50.2 IU/mL) and the predicted lipase activity was also closer to the observed data at these levels, suggesting that ANN is a better optimization method than RSM for lipase production by the recombinant strain.

Neural network models for biological waste-gas treatment systems

This paper outlines the procedure for developing artificial neural network (ANN) based models for three bioreactor configurations used for waste-gas treatment. The three bioreactor configurations chosen for this modelling work were: biofilter (BF), continuous stirred tank bioreactor (CSTB) and monolith bioreactor (MB). Using styrene as the model pollutant, this paper also serves as a general database of information pertaining to the bioreactor operation and important factors affecting gas-phase styrene removal in these biological systems. Biological waste-gas treatment systems are considered to be both advantageous and economically effective in treating a stream of polluted air containing low to moderate concentrations of the target contaminant, over a rather wide range of gas-flow rates. The bioreactors were inoculated with the fungus Sporothrix variecibatus, and their performances were evaluated at different empty bed residence times (EBRT), and at different inlet styrene concentrations (C(i)). The experimental data from these bioreactors were modelled to predict the bioreactors performance in terms of their removal efficiency (RE, %), by adequate training and testing of a three-layered back propagation neural network (input layer-hidden layer-output layer). Two models (BIOF1 and BIOF2) were developed for the BF with different combinations of easily measurable BF parameters as the inputs, that is concentration (gm(-3)), unit flow (h(-1)) and pressure drop (cm of H(2)O). The model developed for the CSTB used two inputs (concentration and unit flow), while the model for the MB had three inputs (concentration, G/L (gas/liquid) ratio, and pressure drop). Sensitivity analysis in the form of absolute average sensitivity (AAS) was performed for all the developed ANN models to ascertain the importance of the different input parameters, and to assess their direct effect on the bioreactors performance. The performance of the models was estimated by the regression coefficient values (R(2)) for the test data set. The results obtained from this modelling work can be useful for obtaining important relationships between different bioreactor parameters and for estimating their safe operating regimes.

Optimization of actinomycin V production by Streptomyces triostinicus using artificial neural network and genetic algorithm

Artificial neural network (ANN) and genetic algorithm (GA) were applied to optimize the medium components for the production of actinomycin V from a newly isolated strain of Streptomyces triostinicus which is not reported to produce this class of antibiotics. Experiments were conducted using the central composite design (CCD), and the data generated was used to build an artificial neural network model. The concentrations of five medium components (MgSO(4), NaCl, glucose, soybean meal and CaCO(3)) served as inputs to the neural network model, and the antibiotic yield served as outputs of the model. Using the genetic algorithm, the input space of the neural network model was optimized to find out the optimum values for maximum antibiotic yield. Maximum antibiotic yield of 452.0 mg l(-1) was obtained at the GA-optimized concentrations of medium components (MgSO(4) 3.657; NaCl 1.9012; glucose 8.836; soybean meal 20.1976 and CaCO(3) 13.0842 gl(-1)). The antibiotic yield obtained by the ANN/GA was 36.7% higher than the yield obtained with the response surface methodology (RSM).

Artificial intelligence based optimization of exocellular glucansucrase production from Leuconostoc dextranicum NRRL B-1146

Two different artificial intelligence techniques namely artificial neural network (ANN) and genetic algorithm (GA) were integrated for optimizing fermentation medium for the production of glucansucrase. The experimental data reported in a previous study were used to build the neural network. The ANN was trained using the back propagation algorithm. The ANN predicted values showed good agreement with the experimentally reported ones from a response surface based experiment. The concentrations of three medium components: viz Tween 80, sucrose and K2HPO4 served as inputs to the neural network model and the enzyme activity as the output of the model. A model was generated with a coefficient of correlation (R2) of 1.0 for the training set and 0.90 for the test data. A genetic algorithm was used to optimize the input space of the neural network model to find the optimum settings for maximum enzyme activity. This artificial neural network supported genetic algorithm predicted a maximum glucansucrase activity of 6.92U/ml at medium composition of 0.54% (v/v) Tween 80, 5.98% (w/v) sucrose and 1.01% (w/v) K2HPO4. ANN-GA predicted model gave a 6.0% increase of enzyme activity over the regression based prediction for optimized enzyme activity. The maximum enzyme activity experimentally obtained using the ANN-GA designed medium was 6.75+/-0.09U/ml which was in good agreement with the predicted value.