Statistical experimental design for bioprocess modeling and optimization analysis: repeated-measures method for dynamic biotechnology process

The statistical design of experiments (DOE) is a collection of predetermined settings of the process variables of interest, which provides an efficient procedure for planning experiments. Experiments on biological processes typically produce long sequences of successive observations on each experimental unit (plant, animal, bioreactor, fermenter, or flask) in response to several treatments (combination of factors). Cell culture and other biotech-related experiments used to be performed by repeated-measures method of experimental design coupled with different levels of several process factors to investigate dynamic biological process. Data collected from this design can be analyzed by several kinds of general linear model (GLM) statistical methods such as multivariate analysis of variance (MANOVA), univariate ANOVA (time split-plot analysis with randomization restriction), and analysis of orthogonal polynomial contrasts of repeated factor (linear coefficient analysis). Last, regression model was introduced to describe responses over time to the different treatments along with model residual analysis. Statistical analysis of biprocess with repeated measurements can help investigate environmental factors and effects affecting physiological and bioprocesses in analyzing and optimizing biotechnology production.     

Design and numerical simulation of a DNA electrophoretic stretching device

DNA stretching is now a key technology in emerging DNA mapping devices such as direct linear analysis (DLA), though DNA stretching in a high throughput manner is still a challenging problem. In this work, we present a new microfluidic channel design to enhance DNA stretching using kinematic analysis and Brownian dynamics-finite element method (BD-FEM). Our group recently showed in experiments that the extensional electrophoretic field arising from a hyperbolic microcontraction can be utilized to stretch T4-DNA. We demonstrate the reliability of our BD-FEM model for the present problem by showing that the numerical predictions are consistent with the experimental data for the hyperbolic channel. We then investigate DNA stretching for four different funnel shapes. Surprisingly the maximum mean DNA stretch is quite similar in all four designs. Finally, we propose a new design with a side-feeding branch to enhance stretching based on a kinematic analysis along different feeding locations. Our numerical simulation predicted that DNA stretching can be dramatically enhanced using side-feeding.     

Experimental designs to investigate capillary electrophoresis-electrospray ionization-mass spectrometry enantioseparation with the partial-filling technique

An experimental design approach is described to evaluate the main electrophoretic parameters involved in the enantioseparation of pharmaceuticals by capillary electrophoresis (CE) coupled to electrospray ionization-mass spectrometry (ESI-MS). For all experiments, the partial-filling technique was applied to avoid the chiral selector entering in the mass spectrometer ion source with a negative effect on the electrospray performance. To carry out enantioseparation, a volatile buffer constituted of 20 mM ammonium acetate at pH 4.0, and a polyvinyl alcohol-coated capillary were used. Methadone was employed as the model compound and three different cyclodextrins (CDs), namely sulfobutyl ether-beta-CD, carboxymethylated-beta-CD and hydroxypropyl-beta-CD, were selected in order to study the countercurrent process. Two different experimental designs were chosen: (i) a full-factorial design to examine the effects and significance of the investigated factors, and (ii) a central composite face-centered design to establish the mathematical model of the selected responses in function of experimental factors. The chiral selector concentration, percentage of the capillary filled with the chiral selector, and drying gas nebulization pressure were three relevant factors taken into consideration. For each CD, the methadone enantiomeric resolution, apparent selectivity, and migration time of the second enantiomer were established as responses. The latter were systematically related to experimental parameters with the help of multiple linear regression. It is noteworthy that the behaviour was different in function of the chiral selector charge. Results revealed that the nebulization pressure involved in the electrospray process and the CD concentration had a significant effect on the enantiomeric resolution, while the effect of the separation zone length was less pronounced. Finally, response surfaces were drawn from the mathematical model and experimental conditions were selected to allow a robust determination of methadone enantiomers by CE-MS.     

Statistical thermodynamics models for polyatomic adsorbates: application to adsorption of n-paraffins in 5A zeolite

Experimental adsorption isotherms of five n-paraffins (ethane, propane, butane, pentane, and hexane) in 5A zeolite were described by means of a statistical thermodynamics model for linear adsorbates (MLA) developed by Ramirez-Pastor et al. (1999) and compared with the well-known multisite Langmuir model (MSL) of Nitta et al. (1984). The experimental data, obtained by different authors in a wide range of temperatures and pressures, were correlated by using an algorithm of multiple fitting. Two main conclusions were drawn from the analysis of experimental data: (i) for small molecules (ethane, propane), MLA is the more accurate model, validating the hypothesis of the linear rigid character of the adsorbate and reinforcing previous results obtained from the analysis of computational experiments developed for dimers and linear trimers; (ii) for large molecules (n-butane, n-pentane, n-hexane), the better performance of the MSL model suggests that the admolecules adsorb in a nonlinear structure. The isosteric heat of adsorption dependence on the number of carbons obtained from our study, ranging between 23.84 kJ/mol for ethane and 59.26 kJ/mol for hexane, showed a very good agreement with previous results reported in the literature, confirming the consistency of our analysis.     

Fast development of separation methods for the chiral analysis of amino acid derivatives using capillary electrophoresis and experimental designs

The use of experimental design in method development was studied for the chiral separation of several amino acid derivatives with capillary electrophoresis. The aim of this study was to define rapidly experimental conditions under which the enantiomers can be sufficiently separated for quantification and to derive a methodology for the separation of new compounds. Three modified cyclodextrins (CDs) were used as chiral selectors: hydroxypropyl-beta-cyclodextrin, carboxymethyl-beta-CD and sulfobutylether-beta-CD. The following factors were examined: the type of cyclodextrin, the CD concentration, the pH and the % of organic modifier (methanol) of the electrolyte. Two types of fractional factorial design were used depending on the type of analyte and on the number of factors selected: a 3(4-2) fractional factorial design (4 factors studied at 3 different levels) and a 2(3-1) fractional factorial design (3 factors at 2 different levels). From the 14 compounds investigated, 12 could be separated with one or another CD and not more than 9 experiments were required. No generalisation of the best analysis conditions was possible within this family of compounds. Specific analysis conditions must be defined for each analyte. Experimental designs have shown to be very useful to determine rapidly conditions under which each enantiomer can be separated with an acceptable resolution.     

Development of generic liquid chromatography-mass spectrometry methods using experimental design

Standard approaches to development of liquid chromatography-mass spectrometry (LC-MS) methods, either ion-pairing or reversed-phase liquid chromatography, have been through trial and error or intentional variation of experimental factors. These approaches to method optimization fail to take into account interactions between experimental factors and therefore the results may not be optimal for the combination of experimental factors. Another approach to optimization is through the use of chemometrics. Chemometric approaches can be more efficient than trial and error or intentional variation because chemometrics make use of multivariate designs; experimental factors are varied simultaneously at the various levels. Therefore chemometrics can take into account interactions between factors. The goal of this study was to develop a generic ion-pair LC-MS method for the analysis of acidic compounds using a chemometric approach called design of experiments (DOE). Four acidic compounds which cover three classes of acidic functional groups: 1-naphthyl phosphate (1), 1-naphthalenesulfonic acid (2), 2-naphthalenesulfonic acid (3), and (1-naphthoxy)acetic acid (4) were used as model compounds to develop the generic method. This study illustrates that LC-MS conditions can be optimized efficiently with minimal amount of experimentation using a chemometric approach to experimental design.     

Multivariate experimental design: towards more reliable electrochemical detection

Design of an experiment approach has recently become an urgent requirement for different experimental measurements. Not only owing to the increased expenses for purchasing chemicals and equipment but also to reduce time required to conduct several one-variable at a time experiments to optimize the operating conditions of an experimental design. Design of experiments has excellent applicability in the analytical process related to method development based on multiple variants used for pharmaceutical, food, and environmental analysis. Application of experimental design has become effective to identify and optimize the significant factors and to achieve adequate results using few experimental trials. Electrochemical sensors represent a class of fast, reliable, and economic tools in analytical chemistry, with vast applicability to different fields. This review aims at presenting the most recently used screening and optimization designs during (2019–2021) for the fabrication and operation variables of electrochemical sensors and how can they be efficiently correlated.     

原油组分低温氧化机理和反应活性实验研究

分析了原油和原油组分低温氧化的机理,通过实验进行了不同油品低温氧化反应,考察了氧化反应前后原油族组成的变化,并研究了单组分(正十六烷、蜡、蒽、沥青质)在不同温度下的低温氧化速率和反应活性,得出了不同原油组分的低温氧化反应的活化能。结果表明,稠油较轻质油有更好的氧化反应活性,在较低温度下稠油更容易被氧化,原油中不同组分及含量是影响氧化反应活性和氧化反应速率的重要因素,重组分的沥青质和长链烷烃在低温下(70~90℃)氧化活性较高,正十六烷和蒽反应活性较之重组分低。揭示了原油组分低温氧化反应机理以及不同组分氧化反应活性的区别,为油田注空气工艺方案设计提供基础。     

Statistical models in assessing fold change of gene expression in real-time RT-PCR experiments

Real-time RT-PCR has been frequently used in quantitative research in molecular biology and bioinformatics. It provides remarkably useful technology to assess expression of genes. Although mathematical models for gene amplification process have been studied, statistical models and methods for data analysis in real-time RT-PCR have received little attention. In this paper, we briefly introduce current mathematical models, and study statistical models for real-time RT-PCR data. We propose a generalized estimation equations (GEE) model that properly reflects the structure of repeated data in RT-PCR experiments for both cross-sectional and longitudinal data. The GEE model takes the correlation between observations within the same subjects into consideration, and prevents from producing false positives or false negatives. We further demonstrate with a set of actual real-time RT-PCR data that different statistical models yield different estimations of fold change and confidence interval. The SAS program for data analysis using the GEE model is provided to facilitate easy computation for non-statistical professionals.     

PARAFASCA: ASCA combined with PARAFAC for the analysis of metabolic fingerprinting data

Novel post‐genomics experiments such as metabolomics provide datasets that are highly multivariate and often reflect an underlying experimental design, developed with a specific experimental question in mind. ANOVA‐simultaneous component analysis (ASCA) can be used for the analysis of multivariate data obtained from an experimental design instead of the widely used principal component analysis (PCA). This increases the interpretability of the model in terms of the experimental question. Aside from the levels of individual factors, variation that can be described by the experimental design may also depend on levels of multiple (crossed) factors simultaneously, e.g. the interactions. ASCA describes each contribution with a PCA model, but a contribution depending on crossed factors may be described more parsimoniously by multiway models like parallel factor analysis (PARAFAC). The combination of PARAFAC and ASCA, named PARAFASCA, provides a view on the data that is both parsimonious and focused on the experimental question. The novel method is used to analyze a dataset in which the effect of two doses of hydrazine on the urinary chemical composition of rats is investigated by time‐resolved metabolic fingerprinting with nuclear magnetic resonance (NMR) spectroscopy. This experiment has been conducted to monitor the dose‐specific urine composition changes in time upon hydrazine administration. Comparison of the PCA, the ASCA and the PARAFASCA models shows that ASCA and PARAFASCA describe the data more dedicated to the experimental question than PCA, but that PARAFASCA is more parsimonious than ASCA, and separates the variation underlying different effects better. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimization of Pb(II) biosorption by Robinia tree leaves using statistical design of experiments

The present study introduces Robinia tree leaves as a novel and efficient biosorbent for removing Pb(II) from aqueous solutions. In order to reduce the large number of experiments and find the highest removal efficiency of Pb(II), a set of full 2(3) factorial design with two blocks were performed in duplicate (16 experiments). In all experiments, the contact time was fixed at 25 min. The main interaction effects of the three factors including sorbent mass, pH and initial concentration of metal-ion were considered. By using Student's t-test and analysis of variances (ANOVA), the main factors, which had the highest effect on the removal process, were identified. Twenty-six experiments were designed according to Doehlert response surface design to obtain a mathematical model describing functional relationship between response and main independent variables. The most suitable regression model, that fitted the experimental data extremely well, was chosen according to the lack-of-fit-test and adjusted R(2) value. Finally, after checking for possible outliers, the optimum conditions for maximum removal of Pb(II) from aqueous solution were obtained. The best conditions were calculated to be as: initial concentration of Pb(II)=40 mg L(-1), pH 4.6 and concentration of sorbet equal to 27.3 g L(-1).     

Extraction and characterization of total phenolic and flavonoid contents from bark of Swietenia macrophylla and their antimicrobial and antioxidant properties

In the current study, the bioactive compounds such as total phenols, flavonoids, hydrolyzable tannins, and gallic acid were extracted from the bark of Swietenia macrophylla using four different solvents such as ethanol, methanol, acetone, and water. Among them, acetone exhibited the highest contents of bioactive compounds. To optimize the extraction process, a statistical approach was adopted using the central composite design (CCD) of response surface methodology (RSM). The five parameters at five different levels were chosen in the design of the experiments. A total of 32 experimental runs given by the design were fitted into the second-order regression model equation. The analysis of the model shows the best fit of the experimental data with an R² of 0.9971 and a model F-value of 191.73. The optimal conditions of acetone concentration (56 %), the volume of acetone (22 mL), agitation speed (173 rpm), extraction temperature (31 °C), and extraction time (28 h) were noted from desirability function and showed a 2.0-fold increase in the contents of bioactive compounds when compared to unoptimized conditions. Further, the antimicrobial activity of 5 % (w/v) extract was tested against two-gram positive strains Bacillus sp, and Staphylococcus aureus, and two-gram negative strains Escherichia coli, and S. marcescens. The extract exhibited the 21 mm and 18 mm clear zone of diameter with 5 mm standard disc against the gram-positive strains tested whereas no clear zone was found against gram-negative strains. Finally, the antioxidant property was electrochemically analyzed using cyclic voltammetry and Differential pulse voltammetry, which confirmed the presence of multiple antioxidants in the extract.     

Design of experiments in 241Am alpha source preparation by electrodeposition: an approach to process optimization

This work describes a procedure to improve the quality of an ²⁴¹Am alpha source obtained by means of electrodeposition. The technique of design of experiments (DoE) was applied in order to perform a multivariate analysis of the experimental variable effects taking into consideration the following: i—amperage, d—cathode–anode distance, t—time and PP—polishing process. A 3⁴⁻² fractional design was employed using four experimental factors, three levels per factor, and three response variables were studied: H_area = electrodeposited active area, %R = activity recovery percentage, and Δ_1/2 = width at half-height. Thanks to this simple design, 9 experiments were enough, done in triplicate, to discern how Δ_1/2 and %R are modified when experimental factors change. Additionally, this work provides tools to perform effect statistical analysis of experimental factors, and to pose linear models applying significant terms. The models obtained were validated by analysis of variance and they were of help to verify the choice of significant factors by means of DoE and to approximate to the optimization of the preparation method of a ²⁴¹Am alpha source by means of contour plots of Δ_1/2 and %R.

     

响应面法优化黄芪多糖的提取工艺研究

为优化对黄芪多糖提取工艺.根据单因素实验结果,选取实验因素与水平,根据Box - Benhnken的试验设计原理,采用三因素三水平的响应面分析法,以获得多元二次线性回归方程,以多糖得率为响应值的响应面和等高线.结果表明,提取黄芪多糖最佳工艺条件:料水比1:13,提取温度94 ℃,提取时间64 min.在此条件下,黄芪多...     

Polymer-tethered ligand-receptor interactions between surfaces II

In this paper, we analyze the thermodynamics of interactions between surfaces mediated by polymer-tethered ligand-receptor binding. From statistical thermodynamics calculations, we obtain an effective two-dimensional binding constant reflecting contributions from the microscopic binding affinity as well as from the conformation entropy of the polymer tethers. The total interaction is a result of the interplay between attractive binding and repulsion due to confinement of the polymer chains. We illustrate the differences between three scenarios when the binding molecules are (1) immobile, (2) mobile with a fixed density, and (3) mobile with a fixed chemical potential (connected to a reservoir), which correspond to different biological or experimental situations. The key features of interactions, including the range of adhesion (onset of binding) and the equilibrium separation, can be obtained from scaling analysis and are verified by numerical solutions. In addition, we also extend our method of treating the quenched case with immobile ligands and receptors developed in a previous paper [Martin, J. I.; Zhang, C.-Z.; Wang, Z.-G. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 2621-2637] as a density expansion in terms of both ligand and receptor densities. Finally, we examine several cases having ligand-receptor pairs with different tether lengths and binding affinities, and/or nonbinding linear polymers as steric repellers. Such systems can exhibit complex interactions such as a double-well potential, or a bound state with an adjustable barrier (due to the repellers), which have both biological and bioengineering relevance.     

Four-level orthogonal array design as a chemometric approach to the optimization of polarographic reaction system for phosphorus determination

It is the purpose of the present work to provide information on the four-level orthogonal array design and data analysis for the optimization of analytical procedures. In the theoretical part, the construction and characteristics of the OA(16)(4(5)) matrix is described in detail, followed by the data analysis strategy, in which the significance of the different factors is quantitatively evaluated by an analysis of variance (ANOVA) method including per cent contribution, and the difference among four levels for each factor is determined by Duncan's multiple F test. Furthermore, a third-order polynomial model representing response surface is established to estimate the effects for the factors with significant influences. In the application part, the proposed four-level orthogonal array design and data analysis method were applied to optimize polarographic reaction system for phosphorus determination. By conducting 16 preplanned experiments that span the maximum working range of the system, the best experimental conditions for achieving the largest response can be obtained. The expected value for each experimental trial calculated by the third-order regression equation established is in good agreement with the corresponding experimental value. To confirm the validity of the optimization procedure, additional experiments using the recommended conditions were performed. The results demonstrate that satisfactory results can be acquired. Therefore, the proposed four-level orthogonal array design as a chemometric approach to optimize the polarographic reaction system for phosphorus determination is rather efficient and effective.     

Quality by Design: Design of Experiments Approach Prior to the Validation of a Stability-Indicating HPLC Method for Montelukast

This paper describes a systematic design of experiments (DoE) approach by applying the principle of quality by design (QbD) to determine the design space for a stability-indicating HPLC method prior to validation. By employing DoE, a simultaneous multivariate approach was carried out for mobile phase pH, flow rate, percentage of organic content and column temperature. A two-level fractional factorial design (2^4?1 + 2 center points = 10 experiments) was employed and statistical analysis of the experimental data uncovered the significant influential chromatographic factors. The experimental data for USP tailing and resolution were analyzed statistically to screen the chromatographic factors. This approach determined the most influential chromatographic factors. During this process, inferences were evaluated from various data tables, for example, analysis of variance, summary of fit, lack of fit, and parameter estimates. The study also explained various plots such as actual vs. predicted plot, Pareto plot, and prediction profiler. The acceptable range of the chromatographic factors was displayed as a Contour plot defining the ‘design space’ of the method. The range of operating conditions that guarantee a satisfactory QbD was deduced to finalize the method prior to validation. The method is simple, rapid, and robust for the determination of montelukast in montelukast sodium oral granules dosage form. The method was validated according to ICH guidelines for accuracy, precision, linearity, range, specificity, ruggedness and robustness (one factor varied at a time). The method has been successfully transferred to the quality control department for quality analysis of manufactured batches and stability samples.     

Effect of substrate wettability in liquid dielectrophoresis (LDEP) based droplet generation: theoretical analysis and experimental confirmation

The generation of droplets for biological reactions at the microscale can be achieved by many techniques, among which the so-called liquid dielectrophoresis technique (LDEP). This is not a new process, but the parameters influencing actuation voltage still need further insight: size and geometry (electrodes width and gap, dielectric thickness), materials (dielectric constant), liquids (surface tension, dielectric constant, conductivity), working conditions (voltage, frequency) and substrate wettability (contact angle). This large experimental space is firstly reduced using non dimensional numbers and then studied in a systematic way thanks to the design of experiments. The contact angle influence is explained thanks to a new analytical model. To summarize, this paper recalls analytical models used to predict the voltage threshold required to develop a liquid rivulet from a mother drop, taking the contact angle into account and providing a large set of experimental results.     

Experimental design and modelling in the investigation of PECVD parameters effects on the structural and gas transport properties of plasma polysiloxane membranes

The experimental design method was used to investigate the PECVD parameters effects on the properties of plasma polysiloxane membranes synthesized using octamethylcyclotetrasiloxane or hexamethyldisiloxane as monomers. On a wide experimental range and with a minimum number of experiments, the use of such a statistical tool enabled us to set up complete and reliable correlations, in the form of polynomial models connecting the gas transport properties (H₂ permeability coefficient, H₂/N₂ ideal selectivity) and the structural properties (growth rate, density, organic/inorganic nature) of synthesized films with the two most influent synthesis parameters of the PECVD process: the input power (represented by the input voltage) and the monomer flux. The polynomial models enabled us not only to statistically confirm the effects of the PECVD parameters displayed by previous classical experimental studies, but also to model, in the mathematical sense, the evolution of each property of materials taking into account the first and second orders effects of both PECVD synthesis parameters. By the use of a performing statistical tool, we managed to improve the knowledge of relations between synthesis parameters/structure/properties relative to our process.