Three Quarter Plackett-Burman Designs for Estimating All Main Effects and Two-Factor Interactions

Plackett-Burman designs and three quarter fractional factorial designs are both well established in the statistical literature yet have never been combined and studied. Plackett-Burman designs are often non-regular and are thus subject to complex aliasing. However, Plackett-Burman designs have the advantage of run-size efficiency (over the usual 2^(k) factorials) and taking three quarters of a Plackett-Burman design further improves this benefit. By considering projections of these designs, we constructed a catalog of designs of resolution V and ranked by D-efficiency

Gradient Estimation Schemes for Noisy Functions

In this paper we analyze different schemes for obtaining gradient estimates when the underlying function is noisy.Good gradient estimation is e.g. important for nonlinear programming solvers.As an error criterion we take the norm of the difference between the real and estimated gradients.This error can be split up into a deterministic and a stochastic error.For three finite difference schemes and two Design of Experiments (DoE) schemes we analyze both the deterministic and the stochastic errors.We also derive optimal step sizes for each scheme, such that the total error is minimized.Some of the schemes have the nice property that this step size also minimizes the variance of the error.Based on these results we show that to obtain good gradient estimates for noisy functions it is worthwhile to use DoE schemes.We recommend to implement such schemes in NLP solversnonlinear programming;finite elements;gradient estimation

Experimental Design for Variable Selection in data bases

This paper analyses the influence of 13 stylized facts of the German economy on the West German business cycles from 1955 to 1994. The method used in this investigation is Statistical Experimental Design with orthogonal factors. We are looking for all existing Plackett-Burman designs realizable by coded observations of these data. The plans are then analysed by regression with forward selection and various classification methods to extract the relevant variables for separating upswing and downswing of the cycles. The results are compared with already existing studies on this topic. --

Statistical modelling optimisation of cellulase enzyme immobilisation on functionalised multi-walled carbon nanotubes for empty fruit bunches degradation

Cellulase obtained from the fermentation of sewage treatment plant sludge (STP) by Trichoderma-reesei RUT C-30 was covalently immobilised on functionalised multi-wall carbon nanotubes. Statistical optimisation using the Plackett–Burman design method was implemented to identify parameters with significant effects on the process of immobilisation. The results obtained from this Plackett–Burman design show that three parameters have a significant effect on immobilisation: pH, temperature, and N-ethyl-N-(3-dimethyl aminopropyl) carbodiimide hydrochloride (EDC) concentration. Based on our Plackett-Burman design results, these parameters were further optimised using a face-centred central composite design. The resulting optimum conditions for cellulase immobilisation, as determined by face-centred central composite design, were pH 4.5, 30°C, and 1 mL of 10mg/mL EDC. The amount of immobilised cellulase was approximately 98% using these optimum conditions. The resulting MWCNT-cellulase composite was further characterized by FTIR and SEM. The FTIR spectrum of MWCNT-cellulase composite showed an amide group peak (O = C-NH) corresponding to cellulase enzyme, which confirms that immobilisation took place

Optimization of Reaction Conditions in the Production of Gadolinium Diethylenetriamine Pentaacetate-Folate

A previous study has performed the laboratory-scale synthesis and characterization of Gadolinium Diethylenetriaminepentaacetate-Folate. Some parameters associated with the synthesis have been defined. In current study was focused on establishment the parameters for scaling up the production of Gadolinium Diethylenetriaminepentaacetate-Folate as a targeted MRI contrast agent. For the purpose of subsequent scaling up the synthesis, the parameters particularly those determining the yield of the reaction product should be established. This report presents the use of The Placket Burman Design and the Response Surface Methodology in establishing the parameters. Thus, following the Placket Burman Design, a number of synthesis reactions were carried out, each with different reaction conditions, with respect to parameters to include: mole ratio of reactants (i.e mole of Gd3+ to DTPA-Folate), time of reaction, temperature, stirring rate, pH and solvent volume. Using this method, a conclusion could be drawn that the three factors were found to be significant. To get final conclusions on the optimal synthesis reaction conditions, the Response Surface Methodology was then applied. For this purpose, again, some synthesis reactions experiments were performed. These were done, in accordance to the Response Surface Methodology, verified by analysis of countour plots, helped to locate the optimal value of the factors. The resulted data showed that for optimal yield of the synthesis reaction there were three dominant parameters. They were mole ratio of reactants, stirring rate process, and the volume of water

Medium optimization for endochitinase production by recombinant Pichia pastoris ZJGSU02 using response surface methodology

Plackett-Burman design and response surface methodology were employed to optimize the medium components for endochitinase production by Pichia pastoris. A Plackett- Burman design of seven factors with 12 runs was applied to evaluate the effects of different medium components. Yeast extract, oleic acid and Tween-80 were found to have significant influence on endochitinase production. The optimal concentrations of three factors were investigated by the response surface methodology using Box- Behnken design. The optimal medium components obtained for achieving the maximum activity of the endochitinase were as follows: Yeast extract 24.36 g/l, tryptone 20 g/l, YNB 5.0 g/l, potassium phosphate 100 mM, methanol 5 ml/l, oleic acid 1.758 ml/l, Tween-80 6.2 ml/l, Pichia trace metals (PTM1) 4.0 ml/ l and biotin 4.00 × 10-4 g/l. Under these conditions, endochitinase activity was up to 88.26 μ/ml, which was about 1.14-fold higher than using the original medium (77.62 μ/ml). This work will be very helpful for large-scale production of endochitinase for future industrial application.Keywords: Recombinant endochitinase, Plackett-Burman design, response surface methodology, fermentatio

Regression Models and Experimental Designs: A Tutorial for Simulation Analaysts

This tutorial explains the basics of linear regression models. especially low-order polynomials. and the corresponding statistical designs. namely, designs of resolution III, IV, V, and Central Composite Designs (CCDs).This tutorial assumes 'white noise', which means that the residuals of the fitted linear regression model are normally, independently, and identically distributed with zero mean.The tutorial gathers statistical results that are scattered throughout the literature on mathematical statistics, and presents these results in a form that is understandable to simulation analysts.metamodels;fractional factorial designs;Plackett-Burman designs;factor interactions;validation;cross-validation

Biossíntese da proteína Catecol-O-metiltransferase membranar humana: optimização com recurso a desenho experimental Plackett-Burman e composto central

Catechol-O-methyltransferase (COMT, EC 2.1.1.6) is an S-adenosyl-L-methionine-dependent methyltransferase enzyme that catalyzes the methylation of catechol substrates (catecholamines, catecholestrogens). Physiologically, it is responsible for the elimination of biologically active or toxic catechols, making it a protein with great clinical relevance as therapeutic target in serious disorders, like schizophrenia and Parkinson´s disease. To fulfill pharmaceuticals requirements, new strategies of optimization and large-scale production of COMT enzyme are crucial. Statistical optimization approaches have demonstrated their enormous value in laboratory and industrial scale, namely in biotechnological production processes, in which an incremental enhancement can be a perpetual improvement. In this work, we aimed the optimization of recombinant human membrane-bound COMT (hMBCOMT) enzymatic activity yields following a statistical optimization as a solving approach. Plackett-Burman design was used as a first optimization step to identify which factors have a significant effect in hMBCOMT productivity and activity levels, and Response Surface Methodology (RSM), by a Central Composite Design (CCD), to optimize the process. We applied Brevibacillus choshinensis cells for the biosynthesis of hMBCOMT and a semi-defined medium for cell growth. This medium was subjected to a first screening using the Plackett–Burman design to evaluate the influence of the culture parameters (chemicals and physicals) in hMBCOMT enzymatic activity levels. Enzymatic activity were measured in a high performance liquid chromatography (HPLC) coupled to a coulochemical detector. Among the eleven variables tested, polypeptone, ammonium sulfate, glucose and temperature were selected owing to their significant effect on human MBCOMT enzymatic activity. The biological human MBCOMT activity obtained with the semi-defined medium in Plackett-Burman design were very promising, while were higher than the obtained with 2SYNm medium, a traditional growth medium for Brevibacillus cells of this work. Typically, we obtained values of 93nmol/h for hMBCOMT total enzymatic activity and 30 nmol/h/mg of specific activity with protein in its native form, without the use of any kind of detergents on protein solubilization step. Based on the results of Plackett–Burman design, a CCD was adopted to define optimal components concentration and temperature in order to maximize our response. The CCD model presented a multiple correlation coefficient value of 0.635 and a significant lack of fit, showing the lack aptness of the model to the process optimization and the failure to attain the optimal concentration of each variable.Catecol-O-metiltransferase (COMT, CE 2.1.1.6) é uma enzima metiltransferase dependente de S-adenosil-L-metionina (SAM) que catalisa a metilação de substratos catecóis (catecolaminas, catecolestrogénios). Fisiologicamente, é responsável pela eliminação de catecóis biologicamente activos ou tóxicos, tornando-a uma proteína de elevado interesse clínico e utilizada como alvo terapêutico em doenças graves, como a esquizofrenia e a doença de Parkinson. Para suprir as necessidades farmacêuticas, novas estratégias de otimização e produção em larga escala desta enzima são fundamentais. Abordagens de otimização estatística têm demonstrado o seu enorme valor à escala laboratorial e industrial, nomeadamente nos processos de produção biotecnológicos, em que um pequeno detalhe melhorado pode significar um grande passo para o sucesso. Neste trabalho, objetivou-se a otimização do nível de atividade enzimática da proteína recombinante COMT, na sua forma membranar, através do recurso a modelos de otimização estatística como uma abordagem resolutiva. Numa primeira fase de otimização e de seleção dos fatores mais significativos para a atividade enzimática da proteína em estudo foi utilizada a técnica de desenho experimental Plackett-Burman. Após esta seleção foi aplicada a Metodologia de Superfície de Resposta (RSM), através de desenho composto central (DCC), para otimização da concentração dos fatores que revelaram ser mais significativos e, consequentemente, do processo. Foi utilizado o sistema de expressão Brevibacillus choshinensis para a biossíntese da proteína membranar COMT e um meio semi-definido para o seu crescimento. Este meio foi submetido a uma primeira triagem através do desenho experimental Plackett-Burman, avaliando-se desta forma a influência dos parâmetros de cultura (produtos químicos e físicos) nos níveis de actividade enzimática da COMT membranar. Os níveis de actividade enzimática foram medidos num sistema de cromatografia líquida de alta eficiência acoplado a um detector amperométrico. Entre as onze variáveis testadas, a polipeptona, sulfato de amónio, glucose e temperatura foram as variáveis selecionadas dado o seu significativo efeito na actividade enzimática da COMT membranar. Os níveis de atividade enzimática obtidos nesta primeira triagem revelaram-se bastante promissores, sendo mais elevados do que os obtidos com o meio 2SYNm, meio de crescimento mais comum para as células usadas neste trabalho. Foram obtidos valores de 93nmol/h para a actividade enzimática total e cerca 30 nmol/h/mg de actividade enzimática específica com a proteína na sua forma nativa, sem o uso de qualquer tipo de detergentes no processo de solubilização. Com base nos resultados do desenho Plackett Burman foi aplicado o desenho Composto Central para a otimização dos quatro fatores em causa a fim de maximizar a nossa resposta. Este apresentou um valor do coeficiente de correlação múltipla de 0,635 e uma falta de ajuste significativa, demonstrando a falta de adequação do modelo para a otimização do processo