Designs Suited for Varietal Trials with Multiple Basals

DAS (1960) gave a method of construction of confounded balanced asymmetrical factorial designs of the type v × 2² by using BIB designs. In the present paper a method has been given for construction of balanced asymmetrical factorial designs of the type (v–t) × 2² by using truncated balanced incomplete block designs obtainable by omitting t treatments. Likewise, partially balanced asymmetrical factorial designs can also be obtained by omitting any particular treatment alongwith its first or second associate treatments from the v treatments of a PBIB design. We can get a large number of new designs not available in literature through this technique. These designs are well suited for varietal trials with multiple basals.     

Fractional Plans to Estimate Main Effects and Two Factor Interactions Inclusive of a Specific Factor

Balanced incomplete block designs are used to construct non‐geometric 2ⁿ fractional factorial plans to estimate all n main effects and n – 1, 2 factor interactions with a specific factor included in each interaction. When the balanced incomplete block design is of Family (A), the resulting fractional factorial plan has the same number of runs as a fold‐over Hadamard matrix giving same variances for the estimates; however, some new designs are shown to be non‐isomorphic to the fold‐over Hadamard matrix plans.     

fullfact: an R package for the analysis of genetic and maternal variance components from full factorial mating designs

Full factorial breeding designs are useful for quantifying the amount of additive genetic, nonadditive genetic, and maternal variance that explain phenotypic traits. Such variance estimates are important for examining evolutionary potential. Traditionally, full factorial mating designs have been analyzed using a two‐way analysis of variance, which may produce negative variance values and is not suited for unbalanced designs. Mixed‐effects models do not produce negative variance values and are suited for unbalanced designs. However, extracting the variance components, calculating significance values, and estimating confidence intervals and/or power values for the components are not straightforward using traditional analytic methods. We introduce fullfact – an R package that addresses these issues and facilitates the analysis of full factorial mating designs with mixed‐effects models. Here, we summarize the functions of the fullfact package. The observed data functions extract the variance explained by random and fixed effects and provide their significance. We then calculate the additive genetic, nonadditive genetic, and maternal variance components explaining the phenotype. In particular, we integrate nonnormal error structures for estimating these components for nonnormal data types. The resampled data functions are used to produce bootstrap‐t confidence intervals, which can then be plotted using a simple function. We explore the fullfact package through a worked example. This package will facilitate the analyses of full factorial mating designs in R, especially for the analysis of binary, proportion, and/or count data types and for the ability to incorporate additional random and fixed effects and power analyses.     

Mathematical model for the alcoholic fermentation in batch culture: Comparison between complete and incomplete factorial (33) designs

Surface response methodology was used to study the effects of three variables, viz. total reducing sugars (116–222 g l^?1), yeast inoculum concentration (10–30%) and supplemented inorganic nitrogen as (NH₄)₂SO₄ (1–3 g l^?1) on the production of ethanol.The complete and incomplete factorial designs (3³) were compared through the residual analysis of variance. Since there was no statistically significant difference at the 5% level, on the basis of cost-efficiency and space limitations, it was recommended to use incomplete factorial design constituting 12 treatments with three repetitions in central point totalling 15 experiments which control the batch alcoholic fermentation.     

Application of fractional factorial designs to screen active factors for antibody production by chinese hamster ovary cells

With ever increasing need for cost-effective large-scale production of monoclonal antibodies, it is essential to develop highly productive and commercially viable processes. Previous research showed that growth and production capacity of the culture media can be improved by micronutrient supplements, such as insulin, vitamins, and growth factors. Since these micronutrients may not act independently of one another, factorial designs can expose critical interactions between nutrients as opposed to a serial approach of changing one factor at a time. In this study, fractional factorial designs were applied to observe the effect of several micronutrients on antibody production and culture longevity in shake flasks. Response surface designs were used to investigate the factors in depth and confirm the results of the fractional factorial study. The results demonstrate that fractional factorial design is an effective tool for rapid development of antibody-producing Chinese hamster ovary (CHO) cells.     

Hierarchical and factorial mating designs for quantitative genetic analysis in tetrasomic potato

Plant breeders need to quantify additive and non-additive components of genetic variance in order to determine appropriate selection methods to improve quantitative characteristics. Hierarchical and factorial mating designs (also known as North Carolina mating designs I and II, respectively) allow one to determine these variance components. The relative advantages of these two designs in the quantitative genetics of tuber yield in tetrasomic potato were investigated. Likewise, the number of female parents to include in design I was also investigated. Data were collected from two independent experiments at two contrasting Peruvian locations: La Molina in the dry coast and San Ramon in the humid mid-altitude. In the first experiment, although design I gave a negative digenic variance (σ² _D), this design provided almost the same estimate of narrow-sense heritability (h²) for tuber yield as that obtained in design II (0.291 and 0.260, respectively). Therefore, design I appears to be appropriate for quantitative genetics research in tetrasomic potato, a crop in which some clones are male sterile. The easy handling of crosses (distinct random females included in the crossing scheme) is another advantage of design I relative to design II. In the second experiment, 12 males were crossed with either two or four females following a design-I mating scheme. The additive genetic variance (σ² _A) was zero (or negative) when two females per male were included but was positive with four females. These results suggest that two females per male may not be enough for design I in tetrasomic potato. Four females per male are preferable to determine σ² _A in design I for this tetrasomic crop. Received: 19 March 2001 / Accepted: 3 July 2001     

Use of uniform designs in combination with neural networks for viral infection process development

This work aimed to compare the predictive capacity of empirical models, based on the uniform design utilization combined to artificial neural networks with respect to classical factorial designs in bioprocess, using as example the rabies virus replication in BHK‐21 cells. The viral infection process parameters under study were temperature (34°C, 37°C), multiplicity of infection (0.04, 0.07, 0.1), times of infection, and harvest (24, 48, 72 hours) and the monitored output parameter was viral production. A multilevel factorial experimental design was performed for the study of this system. Fractions of this experimental approach (18, 24, 30, 36 and 42 runs), defined according uniform designs, were used as alternative for modelling through artificial neural network and thereafter an output variable optimization was carried out by means of genetic algorithm methodology. Model prediction capacities for all uniform design approaches under study were better than that found for classical factorial design approach. It was demonstrated that uniform design in combination with artificial neural network could be an efficient experimental approach for modelling complex bioprocess like viral production. For the present study case, 67% of experimental resources were saved when compared to a classical factorial design approach. In the near future, this strategy could replace the established factorial designs used in the bioprocess development activities performed within biopharmaceutical organizations because of the improvements gained in the economics of experimentation that do not sacrifice the quality of decisions. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 31:532–540, 2015     

Production of a collagenase from Candida albicans URM3622

Culture conditions (pH, time, temperature, inoculum size, orbital agitation speed and substrate concentration) for an extracellular collagenase produced by Candida albicans URM3622 were studied using three experimental designs (one 2⁶⁻² fractionary factorial and two 2³ full factorial). The analysis of the 2⁶⁻² fractionary design data indicated that agitation speed and substrate concentration had the most significant effect on collagenase production. Based on these results, two successive 2³ full factorial design experiments were run in which the effects of substrate concentration, orbital agitation speed and pH were further studied. These two sets of experiments showed that all variables chosen were significant for the enzyme production, with the maximum collagenolytic activity of 6.8 ± 0.4 U achieved at pH 7.0 with an orbital agitation speed of 160 rpm and 2% substrate concentration. Maximum collagenolytic activity was observed at pH 8.2 and 45 °C. The collagenase was stable within a pH range of 7.2–8.2 and over a temperature range of 28–45 °C. These results clearly indicate that C. albicans URM3622 is a potential resource for collagenase production and could be of interest for pharmaceutical, cosmetic and food industry.     

Random and fixed effects in plant genetics

Summary A general model for any type of genetic entry is developed which takes into account both the factorial model of gene effects and the ancestral sources, whether inbred lines or outbred varieties, of the genes.Utilizing the model, various genetic designs of fixed entries are explored for the estimation of genetic effects and the testing of genetic hypotheses. These designs consisted of generation means — parents, crosses, various types of backcrosses, and so on — stemming from one or more pairs of parents, and of hybrid combinations from factorial mating designs. Limitations, from the standpoint of genetic effects that can be estimated and genetic hypotheses that can be tested, are developed in considerable detail.When entries from the factorial mating designs are considered to be random, attention is focused on the estimation of genetic variances, rather than effects, and on the concomitant changes in the tests of genetic hypotheses. While there is considerable improvement over fixed entries in the number of types of genetic variances that can be estimated, and of genetic hypotheses that can be tested, they are still very limited in contrast to what would be most desirable.Paper No. 6018 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh, North Carolina. This investigation was supported in part by NIH Research Grant No. GM 11546 from the National Institute of General Medical Sciences.Preliminary: This paper was presented at the 7th International Biometric Conference. Since then it has come to various people's attention and I have been encouraged to give it a wider distribution. Except for editing, the paper is essentially as originally written.     

Factorial design and response surface optimization of crude violacein for Chromobacterium violaceum production

Initially an eleven variable, sixteen assay 2^15–11 fractional factorial design, was used to determine the key factors in the production of violacein produced by Chromobacterium violaceum, CCT 3496. Subsequently five and three factor central composite designs were executed to determine response surfaces with the aim of optimizing cellular mass and crude violacein production. The 7.5 g l^–1 dry cell mass and 0.17 g l^–1 crude violacein productions obtained with our initial culture medium were increased to 21 g l^–1 and 0.43 g l^–1, respectively, for a medium investigated in the three factor design.     

Optimization of light and temperature for growing Chlorella sp. using response surface methodology

Summary The simultaneous effect of temperature and photon flux density on microalga Chlorella sp. growth was analysed by response surface methodology of two consecutive full factorial designs. Maximum specific growth rate was 0.128 h^-1 at 35°C and 2400 mol photon m^-2s^-1. A photoinhibition effect was observed at high photon flux densities with temperatures far below the optimum. Temperature was the main factor affecting specific growth rate.     

Guidelines for the design and statistical analysis of experiments in papers submitted to ATLA

In vitro experiments need to be well designed and correctly analysed if they are to achieve their full potential to replace the use of animals in research. An "experiment" is a procedure for collecting scientific data in order to answer a hypothesis, or to provide material for generating new hypotheses, and differs from a survey because the scientist has control over the treatments that can be applied. Most experiments can be classified into one of a few formal designs, the most common being completely randomised, and randomised block designs. These are quite common with in vitro experiments, which are often replicated in time. Some experiments involve a single independent (treatment) variable, while other "factorial" designs simultaneously vary two or more independent variables, such as drug treatment and cell line. Factorial designs often provide additional information at little extra cost. Experiments need to be carefully planned to avoid bias, be powerful yet simple, provide for a valid statistical analysis and, in some cases, have a wide range of applicability. Virtually all experiments need some sort of statistical analysis in order to take account of biological variation among the experimental subjects. Parametric methods using the t test or analysis of variance are usually more powerful than non-parametric methods, provided the underlying assumptions of normality of the residuals and equal variances are approximately valid. The statistical analyses of data from a completely randomised design, and from a randomised-block design are demonstrated in Appendices 1 and 2, and methods of determining sample size are discussed in Appendix 3. Appendix 4 gives a checklist for authors submitting papers to ATLA.     

Factorial and time course designs for cDNA microarray experiments

Microarrays are powerful tools for surveying the expression levels of many thousands of genes simultaneously. They belong to the new genomics technologies which have important applications in the biological, agricultural and pharmaceutical sciences. There are myriad sources of uncertainty in microarray experiments, and rigorous experimental design is essential for fully realizing the potential of these valuable resources. Two questions frequently asked by biologists on the brink of conducting cDNA or two-colour, spotted microarray experiments are 'Which mRNA samples should be competitively hybridized together on the same slide?' and 'How many times should each slide be replicated?' Early experience has shown that whilst the field of classical experimental design has much to offer this emerging multi-disciplinary area, new approaches which accommodate features specific to the microarray context are needed. In this paper, we propose optimal designs for factorial and time course experiments, which are special designs arising quite frequently in microarray experimentation. Our criterion for optimality is statistical efficiency based on a new notion of admissible designs; our approach enables efficient designs to be selected subject to the information available on the effects of most interest to biologists, the number of arrays available for the experiment, and other resource or practical constraints, including limitations on the amount of mRNA probe. We show that our designs are superior to both the popular reference designs, which are highly inefficient, and to designs incorporating all possible direct pairwise comparisons. Moreover, our proposed designs represent a substantial practical improvement over classical experimental designs which work in terms of standard interactions and main effects. The latter do not provide a basis for meaningful inference on the effects of most interest to biologists, nor make the most efficient use of valuable and limited resources.     

Enhancement of the bioavailability of an antihypertensive drug by transdermal protransfersomal system: formulation and in vivo study

Timolol Maleate (TiM), a nonselective β-adrenergic blocker, is a potent highly effective agent for management of hypertension. The drug suffers from poor oral bioavailability (50%) due to its first pass effect and a short elimination half-life of 4?h; resulting in its frequent administration. Transdermal formulation may circumvent these problems in the form of protransfersomes. The aim of this study is to develop and optimize transdermal protransfersomal system of Timolol Maleate by film deposition on carrier method where protransfersomes were converted to transfersomes upon skin hydration following transdermal application under occlusive conditions. Two 2³ full factorial designs were employed to investigate the influence of three formulation variables which were; phosphatidyl choline: surfactant molar ratio, carrier: mixture and the type of SAA each on particle size, drug entrapment efficiency and release rate. The optimized formulation was evaluated regarding permeation through hairless rat skin and compared with oral administration of aqueous solution on male Wistar rats. Optimized protransfersomal system had excellent permeation rate through shaved rat skin (780.69?μg/cm²/h) and showed six times increase in relative bioavailability with prolonged plasma profile up to 72?h. A potential protransfresomal transdermal system was successfully developed and factorial design was found to be a smart tool in its optimization.     

Application of Modified Organo-Nanoclay as the Sorbent for Zinc Determination by FAAS: An Optimization Study of an Online Pre-concentration System

An online column pre-concentration technique, coupled with flame atomic absorption spectrometry, was developed using a column filled with nanoclay modified with morin. For this purpose, zinc was determined in the water and biological samples. The sample solution was passed through the modified nanoclay column. The adsorbed zinc was subsequently eluted from the column with nitric acid solution. The optimization step was performed using two-level fractional factorial (2^5-2) and Box-Behnken designs. Firstly, the fractional factorial design was performed for preliminary evaluation of the significant factors. The results showed that pH, amount of morin, and concentration of eluent were significant. The Box-Behnken experimental design was carried out in order to determine the optimum conditions. The optimum conditions were found to be at pH 5.8, 1.8 mg L⁻¹ of morin and 3.0 mol L⁻¹ of eluent concentration. Under these optimum conditions, the limit of detection was found to be 0.11 μg L⁻¹. Furthermore, the relative standard deviation of the ten replicate determinations was <2.8.0%. The method was validated by analyzing the zinc using a certified reference material that is NRCC-SLRS-4 riverine water. The developed procedure was applied to the extraction and determination of zinc in the water and biological samples.     

Statistical optimization of culture media for production of phycobiliprotein by Synechocystis sp. PCC 6701

Synechocystis sp. PCC 6701 has a brilliantly colored pigment, phycobiliprotein containing phycoerythrin. Culture medium was optimized by sequential designs in order to maximize phycobiliprotein production. The observed fresh weights after 6 days were 0.58 g/L in BG-11, 0.83 g/L in medium for Scenedesmus sp. and 0.03∼0.52 g/L in the other tested media. Medium for Scenedesmus sp. was selected to be optimized by fractional factorial design and central composite design since the medium maintained a more stable pH within a desirable range due to higher contents of phosphate. The fractional factorial design had seven factors with two levels: KNO₃, NaNO₃, NaH₂PO₄, Na₂HPO₄, Ca(NO₃)₂, FeEDTA, and MgSO₄. From the result of fractional factorial design, nitrate and phosphate were identified as significant factors. A central composite design was then applied with four variables at five levels each: nitrate, phosphate, pH, and light intensity. Parameters such as fresh weight and phycobiliprotein contents were used to determine the optimum value of the four variables. The proposed optimum media contains 0.88 g/L of nitrate, 0.32 g/L of phosphate under 25 μE·m⁻²·s⁻¹ of light intensity. The maximum phycobiliprotein contents have been increased over 400%, from 4.9 to 25.9 mg/L after optimization.     

A Distribution-Free Multi-Factorial Profiler for Harvesting Information from High-Density Screenings

Data screening is an indispensable phase in initiating the scientific discovery process. Fractional factorial designs offer quick and economical options for engineering highly-dense structured datasets. Maximum information content is harvested when a selected fractional factorial scheme is driven to saturation while data gathering is suppressed to no replication. A novel multi-factorial profiler is presented that allows screening of saturated-unreplicated designs by decomposing the examined response to its constituent contributions. Partial effects are sliced off systematically from the investigated response to form individual contrasts using simple robust measures. By isolating each time the disturbance attributed solely to a single controlling factor, the Wilcoxon-Mann-Whitney rank stochastics are employed to assign significance. We demonstrate that the proposed profiler possesses its own self-checking mechanism for detecting a potential influence due to fluctuations attributed to the remaining unexplainable error. Main benefits of the method are: 1) easy to grasp, 2) well-explained test-power properties, 3) distribution-free, 4) sparsity-free, 5) calibration-free, 6) simulation-free, 7) easy to implement, and 8) expanded usability to any type and size of multi-factorial screening designs. The method is elucidated with a benchmarked profiling effort for a water filtration process.     

Application of factorial and Doehlert designs for optimization of protopectinase production by a Geotrichum klebahnii strain

Two successive factorial designs followed by two response surface methodology were applied to optimize protopectinase production by Geotrichum klebahnii. Factorial designs were used to study the effect of 11 variables (mineral pool and pH) on enzyme production. Only pH and Fe²⁺ had significant effect on the protopectinase production in the conditions of the assay, the interaction between them not being significant. According to this result pH and Fe²⁺ were multivariate according to a Doelhert design. The central points were pH 3.5 and Fe²⁺ 1.8 μmol L⁻¹. The results show a negative effect of pH and a positive (quadratic) effect of Fe²⁺ on enzyme production. The second Doelhert design was centered at pH 3.3. A relative maximum was obtained at pH 2.8 and Fe²⁺ 0.540 μmol L⁻¹, where the enzyme activity obtained was 236 U/mL. This value is two times higher than the value reported elsewhere.     

Comparative genetic analyses of metric traits using diallel and factorial mating designs in bread wheat

Summary For studying the inheritance of metric traits, diallel cross and factorial mating designs are commonly used. Since factorial mating design is less restrictive in crossing plans, the genetic information drawn from it was compared with that from a diallel cross. The comparison was made using graphical, genetic components and combining ability analyses for grain yield, grain weight and spike length in a field experiment of bread wheat (Triticum aestivum L.). Analyses were made on a nine parent diallel cross and a 4 × 5 factorial mating design which was sampled from the diallel cross. In general, there was a high degree of agreement between the results obtained from factorial mating design and diallel cross analyses showing thereby that the former provides almost equivalent genetic information to the latter.