Principle of a fractional factorial design for qualitative and quantitative factors: application to the production of Bradyrhizobium japonicum in culture and inoculation media

Abstract

Summary — To improve the production of Bradyrhizobium japonicum in liquid culture media, different carbon and nitrogen substrates at different concentrations were tested. In order to study simultaneously these qualitative and quantitative factors, a suitable experimental design was necessary. We develop here the principle leading to such fractional factorial designs. The specific design used allowed us to decrease the theoretical number of treatments from 1 024 to 128 and to get estimates of factorial main effects and 2-factor interactions. Five of the 7 tested factors, pH, carbon and organic nitrogen sources, yeast extract concentration and organic nitrogen concentration, were found to have a significant effect on optical density. They also were found to interact with each other. The design allowed us to select 2 media that produced more than 10 10 bacteria/ml.

Effect of Pulsed Electric Fields Treatment and Mash Size on Extraction and Composition of Apple Juices

“…A standard two factors design was used to estimate the effects of the mash size ( S ) as averaged particles volume and the field intensity of electric treatment ( E ) and the interaction between these quantitative factors at two levels. A general linear model including an analysis of variance was applied to the orthogonal polynomial model defined by eq to test the significance rate of the factors . italicX = a 0 + a 1 italicS + a 2 E + a 12 italicS × E in which a 0 , a 1 , a 2 , and a 12 are the constant and linear and interaction coefficients of the model, respectively.…”

Modeling the inhibition of Salmonella typhimurium growth by combination of food antimicrobials

“…These orthonormal polynomials, which have long been used to simplify the computations in polynomial regression, were initially defined and tabulated in Fisher and Yates (1957) and Pearson and Hartley (1976). Although their interest for calculation has now disappeared, their use is still highly recommended in the general context of polynomial regression to obtain meaningful parameters whose estimates are the least correlated possible (Kobilinsky, 1988;Cliquet et al, 1994). As indicated in Appendix B, they are normalized so as to make their coefficients, that is the factorial polynomial effects, comparable.…”

“…This adjustment was first made by fitting a polynomial. As seen in the case of aromatic compounds when AC = 0 (Section 5.2) this choice can be locally inadequate, but the adjustment is very easily handled even when there are many factors involved (Kobilinsky, 1988;Cliquet et al, 1994;Kobilinsky, 1997) and the procedure allows one to quickly find the main features of the data.…”

“…In many cases, it is more convenient to use lin x, quad x, cub x to denote the orthonormal polynomials R 1 (x), R 2 (x), R 3 (x) and then e(lin x), e(quad x), e(cub x) to denote the corresponding effects (Cliquet et al, 1994). This last notation is more in agreement with the one used for factorial effects in Appendix A and we use it in Fig.…”

Development of a Defined Medium for Pythium oligandrum Oospore Production

“…The design of experiments is an eYcient and economical method to study simultaneously a group of variable s and their interactions. Described in 1978 by Box et al, factorial designs have been used extensively in fermentation-relate d ® elds (Dumesnil et al, 1975;Cliquet et al, 1994;Buzzini, 2000).…”