2.1. Plackett–Burman design and BioLector growing conditions
The study assessed the effectiveness of eleven factors on bacterial
growth by designing a series of experiments employing Design of
Expert (Stat Ease Inc.) 7.0.0 software, resulting in 16 trial
configurations (Supplementary Table 1). This study aimed to scrutinize
the Rosetta™ 2 (DE3) the modified insulin strain’s growth kinetics
utilizing the BioLector (mp2-labs, Baesweiler, Germany) system. Two
distinct concentrations of LB broth media, precisely 30 g/L or 50 g/L,
were utilized, and a comprehensive DoE-PBD with 16 parameters was
executed in triplicate on a single plate (Fig. 1). The cells were then
inoculated for 4 h in each well, and the experiments were conducted
under constant agitation (800 rpm) at 37°C in 48-well FlowerPlates
(mp2-labs, Baesweiler, Germany) with a working volume of 1000 µL. This
study continuously monitored scattered light intensities to observe
growth kinetics in real-time (Fig. 1). Furthermore, the induction with
Isopropyl β-D-1-thiogalactopyranoside (IPTG) was performed in each well
at distinct final concentrations (0.2 mM, 0.3 mM, 0.4 mM) compliance
with DoE-PBD parameters, and was conducted overnight at 37°C. The final
insulin density, measured in grams per liter by UV/Vis spectrophotometer
(280 nm) and analyzed by SDS-PAGE, has been considered the response
variable and recorded in the PBD table (Supplementary Table 1; Fig. 1;
Supplementary Fig. 1). The statistical inference conducted on the data
revealed that the model under consideration attained statistical
significance, as deduced from a p -value of 0.05 and an R2
coefficient of determination of 85.37% (Table 1). Notably, the model
terms, encompassing MgSO4, glycerol, glucose, and LB
broth concentration were established to be influential factors, with
p-values that fell below the conventional threshold of 0.05 for
statistical significance. This observation suggests that these terms
exerted a substantial effect on the response variable. Moreover, the
F-statistic was employed to measure the magnitude of association between
each term and the response variable, where the outcomes showed that
higher F-values corresponded to stronger associations.
The half-normal plot is a graphical representation of the distribution
of the residuals in a regression model, which allows for the examination
of the normality assumption of the residuals(Zahn
et al., 1975) . In Fig. 2, a linear pattern in the half-normal plot
indicates that the residuals conform to a normal distribution.
Conversely, any deviation from linearity in the plot suggests that the
residuals deviate from normality, implying that the normality assumption
has been violated. Following the standardized effect, the half-normal
plot depicts the relative significance of the independent variables in a
regression model, where the percentage probability of the standardized
effect for the MgSO4, glycerol, glucose, and LB broth
concentration values are more substantial than those of the other
variables
(Fig.
2).
A Pareto chart also serves as a graphical representation of the
standardized effect exerted by each independent variable on the response
variable (Kenett 1991 ). The effectiveness of the factors is
gauged by employing two statistical thresholds, namely theBenforrini limit and t-value limit, both of which are ascertained
at 3,898 and 2.306, respectively, for a significance level (α) of 0.05.
The Pareto chart elucidates the magnitude of the standardized
effects via bars, with the four bars exhibiting the most prominent
values corresponding to MgSO4, glycerol, glucose, and LB
broth concentration, thereby attesting to their paramount significance
in influencing the response. Consequently, these four variables were
shortlisted for the optimization of the experimental design by applying
the CCD approach, a popular RSM technique
(Fig.3).
The perturbation plot serves as a valuable instrument for discerning and
juxtaposing the effects of multiple factors within a given point in the
design space (Bonnans and Shapiro, 2013 ). It facilitates the
visualization of the response by systematically varying a singular
factor across its entire range while upholding the constancy of all
other factors (Bonnans and Shapiro, 2013 ). A comprehensive
elucidation of the influences exerted by the immediate and interactive
effects of independent variables on insulin yield was attained through
the utilization of perturbation plots. The perturbation plot (Fig. 4)
visually represents the direct effects of variables C, D, E, and H on
insulin yield.