1. Before each growth experiment, one cryovial from the freezer must be removed. The unfreezing procedure should be fast enough to decrease the damage produced by the intra-cellular ice. The microorganisms must always be observed under the optical microscope and also checked for purity. To subcultivate the microorganisms in the broth in which the growth curves are performed, the time and temperature of each subculture must be carefully maintained. To obtain the third preculture, at least three tubes are inoculated.
2. The spectrophotometer should be stabilized 15 min prior to use. Before centrifugation, the absorbance of the third preculture is determined (blank: sterile growth media) in order to gain an approximate notion of the cellular density. This step will allow rapid adjustment of the OD of the bacterial cell in the saline solution (blank: sterile saline solution). The OD54Q of the bacterial cell suspension (in saline solution) used as the inoculum is adjusted at 1.4 (equivalent to 108-109 CFU/mL) in order to begin with the same cellular concentration for the growth experiments.
3. HCL causes burns that are irritating to respiratory system. Caution: Work under a bell, with a propipet.
4. For the pH meter calibration, only the necessary amount of standard buffers is poured in the plastic bottles, and this volume is not returned to the original recipient. Between each pH determination, the pH meter should be on "stand-by," and the electrode should be washed and dried to avoid errors in the sample pH caused by an unclean electrode.
5. Check the initial pH of the LAPTg and MRS carefully before inoculation (or the previous day of the growth experiments).
6. The initial lactobacilli inoculum is 2% v/v (equivalent to 106-107 CFU/mL). This inoculum was previously selected from a tested range (from Q.1 to 10%), because the lag phase was much longer for those experiments performed with inocula lower than 2%. Although for inoculum values higher than 2% there was a decrease in the lag time, the growth curves were not acceptable from the practical point of view, because the final OD did not increase significatively, and also because the times needed to reach those values were not significantly shorter (19).
7. Inoculation of the Lactobacillus suspension in flasks containing the culture media is performed in a random order. The cultures are distributed into tubes from the flasks. The tubes are numbered from 1 to 18 and are later randomly chosen to perform the growth and bacteriocin determinations. For every point of the curve, one tube is removed from the water bath, to avoid the agitation and temperature variations of the flask that occurred when the samples are withdrawn from the same recipient.
8. The temperature of each incubator is controlled with a thermometer within Q.1°C of the set point. For the growth conditions corresponding to the fractional and complete experimental designs, three water baths are needed (at 30, 37, and 44°C).
9. In this incubation system, the temperature variation of lactobacilli culture is minimal because the samples are withdrawn every 3 h. The amount of shakers used depends on the number of blocks of the fractional design, with three being maximal.
10. For nonagitated cultures, every hour a tube is removed from the incubator and the OD measurements are performed in order to cover the entire growth curve time, but focusing mainly on the range in which the absorbance response changes significantly. For the agitated cultures, samples are withdrawn from the flasks every 3 h to minimize the time in which the flasks are outside the incubator.
11. The OD determination is a rapid, nondestructive, and inexpensive technique to measure bacterial growth, and it is useful in many areas of microbiology in which different growth conditions must be tested. The growth parameters can be accurately estimated from absorbance measurements (11,12).
12. The Gilford spectrophotometer was selected to obtain the absorbance data for lactobacilli growth, because of the following characteristics: absorbance range from 0.000 to 3.000 unit of OD (UOD), accuracy of the measurement of ± 0.005 UOD, and reproducibility ± 0.002 UOD. The OD measurements performed with this spectrophotometer are more accurate than those performed with the Spectronic 20.
13. The correction of initial turbidity of the growth media to absorbance value 0 (zero) should be performed before the OD determinations of lactobacilli cultures corresponding to each growth medium or pH, using different glass cuvets. The initial absorbance values of lactobacilli cultures are approx 0.090 ± 0.010 (above the detection threshold of the spectrophotometer used). The nonlinearity of the absorbance measurements was not corrected by diluting the cultures, because of the nonsignificant effect of this factor on the growth rate values previously quantified. This results are in agreement with studies performed by other authors (11,12).
14. An experimental design is an organized and efficient way to obtain data with different treatments. These designs also allow us to establish statistically whether the variations in answers of interest obtained through the application of the different treatments were produced by the action of these treatments, or whether they could be attributed to the randomization of the experimentation. In a factorial design, there are variables, called factors, with levels (at least two) controlled by the researcher to evaluate the variation of the observed characteristic when the value of one or more factors is modified. Other variables, with worthless effects and able to produce nonidentifiable perturbations on the observations, were not controlled by the fixation of levels, but by the randomization of the treatments to the experimental units. A complete factorial design is one used to explore all the possible combinations or treatments of the factors under study and their levels. For example, if a design has four factors with two levels in each one, the number of treatments of the complete design is 2 x 2 x 2 x 2 = 24= 16. A fractional factorial design, on the other hand, allows the utilization of only one fraction of the total of treatments, V2, V4, and so on. In the above example, instead of the 16 treatments used, only 8 or 4 can be used, selected in such a way that the results reflect an "equilibrated" design. Tables are published in books (20) or software (such as MINITAB) that allow one to obtain all the details of the designs for which the number of factors are consigned, for all the effects that can be studied, at two or three levels, and also at the central points.
15. The method of ordinary least squares uses as a loss function the sum of squares of differences between the observed and estimated values. In this function, the constants are the experimental determinations, and the variables are the parameters whose values we are attempting to determine. The least squares method proposes as estimators those parameter values that minimize the loss function.
16. Algorithm of minimization of the loss function: Rosenbrock/quasi-Newton algorithm. To find the minimum of a function, it is first necessary to calculate the first derived function with respect to each parameter and to set the results equal to zero. As the addition of squares sometimes results in an expression with a derived function that cannot be calculated explicitly, the computational algorithms are used to look for the minimal (maximal) of a function modifying their parameters according to pre-established norms. This technique rotates the space of the parameters and aligns one of the co-ordinated axes with the group of points that are around a minimal (maximal). The other axes are situated perpendicular to this one. If the loss function is unimodal and has groups of points around the minimal, the method will have very low error to this point. However, if the function has many peaks, the algorithm can take the results very far from the searched value.
17. The bootstrap method (software S-PLUS) is one of the estimation methods known as resampling, because it uses the sample values to generate a highest number of artificial samples. In the regression situation, the curve is first estimated from the original experimental data. Then the residual values (observed value less estimated value) are assigned randomly to the estimated values of the dependent variable. In this way, a sample different from the observations is obtained, which allows one to estimate another curve, which, if the residues present a regular behavior, should not be substantially different from the one obtained with experimental values. The new curve generates other residual values, which are again randomly assigned to the new estimated values. This process generates a third sample, and the process is again repeated, for example, 1000 times, in such a way that the empirical distributions of the parameter estimators are obtained. The mean value obtained will be used as the estimated value of the parameter, and its error will be calculated as the standard deviation of the values divided by the square root of the total number of generated values. By applying this method, it is possible to calculate the confidence intervals and to perform the test of hypothesis of the parameters by applying the empirical distribution, without making a restrictive hypothesis of normality.
18. The ANOVA method allows one to know whether the growth curves or the production of antagonistic substances for the different combinations of strains, growth media, agitation, pH, and temperatures present similar shapes throughout. If the answer is positive, an analysis is performed to detect if there are statistically significant differences between the data obtained from the different treatments. If the plots are statistically different throughout the time, data from a more reduced group are later compared.
This work was supported by grants from CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas), PIP 359, and from the Ministrio de Salud Pública de la República Argentina (beca Carrillo-Oñativia).
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