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A Rapid Method for Performing a Multivariate Optimization of Phage Production Using the RCCD Approach

Bacteriophages can be used in various applications, from the classical approach as substitutes for antibiotics (phage therapy) to new biotechnological uses, i.e., as a protein delivery vehicle, a diagnostic tool for specific strains of bacteria (phage typing), or environmental bioremediation. The demand for bacteriophage production increases daily, and studies that improve these production processes are necessary. This study evaluated the production of a T4-like bacteriophage vB_EcoM-UFV09 (an E. coli-infecting phage with high potential for reducing environmental biofilms) in seven types of culture media (Luria–Bertani broth and the M9 minimal medium with six different carbon sources) employing four cultivation variables (temperature, incubation time, agitation, and multiplicity of infection). For this purpose, the rotatable central composite design (RCCD) methodology was used, combining and comparing all parameters to determine the ideal conditions for starting to scale up the production process. We used the RCCD to set up the experimental design by combining the cultivation parameters in a specific and systematic way. Despite the high number of conditions evaluated, the results showed that when specific conditions were utilized, viral production was effective even when using a minimal medium, such as M9/glucose, which is less expensive and can significantly reduce costs during large-scale phage production.


Introduction
Phage therapy applies bacteria-infecting viruses, also called phages, to control bacterial infections [1,2]. Since its discovery in the early 20th century, the potential of phages to treat bacterial diseases was quickly recognized. Several studies involving phage cocktails that successfully treated diseases such as cholera, typhoid, and dysentery were developed worldwide in an era before antibiotics. Unfortunately, even with the development of commercial phage-based products, the still insufficient understanding of viral mechanisms, the misuse of phage cocktails over the years, and lastly, the discovery of penicillin mean that phage therapy has almost completely stopped being used [1][2][3][4]. Recently, due to the increase in multidrug-resistant (MDR) bacterial strains, the need for alternative methodologies for controlling pathogenic bacteria has resurfaced, making phage therapy a good alternative [1,3,4]. Although the application of phages for treatment in humans is still re-emerging, essential projects such as the "center for innovative phage applications and therapeutics", of the UC San Diego School of Medicine in the United States, the Phagoburn (European Union financed clinical study) and the Eliava Phage Therapy Center in Georgia such as Escherichia coli. This medium contains several precursors and amino acids that promote high-speed bacterial growth, with a generation time of 20 minutes [42,43]. Despite these advantages, large-scale viral propagation using the LB medium would lead to high manufacturing costs. Alternatively, another less costly culture medium for bacterial growth could be used [33,36]. The minimal medium M9 is composed primarily of salts, ions, and a carbon source and costs almost thirty times less than the LB medium [44]. Although the carbon source is one of the most critical aspects during phage production, other operational parameters can also strongly influence the phage concentration at the end of the process [33,38]. Several studies evaluate how temperature, incubation time, agitation, and MOI can affect viral production, but most of them were performed with only one variable at a time [38,[45][46][47][48][49] and do not consider the influences of these parameters in different medium compositions. To improve phage production in bioreactors, understanding how these variables interact with each other is fundamental for knowing which ones will most affect viral particle production or turn the process economically viable.
Previous analysis has shown that the phage vB_EcoM-UFV09 (Myoviridae family, Tequatrovirus genus) effectively decreased sulfate-reducing bacteria biofilm formed in a continuous flow system (data not shown). This study presents a fast method for analyzing several culture conditions, aiming to optimize the achievement of more advantageous start-up conditions for large-scale phage production. The rotatable central composite design (RCCD) is a statistical approach used to combine different variable levels systematically [36,[50][51][52]. Here, we used the RCCD to determine the best cultivation conditions, or at the very least, to find any indication as to which parameter combinations may produce the best viral yields in a small volume. Our research aimed to establish a starting point for large-scale production, evaluating only the most favorable conditions, thus reducing the number of steps, costs, and time needed to achieve the complete optimized process. The results showed that some carbon sources are preferable for phage production (and that this has no relation to the number of carbon atoms), that some parameter combinations have an antagonistic behavior, and that the model equations were able to indicate the best culture conditions for phage production, at least on the bench scale.

Bacterial Growth Kinetics
Bacterial growth in LB medium can be approximately 30 times more expensive than in M9 medium, using glucose or sodium acetate as a carbon source (see Section 4.2). The growth kinetics of E. coli 30 in M9 and LB media were evaluated. Based on their growth curves, the natural logarithm (ln) of the slope during the exponential growth phase was used to obtain the intrinsic rate of bacterial growth (µ) in each medium ( Figure 1 and Table 1). This analysis allowed the determination of which medium provided the shorter bacterial generation time (g), with more effective growth. The LB medium provided the best growth conditions, with µ being almost four times higher (µ = 1.475) than the best minimal medium evaluated (M9/Glucose, µ = 0.3737), and 8.35 times higher than the poorest minimal medium condition (M9/Acetate, µ = 0.1763). Moreover, the population density in the LB medium (correlated with the OD 600 values obtained after 24 h of incubation) was more than two times higher than the minimum medium with the highest OD 600 value (M9/Glucose, OD 600 = 1.17), and almost five times higher than the minimal medium with the lowest OD 600 (M9/Succinate, OD 600 = 0.54). Considering the µ values (Table 1), the patterns of bacterial growth curves, and especially the OD 600 values, it was possible to observe three distinct behaviors in the overall growth rates ( Figure 1). The first one shows the highest growth effectiveness, where the LB medium stands out both for the higher OD 600 value and for the best µ. The second group demonstrated intermediate effectiveness (M9/Glucose, M9/Glycerol, M9/Lactate, and M9/Pyruvate), and the third showed low bacterial growth (M9/Acetate and M9/Succinate). possible to observe three distinct behaviors in the overall growth rates ( Figure 1). The first one shows the highest growth effectiveness, where the LB medium stands out both for the higher OD600 value and for the best μ. The second group demonstrated intermediate effectiveness (M9/Glucose, M9/Glycerol, M9/Lactate, and M9/Pyruvate), and the third showed low bacterial growth (M9/Acetate and M9/Succinate).

Impacts of Operational Cultivation Variables on Bacteriophage Production
After the 28 assays were performed for each medium individually, it was possible to determine the equation that best synthesizes the influence of the four variables (temperature, incubation time, agitation, and MOI) on the final viral particle production and how these factors are related to each other. The results obtained from the titrations (Table S3) were logarithmized (log 10 ). Table 2 presents the regression coefficients obtained by the surface response regression, and Table 3 presents the equations of the quadratic polynomial model predicted by these results. The equations were used to understand the influence of the variables on viral production, statistical analysis, response surface graphs (Figure 2), and production estimates ( Figure 3).
The presence of the quadratic term in the equations allows the establishment of the optimal value of this variable, aiming for the highest production possible. This value is reached by resolving the derivative equation of this term. b The presence of two variables multiplied by each other in the same term is considered an interaction between these variables (as occurred in M9/Glucose, with the interval "−4.52*X 3 X 4 "). If this interaction has a negative sign, this indicates that the variables involved are antagonistic; thus, production is best when combining the highest value of one and the lowest value of the other, or vice versa. If an interaction has a positive sign, this indicates that the variables involved are synergistic, and the output is best when the highest value or the lowest value of both are combined. When one of the evaluated cultivation variables is not significant for the production model, it means that when using any value within the range of the experiment, the final production will be the same. The M9/acetate, M9/Lactate, and M9/Pyruvate media were not influenced significantly (P > 0.05) by any variable. Because of this, no response surface graph was obtained for these media ( Figure 2).
Cultivation variables that were significant in each experimental unit are summarized in Table 4. MOI was the most significant variable influencing the phage progeny production in three of the seven carbon sources evaluated (3/7; 42.85%), followed by agitation (2/7; 28.57%), which was represented in two carbon sources. Both incubation time and temperature were only significant in one medium: (1/7; 14.28%).  The M9/acetate, M9/Lactate, and M9/Pyruvate media were not influenced significantly (p > 0.05) by any variable. Because of this, no response surface graph was obtained for these media ( Figure 2).
Cultivation variables that were significant in each experimental unit are summarized in Table 4. MOI was the most significant variable influencing the phage progeny production in three of the seven carbon sources evaluated (3/7; 42.85%), followed by agitation (2/7; 28.57%), which was represented in two carbon sources. Both incubation time and temperature were only significant in one medium: (1/7; 14.28%).

Multiplicity of Infection (MOI)
Acetate indicates that the variable influenced the response (by F test; p-value < 0.05); "-" indicates that the variable was not significant.
When a quadratic term is significant in an equation, it is possible to establish the optimal value of this variable, which is reached by solving the derivative equation of this term. This happened in all the media in which the MOI was significant (0.144 PFU/mL in M9/glucose; 0.052 PFU/mL in M9/glycerol, and 0.048 in M9/succinate). If more than one variable is significant in the production process, it is possible to determine how they correlate and influence the final product from the surface response graphs. In the LB medium, the variable that significantly influenced the production was the incubation time ( Figure 2C). The resolution of the derivative quadratic term allowed us to predict the ideal incubation time, which was 9 h and 15 min. Phage production in the M9/Glucose minimal medium was influenced by agitation and MOI ( Figure 2B). In this medium, agitation and MOI showed a negative interaction with each other: if a reduced agitation was used, a high MOI value was required; on the other hand, if high agitation was used, a lower MOI is needed to achieve reasonable production rates. The optimal MOI number, calculated from the derivative of the quadratic term, was 0.144.
Unlike the other carbon sources, the M9/Succinate medium was influenced by three variables ( Figure 2D). From the linear regression equation, it is possible to infer that temperature presented an antagonistic effect on agitation, and the best results were obtained with the combination of low agitation and high temperature. The optimal calculated MOI was 0.0482. The positive value of the incubation time indicates that more extended experiments produced more phage particles; however, the absence of quadratic terms makes it impossible to determine the optimal production time for the other variables.

Prediction of Viral Particle Production in Different Culture Media
Using the best cultivation conditions obtained by the adjusted equations of the experimental units, the production potential of each medium was predicted ( Figure 3). Lower values of the coefficient of determination (R 2 ) represent a minor influence for this variable on phage production and a less accurate data prediction. In M9/Acetate, M9/Pyruvate, and M9/Lactate, the prediction was not possible since no culture variable was significant. Therefore, the values shown are based exclusively on the observed experimental phage production. The media M9/Glycerol, M9/Succinate, and LB showed a similar predicted potential of viral production, but the M9/Glucose medium had the best production values.

Validation of The Mathematical Model
The first assay (Treatment 1) used the best conditions predicted by the model and was the condition that showed the highest yield in absolute numbers, about 1.1 × 10 10 ( Figure 4). Treatment 2 produced fewer phages than the first treatment, with a final mean titer of 3 × 10 9 PFU/mL, and Treatment 3 produced the smallest number of phages, approximately 6.4 × 10 8 PFU/mL. While in Treatment 1, the final number of phages recovered was about 405 times higher (~2.5 logs) than the number of inoculating phages, in Treatment 2 this amount was 16,200 times higher (~4 logs), and in Treatment 3 more than 400,000 times higher (~5 logs). Although the lower MOI produced a smaller viral number, it was in this assay that the most significant difference between the number of recovered and inoculated phages was identified, and consequently, where the best proportional yield occurred. It is essential to highlight that with an extra 1.5 h of incubation, the phage number produced using Treatment 3ʹs conditions became statistically equal to that observed in Treatment 1. Finally, to prove that the RCCD approachʹs modeling is reliable and can predict, or at least indicate, good conditions for a bioprocess, we performed the assay with the worst conditions predicted. These cultivation conditions had the same MOI as Treatment 3, but with different temperatures and agitation. The results ( Figure 4) showed that these modifications were sufficient to decrease the phage production significantly, since in Treatment 4 the number of phages recovered was 1.26 × 10 7 , a number 51 times smaller than that found in Treatment 3.

Validation of The Mathematical Model
The first assay (Treatment 1) used the best conditions predicted by the model and was the condition that showed the highest yield in absolute numbers, about 1.1 × 10 10 ( Figure 4). Treatment 2 produced fewer phages than the first treatment, with a final mean titer of 3 × 10 9 PFU/mL, and Treatment 3 produced the smallest number of phages, approximately 6.4 × 10 8 PFU/mL. While in Treatment 1, the final number of phages recovered was about 405 times higher (~2.5 logs) than the number of inoculating phages, in Treatment 2 this amount was 16,200 times higher (~4 logs), and in Treatment 3 more than 400,000 times higher (~5 logs). Although the lower MOI produced a smaller viral number, it was in this assay that the most significant difference between the number of recovered and inoculated phages was identified, and consequently, where the best proportional yield occurred. It is essential to highlight that with an extra 1.5 h of incubation, the phage number produced using Treatment 3's conditions became statistically equal to that observed in Treatment 1. Finally, to prove that the RCCD approach's modeling is reliable and can predict, or at least indicate, good conditions for a bioprocess, we performed the assay with the worst conditions predicted. These cultivation conditions had the same MOI as Treatment 3, but with different temperatures and agitation. The results (Figure 4) showed that these modifications were sufficient to decrease the phage production significantly, since in Treatment 4 the number of phages recovered was 1.26 × 10 7 , a number 51 times smaller than that found in Treatment 3.

Discussion
Both the OD600 values and the intrinsic growth rate of the E. coli 30 in the LB medium were higher than in the M9 media supplemented with glucose or glycerol (the minimal media with the best growth rates). Our results are similar to those found in other studies that also used complex and minimal media with different carbon sources (including the gluconeogenic ones), and the variations observed in bacterial growth can be explained by differences in the energetic balance, metabolic precursors, and ATP production of each growth medium [53,54]. Some studies correlated medium richness with high phage production and used complex media to perform the experiments [55,56]. However, the use of these media is incompatible with large-scale production, mainly due to elevated production costs. This study showed that even using minimal media, a high phage production can be obtained if the growth conditions (such as temperature, agitation, incubation time, and MOI) are adequately controlled and optimized. For instance, it was

Discussion
Both the OD 600 values and the intrinsic growth rate of the E. coli 30 in the LB medium were higher than in the M9 media supplemented with glucose or glycerol (the minimal media with the best growth rates). Our results are similar to those found in other studies that also used complex and minimal media with different carbon sources (including the gluconeogenic ones), and the variations observed in bacterial growth can be explained by differences in the energetic balance, metabolic precursors, and ATP production of each growth medium [53,54]. Some studies correlated medium richness with high phage production and used complex media to perform the experiments [55,56]. However, the use of these media is incompatible with large-scale production, mainly due to elevated production costs. This study showed that even using minimal media, a high phage production can be obtained if the growth conditions (such as temperature, agitation, incubation time, and MOI) are adequately controlled and optimized. For instance, it was observed that carbon sources with fewer carbon atoms did not necessarily lead to insufficient phage production. They behaved in a non-linear form during the trials, showing high and low progeny for different growth conditions. Despite the highly efficient bacterial growth in the LB medium, phage production in this medium was very similar (or even lower) to other minimal media under some cultivation conditions (Table S2).
Bacterial species have an optimal growth temperature. This key parameter can alter the host physiology and cell membrane structure and affect the availability of phage receptors on the cell surface, decreasing viral infection rates and altering the phage latency time and burst size [36,42,69]. Analyzing the equation (Table 3), it was possible to observe that temperature was significant only in the M9/Succinate ( Figure 2D) medium-where the highest amount of virus was recovered in a temperature close to the optimal for the host growth. One possible reason why this term is significant only in one cultivation condition is that the temperature values utilized in this work were within those used for E. coli growth [70], and because of this, the bacterial growth remained in a range that did not affect the viral propagation.
Agitation is another crucial aspect of phage infection. In addition to its important role in the aeration dynamics and oxygen availability, it increases the probability of contact between the phage particles and the host cells, leading to an irreversible attachment beginning the infection process [33,39,71]. However, if the agitation is too intense, the phage tails can be broken while the absorption process inhibits the infectious process [72]. The equation obtained from the M9/Glucose (Table 4) showed precisely this interaction between the terms MOI and Agitation, with a negative correlation. A reduced number of phages requires higher agitation to achieve good phage production, probably due to the improved contact between phage and cell host at lower phage concentrations (low MOI). However, when the MOI utilized was high, the results indicated that intense agitation was not necessary. The highest agitation also resulted in decreased phage production in M9/Succinate. Agitation was only significant in M9/Glucose and M9/Succinate ( Table 4). The minimal agitation evaluated was enough for infection to be established in all media and, as mentioned before, high agitation reduced the adsorption rate in M9/Glucose and M9/Succinate, probably because of broken phage tails or due to the difficulty of establishing stable adsorption between phage and host [33,72].
Incubation time only influenced the LB medium (Table 3 and Figure 2C). A direct relation was observed, with the increment in incubation time resulting in a corresponding increase in phage production, probably due to a characteristic physiological state of the cells growing in these different carbon sources [69,73]. The nutritional richness of the LB medium provides a high density of host cells, which allows several viral replicative cycles; on the other hand, the complexity of succinate allows for slow but continuous cell growth and more time until a steady state is achieved and phage production is stable throughout the bacterial growth [44,45,74].
When a variable had no significant influence on growth conditions, it was assumed that the production would be the same regardless of the value tested. If viral production was similar at the shortest and longest incubation times, it was assumed that there is no need for long incubation periods, thus optimizing production since less time will achieve the exact yield. Incubation time was not significant for most carbon sources, suggesting that when other cultivation variables were used at their best values, the minimum incubation time evaluated (four hours) was sufficient for the phage to establish an equilibrium state with the bacterial host. The phage-host dynamics have been investigated exten-sively [75][76][77][78][79][80], and, more specifically, the achievement of a stable state between populations may explain the maintenance of the same viral titer from the completion of the first four hours until the end of experiment (12 h) [78,80]. The rapid arrival of the equilibrium state in our study can be explained by the small experimental volume in which the experiments were conducted (5 mL) [33,81,82].
The multiplicity of infection (MOI) is probably one of the most critical cultivation variables for phage production in bioreactors. It will determine the dynamics of infection between the virus and host, and consequently, the batch time until the maximum number of viral particles can be obtained [33,39,83]. When a higher number of phage particles was used (MOI of 1 or more), the equilibrium state was reached quickly since it is statistically likely that all cells present in the bioreactor will be infected, and there will not be enough cells left for subsequent rounds. However, if inoculation occurs with a low phage number (MOI of 0.1 or less), the equilibrium state takes longer to achieve, and more infection cycles occur until populations stabilize [33,39]. Due to this behavior, it is necessary to consider the most advantageous production model: a short batching time coupled with a high initial MOI, or a small viral inoculum at the beginning of the process, but with a longer batching time [33,39]. In this study, MOI was significant in the M9 media supplemented with succinate, glycerol, and glucose, considering the incubation times used in this work.
After all, the significant terms had been identified, and the equations obtained, it was possible to predict the probable viral production in each culture medium using the cultivation parameters indicated by the models (Figure 3). Most of the growth media presented a similar production, except the M9/Glucose, whose production estimate was considerably higher than the others. Although other studies evaluating phage production using minimal medium enriched with glucose have shown promising results, none of them have achieved a production level like that indicated by this prediction [33,38], which was also the case with the experiments performed with this medium in the present work (Table S2). It is important to remember that mathematical predictions do not consider the biological limitations of the organisms involved. Although the model indicates a production potential of 10 25 PFU/mL in the M9/Glucose medium, we know that this value is biologically and physiologically impossible to achieve.
The M9/Glucose medium was considered the best medium (based on the phage titer obtained experimentally, the production costs, and yield predicted for each carbon source) for the next steps of our scale-up process and was used to validate the generated mathematical model. The experiments conducted using the best conditions predicted by the models did produce the most significant number of viral particles (Treatment 1; Figure 4). The experiments performed under ideal conditions but with intermediate and low MOI values (Treatments 2 and 3; Figure 4) resulted in a proportionally smaller number of viral particles recovered at the end of the experiments, but with a more significant difference between the number of phages harvested and the number of inoculated phages. These results can be explained by the establishing of a steady state between the phage and bacterial populations, or perhaps more time is needed to establish the steady state [33,39]. With an additional 1.5 hours of incubation, the number of phages produced by Treatment 3 became statistically equal to Treatment 1. These results are similar to other studies involving phage production and show that MOI is an essential factor to be considered at the beginning of large-scale phage production since it is this variable that will control the number of infection cycles and the batch time [33,39,83]. The worst conditions predicted by the model were also tested (Treatment 4; Figure 4) and resulted in the lowest viral progeny of all the conditions evaluated. This cultivation procedure had the same MOI as Treatment 3 but with different values for other operational parameters (temperature and agitation). These results show that operational modifications were sufficient to cause a considerable decrease in the phage yield (since the number of recovered phages in Treatment 4 was 51 times smaller than that found in Treatment 3). All these findings demonstrate the efficiency of this method for considering the synergistic and antagonistic effects of the different parameters and for indicating the ideal conditions for starting the optimization of large-scale phage production.
Although other studies have already used different growing conditions to determine critical parameters for phage production, our study is the most extensive concerning different combinations of carbon sources and cultivation parameters [29][30][31][32][33]. Although pharmaceutical legislation does not contemplate the particularities of using viruses as bacterial control platforms, we believe that the increasingly influential and encouraging perspectives brought about by phage therapy force the recognition of this methodology as a viable and valuable alternative that requires attention [8,9]. In this way, studies investigating the large-scale production of different phages are essential, since their use is relevant not only in clinical, but also in an environmental and industrial context. This requires much more demanding concentrations and production volumes than simple laboratory production.
We therefore consider that studies like ours clarify that a global optimization of phage production is highly unlikely (since it will be dependent on the host, the culture medium, and the phage used) but that mathematical methodologies such as RCCD can help in the fast and robust determination of the parameters that will interfere in the system under study, helping to facilitate the entire production process.

Bacterial Strain and vB_EcoM-UFV09 Phage
The propagation of the bacteriophage vB_EcoM-UFV9 was performed using the bacterial strain E. coli 30 isolated from an acute bovine mastitis infection provided by the Brazilian Agricultural Research Corporation (EMBRAPA), which previously proved to be a significant biofilm former [84]. The phage was isolated from water samples taken from the São Bartolomeu River (−20.73094 S and −42.88922 W, using the World Geodetic System WGS84 as datum) in the municipality of Viçosa, Minas Gerais state, Brazil. This isolate is part of the microorganism collection at the Molecular Immunovirology Laboratory (LIVM) at the Federal University of Viçosa (UFV), Viçosa, Minas Gerais state, Brazil. The phage genome was sequenced, and the sequence has been submitted in GenBank under the accession number: 2462144.

M9 Minimal Medium
The M9 minimal medium was prepared according to the protocol described by Sambrook and Russel (2001), with a few modifications (12.8 g of Na 2 HPO 4 .7H2O; 5 g of KH 2 PO 4 ; 0.5 g of NaCl; 1 g of NH 4 Cl; 20 mL of MgSO 4 (0.1 M); 200 µL of CaCl 2 (0.5 M); 4 g of a carbon source; and distilled water to complete the volume of 1L). Different carbon source concentrations were evaluated, based on the literature (0.2, 0.3 and 0.4%), and 0.4% w/v was chosen since a decrease in bacterial growth in the lower concentrations was observed, probably associated with carbon source limitations. The highest concentration evaluated (0.4%) was not a bottleneck to bacterial growth (the presence of residual carbon source was assessed using an HPLC). LB broth is a widely used commercial culture medium and was used as the control. Seven culture media were evaluated: six distinct forms of the M9 minimal medium, varying the carbon sources (acetate, lactate, pyruvate, glycerol, succinate, and glucose), and the LB broth (Kasvi, São José do Pinhais, PR, Brazil). Table 5 simulates the production costs of the different culture media used in E. coli growth.

Bacterial Growth Kinetics
The growth kinetics of E. coli 30 in the M9 (with the six different carbon sources) and LB media were compared to evaluate the intrinsic growth rate of this isolate in the different media and carbon sources. An aliquot of grown bacteria (from a single colony, inoculated into the respective media and kept overnight at 37 • C and 150 rpm) was added to a 50-mL tube with 7 mL of sterile medium until the OD 600 reached 0.1. The experiment was performed at 37 • C and 180 rpm agitation. During the incubation period, 300-µL aliquots of each medium were taken at different times (fixed intervals), using the SP-1105 Spectrophotometer (Shanghai Spectrum Instruments Co., Shanghai, China) to monitor the optical density (OD 600 ).

Assembly of RCCD Experiments
The bacterial inoculum was previously grown in each culture medium until it reached an OD 600 of 0.7. Then it was added to a 50 mL tube and diluted with the corresponding culture medium until it reached an initial OD 600 of 0.1 (approximately 3 × 10 8 colonyforming units-CFU/mL) to a 5 mL final volume. These cultures were then subjected to the different cultivation conditions predicted by the RCCD (Table S1). The quantification of viral particles (expressed as plaque-forming units per mL, PFU/mL) was made at the end of each experiment using a well-established double-agar overlay plaque assay. Briefly, 100 µL of each sample were collected, and serial dilutions were performed at the ratio of 1:10 using SM buffer (5.8 g of NaCl; 2 g of MgSO 4 ; 6 g of Tris.HCl; 1 g of powdered gelatin; distilled water to 1 L, with the pH adjusted to 7). A total of 100 µL was withdrawn and mixed with 700 µL of an E. coli 30 culture grown the previous night from each dilution. This suspension was mixed with 5 mL of top agar LB medium (0.7% agar) and then poured into a plate with solid agar (1.4% agar).

Statistical Analysis and Elaboration of Surface Response Graphs
Linear regression (Response surface regression) was applied to each experimental unit to determine the significant terms (variables). The steps to perform this analysis in Minitab were: Stats > DOE (Design of experiments) > Surface response > Analising an Experiment of Surface Response > Answers (Y = logarithmized (log10) phage titre values (PFU/mL) observed). All others parameters were kept as defaults. The final equation models were obtained, and the analyses were performed. Optimization criteria were set to maximize phage production (PFU/mL). The equations derived from each experimental unit allowed the generation of surface response graphics (Stats > DOE (Design of experiments) > Surface response > Surface response graphs), which summarize the influence of the significant variables about the phage particle number and aid in understanding how these variables correlated during the production process. The R 2 value represents how the independent variables explain much variation in the response variable (viral production). The closer these values are to 100%, the more the results correspond to the influence of these significant variables present in the equation. The equations make it possible to understand how each variable influenced phage production (i.e., positively or negatively) and if the interactions between them had an antagonistic or synergistic effect. They were used to interpret and produce the surface response graphs.

Prediction of Viral Particle Production in Different Culture Media
The Minitab software (Minitab, Inc., State College, PA, USA) "predict" tool was used to calculate the phage titer that can be mathematically obtained under the different conditions evaluated (Stats > DOE (Design of experiments) > Surface response > Predict). This analysis is based on the equations obtained for each culture medium and uses the best combinations of the culture parameters to predict the amount of phage that can be produced at the end of a batch.

Model Validation
To validate the model predicted and to evaluate the impact of MOI on phage production, some additional experiments were performed, all with four hours of incubation time, and the same culture medium described previously. The mathematical model was validated for the medium that presented the best potential for commercial use based on the variables evaluated. The best cultivation conditions predicted by the model (40 • C, 100 rpm and MOI = 0.144; treatment 1) and the worst (29 • C, 250 rpm and MOI = 0.00001; treatment 4) were reproduced using the incubation time of four hours (the shortest incubation time tested during this study). To evaluate how the number of phage particles inoculated at the beginning of the experiment can alter the steady-state dynamics of phage and host populations, and the impact of this single operational variable on the final production, we also tested the intermediate and minimum MOI values used in this study under the best cultivation variables (MOI = 0.001 and MOI = 0,00001, treatments 2 and 3, respectively).
The viral quantification was made using the double-agar overlay plaque assay. The average number of phage particles obtained from the four experimental conditions was compared using variance (ANOVA) analysis, followed by a Fisher post-hoc test in case of significance.

Conclusions
The RCCD approach made it possible to evaluate several operational parameters simultaneously, as well as the relationship between them, independent of the phage/host pair. If the complete factorial method had been used, instead of the 196 tests we performed during this study, at least seven thousand tests would have been needed to obtain the same amount of information.
The RCCD approach is an exciting and quick tool for obtaining the best parameters for a start a large-scale phage production optimization. Agitation was the parameter that most influenced phage production, while incubation time was the least influential parameter. Factors such as economic viability, production reliability, and physiological stability make the M9/Glucose medium the one that provided the best performance in vB_EcoM-UFV09 T4-like phage production. Although we used these four different parameters in this work, this tool can be used to evaluate any other parameter, such as dissolved oxygen or micronutrients.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/pathogens10091100/s1, Table S1: Experimental design used by each experimental unit (LB medium and M9 media supplemented with acetate, pyruvate, lactate, glycerol, succinate, and glucose), based on the rotatable central composite design. The variables were: Te = temperature (28 • C ≤ Te ≤ 40 • C); It = incubation time (4 h ≤ It ≤ 12 h); Ag = agitation (100 rpm ≤ Ag ≤ 250 rpm); and MOI = multiplicity of infection (0.00001 ≤ MOI ≤ 0.1). Table S2: Number of phages (PFU/mL) observed at the end of the experiments. Quantification was performed using a double-agar assay. Table S3: Amount of phages (PFU/mL) observed in the end of the experiments. The quantification was made using double-agar assay.