Modeling the effect of oxidative stress on Bordetella pertussis fermentations

A mathematical model is proposed for Bordetella pertussis with the main goal to better understand and describe the relation between cell growth, oxidative stress and NADPH levels under different oxidative conditions. The model is validated with flask experiments conducted under different conditions of oxidative stress induced by high initial glutamate concentrations, low initial inoculum and secondary culturing following exposure to starvation. The model exhibited good accuracy when calibrated and validated for the different experimental conditions. From comparisons of model predictions to data with different model mechanisms, it was concluded that intracellular reactive oxidative species only have an indirect effect on growth rate by reacting with NADPH and thereby reducing the amount of NADPH that is available for growth.


| INTRODUCTION
Whooping cough is a highly contagious respiratory tract disease. The causative agent of this illness is the gram-negative bacterium Bordetella pertussis, which was first isolated by Bordet and Gengou in 1906. 1 Early symptoms of whooping cough resemble the common cold, but then evolve into uncontrollable violent coughing fits, discernable by the "whoop" sound made as air is inhaled.
Prevention of this disease relies on early vaccination. The acellular pertussis vaccine produced by Sanofi Pasteur contains five antigens: fimbriae (types 2 and 3), filamentous hemagglutinin, pertactin and pertussis toxin. The manufacturing process of this vaccine is divided into two main stages: (i) upstream fermentation by which bacteria are grown in two parallel trains each of which contains three reactors of increasing volume in series and (ii) downstream purification of the five target antigens in several steps. In a previous study, the causes of batch-to-batch variation in the production of the antigens were identified in the upstream fermentation process. 2 High levels of nicotinamide adenine dinucleotide phosphate (NADPH) were detected in the supernatant of low antigen-producing fermentations. Since NADPH is known to be involved in detoxification reactions required to combat oxidative stress, it was hypothesized that the occurrence of high oxidative stress may be negatively correlated to the productivity. 3 Zavatti 4 conducted a series of 2 L and 20 L bioreactor experiments in which oxidative stress was induced by either the addition of hydrogen peroxide or a low inoculum dose. These experiments further confirmed that high oxidative stress is correlated to high levels of NADPH, low cell growth and low productivity. 4 Oxidative stress results when an imbalance occurs between the formation of free radicals from oxygen and the capacity of the system to safely consume these compounds. 5 Reactive oxidative species (ROS) cause oxidative stress and are found as singlet oxygen, hydroxyls, superoxides, peroxides, hydroperoxides and the non-radical hydrogen peroxide which are continuously produced during aerobic metabolism. 6,7 Whether ROS function as signaling molecules or cause oxidative damage depends on the delicate equilibrium between their production and scavenging. 8 ROS also serve as second messengers (i.e., intracellular signaling molecules secreted by the cell in response to exposure to extracellular signaling molecules) in a variety of cellular processes including those that help in tolerating various environmental stresses; however, when present in excess, they can be harmful to proteins, lipids and DNA. 6,9 To protect themselves against oxidative stress, living organisms utilize anti-oxidative reactions involving enzymes (catalase and superoxide dismutase counter-mechanisms), small proteins (thioredoxin and glutaredoxin) and molecules (glutathione). 10 The presence of NADPH is important for aerobic organisms to survive oxidative stress since it is a reducing agent that serves to protect against ROS. For example, glutathione reductase can detoxify ROS and use NADPH to replenish its reducing power. 11 Oxidative stress has also been found to promote NADPH production which in turn tends to diminish oxidative stress by promoting reactions that produce a reducing environment. 3,12 Reaction mechanisms that involve ROS have been reported, particularly in the context of antibiotic resistance. [13][14][15] For example, a mechanistic model was developed to show that ROS generation can be increased in Escherichia coli and lead to higher bacteria susceptibility to oxidative attack via antibiotics. 16 Several studies on bacteria have reported that the inhibition of glycolysis allows cells to divert flux into the pentose phosphate pathway to promote NADPH synthesis and enhance the protection against oxidative stress. [17][18][19] On the other hand, B. pertussis does not have an active glycolysis pathway and instead uses gluconeogenesis to process the product of the TCA cycle that is driven by glutamate as the main nutrient. In fact, it has been shown that B. pertussis can synthesize most amino acids and grow in media containing mostly glutamate and proline which is also converted to glutamate. 20 Also, NADPH is produced from the conversions of isocitrate and glutamate to alpha-ketoglutarate and malate to pyruvate, but it is not generated in the pentose phosphate pathway as in the case of E. coli. 21 A metabolic model describing the effect of oxidative stress on the growth of B. pertussis is presented in the current article. The model is based on a previous theoretical model developed by Himeoka and Kaneko 22 to account for the effects of starvation and the stationary growth phase of cells. It should be emphasized that the original model of Himeoka and Kaneko was proposed as a generic description of growth inhibition arising from the interplay between promoters of growth (ribosomes) and waste products (misfolded or mistranslated proteins). In the current study, we adapt the model to describe a particular mechanism of inhibition of B. pertussis growth by ROS (inhibitor) and the role of NADPH (byproduct) as a quencher of ROS. To assess the validity of this model for this specific B. pertussis pathway, we have conducted an experimental flask study in which ROS, NADPH, glutamate and biomass are measured by flow cytometry, spectro-fluorescence, Bioprofile and spectrophotometry, respectively. The experiments are conducted under different conditions of oxidative stress induced by high initial glutamate concentrations, low initial inoculum and secondary culturing following exposure to starvation conditions. Variability in inoculum size or initial glutamate concentration occurs commonly in the manufacturing process due to measurement errors, fluctuations in media composition including casamino acids and differences in seed batches. Also, the behavior of the culture following exposure to starvation conditions is of particular industrial interest since the vaccine is manufactured in a fermentation train of bioreactors of increasing volume and so the exposure to star-  that promote growth through the synthesis of proteins. 23,24 Component B may represent waste products (i.e., misfolded or mistranslated proteins) or other molecules that are produced with the aid of component A but do not facilitate growth. For example, the production of proteins in E. coli related to the stationary phase such as HPF and YfiA is induced under stress conditions such as starvation. 25,26 A lag time is required for growth following stationary or death phases to permit the cells to recover after resources are supplied. The originally reported model was used to quantitatively relate the time in the lag phase to both the starvation time and the maximal growth rate and satisfy the already-known growth laws in the exponential phase.
It also described the dependence of lag time on the speed of the starvation process. For example, if substrate consumption rate during starvation is high, the lag time is short compared to a situation with a low consumption rate. The fact that some of the phenomena VITELLI ET AL. explained by the model of Himeoka and Kaneko were also observed in our experimental studies for B. pertussis, e.g. longer lags following long starvation periods, motivated the use of a modified version of this model in the current work.
Bacteria are consistently challenged to adapt to changes in nutrient availability and stress conditions. The way that bacteria adapt to stasis caused by lack of nutrients or other stressful conditions has led to the idea that defenses against increased levels of intracellular oxidative stress are essential traits of non-growing cells. 27 In nongrowing cells, ROS should accumulate since they are not diluted when the cell increases in volume. 28 Cells with an elevated concentration of ROS should be much more sensitive to additional oxidative stress imposed by external factors. It has been reported that a major overlap exists between the cell use of global regulators to deal with both starvation and oxidative stress. 28 One pathway of adaptation to starvation in bacteria involves the intracellular signal guanosine tetraphosphate which accumulates in response to nutritional deficiency and controls the macromolecular synthesis for entry into starvation and non-growth. 29 NADPH is crucial to decrease oxidative stress through reactions that yield a reducing environment. 12 To avoid reactive oxygen intermediates produced during the respiratory burst, bacteria produce enzymes, such as catalase and superoxide dismutase, which detoxify peroxides by transforming superoxide radicals into hydrogen peroxide and oxygen. 30 NADPH also contributes to the proper functioning of enzymes such as superoxide dismutase, glutathione peroxidase and catalase. B. pertussis produces a catalase and a Fe-superoxide dismutase. 31 NADPH is known to be tightly bound to catalase and to offset the ability of hydrogen peroxide which is the substrate of catalase to convert the enzyme to an inactive state. 32 Also, glutathione peroxidase catalyzes the reaction between reduced glutathione (GSH) and ROS. NADPH is then used to replenish the glutathione to its reduced state (GSSH), 33,34 as shown in Figure 2. Thioredoxin follows a similar mechanism as glutathione with the enzyme thioredoxin reductase and is also replenished to its reduced state by NADPH. 35,36 The chemical reactions for reduced glutathione are shown in Equations (1) and (2).
Both reduced glutathione and thioredoxin are present in the media formulation used in this study.
NADPH is not only vital for the anti-oxidative defense mechanisms of most organisms, but it is also the driving force of most biosynthetic enzymatic reactions, including those responsible for the biosynthesis of all major cell components such as DNA and lipids. [37][38][39] In B. pertussis, NADPH is produced during the metabolism of glutamate entering the TCA cycle and the conversions of isocitrate to alpha-ketoglutarate and malate to pyruvate.
Based on the experimental results, the original model reported by Himeoka and Kaneko 22 is modified to include the following elements: a substrate inhibition term and powers in the expressions of F A and F B (Equations (9) and (10)), a degradation term for ROS (Equation (8)) and a term for the mass transport of NADPH into the supernatant (Equations (6) and (7)). The degradation of ROS is included since these species are highly reactive and will react with other compounds if not quenched by an antioxidant. The mass transfer step is added to account for the secretion of NADPH through the cell membrane into the supernatant.

| Optical density
The sample was diluted by a factor of 20 in 0.9% saline solution and optical density (OD) obtained using optical spectrophotometry by measurement of the absorbance at 600 nm and normalized using the percentage of live cells from flow cytometry (section 3.5.3). The conversion factor from optical density to g/L biomass for B. pertussis is 0.45 ± 0.5.

| Glutamate concentration
The supernatant was collected in order to determine the glutamate concentration (after 20-fold dilution) using the chemistry module of a BioProfile FLEX Analyzer (Nova Medical). Glutamate was measured using an amperometric electrode that contains immobilized enzymes in its membranes. 41 In the presence of oxygen, the enzyme membranes reduce glutamate to produce hydrogen peroxide which is then oxidized at a platinum anode held at constant potential. The resulting current is proportional to the sample concentration.

| Fluorescence spectroscopy
Analysis of the supernatant for extracellular NADPH concentration by fluorescence excitation-emission spectroscopy was carried out with a Cary Eclipse Fluorescence Spectrophotometer (Agilent Technologies).
Each of the supernatant samples was diluted 20 times and analyzed in polymethylmethacrylate cuvettes using a slit width of 5 nm and PMT of 800 V for the peak measurements. Each sample was analyzed over the excitation and emission ranges of 330-370 nm (at 10 nm intervals) and 300-600 nm (at 1 nm intervals

| Oxidative stress
Oxidative stress was measured using the fluorescein derivative carboxy-

| Model fitting
The model given in Equations (3) where y i is the measured value, b y i is the predicted variable, n is the number of calibration samples and μ i is the mean of each variable. Since the intracellular NADPH concentration was not measured, it was not possible to specify its initial level and so was included as an additional parameter to be fitted in the model. The model parameters are defined in Table 2.
Selection criteria are important tools to obtain a model that simultaneously has the appropriate structure and dimensionality. These criteria assess whether a fitted model maintains an optimal balance between its predictive accuracy and number of fitting parameters. For the case that the ratio between the number of samples n to the number of fitted parameters p is n/p < 40, the AIC is as shown in Equation (14): where RSS is the residual sum of square errors. This involved inoculating a secondary flask with cells collected during the exponential growth phase from the primary flask. Figure 5 shows the OD (a), glutamate (b), extracellular NADPH (c) and intracellular ROS (d) concentrations measured over the 48 h of reaction time.
For this experiment, a short lag phase in this culture is observed when the inoculating cells are taken from the exponential growth phase of the primary culture. It is noteworthy that the ROS concentration exhibits a spike rise during the lag phase. In a study by Rolfe et al., 44 it was suggested that oxidative damage during the lag phase is caused by a combination of increased intracellular iron concentration (found in media) and newly available oxygen. Also, the rate of hydrogen peroxide generation was found to be 5-10 times greater when a bacterial culture shifts from the lag to exponential growth phase. 45 Also, when the amounts of NADH and FADH generated by the TCA cycle exceed the capacity of the electron transport chain, this leads to high ROS concentration levels. 46 During the exponential growth phase, the ROS concentration drops to its lowest value where it remains constant. Since only extracellular NADPH is measured, the rate of NADPH accumulation per unit biomass is reported since this rate is expected to be correlated to the production of NADPH per cell. Figure 6 shows reported previously for experiments conducted under starvation conditions. 48 The decrease of ROS in the death phase may be due to reaction with other cellular components or due to leakage of intracellular ROS through severely damaged membranes into the extracellular environment.

| Description of cell flask cultures under different experimental conditions
The model was developed to describe the effect of different experimental conditions as follows: 1. Changes in initial glutamate concentration.
2. Changes in initial inoculum size.

| Effect of changes in initial glutamate concentration
As shown in Figure 8 and Table 3, the growth rate of biomass increases as the initial concentration of glutamate in the media decreases. For example, the doubling time of the bacteria is shortened by $1.01 h when the initial concentration of glutamate is reduced from 11.6 to 6.6 g/L as shown in Table 3. While the growth rates appear similar in the figures, a one-way ANOVA (Table 4) reveals that a significant difference exists between the mean growth rates as the initial concentration of glutamate is changed. Also, the intracellular ROS concentration during the lag and early exponential phases rises as the initial concentration of glutamate increases (Table 3). Since a Oxidative stress caused by nutrient excess has been reported in both mammalian and bacterial cells. 40,49 The tricarboxylic acid (TCA) cycle oxide nutrients and the resulting electrons are transferred to produce NADH and FADH 2 . The electrons are eventually donated to molecular oxygen via the electron transport chain (ETC), but incomplete reduction can lead to the production of superoxides. Therefore, when the breakdown of components from the TCA cycle exceeds the consumption rate capacity of the electron chain cycle as is the case when nutrients are in excess, ROS production increases and can lead to oxidative stress. 40 It has also been shown that high levels of NADH and FADH may inhibit the fluxes in the TCA cycle. 50 Since glutamate is consumed primarily in the TCA cycle, this process will be inhibited if the resulting NADH and FADH reach high enough levels.
On the other hand, the data in Figure 8 indicate that the amount of biomass produced at higher initial glutamate concentrations eventually accelerates and even surpasses the level attained when the glutamate concentration is lower. Such a result is not unexpected since a larger overall glutamate consumption should ultimately yield a higher level of biomass production. The practical implication of this observation is that a fed-batch operation would be best to increase the growth rate of B. pertussis by reducing the impact of initial substrate inhibition by glutamate which is the main carbon source in this process.

| Effect of change in initial inoculum size
Experiments carried out with lower initial density cultures of B. pertussis (i.e., small size inoculum) exhibited higher oxidative stress during the lag phase and early portion of the exponential growth phase ( Table 5)  hydroperoxides. Such protective action could explain the observation of higher oxidative stress in low inoculum cultures when the secretion of a smaller amount of protective protein would be expected than when the inoculum level is higher. It has also been reported that oxidative stress drives the selection of quorum sensing mutants in Staphylococcus aureus populations. 56 Inhibition with respect to biomass concentration was added in the model in Equations (10) and (11) to account for the effect of inoculum size on oxidative stress levels.

| Calibration and validation of the oxidative stress model
The oxidative stress model was calibrated by fitting to experimental data obtained under 13 flask conditions and validated with data from an additional three conditions. The calibration and validation conditions are listed in Tables 6 and 7, respectively.
The system of equations (Equations (3)-(12)) comprising the model is found in section 2, while the definition of each parameter obtained by fitting the model is given in Table 2. The numerical values of the parameters so estimated are listed in Table 8. The fitting procedure is described in section 3.6. This mechanism has not been previously applied to the growth of B. pertussis and therefore the parameter values cannot be compared to those obtained in other studies. However, the initial concentration of NADPH (A o ) and intracellular ROS concentration (Table 8) 58 The difference in starved NADPH concentration may be due to a difference in the duration in starvednutrient conditions. In the experiments presented in this section, the period of starvation was $10 h while the period is not reported by Goldbeck et al. 57 If the starvation period in this earlier study was shorter, one would expect the initial NADPH concentration to be higher than that obtained here (Table 8)   The total root-mean squared errors (RMSE) for the fit of the calibrated and validated values are presented in Table 9 below. The   Table 10. As shown in Figure 13, this simplified model is not able to predict growth following starvation since it does not have a mechanism in place to generate the extended lag phase of starved cells. The key reason that the proposed model is able to predict the larger lag is that NADPH is largely depleted at the end of the primary flask following starvation. Then, a larger time is needed in the secondary flask to build up the necessary amount of NADPH to start growth according to the autocatalytic effect included in F I G U R E 1 1 Model validation of (a) optical density (OD), (b) extracellular glutamate concentration, (c) extracellular NADPH and (d) intracellular reactive oxidative species of a B. pertussis culture with an initial OD of 0.14 and initial glutamate concentration of 8.6 g/L Equation (10). Data obtained from the 60-h primary flask (see Tables 6   and 7) were not used to calibrate and validate the Contois kinetic growth model.   Table 11. This also includes other common substrate inhibition growth models such as Haldane, 65 Luong 66 and Webb. 67 Since the Contois growth kinetics performed better in in the common growth models and within the oxidative stress model, a more in-depth comparison between the oxidative stress and Contois models was done above. The oxidative stress model both improves the predictability of the biomass and the extracellular glutamate concentration.
The improvement in the fitting of the oxidative stress model is particularly significant regarding the extracellular glutamate concentrations as reflected by the significant reduction of the RMSE compared to that obtained using the Contois, Haldane, Luong and Webb models. The AIC criterion (Equation (14)) is used to assess the trade-off between model dimensionality and predictability. As shown in Table 11, the AIC is much lower for the oxidative stress model, indicating that the additional parameters and mechanism included in this model are needed to improve the predictability of the model compared to the simple biomass-substrate model. This further supports the hypothesis that the mechanism of oxidative stress is needed to predict the culture behavior when exposed to starvation conditions. Some of the experiments performed in primary flasks, particularly those involving starvation or different seed, exhibit significant differences from the others in terms of the evolution of ROS and NADPH (Table 6, experiments 9-11). These experiments set very different initial conditions in ROS and NADPH for the following secondary flasks while the remaining experiments ( Table 6,

| CONCLUSIONS
A metabolic model that uses oxidative stress to predict the growth of  Hector Budman: Conceptualization (supporting); investigation (supporting); supervision (equal); writingreview and editing (equal).

ACKNOWLEDGMENT
This work was supported by MITACS grant IT09759 through MITACS-Accelerate Program.

DATA AVAILABILITY STATEMENT
Normalized data available on request from the authors.