RESEARCH ARTICLE – Pharmaceutical Biotechnology

Advanced Kinetic Analysis as a Tool for Formulation Development and Prediction of Vaccine Stability DIDIER CLE´ NET,1 FRE´ DE´ RIC IMBERT,1 PATRICIA PROBECK,1 NAUSHEEN RAHMAN,2 SALVADOR F. AUSAR2 1 2

Bioprocess Research & Development, Sanofi-Pasteur, Marcy L’E´ toile 69280, France Bioprocess Research & Development, Sanofi-Pasteur, Toronto ON M2R 3T4, Canada

Received 11 April 2014; revised 7 July 2014; accepted 10 July 2014 Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.24117 ABSTRACT: We have used a protein-based vaccine, a live virus vaccine, and an experimental adjuvant to evaluate the utility of an advanced kinetic modeling approach for stability prediction. The modeling approach uses a systematic and simple procedure for the selection of the most appropriate kinetic equation to describe the degradation rate of compounds subjected to accelerated conditions. One-step and two-step reactions with unlimited combinations of kinetic models were screened for the three products under evaluation. The most appropriate mathematical model for a given product was chosen based on the values of residual sum of squares and the weight parameter w. A relatively simple n-th order kinetic model best fitted the degradation of an adjuvanted protein vaccine with a prediction error lower than 10%. A more complex two-step model was required to describe inactivation of a live virus vaccine under normal and elevated storage temperatures. Finally, an autocatalytic-type kinetic model best fitted the degradation of an oil-in-water adjuvant formulation. The modeling approach described here could be used for vaccine stability prediction, expiry date estimation, and formulation selection. To the best of our knowledge, this is the first report describing a global kinetic analysis of degradation of vaccine components with high prediction C 2014 Wiley Periodicals, Inc. and the American Pharmacists Association J Pharm Sci accuracy.  Keywords: stability; kinetics; formulation; forced conditions; vaccines; Mathematical models

INTRODUCTION The stability of vaccines is a critical factor influencing their worldwide distribution and has a major impact on vaccine quality, potency, and storage conditions.1,2 The thermal stability of vaccines is of great interest for the vaccine industry, government institutions, and philanthropic organizations attempting to increase the distribution of vaccines to people living in countries with poor infrastructure and unreliable transportation and storage facilities to preserve the vaccines that require refrigeration.2–4 The thermal stability of vaccines can be evaluated through numerous methods that look at physicochemical or biological changes in a vaccine upon exposure to elevated temperatures.4–6 There are essentially two approaches to studying the thermal stability of vaccines: temperature ramping experiments and accelerated stability studies under isothermal conditions. Temperature ramping experiments involve monitoring changes in the biophysical properties of a vaccine while temperature is increased at a given heating rate. In this case, thermal stability is evaluated via monitoring decomposition extent and/or some thermodynamic parameters such as the enthalpy and free energy.7–9 Since thermal ramping experiments can be completed within a few hours, these studies are broadly used in vaccine formulation development and screening of stabilizing conditions.10 Apart from thermodynamics, it is noteworthy to Correspondence to: Salvador F. Ausar (Telephone: +416-667-2700; Fax: +416667-2609; E-mail: [email protected]) This article contains supplementary material available from the authors upon request or via the Internet at http://wileylibrary.com. Journal of Pharmaceutical Sciences  C 2014 Wiley Periodicals, Inc. and the American Pharmacists Association

mention that kinetics also governs the proteins stability. High kinetic stability results in a low denaturation rate of the protein and thus long-term stability.11 For kinetic analysis,12,13 multiheating rate experiments9,14 and isoconversional analyses15 are often used to determine the kinetic parameters for predicting the thermal stability of pharmaceutical products.16,17 Accelerated stability studies are designed to determine the rate of vaccine degradation over time as a result of exposure to temperatures greater than those recommended for vaccine storage.18 Many different stability indicating assays can be used to monitor the rate of vaccine degradation as a function of time and these include viral titer, immunochemical assays, liquid chromatography, and gel electrophoresis, to mention a few.2,4,19 An accelerated stability program can serve for multiple purposes such as selection of stabilizing conditions, shelf life estimation, temperature excursion modeling, and to support manufacturing process changes that may be suspected to alter vaccine stability.18 The most commonly used approaches to analyze data and predict long-term stability from accelerated stability studies consist of fitting data with a simple kinetic model (typically zero- or first-order kinetic models) to obtain the rate constant for two or more temperatures. This experimental procedure is followed by the calculation of the unknown rate constant at required temperature by extrapolation using an Arrhenius dependence of the reaction rate on the temperature.19,20 However, stability predictions based on application of zero- or first-order kinetics are very often too simplified for description of the degradation of biological products, which frequently undergo complex and multistep degradation reactions.21 As such, more sophisticated degradation kinetic models using Vogel– Fulcher–Tammann equation or Prout–Thompkins nucleation models may be useful to describe degradation in biological

Cl´enet et al., JOURNAL OF PHARMACEUTICAL SCIENCES

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products.22–25 Such more complicated approach in which a twostep kinetic model, including an n-th order and an autocatalytic component, was initially used to described the epoxy cure reaction26 and was adapted more recently for protein aggregation kinetics.27 In this report, we use an advanced kinetic modeling approach in which the amount of reaction steps and kinetic models is unlimited and their use is validated by the statistical tools that allow choosing optimal number of the variable parameters used for fitting of experimental data.28 This procedure was applied to evaluate the degradation kinetics of a protein- and virusbased vaccines, and an emulsion-based adjuvant formulation. Accelerated stability studies at three or more isothermal temperatures were conducted and the resulting data were fitted with one-step or two-step kinetic models. The most appropriate model was identified by statistical analysis and was afterward used to extrapolate the long-term degradation at any required storage temperature. It is important to mention that the selection of the kinetic models is purely based on statistical analysis and the goodness of fit without requiring that the chosen model is established as correctly describing the mechanism(s) of degradation of the complex systems under evaluation in this report. Pharmaceutical applications of this approach are discussed.

different temperatures for stability monitoring. The stability of PhtD was evaluated as a function of time by RP-HPLC after desorption from the aluminum adjuvant as previously described.30 By this technique, only the peak area of intact PhtD is integrated and used for the calculation of the concentration of intact protein. Therefore, this provided a direct measurement of protein degradation induced by elevated temperatures. Stability data are presented as the concentration of intact protein as a function of time. The adjuvant formulation based on an oil-in-water emulsion was dispensed in 7 mL amber glass vials (4.6 mL/vial) with fluoropolymer stoppers and incubated under different temperatures for stability monitoring. Since acetone is one of the major degradation products accumulating in the formulation as a result of the oxidation of oil droplets in emulsion, in the stability study, its content was monitored by gas chromatography. Advanced Kinetic Analyses Data analysis was performed using AKTS-Thermokinetics software (version 3.6; AKTS Inc., Advanced Kinetics and Technology Solutions, Siders, Switzerland).31 The tool considers a nonlimited amount of models using “one-step” and “two-step” kinetics. The rate of the reaction is commonly expressed by the Arrhenius equation that describes the empirical relationship between the reaction rate and the temperature.   E d" f (") = k(T)f (") = A exp − dt RT(t)

MATERIALS AND METHODS Materials ALVAC poxvirus recombinant vector vCP2292 containing the melanoma gene inserts NY-ESO-1(M) and TRICOM was produced and purified as previously described.29 Pneumococcal histidine triad protein D (PhtD) was expressed as a recombinant protein in Escherichia coli and purified by serial column chromatography to purity greater than 95% as evaluated by reversed phase HPLC (RP-HPLC) and SDS-PAGE. Aluminum hydroxide (AH) adjuvant (Alhydrogel ) was obtained from Brenntag Biosector (Frederikssund, Denmark). Phosphate-treated aluminum hydroxide (PTAH) was prepared as previously reported.30 All other chemicals were analytical grade reagents. The oil-in-water emulsion was prepared by using the phase inversion temperature process. The concentrated oil-in-water emulsion [more than 30%, w/w, oil in phosphate-buffered saline (PBS)] was then diluted with PBS to its final concentration (∼3%, w/w, oil in PBS). R

(1)

with k, the rate constant, ", the reaction progress, and A, the pre-exponential factor. The units of A are identical to the unit of the rate constant k and will vary depending on the order of the reaction. E, the activation energy, R, the universal gas constant, T, the temperature in Kelvin, and f("), represents a function describing the reaction kinetics. As proposed by Roduit et al.,28 32 ˇ ak–Berggren ´ the truncated Sest (SB) model was applied for f("). f (") = (1 − ")n"m

(2)

where the exponents n and m are generally reported as noninteger. It follows that the general expression describing the rate of reactions which may proceed according to two subreactions has the form:

Stability Monitoring

    E1 E2 d" Purified ALVAC samples containing approximately 7.9 log = A1 exp − (1 − ")n1 + A2 exp − (1 − ")n2 "m2 CCID50 (50% of the cell culture infectious dose) in 10 mM Tris– dt RT RT HCl pH 7.4 were used for all stability studies. Under a laminar (3) flow cabinet, two different ALVAC formulations (ALVAC-1 and ALVAC-2) were prepared by diluting ALVAC stock solution 1:2 For example, by taking n and m equal to 1, one can obtain with formulation buffer. All samples were dispensed in 3 mL glass vials (0.6 mL/vial) with septum closure and aluminum cap the known Prout–Tompkins equation.33,34 As a further examand were incubated under different temperatures for stability ple, the application of two SB models allows describing the monitoring. Virus viability was subsequently tested by CCID50 autocatalytic reactions (with n1 = 1, m1 = 0, n2 = 1, m2 = 1) built up from two subreactions. The autocatalytic reactions are at different time intervals. PhtD formulations were prepared in PTAH adjuvant as pre- divided into two steps: viously described.30 Formulations containing 100 :g/mL PhtD and 0.56 mg/mL aluminum were dispensed in 3 mL glass (1) Primary degradation resulting in the formation of a catalytic vials (0.6 mL/vial) with septum closure and incubated under compound B. Cl´enet et al., JOURNAL OF PHARMACEUTICAL SCIENCES

DOI 10.1002/jps.24117

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RESEARCH ARTICLE – Pharmaceutical Biotechnology k1 ,HR1

A −−−−→ B + C(primary decomposition)

(4)

(2) Secondary degradation in which the product B works as a catalyst. k2 ,HR2

A + B −−−−→ 2B + C(autocatalytic reaction)

to extrapolate the long-term stability behavior of the product under any storage temperature. The confidence intervals were calculated according to an automatic bootstrap analysis of the experimental data.28 This statistical approach, which is based on resampling, was fitted with 1000 loops and provides predictions with a percentile confidence interval at 95% (CI95%).

(5)

RESULTS AND DISCUSSION Such kinetic approach describing the course of the autocatalytic reactions was developed by Sourour and Kamal.26 d" = k2 (1 − ")(Z + A0 (F + ")) dt

(6)

with "=1−

A(t) : reaction progress of A A0

(7)

A0 : initial amount of A(t) at t0 = 0

(8)

B0 : initial amount of B(t) = B0 + A0 − A(t) at t0 = 0

(9)

F=

Z(T) =

B0 A0

k1 (T) : rate constants ratio k2 (T)

(10)

(11)

If Z  0 (i.e., k1  k2 ), the reaction is described by the firstorder kinetics. If Z ∼ 0 (i.e., k1  k2 ), the reaction has clearly autocatalytic behavior: the autocatalytic reaction (3) is much faster than the primary reaction (2). Thus, the general expression given by Eq. (3) allows describing the rate of the reactions. This may proceed according to the n-th order and autocatalytic kinetics with n being the reaction order, and m being a parameter introduced to take into account the eventual autocatalytic component of the reaction when needed. By changing the value of the parameters n1 , m1 , n2 , and m2 the number of possible model combinations becomes infinite. According to an automatic least-squares regression analysis, such kinetic parameters are automatically calculated based on experimental data using a nonlinear least square fitting procedure. In AKTS-Thermokinetics Software, one-step (n-th order, autocatalysis) and two-step (combinations of one step) kinetics can be this way automatically screened. Two situations were further considered: with fitted and fixed constant values (integer) for the reaction orders. In the process of comparing models, not only the quality of regression fit (residual sum of squares or “RSS”) but also the number of data points and the number of parameters in specific models are considered. Such procedure eliminates the overfitting scenario. As detailed elsewhere28 and based on Akaike (AIC) information criterion, those considerations are translated in a w index (w for “weight” between 0 and 1) attributed to each model combination. The model combination that exhibits the highest w value is chosen to describe the reaction kinetics. It is then used DOI 10.1002/jps.24117

Advanced Kinetic Model Accurately Predicts the Degradation of an Aluminum Salt Adjuvanted Protein Vaccine The analysis of stability data using advanced kinetic modeling was evaluated using a protein-based vaccine consisting of the antigen PhtD adsorbed to PTAH. The kinetic model was computed from the experimental data collected in the period of 6 months and compared with degradation profiles collected at 5◦ C and 25◦ C during 2 years. The set of experimental data was determined by RP-HPLC and contained the dependence of concentration of intact protein as a function of time under normal (5◦ C) and elevated (25◦ C, 37◦ C, and 45◦ C) storage temperatures (Fig. 1a). The results show sparse data and the progressive degradation of the protein under elevated temperatures with little to no degradation at normal storage temperature for up to 6 months of incubation. Several kinetic models were applied to fit experimental data and compared by their ability to describe the reaction progress. Table 1 depicts best fitting kinetic models for both possible cases: one-step and two-step reactions. The w fit index was closer to 1 for the n-th order (one-step) reaction, indicating good fit of this model with the experimental data. The two-step model did not enhance quality of fit (higher RSS values) and utilized more fitting parameters. Therefore, n-th order kinetics appeared as the simplest model to describe the reaction progress of a protein adsorbed to aluminum salt adjuvant. However, it is necessary to clearly underline that this result (best description of the reaction course by n-th order kinetics) does not have a mechanistic basis, but it rather only depicts a phenomenological mathematical model applied for fitting the reaction course. Many factors, such as those related to the intrinsic physicochemical stability of protein antigens (susceptibility to oxidation, deamidation, hydrolysis, etc.)35 as well as those that arise from its interaction with the aluminum salt adjuvant (strength of adsorption and microenvironment pH)36 may play an additive role in regulating the kinetics of degradation. The rate of degradation reaction of the protein-based PhtD in aluminum salt adjuvant can thus be described by the following equation:   113.6E3 d" = exp(29.4) exp − (1 − ")5.4 dt RT

(12)

To estimate the predictive power of the obtained model, real time data at 5◦ C and 25◦ C collected for up to 2 years were compared with the predictions in which this model was applied. For comparison, the predictions based on commonly applied firstorder kinetics are also included and presented in Figure 1b. As shown in Figure 1b, real time data collected at 5◦ C are fitted quite well with both, first-order and n-th order kinetic models. In contrast, only the n-th order kinetic model provided a good prediction of the data obtained at 25◦ C. The results shown in Cl´enet et al., JOURNAL OF PHARMACEUTICAL SCIENCES

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Figure 1. (a) Experimental data collected for PhtD formulation incubated under different temperatures for 6 months (5◦ C in blue, 25◦ C in red, 37◦ C in green, and 45◦ C in pink). (b) Predictions from n-th order kinetics (lines) and first-order kinetics (dashed lines) for 5◦ C (blue) and 25◦ C (red). Experimental data are defined as circles. (c) Predictions (lines) for 5◦ C (blue) and 25◦ C (red) with confidence intervals (CI 95%) (dotted lines) according to the n-th order model. Experimental data are defined as both filled and empty circles in all figures. For (b) and (c), only filled circles were used to determine the kinetic model. Empty circles define experimental data not used to determine the kinetic model. Cl´enet et al., JOURNAL OF PHARMACEUTICAL SCIENCES

Table 2 illustrate the correlation between the selected model and the real time data for 5◦ C and 25◦ C in comparison with the fitting in which first-order kinetic model was applied. The results indicate that the n-th order kinetic model can predict protein degradation at 5◦ C and 25◦ C with relative error of prediction lower than 10%. The relative error of prediction with first-order model was markedly higher at the incubation temperature of 25◦ C (Table 2). It is recommended by the software manufacturer to utilize a minimum of 15 data points and a minimum of two elevated temperatures as starting point for computing stability predictions. In order to determine whether the amount of experimental data points influences the accuracy of the prediction model, different amount of data points were used for computing the predictions (see Supplementary Table S1). The results suggested that lower prediction error and a narrower CI95% were obtained when more data points were used for computing the prediction model. These results indicate that increasing the number of data points used in the modeling event would increase both the accuracy and reliability of the predictions. To investigate the effect of the number of temperature conditions on the prediction error, predictions for the degradation of PhtD (at 5◦ C for 2 years) were conducted using the experimental data obtained from two, three, or four temperatures for a maximum incubation time of 6 months. The lowest prediction error was obtained when four temperature conditions were used for computing the predictions suggesting that increasing the number of temperatures produces more accurate predictions. In analogy to what was observed for the effect of amount of data points, the reliability of the prediction (as evaluated by the CI95%) also increased by increasing the number of elevated temperatures (Supplementary Table S2) The results of bootstrap analysis with corresponding CI95% using optimal number of data points and temperatures are presented in Figure 1c for predictions at 5◦ C and 25◦ C. All experimental data were within the CI95% prediction bands, which confirm the reliability of the prediction procedure. Although the CI95% obtained are moderately wide, they are not uncommon in the vaccine stability field. This is most likely due to the variability associated with stability testing of quite complex products, such as proteins adsorbed to heterogeneous suspension of aluminum salt adjuvant or viral particles in suspension. Greater levels of assay variability or insufficient amount of data points could result in larger confidence intervals, and hence less accurate predictions that would make it much more difficult to compare one formulation or drug candidate with another. Based on the results obtained, it appears that greater than twenty experimental data points from four different temperatures are optimal to obtain reliable predictions for a protein adsorbed to aluminum salt adjuvant. In the example presented in Figure 1, a period of 6 months was required for the collection of the data used for computing the predictions. This is a relatively long time for the case of formulation development studies intended to compare the effects of formulation conditions on long-term stability. Shorter duration experiments could be conducted by simply increasing the frequency of stability testing; this would allow the required amount of data points to be obtained at different temperatures in a shorter period of time. Altogether, the results suggest that advanced kinetic analysis can be used to accurately predict the long-term stability of adjuvanted proteins with limited amount of data. To the DOI 10.1002/jps.24117

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RESEARCH ARTICLE – Pharmaceutical Biotechnology

Table 1. Weight (w) and Residual Sum of Square (RSS) Indexes for One-Step and Two-Step Models and the Corresponding Kinetic Parameters Computed for the Process of PhtD degradation Kinetic Model

Fit Indexes

One step Two step

“w”

RSS

0.997 2.5E−7

550 581

ln(A1 ·s) (−)

Ea1 (kJ/mol)

n1

ln(A2 ·s) (−)

Ea2 (kJ/mol)

n2

m2

29.4 12.5

113.6 92.7

5.4 11.6

– 35.3

– 128.6

– 5.7

– 3.8E−4

Table 2. Comparison of Experimental PhtD Concentration Values for up to 2 years at 5◦ C and 25◦ C and Predictions from n-th Order and First-Order Models PhtD Concentration (:g/mL) Prediction Storage Temperature

(◦ C)

Error of Prediction (%)

Incubation Time (year)

Experimental Data

n-th Order

First Order

n-th Order

First Order

1.35 1.7 2 1.35 1.7 2

95.9 85.5 88.4 62.4 55.6 53.2

93.8 92.2 90.7 56.4 53.8 51.8

91.8 88.8 86.0 38.7 30.2 23.9

2.2 7.8 2.6 9.6 3.2 2.6

4.3 3.9 2.7 38.0 45.7 55.1

5

25

Table 3. Weight (w) and Residual Sum of Square (RSS) Indexes for One-Step and Two-Step Models and the Corresponding Kinetic Parameters Obtained After Fitting Procedure Optimization for ALVAC 1 and ALVAC 2 Formulations Kinetic Model

ALVAC 1 ALVAC 2

One step Two steps One step Two steps

Fit Indexes “w”

RSS

2.2E−7 1 3.5E−13 1

1.7 0.3 14.2 0.9

ln(A1 ·s) (−)

Ea1 (kJ/mol)

n1

ln(A2 ·s) (−)

Ea2 (kJ/mol)

n2

m2

47.3 16.0 82.4 34.3

154.2 74.8 248.0 121.9

0.9 1.2 0.9 1.1

– 59.4 – 161.7

– 186.6 – 459.7

– 0.9 – 0.7

– 0 – 0

Experimental data obtained at 25◦ C, 37◦ C, and 45◦ C was used for fitting optimization.

best of our knowledge, this is the first manuscript describing a thermokinetic model for the degradation of a protein antigen adsorbed to aluminum salt adjuvant. Advanced Kinetic Analysis and Long-Term Predictions for a Virus-Based Vaccine Two different formulations of ALVAC were used to evaluate the utility of advanced kinetic modeling in predicting the long-term stability of a virus-based vaccine. Virus thermostability is certainly more intricate than that of proteins due to the multicomponent viral structure. However, in the literature, the same approaches as for protein pharmaceuticals are generally applied: the simplified linear regression, first- or second-order kinetics are typically used to describe the process of virus inactivation and virus-like particles degradation.5,19,37 ALVAC stability was evaluated by monitoring virus infectivity at elevated temperatures using a standardized infectious titer assay. Kinetic analysis was conducted using only data points obtained under accelerated conditions therefore the experimental points obtained at 5◦ C were not considered in the first stage of simulation. The predicted stability profile at 5◦ C, which was computed using kinetic parameters, was compared with real time data obtained for up to 12 months at this temperature. The evaluated kinetic parameters used for simulation of the ALVAC degradation progress are shown in Table 3. The results suggest that a two-step model is the simplest model DOI 10.1002/jps.24117

that best describes the inactivation of ALVAC as denoted by the w values (Table 3). Additionally, the quality of fit (i.e., RSS values) was highly improved when a two-step model was used. The m2 values amount to 0, which indicates that this term is not required to describe the second step. Based on the obtained results, the inactivation of ALVAC can be described by the following equations: ALVAC 1:   74.8E3 d" = exp(16.0) exp − (1 − ")1.2 dt RT   186.6E3 (1 − ")0.9 + exp(59.4) exp − RT

(13)

ALVAC 2:   d" 121.9E3 (1 − ")1.1 = exp(34.3) exp − dt RT   459.7E3 (1 − ")0.7 + exp(161.7) exp − RT

(14)

This observation may suggest the presence of different populations of viruses in specific samples having different kinetics of inactivation. Our results are in agreement with those reported Cl´enet et al., JOURNAL OF PHARMACEUTICAL SCIENCES

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Figure 2. Superposition of experimental data (circles) obtained for up to 1 year at 5◦ C (blue), 25◦ C (red), 37◦ C (green), and 45◦ C (pink) for ALVAC 1 formulation (a and c) and ALVAC 2 formulation (b and d) and predictions from two-step kinetics (lines) obtained without using data points at 5◦ C (a and b) or with data points at 5◦ C (c and d). Dotted lines depict predictions with CI95% at 5◦ C. For (a) and (b), data points at 5◦ C appear as empty circles to indicate that they were not used to determine the kinetic model. (e) and (f) illustrate predictions between 5◦ C and 25◦ C in increments of 5◦ C for ALVAC 1 and ALVAC 2, respectively.

by Higashikawa and Chang38 for the degradation kinetics of retroviral vectors in which virus inactivation was described by two successive n-th order kinetic models. The simulations fit well the ALVAC experimental data collected at 5◦ C as presented in Figures 2a and 2b for both formulations. In order to determine whether the amount of experimental data points influences the accuracy of the prediction model, in the second stage of simulation additionally the data points Cl´enet et al., JOURNAL OF PHARMACEUTICAL SCIENCES

collected at 5◦ C were considered in computations. The new kinetic parameters describing ALVAC degradation progress are shown in Table 4. Little to no change was observed in these kinetic parameters compared to those evaluated in the first stage of simulation, that is, when the data points at 5◦ C were not considered (Table 3). Moreover, the results obtained during second simulation also indicate that the two-step model (two n-th order kinetics with n close to 1) is the simplest model that DOI 10.1002/jps.24117

RESEARCH ARTICLE – Pharmaceutical Biotechnology

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Table 4. Weight (w) and Residual Sum of Square (RSS) Indexes for One-Step and Two-Step Models and the Corresponding Kinetic Parameters Obtained after Fitting Procedure Optimization for ALVAC 1 and ALVAC 2

Kinetic Model

ALVAC 1

One step Two steps One step Two steps

ALVAC 2

Fit Indexes “w”

RSS

1.1E−9 1 1.3E−20 1

2.2 0.6 20.4 1.2

ln(A1 ·s) (−)

Ea1 (kJ/mol)

n1

ln(A2 ·s) (−)

Ea2 (kJ/mol)

n2

m2

Predicted Expiry Date (Years) (Lower CI 95%)

47.1 19.0 83.3 35.9

153.6 82.2 248.5 125.7

0.9 1.2 1.0 1.1

– 60.5 – 187.2

– 189.7 – 528.1

– 0.9 – 0.6

– 0 – 0

– 1.3 – 3.7

Experimental data obtained at 5◦ C, 25◦ C, 37◦ C, and 45◦ C was used for fitting optimization.

best describes the inactivation of ALVAC, as denoted by the w values. Thus, with data points including 5◦ C, the inactivation of ALVAC can be described by the following equations: ALVAC 1:   d" 82.2E3 (1 − ")1.2 = exp(19.0) exp − dt RT   189.7E3 (1 − ")0.9 + exp(60.5) exp − RT

(15)

ALVAC 2:   d" 125.7E3 = exp(35.9) exp − (1 − ")1.1 dt RT   528.1E3 (1 − ")0.6 + exp(187.2) exp − RT

(16)

As shown in Figures 2c and 2d, the kinetic model which included in computations the data points at 5◦ C gave similar long-term predictions at 5◦ C (however, with a narrower CI95%) compared with those obtained from model considering only the points collected at elevated temperatures of: 25◦ C, 37◦ C, and 45◦ C. As observed for the PhtD example above, kinetic models obtained with additional data points at 5◦ C are statistically more robust and predictions are more accurate (narrower CI95%) than those obtained with less data points. This result illustrates once again the impact of the amount of data points used for modeling on prediction accuracies. Regulatory guidance for establishing shelf life, such as ICH Q1A (R2), recommends fitting experimental data by a linear, or higher order functions as long as statistical methods are applied to test the goodness of fit. One of the approaches recommended in ICH Q1A (R2) is to determine the time at which the 95% one-sided confidence limit for the mean curve intersects the acceptance criterion. In good agreement with the guideline, the advanced kinetic analysis approach applied to accelerated stability data could be useful to estimate product expiry and to compare the effect of stabilizers on the long-term stability of the product. Based on advanced kinetic modeling approach discussed in this report, we have determined the expiry date of ALVAC formulations in the presence (ALVAC-2) or in the absence (ALVAC-1) of stabilizer excipients. Expire date was determined based on the intersection of the predicted stability with the lower acceptance criterion for this DOI 10.1002/jps.24117

experimental vaccine (6.4 log CCID50). In particular, the results indicate a threefold increase in the stability of ALVAC 2 with respect to ALVAC 1 with a predicted shelf life of about 3.7 years (Table 4). These results highlight the importance of advanced kinetic analysis reported herein as an important tool for formulation development and for establishing shelflife of vaccines. In using the novel approach, a comparison of different excipients, buffering conditions as well as batch-tobatch variability could be obtained early on in the stability evaluation of the vaccine with few experimental stability data points. According to the described kinetic approach, the long-term predictions of the decay of vaccine stability could be estimated at any storage temperature. Figures 2e and 2f show simulated curved for the prediction between 5◦ C and 25◦ C in increments of 5◦ C for both ALVAC formulations. Altogether, the presented results indicate that a two-step model can accurately describe the stability of the two formulations of ALVAC. Moreover, the results confirm also that advanced kinetic analysis can be used for accurate prediction of the long-term stability of virus-based vaccines even with a limited amount of experimental data points. Advanced Kinetic Analysis and Long-Term Predictions for the Oil-in-water Emulsion-Based Adjuvant Formulation Adjuvants are important substances (or combinations of substances) that are introduced to the vaccine formulation in order to increase and/or modulate the intrinsic immunogenicity of the antigen. The main contributions of adjuvants in vaccines are increasing antibodies’ functional titers, inducing cell-mediated immunity, increasing breadth of response and cross-strain protection, inducing protective responses more rapidly and more efficiently, and also allowing dose sparing (decrease antigen dose and dose number).39 Stability data generated for an emulsion-based adjuvant were used for the evaluation of the advance kinetic modeling approach. Oils such as hydrocarbon lipids are sensitive to oxidation which leads to formation of aldehydes and ketones via peroxide intermediates.40–42 One of the major degradation products accumulating in the formulation as a result of oxidation of oil is acetone.40–42 Therefore, its concentration, being proportional to the extent of adjuvant degradation, was monitored as a function of time at different temperatures. Results of advanced kinetic analysis indicate that the rate of the oxidation of oil with formation of acetone can be best described with an autocatalytic-type kinetic model expressed by the following Cl´enet et al., JOURNAL OF PHARMACEUTICAL SCIENCES

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Table 5. Weight (w) and Residual Sum of Square (RSS) Indexes for One-Step and Two-Step Models and the Corresponding Kinetic Parameters Obtained after Fitting Procedure Optimization for the Oxidation of Oil in Oil-in-water Emulsion Exposed to Accelerated Conditions Kinetic Model

One step Two steps

Fit Indexes “w”

RSS

0.79 0.21

0.82 0.06

ln(A1 ·s) (−)

Ea1 (kJ/mol)

n1

ln(A2 ·s) (−)

Ea2 (kJ/mol)

n2

m2

– 12.0

– 85.3

– 0.0

10.3 7.3

65.9 54.0

0.0 0.0

0.8 1.2

one-step reaction:   65.9E3 d" = exp(10.3) exp − (1 − ")0.0 "0.8 dt RT

(17)

Kinetic parameters for the stability data of the oil-in water adjuvant are depicted in Table 5. The parameter m2 is greater than zero, suggesting that the kinetic model has an autocatalytic behavior with a time lag before the initiation and acceleration of the reaction. According to RSS values, quality of fit seems to be optimal with two-step kinetics model but the best score given by the AIC weight (i.e., w) was obtained with the autocatalytic type model. To avoid overfitting of the data, the simplest model was chosen to describe the reaction progress. As observed for PhtD case study, lower prediction error and narrower CI95% were obtained when more data points were used for computing the prediction model (Supplementary Table S3). The autocatalytic type model determined in this work may well reflect the propagation phase of oil oxidation in which peroxyl radicals are able to abstract hydrogen atoms from other lipid molecules with the formation of further radical species that are responsible for the perpetuation of the reaction.43 In

addition, our results are in good agreement with the simulation models obtained by Litwinienko44 who reported an autocatalytic contribution for the auto-oxidation of unsaturated fatty acids. As shown in Figure 3, the autocatalytic type model fitted well the experimental data obtained at four storage conditions. After 6 months of incubation at 25◦ C, the degradation process of the emulsion exhibited a relatively sharp increase. By comparison, similar extent of degradation was predicted at 5◦ C after 2.5 years. Additionally, it can be observed that the prediction is in agreement with real time data obtained after up to 2 years of incubation at 5◦ C (Fig. 3). A first or n-th order models were not able to fit the experimental data (data not shown). This indicates once again the validity of the acceleratory type kinetic model selected to predict long-term stability of the oil-in-water adjuvant.

CONCLUSIONS A novel approach to analyze the experimental data, to fit them by computed kinetic parameters, and, finally, to predict the long-term stability of vaccine antigens and adjuvants is

Figure 3. Degradation of oil-in-water emulsion: experimental data (empty circles) obtained at 5◦ C (blue), 25◦ C (red), 37◦ C (green), and 45◦ C (pink) and predictions based on autocatalytic type model (lines) obtained from data points up to 6 months (filled circles). Dotted lines depict predictions with CI95% obtained at 5◦ C. Dash-dotted line depicts upper prediction with CI95% by using all data points at 5◦ C. Empty circles depict experimental data points obtained after modeling to illustrate good agreement with prediction. Cl´enet et al., JOURNAL OF PHARMACEUTICAL SCIENCES

DOI 10.1002/jps.24117

RESEARCH ARTICLE – Pharmaceutical Biotechnology

described. Presented results indicate that the long-term stability of vaccines can be predicted with great accuracy. In the case of protein-based vaccine adsorbed to an aluminum adjuvant, the rate of degradation was best described by an n-th order reaction model. The simulations based on this model showed significantly lower prediction errors comparing to simulations in which the traditionally used first-order kinetic model was used to fit experimental data collected at temperature of 25◦ C. In the second case, the ALVAC inactivation rate seems to be governed by a two-step process, which is in agreement with the more complex degradation profile expected for microorganisms. Finally, the autocatalytic kinetic model was found to best describe the degradation of oil-in-water adjuvant formulation. Presented kinetic approach could be employed for many practical applications, including shelf life prediction, estimation of impacts of excursions of temperature from the “cold chain,” lot-to-lot comparison, and evaluation of stabilizers and antimicrobials for biologics and vaccines during formulation development. Future studies should look into the contributions and interactions of individual components in the vaccine to the overall kinetics of degradation of the vaccine as a whole.

ACKNOWLEDGMENTS The authors would like to express his cordial thanks to Ashley Arora and Cristopher Roque for technical assistance in the preparation of this manuscript.

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DOI 10.1002/jps.24117

Advanced kinetic analysis as a tool for formulation development and prediction of vaccine stability.

We have used a protein-based vaccine, a live virus vaccine, and an experimental adjuvant to evaluate the utility of an advanced kinetic modeling appro...
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