Abstract
Studies of the extractable profiles of bioprocessing components have become an integral part of drug development efforts to minimize possible compromise in process performance, decrease in drug product quality, and potential safety risk to patients due to the possibility of small molecules leaching out from the components. In this study, an effective extraction solvent system was developed to evaluate the organic extractable profiles of single-use bioprocess equipment, which has been gaining increasing popularity in the biopharmaceutical industry because of the many advantages over the traditional stainless steel-based bioreactors and other fluid mixing and storage vessels. The chosen extraction conditions were intended to represent aggressive conditions relative to the application of single-use bags in biopharmaceutical manufacture, in which aqueous based systems are largely utilized. Those extraction conditions, along with a non-targeted analytical strategy, allowed for the generation and identification of an array of extractable compounds; a total of 53 organic compounds were identified from four types of commercially available single-use bags, the majority of which are degradation products of polymer additives. The success of this overall extractables analysis strategy was reflected partially by the effectiveness in the extraction and identification of a compound that was later found to be highly detrimental to mammalian cell growth.
LAY ABSTRACT: The usage of single-use bioreactors has been increasing in biopharmaceutical industry because of the appealing advantages that it promises regarding to the cleaning, sterilization, operational flexibility, and so on, during manufacturing of biologics. However, compared to its conventional counterparts based mainly on stainless steel, single-use bioreactors are more susceptible to potential problems associated with compound leaching into the bioprocessing fluid. As a result, extractable profiling of the single-use system has become essential in the qualification of such systems for its use in drug manufacturing. The aim of this study is to evaluate the effectiveness of an extraction solvent system developed to study the extraction profile of single-use bioreactors in which aqueous-based systems are largely used. The results showed that with a non-targeted analytical approach, the extraction solvent allowed the generation and identification of an array of extractable compounds from four commercially available single-use bioreactors. Most of extractables are degradation products of polymer additives, among which was a compound that was later found to be highly detrimental to mammalian cell growth.
Introduction
The past decade has witnessed significant advances in processing and manufacturing technologies in the biopharmaceutical industry, among which has been the rapid adoption of pre-sterilized single-use (SU) plastic bags in the replacement of traditional stainless steel and glass-based fluid mixing and storage vessels (1⇓⇓⇓⇓–6). SU systems promise several significant advantages (7⇓–9) compared with their conventional counterparts with regards to cleaning, sterilization, and validation requirements between batches. Additionally, SU systems offer excellent opportunities for improvements in a biopharmaceutical manufacturing process by providing high flexibility, fast turnaround, and high throughput, which ultimately translates into an increase in operational efficiency and a reduction in overall manufacturing cost (10). A variety of disposable bioprocess bags have now been developed and are available commercially in various formats with different composing materials, capacities, applications, and so on (11).
While SU bioprocess equipment has many appealing features, significant concerns have been raised from end-users due to the possibility of leachables migrating from the plastic materials into a processing fluid and/or final drug products (12, 13). Leachables are generally defined as chemical entities migrating spontaneously into a drug product from a container/closure or in-process system under normal storage/usage conditions. Depending on the nature of the leachable, it may have direct effects on the final drug product by being toxic, carcinogenic, and/or immunogenic (14), or have indirect effects by interacting with active pharmaceutical ingredients and causing modification of their physical–chemical properties. For example, leached rubber agents have been proposed to cause adverse effects on patients (15), and acrylic acids leaching from a prefilled glass syringe have been shown to react with therapeutic proteins stored in the syringe (16).
Although leachables can have a significant impact on the safety, quality, and purity of the final drug product, direct detection and quantitative measurement of leachables in final drug products are normally very challenging given that in most cases leachables exist only in trace level within a very complex matrix. Because of this difficulty, extractable studies are normally conducted first using model solvents under elevated conditions (e.g., higher temperature than that under normal storage conditions and/or use of solvents with higher organic content) to generate information that can be used to predict the leachables, as leachables are normally strongly related to, and often a subset of, extractables (17). It is critical that appropriate extraction conditions be used for the extractable results to be closely relevant for leachables prediction. Ideally, model solvents with extraction properties similar to that from a bio-processing fluid or drug formulation should be used so that maximum overlap between extractables and leachables can be achieved. Because of the strong dependence of extractable results on the extraction conditions, extractable studies tailored to specific applications are warranted to generate information most relevant to the leachables, although generic extractable information may be available from the vendors of components using general conditions. Specific guidance from regulatory authorities does not exist on how to conduct extractables experiments for injectable biopharmaceutical products, however, and currently there is much debate among SU systems users and producers surrounding best practices in the extractables and leachables space. In this report, a specific strategy (solvents, incubation conditions, and compound identification and quantification protocols) was developed to generate extractables information from SU bioprocess bags for use in bio-pharmaceutical manufacturing. The produced extractables were identified with a non-targeted strategy employing an array of complementary analytical techniques. This overall approach allowed the generation of a wealth of extractable information for four commercially available SU bags. The usefulness of the reported approach is indicated by the effective extraction and confident identification of a specific compound, bis(2,4-di-tert-butylphenyl)phosphate (bDtBPP), which was subsequently shown to leach out of certain SU process bags and inhibit the growth of mammalian cells, even at concentrations as low as a few tens or hundreds parts-per-billion (ppb) (18, 19).
Materials and Methods
SU Bags and Solvent Extraction Conditions
SU bags pre-sterilized through gamma radiation were obtained from four different suppliers and are designated herein as bag 1, 2, 3, and 4, with a total fluid capacity of 10 L for each bag. The internal surfaces of the SU bags were extracted with (a) water and (b) an organoaqueous solvent consisting of acetonitrile/ethanol/water (20/20/60, v/v/v) by filling the SU bags with each of the solvents and subsequently incubating at 50 °C for 2 days. A comprehensive analysis of the extracted solutions using multiple analytical techniques was then performed (see below). Bags 1–3 were filled with 500 mL of the extraction fluids, while the fill volume for bag 4 was 250 mL. The internal (fluid-contact) surface areas of the various bags fall in the range of 3000–3400 cm2. In spite of these differences, comparison of extracted quantities across bag types is possible by normalizing the observed concentrations by the solvent fill volume and by the internal surface. Extracted quantities are thus reported in units of nanograms per square centimeter (ng/cm2). Water, acetonitrile, and ethanol were high-performance liquid chromatography (HPLC)-grade.
Analytical Reference Standard Compounds and bDtBPP Synthesis
Amgen has accumulated an extensive library of compounds for use as reference standards, the identities and vendors of which are too numerous to list. Given its impact to cell culture, and the fact that it is unavailable for purchase commercially, the synthesis of a small quantity of bDtBPP for use as a reference standard was undertaken according to the following (un-optimized) procedure.
A solution of 2,4-di-tert-butylphenol (6.5 g, 3.5 mmol) in dichloromethane (65 mL) was cooled to 0 °C. Triethylamine (9.7 mL, 6.9 mmol) was added followed by slow addition of POCl3 (1.8 mL, 0.019 mol) over 10 min. The reaction was stirred for 30 min at 0 °C, and for an additional 16 h at room temperature. Progress of the reaction was monitored by thin-layer chromatography (silica gel, 5% ethyl acetate in hexane, starting material Rf = 0.7). On completion of the reaction, water (1 × 100 mL) was added and the biphasic mixture was stirred vigorously for 1 h. The phases were separated and the organic layer was washed with 6 N NaOH (1 × 100 mL) for 1 h at room temperature. After separation of the aqueous layer, the organic layer was further washed with 1 N HCl (2 × 100 mL) followed by brine solution (1 × 100 mL). The organics were dried over anhydrous Na2SO4, and the solvent was evaporated under reduced pressure to yield 6.5 g of the crude product as a light-yellow, sticky solid. The crude product was dissolved in 12 mL pentane and allowed to crystalize at ambient temperature for 2 days. The precipitated solid was filtered and washed with approximately 12 mL methyl tert-butyl ether to afford bDtBPP (0.800 g, 11.9%) as a white powder. The product mass was confirmed with mass spectrometry (MS) with m/z 475 being observed for the protonated ions, [M + H]+. 1H NMR (400 MHz, CDCl3) was used for product characterization with δ 7.395 (br, 2H, Ar H), δ 7.385 (br, 2H, Ar H), δ 7.113 (q, 2H, Ar H), δ 1.395 (s, 18H, -CH3), and δ 1.307 (s, 18H, -CH3). 31P NMR (162 MHz, CDCl3) measurements showed −δ 10.1. Purity (HPLC) was determined to be 98%.
Analytical Methods
Reversed-Phase HPLC (RP-HPLC)/UV Analysis:
Non-diluted extraction samples of 100 μL were separated on a C18 column (Phenomenex, Torrance, CA) with an Agilent 1200 series HPLC system (Agilent, Santa Clara, CA) using a gradient elution with mobile phases consisting of (A) 95% water/5% acetonitrile/0.05% trifluoroacetic acid (TFA) and (B) 5% water/95% acetonitrile/0.05% TFA at a flow rate of 0.5 mL/min. The initial separation condition uses 15% B for 2 min, then a two-stage gradient from 15% to 55% B in 10 min followed by the second gradient from 55% to 95% B in 9 min. The final flush was performed with 15% B for 4.5 min. UV-Vis absorbance was monitored at 215, 230, 245, and 280 nm with the complete spectra being collected from 190 to 600 nm. The data presented in this study was collected at 215 nm, as data for this wavelength was found to be representative for this study.
RP-HPLC/Mass Spectrometry (RP-HPLC/MS) Analysis:
Non-diluted extraction samples (100 μL) were also analyzed with RP-HPLC/MS using a Thermo LTQ, LTQ-XL, or Q Exactive mass spectrometer (Thermo Scientific, San Jose, CA) coupled with an Agilent 1200 series RP-HPLC using same type of separation column, gradient, and other separation conditions as those used in RP-HPLC/UV analysis. The eluent from the HPLC was subject to electrospray ionization in positive ion mode with mass spectrometry data being collected from 100 to 2000 m/z (LTQ) and from 90 to 1350 m/z (Q Exactive) in full MS and MS/MS modes.
Gas Chromatography/Mass Spectrometry (GC/MS) Analysis:
A GC/MS system coupled with headspace sampler (7890A/5975C) from Agilent Technologies (Santa Clara, CA) was used to analyze volatile and semi-volatile organic compounds in the extracted samples. Non-diluted samples (2 μL) were injected into the GC inlet at 250 °C and subsequently separated with a DB-5HT column and helium carrier gas. The initial oven temperature was set at 50 °C and held for 4 min, and then it was ramped to 300 °C at a rate of 25 °C/min and held at 300 °C for 8 min until the end of the run at 22 min. Electron ionization mass spectrometry data was collected between 35 and 750 m/z. Static headspace GC/MS analysis was also performed for both water- and organic-extracted samples for volatile compounds analysis. Specifically, 2 mL of the extracted samples was transferred into a 20 mL headspace vial, sealed, and heated up to 65 °C for organic-extracted samples and 80 °C for water-extracted samples. The out-gas from the headspace was injected into the GC inlet at 250 °C and analyzed by GC/MS under similar GC and MS conditions as used in the direct injection analysis.
Inductively Coupled Plasma Mass Spectrometry (ICP-MS):
Determination of inorganic elements present in SU bags' extracts was conducted using a Perkin Elmer Sciex (Elan DRC II) ICP-MS system (PerkinElmer, San Jose, CA). Samples were screened for elements within 6–15, 19–39, 42–210, and 230–240 m/z ranges in standard mode analyses. Each sample was diluted 10-fold with water, analyzed, and quantified against an external single point 50 ppb standard mix solution (VWR, Radnor, PA) containing 43 elements. Analysis of potassium, calcium, chromium, iron, and zinc was performed in dynamic reaction cell mode following 10-fold dilution with 0.5% nitric acid, addition of a cadmium internal standard, and was quantified against a five point calibration curve consisting of potassium, calcium, chromium, iron, and zinc standards.
Results and Discussion
The extractable profile of a bioprocessing component is strongly dependent on experimental conditions such as extraction solvent, temperature, and time. To generate extractable information most relevant to the leachables that could be produced in a specific application, it is critical to use appropriate solvent extraction conditions. SU bags are intended to be used with aqueous-based systems, so water is selected as a representative extraction solvent of the bioprocessing bags. As a polar solvent, water permits discovery of potential leachables, but has limited extraction strength towards poorly water-soluble extractables (e.g., hydrophobic compounds, fatty acids, etc.). Adding 20% ethyl alcohol and 20% acetonitrile to water will increase its extractive effectiveness, both in terms of the number of chemical species observed and the concentrations at which they are present in the extracts. Acetonitrile and ethanol are organic solvents miscible in water and are capable of solubilizing a wide range of organic compounds. On the other hand, if a solvent with even higher organic content or higher solvent strength were to be used, the number of expected extractables would be higher still. However, generation of an extremely large number of extractables with solvents of extremely high solvent strength may not necessarily be beneficial; many compounds may have little relevance to the leachables that can be produced in aqueous-based SU bags applications. This will not only put a significant burden on the analytical effort in the identification of this large number of compounds, but also present a possibility that some water-soluble compounds may not be seen in the high organic solvents. Overall, the 40% organoaqueous solvent, together with incubation conditions described below, are designed to represent an aggressive, yet still reasonable, scenario. In addition, both water and the organoaqueous solvent are compatible with the analytical techniques to be used for extractable identification and quantitation. Filling of the bags was accomplished through one of the attached ports on the bags. After filling the ports and other peripheral components were isolated and their contact with the extraction solvent was minimized.
Most SU bag suppliers recommend ∼60 °C as a maximum temperature for SU bags in order to avoid thermal degradation or loss of mechanical integrity. A few temperatures were tested during the collection of preliminary extractable data, and 50 °C was considered to be the most suitable for the given conditions to be used as the extraction temperature without affecting the integrity of the tested systems, and it was found to provide a large number of extractables. Thus, the SU bags were incubated in a conventional oven for 2 days at 50 °C, which is equivalent to approximately 4 days of cell culture at 37 °C, following the Arrhenius-like time-temperature equivalence that is typically used in accelerated ageing studies of polymers (20, 21).
Because of the large variety of additives used in the production of a plastic film, and the multiple degradation pathways of the additives and the polymer itself, the organic compounds extracted from a plastic film are of great diversity in terms of their physicochemical properties. This diversity presents a significant challenge in their analysis. A non-targeted strategy using an array of complementary analytical techniques was used in this study to maximize the number of identified extractable compounds. The analytical techniques employed include RP-HPLC/UV, RP-HPLC/MS, GC/MS, and ICP-MS, which together have high sensitivity and specificity for a wide range of volatile, semi-volatile, and non-volatile compounds as well inorganic elements.
The non-targeted approach and extraction conditions just described were applied to the four SU bag types, generating abundant information about their extractable profiles. As listed in Table I, a total of 53 extractables from the four different SU bags were identified, representing compounds of diverse physicochemical properties. Looking down the list of compounds extracted from bag 1, for example, the value of using multiple complementary analytical tools becomes clear. For bag 1, 13 identified organic extractables are listed. Five of these were detected by GC/MS, identified using National Institute of Standards and Technology (NIST) 08 and NIST 11 GC/MS library searches, and were confirmed with commercially available or custom-synthesized standards. Compared to GC/MS, direct identification with RP-HPLC/UV is less straightforward due to the lower specificity associated with the information provided in a UV spectrum. However, RP-HPLC/UV information can be valuable if the UV spectrum of an unknown compound is included in a UV library, although UV spectra are susceptible to variations due to the experimental conditions such as compound concentration and mobile phase composition. Two of the extractable compounds listed for bag 1 were detected by RP-HPLC/UV and identified from a UV spectrum search of an in-house UV library. The identities of these two compounds were confirmed using commercial standards, which matched both the UV spectra and the LC retention time of the unknown compounds. The rest of the identified extractable compounds were identified using information from RP-HPLC/MS and were also subsequently confirmed with commercial standards. The identification was based on the interpretation of the MS/MS spectra, accurate mass measurement, library search match (NIST 11 and in-house libraries), LC retention properties of the extractables, and correlation with information from other analytical techniques such as GC/MS. Identification of small molecules—especially ones pertaining to plastic additives, polymers, and their degradants products—is not trivial, but a detailed description of the identification process of each compound is outside of the scope of this paper.
Chemical Compounds Identified from Extracts of the Various SU Bags Studied. Observation of the compounds is broken out by the analytical technique used for identification: GC/MS (a), RP-HPLC/MS (b), and/or RP-HPLC/UV (c). The compounds are tentatively grouped according to their proposed source: tris(2,4-di-tert-butylphenyl)phosphite (i), hindered phenolic antioxidants (ii), phthalates (iii), polycarbonate (iv), degradation of polyethylene (v), slip agents (vi), degradation of EVA (vii), and unknown (viii)
Overall, the majority of the identified extractables from these SU bags are degradation products of polymers and their additives. For example, compounds 1–4 in Table I were found in all four SU bags, and are degradants of tris(2,4-di-tert-butylphenyl)phosphite (TBPP), an antioxidant commonly added to polyolefins (22). It is noteworthy that intact TBPP was not detected under the current extraction conditions and not observed even with an organic extraction using a solvent containing 80% acetonitrile (data not shown), which may indicate that the majority, if not all, of the TBPP in the films is degraded into small organic compounds or converted to other forms such as oxidized TBPP (with the phosphite being converted to phosphate). Degradation of TBPP into compounds 1 and 2 was reported to be dominant under heat or hydrolysis conditions (23), although formation of compounds 3 and 4 was not reported under such conditions. In contrast, generation of compound 4 from oxidized TBPP was found to be favorable upon gamma irradiation (18), which has been commonly used for SU bag sterilization. Oxidized TBPP was observable in the extracts with 80% acetonitrile solvent.
Degradants from other antioxidants were also evident; compounds 5 and 6 are related to hindered phenolic antioxidants such as Octadecyl-3-(3,5-di-tert.butyl-4-hydroxyphenyl)-propionate or Pentaerythritol tetrakis(3-(3,5-di-tert-butyl-4-hydroxyphenyl)propionate). Compounds 7–10 are derived from hindered phenolic antioxidants as well, including, for example, butylated hydroxy toluene. It is logical to see degradation products of both phosphite and hindered phenolic antioxidants in film extracts, as the combination of such antioxidants is widely known in the polymer industry to have a synergistic effect and is used to maximize polymer stability (24). Intact additives were also observed, including several different phthalates, used as plasticizers, and fatty acid amides used as slip agents in polymer processing. The fatty acids and fatty acids esters are also commonly used plasticizers and were observed in some of the SU bags.
ICP-MS was employed to determine, evaluate, and quantify the trace metals and inorganic elements present in the SU water extracts only. Inorganic elements—especially heavy metals—can influence the stability, safety, and efficacy of drug products and cell culture. The following elements were found to be present in the bioreactor bags extracts: boron, sodium, silicon, calcium, and potassium. The estimated levels of inorganic components were in the range of parts-per-billion levels and correlate across the SU systems, though silicon levels were determined to be significantly higher for one of the bioreactor bags (bag 4) (Table II).
Inorganic Elements Identified from the Water Extracts of the Various SU Bags Studied
The different extractable profiles observed from the four SU bags examined here reflect the diversity in the polymer films and/or the processing that was used for the manufacture of the SU bags. SU bags are typically made of multiple film layers, with each layer being made of a different polymer material and serving different mechanical or physicochemical functions in the SU bag. Although extractables from the most inner layer (i.e., the fluid-contacting film) may dominate the extractable profile, extractables from the other layers, even the most outside layer, can migrate into the fluid-contacting layer and eventually into the extraction solvent, contributing to the different and complicated extraction profiles of the SU bags from the various vendors. However, the extraction conditions and the non-targeted approach employed in this study proved to be very useful to capture the differences between the various SU bags and provide important extractable profile for them.
A closer look at the data clearly demonstrates the advantages of using the 40% organoaqueous solvent for extractables studies (Figure 1). Compared to the compounds extracted with water, a very similar set of extractables can be generated with the organoaqueous solvent, but with most of the compounds being extracted in much higher quantities. For bag 1, for example (Figure 1A), the abundances of compounds 1, 3, and 4 are approximately 20, 2, and 5 times higher, respectively, in the organoaqueous extracts than in the water extracts. The identification and quantitation of the unknown extractables were significantly facilitated by their higher abundance in the organoaqueous extraction sample. This is especially advantageous in cases when only instruments with relatively low sensitivity are available. In addition to reproducing all the compounds obtained in water extracts, a few extractables absent in the water extract can be observed in the 40% organic extract, corresponding to the compounds of high hydrophobicity and/or low water solubility. An obvious example of this in Figure 1A is compound 2. A second, important example of this can be observed in Figure 1B, where compound 4, bDtBPP, is observed only in the organoaqueous extract. Previous work has demonstrated conclusively that excessive leaching of bDtBPP from SU bags into cell culture medium interferes with the growth of mammalian cells (18,19). In fact, observation of bDtBPP in large quantities in bag 1 extracts was a critical clue leading to that discovery. Looking only at data from water extracts from bag 4 would give the impression that bDtBPP leaching would not be a problem for that bag—an inference that would be incorrect (see below). In truth, bDtBPP extraction into water is not always well correlated with results from a cell-based assay (CBA) designed to test bag suitability for cell culture-related operations, while bDtBPP extraction into the organoaqueous solvent is more reliably predictive. This is demonstrated in Figure 2, where CBA growth results—viable cell density, or VCD, from Hammond et al. (19)—for bags 1–4 are plotted against the quantities of bDtBPP observed in either water or organoaqueous extracts of the same bags. In the CBA, cell culture medium is held in the various bags and then used in cell growth experiments (25), and plots of cell growth versus leached bDtBPP concentration in the media yield a dose-response curve that overlaps neatly with that obtained by spiking bDtBPP directly into media (19, 26). The trend in Figure 2 from the organoaqueous extract data (filled symbols) qualitatively mirrors those dose-response curves, whereas the water extract data (open symbols) does not provide the same level of insight. We must carefully note that we are not implying that it is possible to quantitatively predict bDtBPP leaching into cell culture medium using the 40% organic extraction results, but rather that the organoaqueous solvent gives extraction results that are more (qualitatively) predictive than those of water only. Cell growth for bags 2 and 3 were statistically indistinguishable from controls, and results from bag 1 are obviously affected by bDtBPP. Bag 4, however, presents a very interesting case where the CBA showed a small but statistically significant decrease in cell growth relative to control. This effect was explained by the levels of bDtBPP leached into that CBA media sample (19), but would be completely unexpected if only water extract results were considered. The organoaqueous solvent, therefore, in combination with the incubation conditions used and the non-targeted approach to extractable compound identification, has proven to be an invaluable tool for the evaluation of flexible plastic bio-process equipment.
RP-HPLC/UV chromatograms of extracts for (A) bag 1 and (B) bag 4.
Comparison of cell growth data with quantities of bDtBPP observed in water or organoaqueous solvent extracts. The horizontal dotted line represents the VCD achieved in a control experiment using media not exposed to any SU bag, with the shaded region indicating the variability in control experiment growth. See text for reference to source for cell growth data.
As a final note, we should mention that one parameter we have not carefully controlled for in these studies is the length of time between when the various bags were irradiated and when the extraction studies were performed. A very recent paper reports that cell growth using certain bags can be highly dependent on those bags' ages (post-gamma) (27). Specifically, two bags were reported to cause poor cell growth when recently irradiated, but upon aging, the cell growth improved. The growth issues for those bags is almost certainly bDtBPP-related, so the most logical implication is that the amount of leachable bDtBPP in those bags decreases over time. In our opinion, the possibility that the leachable profile of a given test article could change slowly over time underscores the need for a strategy for the performance of robust extractables experiments. The extraction conditions outlined here give us confidence that although the absolute levels of the observed compounds may vary, their identities should not.
Conclusion
An effective extraction solvent system consisting of 20% acetonitrile, 20% ethanol, and 60% water has been developed and successfully used in the profiling of organic extractables from flexible SU bioprocess equipment. After incubation of the SU bags at 50 °C for 2 days, the organoaqueous solvent extracted a large number of organic compounds of diverse physicochemical properties from the SU bags. The compounds obtained from the organic extraction included all of the extractables generated from water extraction but in much higher abundances, which greatly facilitated the identification process. A non-targeted analytical strategy, employing an array of complementary techniques (RP-HPLC/UV, RP-HPLC/MS, and GC/MS), allowed confident identification of most of the extractables, with a total of 53 compounds being identified from four commercially available SU bags. The majority of the extractables were degradation products of the polymer additives, including antioxidants, slip agents, plasticizers, and so on. The utility of the extraction conditions is reflected by the effective extraction of a compound that was later demonstrated to be highly detrimental to mammalian cell growth. The profusion of extractable information obtained from this extraction protocol, along with the non-targeted analytical approach, indicates its great usefulness in the study of extractables from other bioprocessing materials used primarily for aqueous-based processes.
Conflict of Interest Declaration
The authors declare that they have no competing interests.
Acknowledgements
The authors thank Ping Yeh and Joseph Phillips for helpful discussions and Ken McRae for assistance in accomplishing the contract synthesis of bDtBPP.
- © PDA, Inc. 2015
