Michael Koleto

Compensation for divergence during an analytical batch is a primary motive for including duplicate calibration curves that bracket the unknown samples being measured. The drawback is that this adds time to the analysis. A single calibration curve run with staggered calibrants bracketing the unknowns was compared to running complete duplicate calibration curves, one at the beginning and one at the end of unknown sample analysis in an effort to accelerate discovery bioanalysis. The data, in terms of correlation coefficient (

) and the weighted residuals plot, show that a single calibration curve, with staggered calibrants bracketing the unknown samples, can be used successfully to accelerate discovery (nonregulated) bioanalysis. 

Designing a robust and reproducible generic liquid chromatography–tandem mass spectrometry (LC–MS-MS) method that can support discovery (nonregulated) bioanalysis of different molecules on a daily basis requires balancing scientific rigor with adequacy. Data integrity remains the critical objective. The only assumptions made in the discovery environment are in regard to extraction efficiency, stability, and response function. In essence, the generic method has to be good, or "adequate," enough such that reliable information can be quickly returned to facilitate the decision making process. 

The minimum acceptance criteria are a measure of systematic bias, or 

, the combination of which is a measure of total assay error (1). In addition to these requirements, reproducibility, sensitivity, and selectivity are the other key factors needed to cover the typical 1–10,000 ng/mL range commonly required in discovery pharmacokinetic (PK) bioanalysis. These factors are constrained by typical chromatographic run times of 2 min or less and a minimal sample cleanup step that is usually protein precipitation–based for in-vivo applications. All of this adds to the challenge of developing robust generic LC–MS-MS methods. 

The Calibration Curve — Regression Analysis Considerations

The main role of LC–MS-MS bioanalysis PK studies is to provide drug concentration data for an accurate indication of the new chemical entity (NCE) exposure time profiles. The standard curve serves as a reference line against which the concentrations of the unknown samples are calculated. The standard curve itself is a result of regression analysis that takes into consideration the mean values of all 

 (area ratio) and the line of best fit through each data point to attempt to account for random error.  

The most important consideration for bioanalysis spanning a broad range (1–10,000 ng/mL) is the choice of weighting factor. This is because LC–MS-MS bioanalytical data in almost all cases is heteroscadastic, a statistical term used for data in which the standard deviation changes within the range of measurements. In other words, the error is more or less proportional to concentration, and without proper weighting, the regression is inherently biased by the highest concentration (2). This is especially relevant in discovery bioanalysis where the high point on the curve can be as great as four orders of magnitude away, inherently introducing bias at the critical low end, near the limit of quantitation (LOQ), of the curve. Additionally, the coefficient of determination, or 

 (regression coefficient), actually can be misleading and often is a poor measure of curve fit quality because it fundamentally assumes constant error at all concentrations, which is never the case in bioanalysis (3). 

It is important to determine the best weighting factor, especially when covering the wide dynamic range typical in discovery bioanalysis. Statistically, the 1/

 weighting provides the best fit because it most correctly approximates the variance at the low end of the curve, and by doing so, normalizes the error across the range. This effectively allows for the best fit (2). Because unknown samples are bracketed between two standard curves (one run at the front and one run at the back), the weighting factor chosen also has to account for divergence. The divergence is especially important in LC–MS-MS as factors affecting response are continually changing. At this stage, stability of the NCE is still undetermined, column performance can degrade over time, and ion-source efficiency can be affected as the source becomes coated with sample components. All of these are typical considerations in discovery bioanalysis. 

Running two curves to test for divergence, commonly referred to as 

 technique (Figure 1b), takes time — and time is an important factor in discovery bioanalysis. Another approach to estimate divergence is to run calibrants across the same range in a scattered manner at the beginning and the end of the sample analysis, referred to as 

 technique (Figure 1a). In this case, calibrants at concentrations 1, 5, 50, 500, and 5000 ng/mL are run at the beginning and then 1, 2.5, 10, 100, 1000, and 10,000 ng/mL are run at the end. The 1-ng/mL calibrant is run twice because it is most susceptible to divergence (exceeding the ±20% CV criteria at the LOQ). This article attempts to correlate regression data obtained from the use of a single staggered calibration curve and compare it to the data obtained from the standard approach of running two full calibration curves, one at the beginning and one at the end of sample analysis. The goal of the experiment is to accelerate discovery bioanalysis without compromising data integrity.  

Figure 1: (a) Staggered multipoint calibration curve set-up. Calibrants are prepared from a single stock solution and no QCs are used. The 1 ng/mL sample is repeated twice to ensure the LOQ criteria are met. (b) Standard method using duplicate standard (STD) curves and quality control samples (QCs). The QCs and STDs are from two independent stock solutions to ensure the integrity of the regression. 			

NO, FW: 256.2) was used as the test compound, with reserpine (C

, FW: 609.3; 10 ng/mL) as the analog internal standard (IS). Calibrants were diluted using K2-EDTA rat plasma, and the calibration standards were serially diluted using a Hamilton Starlet Liquid Handler (Hamilton Co., Reno, Nevada).  

Plate 1 (Figure 1a) contained the multipoint staggered calibrants. Calibrants at 1, 5, 50, 500, and 5000 ng/mL were placed in the front of the plate, plasma blanks were placed in the middle, and calibrants 1, 2.5, 10, 100, 1000, and 10,000 ng/mL were placed at the end. Plate 2 (Figure 1b) contained duplicate sets of the calibrants in a low-to-high series, bracketing 50 plasma blanks in the middle, with interspersed quality control samples (QCs) at low, mid, and high concentrations. Both plates were repeated 10 times and the calibration curves were compared for divergence. 

A model 1100 LC pump (Agilent Technologies, Santa Clara, California) was used to perform the chromatography with a CTC PAL autosampler (CTC, Basel, Switzerland). Mobile phase A was water (0.2% formic acid) and mobile phase B was acetonitrile (0.2% formic acid). A gradient was structured as follows, with starting conditions set at 5% B at 0 min and 45% B in 0.01 min with a flow rate of 0.8 mL/min. The % B was ramped to 95% in 1.4 min; the flow rate was increased to 1.3 mL/min. After holding these conditions for 0.2 min, the gradient was ramped back down to the starting conditions. The total run time was 1.8 min. The column used was an 30 mm × 2.1 mm, 3-μm Atlantis C18 column (Waters Corp, Milford, Massachusetts). Analysis was performed on a TSQ Quantum Ultra mass spectrometer using atmospheric-pressure chemical ionization (APCI, Thermo Fisher Scientific, San Jose, California) in the MRM mode using unit resolution in Q1 and Q3. The scan time for both transitions was 0.2 s (resperine, 

Figures 2a and 2b show the results for the staggered and standard multi-point calibration curves, respectively. Both techniques use linear 

 (0.998 vs. 0.999) regression coefficients (coefficients of determination) and thus can be considered comparable. Although reporting 

 is conventional practice, one should take into consideration that the regression coefficient assumes that error is fairly constant across the bioanalytical range, which is seldom the case in bioanalysis. A better way to compare the techniques is to look at the plot of the weighted residuals (Figures 3a and 3b), which is useful in determining divergence as a direct consequence of analytical sensitivity. Based on these graphs, the single calibration curve run in a staggered manner is comparable to duplicate calibration curves. The data thus indicate that the information content required for rigorous quantitation is relatively unaffected and that running a single calibration curve in a staggered setup can be used in discovery bioanalysis without compromising data integrity. One can almost argue that using a single calibration curve in a staggered manner is perhaps more rigorous in terms of adhering to guidelines that require simple statistical models (4).  The larger question remains whether running a duplicate curve at the end of the sample analysis adds any significant value to the experimental end-point, which often determines bioavailability for an NCE. 

Figure 2: Correlation coefficient (r2) results for the (a) staggered (r2 = 0.998) and (b) standard (r2 = 0.999) multipoint calibration curves, respectively. No difference is observed between these two regression techniques. Note that r2 can be a misleading indicator as it assumes a constant bias for each weighted point across the bioanalytical dynamic range, which is seldom the case.			

 weighting provides the best fit because it most correctly approximates the variance at the low end of the curve and by doing so, normalizes the error at the high, low, and mid levels. No practical difference in the divergence was observed using the staggered technique in terms of 

 (0.998 vs. 0.999), slope (1.089 vs. 1.077), or during the comparison of the weighted residuals versus the concentrations (Figures 3a and 3b). This indicates that running a single calibration curve using the staggered technique may be a viable alternative to running duplicate calibration curves.  

Figure 3: The plot of the weighted residuals for the (a) staggered and (b) standard techniques. This plot is perhaps most useful in determining divergence as a result of the impact of sensitivity. Note the scale on the y-axis for the LOQ. Based on these data, a single calibration curve using the staggered technique provides comparable data and can be used in discovery bioanalysis.			

The authors would like to thank Rohan A. Thakur for his contribution to this article. The authors also wish to thank Richard Lelacheur, Vice President, PharmaNet USA for his input and discussions. 

(4)  "Guidance for Industry: Bioanalytical Method Validation," US FDA (2001). 

is Associate Director with PharmaNet in Princeton, New Jersey. 

Articles

A single calibration curve run with staggered calibrants bracketing the unknowns is compared to running complete duplicate calibration curves, one at the beginning and one at the end of unknown sample analysis in an effort to accelerate discovery bioanalysis.

Single Multipoint Calibration Curve for Discovery Bioanalysis

The use of dried blood spots (DBS) as a sampling technique was pioneered by Dr. Robert Guthrie at the University of Buffalo in the 1960s. The challenge he faced was to obtain blood samples from newborns to screen for phenylketonuria, a genetic metabolism disorder. Dr. Guthrie used a filter paper disk to sample blood via a heel-prick, which he then could place directly atop an agar culture plate used to screen for phenylketonuria (1). Today, the DBS technique is used routinely by hospitals in the developed world to screen newborns for inherited metabolic disorders and its success is related to several practical advantages; the DBS technique is less invasive, requires smaller sample volumes, is easier to transport and store, and reduces risk due to infectious pathogens (2,3). Recently, the pharmaceutical industry has been debating the utility of DBS for pharmaceutical analysis versus the established norm of plasma bioanalysis, primarily in an effort to reduce drug development costs.  

In discovery fast pharmacokinetics (PK), however, the advantages are straightforward, especially in terms of animal welfare (4,5). A key advantage is reduced cumulative stress on the animal. There are several factors that can stress the animal and therefore influence the PK profile; bruising, hemorrhaging, and thrombosis resulting from animal handling and venipuncture, surgical implantation of the cannulas for both dosing and sampling, and the associated adverse effects such as blockage, accidental removal, and infection, are all stress factors on the animal. Sampling smaller amounts of blood volume by using the DBS sampling technique has the potential advantage of dramatically reducing the stress factors on the animal, ultimately resulting in better PK data. 

One current limitation of the DBS technique is its amenability to automation when compared to established liquid-handling robotics, which make samples ready for analysis by liquid chromatography–mass spectrometry (LC–MS). Robotic liquid handlers enable complete workflow automation of plasma sample clean-up using protein precipitation techniques, allowing a large number of samples to be analyzed simultaneously. In most laboratories, a sample aliquot from a DBS card requires a manual step of coring the center of the dried sample on the card, a step that represents a bottleneck for high-throughput applications. In discovery PK applications in which a multitude of compounds are analyzed every day, tuning of the triple-stage quadrupole MS system for the multiple reaction monitoring (MRM) step specific for the compound of interest represents another step where throughput improvements can be made. While some companies have robotic platforms for DBS work, they are still first generation and do not compete with liquid-handling robotic platforms in terms of efficiency. This article introduces the advantages of accurate mass high-resolution LC–MS (HRMS) coupled to DBS sampling for fast PK applications in a discovery environment to overcome the transition from plasma bioanalysis to a DBS-based workflow. 

Verapamil (Sigma Chemicals, St. Louis, Missouri) was administered orally and intravenously to catheterized male rats at doses of 2 mg/kg (in 0.5% carboxymethylcellulose) and 1 mg/kg (in 10% hydroxypropyl-β-cyclodextrin), respectively. Blood was heparinized and collected at various timepoints, and immediately spotted in 30-μL aliquots to FTA DMPK-C cards (GE Whatman, Florham Park, New Jersey) via air-displacement pipette. The spots were dried overnight under ambient conditions. 

Verapamil standards and QC samples were prepared in fresh heparinized whole blood from spiking solutions. Spiking solutions for standards and QC samples were prepared by serial dilution from independent stock solutions (all in methanol). Pools were immediately spotted as described above and allowed to dry.  

Punches (6-mm) were removed from each spot and extracted in 90% methanol–10% water using diphenhydramine as an internal standard. The supernatants were analyzed by LC–MS (HRMS, Exactive, Thermo Fisher Scientific, Madison, Wisconsin) using a resolution setting of R = 25,000, which resulted in a scan speed of 4 scans/s. The mass spectrometer was verified to be in calibration by using a mixture of Ultramark caffeine, and MRFA, but no other optimization was done. A model 1100 high-pressure liquid chromatograph (Agilent Technologies, Palo Alto, California) coupled to a CTC Pal autosampler (Leap Technologies, Carrboro, North Carolina) was used to perform the chromatography and inject the sample. 

 Figure 1: Extracted ion HRMS chromatogram of verapamil (m/z 455.2892) at R = 25,000 (left panel top), and the verapamil spectrum at 1.61 min (right top panel). Total ion chromatogram (bottom left panel) and chemical noise at 1.61 min (bottom right panel). 			

Figure 1 shows the HRMS chromatogram and mass spectra of verapamil from the 6-mm core. While a resolution of R = 25,000 provides more than adequate specificity (right top panel, Figure 1), the presence of coeluted peaks can be seen easily due to the full-scan HRMS acquisition, indicating the extent of clean-up achieved by protein precipitation as a clean-up technique (right bottom panel, Figure 1). The advantages of full-scan HRMS become apparent over the traditional triple-quadrupole–based MRM assay, and one of these advantages is that every sample injected on the HRMS system can be monitored for ion suppression. The data file can be queried postacquisition (Figure 2), and in this example, the data file was queried for the ions (

 494, 522, 786, 804) representing the commonly suspected phospholipids. This cannot be done pragmatically on a triple-quadrupole system and requires a separate experiment to characterize the extent of ion suppression. During bioanalysis performed using MRM, it is simply assumed that the components responsible for ion suppression are not coeluted. However, when there is a discrepancy in the bioanalysis, the MRM data file is devoid of any information indicative of what might have caused the variance. Using HRMS, every sample injected can be queried for known components, and acquired data file mined for unknown causes of variance due to the full scan MS nature of the data acquisition. 

Figure 2: Postacquisition extracted ion chromatograms of common phospholipids and lysophospholipids displayed relative to the retention time of verapamil, showing the advantage of full-scan HRMS, as every injection can be monitored for interferences.			

The 6-mm core size provided adequate sensitivity (1 ng/mL) for the parent. The standard curve between the range of 1 ng/mL to 500 ng/mL, with QC samples at 5 ng/mL, 50 ng/mL and 250 ng/mL was linear (

 of 0.999) and the results are shown in Figure 3. The results indicate that the HRMS system operating in the full-scan mode meets the basic precision and accuracy requirements of non-GLP bioanalysis. Note that the QC levels represent a second independent weighing, used to substantiate the results obtained from the calibration curve (calibrants weighed independently), and have a precision result of less than 6% across the range. This is standard practice put in place to ensure integrity in a semihigh-throughput bioanalytical operation.  

Figure 3: Calibration curve results in the range 1â500 ng/mL including QC samples at 5, 50, and 250 ng/mL using the Exactive HRMS system at 25,000 resolution.			

After the sensitivity criteria were established, the plasma was harvested from the incurred whole blood and the DBS samples were analyzed using HRMS. Figure 4 shows the PK curves (IV versus PO), indicating a good fit for both sets of graphs. The PK parameters are shown in Table I and show no significant difference in terms of the normalized clearance (milliters per minute per kilogram) and the volume of distribution (liters per kilogram) between plasma bioanalysis and DBS.  

Figure 4: Comparison between DBS and plasma PK profiles for the IV and oral dose indicating a good fit between the two different sampling techniques.			

The FTA DMPK-C card discussed earlier was chosen because it was uncoated and as per the manufacturer, it did not contain impregnated chemicals with a potential to interfere with LC–MS. Additional interferences from the DBS card add to the sample clean-up load, which is substantial in any biological matrix, and thus, can contribute to problems during bioanalysis. Recovery does seem related to card thickness (and pore size), which affects spreadability of the spotted blood, thereby influencing drying time. Hopefully, there will be some quality control similar similar to the Newborn Screening Quality Assurance Program (NSQAP), which monitors lot-to-lot card quality for the pediatric applications. However, both the bioanalytical data, as well as the resulting PK parameters in terms of the clearance and the volume of distribution, prove that DBS as a sampling technique is a viable alternative to plasma analyses. Because both the DBS sample and the plasma aliquot were harvested from the same whole blood sample, one would expect the PK parameters to agree, which they do, indicating that the advantages provided by DBS can be realized by discovery fast PK bioanalysis.  

Table I: Clearance and the volume of distribution results between the plasma bioanalysis and DBS bioanalysis (normalized for dilution effect using a factor of 0.55 plasma to blood)			

The authors would like to thank Casey Tyrrel and Paul Taylor, Taylor Technology, and Jamie Boulet, Janet Dell, and  John and Gary Wronowski, Product Safety Labs. 

Rohan A. Thakur and Michael Koleto, Dahai Dong, and Benjamin Begley

 are with Taylor Technology, Princeton, New Jersey. 

 is with Product Safety Labs, Dayton, New Jersey.  

(2) P.M. Edelbroek, J. van der Heijden, and L.M. Stolk, 

(3) J.V. Mei, J.R. Alexander, B.W. Adam, and W.H. Hannon

(4) M. Barfield, N. Spooner, R. Lad, S. Parry, and S. Fowles, 

J. Chromatogr., B (Analytical Technologies in the Biomedical and Life Sciences) 

This article introduces the advantages of accurate mass high-resolution mass spectrometry LC–MS (HRMS) coupled to the dried blood spot (DBS) technique for fast PK applications in a discovery environment. Compared with the established norm of plasma bioanalysis using triple quadrupoles, HRMS coupled to DBS is a viable alternative. The benefit is access to critical new information (HRMS bioanalysis) and significantly less stress on the animal (DBS), both factors that potentially improve the quality of early PK data.

Michael Koleto

Articles

Single Multipoint Calibration Curve for Discovery Bioanalysis

Dried Blood Spots and High-Resolution Mass Spectrometry for Discovery Fast PK Bioanalysis