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Two scenarios demonstrate the need to use the percent of parent drug loss rather than the percent of degradation products formed when reconciling mass balance calculations.
Mass balance correlates the measured loss of a parent drug to the measured increase in the amount of degradation products. It is a good quality control check on analytical methods to show that all degradation products are adequately detected and do not interfere with quantitation of the parent drug (i.e., stability-indicating methods). Regulatory agencies use mass balance to assess the appropriateness of the analytical method as a stability-indicating method and determine whether all degradants have been accounted for (1–4).
Figure 1: In the reaction shown above, the parent drug, an ester, degrades to produce an acid hydrolysis product with a different molecular weight relative to the parent drug. The amount (percent) of degradant is not numerically equal to the percent of drug degraded and correction factors are needed to properly reconcile mass balance.
In mass balance calculations, the loss of parent drug or the amount of drug remaining is determined from a sample assay, and the measured increase in degradation products is determined by a degradation method. The fundamental approach for determining mass balance is to quantitate the degradation peaks using degradation methods and then reconcile the measured loss in the parent drug with the amount of degradation products. If the loss in potency can be reasonably accounted for by the amount of degradants measured, then mass balance is achieved.
It has come to our attention that under certain circumstances it is not appropriate to estimate mass balance directly from the amount of degradation products formed but rather the percent parent drug lost. This percentage, which corresponds to the amount of degradant formed, is the ultimate quantity that should be used to reconcile mass balance. The amount of degradant is converted to the corresponding percent parent drug degraded by means of the ratio of molecular weight of the parent drug relative to that of the degradant. Thus, the operative entity used in reconciling mass balance is the percent of parent drug degraded. In this article, we present two scenarios to illustrate the necessity of making this conversion.
Scenario 1: Molecule degrades to form a lower molecular weight degradant
Because of the paucity of structural information about the degradation products of drugs and their unavailability in early phases of drug development, scientists quantitate degradants using area-percent normalization (area %). There is an underlying assumption of an identical response factor (area relative to amount) for parent drug and degradant. Discrepancies in mass balance when degradants are measured by area normalization have been rightly explained by citing differences in detector response for the parent drug and degradant. This is particularly true for analyses involving ultraviolet (UV) detection. Appropriate correction often is applied to area percent, including using relative UV response to convert area percent to weight–weight percent (5).
An overlooked cause for possible discrepancies in mass balance is the difference in molecular weight between the parent drug and the degradant. To get the percent of parent drug degraded, which is the useful term in a mass balance calculation, one often assumes, sometimes unknowingly, that the percent of degradant formed corresponds to the percent parent drug degraded. This assumption would be invalid if the degradant had a molecular weight that differed significantly from that of the parent drug.
Consider the case in which drug P degrades to form A, a degradant with a lower molecular weight:
One example is the hydrolysis reaction shown in Figure 1, in which the ester parent drug could degrade by hydrolysis to produce an acid hydrolysis product with a different molecular weight relative to the parent drug. The assumption that the amount (i.e., percent) of degradant is equal in numerical value to the corresponding percent of drug degraded is incorrect, as explained in the following section.
Differing detector response. Consider the case in which the amount of degradant is determined by area normalization and the detector response of degradant A differs from that of the parent drug P. To convert the percent degradant to percent parent drug degraded, two corrections must be applied to the former result. First, a relative response factor is needed to convert area percent results to weight–weight (wt/wt) percent results. The second correction, which often is overlooked, is the need to correct for the difference in molecular weight between the parent and the degradant as follows:
percent drug degraded = percent degradant (wt/wt) X (Mp ÷ MD)
in which Mp is the molecular weight of parent drug and MD is the molecular weight of degradant.
For example, if the amount of degradant quantitated is 0.5% (wt/wt), then the corresponding amount of parent drug degraded is:
percent parent drug degraded = 0.5% × (Mp ÷ MD)
and not 0.5%. Therefore, the number that should be reconciled with the potency of the drug to determine mass balance is (0.5% X [Mp ÷ MD]). That is, if the loss in potency as determined from the assay is equal to (0.5% X [Mp ÷ MD]), then there is perfect mass balance.
This second correction is necessary because the response factors calculated on the basis of concentration assume equal moles for the same mass of compound. Because the number of moles is a function of molecular weight, a significant difference in molecular weight can lead to errors in the estimation of percent degraded. When the molecular weights of a parent drug and a degradant are similar, then the ratio of molecular weights (Mp ÷ MD) is unity, and the percent degraded is equal to the percent degradant. Thus, the amount of degradant is equal to percent drug degraded.
Table I illustrates the effect of molecular-weight differences between the parent drug and the degradant on the error in a mass balance calculation. The analysis is a simulation of a drug with a molecular weight of 300 Da and degradants with molecular weights of 300, 250, and 350 Da. Error analyses are completed assuming degradants at levels of 0.5, 1.0, and 5.0%.
Table I shows that the error in mass balance calculation increases as the difference in molecular weight between the parent drug and the degradant increases. It also shows that the percent error is almost independent of the amount of degradant (at typical levels expected in pharmaceutical drugs). Thus, even in cases in which the level of degradant is low, the correction advocated in this article is appropriate and warranted.
Table I: The effect of differences in molecular weight of drug and degradant on the error in mass balance calculation.
Equivalent detector response. When the detector response is equivalent between the parent drug and the degradants, then area percent results can translate directly into weight–weight results. Thus, only a correction for molecular weight must be done as previously described.
Scenario 2: Molecule degrades by forming an adduct with a high molecular weight excipient
Consider the example in which the parent drug P forms an adduct with excipient E, as follows:
in which P – E is the degradant.
For example, consider the condensation reaction between a drug with a primary amine functionality and citric acid (see Figure 2). In this case, the parent drug undergoes a condensation reaction with citric acid to form an amide citrate adduct.
Figure 2: In this reaction, the parent drug undergoes a condensation reaction with citric acid to form an amide citrate adduct. The molecular weight of the adduct is greater than the parent drug, and the percent of degradant calculated on a weightâweight basis does not equal the percent of parent drug degraded. The difference in molecular weights necessitates a correction to the percent degradant to calculate percent drug degraded.
In cases in which the molecular weight of the adduct is significantly greater than the parent drug (as is the case just described), the percent of degradant calculated on a weight–weight basis is not equal to the percent parent degraded. Rather, the calculated percent degradant should be corrected for the difference in molecular weight as illustrated below:
percent degraded = percent degradant (wt/wt) X (Mp ÷ MD)
To further illustrate this point, consider the case in which the molecular weight of P – E is twice that of P and P degrades in a stability study to give 2% degradant (P – E). Mass balance is reconciled after converting the amount of degradant to percent parent degraded as follows:
percent parent degraded = 2% X (Mp ÷ MD) = 1.0%
For mass balance to hold, the assay result (amount of drug remaining) is 100 – 1.0% and not (100 – 2.0%).
These scenarios demonstrate that when the molecular weight of the parent drug differs significantly from that of the degradant, proper attention should be paid to the implications of this difference and appropriate corrections should be carried out to obtain a good mass-balance result. This process involves converting the percent degradant result to the corresponding percent parent degraded, because percent parent degraded is the operative number that should be accounted for in a mass balance calculation.
The authors gratefully acknowledge the valuable insights provided by Bruce Johnson and Steve Hagen of Pfizer, Inc. in their review of this article. We also thank Brian Weekley, Peter Angus, and Derek Jackson of Pfizer, Inc. and Loren Wrisley of Wyeth for valuable discussions over the years on the subject of mass balance.
Patrick Lukulay, PhD,* is a senior principal scientist–Analytical Research and Development, Pharmaceutical Sciences, Pfizer Global Research and Development, Ann Arbor Laboratories, 2800 Plymouth Road, Ann Arbor, MI 48105, tel. 734.622. 5524, fax 734.622.7800, Patrick.Lukulay@pfizer.comGerard Hokanson, PhD, is an executive director–Global Quality Assurance, Pfizer Global Research and Development, 50 Pequot Avenue, New London, CT 06320.
*To whom all correspondence should be addressed
Submitted: Feb. 22, 2005. Accepted: July 12, 2005.
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