Errors in the Measurement of Plasma Free Testosterone 1

In their investigations on the effect of weight loss on serum androgens in obese women with and without polycystic ovary syndrome (PCOS), Jakubowicz and Nestler (1) measured the concentrations in plasma of testosterone, free testosterone, and sex hormone-binding globulin (SHBG). Among their observations was that, although testosterone and free testosterone fell significantly after weight loss in patients with PCOS, this was not true in the weight-matched patients without PCOS. I believe that some of the conclusions need to be changed because the values for plasma free testosterone appear to be incorrect. This is based on internal inconsistencies in the data, disagreements with calculated values for free testosterone, and substantial discrepancies from the percentage of free testosterone in the literature obtained using a variety of other methods. The data in question appeared in Table 2 of Jakubowicz and Nestler (1) and are reproduced in Table 1 (below), along with calculations I have made. Two different kinds of calculation are in the table. The row labeled “Percent of Free Testosterone” is derived from the original data (1) and follows from the definition of percent free testosterone: (free testosterone/testosterone) × 100. The data in bold-face are our calculations of testosterone and percent of free testosterone using equations derived from the law of mass action as described (2). To make these calculations, we used the values for testosterone and SHBG in the table, an assumed serum albumin of 4.5 gm/dL, an association constant (Ka) for the interaction of testosterone and SHBG of 1 × 109 L/mol, and a Ka for the interaction of testosterone and albumin of 3 × 104 L/mol (2–4). There is an internal inconsistency in the published data (1) that is most easily appreciated by comparing the percent of free testosterone in the PCOS group before and after diet. It is unchanged in the face of 4.5-fold increase in SHBG, which is physicochemically not possible. The percent of free testosterone is a function of the concentrations of SHBG, albumin, and total testosterone, the relative concentrations of testosterone and SHBG, and the Ka that characterizes the interaction. However, when the ratio SHBG/T is large, the percent of free testosterone is a function only of the concentration of SHBG and the Ka (5). Since Ka is a physical constant, and therefore invariant, the percent of free testosterone must decrease when SHBG increases. (The contribution of albumin is relatively small, and it undoubtedly does not undergo large changes with weight loss; we will neglect it for purposes of this discussion.) In vivo, there is the potential for the confounding of this straightforward calculation. For instance, if a compound that competed for SHBG binding appeared in the plasma of PCOS patients after dieting, it could increase the percent of free testosterone, thus offsetting the increase in SHBG. However, in the face of an SHBG of 78 nmol/L, the concentration of such a compound, having the same Ka as testosterone, would have to be about 135 nmol/L. There are no steroids in plasma that bind to SHBG with an appropriate affinity that circulate in such high concentrations. Additionally, it is known that free fatty acids may decrease the binding of steroids to SHBG (6). However, they do not do so at physiologic concentrations (7), and hence, changes in their concentration could not account for the discrepancies presented in the table. The foregoing addresses an internal inconsistency in the data. In addition, the actual concentration of free testosterone reported by Nestler and Jakuobowicz differs substantially both from the calculated concentration (see table) and from that measured by a variety of other methods. In general, the way that percent of free testosterone is measured is to add a radioactive tracer of testosterone (free of radiochemical impurities that would bind differently from testosterone) to plasma in vitro, at a concentration that is small compared with endogenous levels, and then to separate bound from free testosterone at 37 C without disturbing the original distribution of testosterone between its free and bound states. At equilibrium, the tracer reflects the distribution of endogenous testosterone, and is used to calculate the percent of free testosterone. In addition to the constraint that equilibrium not be disturbed, it is important that the plasma sample not be diluted or, if it is, to take into account the effect of dilution on the original equilibrium. To accomplish the foregoing, a number of methods are used: equilibrium dialysis (8, 9), ultrafiltration (10, 11), flow dialysis (12), and steady state gel filtration (13). Furthermore, there are numerous authors who, as we have done, calculate the free and percent of free testosterone (2, 4) after determining total testosterone by immunoassay and SHBG by one of a variety of methods (reviewed in ref.14). In the papers cited, the mean percent of free testosterone in normal women is: 0.96 (9), 0.74 (8), 0.87 (10), 1.18 (11), 1.02 (13), 1.38 (12), 1.45 (2), and 1.36 (4). In those papers that examined hirsute women the values are: 1.74 (9), 1.22 (8), 2.09 (11), 1.68 (13), and 2.21 (12). If we take the post-weight loss measurements in the table to be normal, then the percent of free testosterone we calculated from the authors’ data (1) agrees with the published values for percent of free testosterone in normal and hirsute women reasonably well, better than do the measured values. Using the calculated numbers, it can be seen (see Table 1) that there is a very much more impressive fall in the plasma free testosterone concentration in the PCOS patients after diet (76% decrease) than was indicated by the original data (34% decrease). Further, the obese controls, like the PCOS patients, underwent a large (50%) decrease in free testosterone concentration. This result is qualitatively different from the 9% increase in plasma free testosterone obtained by its direct measurement. Thus, in this regard, the obese controls were not qualitatively different from the patients with PCOS. Because the measured values for SHBG (1) are within the range of those obtained by a variety of methods (14), and because the normal values for testosterone (1) agree with a previous survey of the literature (4), the error in the percent of free testosterone most likely can be attributed to the inaccuracy of the measurement of free testosterone. The free testosterone was measured (1) using a kit which purports to measure directly the concentration of free testosterone in plasma samples. It appears likely that this claim is not correct.