123© 2013 David G. Wild. Published by Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/B978-0-08-097037-0.0000...
124 The Immunoassay Handbook
the proteins. The concentration of FT4 can be calculated
by equations derived from the Law of...
125CHAPTER2.6FreeAnalyteImmunoassay
TABLE 1 Spreadsheet for Calculation of Free Analyte Concentration
126TheImmunoassayHandbook
TABLE 2 Free Analyte Immunoassay
127CHAPTER 2.6 Free Analyte Immunoassay
Effect of Serum Proteins
on Free Analyte
Concentration
As in the previous sections...
128 The Immunoassay Handbook
Using the equations in the spreadsheet, one can challenge
these hypotheses by calculating the...
129CHAPTER 2.6 Free Analyte Immunoassay
the buffer compartment should be equal to the FT4 con-
centration of the undialyze...
130 The Immunoassay Handbook
This redistribution is dictated not only by the concentra-
tion and affinity of the antibody u...
131CHAPTER 2.6 Free Analyte Immunoassay
30-fold range can be observed, with severely ill patients
having binding capacitie...
132 The Immunoassay Handbook
and concentration of antibody so that the K[P] is kept at
1% of the binding capacity of a nor...
133CHAPTER 2.6 Free Analyte Immunoassay
However, reduction of the concentration of T3 cellulose
in the assay resulted in t...
134 The Immunoassay Handbook
amount of labeled antibody binding to the solid phase
(estimated after separating the liquid ...
135CHAPTER 2.6 Free Analyte Immunoassay
TESTS OF VALIDITY (ACCURACY)
Using the Law of Mass Action model described earlier,...
136 The Immunoassay Handbook
following the addition of TBG than following addition of
equimolar concentrations of TTR or H...
137CHAPTER 2.6 Free Analyte Immunoassay
Ellis, S.M. and Ekins, R. Direct measurement by immunoassay of the free thyroid
ho...
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The immuassay handbook parte22

  1. 1. 123© 2013 David G. Wild. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/B978-0-08-097037-0.00009-9 The free hormone hypothesis, originally advanced by Robbins and Rall in the late 1950s, states that, in the case of those hormones that exist in blood in free and protein-bound forms, the free hormone concentration constitutes the only determinant of physiological activ- ity. This hypothesis is widely accepted for the thyroid hormones (thyroxine, T4, and 3,3′5-triiodothyronine, T3) and some steroid hormones (e.g., testosterone). It may also apply to other analytes, such as vitamins and drugs, but evidence demonstrating a closer correlation of the free analyte concentration, rather than the total analyte concentration, to biological activity is scarce. This is primarily due to the very limited availability of accurate methods to measure free vitamins and drugs. Development of methods to measure free analytes (e.g., free thyroxine (FT4)) started in the 1970s, mainly through the pioneering work of Ekins and colleagues (e.g., Ekins & Ellis, 1975; Ekins et al., 1980). Over the last two decades, a large number of methods have been developed and latterly many have been automated (e.g., see THYROID or Demers, 1999). This makes their use in clinical practice very attrac- tive. In Europe, most laboratories measure FT4, rather than total T4 (TT4), whereas in the USA, FT4 measure- ment accounts for a lower proportion of the thyroid test- ing than in Europe. The main reason for the continued use of total T4 measurement in the USA is the continuing con- troversy regarding the accuracy and validity of some com- mercial methods. The primary aim of this chapter is to explain the basic mechanisms that dictate the free analyte concentration in the serum and how these mechanisms can be applied to develop valid free hormone assays. In addition, simple experimental designs will be described which can be used to challenge the validity of any free analyte assay. Basic Principles Governing the Free Hormone Concentration Following the endogenous release of certain hormones, such as thyroid and steroid hormones, into the blood cir- culation, they become bound to the transport proteins. Similarly, exogenous administration of some drugs and vitamins leads to the formation of binding protein–analyte complexes, with a small fraction of the drug or vitamin remaining unbound. The binding of the analyte to the serum proteins is reversible and, at equilibrium, the rate of dissociation of the analyte from the serum proteins is equal to its association rate. The proportion of analyte bound by the serum proteins is dictated by the relative affinity and concentration of each of the binding pro- teins. It is now widely accepted (at least in the case of thyroid and steroid hormones) that the free analyte fraction, rather than the fraction bound to the serum proteins, is the entity that binds to receptors and exerts biological activity. This does not mean that the hormone-binding protein complex has no function. Its role is to assure that a relatively constant supply of hor- mone to the organ tissues is maintained. This is achieved by dissociation of the hormone from the complex. Thus, when free hormone is removed from the pool as it is taken up by the tissues, sufficient free hormone becomes available by the dissociation of the complex to ensure a near constant supply of free hormone to the tissues. This property of the hormone–protein complex (i.e., dissoci- ation of hormone from protein while maintaining a near constant free hormone concentration) has been utilized to develop methods that measure the free hormone concentration. Throughout the remainder of this chapter, free thy- roxine (FT4) has been used as an example to illustrate the principles involved, both in the calculation of the free concentration and also in the development of methods for its measurement. This is because FT4 has been the most extensively studied hormone. However, the principles discussed apply to all free analyte measurements. Calculation of Free Analyte Concentration In the case of T4, following its release from the thyroid gland into the blood circulation, it becomes bound by three separate binding proteins. These are thyroxine-binding globulin (TBG), human serum albumin (HSA), and transthyretin (TTR). Typical concentrations of total thy- roxine and the binding proteins and the equilibrium con- stants (Keq) of the binding proteins (to T4) in a normal individual are shown below. Concentration of TT4 =1×10−7 mol/L Concentration of TBG=3.57×10−7 mol/L, Keq =2.2×1010 L/M Concentration of HSA=6.18×10−4 mol/L, Keq =1.3×106 L/M Concentration of TTR=5.56×10−6 mol/L, Keq =3.9×107 L/M The proportion of T4 binding to the proteins is dictated by the relative binding capacity (affinity (Keq or K) multi- plied by concentration) of each protein. Thus, at equilib- rium, the amount of T4 bound by TBG will be equal to: (1) The concentration of free T4 is controlled by the equilib- rium between the bound T4 and the free binding sites of Free Analyte Immunoassay Nic D. Christofides (nicchristofides@hotmail.com) C H A P T E R 2.6
  2. 2. 124 The Immunoassay Handbook the proteins. The concentration of FT4 can be calculated by equations derived from the Law of Mass Action. Thus, it can readily be shown that: (2) where PBT4 denotes the concentration of protein-bound T4, K, the net affinity of the proteins (toward T4), and [Pfree], the concentration of the unbound (free) binding sites of the proteins. Using this equation and knowing the total concentra- tion and affinities of the binding proteins and of T4, one can easily predict the in vivo serum FT4 concentration. In the next section, the construction of a simplified spreadsheet is described which can be used to calculate the in vivo FT4 concentration in serum. The spread- sheet can also be expanded to include immunoassay reagents (such as the antibody and other chemicals) and thus can be used to predict their influence on the FT4 concentration. Spreadsheet for Calculation of Free Analyte Concentration This can be performed using a computer spreadsheet. Once again FT4 is used as the example analyte. The pro- gram can be made available from the author. The program can be used to calculate both the in vivo and in vitro (e.g., by immunoassay) FT4 concentrations. Table 1 shows the calculations performed to derive the in vitro FT4 concentration, and Table 2 shows an example set of data. The in vivo FT4 concentration can be calcu- lated using the same program, by removing the reagent contribution (i.e., enter “zero” for the reagent concentra- tion and volume). The calculation steps are also outlined below. 1. Enter the volumes of serum, antibody, and other reagents in column C (cells 4–6). The total reac- tion volume is calculated by adding the three indi- vidual volumes (in cell C7); the dilution factor incurred by the serum, in the reaction vessel, is calculated by dividing the total reaction volume by the serum volume (i.e., C7/C4). If one wants to esti- mate the in vivo FT4 concentration, enter 0µL for volume of antibody (C5) and for volume of other reagents (C6). 2. Enter the serum concentrations (in g/L) of the binding proteins (TBG, HSA, and TTR), TT4, and the concentration of antibody used in the immuno- assay reagents in column C (cells C13–C16); if any other binder is used in the immunoassay reagents (such as bovine serum albumin, BSA), enter the concentration in C20. 3. Enter the molecular weights of the binding proteins and of TT4 in column D. 4. In column E calculate the molar concentrations of the binding proteins by dividing the inputs of col- umn C by the molecular weights in column D. 5. The molar concentration of binding proteins and TT4 in the immunoassay “tube” is calculated in column F. 6. Enter the affinity constants (K) of the individual binding proteins (including that of the antibody, if the program is to be used for simulations on immu- noassay performance) in column G. 7. The binding capacity (i.e., K[Ptotal]) is calculated by multiplying column G by column F and placing in column H. 8. Calculate the sum of column H and place in cell H25. 9. The concentration of T4 bound by each protein is calculated by multiplying column F by column H (divided by cell H25) and placing in column I. 10. The concentration of total protein bound T4 (PBT4) is calculated by subtracting the fraction, cell F16/H25, from cell F16 (concentration of TT4) and this is placed in cell H26. 11. The concentrations of free binding sites for each protein are calculated by subtracting column I from column F, placing in column J. 12. Calculate the product K[Pfree] by multiplying col- umn G by column J and placing in column K. 13. Calculate the sum of column K and place in cell H27. 14. Calculate the FT4 concentration (in M/L) by divid- ing H26 by H27 and placing in cell H28. 15. One can calculate the proportion of T4 carried by each protein by dividing column H by the cell H25 and placing in column L. 16. The fraction of the antibody which remains unbound can also be estimated by dividing J19 by F19 and placing the calculation in M19. The spreadsheet program assumes that one substance (in this case T4) is bound by the binding proteins but could be expanded to include the binding of other substances, which may compete (e.g., T3). The simulations presented in later sections have used the spreadsheet program out- lined above, since in the case of FT4, the contribution of T3 does not greatly affect the FT4 profiles obtained. However, the program will greatly underestimate the FT4 concentration if large amounts of binding inhibitors (such as nonesterified fatty acids) are present in the serum. Another possible limitation of this and other software programs is that it assumes that full equilibrium between T4 and any binding proteins has been reached, which may not be the case with some immunoassay methods. It is thus suggested that the results obtained are used in a qual- itative fashion (i.e., to establish whether the hormone concentrations will increase or decrease) rather than quantitatively. A similar program can be constructed for other free ana- lytes (e.g., FT3, cortisol, testosterone, etc.) following input of the relevant affinities and concentrations of the binding proteins (and concentration of the total analyte). It is how- ever important to note that, in the case of FT3, as the T4-binding affinity is greater than that of T3, the contribu- tion of T4 on the calculation of FT3 concentration will be significant and will require the construction of a more complex program.
  3. 3. 125CHAPTER2.6FreeAnalyteImmunoassay TABLE 1 Spreadsheet for Calculation of Free Analyte Concentration
  4. 4. 126TheImmunoassayHandbook TABLE 2 Free Analyte Immunoassay
  5. 5. 127CHAPTER 2.6 Free Analyte Immunoassay Effect of Serum Proteins on Free Analyte Concentration As in the previous sections, free thyroxine is used as the example analyte. Using the spreadsheet program, one can perform simu- lations to predict the concentration of FT4 in any conceiv- able circumstance, e.g., when the concentration and affinity (K[Ptotal]) of individual proteins are altered or when the concentration of TT4 is changed. Figure 1 shows the effect, on FT4, of altering the endogenous protein concentrations (while maintaining a constant TT4 concentration). In this example the concentration of individual proteins (TBG, HSA, and TTR) was changed (from 1/4 to 4-fold of normal concentration) while the TT4 concentration was kept at 100nmol/L (euthyroid concentration). It is clear from the graph that an increase in the concentration of the proteins leads to a decrease in FT4 concentration, whereas a reduction in the concentration of the proteins leads to an increase in FT4. Also evident from this figure is that the FT4 concentration is predominantly influenced (and controlled) by the TBG concentration (and affinity), rather than the other two binding proteins. This is the rea- son why the T4/TBG ratio has been used as an “indirect” measure of FT4. However, it can be predicted that this ratio will not accurately describe the FT4 concentration since the calcu- lation uses the total TBG concentration rather than con- centration of the free binding sites. Figure 2 shows the predicted (using the spreadsheet program) FT4 concentra- tion and the FT4 “index,” calculated from the TT4/TBG ratio (and calibrated in “FT4 units”) in a euthyroid serum spiked by different concentrations of T4. The results show that the T4/TBG ratio is linearly related to the TT4 concentration whereas a curvilinear relationship is observed between FT4 and TT4. At high TT4 concentrations (when the concentration of free sites on TBG is reduced), the T4/TBG ratio becomes nega- tively biased (in comparison to FT4), whereas at low TT4 concentrations (when the concentration of free sites on TBG is increased) the T4/TBG is positively biased. This is also illustrated (as a bias plot) in Fig. 3. It can be predicted that biased T4/TBG results will also be obtained in situa- tions where the TBG affinity to T4 is reduced or in situa- tions when the serum contains substances that can bind to TBG (and thus reduce the concentration of unoccupied binding sites). Of course, if the reduction in binding sites is not taken into consideration, the same will be true of estimates of FT4 obtained by the spreadsheet program. Nonetheless, the spreadsheet calculations can help in the understanding of the mechanisms that may influence the FT4 concentrations in certain clinical conditions. For example, the FT4 concentrations in severely ill patients is approximately 30% higher than the FT4 concentration typically seen in ambulatory patients, despite the fact that the corresponding TT4 concentration in these patients is approximately 50% lower than the ambulatory patients. A number of hypotheses have been put forward to explain the discordance between TT4 and FT4. These include: G the presence of substances in the serum of ill patients that bind to albumin, reducing the concentration of unoccupied T4-binding sites; G decrease in albumin concentration; G decrease in the binding affinity of albumin for T4; G decrease in the binding affinity of TBG for T4 or reduc- tion in the concentration of TBG. FIGURE 1 FT4 concentration following changes in the protein concentrations. FIGURE 2 Biasing effects of the T4/TBG ratio. FIGURE 3 Bias plot showing the expected difference (%) between the T4/TBG ratio (calibrated in pmol/L) and FT4, in a euthyroid serum spiked with increasing amounts of T4.
  6. 6. 128 The Immunoassay Handbook Using the equations in the spreadsheet, one can challenge these hypotheses by calculating the FT4 concentration in the different situations and establish the most likely cause of any TT4/FT4 discordance. It can be shown that, no matter how far one reduces the affinity and concentration of HSA and TTR, the presence of low TT4 concentration (50% lower than normal) will not cause an elevation in the FT4 concentration. However, the 30% increase in FT4 (in the presence of a 50% reduction of TT4) could result if either the concentration or affinity of TBG was reduced by 75–80% (or when the concentration and affinity are both reduced by 50%). Thus, one can show that the reason for the FT4/TT4 profile seen in ill patients is most likely to be due to a reduction in either the concentration or affinity of TBG. Both of these possibilities have indeed been demon- strated to occur in some non-thyroidal illness (NTI) patients (Csako et al., 1989, Wilcox et al., 1994). In Vitro Measurement of Free Analyte Concentration There are a number of different methodologies that can be used to quantify free analyte concentrations in biological fluids. All the methods involve “sampling” some of the free form in the serum sample and then quantitating the amount of free analyte sampled. The basic requirement, irrespective of methodology, is that the concentration of the free form sampled reflects the in vivo free analyte con- centration. This section will examine whether this require- ment has been met by the various methodologies. DIRECT EQUILIBRIUM DIALYSIS Direct equilibrium dialysis (ED) is a method that is con- sidered by many investigators as the reference method for measuring free hormones. Figure 4 is an illustration of the mechanisms involved in this method. The ED cell is made up of two compartments that are separated from each other by a semipermeable membrane. This membrane allows small molecules to freely diffuse from one compartment to another but prevents large mol- ecules (such as proteins) from doing so. The serum sample is placed in one compartment and buffer is placed in the second compartment. During an incubation period, T4 (and other small molecules) diffuse through the mem- brane, from one compartment to the other. When equilib- rium is reached, typically after 16–24h, the concentrations of FT4 and other small molecules in the two compartments are equal. However, as illustrated in Fig. 4, the number of FT4 molecules present in the buffer compartment is much larger than found in the serum compartment, although the FT4 concentration (per millilitre) is similar. The number of FT4 molecules is dependent on the ratio of the volumes in the two compartments, e.g., in Fig. 4, 200µL of serum is equilibrated against 2.4mL buffer resulting in the pres- ence of a 12-fold greater number of FT4 molecules in the buffer compartment. This “extra” FT4 is derived from the binding proteins (i.e., T4 which is normally bound to the serum proteins becomes dissociated and diffuses through to the buffer compartment). A crucial requirement of an authentic FT4 assay is that the amount of FT4 sampled (or in the case of ED, the amount of T4 diffusing from the serum compartment to the buffer compartment) does not alter the in vivo FT4 concentration, i.e., the concentration of FT4 measured in FIGURE 4 Schematic representation of a direct dialysis FT4 method. The serum (200µL), containing normal concentrations of binding proteins, is placed in the serum compartment. Buffer (2.4mL) is placed in a second compartment and is separated from the serum by a semipermeable membrane. At equilibrium the concentration of FT4 in the two compartments is equal. Measurement of the FT4 concentration present in the buffer compartment should therefore reflect the FT4 concentration present in the serum.
  7. 7. 129CHAPTER 2.6 Free Analyte Immunoassay the buffer compartment should be equal to the FT4 con- centration of the undialyzed serum. Whether the direct ED method used fulfills this requirement will depend on a number of factors. These include: G the buffer composition and pH of the dialysis buffer (these will affect the affinity of the binding proteins); G temperature used (affinity of proteins is temperature dependent); G magnitude of nonspecific binding (NSB) of T4 (increased NSB will cause further dissociation of T4 from its binding proteins); G nature of the membrane (i.e., should only allow diffu- sion of small molecules); G the volume of buffer relative to the volume of serum. These factors are very important since they will dictate the concentration of T4 dissociating from the buffer proteins and consequently the measured FT4 concentration. A proposed reference method, based on direct ED fol- lowed by ID-MS has recently been proposed (Thienpont et al., 2010). This method has been recommended in the NCCLS approved guideline C-45A. The Effect of a Reduced Protein-Bound T4 Concentration on FT4 Concentration The FT4 concentration expected following the removal of increasing amounts of T4 can be calculated using the spreadsheet program (see Fig. 5). As the amount of T4 being removed from a euthyroid serum increases, the serum FT4 becomes progressively decreased. It is, how- ever, clear that one would need to remove a very large amount of T4 from the serum before observing a large reduction in serum FT4 concentration. For example, dis- sociation (and removal) of 1000pmol/L of the TT4 will cause a reduction in FT4 concentration of less than 2% (or <0.2pmol/L). Serum Dilution In the example given above, I have considered diffusion of FT4 from the serum compartment through the dialysis membrane to the buffer compartment. An identical effect, i.e., dissociation of T4 from its binding proteins and near constancy of the FT4 concentration, will also be seen if a serum is diluted in an inert buffer. Indeed, as far as the mechanisms involved, the presence or absence of the dialy- sis membrane is irrelevant. Figure 6 shows the calculated (using the spreadsheet program) FT4 concentrations of three serum samples diluted by an inert buffer (such as 10mmol/L HEPES buffer, pH 7.4). One of the sera had a normal T4-binding capacity, another had a binding capac- ity which was fourfold higher than normal and the final serum had a binding capacity which was fourfold lower than normal. (The binding capacity is the affinity multiplied by the concentration of the binding proteins.) The results show that only when the dilution factor is increased more than 1000-fold does the FT4 concentration decrease signifi- cantly (by more than 10%) in the normal- and high-binding capacity sera. However, dilution of the low-binding capacity serum reduces the dilution window and causes a greater reduction of FT4 concentration than those seen in the serum with normal-binding capacity. These data suggest that in order to obtain unbiased FT4 results in low-binding capacity sera, the dilution of the assay used (equally appli- cable to all free hormone methodologies) should be kept to a minimum. Any assays that employ high serum dilutions will produce negatively biased results in such patients. IMMUNOASSAYS FOR FREE ANALYTES All immunoassays for FT4 (and other free analytes), irre- spective of assay architecture, have a number of common features. These are: G a serum dilution step; G addition of an antibody; G quantification of free (unoccupied) binding sites of the antibody. However, the assays do vary significantly, not only in architecture (i.e., the procedures used for quantification of the free binding sites of the antibody) but also on the level of disturbance of the T4/protein equilibrium exerted by the assay reagents and protocols. When an antibody is added to a diluted serum the fol- lowing sequence of events occurs. As the antibody binds to the FT4 more FT4 becomes available by the dissociation of the protein–T4 complex. The result is that T4 becomes redistributed between the serum proteins and antibody. FIGURE 5 The relationship between the amount of TT4 removed from serum (in pmol/L) and reduction (%) in FT4 concentration.
  8. 8. 130 The Immunoassay Handbook This redistribution is dictated not only by the concentra- tion and affinity of the antibody used (relative to the serum binding capacity), but also by whether any other ingredi- ents (e.g., BSA), included in the buffer formulation, can affect the binding of T4 to the serum proteins. The reac- tions involved can best be described using two simple equations. Equation (2) (also shown previously) describes the in vivo serum FT4 concentration. where PBT4 denotes the concentration of protein-bound T4, K, the net affinity of the proteins (toward T4), and [Pfree], the concentration of the unbound (free) binding sites of the proteins. Equation (3) describes the in vitro (i.e., in the immunoassay tube) serum FT4 concentration. (3) where PBT4 and IAT4 denote the concentration of T4 bound to the serum proteins and to the immunoassay reagents (including the antibody), respectively. K[Pfree]+K[IAfree] denote the binding capacities (i.e., affinity×concentration of free binding sites) of the serum proteins and immunoassay reagents, respectively. The spreadsheet program can be used to calculate both the in vitro (i.e., in the immunoassay tube) and the in vivo FT4 concentrations. It has been used to determine: G the effects of adding antibodies (with different K[P]) on the FT4 response to serum dilution; G the biasing effects (on FT4) of antibodies that have dif- ferent binding capacities (K[Ab]) in different patient populations (i.e., sera having varying binding capacities (K[Pfree]); G the biasing effects (on FT4) of exogenous binders (e.g., different amounts of BSA added to immunoassay reagents); G the optimal affinity constant (Keq) requirement for the antibody used in the immunoassay. Effect of Antibody Addition on the Free Analyte Sample Dilution Profile Figure 7 shows the serum dilution profiles expected when the affinity (K) and concentration of the antibody ([Pab]) are varied from 0 (i.e., no antibody added) to situations where the K[Pab] is 0.2%, 0.5%, 1%, and 15% of the total binding capacity in the immunoassay tube i.e., the K[Pab]/(K[Pab])+K[Ptotal] ratio was 0.002, 0.005, 0.1, and 0.15. In these situations, the antibody will sequestrate (or “pull off”) 0.2–15% of the serum total T4. The concentra- tions of the binding proteins and of T4 in the euthyroid serum sample used for these simulations were as described earlier in the chapter; the immunoassay protocol used 25µL sample in a total reaction volume of 125µL (with the only T4 binder in the reagents being the antibody). The serum was used at dilution factors of 1 (i.e., no additional dilution above the one already used in the assay, which was a fivefold dilution) to 160. The results show that the FT4 concentration is robust to serum dilution, as long as the combined effects of antibody concentration and affinity (K[Pab]) are kept to a minimum, compared to the overall concentration and affinities of the native binding proteins, e.g., the K[Pab]/(K[Pab])+K[Ptotal] ratio should be less than 0.5% in order to maintain robust- ness of FT4 on serum dilution. At higher K[Pab], the FT4 concentrations decrease in parallel to the dilution factor; the dilution-induced reduction in FT4 becomes greater as the K[Pab] increases. The clinical significance of the serum dilution profile is discussed later in this chapter. Effect of Antibody on the Free Analyte Concentration of Different Patient Populations Figure 8 depicts the biasing effects of adding antibodies (of different K[Pab]) in sera whose binding capacities span the range that would normally be seen in patients undergoing thyroid function testing (Nelson et al. suggested that a FIGURE 7 Effect of antibody on free T4 concentration. FIGURE 6 Effect of serum dilution on FT4 levels.
  9. 9. 131CHAPTER 2.6 Free Analyte Immunoassay 30-fold range can be observed, with severely ill patients having binding capacities that are eightfold lower and pregnancy sera (or patients with TBG excess) that are fourfold higher than the ambulatory subjects). Other cat- egories that have low serum binding capacities include patients with TBG deficiency, hyperthyroid patients, and newborns with respiratory distress syndrome. The results show that the use of antibodies with high K[Pab] will cause a negative bias in sera with low binding capacities, whereas a positive bias will be seen in patients whose sera have high binding capacities. Only assays that use antibodies with a low K[Pab], e.g., when the K[Pab]/ (K[Pab])+K[Ptotal] is less than 1%, will produce results that are close (i.e., <10% difference) to the true FT4 concentration. Effect of BSA Present in Immunoassay Reagents on Free Analyte Concentration Exogenous proteins, such as BSA, are commonly included in the reagents of most immunoassays, in order to reduce NSB of antibodies or of the analyte. In the case of the immunological measurement of FT4 and FT3, inclusion of BSA in the reagents was thought to make the assay robust to nonesterified fatty acids (NEFAs).* Figure 9 simulates the effects of including different concentrations of exogenous BSA in immunoassay reagents on the FT4 concentration in sera having different T4-binding capaci- ties. The immunoassay protocol used 25µL sample in a total reaction volume of 125µL. The results in Fig. 9 * NEFAs are normally generated in vitro through the actions of lipoprotein lipases, and because they are able to bind to the thyroid binding proteins, they cause a “false” elevation in FT3 and FT4 concentrations. This is usually not a major problem, as the concentration of NEFAs in the serum is normally too low to have any significant effects. However, a significant in vitro generation of NEFAs, which can cause an elevation of FT4, can occur when patients have been given heparin. Heparin is sometimes used to prevent clotting in infusion cannulae. In vivo administration of heparin stimulates the production of lipoprotein lipases and these act to release NEFAs. clearly show that inclusion of BSA in the immunoassay reagents of a free hormone assay will cause variable biases in results. Increasing the amount of BSA in the reagents causes increasingly negative biases in sera with low bind- ing capacities, whereas sera with high binding capacities become positively biased. As far as the notion that inclu- sion of BSA will protect against NEFA interference (since the NEFAs will be bound by the BSA), BSA actually causes the FT4 concentrations to be negatively biased, since the patients who are most likely to receive heparin are those with low serum T4-binding capacities. So it is inadvisable for patients receiving heparin to have their FT4 or FT3 levels assayed, since the alterations occurring in the serum composition due to NEFA generation cause the in vitro FT4 concentration to differ from the in vivo concentration. Optimization of Antibody Affinity and Concentration The spreadsheet program has so far been used to predict the free analyte concentrations when the analyte/protein equilibrium has been disturbed by exogenous addition of buffer (i.e., serum dilution), analyte binders (i.e., antibod- ies and BSA), or by alteration of the binding protein con- centrations and affinities. The results of these simulations suggest that in order to develop a valid and accurate free analyte assay, one should keep the disturbance of the ana- lyte/protein equilibrium to a minimum. If the delicate equilibrium in the sample is upset, the advantages of free analyte measurement vs total analyte measurement may be lost, as the assay results become like those of a total analyte. The results presented in the above sections suggest that addition of the antibody to the serum causes a reduction in its FT4 concentration. The magnitude of the reduction depends on the binding capacity of the antibody (K[Pantibody]) and thus, in order to minimize bias the antibody binding capacity has to be kept at a low level. The simulations performed suggest that the optimum binding capacity of the antibody should be less than 1% of the binding capacity typically seen in a normal serum. Using the spreadsheet program, one can vary both the affinity FIGURE 8 Biasing effects of antibodies. FIGURE 9 Biasing effects of antibodies. BC: binding capacity.
  10. 10. 132 The Immunoassay Handbook and concentration of antibody so that the K[P] is kept at 1% of the binding capacity of a normal serum. As explained previously, in these circumstances the antibody will sequestrate (pull off) 1% of the serum TT4. The percent- age of free binding sites on the antibody (calculated in cell M19) can then be monitored, along with the FT4 concen- tration, as the concentration of total T4 (cell C16 in the spreadsheet program) is altered. Figure 10 shows the results of these simulations. It is clear that the use of high affinity antibodies (1×1011 L/mol) at a concentration (in the tube) of 1.79×10−10 mol/L will result in a FT4 assay having excellent sensitivity but with a very reduced range, making it unsuitable for routine use. As the affinity of the antibody is decreased (but keeping the K[P] constant by adjusting the antibody concentra- tion), the dose–response curve becomes shallower, but with an increased range. At affinities of less than 1×1010 L/M, the curve becomes too shallow making it unsuitable for routine use. It was thus surprising that two FT4 assays having curves with the required characteristics (in terms of curve shape and range) were claimed to have used anti-T4 antibodies of affinities of less than 1×1010 L/M (Christofides et al., 1992; Christofides & Sheehan, 1995). This claim stimulated some debate in the literature, with Ekins (1992, 1998) suggesting that an error had been made in the measurement of the affinity constants of the anti- bodies and that only antibodies with affinity constants of more than 1×1011 L/M can produce the necessary curve shape. The data presented below show how antibodies with affinities of less than 1×1010 L/M can indeed be used in the measurement of FT4. The first experiment used a T4 antibody (K of 8×109 L/M, as measured by classical Scatchard plot analysis, using gravimetrically prepared T4 standards, which were diluted in buffer). The assay proto- col, based on a back-titration format (see next section), was as follows. Twenty-five microliters aliquots of serum FT4 standards (calibrated in ED) were pipetted into wells coated with a donkey anti-sheep antibody. One hundred microliters of sheep anti-T4 antibody was added, and the wells were incubated for 15min at 37°C. The wells were then washed and 100µL of a solution containing T3 conju- gated to horseradish peroxidase (HRP) was added (T3-HRP was used in order to reduce the possibility of dis- sociation of the antibody-bound T4). This second incuba- tion period was varied from 0.25 to 6h. The wells were then washed and the HRP substrate added. The emitted luminescence was measured in a luminometer. The dose–response curves are shown in Fig. 11. As predicted by Ekins (e.g., Ekins, 1998), the dose–response curve obtained with an antibody having an affinity of less than 1 × 1010 L/mol, when the assay was near equilibrium (after 6 h incubation) was too shallow to be a useful assay. However, as the incubation time was decreased, the slope of the dose–response curve became progressively steeper with the curve produced after 0.25 h incubation period having the necessary slope and range. In a second experiment an anti-T4 mouse monoclonal antibody with an affinity constant of 5×109 L/M was labeled with 125I and used in a “labeled” antibody method (see LABELED ANTIBODY METHODS). Fifty microliters of serum FT4 calibrators were pipetted into polystyrene tubes, followed by 100µL of the tracer antibody and 100µL of a solution containing T3, which was covalently linked to magnetizable cellulose separation suspension (SS). The concentration of the SS was varied from a “neat” concentration to one that was 1000-fold lower. The tubes were incubated at 37°C for 60min and then placed on a magnetic base for 20min. The liquid super- natant was removed and the pellet counted in a gamma counter (NE1600). Figure 12 shows the dose–response curves (plotted as percentage of the total antibody bind- ing to the SS vs FT4 concentration) of the assays using different SS concentrations. The data were also plotted (in Fig. 13) as %B/B0 vs FT4 concentration. It is clear that the slopes obtained in the assays using high concen- trations of T3 cellulose are too shallow, making the assays unsuitable for routine use. This outcome is in line with the prediction that FT4 antibodies having affinities of <1×1010 L/M will produce curves that are too insensitive. FIGURE 11 Does–response curves using the same antibody (over different incubation times). FIGURE 10 Simulated FT4 does–response curves using antibodies of varying affinity constants ●---● depicts an antibody with a Keq of 1×1010 L/mol, ●– – – –● depicts an antibody with a Keq of 2×1010 L/mol, ●—● depicts an antibody with a Keq of 3×1010 L/mol, ●······● depicts an antibody with a Keq of 5×1010 L/mol and ●-·-·-·● depicts an antibody with a Keq of 1×1011 L/mol. The assumptions made for this simulation include that the antibody concentrations used are sufficient to seques- trate (i.e., pull off) 1% of the serum TT4 and that the FT4 assays proceeded to equilibrium.
  11. 11. 133CHAPTER 2.6 Free Analyte Immunoassay However, reduction of the concentration of T3 cellulose in the assay resulted in the generation of a dose–response curve that had the required (for a FT4 assay) characteris- tics. The ED50 (i.e., the concentration of FT4 required to reduce the amount of antibody bound by 50%) of the dif- ferent assays presented in Fig. 13 ranged from >100pmol/L for the assay using “neat” T3 cellulose to 13pmol/L for the assay using the T3 cellulose at a con- centration of 1 in 1000. It is clear from the results of these two experiments that, if the assays are taken to (near) equilibrium then the theo- retical predictions (i.e., that it is impossible to produce a workable FT4 assay using antibodies with affinities of <1×1010 L/M) hold true. However, the use of nonequilib- rium conditions and/or the optimization of the assay reac- tants, e.g., adjusting the concentration and affinity of the T3 cellulose (for the separation of bound from free anti- body) permits the development of FT4 assays that have the necessary sensitivity and range. Back-Titration (Two-Step) Method for Free Analyte Immunoassay In this method, the serum is allowed to react with an anti- body that has been immobilized on a solid support. During this first incubation (which should be performed at 37°C), the antibody binds to the analyte in the serum. After the first incubation is completed the reaction mixture is removed by aspiration and the immobilized antibody washed. The unoccupied binding sites of the antibody can then be quantified by incubating it with labeled analyte. See Fig. 14. The use of a labeled analog of the analyte, having a lower affinity than the endogenous hormone toward the antibody, is preferable as this can reduce dissociation of the bound analyte from the antibody. The amount of tracer binding to the antibody can then be interpolated into concentration using the calibration curve, which is a plot of amount of tracer bound by the antibody against free analyte concentration. The free analyte values assigned to the calibrators are normally derived by calibration in a direct ED method. Labeled Analog Tracer Method In this method, the serum is incubated simultaneously with the antibody (this is usually immobilized on a solid surface) and a labeled derivative of the analyte (the labeled analog tracer). During a single incubation period (at 37°C), the analog tracer competes with the free analyte for the limiting number of antibody binding sites. The amount of tracer binding to the antibody is inversely proportional to the concentration of the analyte. At the end of the incu- bation, the antibody is separated from the rest of the reac- tants and the amount of bound tracer quantified (the measurement of the tracer depends on the nature of the label used, e.g., 125I, enzyme, or fluorophore) and then converted into dose by interpolation from a calibration curve. The free analyte concentrations assigned to the cali- brators are normally derived by using direct ED as the ref- erence method. See Fig. 15. An important requirement for this methodology (and also the labeled antibody method) is that the analog used does not have an affinity toward any of the serum binding proteins. If the analog has affinity toward any of the serum binding proteins then the free analyte concentra- tions obtained with such an assay will be dependent on the protein concentration. Binding of the analog to pro- teins can be eliminated by conjugating it to large proteins (Georgiou & Christofidis, 1996; Tsutsumi et al., 1987). This conjugation causes a sufficient steric hindrance to eliminate binding to the serum proteins. Labeled Antibody Methods Once again, free thyroid hormones will be used as the example. Thyroid hormone (e.g., T4 or a T4–protein con- jugate) is immobilized onto a solid surface (e.g., microtiter well surface). The serum sample and a labeled anti-T4 antibody solution are added to the solid phase and the mix- ture incubated at 37°C. During the incubation period, the antibody partitions itself between the liquid phase (con- taining the endogenous FT4) and the solid phase. The FIGURE 12 Does–response curves using different concentrations of SS. FIGURE 13 Does–response curves using different amounts of SS.
  12. 12. 134 The Immunoassay Handbook amount of labeled antibody binding to the solid phase (estimated after separating the liquid reactants from the solid phase) is thus inversely related to the amount of FT4 in the serum and can be quantified by interpolation from sera containing known concentrations of FT4 (the values are commonly obtained from ED). FT3 assays can be developed using immobilized T3 or a T3 conjugate and a labeled anti-T3 antibody tracer. A variation of this method has been successfully employed (Christofides et al., 1992, 1995, 1999a,b) in developing commercial immunoassays for FT4 (see Fig. 16). This utilizes the weak cross-reactivity (<1%) of the labeled anti-T4 antibody to an immobilized T3–protein conjugate. The weakly cross-reacting T2-protein conjugate has been used in the development of a FT3 assay. The use of this “heterologous assay” approach has a number of advantages. The first advantage, which is com- mon with all heterologous assays, is that the dose–response curve becomes steeper. Other advantages include faster kinetics, a much higher signal and making the assay more robust to interference by endogenous anti-thyroid hor- mone antibodies. Note however that the presence of a high concentration of anti-T3 autoantibodies with a very high affinity toward the immobilized antigen can still cause interference. Important requirements for these types of assays are lack of binding of thyroid binding pro- teins to the immobilized antigen (this is generally met by linking the antigen to a large molecule) and, in common with all free thyroid hormone assays, minimizing the dis- turbance of the endogenous T4/protein equilibrium. FIGURE 14 Two-step free T4.
  13. 13. 135CHAPTER 2.6 Free Analyte Immunoassay TESTS OF VALIDITY (ACCURACY) Using the Law of Mass Action model described earlier, one can design a number of experiments to compare the performance of any free analyte assay with the ideal assay. Examples of experiments that can be performed are given in this section. Spiking Serum Samples with Binding Proteins The response expected is a gradual decrease in free analyte concentration, as more protein is added. In the case of FT4, in the absence of any interference in the assay, one should expect that the % decrease in FT4 would be greater FIGURE 15 Labeled analog free T4 assay. FIGURE 16 Labeled antibody free T4.
  14. 14. 136 The Immunoassay Handbook following the addition of TBG than following addition of equimolar concentrations of TTR or HSA. The problem with this test is that the magnitude of the decrease in free analyte concentration will depend not only on the concen- tration (and affinities) of the added proteins but also on the concentration and affinities of the endogenous proteins. Thus, one cannot readily compare the experimental results with those expected from theory, unless the concentration and affinities of both the exogenous and endogenous pro- teins are known. Nonetheless, this test is useful in deter- mining any gross problems with the assay, e.g., if the tracer used in the assay has an affinity toward any of the binding proteins then adding this protein in the serum will result in an apparent increase (or no change) in the FT4 concentra- tion rather than the expected decrease. Spiking Serum Samples with Binding Blocking Agents The response expected is a dose-dependent increase in free analyte concentration. Blockers that can be used for thyroid hormones include drugs such as furosemide, ketoprofen, phenylbutazone, mefenamic acid, diphenyl- hydantoin, probenecid, sulindac, fenclofenac, and salicylic acid; other substances include anilino naphthalenesul- fonic acid and nonesterified fatty acids (e.g., oleic acid). This test, like the protein spiking test (above), can be viewed as qualitative rather than quantitative, since the increase in free analyte concentration expected will depend on both the concentration (and affinity) of the spiked substance and the concentration and affinity of the endogenous proteins. Dilution Test A quantitative test that can readily be performed with any free analyte assay is the serum dilution test. Dilution of serum should produce near-constant free analyte results if the assay is valid, but decreased free analyte values if the assay is invalid. In the case of thyroid hormones it has been proposed (Christofides et al., 1999a; Christofides et al, 1999b) that this test can be used to predict the perfor- mance of the assay in different patient categories. This is because serum dilution will, in effect, produce a panel of samples whose serum binding capacities reflect the spec- trum of binding capacities seen in patients undergoing thyroid function tests. For example, it has been shown that there is a 20- to 30-fold span of binding capacities of patients having thyroid function tests; this span can be reproduced by diluting a third-trimester pregnancy serum to 20-fold or 30-fold. Any decrease of FT4 seen following dilution would indicate that this assay would underesti- mate the FT4 concentrations in any patients who have low T4-binding capacities, e.g., hospitalized patients. The buf- fer that is commonly used in the serum dilution experiment is 10mmol/L HEPES (N-[2-hydroxyethyl] piperazine-N -[2-ethane]sulfonic acid), which can be obtained from Sigma, catalog no. H7523, pH 7.4. One possible problem with this approach is that dilution of sera to these extents (i.e., 20- to 30-fold) will excessively lower the protein content of the assay reagents and may intro- duce significant nonspecific effects. It may thus be prudent to reduce the dilution window to no more than four- to eightfold dilution (to reflect severe hypoproteinemia), to assure that there is sufficient protein present in the assay reagents to prevent these nonspecific events from happen- ing. The presence of a dilution-dependent reduction in FT4 concentrations indicates that the assay will produce negatively biased results with sera having low T4-binding capacities. Comparison with a Reference Method The composition of the patient panel used in such a com- parison is of paramount importance, since an apparently excellent relationship can be obtained between an invalid free analyte assay and the reference method if the panel excludes patients with high or low analyte binding capaci- ties. Thus, the panel chosen for this evaluation should include patient sera from severely ill, hospitalized patients, and pregnancy sera (preferably sera from the third trimes- ter). More importantly, the reference method chosen should be one that has, itself, been proved to be a valid free hormone assay. Concluding Remarks To measure free hormones or drugs in patient samples, there must be minimal disturbance of the equilibrium between the analyte and its binding proteins. Assays should not be judged on their assay architecture but on the level of disturbance they exert on this equilibrium. The fact that an assay is based on accepted physico-chemical principles (e.g., ED) does not necessarily make it a valid assay. Con- versely, when a particular assay is shown to be invalid it does not necessarily mean that all assays based on this architecture are also invalid. References and Further Reading Christofides, N.D. and Sheehan, C.P. Enhanced chemiluminescence labeled-antibody immunoassay (Amerlite MAB) for free thyroxine: design, development, and tech- nical validation. Clin. Chem. 41, 17–23 (1995). Christofides, N.D., Sheehan, C.P. and Midgley, J.E.M. One-step, labeled anti- body assay for measuring free thyroxine. I. Assay development and validation. Clin. Chem. 38, 1118 (1992). Christofides, N.D., Wilkinson, E., Stoddart, M., Ray, D.C. and Beckett, G.J. Assessment of serum thyroxine binding capacity-dependent biases in free thy- roxine assays. Clin. Chem. 45, 520–525 (1999a). Christofides, N.D., Wilkinson, E., Stoddart, M., Ray, D.C. and Beckett, G.J. Serum T4 binding capacity-dependent bias in the AXSYM FT4 assay. J. Immunoassay 20, 2101–2121 (1999b). Csako, G., Zweig, M.H., Glickman, J., Ruddel, M. and Kestner, J. Direct and indirect techniques for free thyroxin compared in patients with nonthyroidal illness. II. Effect of prealbumin, albumin, and thyroxin-binding globulin. Clin. Chem. 35, 1655–1662 (1989). Demers, L.M. Thyroid function testing and automation. J. Clin. Ligand Assay 22, 38–41 (1999). Ekins, R.P. and Ellis, S. The radioimmunoassay of free thyroid hormones in serum. In: Thyroid research: proceedings of the seventh international thyroid conference, Boston (eds Robbins, J. and Braverman, L.E.), 597–600 (Excerpta Medica, Amsterdam, 1975). Ekins, R., Filetti, S., Kurtz, A.B. and Dwyer, K. A simple general method for the assay of free hormones (and drugs); its application to the measurement of serum free thyroxine levels and the bearing of assay results on the ‘free thyroxine’ concept. J. Endocrinol. 85, 29–30 (1980). Ekins, R. One-step, labeled antibody assay for measuring free thyroxin. I. Assay development and validation (Letter). Clin. Chem. 38, 2355–2357 (1992). Ekins, R. The science of free hormone measurement. Proc. UK NEQAS Meeting 3, 35–59 (1998).
  15. 15. 137CHAPTER 2.6 Free Analyte Immunoassay Ellis, S.M. and Ekins, R. Direct measurement by immunoassay of the free thyroid hormone concentrations in serum. Acta Endocrinol. 177(Suppl), 106 (1973). Georgiou, S. and Christofidis, I. Radioimmunoassay of free thyroxine (T4) using 125I-labeled T4-IgG complex with very large molecular weight. Clin. Chim. Acta 244, 209–220 (1996). NCCLS. Measurement of free thyroid hormones; approved guidelines reference no. C-45A, Vol. 24, No. 31. Nelson, J.C. and Wilcox, R.B. Analytical performance of free and total thyroxine assays. Clin. Chem. 42, 146–154 (1996). Robins, J. and Rall, J.E. The interaction of thyroid hormones and protein in bio- logical fluids. Recent Prog. Horm. Res. 13, 161–208 (1957). Thienpont, L., et al. Report of the IFCC Working group for standardization of thyroid function. Clin. Chem. 56, 919–920 (2010). Tsutsumi, S., Ishibashi, K., Miyai, K., Nagase, S., Ito, M., Amino, N. and Endo, Y. A new radioimmunoassay of free thyroxine using 125I-labelled thyroxine-protein complex uninfluenced by albumin and thyroxine-binding globulin. Clin. Chim. Acta 170, 315–322 (1987). Wilcox, R., Nelson, J.C. and Tomei, R.T. Heterogeneity in affinities of serum proteins for thyroxine among patients with non-thyroidal illness as indicated by the serum free thyroxine response to serum dilution. Eur. J. Endocrinol. 131, 9–13 (1994).

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