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:
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
Calculation of Free
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
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
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
8. Calculate the sum of column H and place in
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
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
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
TABLE 1 Spreadsheet for Calculation of Free Analyte Concentration
127CHAPTER 2.6 Free Analyte Immunoassay
Effect of Serum Proteins
on Free Analyte
As in the previous sections, free thyroxine is used as the
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
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.
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
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.
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
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
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
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.
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
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
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
G the biasing effects (on FT4) of exogenous binders (e.g.,
different amounts of BSA added to immunoassay
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
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.
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
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
Optimization of Antibody Affinity
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
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.
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.
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
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.
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.
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
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.
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
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
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
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
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
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Christofides, N.D., Sheehan, C.P. and Midgley, J.E.M. One-step, labeled anti-
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