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Journal of Virology, October 2001, p. 9177-9186, Vol. 75, No. 19
Department of Pathology1 and the
Institute of Environmental Medicine,2
New York University School of Medicine, New York, New York 10016, and Research Center for AIDS and HIV Infection, Veterans
Affairs Medical Center, New York, New York
100103
Received 15 February 2001/Accepted 29 June 2001
Human immunodeficiency virus-type I (HIV-1) infection elicits
antibodies (Abs) directed against several regions of the gp120 and gp41
envelope glycoproteins. Many of these Abs are able to neutralize
T-cell-line-adapted strains (TCLA) of HIV-1, but only a few effectively
neutralize primary HIV-1 isolates. The nature of HIV-1 neutralization
has been carefully studied using human monoclonal Abs (MAbs),
and the ability of such MAbs to act in synergy to neutralize HIV-1 has
also been extensively studied. However, most synergy studies have been
conducted using TCLA strains. To determine the nature of Ab interaction
in HIV-1 primary isolate neutralization, a panel of 12 anti-HIV-1 human
immunoglobulin G (IgG) MAbs, specific for epitopes in gp120 and
gp41, were used. Initial tests showed that six of these MAbs, as well
as sCD4, used individually, were able to neutralize the dualtropic
primary isolate HIV-189.6; MAbs giving significant
neutralization at 2 to 10 µg/ml included 2F5 (anti-gp41), 50-69 (anti-gp41), IgG1b12 (anti-gp120CD4bd), 447-52D
(anti-gp120V3), 2G12 (anti-gp120), and 670-D
(anti-gp120C5). For studies of reagent interaction, 16 binary combinations of reagents were tested for their ability to
neutralize HIV-189.6. Reagent combinations tested included one neutralizing MAb with sCD4, six pairs consisting of two
neutralizing MAbs, and nine pairs consisting of one neutralizing MAb
with another non-neutralizing MAb. To assess the interaction of the
latter type of combination, a new mathematical treatment of
reagent interaction was developed since previously used methods could
be used only when both reagents neutralize. Synergy was noted
between sCD4 and a neutralizing anti-gp120V3 MAb.
Antagonism was noted between two pairs of anti-gp41 MAbs (one
neutralizing and one non-neutralizing). All of the other 13 pairs of
MAbs tested displayed only additive effects. These studies suggest that
Abs rarely act in synergy to neutralize primary isolate
HIV-189.6; many anti-HIV-1 Abs act additively to mediate
this biological function.
Passive immunization has established
the role of antibodies (Abs) in the prevention and treatment of many
viral infections, including polio, measles, rubella, mumps,
varicella-zoster, rabies, and hepatitis A and B (6, 7, 33, 38,
39, 47, 53, 83, 88, 89). Similarly, administration of polyclonal
or monoclonal Abs (MAbs) has been shown to prevent the infection of
chimpanzees and SCID mice with human immunodeficiency virus type 1 (HIV-1) (27, 28, 32, 82, 85) and of macaques with SHIV
(5, 61, 63, 86). Moreover, administration of immunoglobulin (Ig) preparations from the sera of HIV-infected individuals (HIVIG) into HIV-infected patients was associated with
reduced p24 antigen (Ag) levels and/or increased
CD4+ T-lymphocyte counts (46, 48, 56, 78,
96). Thus, Abs have been shown to have an important role in
preventing HIV-1 infection and may participate in some aspects of
controlling an established infection.
While the role of non-neutralizing Abs in preventing HIV-1 infection in
in vivo models has not been confirmed as it has been in other virus
systems (9, 11, 21, 37, 41, 45, 65, 67, 68), neutralizing
MAbs (NMAbs) and HIVIG with neutralizing activity have been most
frequently used and advocated for passive immunization against HIV-1.
However, a major obstacle in developing effective prophylactic or
therapeutic passive immunization strategies against HIV-1 is the
paucity of Ab preparations that effectively neutralize primary HIV-1
isolates. Only a few MAbs have been shown capable of neutralizing a
wide array of primary HIV-1 isolates (25, 35, 93). In
addition, while most HIV+ sera have neutralizing
activity against many primary isolates, and essentially all primary
isolates can be neutralized by at least some sera, when panels of sera
from HIV-1-infected individuals are tested against diverse primary
isolates, only about 52 to 65% of the serum-virus combinations show
neutralization, and both the Ab titers in sera and the levels of
neutralization achieved are generally low (54, 70, 71, 76,
98). Furthermore, experiments of passive immunization in animal
models suggest that a concentration of Ab inducing 99% neutralization
in vitro may be necessary for significant protective effects in vivo
(32, 79, 86), although it should be noted that the animal
infectious doses used in these experiments far exceed the probable
infectious dose to which humans are normally exposed.
These data suggest that, while Abs have potential promise as
immunotherapeutic and prophylactic reagents, their use is also fraught
with problems. Therefore, the finding that two or more Abs can act in
synergy to neutralize virus infectivity suggests that appropriately
selected combinations of Abs may be useful in protecting against
infection in vivo, can help to delineate mechanisms that protect cells
from infection, and may be useful in the design of passive and active
immunization strategies. This phenomenon of Ab synergy has been
described in the neutralization of many viruses; for example, enhanced
neutralization by pairs of Abs has been described for the following
viruses: vesicular stomatitis virus (97), West Nile virus
(80), Sindbis virus (20), Japanese
encephalitis virus (50), La Crosse virus
(51), Newcastle disease virus (84), rubella
virus (34), respiratory syncytial virus (2),
and bovine herpesvirus type 4 (26). These studies
suggested that one of the Abs in each pair could increase the binding
or increase the avidity of the other Ab, resulting in a greater degree
or greater breadth of neutralization.
The cooperativity of pairs of MAbs in neutralizing HIV-1 has been
extensively studied over the past several years. Neutralization synergy
was detected with a variety of anti-HIV-1 Abs to different gp120 or
gp41 epitopes. Synergistic neutralization has been demonstrated most extensively between anti-gp120V3 Abs and
anti-gp120CD4bd MAbs or sCD4 (1, 13, 17,
55, 60, 66, 69, 81, 91, 92, 95). In addition, synergy between
two anti-gp120CD4bd MAbs or between
anti-gp120CD4bd and
anti-gp120C5 MAbs has been reported
(55). The same effect has also been seen with double or
triple combinations of an anti-gp120V2 MAb with
an anti-gp120V3 and an
anti-gp120CD4bd MAb (58, 95), with a
combination of anti-gp120V3, anti-gp41 and
anti-gp120 MAbs (58), and with combinations of anti-gp41,
anti-gp120 MAbs, and HIVIG (58, 62). Moreover, in an HIV-1
env-mediated cell fusion assay which contrasts with the
cell-free virus neutralization assays used by other investigators studying synergistic neutralization of HIV-1, Allaway et al.
(1) observed synergistic interactions between the
anti-gp41 NMAb 2F5 and anti-gp120CD4bd MAbs, and
between anti-gp120V3 and
anti-gp120CD4bd MAbs.
Primary isolates are clearly more relevant to human infection than are
T-cell-line-adapted (TCLA) strains of HIV-1; however, most synergy
studies have been conducted using TCLA strains of HIV-1. Only one group
(62) has shown synergy against primary isolates by mixing
human MAbs with a polyclonal preparation of IgG. Such an Ab cocktail
consists of multiple Ab populations with diverse specificities against
a variety of epitopes in gp120 and gp41, making it difficult to
dissect the effect observed. The observed effects with such a
preparation could derive from the sum of the synergistic, additive, and
antagonistic effects of each Ab. To circumvent these ambiguities,
combinations of MAbs could be studied, but there are few data
concerning the ability of MAb combinations to neutralize primary
isolates, a result, in part, of the paucity of human MAbs isolated from
HIV-1-infected individuals which are able to neutralize primary
isolates. However, it has been shown with other viruses that
neutralizing activity can be conferred by combinations of two
non-neutralizing MAbs or by one NMAb and one non-NMAb (2, 26, 34,
59). Consequently, a study of HIV-1 neutralization was
undertaken using pairs of human MAbs directed against gp120 or gp41,
whether of two NMAbs or of one NMAb and one non-NMAb. For this, the
dualtropic primary isolate HIV-189.6 was
tested with single reagents or binary combinations of 12 human
anti-HIV-1 IgG MAbs specific for epitopes in gp120 and gp41.
Antibodies.
Humans MAbs were used in this study. They
included MAbs directed against five regions of gp120: V3 (MAb 447-52D
[35]), CD4bd (MAbs IgG1b12 [15, 16] and
654-D [55]), CD4i (MAb 4.8D [72, 90]), C5
(MAbs 450-D [49] and 670-D), and MAb 2G12, directed against a complex gp120 epitope (93). MAbs to three
regions of gp41 were also used: MAbs 50-69 and 246-D to cluster I
(99), MAbs 98-6 and 1281 to cluster II (99),
and MAb 2F5 to an epitope adjacent to cluster II at amino acids 662 to 667 (12). MAbs 2F5 and 2G12 were provided by J. Mascola
(Henry M. Jackson Foundation); MAb IgG1b12 was provided by D. Burton.
Recombinant sCD4 and MAb 4.8D were obtained from the NIH AIDS Research
and Reference Reagent Program. All other MAbs were produced in our laboratory.
Neutralization assay.
The GHOST cell neutralization assay
was used throughout (18). GHOST-R5 or GHOST-X4 cells were
used as target cells with the dualtropic primary isolate
HIV-189.6 or the X4 primary isolate HIV-1MNp (John Sullivan, University of
Massachusetts Medical School, Worcester), respectively. The latter
isolate was derived from the spleen cells of patient MN and was never
cultured in cell lines. The GHOST cells were maintained in Dulbecco
modified Eagle medium supplemented with 10% fetal calf serum, 1%
glutamine, 2% penicillin and streptomycin, and 500 µg of Geneticin,
50 µg of hygromycin, and 1 µg of puromycin/ml. Cell monolayers,
when confluent, were resuspended using 0.25% trypsin. The cells were
carried for 15 passages and then replaced with fresh cells from stocks
frozen at the second or third passage. For the GHOST cell
neutralization assay, 6 × 104 GHOST
cells/well/0.5 ml were seeded into wells of 24-well tissue culture
plates and allowed to grow for 24 h. HIV-1 virus stock was diluted
to a predetermined concentration which had been found to result in
~1,000 infected cells per 15,000 total cells measured cytofluorometrically at the end of the assay. Serial dilutions of sCD4,
MAbs, or mixtures (present at a constant ratio in each experiment) were
prepared in culture medium, and then equal volumes of appropriately
diluted virus and MAbs were mixed and incubated at 37°C for 1 h
before being applied to the GHOST cells in the presence of DEAE-dextran
at 8 µg/ml. After overnight incubation, the virus-Ab-containing
medium was removed, the cell monolayers were washed, and the cells
incubated for 3 to 4 days. For harvest, cells were resuspended using 1 mM EDTA, fixed in 2% formaldehyde, and then analyzed using a FACScan
flow cytometer (Becton Dickinson). The percent neutralization was
calculated using the number of infected cells observed in the absence
of Ab as the denominator. The irrelevant human MAb 860-55D specific for
parvovirus B19 (3) was used at 10 µg/ml as a negative
control in each experiment.
Calculation of neutralization and synergy.
Most of the
methods used to analyze and define synergy are based on the analytical
method of Chou and Talalay (19). Briefly, this method
yields a parameter (the combination index) that describes the
interactions among the Abs in a given combination. This method takes
into account the potency (median effect dose values or antibody concentration at 50% neutralization [EC50])
and the shape (sigmoidicity) of the dose effect curve based on the
median effect equation of Chou and Talalay. This requires that both Abs
used in a combination be capable of neutralizing the virus used in the
experiment. Because the majority of MAbs used in this study were not
able to neutralize primary isolate HIV-189.6 by
themselves, the Chou and Talalay method could not be used to analyze
the effect of most of the Ab combinations tested. Therefore, as
described in the Appendix, we developed a mathematical method to
analyze the combination effect of two MAbs based on the comparison of
the experimental effect of the combination of two MAbs to the effect
predicted under the hypothesis that the two MAbs act neither in synergy nor in antagonism but rather in a statistically independent manner. (See the Appendix for a comparison of our method and other previously used methods.)
0022-538X/01/$04.00+0 DOI: 10.1128/JVI.75.19.9177-9186.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.
Additive Effects Characterize the Interaction of Antibodies
Involved in Neutralization of the Primary Dualtropic Human
Immunodeficiency Virus Type 1 Isolate 89.6
ABSTRACT
Top
Abstract
Introduction
Materials and Methods
Results
Discussion
Appendix
References
INTRODUCTION
Top
Abstract
Introduction
Materials and Methods
Results
Discussion
Appendix
References
MATERIALS AND METHODS
Top
Abstract
Introduction
Materials and Methods
Results
Discussion
Appendix
References
p1p2. In the absence
of both synergy and antagonism, the predicted percent neutralization
under these conditions is 100 × p12.
Note that, for a meaningful comparison, the combination of the two MAbs
must consist of a mixture made according to the doses D1 and D2. In
most of our experiments D1 = D2; in these cases, the mixture has
equal concentrations of each MAb. If there is neither synergy nor
antagonism then, except for statistical variation (see details in the
Appendix), the difference between the observed and the predicted
percent neutralizations should be small. Significant differences
between the observed experimental percentage neutralization and the
predicted percentage neutralization (for each combination of reagents)
were defined by 90% confidence intervals for
p12, where the width of these intervals were
based on the variation within and between experiments with each MAb.
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RESULTS |
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Top
Abstract
Introduction
Materials and Methods
Results
Discussion
Appendix
References
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Neutralization of HIV-189.6 by individual MAbs specific
for gp120 or gp41, and by sCD4.
The capacity of a single MAb to
neutralize HIV-189.6 is represented in Fig.
1 and 2.
Two groups of MAbs were tested: MAbs directed against gp120 (Fig. 1)
and MAbs directed against gp41 (Fig. 2). MAb 860-55D, specific for
human parvovirus B19, was used as a negative control. This latter Ab
was tested in each of 24 experiments at 10 µg/ml, and the percent
neutralization it produced was used to calculate the 95% confidence
limit of the assay. This value, 14%, was used as the cutoff point
below which neutralization was considered nonsignificant.
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HIV-189.6 neutralization by MAb combinations.
As
shown above, only four of the 12 anti-HIV-1 MAbs were able to effect
strong neutralization of HIV-189.6. In order to
assess the interaction between two non-NMAbs or between one NMAb and one non-NMAb, a new mathematical treatment of reagent interaction was
developed, since previous methods could not be used unless both
reagents neutralize. Accordingly, the observed percentages of
neutralization achieved when a fixed ratio of two MAbs was tested at
several concentrations were compared to the percentages of
neutralization predicted based on calculations of the level of
neutralization that would be achieved if the two MAbs were acting in an
additive manner. Significant differences between observed experimental
values, and predicted additive effects were defined by the 90%
confidence limits based on the variation within and between
experiments. Figure 4 shows the observed
dose-response neutralization curve (effect "obs") for each tested
combination of MAbs against HIV-189.6 and the
predicted additive effect (effect "pred") for that pair of MAbs.
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), as well as the predicted
additive effects (pred, 
) are shown on the y axis for
16 binary combinations of reagents, as the means of 2 or 4 independent
experiments. The total amount of the combined MAbs used in the
virus-MAb mixture for the neutralization assay is shown on the
x axes.
Combinations of two anti-gp120 MAbs. The anti-gp120V3 loop MAb (447-52D) was combined with MAbs directed against gp120 epitopes CD4bd (MAbs IgG1b12 or 654-D), CD4i (MAb 4.8D), or C5 (MAbs 450-D or 670-D). As shown in Fig. 4a to e, the effect observed with all of these combinations was, in each case, similar to the predicted additive effect, whether the combination represented two neutralizing antibodies (e.g., 447-52D and IgG1b12) or one NMAb and one non-NMAb (e.g., 447-52D and 670-D). The difference between the observed effect and the predicted additivity was not significant based on the 90% confidence limit. The same additive effect was observed when 447-52D and IgG1b12 were tested against another primary isolate, HIV-1MNp. Furthermore, the results with HIV-189.6 were similar whether GHOST-R5 or GHOST-X4 cells were used (data not shown).
Combinations of one anti-gp120 MAb and one anti-gp41 MAb. The envelope of HIV-1 is composed by glycoprotein gp120 noncovalently associated with glycoprotein gp41. In the native envelope of HIV-1, epitopes in gp41 are partially or completely hidden by their association with gp120 or by the structure of these molecules assembled into trimers (8, 75, 77). However, some anti-gp41 MAbs have been shown to neutralize HIV-1, including MAbs 2F5 (25, 94), 98-6 (43), clone 3 (22), and 50-69 (see Fig. 2). Therefore, we examined whether anti-gp120 MAbs could increase the neutralizing activity of anti-gp41 MAbs. As shown in Fig. 4f to k, all six combinations of anti-gp120 and anti-gp41 MAbs tested, whether consisting of two NMAbs (2F5 with 447-52D or 2G12) or of one neutralizing and one non-NMAb (447-52D with 246-D), displayed an observed effect comparable to the predicted additive effect.
Combinations of two anti-gp41 MAbs. Finally, we examined the effect of combinations of two anti-gp41 MAbs on HIV-1 neutralization. This type of combination has not been examined to date on either TCLA or primary isolates of HIV-1. Three combinations of anti-gp41 MAbs were tested for their ability to neutralize HIV-189.6: the effect observed with the two neutralizing anti-gp41 MAbs, 50-69 and 2F5, was similar to the predicted additive effect (Fig. 4l). These two MAbs recognize distinct epitopes in gp41. Two other anti-gp41 combinations (MAb 98.6 with either 2F5 or 50-69 [Fig. 4m and n]) displayed a significant difference between the observed and the predicted additive effects. For these latter two combinations, the observed effect of each mixture was significantly less than that of the predictive additive effect. Interestingly, antagonism occurred between two MAbs (50-69 and 98-6), which recognize different gp41 epitopes (cluster I and cluster II, respectively [99]) and between two MAbs (98-6 and 2F5) which recognize different epitopes in a contiguous portion of the cluster II region of gp41.
Additivity characterizes the interaction of most MAbs
tested.
Table 1 summarizes the
results of the 16 combinations of reagents tested for neutralization of
HIV-189.6. Of the 16 combinations, 13 demonstrated additivity. Synergy was observed only between sCD4 and an
anti-gp120V3 MAb, while antagonism was
demonstrated between two combinations of anti-gp41 MAbs, one of which
was non-neutralizing for HIV-189.6 (MAb 98-6)
while the other member of the pair (either MAb 50-69 or MAb 2F5) could
neutralize this virus.
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DISCUSSION |
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Top
Abstract
Introduction
Materials and Methods
Results
Discussion
Appendix
References
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Various combinations of human MAbs have been studied over the past several years which have shown additive, synergistic, or antagonistic effects on the neutralization of HIV-1 (13, 14, 40, 55, 57, 58, 61, 62, 81, 91, 92). In most of these studies, TCLA strains of HIV-1 were used, and most frequently the authors of these reports have used a computer model developed by Chou and Talalay (19) to analyze and define synergy. This method was originally developed to define the interaction of drug combinations and requires that each reagent in the combination display an effect which can be represented by a dose-response curve (see Appendix). This requirement excludes the possibility of analyzing combinations of reagents such as Abs where at least one member of the pair is non-neutralizing, i.e., displays no dose-response curve in the neutralization of the test virus strain. Moreover, this computer model can define an interaction as synergistic when the increase in neutralization observed is due to intra-experimental variation (81).
Since most Abs to the envelope glycoproteins do not neutralize HIV-1 primary isolates, yet are present as a complex polyclonal mixture in HIV+ sera, defining the functional interaction of non-neutralizing Abs and of neutralizing and non-neutralizing Abs could reveal important interactions useful for designing active and passive immunization regimens against HIV-1. To conduct such studies, it was necessary to develop a mathematical method that would be generally applicable for the analysis of the effects of Ab combinations, be they representatives of neutralizing or non-neutralizing Abs. Such a method was developed (see Appendix) and applied here. We demonstrated a synergistic interaction between sCD4 and an anti-gp120V3 loop MAb, 447-52D, confirming other studies showing synergistic effects between sCD4 and anti-gp120V3 MAbs (1, 81). However, additivity characterized the vast majority of MAb interactions, while antagonism was noted in two cases.
As noted above, some combinations of Abs against gp120 have previously been found to have a positive cooperative effect in neutralizing HIV-1; however, our results indicate that synergy appears to be the exception rather than the rule. Thus, all five combinations of anti-gp120 MAbs tested (Fig. 4a to e), whether of two NMAbs or of one NMAb and one non-NMAb, displayed only additive effects in neutralizing the dualtropic primary isolate HIV-189.6. Interestingly, one combination, MAbs 447-52D (anti-gp120V3) and 654-D (anti-gp120CD4bd), had previously been shown to synergize in neutralizing the TCLA HIV-1IIIB strain (55); however, we show here that this combination has only an additive effect against primary isolate HIV-189.6. This result supports the hypothesis that epitope presentation, conformation and/or flexibility of the HIV-1 envelope appear to differ between TCLA and primary HIV-1 isolates (10, 30, 74, 100).
While several anti-gp41 MAbs have displayed neutralizing activity against HIV-1, only one, MAb 2F5, has shown broad activity against primary isolates (22, 25, 43, 94). In this study we report that another anti-gp41 (50-69), specific for cluster I, is able to neutralize primary isolate HIV-189.6. The analysis of the ability of various anti-gp41 MAbs to neutralize this primary isolate in combination with anti-gp120 MAbs (447-52D or 2G12) showed only additive effects (Fig. 4f to k). Similar results were obtained with the TCLA strain of HIV-1IIIB (55). However, Li et al. showed that the combination of an anti-gp120V3 MAb (694/98D) and anti-gp41 MAb (2F5) could display synergy against SHIV-1vpu (expressing the envelope of HIV-1IIIB) (57).
Among the three pairs of anti-gp41 MAbs tested, two displayed antagonism in the neutralization of HIV-189.6. Thus, when MAb 98.6 (which does not neutralize HIV-189.6) was used in combination with MAb 2F5 (Fig. 4m) or with MAb 50-69 (Fig. 4n) (both of which neutralize HIV-189.6 [Fig. 2]), the potency of neutralization was reduced. This is the first time that antagonism has been shown between two anti-gp41 MAbs, although a similar antagonistic effect in HIV-1 neutralization has been previously reported with a pair of anti-gp120 MAbs directed against gp120 (with Abs to gp120V3 and anti-gp120CD4bd [40]). Antagonism between Abs has also been demonstrated in other virus systems (42, 64). Several explanations could explain this phenomenon of antagonism: negative cooperativity between two MAbs could reflect conformational rearrangements induced by one of the Abs, inhibiting subsequent interactions with the neutralizing Ab of the pair. Abs might also interfere with each other's binding by steric hindrance (26); the antagonism between MAbs 98-6 and 2F5 might be an example of this. Thus, Gorny and Zolla-Pazner (36) recently showed that MAbs 98-6 and 2F5 could bind to peptides and peptide complexes representing the prefusogenic and fusogenic forms of gp41. In that study, 98-6 had a higher affinity for the peptide complexes representing the fusogenic form, than did 2F5. Thus, the binding of 98-6, which fails to neutralize HIV-189.6, could interfere with the binding of 2F5, leading to the antagonism noted (Fig. 4m). In contrast, MAbs 50-69 and 2F5 recognize distinct epitopes in gp41 and display independent (additive) reactivity against HIV-189.6.
The data presented in this study suggest that many anti-HIV-1 Abs act additively to neutralize HIV-189.6. While synergy and antagonism have been documented here and elsewhere, it would appear that the predominant phenomenon characterizing Ab interaction is additivity. Given that relatively few anti-HIV-1 Abs characterized to date have broad neutralizing activity and given the extreme polyclonality of the human Ab response to HIV-1, it seems plausible that the additive interactions between Abs may contribute whatever neutralizing activity is observed in HIV+ sera and that antagonism probably does not account for the modest neutralizing activity in these sera. Continued studies of MAb combinations and of MAbs mixed with HIVIG preparations should illuminate the search for reagents useful in passive immunization regimens and in the design of antigens that will elicit the most effective protective Ab responses.
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APPENDIX |
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Top
Abstract
Introduction
Materials and Methods
Results
Discussion
Appendix
References
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There are a number of definitions of synergy in the literature. The purpose of this appendix is to give a general but mathematically precise definition that is nevertheless intuitive and comprehensive for nonmathematicians. Synergy is defined by a mathematical definition and specifically in terms of the problem which motivated this study, i.e., the definition of synergy among MAbs in neutralizing the HIV-1 virus. The present approach is contrasted with those of Mascola et al. (62) and Chou and Talalay (19).
Mathematical definition. Let X and Y be random
objects and let f be a function with value Z = f(X,Y). Z may be
viewed as the response of a system to the simultaneous stimuli X and Y. Let Eind denote the expected value of Z under the
hypothesis that X and Y are statistically independent random objects.
Then (using discrete variables for illustration),
Eind = 
f(x,y) pX(x) pY(y), where the sum is over all possible values
(x,y) and pX(x) is the probability of the event
that X = x. Similarly, pY(y) is the
probability of the event that Y = y.
pX,Y(x,y) is the probability of the event that
simultaneously X = x and Y = y. Let E denote the expected
value of Z with no assumptions about the dependence or
independence of X and Y: E = f(x,y)
pX,Y(x,y), where the sum is
again over all possible values of the pair (x,y).
We say that (i) there is synergy between X and Y if E > Eind, (ii) there is independence between X and Y if E = Eind, and (iii) there is antagonism between X and Y if E < Eind.
A "synergy index" (SI) may be defined as the percent excess of E
over Eind, i.e., SI = 100(E Eind)/Eind, whose negative values indicate antagonism.
Synergy between neutralizing MAbs. The intuitive definition of synergy is sometimes stated as the event when the combined action of two agents exceeds the sum of their actions alone. Note that if the "action," i.e., the desired effect, is measured by the percent or the fraction of the virus that was neutralized, then this intuitive definition is meaningless when both agents neutralize more than half of the viruses. Thus, if we are to calculate the sum of anything, it has to be the amounts of agents used and not their effect. Also, presumably, "more is better," so any comparisons between combined and separate effects must be such that the individual dosages of two MAbs in the mixture are exactly the same dosages at which they were separately measured for percent neutralization.
Consider the special case of the mathematical definition where X is the
characteristic function or indicator (1 or 0, according to occurrence
or nonoccurrence) of the event when a virus particle is neutralized by
MAb1 and Y is the indicator of the event when a
virus is neutralized by MAb2. Let f(x,y) = 1 (1 x)(1 y); then Z = f(X,Y) is the
indicator of the event that the virus is neutralized by at least one of
the two MAbs.
It follows that Eind = 1 q1q2, where now
Eind becomes the probability that the virus
particle is neutralized by at least one of the two antibodies, whereas
q1 is the probability that MAb1 alone fails to neutralize and
q2 is the probability that MAb2 alone fails to neutralize the virus particle.
In the above, synergy was defined between two random objects, but the
definition easily generalizes to any number of objects. For example, if
there are four antibodies in a neutralizing experiment, then the
probability that at least one of the four succeeds is 1 q1q2q3q4,
provided that we assume mutual independence among the antibodies.
Experimental error. In practice, E is estimated
by Z* which is an average of some replications of Z, and
Eind is estimated by Eind* = 1 q1*q2*, where
1 q1* and 1 q2* are the fractions of neutralization achieved
by each antibody. Independence is rejected in favor of synergy or
antagonism if |E* Eind*|/S exceeds a fractile of a Student t test distribution. Equivalently,
independence is rejected if E* is not inside the corresponding
confidence interval for Eind. The standard
deviation S may be obtained from the relation S2 = S2(E*) + S2(Eind*) because E* and
Eind* are based on different experiments that
are, of necessity, independent so that the variance of E* Eind* is the sum of their variances.
Comparison with other methods. We now reintroduce the
neutralization model in a more intuitive way and compare it to other
methods found in the literature. The probability p of neutralization is
defined this way: starting with one or more MAbs at some total concentration (dose) D, a virus particle is introduced, which is then
either neutralized or not. Let p = p(D) denote the probability that the virus is neutralized at dose D, so that q = 1 p is the
probability it is not neutralized at that dose. In an actual experiment, a large number (N) of virus particles will be
introduced. Then, the percent neutralization achieved will be ca. 100p;
the expected number neutralized will be Np and the variance
of the number neutralized will be Npq.
The dose is varied as D1,D2, ... , Dk, resulting in the dose responses p(D1), ... ,p(Dk). One may plot p against D and get a dose-response curve by joining these data points with straight lines. This is repeated for each of two MAbs as well as for a combination, i.e., a mixture of the two.
Both synergy and antagonism and their absence are defined as described
above: there is neither synergy nor antagonism in the combination of
MAbs if the two events ("MAb1 neutralizes"
and "MAb2 neutralizes") are statistically
independent. In this case, the probability Eind
that the combination neutralizes is Eind = Prob
(at least one of the two MAbs neutralizes) = p1 + p2 p1p2 = 1 q1q2, where
p1 is the probability that the
MAb1 portion of the mix neutralizes and
p2 is the probability for
MAb2. According to our definition, there is
synergy between the MAbs at a fixed concentration D whenever the
neutralization probability E of the mixture is greater than what it
would be for independently acting MAbs, i.e., if E > Eind. This is not the definition used in the literature of virology, but we will show that this definition nevertheless implies some definitions suggested by both Mascola et al.
(62) and Chou and Talalay (19).
We prefer the definition developed here because it does not require the additional assumptions made by these previously cited authors in their description of the dose-response curves associated with the individual and with the combined MAbs. In order to answer our question, whether the two MAbs act synergistically or not, it is not necessary to model the dose-response relationships, which is what the authors in the other studies have done. Rather, we simply measure E and compare it to Eind, making the necessary allowances for statistical error in the measurements.
We now compare and relate our model-free definition of synergy and antagonism to the definitions used by Mascola et al. and by Chou and Talalay. At the risk of excess, we repeat that none of the following dose-response modeling is necessary for our problem. Nevertheless, these models must be examined because of their pervasive use in the literature.
Mascola et al. model the dose-response curve for a single MAb as follows: q(D) = 1/[1 + (D/k)] in the "first order" case. Here, k is a constant obtained by fitting this curve to dose-response data, obviously, q(k) = p(k) = 1/2. These authors mention the general case wherein D/k is replaced by D/k to some power B, and this second constant B is also to be learned from the data. However, these authors seem not to employ the general case because they model the dose-response for a mixture of two MAbs as follows: q12(D1,D2) = 1/[1 + (D1/k1) + (D2/k2)]. Mascola et al. refer to this as the "predicted effect" and assert synergy between the MAbs if the measured effect of the mixture exceeds this predicted effect. Note that this expression contains no product term. In fact, the corresponding odds ratio is as follows: p12/q12 = (D1/k1) + (D2/k2), which is exactly the Chou and Talalay index for the case of mutually exclusive drugs, e.g., for two MAbs having the same target epitope. This is puzzling because Mascola et al. do not suggest that 2F5 and 2G12 (let alone the polyclonal HIVIG in their triple mixture) target the same epitope or are for some other reasons mutually exclusive in their action. We do not need to sort out this complication, because it is not necessary to model the dose-response curve to detect synergy or antagonism.
In the case of distinct target epitopes (such as those recognized by 2F5 and 2G12), our simple setup, together with the model of Mascola et al. for single MAbs, yields by statistical independence of the actions of the two MAbs the following: q12(D1,D2) = 1/[1 + (D1/k1) + (D2/k2) + (D1/k1)(D2/k2)].
The corresponding odds ratio is p12/q12 = (D1/k1) + (D2/k2) + (D1/k1)(D2/k2), which is exactly the Chou and Talalay index for the case of drugs that are not mutually exclusive, e.g., for two MAbs having distinct target epitopes. Thus, we see that there is no contradiction, at least in the "first-order" case, between our statistical but model-free definition of synergy and the more complicated model-based definitions of Mascola et al. and Chou and Talalay.
The theory of Chou and Talalay is based on enzyme kinetics. Its central tenet, the "mass action law" (based on Michaelis-Menten theory) is that the odds ratio curve corresponding to any dose-response curve has the form p12/q12 = [(D1/k1) + (D2/k2) + (D1/k1)(D2/k2)]B; however, the product term is dropped in the case of mutually exclusive drugs. (We ignore this case.)
We now assert that if B is different from 1, then such a dose-response curve cannot describe the statistically independent actions (as in our model-free setup) of two MAbs. This is because the dose-response and odds ratio curves of the individual MAbs also must follow this form, and we know that, as in Mascola et al., q1 = 1/[1 + (D1/k1)B1] and q2 = 1/[1 + (D2/k2)B2]. Thus, q12 = q1q2 = {1/[1 + (D1/k1)B1]}{1/[1 + (D2/k2)B2]} and then the corresponding odds ratio function has the form p12/q12 = (D1/k1)B1 + (D2/k2)B2 + (D1/k1)B1(D2/k2)B2. This form does not agree with that of Chou and Talalay, not even if B1 = B2 = B, unless B = 1.
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ACKNOWLEDGMENTS |
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This study was supported in part by grants from the National Institutes of Health (AI 32424, AI 36085, HL 59725, and AI 27742) and by the Research Center for AIDS and HIV Infection.
We acknowledge the provision of antibodies, either directly or indirectly, from Denis Burton, Hermann Katinger, James Robinson, and John Mascola.
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FOOTNOTES |
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* Corresponding author. Mailing address: VA Medical Center (Room 18124N), 423 E. 23rd St., New York, NY 10010. Phone: (212) 951-3211. Fax: (212) 951-6321. E-mail: zollas01{at}popmail.med.nyu.edu.
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REFERENCES |
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Top
Abstract
Introduction
Materials and Methods
Results
Discussion
Appendix
References
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Journal of Virology, October 2001, p. 9177-9186, Vol. 75, No. 19
0022-538X/01/$04.00+0 DOI: 10.1128/JVI.75.19.9177-9186.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.
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