Env-glycoprotein heterogeneity as a source of apparent synergy and enhanced cooperativity in inhibition of HIV-1 infection by neutralizing antibodies and entry inhibitors

Abstract

We measured the inhibition of infectivity of HIV-1 isolates and derivative clones by combinations of neutralizing antibodies (NAbs) and other entry inhibitors in a single-cycle-replication assay. Synergy was analyzed both by the current linear and a new nonlinear method. The new method reduced spurious indications of synergy and antagonism. Synergy between NAbs was overall weaker than between other entry inhibitors, and no stronger where one ligand is known to enhance the binding of another. However, synergy was stronger for a genetically heterogeneous HIV-1 R5 isolate than for its derivative clones. Enhanced cooperativity in inhibition by combinations, compared with individual inhibitors, correlated with increased synergy at higher levels of inhibition, while being less variable. Again, cooperativity enhancement was stronger for isolates than clones. We hypothesize that genetic, post-translational or conformational heterogeneity of the Env protein and of other targets for inhibitors can yield apparent synergy and increased cooperativity between inhibitors.

INTRODUCTION

The functional human immunodeficiency virus type 1 (HIV-1) envelope glycoprotein complex (Env) is a trimer of hetero-dimers that each consists of the outer gp120 subunit attached non-covalently to the transmembrane glycoprotein, gp41. The docking of gp120 onto the primary receptor, CD4, triggers conformational changes that allow interactions with the CCR5 or CXCR4 co-receptor; these interactions in turn activate a refolding of the Env complex that unleashes the fusogenic potential of gp41, ultimately allowing the viral core to enter the cytoplasm of the target cell (Doms and Peiper, 1997; Pantophlet and Burton, 2006). Neutralizing antibodies (NAbs) interfere with this process at different stages by binding to different epitopes; some recognize gp120 and impede receptor interactions; others interact with gp41 and interfere with later stages of entry (Klasse and Sattentau, 2002; Ugolini et al., 1997; Zwick and Burton, 2007). The induction of broadly active and potent NAbs is a crucial but elusive requirement for an effective vaccine to prevent HIV-1 infection. The access to epitopes on the native Env complex is restricted, as is the immunogenicity of the few epitopes that bind broadly active NAbs (Burton et al., 2004; Karlsson Hedestam et al., 2008; Klasse et al., 2011; Pantophlet and Burton, 2006; Poignard et al., 1996b; Poignard et al., 2001; Zwick and Burton, 2007). Env-vaccine design aims to induce protective levels of NAbs against these neutralization epitopes. But how well do NAbs act in combination? Do they have stronger or weaker effect when combined than when acting individually?

Various small organic molecules, as well as peptides and proteins, can also inhibit HIV-1 entry, again by acting at different stages of the entry process. Some such compounds are used in therapy or may become components of microbicides or oral prevention regimens to block sexual transmission (Grant et al., 2010; Klasse et al., 2008; Lederman et al., 2006; Veazey et al., 2005). The use of inhibitor combinations has long been standard for treating HIV-1 infection, but it may also be advantageous for prevention. For example, more than one inhibitor may be needed in a microbicide to counteract HIV-1 sequence diversity, while any enhanced potency of a combination may allow lower amounts of each drug to be used, reducing cost and improving safety (Grant et al., 2008; Ketas et al., 2007b). The quantitative analysis of combinatorial effects is therefore important both in prevention and therapy.

Synergy is a special case of combined effects (Berenbaum, 1977; Greco et al., 1995; Loewe, 1953). Its potential occurrence between NAbs and other entry inhibitors merits a rigorous, quantitative investigation. Synergy can be defined as a greater potency of combined inhibitors than would be predicted from their individual effects (Loewe, 1953); weaker than predicted potency is called antagonism; when the combined potency is neither enhanced nor reduced, it is categorized as additivity. The method most commonly used to quantify synergy in the inhibition of HIV-1 replication analyzes the inhibitor-concentration dependence after a linear transformation of the data (Chou and Talalay, 1981, 1984). Here, we compare that method with a new, non-linear approach.

What types of infectivity-inhibition assays are suitable for synergy analyses? Valid synergy assessments require proportionality between the infectious dose and the resulting propagation of the virus, which can only be guaranteed in certain titration zones of single-cycle replication assays; the distortions inherent in multi-cycle replication can create artifactual, or obliterate authentic, synergy (Ferguson et al., 2001). Moreover, PBMC assays based on production of the HIV-1 p24 Gag antigen lack precision (Choudhry et al., 2006; Heredia et al., 2007a; Heredia et al., 2007b; Ketas et al., 2007). Despite that problem, PBMC or T-cell-line assays with a p24 read-out have been used extensively in studies of synergy involving NAbs and other inhibitors (Dorr et al., 2005; Eron et al., 1992; Gantlett et al., 2007; Johnson et al., 1989; Johnson et al., 1990; Johnson et al., 1992; Kennedy et al., 1991; Laal et al., 1994; Li et al., 1997; Mascola et al., 1997; McKeating et al., 1992; Nakata et al., 2008; Strizki et al., 2005; Tremblay et al., 1999; Tremblay et al., 2005a; Tremblay et al., 2005b; Tremblay et al., 2002; Tremblay et al., 2000; Vermeire et al., 2004; Xu et al., 2001; Zwick et al., 2001). Here, we explored whether data obtained from a PBMC assay are amenable to synergy analysis.

Cooperativity differs from synergy in that it can occur for each individual ligand; it typically arises when ligands interact with multimeric proteins (Hill, 1913; Koshland et al., 1966; Monod et al., 1965). At least some NAbs may show negative coperativity in binding to the trimeric HIV-1 Env complex (Gustchina et al., 2010). However, cooperativity as measured by slope coefficients is subject to other molecular influences, and slope differences complicate synergy determinations (Chou and Talalay, 1981; Greco et al., 1995; Hoffman and Goldberg, 1994; Loewe, 1953; Weiss, 1997). We have therefore also investigated the relationship between synergy and changes in cooperativity.

Overall, we found that synergy between NAbs was weaker than between certain other entry inhibitors, and that both synergy and cooperativity enhancement were stronger for HIV-1 isolates than derivative clones. We suggest that heterogeneity among the target molecules, both viral and cellular, is a general source of apparent synergy and enhanced cooperativity between entry inhibitors. Although the molecular basis of these phenomena may differ from what has previously been assumed, the resulting effects may nevertheless be biologically important. We propose changes in both in the methods and the interpretations of combinatorial analyses of viral inhibitors. We emphasize that both the synergy and cooperativity phenomena observed can be regarded as apparent, i.e. as merely fulfilling the criteria of their respective mathematical definitions. We also try to keep the two problems we have addressed strictly separate: first, under what conditions these quantities can be measured correctly; and second, how certified observations of synergy and changes in cooperativity should be interpreted in molecular terms.

RESULTS

Comparison of linear and non-linear methods for determining inhibitory concentrations

The commonly used method for evaluating synergy is based on linear transformation of infectivity-inhibition data (Chou and Talalay, 1981, 1984). Our new one uses non-linear regression to fit a non-linear function, based on the Law of Mass Action, to untransformed data: I=(C/K_i)^η/(1+(C/K_i)^η)), where I = relative inhibition of infectivity; K_i is the half-maximal inhibitory concentration by analogy with the dissociation constant, K_d, in the Law of Mass Action; C = concentration of an inhibitor; η = slope coefficient or cooperativity factor, corresponding to the Hill constant of binding. One advantage of this non-linear function is that it can be fitted without assuming any reduction in the plateau of maximum inhibition (which is beyond the resolution of our current data); it also avoids the problem that data transformed by the other method, so as to become linear, are often far from linear. In addition, unlike the linear function, the non-linear one does not require values that lie just above 100% (or below 0%) inhibition to be censored, whereby loss of many high-quality data points is avoided. Here we did not, however, include such data in the non-linear analysis; we opted for a comparison of how the two methods perform based on exactly same data. In a previous informal comparison of the linear method with a different non-linear one, only 38 out of 136 published data sets yielded conclusions about synergy that were in close agreement (Greco et al., 1995). As laid out in what follows, it should be noted that there are other differences between the standard approach and ours than how inhibitory concentrations are calculated (see also Supplement).

To generate data for our own comparative synergy analyses, we titrated four NAbs, other entry inhibitors and one non-nucleoside reverse-transcriptase inhibitor (NNRTI), both alone and in selected combinations, against HIV-1 isolates CC1/85 and IIIB, as well as against clones derived from these viruses (9-6, 9-7, and 9-8 for CC1/85; NL4.3 and LAI for IIIB). The residual infectivity was quantified on Tzm-bl cells. The linear and non-linear methods were used for calculating synergy indices for data from 316 such inhibition experiments, including all six possible pair-wise combinations of the four NAbs.

Some examples of how the two methods can generate different synergy or antagonism outcomes are illustrated in Fig. 1 and Table 1. For each combination, the left-hand panel in Fig. 1 shows the median-effect plot of the Chou-Talalay method. The linear transformation involves calculating the ratio between the “fraction affected”, f_a (i.e. the fraction of virus prevented from replicating) and the “fraction unaffected”, f_u (i.e. the residual infectivity). The logarithm of that ratio is plotted as a function of the logarithm of the concentration of each inhibitor or their combination. Although this transformation is the standard basis for calculating synergy, it is hypersensitive to errors in the upper and lower zones of inhibition. Thus, a change from 90% to 99.999% inhibition involves a 1000-fold greater change in the f_a/f_u ratio than a change from 90% to 99%, although the difference between 99% and 99.999% is well within the margin of error for the assay. The plots in each right-hand panel show the fits by non-linear regression of the non-linear function described above to untransformed fractional data. The degree of inhibition is plotted as a function of inhibitor concentration on a log scale (Fig. 1).

Figure 1. Synergy analyses of HIV-1 inhibitor combinations by linear and nonlinear methods.

Left-hand panels show median-effect plots of the linearly transformed data. Y-axis: the log₁₀ of the ratio of the fraction of inhibited infectivity over the fraction remaining. X-axis: the log₁₀ of the concentration of each inhibitor, or their sum in combinations. Right-hand panels show the non-linear function fitted to the same data; relative inhibition of infectivity is plotted on the y-axis as a function of the concentration of individual inhibitors, or their sum, on a log scale on the x-axis. A. Inhibition of CC1/85 by VCV (blue, circles), T-20 (red, squares), and their combination at a molar ratio of 17/75 (green, triangles). The shift to the left of the green curve indicates strong synergy. B. Inhibition of CC1/85 by NAb 2F5 (blue, circles), T-20 (red, squares), and their combination at a ratio of 120/27 (green, triangles). The shift to the right of the green curve indicates antagonism. C. Neutralization of CC1/85 by NAbs b12 (blue, circles), 2G12 (red, squares), and their combination at a molar ratio of 1/1 (green, triangles). The intermediate position of the green curve indicates approximate additivity. D. Neutralization of the X4 isolate IIIB by NAbs b12 (blue, circles), 2G12 (red, squares), and their combination at a molar ratio of 1/1 (green, triangles). The intermediate position of the green curve indicates approximate additivity. E. Inhibition of IIIB by AMD3100 (blue, circles), Nevirapine (red, squares), and their combination at a molar ratio of 1/1 (green, triangles). The poor fit of the linear function results in a spurious indication of antagonism, whereas the non-linear method yields an outcome that is close to additivity (Table 1). The graphs are simplified for the purpose of illustration: only three curves are shown in each, the inhibition by the combined inhibitors being expressed as a function of the sum of their concentrations. The computations of the synergy indices are performed on values obtained by fitting the function to four separate data series, each having individual inhibitor concentrations on the x axis.

Table 1.

Comparison of linear and non-linear methods of synergy assessment

Virus	Inhibitor	Lin/Non-lina	Lin/Non-lina	Lin/Non-lina		Lin/Non-lina
		Half-max. inhib. conc. (Dm/Ki)b	Half-max. inhib. conc. c.i. (fold)c	R2/R2d		CI/σ e
CC1/85	VCV	20/20	5.0/1.5	0.98/0.99	0.79/0.99	0.21/0.18
	T-20	110/110	5.5/1.4	0.99/0.99
CC1/85	2F5	180/190	29/1.8	0.95/0.98	0.98/1.0	4.3/5.0
	T-20	61/54	11/1.4	0.98/0.99
CC1/85	b12	2.7/3.2	13/1.6	0.88/0.99	0.90/0.98	0.87/1.0
	2G12	6.7/6.9	1.8/1.2	0.99/1.0
IIIB	b12	2.6/3.4	14/1.6	0.87/0.98	0.84/0.99	0.89/0.95
	2G12	14/13	4.4/1.5	0.97/0.99
IIIB	AMD3100	0.027/0.97	104/1.4	0.76/1.0	0.74/0.99	11/1.4
	Nevirapine	20/24	8.3/1.3	0.97/0.99

^aThe values obtained by the linear and non-linear methods are expressed as the numerators and the denominators in ratios, respectively.

^bThe half-maximal inhibitory concentrations (nM) in the linear function (log (f_a/f_u) = m log(D/D_m)) is D_m, and in the non-linear function (I=(K_i/D)^η/(1+(K_i/D)^η)), it is K_i.

^cThe 95% confidence interval (c.i.) of the half-maximal inhibitory concentrations obtained by the respective fits are described by their fold variation from the lower to the upper limit.

^dThe R² values describe the closeness of the fit: R²=1 represents the ideal fit. The values in the lower two boxes to the left pertain to the individual inhibitors, the values in the taller box to the right, to their combination.

^eThe combination index (CI) of the linear, and the synergy indicator σ of the nonlinear method, indicate synergy when <1, additivity when =1, and antagonism when >1.

Synergistic inhibition of the HIV-1 R5 isolate CC1/85 by the CCR5 small molecule ligand vicriviroc (VCV) and the gp41 HR2 peptide T-20 is suggested by the displacement of the combination curve (green) to the left of the individual curves (red and blue) (Fig. 1A) Conversely, the gp41-directed NAb 2F5 and the HR2 peptide T-20 were antagonistic, and the combination curve is shifted to the right of both individual curves (Fig. 1B). The latter outcome was expected because T-20 contains the 2F5 epitope; the peptide binds the NAb to form an inert complex. Subtler synergy or additivity arose when isolates CC1/85 and IIIB were neutralized by NAbs b12 and 2G12 in combination (Figs. 1C and 1D). Here, the curves for the combinations fell mostly between those for the individual NAbs. Finally, an experiment with the CXCR4 ligand AMD3100 combined with the NNRTI Nevirapine generated several data points that represented nearly complete inhibition (Fig. 1E). Such data are less amenable to analysis by the linear than the non-linear method. Thus, the linear transformation (Fig. 1E, left-hand panel) gave a poorer curve fit than the non-linear one (right-hand panel) (Table 1). Table 1 shows that poor fits can substantially distort the outcome of the analyses.

It should be noted that the slopes of the curves in Fig. 1 differ and deviate from 1. Such complicating factors make synergy or antagonism hard to detect by inspecting the data. For example, when the slopes for the individual inhibitors differ, the combined curve will theoretically be bent, with different slopes at high and low inhibitor concentrations. A linear curve may therefore fit poorly even to theoretically perfect data. Greater complications arise with predictions of the combined fractional effect than when the inhibitory concentrations are compared for individual and combined inhibitors (Ferguson et al., 2001; Greco et al., 1995). Calculating a synergy index using Loewe’s formula is the best way to make the latter comparison (Greco et al., 1995; Loewe, 1953). We use this formula throughout, whereas Chou and Talalay apply it only to what is deemed to be mutually exclusive inhibition.

For clarity, we designate the synergy indices calculated by the linear method as CI (combination index; (Chou and Talalay, 1981, 1984)) and those by the non-linear one as σ (sigma) (Table 1). CI and σ both indicate synergy when <1, additivity when =1 and antagonism when >1. The non-linear method gave narrower confidence intervals of the half-maximal inhibitory concentrations (D_m and K_i) and higher R² values (i.e. better fits), both for individual inhibitors and for combinations. In individual experiments, the nonlinear method indicated marginally stronger synergy than the linear for the combination of VCV with T-20, and somewhat stronger antagonism for 2F5 combined with T-20 (Table 1). In the two examples of NAbs b12 combined with 2G12 against isolates CC1/85 and IIIB, the linear method indicated modest synergy, the non-linear method mere additivity (Table 1). The displayed data for the AMD3100 and Nevirapine combination were dealt with conspicuously less well by the linear method, which works poorly when inhibition approaches 100% (Figure 1E). Thus, R² was low, the imprecision of the D_m value was substantial, and the CI value of 11 indicated strong antagonism (Table 1). In contrast, the non-linear method generated excellent fits to the same data and indicated only modest antagonism (σ_50% = 1.4), which was close to the mean from four replicate experiments (σ_50% = 1.6 ± 0.27). Overall, these various examples illustrate analytic artifacts that the linear method is more prone to than is the non-linear one.

To compare the validity of the two methods further, we combined each inhibitor with itself in all experiments by adding it twice, each time at half the total concentration. A synergy analysis of such controls should theoretically give exact additivity (i.e. CI = σ = 1). We therefore refer to these titrations as additivity controls. The deviation of the additivity controls from ideality, as analyzed by the two methods, is shown in Supplementary Table 1. When we analyzed a total of 632 such titrations (two additivity controls from each of 316 experiments), the variability, expressed as the fold-spread from minimum to maximum, was greater for the linear method. However, both methods frequently indicated spurious synergy as well as antagonism, particularly at the higher levels of inhibition. The fold-spread CI or σ at 50% inhibition was 11-fold narrower for the non-linear than the linear method; at 75% inhibition it was 45-fold narrower; at 90% 180-fold (Supplementary Table 1). Further comparisons of the variability of the results obtained by the two methods are given in the Supplement.

We conclude that although neither method is acceptably accurate or precise at the higher levels of inhibition, the non-linear one yields more valid results. Hence, from here on, we only cite results obtained with the non-linear method and focus on the mid-range zone of inhibition. Furthermore, we avoid the standard classification of combinations as mutually exclusive and non-exclusive, as well as the concomitant modifications of the formula for calculating combination indices (Chou and Talalay, 1981). Both theoretical and pragmatic reasons for this choice are given in the Supplement.

Single- vs. multi-cycle replication

Multi-cycle replication of viruses can distort synergy analyses (Ferguson et al., 2001). It was therefore imperative to determine how many replication cycles can occur in the Tzm-bl assay under the conditions we used; although the input virus is not defective, the limited culture period (40 h) might prevent any progeny virus from initiating new cycles. Accordingly, we compared the infectivity of the 9-7 clone in the Tzm-bl cell and PBMC assays, both in the presence and absence of a protease inhibitor, Atazanavir, that prevents the formation of infectious progeny viruses. The luciferase signal generated in the Tzm-bl assay was proportional to the virus input, whereas the amount of p24 antigen produced in the PBMC assay varied exponentially with the input (Supplementary Figure 1). Furthermore, Atazanavir had a negligible effect in the Tzm-bl assay, confirming that progeny virus did not contribute to the endpoint. In contrast, the protease inhibitor eliminated p24 production in the PBMC assay, suggesting that the first replication cycle contributes only marginally. Both lines of evidence thus strongly indicate that the Tzm-bl assay records single-cycle replication while the PBMC assay involves multiple cycles.

We then explored whether multi-cycle replication would allow meaningful synergy assessments. The most accurate synergy measurement we identified, σ_50% (Table 1, Supplementary Table 1), varied drastically with the time of sampling, and as much for the additivity controls as for the NAb b12-2G12 combination (Figure 2). The variation in σ_50% among three repeat experiments was also extensive (Figure 2). Hence, the results from the PBMC assay were unsuitable for synergy analyses. Multiple cycles of replication complicate synergy calculations based on fractional effects (Ferguson et al., 2001). However, the large errors we found in concentration-based synergy calculations by Loewe’s formula can be attributed to the imprecision of the PBMC assay.

Figure 2. Lability of synergy measurements in a multi-cycle replication assay.

The dependence of apparent synergy on the duration of PBMC cultures, and hence the number of replication cycles, was investigated by taking samples for p24 quantification from days 5 to 16 after infection with the clonal virus 9-7. Each diagram shows the results from three experiments (Exp 1, blue circles; Exp 2, red squares; Exp 3, green triangles; symbols for each experiment are connected by lines). A. Synergy index at 50% inhibition, σ_50%, for the combination b12 + 2G12 used at a constant ratio close to their IC₅₀ ratio; B. σ_50% for the additivity control b12 + b12. C. σ_50% for the additivity control 2G12 + 2G12. The results varied over time from considerable synergy to antagonism for the b12 + 2G12 combination. However, the additivity controls for both NAbs gave even more divergent results over time, and since any deviation from 1 is an error in B and C, it is likely to be so in A as well.

Comparing isolates and clones for synergy in entry inhibition

The combination of the CCR5 ligands VCV (small molecule) and PRO 140 (MAb) was synergistic against the CC1/85 R5 isolate and the derivative clones 9-6 and 9-7, with a σ_50% value of 0.33–0.35. Synergy was weaker (σ_50% = 0.58) for this combination against the other CC1/85 clone, 9-8 (Table 2). The strongest synergy recorded (σ_50% = 0.22) was for VCV combined with T-20 against CC1/85, but it was weaker (σ_50% = 0.68–0.84) for the same combination against the three R5 clones. In contrast, the corresponding combination of the CXCR4 ligand AMD3100 with T-20 was not synergistic for any of the X4 isolates or clones (σ_50% = 0.90–1.2). VCV combined with the NNRTI Nevirapine was moderately synergistic against the CC1/85 isolate (σ_50% = 0.58), weakly synergistic or additive against the 9-6, 9-7 and 9-8 clones (σ_50% = 0.85–0.93). There was a tendency towards antagonism between AMD3100 and Nevirapine for the X4 viruses, particularly for IIIB (σ_50% = 1.6).

Table 2.

Synergy (σ_50%) in blocking the infection of Tzm-bl cells by R5 and X4 HIV-1 isolates and clones

Combination	Virus
	R5				X4
	CC1/85	9-6	9-7	9-8	IIIB	LAI	NL4.3
VCV + PRO 140	0.35a±0.075 (n=5)	0.33±0.035 (n=7)	0.35±0.045 (n=4)	0.58±0.27 (n=4)	-	-	-
VCV/AMD3100b + T-20	0.22±0.023 (n=4)	0.68±0.066 (n=8)	0.84±0.062 (n=5)	0.84±0.075 (n=6)	1.2±0.23 (n=8)	0.90±0.141 (n=6)	1.1±0.094 (n=7)
VCV/AMD3100b + Nevirapinec	0.58±0.099 (n=3)	0.93±0.10 (n=3)	0.87±0.058 (n=3)	0.85±0.036 (n=3)	1.6±0.27 (n=4)	1.3±0.30 (n=3)	1.1±0.14 (n=3)
CD4-IgG2 + 17b	1.1±0.23 (n=4)	0.62±0.16 (n=4)	0.78±0.16 (n=6)	0.73±0.12 (n=5)	1.1±0.14 (n=4)	1.2±0.18 (n=3)	0.79±0.099 (n=5)
b12 + 2G12	0.88±0.12 (n=4)	0.72±0.066 (n=3)	0.60±0.038 (n=5)	0.75±0.051 (n=4)	0.77±0.13 (n=3)	0.66±0.033 (n=3)	0.85±0.081 (n=4)
b12 + 2F5	0.73±0.16 (n=3)	1.1±0.050 (n=3)	1.6±0.39 (n=3)	0.71±0.12 (n=4)	0.95±0.065 (n=3)	0.75±0.014 (n=3)	1.2±0.17 (n=3)
b12 + 17b	0.68±0.15 (n=3)	1.5±0.12 (n=4)	1.2±0.289 (n=4)	1.9±0.28 (n=3)	1.2±0.21 (n=4)	0.93±0.066 (n=3)	0.69±0.10 (n=3)
2G12 + 2F5	0.50±0.094 (n=3)	1.6±0.78 (n=3)	0.69±0.141 (n=3)	0.60±0.055 (n=3)	0.67±0.16 (n=3)	0.60±0.17 (n=3)	1.00±0.105 (n=3)
2G12 + 17b	0.64±0.049 (n=8)	1.2±0.13 (n=7)	0.78±0.097 (n=6)	0.80±0.063 (n=9)	0.53±0.12 (n=7)	0.72±0.11 (n=7)	1.2±0.16 (n=8)
2F5 + 17b	1.4±0.50 (n=6)	1.6±0.47 (n=6)	1.1±0.28 (n=5)	0.83±0.20 (n=6)	0.65±0.19 (n=4)	0.50±0.050 (n=4)	0.98±0.125 (n=4)

^aThe values are the mean values of σ_50%from n (3 ≤ n ≤ 9) replicate experiments± SEM. σ_50% denotes synergy when <1, additivity when = 1, and antagonism when >1. Mean σ_50% values − 2 SEM >1 are shown in underlined italics; mean σ_50% values + 2 SEM < 1 are in bold. Values marked thus indicate synergy or antagonism ascertained with 95% confidence.

^bVCV was used against R5 viruses, AMD3100 against X4 viruses.

^cNevirapine is an NNRTI and thus the only inhibitor tested that blocks a post-entry step.

The receptor mimic CD4-IgG2, a tetravalent soluble CD4 construct, enhances the binding of the 17b antibody to monomeric gp120. Conversely, 17b inhibits soluble CD4 binding to gp120 (Moore and Sodroski, 1996). In line with this lack of mutually enhanced binding, CD4-IgG2 was not consistently synergistic together with 17b (Table 2). For this pair, synergy was no stronger or more consistent than for some of the NAb-NAb combinations (see below). For example, the combination of b12 with 2G12 gave σ_50% values < 1 for all viruses (Table 2).

Moderate synergy was detected sporadically for the six NAb-NAb combinations against the seven test viruses (Table 2). Overall, the virus-NAb combinations gave σ_50% + 2 SEM values that sometimes fell below 1, but only twice were the values of σ_50% >2 SEM above 1 (for b12 + 17b against clones 9-6 and 9-8). The inconsistent outcome may reflect the considerable variability inherent to even the most precise assessment of synergy (i.e. σ_50%). Although we performed 3–9 replicates of each experiment, it was still difficult to identify, or exclude, genuine moderate synergy in a matrix containing as many as 67 virus-inhibitor combinations, given the experimental variation (Supplementary Table 1): the mass-significance problem and the magnification of the experimental variation by the synergy calculations together exacerbate the difficulties of interpretation. Against that background it can be noted that with 95% confidence intervals, three σ_50% values out of 67 deviating significantly from 1 would be expected by chance, although that could be in either direction as for the additivity controls (Supplementary Table 1). In contrast to that expected noise, 32 σ_50% values were significantly below 1; three were above. In other words, it is beyond doubt that synergy occurs with combinations of these inhibitors. Nevertheless, we conclude that multiple replicates in assays with high precision, as well as focusing on half-maximal effect where σ varies least, are necessary steps to render synergy analyses of viral inhibition meaningful.

The strongest synergy among the NAb combinations was observed for 2G12 + 2F5 against CC1/85 (σ_50%= 0.50), 2G12 + 17b against IIIB (σ_50%= 0.53), and 2F5 + 17b against LAI (σ_50%= 0.50). Although the other entry inhibitors were generally more synergistic than the NAbs, the above NAb-NAb combinations showed stronger synergy than did VCV + PRO 140 against 9-8 (σ_50% = 0.58) or VCV + T-20 against the three R5 clones (σ_50% = 0.68–0.84). The b12 + 17b combination yielded a particularly stark contrast between the R5 isolate (σ_50% = 0.68) and the three R5 clones (σ_50% 1.2–1.9).

More robust patterns were revealed when data were pooled across all ten inhibitor combinations. When this was done, synergy measurements were shown to differ between viral isolates and clones. Thus, overall, σ_50% values tended to be lower for isolates than clones (p = 0.051). However, this outcome was restricted to the R5 viruses, for which the difference was significant (p = 0.0061; NS for X4 virus, p = 0.45).

Optimizing the sensitivity of synergy detection

We explored whether the ratio at which two inhibitors were mixed affected the detection of synergy. In summary, we found that using two inhibitors at a ratio as close as possible to that of their respective half-maximal inhibitory concentrations, K_i, modestly enhanced the sensitivity of synergy detection. The σ_50% values correlated weakly but highly significantly with the deviation from the intra-experimental K_i ratio (Supplementary Figure 2, Spearman rank correlation coefficient, r=0.22, p=0.0001). In other words, the more the actual concentration ratio for the two inhibitors deviated (in either direction) from the ratio of their K_i values, as measured in the same assay, the higher were the values of σ_50% (i.e., the weaker the indication of synergy). The theoretical background for this effect on the sensitivity of synergy detection is given in the Supplement.

Cooperativity and its relationship to synergy

We favor restricting synergy measurement to half-maximal inhibition, which is more precise (Table 1, Supplementary Table 1) and also slope-independent; the slope, an indicator of cooperativity, provides complementary information. It is common for ligands to bind cooperatively to multiple sites on oligomeric proteins. Cooperativity differs from synergy in that a single agent can cooperate with itself, as in the classic case of the binding of oxygen to tetrameric hemoglobin (Hill, 1913; Koshland et al., 1966; Monod et al., 1965), whereas two different agents are required for synergy. In our non-linear function, the quantity η (eta) corresponds to the Hill coefficient and therefore may partly reflect classic cooperativity but can be influenced by other factors too. Henceforth we refer to the apparent cooperativity, measured by the slope coefficient, merely as cooperativity, regardless of the underlying molecular mechanism.

We investigated whether individual inhibitors and their combinations show cooperativity, and how changes in cooperativity relate to synergy. First, we examined how accurately and precisely we could measure a change in cooperativity, η_rel, which we calculate as ((η_AB/η_A) + (η_AB/η_B))/2. In that formula, η_AB is the cooperativity factor for inhibition by the combination, while η_A and η_B are the corresponding factors for inhibition by the individual components. Again, we used additivity controls, for which ((η_AB/η_A) + (η_AB/η_B))/2 should equal 1. Thus, although the individual inhibitors have different intrinsic cooperativities, these values should not change when the inhibitors are combined with themselves. We were encouraged to find that these additivity controls did indeed vary little. Thus, the range of change in η among the 632 controls was only 4.4-fold, whereas for σ_50% it was 79-fold (for minima and maxima, see Supplementary Tables 1 and 2). In conclusion, the η_rel values were measured more accurately than σ_50% (which in turn was more accurate than σ_75%, σ_90% or linearly derived CI values, as shown in Table 1 and Supplementary Table 1).

Combining two inhibitors increased cooperativity to differing extents (Table 3). The effect was particularly strong and consistent for the VCV + PRO 140 and 2G12 + 17b combinations against R5 viruses. We observed no example of a decrease in η of more than 2 SEM below the mean; overall, η_rel ranged from ~1 (i.e. no change) to 2.

Table 3.

Change in cooperativity, η_rel

Combination	Virus
	R5				X4
	CC1/85	9-6	9-7	9-8	IIIB	LAI	NL4.3
VCV + PRO 140	1.8±0.11	1.5±0.060	2.0±0.19	1.4±0.15	-	-	-
VCV/AMD3100 + T-20	1.5±0.15	1.4±0.045	1.4±0.089	1.2±0.092	1.2±0.13	1.2±0.033	1.0±0.079
VCV/AMD3100 + Nevirapine	1.2±0.034	1.1±0.072	1.0±0.017	1.1±0.038	1.2±0.064	1.0±0.20	1.0±0.050
CD4-IgG2 + 17b	1.3±0.16	1.0±0.14	1.2±0.068	1.6±0.27	1.4±0.16	1.3±0.083	1.1±0.047
b12 + 2G12	1.2±0.048	1.1±0.030	1.1±0.042	1.2±0.11	1.6±0.060	1.2±0.077	1.1±0.046
b12 + 2F5	1.1±0.130	1.4±0.28	1.1±0.019	0.93±0.057	1.2±0.096	1.0±0.048	1.1±0.052
b12 + 17b	1.0±0.30	1.0±0.078	1.0±0.043	1.1±0.075	1.3±0.132	1.1±0.048	1.2±0.039
2G12 + 2F5	1.6±0.30	1.6±0.34	1.4±0.15	1.6±0.32	1.7±0.191	1.5±0.0081	1.4±0.23
2G12 + 17b	1.6±0.17	1.8±0.16	1.3±0.077	1.8±0.077	1.4±0.065	1.5±0.35	1.3±0.099
2F5 + 17b	1.3±0.19	1.2±0.11	1.1±0.13	1.2±0.118	1.3±0.091	0.9±0.12	1.3±0.058

^aThe values are the mean values of fold change in η (calculated as η_rel = ((η_AB/η_A) + (η_AB/η_B))/2) from n (3 ≤ n ≤ 9) replicate experiments ± SEM. Mean values of η_rel + 2 SEM > 1 are given in bold. There were no mean values of η_rel + 2 SEM < 1. Note that n for each combination of inhibitors and virus is the same as in Table 2 and is given only there.

As with synergy, the cooperativity change for inhibitor combinations differed between isolates and clones. Thus the η_rel values were significantly greater for isolates than clones (p=0.0031), more so among the X4 than the R5 viruses (IIIB vs. LAI and NL4.3, p=0.0005; CC1/85 vs. 9-6, 9-7 and 9-8, p=0.095, NS).

Indirectly, the limited change in cooperativity for the additivity controls (Supplementary Table 2) also validates the determination of intrinsic η for all the inhibitors we used (Table 4). Most of the intrinsic η values were <1. It should be noted that negative cooperativity does not necessarily confer values <1, although it does reduce the slope value below the maximum value that is set by the number of interacting subunits (Weiss, 1997). In contrast, heterogeneity, i.e. the width of inhibitory effects over a population of target molecules, often reduce the slope values to <1 (Greco et al., 1995; Hoffman and Goldberg, 1994). The R5 isolate had lower values of η than its derivative clones (p < 0.0001), and the X4 isolate and clones had significantly higher values of η than the R5 viruses (p < 0.0001). These differences are interpreted in the Discussion.

Table 4.

Intrinsic cooperativity, η, of inhibitors of HIV-1 infection

Inhibitor	Virus
	R5				X4
	CC1/85	9-6	9-7	9-8	IIIB	LAI	NL4.3
PRO 140	0.80a±0.039 (n=12)	0.90±0.027 (n=14)	1.0±0.055 (n=8)	1.0±0.050 (n=8)	-	-	-
VCV	0.64±0.030 (n=25)	0.86±0.035 (n=36)	0.94±0.024 (n=24)	0.93±0.015 (n=26)	-	-	-
AMD3100	-	-	-	-	1.2±0.065 (n=24)	1.0±0.038 (n=18)	1.2±0.081 (n=20)
T-20	0.59a±0.027 (n=16)	0.80±0.022 (n=22)	1.1±0.054 (n=12)	0.98±0.98 (n=18)	1.2±0.064 (n=22)	1.4±0.12 (n=16)	1.0±0.12 (n=24)
Nevirapine	0.68±0.080 (n=6)	0.84±0.018 (n=6)	0.83±0.050 (n= 6)	0.83±0.028 (n= 6)	0.92±0.031 (n=8)	0.71±0.034 (n=6)	0.86±0.017 (n= 6)
CD4-IgG2	0.74±0.027 (n= 8)	0.65±0.030 (n= 8)	0.84±0.048 (n=12)	0.88±0.042 (n=10)	1.1±0.053 (n=8)	0.88±0.047 (n=6)	0.81±0.044 (n=10)
17b	0.84±0.054 (n= 42)	0.60±0.031 (n=42)	0.70±0.023 (n=42)	0.53±0.026 (n=46)	0.74±0.091 (n=38)	1.0±0.14 (n=34)	0.66±0.023 (n=40)
b12	0.79±0.030 (n= 20)	0.71±0.018 (n=20)	0.80±0.015 (n=24)	0.80±0.016 (n=24)	0.88±0.014 (n=20)	1.0±0.023 (n=18)	0.88±0.027 (n=20)
2G12	0.54±0.036 (n=30)	0.95±0.031 (n=26)	0.74±0.023 (n=28)	0.87±0.036 (n=32)	0.76±0.025 (n=26)	1.1±0.038 (n=26)	0.79±0.028 (n=30)
2F5	0.57±0.035 (n=32)	0.48±0.021 (n=28)	0.69±0.021 (n=24)	0.73±0.037 (n=32)	0.72±0.032 (n=24)	1.3±0.061 (n=24)	0.69±0.035 (n=30)

^aThe values are the means of intrinsic cooperativity factors, η, obtained by fitting the non-linear function (I=(C/K_i)^η/(1+(C/K_i)^η)) to data from n (6 ≤ n ≤ 46) replicate titrations ± SEM. Since most inhibitors were included in different combinations, the results titrations of individual inhibitors, which were pooled here, had higher n values and gave greater precision than those listed in Tables 2 and 3. Mean values of η + 2 SEM < 1 are given in bold; mean values of η − 2 SEM > 1 are given in underlined italics. The factors that raise and lower η (number of subunits of oligomeric targets, positive and negative cooperativity, and heterogeneity among target molecules) are outlined in the Discussion.

We have given several reasons for believing that σ_50% and η_rel measure distinct and partially independent biological quantities. Indeed, σ_50% and η_rel did not correlate (Figure 3A, Spearman r=0.021, p=0.72). Instead, the change in cooperativity correlated well with the ratio of σ_50%/σ_90% (Figure 3B, Spearman r=0.80, p<0.0001). Different degrees of synergy at different levels of inhibition are commonly reported (Greco et al., 1995). However, as we show here, synergy measurements are subject to extreme error at the higher levels of inhibition, as well as being theoretically unjustified (Loewe, 1953). The more accurate determination of change in cooperativity therefore provides a valuable complement to the slope-independent synergy measurement at 50% inhibition. In theory, synergy can occur as a perfectly parallel displacement of the inhibition curves. This is exemplified by values of σ_50% <1 in Table 2 that correspond to values of η_rel ~ 1 in Table 3. Conversely, cooperativity can increase markedly when the same combination is merely additive at 50% inhibition. These discrepancies account for the lack of correlation between σ_50% and η_rel. The two effects can also occur together, however, as illustrated by the VCV + PRO 140 combination (Tables 2 and 3), and both are worth evaluating. We suggest that non-linearly determined σ_50% and η_rel values together capture biologically important and partly independent combinatorial effects with optimal accuracy and precision.

Figure 3. Variable relationship between synergy and enhanced cooperativity.

A. The average increase in cooperativity (fold change in η, η_rel) is plotted on the y-axis as a function of synergy as measured by the non-linear method at 50% inhibition (σ_50%) on the x-axis. The individual results from 297 experiments (antagonistic combination excluded) are shown as dots. The two variables were uncorrelated (Spearman r = 0.021, p = 0.72), indicating at least partial independence. B. The average fold change in cooperativity, η_rel, is plotted on the y-axis against the ratio of synergy indices at 50% and 90% inhibition, σ_50%/σ_90%, for all combinations against all viruses (antagonistic combination excluded, n=297). The correlation was strong and highly significant (Spearman rank correlation, r = 0.80, p < 0.0001).

A summary listing all the differences between the standard approach to synergy in the inhibition of HIV-1 infectivity and our proposed framework for combinatorial analysis can be found at the end of the Supplement.

DISCUSSION

Multiple studies have addressed whether NAbs synergize in blocking HIV-1 infection, the outcomes ranging from strong synergy to mere additivity or even antagonism (Allaway et al., 1993; Buchbinder et al., 1992; Cavacini et al., 1993; Hrin et al., 2008; Kennedy et al., 1991; Laal et al., 1994; Li et al., 1997; Li et al., 1998; Mascola et al., 1997; McKeating et al., 1992; Montefiori et al., 1993; Potts et al., 1993; Thali et al., 1992; Tilley et al., 1992; Verrier et al., 2001; Vijh-Warrier et al., 1996; Xu et al., 2001; Zwick et al., 2001). Those studies used both T-cell line-adapted (TCLA) viruses and primary isolates in infectivity assays that allow multi-cycle replication to different extents. One study compared multi-cycle replication with single-cycle pseudovirus infection: in a multi-cycle PBMC assay the triple-NAb combination b12, 2F5, and 2G12 showed synergy at both 50% and 90% inhibition of the JR-CSF primary isolate (CI=0.6–0.8); in a single-cycle assay with a JR-CSF Env-pseudotyped virus, weak antagonism occurred at 50% inhibition (CI=1.2) but strong synergy at 90% (CI=0.4) (Zwick et al., 2001). Hence, single- and multi-cycle-replication assays can clearly give different results. We found that widely different degrees of synergy or antagonism arose in a multi-cycle experiment at different times of sampling. Different synergy indices at middle and high levels of inhibition are also problematic; in our analyses, CI values were more error-prone at 90% inhibition than at 50%. Furthermore, most of the cited studies used the linear transformation method, which, as illustrated here and previously explained, can contribute to errors (Suhnel, 1998). For example, the median-effect linearization of combination data will often result in curves that are actually non-linear, and the commonly found CI values ≫1 in the region close to zero inhibition are calculation artifacts (Greco et al., 1995).

It is not surprising that the above sources of error together can generate the highly divergent results that are found in the literature on HIV-1 NAb-NAb synergy. We conclude, nevertheless, that synergy can sometimes occur between different NAbs as measured by the more precise non-linear method in the most reliable zone, i.e. at 50% inhibition. The synergy we observed was, however, only moderate and sporadic (Table 2); it was markedly less pronounced and consistent than when a small-molecule CCR5 inhibitor was combined with a CCR5 MAb. We will now discuss possible mechanisms for these different synergies, and then suggest the best approach for analyzing the divergent combinatorial effects that frequently arise at different levels of inhibition.

Because an IgG molecule is bulky, similar in size to a gp120-gp41 hetero-dimer, the binding of a single NAb could be sufficient to inactivate the function of that protomer sterically; indeed, models of neutralization stoichiometry suggest that a single molecule of certain NAbs can inactivate an entire Env trimer (Burton et al., 2001; Klasse, 2007; Magnus and Regoes, 2010; Yang et al., 2006). What, then, would the binding of a second NAb to a different (or even the same) Env protomer in the trimer accomplish? A similar argument can be applied to all the obligate components of an entry complex, including CD4 and CCR5 or CXCR4. When one necessary step of the fusion process is blocked, impeding a second would conceivably be redundant. But does this reasoning erroneously assume all-or-nothing, static equilibrium effects? Perhaps models of these inhibitory processes should instead be both kinetic and dynamic, allowing for ligand association and dissociation over time, as well as for binding competition among Env, NAbs, and receptors. The binding of two NAbs to the same Env protomer could significantly increase the proportion of time that the antigen is occupied and thereby non-functional. In addition, the binding of some NAbs irreversibly inactivates a protomer by inducing the dissociation of gp120 from gp41 (Poignard et al., 1996a; Ruprecht et al., 2011), a process that might be accelerated for combinations of NAbs. Whether any such dynamic or kinetic effects could yield synergy is an unsolved problem.

HIV-1 entry into susceptible cells is a non-linear process, involving complex consecutive molecular interactions. The virions may attach to ancillary receptors, then dock onto a requisite number of CD4 molecules, and thereafter recruit several chemokine receptor molecules (Klasse et al., 1999; Kuhmann et al., 2000; Platt et al., 2005; Sougrat et al., 2007). These interactions ultimately trigger the fusion reaction in which an unknown number of Env trimers participate in forming a fusion pore through which the viral core can enter the cytoplasm. The inhibition of this process may have critical thresholds at the levels of both the virion and the Env trimer (Herrera et al., 2006; Klasse, 2007; Klasse and Moore, 1996; Magnus and Regoes, 2010; Magnus et al., 2009; Schonning et al., 1999; Yang et al., 2005). Because of this complexity, inhibition may not increase with binding in a simple proportional, incremental manner. Therefore, when the kinetics, dynamics, and threshold effects of inhibition are taken into account, synergy in biological activity might result without synergistic binding of NAbs or other inhibitors to components of the entry machinery.

MAbs and soluble CD4 (sCD4) do, however, affect each other’s binding to the gp120 monomer. For example, CD4-binding-site (CD4bs) MAbs enhance the binding of some V3-directed MAbs, and sCD4 greatly increases the binding of MAbs to the CD4i epitopes in the bridging sheet (Moore and Sodroski, 1996). But not a single case of mutually enhanced binding is known: when two ligands are added to gp120, the binding of one ligand is enhanced while that of the other is unaffected or reduced, or else there is mutual inhibition (Moore and Sodroski, 1996). These effects fall short of the potentiated binding of both ligands at a linked equilibrium, which would provide a straightforward molecular basis for synergy through interactions in the ternary complex. Indeed, we did not observe any more consistent synergy when CD4-IgG2 was combined with the CD4i MAb 17b than when 17b was combined with the CD4bs MAb b12 or with the mannose-epitope-specific MAb 2G12 (Table 2). Yet CD4-IgG2 uni-directionally enhances 17b binding to gp120, whereas the binding of 17b and b12 is mutually antagonistic, and 17b and 2G12 have no effect on each other’s binding (Moore and Sodroski, 1996). It should be noted, however, that these bi- or uni-directional effects of MAb binding could differ between the gp120 monomer and the functional Env trimer. Synergy in NAb binding to trimers also does not correlate with synergistic virus neutralization, although the binding assays have involved uncleaved Env precursors that are irrelevant to HIV-1 entry and its inhibition (Thali et al., 1992; Zwick et al., 2001). No assay preferentially detects NAb binding to functional Env, and no soluble Env trimer presents all conserved neutralization epitopes (Burton and Poignard, 2009).

Some, but not all, NAbs to the V3 region of gp120 reportedly synergize with CD4bs NAbs and recombinant CD4 constructs (Allaway et al., 1993; Laal et al., 1994; Potts et al., 1993; Thali et al., 1992; Tilley et al., 1992; Verrier et al., 2001; Vijh-Warrier et al., 1996). Even different NAbs against overlapping epitopes within the same CD4bs cluster on Env have been reported to synergize (Laal et al., 1994). In one study, synergy was detected between sCD4 and a V3 NAb, but for no combination of Env-directed MAbs (Verrier et al., 2001). As outlined above, it is difficult to explain such differential findings if the requirement for neutralization were simply a certain degree of sCD4 or NAb occupancy on indistinguishable Env protomers (Burnet et al., 1937; Burton, 2001; Klasse and Sattentau, 2002). We found cases of synergy for all NAb combinations as well as for CD4-IgG2 combined with 17b. Although the detection of moderate synergy is to some extent subject to chance, its sporadic occurrence across the NAb panel argues against a role for special molecular interactions within the ternary complex consisting of two NAbs and one Env spike or protomer; that some combinations gave more synergy than others can have other explanations than mutually enhanced binding.

We propose instead that antigenic differences in Env within each virus population may contribute to the occasionally synergistic effects. The only discernable overall pattern in our own data was that synergy was stronger for the R5 isolate than for its corresponding clones. A similar difference among X4 isolates and clones has been reported previously (Vijh-Warrier et al., 1996). Genetic variation within the viral quasispecies is one obvious source of Env heterogeneity, but we suggest that other contributors include variable carbohydrate processing (with direct and indirect effects on NAb recognition), and the conformational flexibility of the Env complex (Harris et al., 2011; Kwong et al., 2002; Kwong et al., 1998; Pantophlet and Burton, 2006; Wyatt and Sodroski, 1998). Functional and non-functional Env complexes (not only trimeric) on the surface of virions have been described (Moore et al., 2006; Pancera and Wyatt, 2005; Poignard et al., 2003), but here we are postulating heterogeneity also within the functional subset. Overall, any difference that affects the antigenicity of functional Env trimers could explain why NAbs with distinct specificities can apparently synergize when combined. Indeed, antigenic heterogeneity could even account for synergy between two NAbs directed to the same epitope cluster, e.g. the CD4bs (Laal et al., 1994).

We also tested combinations of inhibitors of HIV-1 entry other than NAbs. Thus, we found that T-20 synergized with the CCR5 ligand VCV but not with the CXCR4 ligand AMD3100 (Table 2). In earlier reports, fusion-blocking gp41-derived heptad-repeat 2 (HR2) peptides such as T-20 have shown variable degrees of synergy with co-receptor ligands against some HIV-1 isolates but mere additivity against others (Nakata et al., 2008; Tremblay et al., 2005a; Tremblay et al., 2005b; Tremblay et al., 2002; Tremblay et al., 2000; Veazey et al., 2005). Interactions between Env and co-receptors elicit the gp41 pre-hairpin-intermediate, which is the target for T-20, but co-receptors are also involved in promoting later, T-20-insensitive steps of the fusion reaction (Matthews et al., 2004; Mkrtchyan et al., 2005; Nagashima et al., 2001). The lower the CCR5 expression levels on the target cells, the more potently T-20 acts against R5 viruses, an explanation being that the fewer the co-receptor molecules available the more time T-20 has to intercede (Platt et al., 2005; Reeves et al., 2002). Similarly, CCR5 inhibitors may potentiate the action of T-20, but other observations of synergy in entry inhibition are less readily explained by such an effect: CD4-IgG2, which prevents binding to cellular CD4 but induces the co-receptor binding site on Env, also synergizes with T-20 (Nagashima et al., 2001); sulfated polyanions that block both HIV-1 attachment and co-receptor interactions can synergize with an HR2 peptide, as well as with a CCR5 ligand (Gantlett et al., 2007).

The sequence of events in entry, which is common to most strains of HIV-1, does not provide a comprehensive explanation for the variable observations of synergy among different inhibitors and viral strains. That synergy between HR2 peptides has only been observed with certain HIV-1 strains might be related to amino-acid variation in the V3 region of gp120, which strongly influences the sensitivity to inhibitors of both classes (Anastassopoulou et al., 2011; Berro et al., 2009; Derdeyn et al., 2000; Derdeyn et al., 2001; Kuhmann et al., 2004; Ogert et al., 2010). Therefore, heterogeneity among Env and co-receptor molecules could conceivably contribute to explaining these diverse phenomena. In this regard, we note that T-20 and VCV synergized more strongly against the R5 isolate CC1/85 than against all three clones derived from it, whereas no synergy was observed for AMD3100 combined with T-20 against X4 viruses. On the heterogeneity-based interpretation, our results would thus suggest that cell-surface CCR5 is more heterogeneous than CXCR4, particularly in how it interacts with Env. Although there is evidence that both co-receptors are heterogeneous, the relative extent is unknown (Anastassopoulou et al., 2009; Baribaud et al., 2001; Berro et al., 2011; Lee et al., 1999). It is also possible that, compared with X4 gp41, R5 gp41 varies more on each virion in how it interacts with T-20 and other HR2 peptides: the lower sensitivity of R5 viruses to such peptides is strongly influenced by the conformationally flexible and sequence-variable V3 region, as is their fusogenicity in general (Derdeyn et al., 2000; Derdeyn et al., 2001). Finally, mutants of HR2 peptides and a 5-helix-bundle construct, with reduced affinity for each other, can synergize strongly in blocking infection (Kahle et al., 2009). Heterogeneity might contribute to that example of synergy as well, in that the pre-hairpin intermediate of gp41 assumes different conformations during the fusion process, the HR1 region becoming more exposed, the HR2 region less so (Abrahamyan et al., 2005; Kahle et al., 2009). Since the multiple co-receptor interactions of Env trimers on a single virion would be asynchronous, the greater activity of HR1 peptides against some trimers would be complemented by the greater activity of HR2 peptides against others, creating synergy.

A related but simpler case is the strong synergy observed here and previously between a MAb and a small molecule that both bind to CCR5 (Ji et al., 2007; Latinovic et al., 2011a; Murga et al., 2006). Although the small CCR5 ligand may enhance the binding of the MAb (Latinovic et al., 2011b), the binding of the two ligands can also be antagonistic (Murga et al., 2006). Furthermore, the MAb and the small molecule can be active in different (Safarian et al., 2006) or the same (Ji et al., 2007) time windows and still synergize. The best explanation for their synergy might therefore be that they have distinct affinities for different forms of CCR5, which the virus can use (Anastassopoulou et al., 2009; Berro et al., 2011; Lee et al., 1999). Thus, combining two co-receptor ligands may potentiate both, one ligand compensating for when the other binds weakly to a subset of targets and vice versa. We note the smaller difference in synergy between the R5 isolate and its clones for the CCR5-ligand combination than for VCV + T-20 (Table 2). Hence Env heterogeneity may have a greater impact when the target molecules consist of both CCR5 and Env (i.e., VCV + T-20) rather than only CCR5 (i.e., VCV + PRO 140).

Many studies also report synergy between agents that block distinct steps in HIV-1 replication, e.g., among inhibitors of entry, the reverse transcriptase and the protease (Johnson et al., 1989; Johnson et al., 1990; Johnson et al., 1992; Johnson et al., 1991; Nakata et al., 2008; Strizki et al., 2005; Tremblay et al., 2005a; Tremblay et al., 2005b; Vermeire et al., 2004). We observed moderate synergy between the NNRTI Nevirapine and the CCR5 ligand VCV against the CC1/85 R5 isolate and to a smaller extent against the R5 clones; in contrast, Nevirapine and the CXCR4 ligand AMD3100 tended to be weakly antagonistic against the X4 viruses (Table 2). The weak antagonism may be due to fortuitous binding between the two molecules (although we have no evidence for this), but what could explain synergy when separate replicative steps are targeted? Since each blocked event is necessary for HIV-1 replication, why is blocking a second one not merely redundant? Again, viral heterogeneity could be the explanation, one inhibitor acting against variants that are relatively resistant to the other, and vice versa. In some cases, the viral quasispecies may be sufficiently pan-sensitive to exclude such effects, particularly when ligands are directed to the more invariable non-viral sites (e.g., CD4), or to relatively conserved sites on viral proteins other than Env. In the case of the combination of a co-receptor blocker and an NNRTI, differential sensitivity among Env trimers to inhibition by, e.g., VCV could be complemented by any heterogeneity in the reverse transcriptase that affects the action of, e.g., Nevirapine. The only requirement for this mechanism of synergy is that the maxima in sensitivity to the two inhibitors do not exactly coincide in the virion population.

In biochemistry or pharmacology, synergy is generally observed, and readily explained, when two parallel, mutually redundant pathways are blocked (Yeh and Kishony, 2007). Such situations differ from the consecutive steps of the HIV-1 replication cycle, with one informative exception. Thus, when both CCR5 and CXCR4 are expressed on the same target cells, a mixture of R5 and X4 HIV-1 isolates can be completely blocked only by a combination of ligands against both co-receptors. In that black-and-white situation, clear synergy was indeed observed when CCR5 and CXCR4 ligands were combined in a multi-cycle infectivity assay (Nakata et al., 2008). The heterogeneity that we postulate among Env, CCR5, and other target molecules would have more shades of grey. However, the basic principle of tightening the blockade by combining inhibitors would still apply. It can be shown by a schematic example when the outcome would be synergy rather than additivity. Suppose the inhibitor A has a K_d = 1 nM for half the target molecules and a K_d = 100 nM for the other half. Inhibitor B has the converse affinities. At 100 nM, each inhibitor alone therefore achieves ~ 75% occupancy on the total population of target molecules. When they are combined, however, 75% occupancy is achieved at 3 nM of each. Suppose that is the minimal inhibitory occupancy. Then the σ_50% for the combination at equal concentrations will be ~ 0.06, which indicates strong synergy.

We investigated the slope of the inhibition curves. The fitted quantity η in our formula corresponds to the cooperativity coefficient in Hill’s equation for ligand-receptor binding (Hill, 1913). It is notable that η was < 1 for all individual inhibitors against all viruses, with the exceptions of each of AMD3100 and T-20 against all X4 viruses. Among R5 viruses, the values of η were markedly lower for the isolate than the clones, perhaps because the greater genetic heterogeneity widens the spectrum of sensitivities, which would reduce the slope coefficient (Greco et al., 1995; Hoffman and Goldberg, 1994). The η-values were also lower overall for R5 (primary-isolate-derived) than X4 (TCLA) viruses, possibly because there are fewer functional Env trimers on TCLA virions (Moore and Klasse, 1992; Moore et al., 1992). The difference between the minimum number of Env trimers required for entry and the total number on each virion is the number that is spare (Klasse and Moore, 1996). The larger the proportion of spare trimers the greater the potential number on each virion that are heterogeneously sensitive to inhibition, and the greater the heterogeneity the less steep the inhibition curve would be. By analogy, pseudoviruses, which have fewer Env spikes than natural viruses but were not included in this study, could be expected to show higher intrinsic values of η (Table 5).

Table 5.

Summary of relationships between synergy and cooperativity in the inhibition of HIV-1 entry

	Synergy index, σ50%, for combinations	Change in cooperativity, ηrel, for combinations	Intrinsic cooperativity for individual inhibitors, η
Range of values	~0.20 – ~1.9a	~1.0 – ~2.0a	~0.50 – ~1.5a
Isolates/clonesb	Low (R5)	High (mainly X4)	Low (R5)
R5 (PI)/X4 (TCLA)b	NSc	NSc	Low
Correlates	Weakly with deviation of used ratio from Ki ratio	Strongly with σ50%/σ90%, synergy skewness	Inversely with SD/EC50d
Moderate Emax differences as confounding factor	Weake	Strong	Strong
Plausible influence of heterogeneity in Env and of trimer number per virion	Yes	Yes	Yes

^aRanges are based on values that deviate by more than 2 SEM from 1 in Tables 2–4.

^bThe ratios of the values obtained for isolates and clones or R5 and X4 viruses are described.

^cNS = non-significant deviation from 1.

^dThe ratio of the standard deviation of the half-maximal effective concentration over the mean of the latter among a hypothetical population of heterogeneous receptors was shown to have an inverse relationship to the slope coefficient or cooperativity factor (Hoffman and Goldberg, 1994).

^eLarge E_max differences among individual inhibitors and combinations will

invalidate regular concentration-based or fractional synergy analyses.

When the cooperativity factor for inhibitors other than NAbs was analyzed by the Chou-Talalay median-effect principle in an X4 pseudovirus-PBMC assay with a 4-log dynamic range, the slopes of the viral inhibition curves were inhibitor-class-specific (Shen et al., 2008; Zhang et al., 2004). NRTI and integrase inhibitors had slopes of ~1, NNRTIs and fusion-blocking peptides of ~1.7, while protease inhibitors had the highest slopes of 1.8–4.5. Furthermore, the differences in slope affect how HIV-1 escapes the different classes of ARV. Thus, escape from drugs with low slope values takes the form of increased IC₅₀ values, whereas escape from inhibitors with high slope values is manifested by a reduction of the slope (Sampah et al., 2011). We obtained comparable slope values >1 for T-20 with two of three X4 viruses (Table 4), but the corresponding values for the R5 viruses (not studied in (Shen et al., 2008)) were lower (0.59–1.1). The slope (η) influences the instantaneous inhibitory potential (the log reduction in single-round infectivity at clinical drug concentrations), which correlates better with in vivo efficacy than does IC₅₀ or the inhibitory quotient (the ratio of plasma drug concentration over IC₅₀) (Shen et al., 2008). Although many other factors than instantaneous inhibitory potential and inhibitory quotient influence clinical outcome during ART, both correlate with long-term viral suppression (Henrich et al., 2010; Shen and Siliciano, 2010). It may therefore be worth considering how efficacy is affected by synergy and changes in cooperativity at inhibitor concentrations close to and above IC₅₀. Suppose the combination A+B is synergistic in the mid-zone (σ_50%=0.5), whereas C+D is not (σ_50%=1.0). A+B involves no slope change (η_rel=1), but C+D shows enhanced cooperativity (η_rel=2). For simplicity, all single-inhibitor K_i values are the same and all intrinsic η values = 1. Then at an inhibitory quotient of 1, C+D reduces the remaining infectivity 1.5-fold less than A+B; but at inhibitory quotients of 10 and 100, C+D reduces the remaining infectivity, respectively, 5- and 50-fold more than A+B. The example shows that at high concentrations, which may be medically relevant, changes in cooperativity can give more drastic combinatorial effects than synergy that is manifested merely as a parallel curve shift.

It can be argued that a high slope of inhibition would be crucial for vaccine-induced NAbs. For their protective capability may be determined not by their mid-range potency but by how much they can reduce the infectivity of virus deposited in the mucosae. The values of η we measured here for the NAbs were low, <1 or ~1, with one exception (2F5 against LAI, η=1.3). Hence it should be investigated whether other, newly discovered, broadly acting and potent NAbs (Walker et al., 2011; Walker et al., 2009; Zhou et al., 2010) perform better in this regard. Overall, the relationship between the in vitro potency and the in vivo protective capacity of NAbs remains to be fully elucidated (Hessell et al., 2009).

We extended the slope analysis to combinations of inhibitors and found near-uniform elevations of η (i.e. η_rel >1) (Table 3). This quantity, change in slope upon combination, may be useful in dealing with the problem of inconsistent synergy over different degrees of inhibition. Such skewness in synergy - usually manifested as lower CI_90% than CI_50% values - is a common finding (Allaway et al., 1993; Buchbinder et al., 1992; Gantlett et al., 2007; Hrin et al., 2008; Ji et al., 2007; Mascola et al., 1997; Murga et al., 2006; Nakata et al., 2008; Strizki et al., 2005; Tilley et al., 1992; Tremblay et al., 2002; Tremblay et al., 2000; Xu et al., 2001; Yoshimura et al., 2006; Zwick et al., 2001). The CI_90% or σ_90% value is theoretically often invalid and is, in any case, practically impossible to determine with acceptable precision (Supplementary Table 1). However, η_rel correlates strongly with the σ_50%/σ_90% ratio (Figure 3B) and is more readily determined with precision than σ_90% (Supplementary Table 2). The η_rel quantity is therefore appropriate for characterizing combinatorial effects at higher levels of inhibition, as a complement to the slope-independent, σ_50% value (Table 5). However, adding the measurement of η and η_rel to the standard arsenal of inhibition analyses, as we advocate, raises the question of how these quantities should be interpreted biologically.

Originally, the Hill coefficient, n, was suggested to reflect the number of ligands interacting with each receptor complex, but the value of n is generally lower than that stoichiometric number and only approaches it under conditions of extreme positive cooperativity (Hill, 1913; Weiss, 1997). In some binding schemes, 10 sites for the ligand on the receptor can give n = 2 without any cooperativity; negative cooperativity reduces n further below its theoretical maximum, but not below 1 (Weiss, 1997). In contrast, heterogeneity in the population of target molecules, whether Env, co-receptor or reverse transcriptase, can bring the value of the slope coefficient below 1. The greater the heterogeneity in target molecule sensitivity, expressed as SD/EC₅₀ (the standard deviation of the half-maximal effective concentration divided by the mean of the latter) the smaller will be the slope coefficient, n (Hoffman and Goldberg, 1994), or in our case η (Table 5). This basis of reduced η-values for individual inhibitors also explains why η_rel becomes >1 for combinations. Thus, the virions that are least sensitive to one inhibitor will statistically have a more ordinary sensitivity to another; the resulting reduction in the heterogeneity in sensitivity to the combined action of the two inhibitors raises the value of η. In this regard, it is notable that the broad and potent neutralizing capacity of sera from some HIV-1-infected persons has been attributed to the combined action of NAbs directed to several different Env epitopes (Scheid et al., 2009), although in most subjects only one or two specificities may be involved (Walker et al., 2011; Walker et al., 2010). Hypotheses now worth testing are whether the values of η are higher for polyclonal sera than for their constituent specificities, and whether η_rel for pooled NAbs > 1. Since it was the breadth of the neutralizing capacity rather than its potency that could be reconstituted by the pooling of NAb clones (Scheid et al., 2009), a generalized version of the heterogeneity hypothesis might have further test implications: individual NAbs would be predicted to give lower values of η for a mixture of different isolates than for individual ones, and the greater the diversity of the virus mix, the higher the predicted η_rel values for cross-neutralizing pools of NAbs.

In summary, the synergy in neutralization that we observed was modest, sporadic, and interspersed with some cases of antagonism. In contrast, the positive change in cooperativity upon combination was nearly ubiquitous and frequently strong (Table 5). In particular, combining 2G12 with 2F5 or 17b gave consistently high values of η_rel (1.3–1.8) across the panel of viruses (Table 3). Heterogeneity among target molecules may provide a mechanistic basis for both synergy and enhanced cooperativity. Genetic heterogeneity in env may contribute to synergy among NAbs in a way that the data for R5 viruses support; heterogeneity in the glycan shield can both stem from genetically determined differences at glycosylation sites and be affected by non-uniform carbohydrate processing. The involvement of the NAb 2G12, which is directed to a mannose-dependent epitope (Sanders et al., 2002; Scanlan et al., 2002), in some of the strongest synergy, as well as in enhanced cooperativity, suggests a role for glycan-shield heterogeneity. Conformational heterogeneity may instead particularly affect the antigenicity of the 17b and 2F5 epitopes (Dimitrov et al., 2007; Finnegan et al., 2001, 2002; Harris et al., 2011; Sattentau et al., 1995; Shen et al., 2010). Each of these NAbs also gave many instances of marked synergy and slope increases when combined with 2G12; they synergized considerably less together, suggesting that two different kinds of heterogeneity together are particularly conducive to synergy and enhanced cooperativity.

New assays for quantifying the inhibition of HIV-1 infectivity over a wide dynamic range, and the concomitant focus on slope analysis, constitute significant advances (Sampah et al., 2011; Shen et al., 2008; Zhang et al., 2004). Such experimental systems may also allow rigorous determinations of the maximal extent of inhibition, E_max, which is currently beyond the scope of our data. Determining that additional quantity could improve our analyses, since real differences in E_max may masquerade as variation in η (Table 5). Since these in vitro measurements might predict the efficacy of NAbs and viral inhibitors in vivo, they seem worth pursuing in the quest for better preventive and therapeutic strategies.

MATERIALS AND METHODS

Cells and viruses

Tzm-bl cells were obtained from the NIH AIDS Research and Reference Reagent Program (ARRRP). They express the luciferase gene under control of the HIV-1 LTR (Wei et al., 2002), which is activated by viral Tat upon infection. The 293T cell line was obtained from the American Type Culture Collection (ATCC; Manassas, VA). Tzm-bl and 293T cells were maintained in Dulbecco’s modified Eagle medium (DMEM; Invitrogen Inc., Carlsbad, CA) supplemented with 10% fetal bovine serum (FBS; Invitrogen) and 100 U/ml penicillin + 100 μg/ml streptomycin (1× PenStrep; HyClone, Logan, UT). All cells were incubated at 37 °C in a 5% CO₂ atmosphere.

The primary R5 HIV-1 isolate CC1/85 and its env-derivative chimeric clonal viruses NL4.3/9-6, NL4.3/9-7, and NL4.3/9-8 have been described (Kuhmann et al., 2004; Trkola et al., 2002). These clones are hereafter described as 9-6, 9-7, and 9-8. The HIV-1 isolate IIIB and the derivative clonal viruses LAI and NL4.3 were obtained from the ARRRP. Stocks of infectious clones were prepared by transfecting the full-length proviral plasmids into 293T cells by Lipofectamine 2000 (Invitrogen).

Antibodies and reagents

NAbs 2G12 to a mannose-dependent epitope on the outer domain of gp120, b12 to the CD4bs, 17b to a CD4-induced epitope overlapping the co-receptor binding site, and 2F5 to a membrane-proximal epitope on gp41 were all provided by the IAVI Neutralizing Antibody Consortium Repository. The humanized anti-CCR5 MAb PRO 140 was obtained from Bill Olson (Progenics Pharmaceuticals), and the small molecule CCR5 inhibitor vicriviroc (VCV) from Julie Strizki (Schering-Plough; now Merck). Michael Greenberg (Trimeris) supplied the gp41-derived HR2 fusion-blocking peptide T-20. AMD3100, a small-molecule CXCR4 inhibitor, was obtained from Gary Bridger (AnorMed; now Genzyme). Nevirapine, a non-nucleoside reverse transcriptase inhibitor, was purchased from Boehringer Ingelheim.

Infectivity assays

Neutralization and entry inhibition experiments were carried out using Tzm-bl cells (Wei et al., 2003). One day before infection, 1 × 10⁴ Tzm-bl cells in 200 μl DMEM-FBS were seeded into each well of 96-well plates. NAbs were serially diluted in 2-fold steps in DMEM. A 50 μl aliquot of each dilution was then mixed with 50 μl of virus suspension (pre-titrated to yield a luminescence of ~5 × 10⁵ counts per second) per well, and incubated at 37ºC for 1 h. The mixture (100 μl per well) was then added to the cells, which were incubated at 37ºC for 40 h. Each NAb concentration was tested in quadruplicate. The other inhibitors (T-20, VCV, AMD3100, Neviparine, PRO 140) were titrated similarly, except that the 50 μl aliquots from each dilution step were incubated with the Tzm-bl cells for 1 h at 37ºC before addition of 50 μl of virus for a further 40 h. The cells were then washed with PBS, lysed and freeze-thawed. The luciferase activity in the lysate was measured by the Bright-Glo method (Promega) on a Victor3 1420 plate-reading luminometer (Perkin Elmer, Wellesley, MA). Background luminescence values from control wells with cells and no virus were subtracted. Inhibitory concentrations were calculated by non-linear regression in Prism (Graphpad, see Modeling section below).

Inhibitors were then combined in proportions approximately corresponding to the ratios of their IC₅₀ (K_i) values derived from the single-inhibitor titrations. As controls, each inhibitor was combined with itself at equimolar concentrations. All such combinations were titrated at fixed ratios in octuplicate in parallel with single inhibitors in quadruplicate.

To examine the influence of multi-cycle replication, we also used an infectivity assay based on p24 production by HIV-1-infected primary lymphocytes. Peripheral blood mononuclear cells (PBMC) were isolated from blood obtained at the New York Blood Center (New York, NY), then cultured in Culture Medium, which was RPMI 1640 supplemented with 10% FBS, 10 mM L-glutamine (Cellgro), and 100 U/ml IL-2 (ARRRP, contributed by Hoffman-LaRoche, Inc.). Half the PBMC culture was stimulated with 5 μg/ml of phytohemagglutinin (PHA; Sigma, St. Louis, MO), half with an anti-CD3 MAb (supernatant from the OKT3 hybridoma) in Culture Medium, directly after isolation. After 3 days, the differently stimulated cells were mixed in equal proportions, washed, and suspended in Culture Medium supplemented with 100 μg/ml of penicillin/streptomycin for the remainder of the culture. The PBMC were seeded at 1.4 × 10⁶ cells/ml in 100 μl per well in 96-well plates. NAbs b12 and 2G12 (the only ones included in the PBMC experiment) were diluted serially in two-fold steps and incubated with virus for 1 h before adding the mixture to cells. HIV-1 replication was measured as Gag-p24 content in mixed cell-culture suspension by an in-house ELISA on different days over 2 weeks of culture (Ketas et al., 2003). The ELISA detects both p24 and Gag precursor (p55), so that antigen detection is not affected by the presence of the protease inhibitor (data not shown). The amount of residual Gag from the input virus was measured in 9 replicates per plate and subtracted from test values. Net Gag production in the test wells was compared with that in the control wells (no inhibitor in 21 replicates per plate). The yield corresponded to 0.1–3 ng p24 per ml, which was defined as 100%.

Modeling

We compared the current standard method for synergy analysis (Chou and Talalay, 1981, 1984) with a new one that we devised. The “median-effect principle” of Chou’s method is based on a linear transformation of the inhibition data. A linear function is then fitted: (log (f_a/f_u) = m log(D/D_m)), where f_a = fraction affected (i.e., the normalized proportion of inhibited infection); f_u = fraction unaffected (i.e., 1- f_a, or the relative residual infectivity); m is a constant affecting the slope of the linear curve; D_m is the “median effect dose”, the equivalent of the half-maximal inhibitory concentration; D is the concentration of inhibitor yielding a degree of inhibition corresponding to f_a. The combination index, CI = (D_(AB)A/D_A) + (D_(AB)B/D_B) is next calculated from the fitted values of D when inhibitors A or B are used alone (D_A or D_B) or as constituents of the combination (D_(AB)A and D_(AB)B). This formula has been suggested to apply to the case of two inhibitors with mutually exclusive actions only (Chou and Talalay, 1981, 1984). An alternative formula, CI= (D_(AB)A/D_A) + (D_(AB)B/D_B) + (D_(AB)A/D_A) * (D_(AB)B/D_B), has been proposed to apply to the case of non-exclusive inhibitors (Chou and Talalay, 1981, 1984). We only used the simpler formula here. For a justification of this choice, see the Supplementary Information. Chou’s and Talalay’s method is available in software form (CalcuSyn, Bisoft), but we fitted the published functions as polynomials of the first order in Prism (Graphpad).

We also used non-linear regression (Prism, Graphpad) to fit all data to a non-linear function that is similar in form to the law of mass action: I=(C/K_i)^η/(1+(C/K_i)^η)), where I = relative inhibition of infectivity; K_i is the half-maximal inhibitory concentration by analogy with the dissociation constant, K_d, in the Law of Mass Action; C = concentration of an inhibitor; η = a cooperativity factor, related to the Hill constant.

The synergy indicator was calculated according to Loewe’s formula (Loewe, 1953) as σ = (K_i(AB)A/K_iA) + (K_i(AB)B/K_iB), where K_iA = inhibitory concentration of A when used alone; K_iB = inhibitory concentration of B when used alone; K_i(AB)A = inhibitory concentration of A when used in combination with B; and K_i(AB)B = inhibitory concentration of B when used in combination with A.