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Title: Estimating the Probability of Polyreactive Antibodies 4E10 and 2F5 Disabling a gp41 Trimer after T Cell-HIV Adhesion}
Article:
Abstract:
A few broadly neutralizing antibodies, isolated from HIV-1 infected individuals, recognize epitopes in the membrane proximal external region( MPER) of gp41 that are transiently exposed during viral entry. The best characterized, 4E10 and 2F5, are polyreactive, binding to the viral membrane and their epitopes in the MPER. We present a model to calculate, for any antibody concentration, the probability that during the pre-hairpin intermediate, the transient period when the epitopes are first exposed, a bound antibody will disable a trivalent gp41 before fusion is complete. When 4E10 or 2F5 bind to the MPER, a conformational change is induced that results in a stably bound complex. The model predicts that for these antibodies to be effective at neutralization, the time to disable an epitope must be shorter than the time the antibody remains bound in this conformation, about five minutes or less for 4E10 and 2F5. We investigate the role of avidity in neutralization and show that 2F5 IgG, but not 4E10, is much more effective at neutralization than its Fab fragment. We attribute this to 2F5 interacting more stably than 4E10 with the viral membrane. We use the model to elucidate the parameters that determine the ability of these antibodies to disable epitopes and propose an extension of the model to analyze neutralization data. The extended model predicts the dependencies of for neutralization on the rate constants that characterize antibody binding, the rate of fusion of gp41, and the number of gp41 bridging the virus and target cell at the start of the pre-hairpin intermediate. Analysis of neutralization experiments indicate that only a small number of gp41 bridges must be disabled to prevent fusion. However, the model cannot determine the exact number from neutralization experiments alone.
Introduction:
A small but growing number of HIV-1 broadly neutralizing monoclonal antibodies( mAbs) have been isolated from HIV-1 infected individuals( reviewed in[1]). A subset of these( 4E10, 2F5, m66. 6 and Z13e1) bind to epitopes at the base of gp41, along a segment adjacent to the viral membrane known as the membrane proximal external region( MPER) that links the gp41 transmembrane domain to its ectodomain 2, 3. Two, 4E10 and 2F5, have been extensively characterized. Each has been shown to be polyreactive[4]–[6], with an elongated heavy chain complementarity determining region 3( CDRH3) that has a hydrophobic surface that does not contact the peptide antigen[7],[8], but that contributes to the ability of 4E10 and 2F5 to bind to the virion membrane and to broadly neutralise[9]–[13]. Recently, self-antigens have been identified that these antibodies recognize[14]. Of the two mAbs, 2F5 interacts more strongly with membrane as demonstrated by its ability to bind to virus-like particles bearing no envelop glycoprotein( Env spikes)[6]. Detailed structural studies and surface plasmon resonance measurements( SPR) have shown that the epitopes for 4E10 and 2F5 are within the MPER, lying along the viral surface with parts immersed in the viral membrane[15]–[17]. The binding of these antibodies to their epitopes on the viral membrane appears to be step-wise[4],[17],[18] with the membrane associated antibody and the MPER undergoing conformaional changes[15],[16],[18] that result in a more stably bound complex[4],[8],[17],[18]. For both mAbs and their Fabs, the rate constants that describe the kinetics of the two step process have been determined for binding to liposome-gp41 peptide conjugates[4]. The epitopes recognized by 4E10 and 2F5 on gp41 are displayed on the viral membrane after the binding of HIV-1 to the target cell has occurred and the processes that result in membrane fusion have begun[2]. This stage, between pre- and postfusion, called the pre-hairpin intermediate[19], has a lifetime that has been estimated to range from a few seconds to many minutes[20]–[23]. The tenet that 4E10 and 2F5 only recognize epitopes on the MPER during the pre-hairpin intermediate appears to strictly hold only for HIV-1 isolates that are highly resistant to neutralization[24]. For HIV-1 isolates that are less resistant to neutralization, the MPER epitopes may be accessible to antibody binding before the pre-hairpin intermediate stage has been initiated. Alternatively, enhanced susceptibility to MPER neutralizing antibodies could be a result of prolonged exposure of the intermediate state during viral entry[25]. Although numerous studies have determined rate constants for the binding of 4E10 and 2F5 to peptide epitopes in solution and peptides conjugated to liposomes[2],[4],[10],[12],[13],[15],[17],[18], and estimates of the lifetime of the exposure of the MPER on HIV-1 have been obtained[20]–[22],[26], a quantitative description of how these parameters determine the mAb concentrations that are effective in inhibiting fusion has been lacking. Here we present a model that allows us to calculate, as a function of the serum antibody concentration, the probability of a trivalent MPER being disabled by polyreactive mAbs. A question we also consider is how the probability of disabling a single epitope is related to the probability of blocking membrane fusion of HIV-1 and target cell when, at the start of the pre-hairpin intermediate stage, epitopes bridge the two membranes. We present a model that predicts the form of a neutralization curve, i. e., the percent neutralization versus the antibody or Fab concentration, and how the for neutralization depends on, as well as on the rate constants that characterize antibody binding and the rate of fusion of gp41. We use the model to fit neutralization experiments where neutralization is achieved with either 4E10 or 2F5 IgG or Fab. Our analysis of these experiments indicates that at the start of the pre-hairpin intermediate only a few gp41 trimers are involved in bridging the virion and target cell. As the bonds break sequentially those that remain come under additional strain and are disabled more easily.
Discussion:
The probability of disabling a trivalent gp41 in the pre-hairpin intermediate depends on a number of factors including the concentration of mAb available to bind to gp41 and the number of gp41 bridging the virus and target cell. We expect that for a fixed antibody concentration, as the number of gp41 attachments increases, the probability decreases( it becomes harder to disable a bond) reaching a plateau where the probability( in our model) is independent of the number of bonds present. In this limit, increasing the number of bonds increases the contact area between virus and target cell while the bond density remains uniform[37]. For this limit we presented a kinetic model and used it to calculate, for a given concentration of polyreactive mAbs or Fabs, the probability that during the pre-hairpin intermediate, a trivalent gp41 will be rendered incapable of completing the fusion process when a single Fab or mAb binds to one of the three exposed MPERs. The model predicted that for the antibody to be effective in neutralizing HIV-1, the time it takes to disable an epitope must be shorter than the time the epitope remains in the long-lived conformation induced by antibody binding. For 4E10 and 2F5, whose dissociation rate constants for the breakup of the long-lived complex s−1( Table 1 and[4],[17]), the time to disable an epitope must be about five minutes or less. Increasing the time the antibodies remain bound in the long-lived conformation( lowering) would not improve their neutralization capabilities. Rather, it is the rate of formation of the long-lived conformation that is the limiting step in determining the ability of these antibodies to disable epitopes. The effective forward rate constant for this step, the parameter in the model, given by Eq.( 10), equals the product of the forward rate constant for binding of the antibody in solution to the epitope,, and the probability that the bound complex undergoes a conformational change rather than dissociating,. In the encounter model, which we believe well characterizes the kinetics of binding of 2F5, is the overall rate constant for the binding of the antibody from solution to the membrane, diffusion of the membrane bound antibody to the epitope, and binding of the antibody to the epitope through a surface reaction. Increasing the antibody's affinity for the membrane or its affinity for the MPER is predicted to result in higher values of, higher values for the probability of disabling an epitope and lower values for the. Increasing the affinity of the antibody by lowering its dissociation rate constant for the MPER,, will increase the probability of forming a long-lived complex, while increasing the affinity by increasing the forward rate constants will increase the rate of formation of the initial antibody-MPER complex. From previous SPR studies of 2F5 and 4E10 Fab and IgG binding to peptide-lipisome conjugates[4] we determined the values of for these four ligands. These values led us to predict that 2F5 IgG would exhibit a much stronger avidity effect than 4E10 IgG. The prediction was tested by comparing neutralization experiments using Fab and IgG and plotting the ligand concentration in Fab sites per mole. If there were no avidity effect, such a plot should yield two identical curves. In the plots in Figure 5A and 5B the prediction was born out. The mAb 2F5 was much more effective than its Fab, while the mAb 4E10 was only marginally better than its Fab. In the model the strong avidity of 2F5 IgG arises as result of its being able to form cross-links between the MPER and the viral membrane. This result is consistent with experiments showing that 2F5 interacts more stably with the viral membrane than does 4E10[6]. We cannot rule out that an additional contribution to the avidity comes from the mAb cross-linking different MPERs on the same virion, something not in the model. Indeed, in light of recent studies showing that Env spikes are clustered on mature HIV-1[33], and because 2F5 and 4E10 interact with gp41 after it has attached to the target cell membrane and clustered in the contact region between the two membranes, it is to be expected that some cross-linking of MPERs occurs. Still, 4E10 shows little improvement over its Fab in neutralization, indicating that for 4E10 there is little or no cross-linking of MPERs. In contrast, 2F5 shows a high avidity, but what contribution, if any, comes from 2F5 cross-linking two MPERs rather than MPER and viral membrane, is unknown. Although, the model we presented to calculate delineated the roles of the rate constants in determining the ability of 2F5 and 4E10 to disable an epitope, it couldn't be directly applied to analyze neutralization experiments. To do this we considered an HIV and target cell bridged by N gp41 at the start of a neutaliation experiment and asked the question, what is the probability of sequentially disabling all N gp41s before one of them fused? To answer this question required a model that quantified the influence of the number of bridging bonds on bond breakage. We proposed an expression for, the probability of disabling a bond when bonds are present, given by Eq.( 14). The expression was chosen so that it had the correct limiting behavior, that when was large was independent of and when was small the probability of disabling increased as the bonds came under additional strain. Using this expression for we were able to obtain an expression for the probability of disabling all bonds before fusion occurred, Eq.( 18). One prediction of the model, Eq.( 20) is how the depends on the model parameters. For a mean time of fusion of 10–30 min()[20]–[22],, the value for 4E10 in Table 2, and, nM. For, the value for 2F5 from Table 1, nM. These predicted values, obtained for values of from SPR experiments with peptide-vesicle conjugates, are consistent with the values determined from neutralization experiments[8]–[11],[13],[24],[28],[36],[41] and lend some support to the model. The model also predicted that for a series of neutralization experiments with different mAbs and Fabs, a plot of the fraction of virus neutralized in each experiment versus, should lie on a single curve. After we fit Eq.( 18) to four experiments that used 2F5 and 4E10 mAb and Fab, and replotted the data as a function of, the data did lie on a universal curve( Figure 7A). From the analysis of these data we could not determine the number of gp41 bridging the virus and target cell at the start of the experiment, but the analysis indicated that these bonds are few in number and under considerably more strain then if there were a large number of attachments in the contact region. There are relatively few Env spikes on HIV-1. The average number has been reported to be between seven and 14 spikes per HIV-1[30],[33],[42],[43]. Zhu et al. found spikes per HIV-1 with a range of four to 35[30]. Using electron tomography about five to seven spikes have been observed in the contact region between virion and CD+ T cell in the prefusion stage[34]. This was the case when the virion was either SIV or HIV. However, it is not known how many gp41 membrane spanning trimers are established after the loss of gp120 and the entrance into the pre-hairpin intermediate. Attempts have been made to determine the stoichiometry of HIV entry, but as yet reliable estimates of the minimum number of attachments required for fusion to occur have not been established[32],[39],[40],[44]. It therefore remains to be seen whether this picture, where just a few weak attachments are mediating fusion and neutralization can be achieved by disabling these, is a reasonable description of what is occurring in the neutralization experiments we have analyzed.
Most people who become infected with HIV generate a strong antibody response to the infecting virus population . Unfortunately , the protection offered by the antibody is short lived as the virus rapidly mutates and renders the antibodies impotent in preventing further infection . There are a few antibodies , however , that have been isolated from infected individuals that can block infection by many different viral strains . Among these are several that target sites on the HIV that are exposed only after the virus has attached to a cell . These antibodies have a brief window of time to prevent fusion of the virus and cell . They are special in that they bind both to the viral membrane and to sequences on the gp41 protein that lie along the viral surface . Here , we present a model that predicts the concentrations at which these antibodies effectively neutralize the virus . The model tells us what properties of antibody binding are key in determining efficient neutralization and what properties have little influence . A prediction of the model is that in a standard neutralization assay there are only a small number of attachments between virus and cell and disabling these is sufficient to prevent infection .