Abstract
Due to the low density of envelope (Env) spikes on the surface of HIV-1, neutralizing IgG antibodies rarely bind bivalently using both antigen-binding arms (Fabs) to crosslink between spikes (inter-spike crosslinking), instead resorting to weaker monovalent binding that is more sensitive to Env mutations. Synthetic antibodies designed to bivalently bind a single Env trimer (intra-spike crosslinking) were previously shown to exhibit increased neutralization potencies. In initial work, diFabs joined by varying lengths of rigid double-stranded DNA (dsDNA) were considered. Anticipating future experiments to improve synthetic antibodies, we investigate whether linkers with different rigidities could enhance diFab potency by modeling DNA-Fabs containing different combinations of rigid dsDNA and flexible single-stranded DNA (ssDNA) and characterizing their neutralization potential. Model predictions suggest that while a long flexible polymer may be capable of bivalent binding, it exhibits weak neutralization due to the large loss in entropic degrees of freedom when both Fabs are bound. In contrast, the strongest neutralization potencies are predicted to require a rigid linker that optimally spans the distance between two Fab binding sites on an Env trimer, and avidity can be further boosted by incorporating more Fabs into these constructs. These results inform the design of multivalent anti-HIV-1 therapeutics that utilize avidity effects to remain potent against HIV-1 in the face of the rapid mutation of Env spikes.
Significance IgG antibodies utilize avidity to increase their apparent affinities through simultaneous binding of two antigen-binding Fabs – if one Fab dissociates from an antigen, the other Fab can remain attached, allowing rebinding. HIV-1 foils this strategy by having few, and highly-separated, Envelope spike targets for antibodies, forcing most IgGs to bind monovalently. Here we develop a statistical mechanics model of synthetic diFabs joined by DNA linkers of different lengths and flexibilities. This framework enables us to translate the energetic and entropic effects of the linker into the neutralization potency of a diFab. We demonstrate that the avidity of multivalent binding is enhanced by using rigid linkers or including additional Fabs capable of simultaneous binding, providing the means to quantitatively predict the potencies of other antibody designs.
Introduction
Despite decades of research since its discovery, Human Immunodeficiency Virus-1 (HIV-1) continues to threaten global public health (1). While there have been advances in our understanding of the mechanisms of infection and the development of preventative and therapeutic strategies, there remains no cure for HIV-1 infection. Antiretroviral therapy with small molecule drugs can control the progression of the virus, allowing those infected with HIV-1 to live longer and healthier lives, but the treatment includes detrimental side effects, and when discontinued or not taken as prescribed, leads to viral rebound to pre-treatment levels (2). A major factor confounding the development of a prophylactic vaccine is the rapid mutation of HIV-1 which leads to the emergence of many new strains, even within a single individual (3). Thus, most antibodies raised by the host immune system are strain-specific or neutralize only a subset of strains, leading to viral escape from host antibodies.
Recent interest has focused upon the isolation of broadly neutralizing IgG antibodies (bNAbs) from a subset of HIV-1–infected individuals (4). These antibodies bind to and block the functions of the HIV-1 envelope (Env) spike, the viral protein responsible for the fusion of HIV-1 to the host cell (5). The discovery and characterization of HIV-1 bNAbs has brought new impetus to the idea of passively delivering antibodies to protect against or treat HIV-1 infection. bNAbs can prevent and treat infection in animal models (6–12) and exhibited efficacy against HIV-1 in human trials (13–16). However, HIV-1 Env mutates to become resistant to any single bNAb, as even the most potent NAbs developed in an infected individual normally fail to neutralize autologous circulating viral strains (17–20). As a result, antibodies that develop during HIV-1 infection appear to be unable to control the virus in an infected individual.
We previously proposed that one mechanism by which HIV-1 evades antibodies more successfully than other viruses arises from the low surface density of Env spikes that can be targeted by neutralizing antibodies (21, 22). Compared to viruses such as influenza A, dengue, and hepatitis B, the density of Env spikes on the surface of HIV-1 is about two orders of magnitude smaller (22). For example, influenza A has ≈450 spikes per virion, whereas each HIV-1 virion incorporates only 7-30 Env spikes (average of 14) (22–26), even though both influenza A and HIV-1 are enveloped viruses with ≈120 nm diameters (Fig. 1A). The HIV-1 spikes are the machinery by which the virus binds its host receptor CD4 and coreceptor CCR5/CXCR4 to mediate the fusion of the host and viral membranes that allows its genome to enter target cells (5). As a consequence of its small number of spikes, HIV-1 infection of target cells is inefficient; the transmission probabilities for sexually-acquired HIV-1 infection range from 0.4 to 1.4% (27). However, the reduced infectivity of HIV-1 comes with a concomitant reduction in the ability of antibodies to control the virus, as the surface spikes serve as the only targets for neutralizing antibodies that can block infection of target cells (4).
The close spacing of spikes on typical viruses allows IgG antibodies to bind bivalently to neighboring spikes (inter-spike crosslinking) using both of their antigen-binding arms (Fabs). However, most spikes on HIV-1 virions are too far apart (typically over 20 nm separation) (22) to permit inter-spike crosslinking by IgGs whose antigen-binding sites are separated by ≤15 nm (28). While each homotrimeric HIV-1 spike includes three binding sites (epitopes) for an antibody, the architecture of HIV-1 Envs prohibits simultaneous binding of two Fabs within a single IgG to the same Env (intra-spike crosslinking) (29, 30). We suggested that predominantly monovalent binding by anti-HIV-1 antibodies expands the range of Env mutations permitting antibody evasion, since reagents capable of bivalent binding through inter- or intra-spike crosslinking would be less affected by Env mutations that reduce but do not abrogate binding and thus may be more potent across multiple strains of HIV-1 (21, 22). The hypothesis that HIV’s low spike numbers and low densities contributes to the vulnerability of HIV-1 bNAbs to spike mutations is supported by independent biochemical and EM studies demonstrating that HIV-1 has an unusually low number of spikes that are not clustered (23–26, 31), and that bivalent IgG forms of anti-HIV-1 NAbs are only modestly more effective than monovalent Fabs, by contrast to bivalent IgGs against other viruses, which can be 100s- to 1000s-fold more potent than counterpart monovalent Fabs (21, 22, 29, 30).
An antibody’s neutralization potency against a virus is related to its antigen-binding affinity, which is defined as the binding strength between a Fab and its antigen (32) described by the equilibrium dissociation constant KD = [Fab][Ag]/[Fab–Ag], where [Fab], [Ag] and [Fab–Ag] are the concentrations of the antibody Fab, antigen, and the complex, respectively (33). In bivalent molecules interacting with binding partners that are tethered to a surface, the apparent affinity, or avidity, can be enhanced by multivalent binding. Such multivalent interactions are seen in many biological contexts including cell-cell communication, virus-host cell interactions, antibody-antigen interactions, and Fc receptor interactions with antigen-antibody complexes (34). Avidity effects benefit these interactions from both kinetic and thermodynamic standpoints. Binding bivalently to tethered binding partners is advantageous kinetically because if one arm dissociates, the likelihood of it finding its binding partner is greater due to the constraint of being tethered (35). Avidity effects are also advantageous thermodynamically; whereas binding the first arm results in losses of translational and rotational degrees of freedom, the subsequent binding of the second arm incurs a smaller entropic cost, thereby increasing the likelihood of the bivalent state (35).
In the context of an IgG with two antigen-binding Fabs, the ability to bind bivalently to a virus is dependent on geometric factors such as the separation distances and orientations of tethered epitopes either on adjacent spikes during inter-spike crosslinking (Fig. 1A, red box) or on individual spikes if intra-spike crosslinking can occur (Fig. 1A, blue box) (36). Because the large distances between HIV-1 spikes makes inter-spike crosslinking unlikely, in this work, we focus exclusively on the latter mechanism of achieving bivalent binding. Although IgGs are too small to intra-spike crosslink (Fig. 1A, gold box) (29, 30), we previously engineered larger reagents (homo- and hetero-diFabs) that were designed to bind to a single Env, resulting in mean neutralization potency increases over a panel of HIV-1 strains (21). These diFab constructs were composed of two IgG Fabs joined by different lengths of double-stranded DNA (dsDNA), which served as both a rigid linker and a molecular ruler to probe the conformations of HIV-1 Env on virions (21) (Fig. 1B). The dsDNA was flanked by two short single-stranded DNA (ssDNA) segments, where the primary differences between the two types of DNA is that dsDNA is more rigid and shorter than the more flexible and longer ssDNA .
In this work, we expand upon these earlier results and theoretically analyze whether changing the flexibility of the linker joining the two Fabs could also enhance neutralization potency. This enables us to compare a spectrum of possibilities from a rigid linker solely comprising dsDNA to a fully flexible linker composed of only ssDNA. To that end, we developed a statistical mechanical model to systematically evaluate the effects of linker length and rigidity on synergistic neutralization by a diFab. We then generalize our model to a triFab design and demonstrate that simultaneously binding to three Env epitopes can greatly boost avidity. Insights from our synthetic constructs can be adapted to antibody design in other systems in which length and rigidity of linkers in multivalent reagents must be balanced to elicit the most effective response.
Results
Estimating the Parameters of diFab Binding from Crystal Structures
While HIV-1 Env fluctuates between multiple conformations, we assume that a diFab neutralizes the virus by binding to one specific state of Env at which the distance between the C-termini of the two Fabs (where the DNA is joined) is defined to be llinker (Fig. 2A). For example, the predicted distance based on modeling adjacent 3BNC60 Fabs on a low-resolution open structure of an HIV-1 trimer (37) was ≈20 nm. More recently, we used the 3BNC117 Fab-gp120 portion of a cryo-EM structure to measure the distance between adjacent Fab CH1 C-termini in the closed conformation of Env and then modeled a 3BNC60-gp120 protomer into three recent cryo-EM structures of Env trimers in different conformations: an open Env bound by the b12 bNAb in which the coreceptor binding sites on the V3 loops are not exposed (38), an open CD4-bound Env structure with exposed V3 loops (38), and a partially-open CD4-bound Env in which the gp120 subunits adopted positions mid-way between closed and fully open (39). From these structures, we measured distances of 15.8, 20.3, 20.4, and 20.1 nm between C-termini of Fab CH1 domains modeled onto the closed, b12-bound open, CD4-bound open, and CD4-bound partially-open Env conformations, respectively. Based on these values, we set llinker=20 nm.
A further model parameter, lflex=1 nm, shown in Fig. 2A was included to account for the flexibility of the Fab. More precisely, this parameter accounts for variations in the distance between the C-termini of the two Fab CH1 domains to which the DNA was attached due to the following factors: (i) the Fab CH1-CL domains can adopt different conformations with respect to VH-VL (40) such that the locations of the CH1 C-terminus could shift by up to ≈1 nm; (ii) residues C-terminal to CH1 residue 217 were found to be disordered in the 3BNC60 Fab structure (41), thus the position of the CH1 residue to which the DNA was attached (Cys233) is uncertain within ≈1 nm; (iii) the ssDNA is covalently linked to the CH1 residue Cys233 using an amine-to-sulfhydryl crosslinker (Sulfo-SMCC), which exerts unknown effects on the length and the degree of flexibility between the ssDNA and Fab.
Relating Neutralization to the Probability that an HIV-1 Spike is Bound
To model diFab efficacy in terms of the properties of the linker, we first related the ability of a diFab to neutralize an HIV-1 virion to the probability that an Env spike on the surface of HIV-1 will be bound by an antibody. We assume that the spikes are sufficiently far apart to preclude inter-spike crosslinking (Fig. 1A, red boxes) and focus exclusively on intra-spike crosslinking between the three identical sites on the Env homotrimer (Fig. 1A, blue boxes). We further assume that viral infectivity varies linearly with the number of unbound Env, rising from zero (when all spikes are bound by diFabs) to maximum infectivity (when all spikes are unbound) as discussed in Appendix A (42, 43, 44).
Given these assumptions, the ability of a diFab to neutralize HIV-1 is proportional to the probability that at least one of the binding sites on an Env spike will be bound (Appendix A). For example, if each Env protein has a 75% chance to be bound by a diFab, an average of 75% of the spikes on each virion will be bound, and by the linearity assumption, the HIV-1 virions will be 75% neutralized. This enables us to relate the experimentally-determinable % neutralization for diFabs to the theoretically-tractable probability that a single Env spike will be bound either monovalently or bivalently by a diFab. Avidity effects will allow an optimal diFab to bind more tightly to a spike, increasing the binding probability and the neutralization potency.
The Avidity of a diFab is Dictated by its Linker Composition
To calculate the probability that any of the Fab binding sites on an HIV-1 spike are occupied, we enumerated three potential states of the spike, which represent a single diFab bound to zero, one, or two binding sites (Fig. 2A). The entropy of the linker was characterized by treating the dsDNA as a 1D rigid rod and the ssDNA as a random walk. The former assumption is valid provided the dsDNA in each linker is less than the 150 bp persistence length of dsDNA (45), a reasonable restriction given that only 60 bp dsDNA are required to span llinker=20 nm. Free ssDNA is flexible with a persistence length ξssDNA = 1.5 nm (≈ 2.3 bases) (46, 47) that we analyze using the ideal chain polymer physics model (48).
When a diFab transitions from the unbound state (with probability p0) to a monovalently-bound state (with probability p1), it loses translational and rotational entropy but gains favorable binding energy (49) leading to the relative probability where [Ab] is the concentration of the diFab and is the equilibrium dissociation constant of the first diFab arm binding to Env. can be experimentally determined as the IC50 (concentration of antibody capable of neutralizing 50% of the virus) of a Fab neutralization profile, with a smaller IC50 signifying a more potent antibody. We use the typical value reported for a CD4-binding site bNAb dissociating from a soluble, trimeric HIV-1 Env (50). Importantly, the transition from an unbound to a monovalently-bound diFab is independent of the amount of dsDNA and ssDNA in the diFab’s linker.
We now turn to the transition from a monovalently-bound diFab to a bivalently-bound diFab. The ability to simultaneously bind two epitopes depends on the linker composition (the quantity of dsDNA and ssDNA), since the distance llinker between the C-termini of bivalently-bound Fabs must be spanned by the rigid dsDNA segments as well as the two flanking ssDNA strands (Fig. 2A). More precisely, we enumerate the configurations of the ssDNA random walk and the dsDNA in the bivalently bound state (Fig. 2B), permitting us to compute the entropic cost of bivalent binding (Appendix B). Within this framework, the probability of the bivalently bound state (p2) compared to the monovalently bound state is given by the product of a constant α that is independent of the linker composition and a term n(ldsDNA, lssDNA) that depends on the quantity of dsDNA and ssDNA, namely, where and represent the length of d dsDNA base pairs and s ssDNA bases in the linker, respectively.
Eqs. 1 and 2, together with the normalization condition p0 + p1 + p2 = 1, enable us to compute the probability that a diFab will neutralize a virion, from which we can write the concentration of 50% inhibition,
The value of α = 5 × 106 was calibrated from previous measurements where a diFab with d=62 bp and s=12 bases neutralized HIV-1 approximately 100-fold better than the Fab alone (21). Fig. 2C compares the probability that a diFab will be bivalently bound (p2) rather than monovalently bound (p1) for different linkers. The model shows that bivalent binding is most likely when llinker ≈ ldsDNA, when the rigid dsDNA approximately spans the length between the two bound Fabs. This peak shifts leftwards with the root-mean-squared length of the flexible ssDNA, demonstrating that ssDNA can make up for dsDNA that is slightly too short or too long, provided the flexibility of the ssDNA is taken into account. Fig. 2D shows the corresponding IC50s for these constructs. Although adding more flexible ssDNA leads to a broader segment of dsDNA lengths capable of enhanced neutralization, the optimal diFab potency is achieved by including less ssDNA and maximizing the rigidity of the linker.
The diFab Model Allows Bivalent Binding Only when the dsDNA Length is Approximately Equal to the Length of the Linker it Spans
To gain a qualitative understanding of our results, we examined Eq. 4 in two limits: near the optimal geometry ldsDNA ≈ llinker where the ability to bind bivalently is maximum, and far from the optimal limit when the diFab is too short or too long to permit bivalent binding through intra-spike crosslinking.
Near the optimal geometry, HIV-1 neutralization occurs predominantly from the bivalently-bound configuration rather than the monovalent state, . Hence, the system is well approximated with each spike either being unbound or bivalently-bound, with the dissociation constant for a single Fab boosted by the avidity factor α n, namely,
If the potency of diFab 1 is , and the potency of diFab 2 with a different linker is , the latter diFab’s potency will be shifted relative to the former by the ratio of n factors, namely,
In other words, the relative potency of both diFabs is determined solely by the entropy, rather than the energy, of the linker when bivalently bound.
In the opposite regime where the diFab linker is too small (ldsDNA + lssDNA ≲ llinker) or too large (ldsDNA − lssDNA ≳ llinker), the diFab loses the ability to bind bivalently and the IC50 attains a constant value shown as a black dashed line in Fig. 2D.
The Avidity of a triFab is Capable of Binding Three Env Sites is Further Enhanced over that of the diFab
While the diFab constructs were inspired by two-armed IgG antibodies, a triFab construct that could simultaneously bind to three Env epitopes (Fig. 1B) should exhibit even greater avidity and hence neutralize HIV-1 more potently. For simplicity, we assume that both dsDNA segments have the same length, as do all ssDNA segments. As derived in Appendix C, the IC50 of such a construct is given by
Fig. 3A and B compare the neutralization potencies across the design space of diFabs and triFabs, demonstrating that joining three Fabs can result in IC50s far smaller than what is possible for even the theoretically optimal diFab design.
The neutralization potency of a triFab near its optimal geometry (α n ≫ 1) is dictated purely by the trivalently bound state,
Note that the boost in avidity in going from a Fab to a diFab is equivalent to the boost between a diFab and triFab. Since diFabs have been shown to achieve a 100-1000 fold decrease in IC50 over a Fab, a triFab should be able to achieve a 104-106 fold decrease in IC50 relative to the Fab, providing a powerful framework with which to achieve very high neutralization. To further enhance potency, more than three Fabs could be joined together into a multiFab. By joining multiple types of Fabs that bind to different epitopes (e.g., the broadly neutralizing CD4-binding 3BNC117 with a V1V2-binding PG16), multiFabs may enhance the potency of neutralization as well as help combat HIV-1 heterogeneity as has been seen in combination influenza antibodies (51) and HIV-1 mosaic vaccines (52).
An Optimal Linker is Maximally Rigid and Perfectly Spans the Distance between Env Epitopes
Counter to what might be intuitively expected, adding flexibility to a linker by increasing the number of ssDNA bases need not improve the diFab’s neutralization potential. This effect arises because flexible ssDNA has a large number of degrees of freedom that are constrained when the diFab bivalently binds, leading to a larger entropic penalty (or smaller boost in avidity). Indeed, the full diFab and triFab design space shown in Fig. 3 demonstrates that an optimal construct is a perfectly rigid linker composed of only dsDNA whose length matches the distance between HIV-1 epitopes (ldsDNA ≈ llinker). However, we caution that such diFabs may not operate optimally for both experimental and theoretical reasons including: (1) the range of dsDNA lengths that permit bivalent binding narrows as the amount of ssDNA decrease, and in the extreme limit of a linker with no ssDNA, being slightly too short or too long by as little as a few base pairs may preclude bivalent binding; (2) charge interactions between the dsDNA and either the Fab or Env may disrupt diFab functionality; (3) a lack of sufficient flexibility at the Fab-dsDNA junction may preclude bivalent binding; and (4) in the limit of a rigid linker (ssDNA≲10 bases) the ideal chain model breaks down and the bending of ssDNA must be accounted for (e.g., via the worm-like chain model) which may result in higher IC50s than predicted by our model.
Because of these considerations, it is worthwhile to use a diFab whose dsDNA length ldsDNA matches the distance between Fab epitopes (llinker) found in crystal structures, and to flank this dsDNA with short segments of ssDNA (≈10 bases) to buffer against uncertainties in the measurements. As seen in Fig. 3, such constructs lie within a wide basin with strong neutralization potential. Of note, this strategy far surpasses a purely flexible linker (lssDNA ≈ llinker, ldsDNA = 0) which cannot bivalently bind because of the large entropic cost. Other methods of introducing flexibility, such as introducing ssDNA breaks in the dsDNA linker, are also predicted to increase the entropic cost of bivalent binding and hence increase the IC50 (see Appendix C).
Discussion
The low density of Env spikes on HIV-1 potentially enables the virus to mitigate the host antibody response by hindering IgGs from using both antigen-binding Fabs to bind bivalently, thereby expanding the range of HIV-1 mutations permitting antibody evasion (21, 22). Indeed, a mutant simian immunodeficiency virus (SIV) with a higher number of Env spikes reverted to its normal spike count of ≈14 when propagated in non-human primate hosts (53). This suggests that while HIV-1 may be more infectious with more Env trimers (54), the immune system applies selective pressure that keeps the Env spike count per virion low, presumably to prevent anti-HIV-1 IgGs from utilizing avidity effects to counter the lower intrinsic Fab-Env affinities that result from rapid mutation of Env. Antibody isotypes such as dimeric IgA or pentameric IgM have increased valencies (four and ten Fabs, respectively) compared to the two Fabs of an IgG, thus allowing for increased avidity effects during antibody binding to a pathogen. However, most of the neutralizing activity in the sera of HIV-1–positive individuals is attributed to IgGs (55, 56), and converting an anti-HIV-1 IgG antibody to an IgA or IgM has minimal effects on potency in standard neutralization assays (57, 58), possibly because there are so few Env spaced sufficiently far apart that these other antibody classes are also forced to bind monovalently.
Bivalent binding to single Env trimer (intra-spike crosslinking) is another way to utilize avidity effects to counteract the low spike density of HIV-1. Although the architecture of Env trimers prohibits this mode of binding for conventional, host-derived IgGs (29, 30), we analyzed how synthetic diFabs (Fabs from a neutralizing anti-HIV-1 IgG joined by a linker containing rigid dsDNA flanked by flexible ssDNA shown in Fig. 1B) could be designed to achieve optimal intra-spike crosslinking.
HIV-1 Env trimers adopt multiple conformations on virions (24, 59) and in the soluble native-like forms used for structural studies (60). For example, binding of the host CD4 receptor induces outward displacements of the three Env gp120 subunits, resulting in an open conformation in which the coreceptor binding sites on the trimer apex V3 loops are exposed (38, 39, 61, 62) and that rearranges further upon coreceptor binding and subsequent membrane fusion. We measured the distances between adjacent 3BNC117 epitopes in a new cryo-EM structure (63) and estimated the average position of the C-terminal CH1 domain residue to which the DNA of a 3BNC117 diFab would be covalently attached (40). Based on these measurements, we assumed that a diFab neutralized HIV-1 when the linker spans a length llinker=20 nm. We further assumed that the Fab CH1-CL domains can stretch relative to the VH-VL domains by lflex =1 nm (see Fig. 2A). Lastly, we considered a Fab whose ability to dissociation (as given by the midpoint of a neutralization assay) equals to . Each of these values can be readily adapted to other HIV-1 strains and Fabs.
With these parameters in hand, we developed a statistical mechanics-based model to predict the neutralization of a diFab whose linker is composed of d base pairs dsDNA and s bases ssDNA (Fig. 1B), enabling us to tune both the length and rigidity of the linker. By assuming that (i) each homotrimeric spike is unable to help infect a host cell when any one of its three epitopes are bound by Fab and (ii) that the infectivity of a virion varies linearly with the number of unbound Env, we showed that the neutralization of a virion is proportional to the probability that any single Env protein is bound by a Fab (Appendix A). This framework enabled us to translate the linker-dependent entropy and energy of binding to an HIV-1 Env trimer into the predicted neutralization potency for each diFab.
It is worthwhile to point out several factors that the model neglects. First, the model does not consider potential, but presumably rare, diFab binding between adjacent Env trimers. Second, our model assumed that the % neutralization of HIV-1 decreases linearly with the number of unbound Env trimers (Appendix A). While such a linear relationship was observed when less than half of HIV-1 spikes were bound (54), it may break down if, for example, at least 2-3 unbound Env trimers are needed to infect a cell. We also assumed that each virion had exactly 14 spikes, neglecting the relatively small observed spike number variations (23–26). However, relaxing these assumptions yielded nearly identical results (Appendix A), suggesting that our results are robust and should apply to more general descriptions of HIV-1 neutralization.
We determined that an optimal linker will maximize its rigidity, trading flexible ssDNA for rigid dsDNA. The larger flexibility of ssDNA implies that there will be a higher entropic penalty for bivalently binding, thereby resulting in a worse (larger) IC50. This general statement applies to all forms of increased flexibility including: (1) trading dsDNA for an equivalent length of ssDNA; (2) adding ssDNA without decreasing the length of dsDNA; or (3) introducing ssDNA gaps in the dsDNA (Appendix C).
In additional to tuning the length of dsDNA and ssDNA in the linker, an additional biologically-inspired approach to further increase avidity is to construct multiFabs that target more than two epitopes. As has been seen in other biological systems (64–66), higher valencies can elicit tighter binding. Hence, a triFab that allows three Fabs to simultaneously bind to an HIV-1 Env trimer is predicted to have a lower IC50 than an optimal diFab; indeed, our model predicts that the boost from avidity of an optimal diFab over a Fab is equivalent to the boost of an optimal triFab over an optimal diFab, and hence we expect that triFabs should be able to achieve IC50s 104-106 fold smaller than Fabs. MultiFabs that link together Fabs targeting different epitopes (e.g., the broadly neutralizing CD4-binding site antibody 3BNC117 and the V2-binding PG16 antibody) (52) could better combat the heterogeneity of HIV-1 strains, providing guidance for constructing optimal anti-HIV-1 therapeutics that remain potent against HIV-1 in the face of the Env mutations arising during HIV-1 replication.
Supporting Information
The supporting information includes appendices and a Mathematica notebook that reproduces the figures in this manuscript.
Author Contributions
T.E., A.P.W., R.P. and P.J.B. conceived the project; T.E., S.Y., and R.P. developed the model and performed analyses; T.E., R.P., and P.J.B. wrote the paper with input from other authors.
Acknowledgements
We thank Anthony Bartolotta, Justin Bois, Jim Eisenstein, Vahe Galstyan, Peng He, Willem Kegel, David Hsieh, Giacomo Koszegi, Pankaj Mehta, Jiseon Min, Olexei Motrunich, Noah Olsman, Vahe Singh, and Richard Zhu for useful discussions, Christopher Barnes for measuring modeled 3BNC60-Env complexes, and Marta Murphy for help preparing figures. This research was supported by NIH NIAID grants 1R01AI129784 and HIVRAD P01 AI100148 (P.J.B.), the Bill and Melinda Gates Foundation Collaboration for AIDS Vaccine Discovery Grant 1040753 (P.J.B.), La Fondation Pierre-Gilles de Gennes (R.P.), the Rosen Center at Caltech (R.P.), R01 GM085286, and 1R35 GM118043-01 (MIRA) (R.P.), and a Caltech-COH Biomedical Research Initiative (P.J.B.). We thank the Burroughs-Wellcome Fund for their support through the Career Award at the Scientific Interface (S.Y.) as well as for the Physiology Course at the Marine Biological Laboratory where part of this work was done.
Footnotes
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Expanded main text and revised and figures