Stoichiometry for entry and binding properties of the Env protein of R5 T cell-tropic HIV-1 and its evolutionary variant of macrophage-tropic HIV-1

ABSTRACT Human immunodeficiency virus type 1 typically requires a high density of CD4 for efficient entry as a mechanism to target CD4+ T cells (T-tropic), with CCR5 being used most often as the coreceptor. When target T cells are limiting, the virus can evolve to infect cells with a low density of CD4 such as macrophages (M-tropic). The entry phenotype is known to be encoded in the viral Env protein on the surface of the virus particle. Using data showing a dose response for infectivity based on CD4 surface density, we built a model consistent with T-tropic viruses requiring multiple CD4 molecules to mediate infection, whereas M-tropic viruses can infect cells using a single CD4 receptor molecule interaction. We also found that T-tropic viruses bound to the surface of cells with a low density of CD4 are released more slowly than M-tropic viruses which we modeled to be due to multiple interactions of the T-tropic virus with multiple CD4 molecules to allow the initial stable binding. Finally, we found that some M-tropic Env proteins, as the gp120 subunit, possess an enhanced affinity for CD4 compared with their T-tropic pair, indicating that the evolution of macrophage tropism can be reflected both in the closed Env trimer conformation on the virion surface and, in some cases, also in the open confirmation of gp120 Env. Collectively, these studies reveal differences in the stoichiometry of interaction of T-tropic and M-tropic viruses with CD4 and start to identify the basis of binding differences at the biochemical level. IMPORTANCE Human immunodeficiency virus type 1 normally targets CD4+ T cells for viral replication. When T cells are limiting, the virus can evolve to infect myeloid cells. The evolutionary step involves a change from requiring a high surface density of CD4 for entry to being able to infect cells with a low density of CD4, as is found on myeloid lineage cells such as macrophage and microglia. Viruses able to infect macrophages efficiently are most often found in the CNS late in the disease course, and such viruses may contribute to neurocognitive impairment. Here, we examine the CD4 binding properties of the viral Env protein to explore these two different entry phenotypes.

the coreceptor, which usually is the chemokine receptor CCR5 but can be CXCR4 (2).The gp41 subunit is a transmembrane protein embedded within the viral envelope membrane; gp41 undergoes conformational changes once gp120 binds to the host cell receptors to mediate fusion between the viral and host membranes allowing the viral capsid to enter the cell (3,4).
Structural studies of the gp120 domain and of the gp120/gp41 trimer (truncated at the transmembrane domain of gp41) have led to the concept of the Env protein existing in a closed or open conformation, with the closed conformation being the unbound form and the open conformation representing the CD4-bound state (3,5).Studies using single-molecule dynamics have further shown that the protein can move between these states (6)(7)(8)(9).In the native state, the Env trimers are in the closed unligated conformation, while binding to CD4 results in an opening of the gp120 structure and exposure of CD4-induced features that are either occluded or do not exist in the closed conformation (7,10).Taken together, these studies point to the Env-mediated entry process involving a complex set of changes in the conformation of the Env protein leading ultimately to receptor and coreceptor binding followed by membrane fusion between the host and viral membranes.
HIV-1 has two distinct entry phenotypes based on coreceptor use and on primary receptor CD4 use.When CD4+ T cells expressing CCR5 become limiting, the virus will evolve to switch from using CCR5 as its coreceptor (R5 virus) to using CXCR4 (X4 virus) on CD4+ T cells lacking CCR5 (11).The typical form of HIV-1 requires a high surface density of CD4, as is found on CD4+ T cells, to target T cells for infection (T-tropic viruses) and avoid myeloid cells which express a low density of CD4 on their surface.The virus can follow a different evolutionary path in compartments that largely lack CD4+ T cells, such as in the central nervous system (CNS).This alternative entry phenotype involves an expansion of host target cells from CD4+ T cells to myeloid cells, such as macrophages and/or microglia (12)(13)(14).To infect macrophages, the virus must evolve the ability to enter cells with a low density of CD4, becoming macrophage-tropic (M-tropic viruses) (15)(16)(17).M-tropic virus is rarely found in the blood, is not the transmitted form of the virus, and is typically found in the CNS where it can be associated with HIV-associated dementia (14).Thus, the evolutionary path from T-tropic to M-tropic virus represents both an expansion of host cells but also an important pathogenic mechanism.Two consistent features of M-tropic viruses (as encoded in their Env proteins) are the ability to enter cells with a low density of CD4 and enhanced sensitivity to neutralization by soluble CD4 (15,18).As these viruses appear to be resistant to antibodies that bind to CD4-induced epitopes, this argues that the unliganded M-tropic Env protein is likely in a closed conformation.Several studies have examined the basis for the M-tropic Env phenotype in specific isolates, but no uniform explanation for the ability to a use low density of CD4 has yet emerged (19)(20)(21)(22)(23)(24)(25)(26).
Previous studies have examined the number of Env/CD4 interactions required for virus entry using a strategy of making heterotrimers with mixtures of active and inactive gp120 subunits and modeling the loss of infectivity; results from these studies have suggested that from one to seven interactions are needed to mediate infectivity, depending on the isolate (27)(28)(29)(30)(31). Two limitations of these previous studies are the lack of distinction between M-tropic and T-tropic viruses and the inclusion of tissue cultureadapted viruses (which can acquire entry properties not seen in vivo).In this study, we have used five pairs of T-tropic and M-tropic env gene clones to express the Env proteins, with each pair coming from a different person (and without tissue culture passage), to compare features of T-tropic viruses with paired M-tropic evolutionary variants.We modeled the relationship between surface CD4 density and entry efficiency and fit a model where M-tropic viruses can enter cells after engaging a single CD4 molecule while T-tropic viruses require interaction with three CD4 molecules.We also measured the rate of virion dissociation from the surface of cells with a low density of CD4 and paradoxically observed a slower rate for the T-tropic virus, which we modeled as being the result of binding multiple CD4 molecules to allow the initial stable cell attachment of the T-tropic variant.Finally, we measured the binding affinity of the gp120 form of the Env protein for both M-and T-tropic viruses and found that some of the M-tropic viruses bound CD4 more tightly than their paired T-tropic Env even in the open conformation.These results help inform the nature of the evolutionary path from R5 T cell tropism to macrophage tropism and point to the presence of determinants in both the closed and open conformation that can contribute to this phenotype.

M-and T-tropic HIV-1 variants differ in their dependency on CD4 density for efficient infection
In a previous work, we created five pairs of M-tropic env genes and T-tropic env genes cloned in expression vectors, where each pair was isolated from the same person so each pair was a relevant biological comparison (32).These clones can be used to pseudotype an HIV-1 reporter virus that does not express its own surface Env protein but rather an Env protein of our choosing using a cotransfection strategy (33).In Fig. 1, we reproduce the entry phenotype results from infecting Affinofile cells at high and low densities of surface CD4.env genes from the HIV-1 isolates JR-CSF and BAL are used as T cell-tropic virus and M-tropic virus controls, respectively.The nomenclature of each env gene used in pseudotyping is a number to distinguish the different participants followed by a P, for plasma source and T-tropic, or a C, for CSF source and M-tropic.The final number in the name is a clone designation.As can be seen in Fig. 1, infectivity on low CD4-density Affinofile cells by the T cell-tropic viruses is very low and in some cases undetectable, while all of the M-tropic viruses retain between 20% and 45% of their infectivity at low CD4 density compared with their infectivity as measured on Affinofile cells expressing a high density of CD4 (defined as 100%).

Model of the stoichiometry of CD4 usage by M-and T-tropic viruses
In Fig. 1 we validated the entry phenotype of the five Env protein pairs at low versus high surface density of CD4.We have previously measured the dose response of virus entry as a function of varying CD4 density on the surface of Affinofile cells for these five pairs of the expressed Env proteins (See Table S1) (34).Here, we use that data to model infection efficiency as a function of CD4 density to infer the number of CD4 receptors needed for viral entry for the M-and the T-tropic viruses.The model keeps track of the population of cells free of virions attached to CD4 receptors (C0), cells where a virion is attached to one, two, or three CD4 receptors (C1, C2, and C3, respectively) and cells that are infected with HIV-1 (I).See Fig. S1 for a schematic representation of the model and a description of the model formula.We fit the model to the fraction of the maximum signal obtained after infecting Affinofile cells with different expression levels of CD4.We found that only a small fraction of T-tropic viruses infect cells using one CD4 receptor when the CD4 density is low [<10 4 antibody binding sites (ABS) per cell], whereas when the CD4 density is high (>10 4 ABS per cell), they are able to effectively infect using three CD4 receptors for entry (Fig. 2).In contrast, M-tropic viruses are able to infect cells using one CD4 receptor when CD4 density is low, and they switch to using three CD4 receptors for entry for maximal infectivity when CD4 density becomes high (Fig. 2).This model fits well for all five pairs of M-and T-tropic viruses.In addition, comparing the estimated parameters for the T-tropic and the M-tropic viruses (Tables S2 and S3), we found that the difference between the two viruses is primarily their ability to use one CD4 receptor molecule for entry, while their ability to use three CD4 receptors is similar.

The population of T-tropic virus that binds to cells with a low density of CD4 has a distinct interaction with the cells
In Fig. 1, we showed that T-tropic viruses have very little infectivity in cells that express a low density of CD4.We were interested next in looking at the small amount of T-tropic virus that was able to constitute an infectious event where the goal was to measure how tightly M-and T-tropic variants bound to cells at low CD4 density.The design of this experiment was to bind virus to the surface of the cells with a low surface density of CD4 at 4°C (using spinoculation), remove the excess unbound virus, and then hold the cells and virus at 4°C to determine the rate at which infectivity was lost.Binding virus to cells at 4°C is expected to allow interaction with CD4 but to preclude the subsequent steps of membrane fusion.At varying time points, the medium was replaced with 37°C medium and the infection allowed to proceed.Since the virus not attached to cells was removed, we assume any virus released into the medium during the period when the cells were held at 4°C would have a very low probability of rebinding to cells and its potential infectivity would be lost, thus allowing a measure of virus release as lost infectivity.To compensate for the low infectivity of T-tropic viruses on low CD4-expressing cells, 10 times the amount of infectious virus units as the M-tropic variants (as measured at high CD4 density) was used to allow similar numbers of infectious events for the M-and T-tropic viruses to be recorded at time zero.These experimental conditions were used for two pairs of M-and T-tropic Env protein pseudotyped viruses (4051 and 4059) with the results shown in Fig. 3.There is an initial period of no loss or even a slight increase in infectivity followed by a loss of infectivity over time.Surprisingly, the infectivity of the T-tropic virus decayed more slowly relative to its M-tropic virus pair in both cases, suggesting the T-tropic virus was bound tighter to the low-density CD4 cells than the M-tropic viruses.
In an initial analysis, we estimated the dissociation rate assuming a first-order decay for release of virus from the cell.Using the % RLU infection at 8 and 24 hours, we Figure 4 shows a schematic and kinetic scheme for the new model where we assume a two-step dissociation process to describe the dissociation data for the T-tropic virus.In the new model, we assume that the only T-tropic viruses stably bound to the cell surface do so by interacting with two CD4 molecules via two trimers such that the virus must release from both CD4 molecules to leave the cell.In this model, the dissociation rate

Research Article mBio
k app allows for release from one CD4 molecule (k −t ) and reformation of that interaction (k +t ).Only when the second CD4 molecule is released at a moment when the first CD4 molecule is not engaged is the virus released.We then made the assumption that the timescale of the reversible binding process, wherein one trimer is released and then rebinds, is smaller than the timescale of the release of the second trimer molecule.This leads to a rapid equilibrium assumption such that k −t tCCt = k +t ttCC and derives a single decay rate for the total pool of tCCt + ttCC (35): (1) where [L] is the "local" concentration of the trimer.The local concentration of the trimer was estimated as the concentration of a single trimer in a hemisphere centered at the occupied CD4-trimer complex with radius the approximate distance to another trimer (Fig. 4C) (36).Given that there are approximately 20 trimers on a virus with a 100nm (0.01 µm) diameter, we estimate the average distance between trimers to be 0.045 µm, assuming there are 20 circular patches of surface area on the virus.Thus, L = 1trimer We then plotted this expression in Fig. 4D to see the dependence of k −t on k +t .The dashed line in the plot is the decay rate for the M-tropic virus.We can see that for our computed apparent decay rate and local concentration of trimer, k −t is a monotonically increasing function of k +t , where k +t is unknown.Only for k +t < 7.5/Ms do we have values where k −t §amp;lt; k −m .This is an extremely slow association rate that is very unlikely, as most association rates are within the 10 5 -10 8 /Ms range (37), especially considering this is for a virion already attached to the cell remaking a bivalent interac tion.Thus, our model explains how T-tropic viruses can decay from the cell surface at a slower rate compared with the M-tropic virus (k app < k −m ) in spite of a weaker interaction between the T-tropic Env trimer with a single CD4 molecule compared with the M-tropic Env (k −t > k −m ).While we have not measured k -t or k +t directly, by extrapolating from Fig. 4D ,we can see that if k +t were only 10 4 /Ms, this would make the dissociation rate of a T-tropic virus from a single CD4 molecule (k -t ) 30-fold faster than the rate for the Mtropic virus (k -m ).

Some M-tropic Env proteins also have a post-CD4-binding determinant of macrophage tropism
The preceding experiments used the native Env trimer on the surface of the virus to examine differences between M-and T-tropic Env proteins interacting with cell surface CD4.We next explored whether the differences we showed at the trimer level were conserved at the gp120 Env monomer level.It is known that the gp120 form of Env is in an open conformation that displays antibody epitopes that are hidden in the trimer but exposed after binding CD4, suggesting gp120 is in a conformation that approximates the structure bound to CD4 (3,38).We purified the gp120 form of the five Env pairs to test their binding properties to CD4 to determine if the differences between M-and T-tropic Env proteins we observed in the virion-associated trimer form of Env would extend to the purified gp120 form.Binding was assessed using a surface plasmon resonance (SPR) strategy of flowing gp120 over CD4 that was immobilized to carboxymethylated dextrancoated gold plated chips.The binding of each gp120 Env to CD4 gave binding affinities in the low nanomolar range (Fig. 5A).In three out of the five Env pairs, the M-tropic gp120 Env protein bound CD4 tighter as compared with its paired T-tropic gp120 Env protein (Fig. 5B).Taken together, these data indicate that the gp120 Env proteins that as part of trimers on virions have the M-tropic phenotype can also have amino acid changes that result in tighter CD4 interaction as gp120 than their paired T-tropic Env protein comparator.This result suggests that the evolution of the M-tropic phenotype follows multiple pathways such that the phenotype is always expressed at the level of the Env trimer but in some cases can also be expressed in the gp120 Env open conformation.

DISCUSSION
This study focuses on the features of the Env protein of M-tropic viruses in order to explore how they differ from T-tropic viruses.One focal point of this study was to examine how many CD4 molecules are needed to initiate infection for T-tropic and Mtropic Envs.Analyzing our previously collected experimental data led us to devise a model that suggests T-tropic viruses typically use three CD4 molecules in order to infect efficiently whereas M-tropic viruses are able to enter after engaging a single CD4 molecule.We used this difference in the number of CD4 molecules needed for infectivity to model multivalent binding to allow stable association of T-tropic viruses with the cell surface leading to slower dissociation compared with M-tropic viruses.We also show some M-tropic Env proteins in the gp120 form have a higher affinity for CD4 compared with T-tropic gp120 Env, adding to the M-tropic phenotype that is defined by CD4 dependency at the Env trimer level.
The question of the number of trimer/CD4 molecule interactions needed for entry has been studied previously using a different approach where heterotrimers were created on the surface of the virion using active and inactive gp120 subunits and measuring infectivity as a function of the changing ratio of active to inactive Env proteins assembled in a trimer (28).In one case, the M-tropic virus YU-2 was modeled to use a single Env trimer/CD4 interaction, consistent with what we observed for M-tropic viruses using a strategy of varying CD4 density; yet in another study, the M-tropic virus JR-FL was modeled to require two Env/CD4 interactions for infection (28)(29)(30).However, this approach has also given discrepant values for the Env protein from the HIV-1 IIIB isolate (as found in either the pNL4-3 clone or the HXB-2 clone) with values ranging from 2 to 5, with the confounding feature being this variant was passaged extensively in culture before clones were made (27,28).These approaches, along with the use of the Affinofile cell assay, all measure infectivity, and thus, it is unknown what the precise step is where these differences occur (CD4 binding versus the ease of downstream conformational changes).In this regard, Quitadamo et al. showed that a tagged sCD4 molecule bound poorly to cells expressing a T-tropic Env protein but gave detectable binding to cells expressing an M-tropic Env protein (39).Our modeling data for infectivity as a function of CD4 density is consistent with M-tropic viruses needing to interact only with a single CD4 to initiate infection while T-tropic viruses require three interactions (Fig. 2).
Several structural studies have shown CD4 molecules binding to an Env trimer can give different conformations of the trimer depending on whether one, two, or three CD4 molecules are bound, with the implication being that a trimer must be fully occupied with CD4 to allow the subsequent conformational changes to occur, leading to viral membrane fusion (8,(40)(41)(42).Our modeling of infectivity as a function of surface CD4 density for R5 T-tropic viruses is consistent with this observation in that there is a strong dependence on surface CD4 density for infectivity implying the need to interact with multiple CD4 molecules.The model does not distinguish between the need for multiple CD4 molecules interacting with different trimers or a single trimer.However, our modeling for M-tropic virus suggests interaction with one CD4 molecule is sufficient to initiate infection.It should be pointed out that M-tropic viruses still have increasing infectivity with increasing cell surface density of CD4 but in more of a linear relationship compared with T-tropic viruses.It is possible that the M-tropic trimer can initiate a conformational change based on an interaction with a single CD4 molecule, or alternatively, the M-tropic trimer may require multiple engagements but makes a more stable first engagement so that step does not become rate limiting before initiating the subsequent interactions with CD4.
When we bound T-tropic virus to cells with a low CD4 density (and in the cold to prevent fusion), we found that infectivity decayed more slowly compared with bound M-tropic viruses (Fig. 3).Given the poor infectivity of T-tropic viruses at low CD4 density, we modeled the slow decay (which we assume is virion release/dissociation from the cell surface) as being the result of T-tropic viruses binding two (or more) CD4 molecules to be retained on the cell surface compared with one interaction for M-tropic viruses (Fig. 4).We have considered two other factors that could account for the time-dependent reduction in infectivity of surface bound virus: irreversible cold inactivation of virus and CD4-induced shedding of gp120.We previously tested cold inactivation of these virus pairs and found one pair (4051) had a difference in cold sensitivity while the other pair (4059) showed similar cold sensitivities (15), so irreversible cold inactivation does not explain the behavior of both pairs for infectivity decay rates.Also, the slow loss of infectivity for the cold-resistant viruses is inconsistent with the enhanced loss of infectivity seen in Fig. 3, suggesting virus inactivation is not what is being measured.However, it is possible that cold sensitivity of a CD4-bound trimer is different from the unbound trimer, but this has not been tested (43,44).Additionally, gp120 shedding, which could affect infectivity, is temperature-dependent and has been reported not to occur at 4°C, which was the temperature used in our experiment (43,44).Chojnacki et al. have shown that the Env trimers are clustered on the surface of the virus (45).While we have modeled a more uniform trimer distribution, the effect of clustering would suggest an even smaller k +1 if CD4 molecules were also clustered (46); additionally, clustering of trimers could overcome the strain of membrane curvature in making a second interaction with CD4.
The SPR analysis allowed us to compare T-tropic and M-tropic binding kinetics as gp120 monomers to allow comparison with the trimer phenotype measured using infectivity.Previously, it was shown that the presence of artifactual gp120 dimers, generated when overexpressing gp120 in mammalian cells, makes interpretation of binding kinetic data difficult because the inclusion of dimers affects on-rate estimations (47,48).Thus, the use of monomers requires a size exclusion purification strategy to remove dimers during purification (Fig. S2).The gp120 Env proteins from participants 4051, 4059, and 5002 were characterized by having a faster association rate for the M-tropic Env compared with the T-tropic Env.A previous SPR experiment examined differences between a parent and microglia lab-adapted gp120 (HIV-Bori 15 ) and found the difference in affinity between the two was a threefold reduced dissociation rate, leading to the conclusion that this lab-adapted gp120 had a higher affinity for CD4 (49)(50)(51).Our gp120 pairs came from participants where evolution occurred in vivo; however, participant pairs that displayed a significant difference in affinity did not have a reduced dissociation rate like the aforementioned study.A more recent experiment by Quitadamo et al. showed with paired BR-and LN-derived gp120s, the BR-derived gp120 bound CD4Ig with higher affinity (39).This aligns with our findings; however, the magnitude of difference found in our samples was more pronounced.We note that only three of the five pairs showed enhanced binding of the M-tropic gp120 to CD4 relative to the T-tropic gp120.All five pairs have the M-tropic phenotype for entry in the trimer form on the virion surface.This suggests that all M-tropic viruses are likely to express the M-tropic phenotype at the level of the trimer and that only a subset of the M-tropic Env proteins will follow an evolutionary path that will also display enhanced binding of the gp120 form to CD4.

Construct design
Each gp120 originated from a prior study where we used single genome amplification to isolate and clone full-length env gene sequences from study participants (32); accession numbers are shown in Table 1.The sequence encoding gp120 was synthesized and cloned (Genescript Biotech, Piscataway, NJ) into an expression vector.The restriction enzyme site XbaI (TCTAGA) was used as the 5′ flanking region followed by the Kozak sequence (CCACC).All gp120 constructs included a CD5 leader sequence for cellular secretion.The 3′ flanking region included two stop codons (TGATGA) and a HindIII site (AAGCTT).Lastly, all of the gp120 proteins contain an internal HRV3C protease cleavage site followed by a 6× histidine tail for the protein purification strategy.DNA transforma tions were conducted with the DH5α strain of E. coli.

Expression of gp120 proteins
gp120 proteins were expressed via transient transfection of Expi293F (Thermo) cell cultures using 1 mg of endotoxin-free plasmid per 1 L culture at 3.0 × 10 6 cells/mL cell density.Each culture supernatant was harvested on the third day post-transfection by centrifugation at 4,000 × g for 30 minutes.The culture medium was filtered through a 0.22-µm membrane and then subjected to tangential flow filtration to reduce the volume and perform a buffer exchange into 50 mM sodium phosphate pH 7.4, 500 mM NaCl, and 20 mM imidazole (NiNTA buffer A). gp120 proteins were captured via NiNTA chromatography using 1 mL HisTrap FF columns (Cytiva).The columns were washed to baseline in NiNTA buffer A; then, proteins were eluted with 50 mM sodium phosphate pH 7.4, 500 mM NaCl, and 500 mM imidazole.Eluates were dialyzed into 50 mM Tris-Cl pH 8.0 and 150 mM NaCl and then cleaved with HRV 3C protease at 1 U per 100 µg gp120.The digests were passed over re-equilibrated HisTrap columns to remove undigested proteins and non-specific binding contaminants.Flowthroughs were concentrated and then subjected to size exclusion chromatography over a Superdex 200 prep grade 16/60 column (Cytiva) in PBS.Monomer-containing fractions as identified by reducing and non-reducing SDS-PAGE were collected, combined, and concentrated (Fig. S2).Equal volumes of PBS + 0.1% Tween 20 were added to the samples for 0.05% Tween 20 final concentration.Samples were divided into 50-µL aliquots, flash frozen in liquid nitrogen, and stored at −80°C until used.

SPR analysis
The surface plasmon resonance analysis was conducted on a Biacore 8K at the UNC Macromolecular Interactions Facility.Amine coupling kit (BR100050) reagents were used for covalent immobilization of free amine groups on the CD4.The isoelectric point of CD4 was calculated to be near 8; thus, the CD4 was dissolved in dH 2 0 to elicit a net positive charge.Four-domain CD4 (Cat: 10400-H08H-B) from Sino Biological was immobilized to Series S CM5 sensor chips from Cytiva (29104988).
Approximately 75 nM yielded between 1,000 and 3,000 response units.A threefold dilution series from 180 to 3.3 nM was completed for all gp120 proteins in 150 mM NaCl PBS 0.05% Tween.All experimental conditions occurred at 25°C, 360 seconds contact time, 3,000 seconds dissociation time, at a flow rate of 30 µL/min using a single cycle kinetics method.Four replicates were collected for each gp120 over 2 days of experimentation (two per day).

Affinofile cell infection
A 96-well plate was seeded with Affinofile cells at a cell density of 1.8 × 10 4 cells/well and incubated at 37°C on day 0. On day 1, cells were induced to express high levels of CCR5 and high or low levels of CD4 using Ponasterone A and Doxycycline in DMEM-F10/B medium, respectively (34).Cells were infected on day 2 with viruses that were generated as pseudotypes with a luciferase reporter envvirus 18 hours after induction of CCR5 and CD4 by adding 50 µL of diluted virus in medium to achieve an 800,000 RLU signal at high CD4 density.After adding virus, the plates were then spun at 2,000 rpm for 2 hours at 37°C.Infectivity was measured 48 hours later using a luciferase reporter system with a luminometer.

Virus dissociation experiment procedure
On day 0, approximately 1.8 × 10 4 Affinofile cells/well were seeded in 96-well plates.The cells were used with uninduced low levels of CD4.Using 4051 and 4059 pairs of virus, cells were exposed to virus at 4°C by spinoculation for 2 hours at 2,000 rpm.T-Tropic viruses were used at 10 times the concentration of their M-tropic virus pair.Following spinoculation, cells were placed on ice, washed with cold PBS to remove unbound virus, and then overlayed with cold medium.One plate of cells had warm medium added immediately (T 0 ) and was placed in the 37°C incubator, while the other plates were incubated at 4°C and at various times replaced with warm medium.

Prediction of number of receptors needed to bind cells
We constructed a mathematical model using ordinary differential equations to model the steps in the infection of Affinofile cells.This model is based on the previous framework proposed by Kuhmann et al. (52).The model considers the population of Affinofile cells in different stages of infection depending on the number of CD4 receptors attached to a virion and whether the virion enters the cell (i.e., infection) (see Fig. S1, Equation and Model Schematic).

FIG 1
FIG 1 Infection of Affinofile cells expressing low CD4 and high CCR5 levels of surface density.Affinofile cells expressing either a high or low density of CD4 were infected with a luciferase reporter virus with the indicated Env protein pseudotype.Infectivity levels were measured after 48 hours as luciferase activity in the cell lysate.The infectivity at low CD4 density is shown as the percentage of infectivity at high CD4.The experiment represents the result of an infection with two biological replicates for each individual virus.

FIG 2
FIG 2 Model of infectivity based on the number of CD4 molecules required.For T-tropic viruses (upper panels), infection is minimal at low CD4 densities, with significant infectivity apparent at high CD4 density and requiring three CD4 receptors (red lines) to enter cells.In contrast, M-tropic viruses (lower panels) can infect cells efficiently using only one CD4 receptor when CD4 density is low, and these viruses switch to using three CD4 receptors when CD4 density is very high.Values of infectivity from the model are shown using three CD4 molecules (red line) and one CD4 molecule (blue line) with the experimental data shown as points (black circles).A non-linear regression curve fit (black dotted line) through the experimental data points (black circles) is also shown.Total infectivity in the model is the sum of the red and blue lines.
computed the decay rates with k decay = log %RLU 8hrs − log %RLU 24hrs 24 − 8hrs .The decay rates are 8.91 × 10 −5 /s and 7.78 × 10 −5 /s for the 4051 and 4059 M-tropic viruses (k -m ), respectively.When we apply a first-order decay model for the T-tropic viruses as well, they show slower decay rates of 6.99 × 10 −5 /s for 4051 and 4.28 × 10 −5 /s for 4059 (k -t ).However, given the low infectivity of T-tropic viruses for cells with a low density of CD4 and the need to put 10 times as much virus on the Affinofile cells to get similar numbers of infectious events between the T-and M-tropic viruses, we consider a first-order decay model far to simplistic for the T-tropic virus.For this reason, we developed a new model to determine if there is an alternative description of the dissociation process that can explain a weak affinity of the T-tropic virus for CD4 while giving the appearance of tighter binding.

FIG 3
FIG 3 Dissociation of M-and T-tropic viruses from cells expressing a low density of CD4.Infection of Affinofile cells expressing low densities of CD4 on their cellular surface was completed using two (4051 and 4059) M and T luciferase reporter virus pairs.The measured RLUs at the 0-hour time point were set to 100%, and infectivity thereafter for 2, 4, 8, and 24 hours was recorded.The percentage at each time point is a representation of the RLU recorded over the RLU 0-hour time point.

2 3
π 0.045μm 3 N A = 8.86 µM.Solving equation (1) for k −t as a function of k app and k +t L leads to the following expression:

FIG 4
FIG 4 Dissociation model of M-and T-tropic viruses.Schematic (A) and kinetic scheme (B) of two CD4 receptors on an Affinofile cell bound to two trimers of a T-tropic virus, then releasing one trimer from one CD4, with a chance to rebind or subsequently release the second trimer.(C) The local volume of the hemisphere with radius r is used to compute the local concentration of trimer (D).The estimated relationship of the off rate of each trimer plotted as a function of the on rate, using a rapid equilibrium assumption, the apparent decay rate from the data, and the local concentration of trimer is computed in the text.

FIG 5
FIG 5 Analysis of gp120 binding affinity for four-domain CD4 using SPR.Four replicates were completed per sample where experiments were run in duplicate across 2 consecutive days.(A) Individual binding parameters are shown for each gp120 Env protein.(B) The K D for each measurement of each gp120 Env protein is shown and compared between the M-and T-tropic pairs.Statistical significance testing was done using a Wilcoxon rank-sum test (**P < 0.001).gp120 proteins derived from the M-tropic viruses are in blue, and T-tropic viruses are in red.

TABLE 1 env
clone accession numbers Methodology, Writing -review and editing | Ruian Ke, Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Supervision, visuali zation, Writing -original draft, Writing -review and editing | Karin Leiderman, Con ceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, software, Supervision, visualization, Writing -original draft, Writing -review and editing | Sarah B. Joseph, Conceptualization, Data curation, Formal analysis, Funding acquisition, Methodology, Supervision, Writing -review and editing | Ronald Swanstrom, Con ceptualization, Formal analysis, Funding acquisition, Project administration, Resources, Supervision, Writing -original draft, Writing -review and editingDIRECT CONTRIBUTIONThis article is a direct contribution from Ronald Swanstrom, a Fellow of the American Academy of Microbiology, who arranged for and secured reviews by Wesley Sundquist, University of Utah, and Eric Freed, National Cancer Institute.