Conceived and designed the experiments: NMD. Performed the experiments: SNM. Analyzed the data: SNM NMD. Contributed reagents/materials/analysis tools: SNM NMD. Wrote the paper: NMD.
The authors have declared that no competing interests exist.
Reduced expression of CCR5 on target CD4^{+} cells lowers their
susceptibility to infection by R5tropic HIV1, potentially preventing
transmission of infection and delaying disease progression. Binding of the HIV1
envelope (Env) protein gp120 with CCR5 is essential for the entry of R5 viruses
into target cells. The threshold surface density of gp120CCR5 complexes that
enables HIV1 entry remains poorly estimated. We constructed a mathematical
model that mimics Envmediated cellcell fusion assays, where target
CD4^{+}CCR5^{+} cells are exposed to effector
cells expressing Env in the presence of a coreceptor antagonist and the fraction
of target cells fused with effector cells is measured. Our model employs a
reaction networkbased approach to describe protein interactions that precede
viral entry coupled with the ternary complex model to quantify the allosteric
interactions of the coreceptor antagonist and predicts the fraction of target
cells fused. By fitting model predictions to published data of cellcell fusion
in the presence of the CCR5 antagonist vicriviroc, we estimated the threshold
surface density of gp120CCR5 complexes for cellcell fusion as ∼20
The entry of HIV1 into target cells requires the formation of complexes between the
viral envelope protein (Env) and the cellular receptor, CD4, as well as a
coreceptor, either CCR5 or CXCR4. CCR5 appears to play a central role in HIV1
transmission and disease progression to AIDS. Viruses transmitted across individuals
are predominantly R5 viruses, i.e., require CCR5 for entry
Env is a trimer of noncovalently attached extracellular gp120 and transmembrane gp41
glycoprotein heterodimers
Here, we developed a mathematical model that mimics cellcell fusion assays widely
employed to investigate HIV entry into target cells (e.g.,
We modelled cellcell fusion assays where target cells expressing CD4 and CCR5
are exposed to effector cells expressing Env in the presence of a coreceptor
antagonist and the percentage of target cells fused with effector cells is
measured (e.g., see
A) High CCR5 expression on a target cell allows the formation of the requisite gp120CCR5 complexes for cellcell fusion. B) Low CCR5 expression or C) the presence of a coreceptor antagonist reduces the surface density of gp120CCR5 complexes and prevents fusion.
A coreceptor antagonist typically binds to an allosteric site on CCR5 and
inhibits CCR5 binding to gp120
In
A) Distribution,
With the above distribution of CCR5 expression and given a threshold CCR5
expression level necessary for fusion,
We next predicted the equilibrium surface densities of the various reacting
species across a single target celleffector cell pair
(Eq. 5), calculated using Eqs.
(6)–(9), as functions of the concentration of the coreceptor
antagonist,
Equilibrium surface densities of A) unbound gp120,
In
The fraction of cells fused,
Our model thus describes the outcome of a cellcell fusion assay in the presence of a coreceptor antagonist. Below, we present comparisons of our predictions with experiments.
Recently, Heredia
A) Fit of model predictions of
To validate our parameter estimates, we compared our model predictions with
independent data of cellcell fusion as a function of vicriviroc
concentration in the presence of rapamycin, reported by Heredia
The above experiments have employed the HIV1 JRFL Env. Also, rapamycin is
known to have a cytostatic effect on cells
Fits of model predictions (lines) of the relative extent of cellcell
fusion,
100−
Env clone  Threshold complex surface density,

Cooperativity factor,

IC_{50} (nM) 
RHPA.A19.2000  19.9 (19.5–20.2)  0.011 (0.005–0.031)  79.5 
PRB958_06.TB1.4305  19.6 (18.6–20.1)  0.009 (0.002–0.026)  242.1 
PRB926_04.A9.4237  20.2 (20.1–20.3)  0.021 (0.012–0.033)  29.0 
6244_13.B5.4576  20.0 (18.7–20.4)  0.020 (0.003–0.130)  143.3 
1054.TC4.1499  20.1 (19.3–20.3)  0.020 (0.005–0.058)  100.9 
62357_14.D3.4589  20.1 (20.0–20.2)  0.015 (0.009–0.021)  44.4 
9021_14.B2.4571  20.2 (19.3–20.4)  0.028 (0.005–0.100)  71.4 
1006_11.C3.1601  20.1 (19.7–20.3)  0.013 (0.005–0.030)  46.0 
6240_08.TA5.4622  19.7 (18.5–20.2)  0.013 (0.004–0.040)  798.5 
SC05.8C112344  20.3 (18.2–20.5)  0.082 (0.003–0.741)  1287.0 
700010058.A4.4375  19.4 (16.4–20.2)  0.005 (0.001–0.030)  201.1 
REJO.D12.1972  20.4 (20.2–20.5)  0.128 (0.032–0.473)  17.6 
PRB931_06.TC3.4930  18.3 (17.4–19.0)  0.002 (0.001–0.004)  469.8 
SC45.4B5.2631  17.8 (16.7–18.5)  0.002 (0.001–0.003)  699.3 
62615_03.P4.3964  20.3 (19.5–20.4)  0.042 (0.007–0.200)  43.2 
700010040.C9.4520  20.4 (20.3–20.4)  0.061 (0.038–0.096)  13.9 




The role of CCR5 in mediating HIV1 entry has important implications for HIV1
transmission and disease progression to AIDS as well as for strategies of
intervention
Our estimate of the threshold surface density of gp120CCR5 complexes necessary for
HIV1 entry may facilitate optimal utilization of coreceptor antagonists for
preventive and therapeutic intervention. For instance, the estimate suggests that a
potent coreceptor antagonist must reduce the surface density of gp120CCR5 complexes
to below
Our study may also inform the substantial ongoing efforts to elucidate the origins of
the differences between SIV infection of natural and nonnatural hosts (reviewed in
Recent studies have argued that the mechanism of viral entry into cells may be
distinct from cellcell fusion: while cellcell fusion involves membrane fusion at
the cell surface, HIV1 entry appears to involve receptor and coreceptor mediated
endocytosis
We recognize approximations in our model that hold for cellcell fusion but may not
apply to viral entry in vivo. First, our model describes the protein interactions
that precede viral entry using a continuum, mass actionbased approach. Such a
continuum approximation is expected to be accurate for cellcell fusion, where the
number of protein molecules per cell is large (>10^{3}). The advantage of
the continuum approach is the simplicity of the resulting model equations and their
facile application to data analysis. With viruscell interaction, however, because
virions express far fewer gp120 molecules (14±7 Env trimers per virion
The spatial distribution of CCR5 across the surface of a target cell and its role on
viral entry remains to be established. While one study suggests that CCR5 molecules
are localized within lipid rafts
Finally, we note that our model assumed that each gp120 monomer in an Env trimer is
independently accessible to CCR5. In contrast, steric constraints may result in
increasingly hindered successive binding of CCR5 to the second and third gp120
monomers of an Env trimer. Conversely, cooperative binding may render successive
binding easier
We have analysed experimental data of HIV1Env mediated cellcell fusion
published recently by Heredia et al.
In the experiments performed by Hu et al.
We considered first the interactions between proteins across a single target
celleffector cell pair in the absence of a coreceptor antagonist (
We defined
We next considered a single target celleffector cell pair in the presence of
a CCR5 antagonist,
Here, gp120 can bind to a complex of CCR5 and
We assumed that the concentration of
In a cellcell fusion assay, target cells with different expression levels of
CCR5 form different surface densities of gp120CCR5 complexes at
equilibrium. We defined
In the presence of the coreceptor antagonist, the expression level of CCR5
that results in the formation of complexes at the surface density
We performed model calculations using parameter estimates representative of the
cellcell fusion assays we considered
Parameter  Description  Value 
Source 

Surface density of gp120 on effector cells 



Mean surface density of CCR5 on target cells 



Standard deviation of the surface density of CCR5 across cells 

Bestfit ( 

Equilibrium association constant of gp120 with CCR5 



Threshold surface density of gp120CCR5 complexes 

Bestfits ( 

Cooperativity factor in the ternary complex model Eq.(5)  0.03  Bestfits ( 

Equilibrium association constant of a coreceptor antagonist with CCR5 


Typical values; variations are indicated in the text and in figure legends.
We solved the above equations and fit model predictions to data using a computer program written in MATLAB. We employed the inbuilt routine NLINFIT, which uses the LevenbergMargquardt algorithm for nonlinear least squares, for fitting model predictions to data and for obtaining 95% confidence intervals. For some of the data sets of transmitted/founder Envmediated cellcell fusion in the presence of maraviroc, NLINFIT yielded confidence intervals that included negative parameter values. We therefore determined 95% confidence intervals on the bestfit parameter values for the transmitted/founder Envmediated cellcell fusion data sets by performing 200 bootstrap replicates each, again in MATLAB.
(TIF)
(DOC)
We thank Alonso Heredia for providing details of their experimental observations and Pradeep Nagaraja and Prithwiraj M. Mukherjee for help with parameter estimation.