TABLE 1 Mathematical
model for cellular APO and viral Vif related
virus production
Chemical Species
|
Variable
|
Related Equation
|
|
Number of
|
|
|
|
|
Viral RNA
|

|

|
(1)
|
|
Viral protein
Tat
|

|

|
(2)
|
|
Viral protein
Gag
|

|

|
(3)
|
|
Viral protein
Vif
|

|

|
(4)
|
|
Cellular RNA
of APO
|

|

|
(5)
|
|
Cellular
protein APO
|

|

|
(6)
|
|
Vif-APO
complex
|

|

|
(7)
|
|
Gag-Vif
complex
|

|

|
(8)
|
|
Gag-APO
complex
|

|

|
(9)
|
Accumulated Number of
|
|
|
|
|
Virions
produced
|

|

|
(10)
|
|
Vif packaged
in virions
|

|

|
(11)
|
|
APO
packaged in virions
|

|

|
(12)
|
Average Number of
|
|
|
|
|
Packaged Vif
per virion
|

|

|
(13)
|
|
Packaged APO per virion
|

|

|
(14)
|
All variables
denote the number of molecules or virions.
TABLE 2 Parameter
values
Parameter Explanation
|
Parameter
|
Base Value ( )
|
Reference
|
Number of integrated
provirus
|

|
1 (t >=
6h), 0 (t < 6h)
|
(8)
|
Basal
transcription rate for viral RNA
|

|
15 transcripts/h
|
(9)
|
Increase in
viral RNA transcription by Tat transactivation
|

|
1485
transcripts/h
|
24.75
transcripts/min (9)
|
Transcription
rate of APO RNA
|

|
15 transcripts/h
|
Assigned to
be the same as 
|
(Eukaryotic)
steady-state translation rate
|

|
270 proteins/h
|
4.5 proteins/min
(9)
|
Probability
of viral RNA to encode Tat
|

|
0.01
|
Fraction of
tat RNA in spliced RNA: 0.05 (9), we assigned
as 5 fold of
spliced RNA (34).
|
Probability
of viral RNA to encode Gag
|

|
1
|
(35,36)
|
Probability
of viral RNA to encode Vif
|

|
0.05
|
(35,36)
|
Number of Gag
per Virion for assembling
|

|
2000
|
(35,37,38)
|
Association
constant of Tat with TAR
|

|
5.2453×10-5/molecule
|
28.57/μM (9).
|
Association constant
of Vif and APO
|

|
9.1798×10-5/molecule
|
Assumed to be
50/μM (21,39).
|
Association constant
of Gag and Vif
|

|
2×10-6/molecule
|
Selected to
keep steady state of to be about
100. Range of was reported to
be 60-100 (35) in acutely
infected cells.
|
Association constant
of Gag and APO
|

|
2×10-6/molecule
|
Assigned to
be same as .
|
Rate of Gag
export through virions budding
|

|
0.08/h
|
Selected to
keep the steady state of about 3900 (40).
|
Degradation
rate of viral RNA
|

|
0.1733/h
|
Half life: 4h
(9)
|
Degradation
rate of cellular RNA of APO
|

|
0.1733/h
|
Selected to
be the same as .
|
Degradation
rate of Tat
|

|
0.1733/h
|
Half life: 4h
(9)
|
Degradation
rate of Gag
|

|
0.1054/h
|
10% Gag (p24) degradates in 1h (41)
|
Degradation
rate of Vif
|

|
0.4673/h
|
Half life: 89min
(21)
|
Degradation
rate of APO
|

|
1.4341/h
|
Half life: 29min
(21)
|
Degradation
rate of Vif-APO complex
|

|
2.0794/h
|
Half life: 18min
(21)
|
The units of association
constants ( , , and ) were converted to molecule-1 according to a
fixed T cell volume. We took the diameter
of a T cell as 12μm (42).
Sensitivity and perturbation analysis was performed for all parameters
(Fig. 3). In the analysis, the
parameters for probability of viral RNA to encode certain protein ( , and ) may be larger than 1.
This is simply a mathematical treatment to increase the synthesis rate
of the corresponding protein.
TABLE
3 Variables and
parameter(s) used in simulation corresponding to experimental measurements and
conditions.
Experiment
Reference /
Simulation
Result
|
Measurements
in Experiment /
Variables
in Simulation
|
Conditions
in Experiment /
Parameter(s)
in Simulation
|
Fig. 3 B in (18)
|
Protein level of A3G
|
Vector Vif:APO-3G (μg:μg) = 4:2, 1:2,
0.25:2, 0:2
|
Fig. 2 A in this work
|
Normalized at 24h
|
= 4, 1, 0.25, 0. 
|
Fig. 1 B in (19)
|
Relative amount of A3G packaged into
virions at 48h post-infection
|
Vector HA-A3G:pNL4-3ΔVif (μg:μg) = 0:60,
1:60, 2:60, 5:60, 10:60, 20:60
|
Fig. 2 B in this work
|
at 48h
simulation time
|
= 0, 0.5,
1, 2.5, 5, 10. = 0
|
Fig. 2 B in (20)
|
Percentage of packaged A3G in total A3G
at 24h post-infection
|
1. Constant pNL4-3 (expressing constant
amounts of Vif) = 2.5μg, varying pcDNA-APO3G. = 0, 0.5, or 2.5μg, total DNA
was adjusted to 5μg.
2. Constant Vif-defective pNL4-3Vif(-) =
2.5μg, varying Vif expression vector pNL-A1 = 0, 0.5, or 2μg, total DNA was
adjusted to 6μg.
|
Fig. 2 C in this work
|
at 24h simulation
time
|
,

|
Fig. 4 A in (21)
|
Relative viral infectivity in subsequent
infection
|
WT and ΔVif provirus 3μg and A3G = 0,
0.01, 0.02, 0.05, 0.1 or 0.2μg adjusted with an empty vector to 4μg total.
|
Fig. 2 D in this work
|
at 48h
simulation time
|
or 0 (for ΔVif),
=0, 0.1, 0.2, 0.5, 1 or 2
|
Shaded row denotes the experiments; the row
directly below represents the corresponding simulations.
FIGURE
LEGENDS
Figure
Legends
FIGURE 1
Schematic of cellular APO
and viral Vif related virus production. Viral RNA
is transcribed from provirus integrated in cellular genome and yields viral
proteins Tat, Gag and Vif. Tat
transactivates viral transcription to accelerate viral RNA synthesis. Gag is a polyprotein used to form the
main virus structure. Regulatory protein
Vif acts as anti cell defense factor to form complex with cellular cytidine deaminase
enzyme APO and promote its degradation through
ubiquitination. Both Vif and APO are able to be incorporated into nascent formed
virion.
FIGURE
2
Comparison
between experiments and simulations.
(A) Viral Vif
downmodulates cellular protein APO. Note the direction of horizontal axis is
reversed. (B) Overexpressing APO
increase the relative ratio of packaged APO
into virions. (C) 2D plot of the
percentage of packaged APO in total APO, by
varying transcription rate of APO RNA and rate of Vif expressing. (D) Negative correlation between viral
infectivity and simulated . Note the
vertical axis direction of is reversed. See text and Table 3 for details.
FIGURE
3
Parameter
sensitivity analysis. Vertical axis denotes relative parameter
sensitivity value on the steady state value of variable , and accumulated
number for at 48h
post-infection. The locations of
bars are in descending order from left to right for sensitivity on variable . The value bars
are grouped by each parameter. Note
the sensitivity values on variables and are scaled down
for plot convenience.
FIGURE
4
Perturbation
analysis. Each parameter was varied by 4 magnitude
to explore its influence on the steady state value of variable , and the accumulated
value of at 48h post-infection. Values on variables and are scaled down
as legend indicated. (A) Gag
related parameter and . (B) Tat related
parameter , and .
FIGURE 1

FIGURE
2

FIGURE
3

FIGURE
4

Paper Manuscript: Open in New Window, PDF; Supplementary File: Open in New Window, PDF
Poster and Slides in From Structure to Systems Based Drug Discovery Symposium, Beijing, 8/2007: Open in New Window
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