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)


VifAPO
complex

_{}

_{}

(7)


GagVif
complex

_{}

_{}

(8)


GagAPO
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)
steadystate 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 60100 (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 VifAPO 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:APO3G (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 postinfection

Vector HAA3G:pNL43ΔVif (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 postinfection

1. Constant pNL43 (expressing constant
amounts of Vif) = 2.5μg, varying pcDNAAPO3G. = 0, 0.5, or 2.5μg, total DNA
was adjusted to 5μg.
2. Constant Vifdefective pNL43Vif() =
2.5μg, varying Vif expression vector pNLA1 = 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
postinfection. 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 postinfection. 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
