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ODE Model


TABLE 1     Mathematical model for cellular APO and viral Vif related virus production

Chemical Species


Related Equation


Number of





Viral RNA



Viral protein Tat



Viral protein Gag



Viral protein Vif



Cellular RNA of APO



Cellular protein APO



Vif-APO complex



Gag-Vif complex



Gag-APO complex


Accumulated Number of





Virions produced



Vif packaged in virions



APO packaged in virions


Average Number of





Packaged Vif per virion



Packaged APO per virion


All variables denote the number of molecules or virions.


TABLE 2     Parameter values

Parameter Explanation


Base Value ()


Number of integrated provirus

1 (t >= 6h), 0 (t < 6h)


Basal transcription rate for viral RNA

15 transcripts/h


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


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



Probability of viral RNA to encode Vif



Number of Gag per Virion for assembling



Association constant of Tat with TAR


28.57/μM  (9).

Association constant of Vif and APO


Assumed to be 50/μM (21,39).

Association constant of Gag and Vif


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


Assigned to be same as .

Rate of Gag export through virions budding


Selected to keep the steady state of  about 3900 (40).

Degradation rate of viral RNA


Half life: 4h (9)

Degradation rate of cellular RNA of APO


Selected to be the same as .

Degradation rate of Tat


Half life: 4h (9)

Degradation rate of Gag


10% Gag (p24) degradates in 1h (41)

Degradation rate of Vif


Half life: 89min (21)

Degradation rate of APO


Half life: 29min (21)

Degradation rate of Vif-APO complex


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



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.



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.



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.



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 .








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