Supplemental Material

 

1.    Model Development

1.1  Viral components

1.2  Cellular components

1.3  Interactions among cellular and viral components and virion production

 

2.    Perturbation Analysis

       FIGURE S1


 

1.    Model Development

 

The model describes the virus production network shown schematically in Fig. 1.  Viral components involve integrated provirus (), viral RNA (), structure protein Gag, regulatory protein Tat and viral infectivity factor Vif, which can be packaged into newly synthesized virions by forming complex () with Gag.  Cellular components include cytidine deaminase enzyme APO and RNA of APO ().  The interactions among viral and cellular components were modeled by Vif-APO complex (), through which degradation of APO was accelerated, and Gag-APO complex (), through which APO can be incorporated into nascent synthesized virions.  The average number of Vif and APO incorporated per virion was defined by  and .

 

1.1  Viral components

Before integrated provirus is produced, reverse-transcription of viral RNA, nuclear transport of the viral DNA and its integration to the cellular genome must precede and consume proximately 6-12h, finally about 1-2 proviruses per cell are finally integrated into the genome (1).  In our simulation, we let the number of integrated provirus pv=0 when t<6h and pv=1 when t>=6h.

The rate of synthesis was expressed by the rate of transcription from integrated provirus, its degradation and its recruitment into new virions:

    (1)

The rate of viral RNA transcription combines a eukaryotic basal transcription rate and a Michaelis-Menten form for the effect of Tat transactivation (2), and the rate of viral RNA recruitment is two times the rate of virion production, based on the fact that two genomic-length viral RNA molecules are assembled into one new virion (3).

After viral RNA being transcribed, the processes involving viral RNA splicing and export from nucleus into cytoplasm are complicated (4-8).  In the initial stage, spliced viral RNA are produced and exported from nucleus into cytoplasm.  These spliced RNA encode several regulatory proteins, including Tat, the activator for viral RNA synthesis, and another viral protein Rev.  Rev is translated in cytoplasm and transported back into nucleus in order to bind with full-length viral RNA and keep them unspliced, whereby full-length RNA is transported into and accumulated in cytoplasm.  Full-length viral RNA encode viral structure proteins like Gag and Env, which are necessary for assembling nascently formed virus particles (3).  These full-length RNA finally become dominant in cytoplasm, while spliced RNA remain a small fraction in the whole viral RNA pool (9).  Several models (1,2,10,11) have been developed to study HIV-1 viral RNA splicing and/or Rev in detail.

Our model was designed to explore the effects of cellular factor APO on viral components; therefore the early events about the transcription and transportation of viral RNA were not explicitly presented in the equations.  Variable  denotes the ensemble of viral RNA, and in simulation the translation rates of viral proteins (Tat, Gag and Vif) were represented by multiplying the probability of viral RNA to encode them (, and ) with the term denoting eukaryotic steady-state translation rate :

                                                                                 (2)

      (3)

                      (4)

 

1.2  Cellular components

The dynamics of APO and its RNA were represented by following equations:

                                                              (5)

    (6)

It should be noted that all chemical species other than these two in this model were zero when t<6h since pv=0.  Variable  was related to APOBEC, a family of DNA or RNA cytidine deaminase enzymes (12).  APOBEC3G (A3G) and APOBEC3F (A3F) in this family are co-expressed in many tissues (13), and one copy of each gene is encoded on chromosome 22 (14).  Both proteins are able to be incorporated into newly formed virions and reduce virus infectivity in subsequent infection (12,13), which are also antagonistic to viral protein Vif (13,14), and share similar expression pattern (13).  In many early and subsequent experiments conducted, only A3G was involved (15-21).  As a simplified model, we did not distinguish A3G and A3F (or any other proteins in APOBEC family) due to their functional similarity. The transcription rate of APO RNA () was assigned to be the same as the basal transcription rate of viral RNA ().  Variations of APO related parameters were also performed in comparison with experiments and perturbation analysis.

 

1.3  Interactions among cellular and viral components and virion production

The association constant  denotes the strength of binding between Vif and APO to form corresponding complex  targeted for ubiquitination and degradation:

                     (7)

Experimental evidences show the association of Vif and APO is not very strong (13,17).  As quantitative measurement on the association constant was not available, we assumed it to be 50/μM, since usually a relative weak binding constant range was 1-100/μM.

Complexes  and  are simplified forms to represent the incorporation of Vif and APO into nascent virions:

                 (8)

                   (9)

Vif was reported to directly associate with Gag (22), it also had been reported that specific interaction between Vif and viral RNA may be functionally important for its recruitment into virions (23-25).  For APO, its interactions with non-specific RNA may be needed to form complexes with Gag (26).  Therefore in simulation, the association constants  and  were actually the measurements of the abilities of Vif and APO incorporating into virions, respectively.  But due to no direct measurements on these properties, we selected the base value of  to allow the steady state of average number of incorporated Vif per virion () to be about 100 (27), based on the direct correlation between  and Gag-Vif complex (Eq. 11, 13).  In addition we assigned the base value .

The rate of virion production is equal to the exporting rate of total Gag protein in all its existing forms  divided by number of Gag per virion () for assembling:

     (10)

Parameter  stands for the rate of Gag export for virion budding (Eq. 3), as well as the exporting rate of incorporated Vif and Gag:

               (11)

                   (12)

Also due to no direct measurements on , it was selected to keep the steady state of viral RNA () about 3900 (28), based on the rate of viral RNA packaging into new virion particles is correlated with the rate of Gag assembling and budding (Eq. 1).

 and  are average number of incorporated Vif and APO per virion, represented as their accumulated exported number ( and ) over accumulated number of virions produced respectively:

            (13)

        (14)

 


 

2.    Perturbation Analysis

FIGURE S1        Perturbation analysis.  Each parameter was varied by 4 magnitude to explore its influence on steady state value of variable ,  and accumulated value of  at 48h post-infection.  Values on variables  and  are scaled down as legend indicated.  Definition: .

 

 

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