TABLE 1.
Notations used in the differential equations model and the values assigned to each parametera
| Notation | Description | Value |
|---|---|---|
| β | Fraction of the viral polyprotein used as replicase (1 − β is the fraction used as structural proteins) | 0.9b |
| ɛ | Strand degradation rate | 0.005c |
| ɛΤ | Degradation rate of the translational complex | 10−5d |
| ɛp | Degradation rate of the viral polyprotein | 1.5 × 10−3e |
| Γ± | Probabilities of replication for the genomic (+) and antigenomic (−) master strands | 0-1 |
| Λ± | Probabilities of replication for the genomic and antigenomic mutant strands | 0-0.1 |
| kR | Effective rate of interaction between the master genomic strands and the available ribosomes | 0.04d |
| k1 | Rate of dissociation of the master genomic strand from the translational complex | 0.02d |
| k2 | Encapsidation probability of genomic strands | 0.75 |
| m | No. of monomers of structural protein necessary for building up a virion | 200f |
| μ | Avg mutation rate | 0-1 |
| Rtot | Constant concentration of ribosomes inside the cell | 1 |
| σ | Rate of elimination of mature virions (either by degradation or by leaking out of the cell) | 3.5 × 10−3g |
Initial conditions: x0+(0) = 0.01 and x0−(0) = x1+(0) = x1−(0) = Tc(0) = p(0) = V(0) = 0 if not otherwise specified.
The nonstructural genomic components represent ∼90% of the genome in picornaviruslike viruses (1).
RNA stability depends on intrinsic properties of the molecule, such as sequence structure and the presence of CAP, VPg, or a poly(A) tail, as much as the action of cellular RNases, and thus it must be independent of the replication model. We assume that mutations have negligible effects on RNA stability. Since we found no useful values in the literature, we performed a sensitivity analysis for ɛ in the range 0.002 to 0.01 by exploring more than a million parameter combinations. We obtained a good qualitative convergence of equilibrium concentrations inside this range.
These values were chosen in such a way that the ratio of formation rate to degradation rate plus dissociation rate lies in the same range as in reference 6.
Once the polyprotein has been produced, we assume that either it can be degraded at rate given by ɛp or is cleaved with absolute efficiency into the mature peptides, which is equivalent to a cleavage rate of 1, as in the range reported in reference 6. The exact value employed in our simulations was obtained from the same sensitivity analyses described for ɛ.
For picornaviruslike viruses, the number of monomers of structural proteins required for encapsidation is in the range of hundreds to thousands. The value has been fixed to make it similar to that for the potyviruses (36).
The virion degradation rate has been fixed at 2 orders of magnitude smaller than the formation rate (k2) as reported for VSV (14).