Viral capsids: Kinetics of assembly under transient conditions and kinetics of disassembly

The available kinetic models of assembly of viral protein capsids are focused primarily on the situations in vitro where the amount of protein is fixed. In vivo, however, the viral protein synthesis and capsid assembly occur under transient conditions in parallel with viral genome replication. Herein, a kinetic model describing the latter case of capsid assembly is proposed with emphasis on the period corresponding to the initial stage of viral genome replication. The analysis is aimed at small icosahedral capsids. With biologically reasonable values of model parameters, the model predicts rapid exponential growth of the populations of monomers and fully assembled capsids during the transient period of genome replication. Under the subsequent steady-state conditions with respect to replication, the monomer population is predicted to be nearly constant while the number of fully assembled capsids increases linearly. The kinetics of capsid disassembly, described briefly as well under conditions of negligible monomer concentration, exhibit a short induction period when the number of proteins in a capsid is only slightly smaller than in the beginning, followed by more rapid protein detachment. According to calculations, the latter kinetics may strongly depend on protein degradation.

Figure 1

Specification of the protein detachment rate: (a) the activation energy of detachment from the rim as a function of $i$; (b) the rate constants of detachment from the rim (filled circles) and close-packed area (open circles).

Figure 2

Specification of protein attachment, detachments and degradation rates: ${log}_{10}(k_i{n}_1/V)$ (for $n_1={10}^2,{10}^3$, and ${10}^4)$, ${log}_{10}\left(r_i\right)$, and ${log}_{10}\left({\kappa }_i\right)$ as a function of $i$.

Figure 3

Numbers of monomers and fully assembled capsids as a function of time for $w_{\circ }=30$ and 100 ${\min }^{-1}$. The kinetics were calculated taking degradation of monomers into account. Degradation of $i$-mers (with $i\ge 2)$ was either considered to occur (thick lines) or to be negligible (thin lines). In the case of monomers, the corresponding curves are not distinguishable by eye.

Figure 4

Distribution of dimers, trimers, and partially assembled capsids in the end of the kinetics calculated with $w_{\circ }=100$ ${\min }^{-1}$ (thick lines in Fig. 3).

Figure 5

Kinetics of capsid disassembly with and without protein degradation. Lines 1 and 2 exhibit the average measure of capsid assembly, ${\sum }_{i=2}^{m}i{p}_i$, in these two cases. Line 3 shows $m{p}_m$. The latter value corresponding to the fully assembled capsid is the same in both cases.