Dynamical formation of empty viral capsids, Part 2

The geometry of directional attractions is chosen such that a particular capsid structure is the free energy minimum. Assembly pathways are not pre-assumed in this model, and once the subunit structure is specified there are few remaining adjustable parameters: subunit concentration, binding energy, and the angle tolerance for directional attractions. Dynamical simulations were carried out over a wide range of these parameters; some results of these simulations are shown in Figure 2.

Figure 2 

Figure 2: Fraction of subunits in complete capsids, fC, as a function of system parameters. Subunit concentration and time are in reduced units and bond energy is in units of the thermal energy, kBT. At low concentrations and bond energies, capsids do not form within the time simulated. When concentrations or bond energies become too large, however, ordered capsids do not form.

At low subunit concentrations or binding energies, the driving forces for assembly are weak; increasing concentration or binding energy leads to faster and more successful assembly. This trend is nonmonotonic, however; above some optimal parameter values a stronger driving force for assembly leads to less efficient capsid formation. Although capsids are more thermodynamically favored with increasing parameter values, structures with strained bonds or defects also become more stable. As defects become trapped in a growing capsid by further addition of subunits, the thermodynamically stable state becomes kinetically inaccessible.

Figure 3 

Figure 3: Snapshots from dynamical trajectories. For the case shown on the left, system parameters were such that the dynamics produced a high yield of correctly assembled capsids. For the case on the right, strained bonds were stable enough that they did not anneal before additional subunits bound. Note that a properly assembled capsid is the thermodynamically favorable state in both cases. In fact, the ordered capsid is actually more thermodynamically favored in the case on the right.