Self-assembly of polyhedral shells: A molecular dynamics study

The use of reduced models for investigating the self-assembly dynamics underlying protein shell formation in spherical viruses is described. The spontaneous self-assembly of these polyhedral, supramolecular structures, in which icosahedral symmetry is a conspicuous feature, is a phenomenon whose dynamics remain unexplored; studying the growth process by means of computer simulation provides access to the mechanisms underlying assembly. In order to capture the more universal aspects of self-assembly, namely the manner in which component shapes influence structure and assembly pathway, in this exploratory study low-resolution approximations are used to represent the basic protein building blocks. Alternative approaches involving both irreversible and reversible assembly are discussed, models based on both schemes are introduced, and examples of the resulting behavior described.

Figure 1

(Color online) Capsomer model used for $T=1$ simulation with permanent bonding; the spheres and interaction sites (small spheres) comprising the capsomer and the effective trapezoidal shape are shown.

Figure 2

(Color online) Views of $T=3$ capsomer model.

Figure 3

(Color online) Capsomers model used for reversible bonding $(T=1)$; different views of the sphere-based structure and its effective shape are shown.

Figure 4

(Color online) Complete $T=1$ shell (as produced by the simulation) with 60 capsomers; capsomers are shown reduced in size so that bonds are visible.

Figure 5

(Color online) Complete $T=3$ shell shell with 180 capsomers of three (color-coded) types.

Figure 6

Dimer, trimer, and (opened-up) pentamer configurations with labeled interaction sites; the color identification (for $T=3$) is included in the triangular configuration.

Figure 7

(Color online) Example of mutant capsid structure (permanent bonding); capsomer size is reduced, as in Fig. 4, to show the bonds (yellow particles are fully bonded, blue are not).

Figure 8

Number of complete shells vs time for permanent bonding.

Figure 9

(Color online) Sanpshots from a $T=3$ simulation with permanent bonding: the images show an early state (including the container for reference); three views at different times showing only the growing shells; the entire system corresponding to the third of these views; the final state (capsomers are colored by type).

Figure 10

Number of complete shells vs time for reversible bonding.

Figure 11

(Color online) Snapshots from a simulation with reversible bonding: early state; two views after $0.5\times {10}^6$ steps showing the full system and the 132 clusters of size $⩾10$ (color coding—red particles have all five bonds in place, blue have $<5$); the 34 clusters of size $⩾50$ after $2.5\times {10}^6$ steps; two views of the final state after $8\times {10}^6$ steps showing the entire system, and just the 39 complete shells with container.

Figure 12

Capsomer fractions with different bond counts vs cluster size for reversible bonding and unweighted assembly.

Figure 13

As in Fig. 12, for trimer-weighted assembly.

Figure 14

Cluster size distribution vs time for the trimer-weighted case.

Figure 15

Ranked cluster sizes for trimer-weighted assembly (only every fifth cluster is included); all site pairs are required for bonding.

Figure 16

As in Fig. 15, but bonding requires only a single site pair.

Figure 17

Size histories of selected clusters that grow into complete shells (see Sec. 6C).

Figure 18

(Color online) Tapered cylindrical particles that have condensed into spherical clusters.

Figure 19

(Color online) Soma cube components and self-assembled puzzle solution.