Molecular dynamics simulation of reversibly self-assembling shells in solution using trapezoidal particles

The self-assembly of polyhedral shells, each constructed from 60 trapezoidal particles, is simulated using molecular dynamics. The spatial organization of the component particles in this shell is similar to the capsomer proteins forming the capsid of a $T=1$ virus. Growth occurs in the presence of an atomistic solvent and, under suitable conditions, achieves a high yield of complete shells. The simulations provide details of the structure and lifetime of the particle clusters that appear as intermediate states along the growth pathway, and the nature of the transitions between them. In certain respects the growth of size-60 shells from trapezoidal particles resembles the growth of icosahedral shells from triangular particles studied previously, with reversible bonding playing a major role in avoiding incorrect assembly, although the details differ due to particle shape and bond organization. The strong preference for maximal bonding exhibited by the triangular particle clusters is also apparent for trapezoidal particles, but this is now confined to early growth and is less pronounced as shells approach completion along a variety of pathways.

Figure 1

The component spheres and effective shape of the trapezoidal particle; the small spheres denote the attraction sites.

Figure 2

Late state of the $e=0.090$ run, with the solvent omitted and particles not in complete shells shown semitransparently; complete shells that cross periodic boundaries appear open, an artifact of the visualization.

Figure 3

Time-dependent cluster size distribution (mass fraction) for $e=0.090$; the final peaks correspond to monomers and complete shells; each grid interval along the time axis (MD units) corresponds to $\sim 3\times {10}^6$ time steps.

Figure 4

Number of complete shells (solid lines) and combined number of complete shells and large (size $>50$) clusters (dashed lines) as functions of time.

Figure 5

Bond counts for different cluster sizes ($e=0.090$); solid lines show the minimum and maximum observed counts, triangles the ranges of counts accounting for $>$80$\%$ of cases, and squares the most frequent counts.

Figure 6

Event fractions corresponding to cluster size changes ($e=0.090$).

Figure 7

Growth histories of several shells; the large spike for one of the shells corresponds to a temporary merger of two big clusters.

Figure 8

Total and intermittent cluster lifetimes (MD units), the latter also subdivided according to whether, in the subsequent event, the size change is up or down ($e=0.090$).

Figure 9

Clusters of size 30, oriented to show their perimeters; the majority of the particles are also present in the final shells into which the clusters develop, with the few that escape shown in a lighter color or shade.

Figure 10

Clusters of size 50, oriented to show the variation in hole number and shape.

Figure 11

An example of shell growth (color coding as in Fig. 9); in the final image the shell is about to close.

Figure 12

Stages in the successful merging of two clusters; the last image shows the state an instant before final bonding.