Knot-Controlled Ejection of a Polymer from a Virus Capsid

We present a numerical study of the effect of knotting on the ejection of flexible and semiflexible polymers from a spherical, viruslike capsid. The polymer ejection rate is primarily controlled by the knot, which moves to the hole in the capsid and then acts as a ratchet. Polymers with more complex knots eject more slowly and, for large knots, the knot type, and not the flexibility of the polymer, determines the rate of ejection. We discuss the relation of our results to the ejection of DNA from viral capsids and conjecture that this process has the biological advantage of unknotting the DNA before it enters a cell.

Figure 1

Schematic of initial configurations: (left) a spooled chain, (right) a random configuration is achieved by packing the chain through a hole at the bottom of the capsid, which is closed before equilibration.

Figure 2

Fraction of beads remaining in the capsid as a function of time for unknotted flexible (●) and semiflexible (○) polymers and for flexible polymers with $3_1$ (▴), $4_1$ (■), and $6_1$ (◆) knots. The knots have a clear effect on the shape of the ejection curve, and the rate of ejection is primarily determined by knot type.

Figure 3

Fraction of beads remaining in the capsid as a function of time for semiflexible polymers: (i) unknotted polymer (○); (ii) polymer with a $6_1$ knot initially at the midpoint of the polymer chain (▵); and (iii) a polymer with a $6_1$ knot initially near the capsid entrance (□).

Figure 4

Average ejection rates for $C_1$ knots: flexible polymers in the smaller capsid (●); semiflexible polymers in the smaller capsid (▵); flexible polymers in the larger capsid (■); semiflexible polymers in the larger capsid (◇). For more complex knots, the rates for flexible and semiflexible polymers are very similar.

Figure 5

Fraction of beads remaining in the capsid as a function of time for semiflexible polymers with three knots randomly selected from $3_1$, $4_1$, $5_1$, $5_2$, and $6_1$ (▵) and the prime knot ${12}_1$ (○).