Minimum energy paths for conformational changes of viral capsids

In this work we study conformational changes of viral capsids using techniques of large deviations theory for stochastic differential equations. The viral capsid is a model of a complex system in which many units—the proteins forming the capsomers—interact by weak forces to form a structure with exceptional mechanical resistance. The destabilization of such a structure is interesting both, per se, since it is related either to infection or maturation processes and because it yields insights into the stability of complex structures in which the constitutive elements interact by weak attractive forces. We focus here on a simplified model of a dodecahedral viral capsid and assume that the capsomers are rigid plaquettes with one degree of freedom each. We compute the most probable transition path from the closed capsid to the final configuration using minimum energy paths and discuss the stability of intermediate states.

Figure 1

Schlegel diagram of the dodecahedron with the indexing convention used here.

Figure 2

Representatives of the symmetry classes of admissible states for the energy (39). White pentagons represent detached pentamers. (a) is the closed capsid, (j) is the totally disgregated capsid.

Figure 3

The squared distance between two capsomers in the problem of the disgregation of the capsid. Schematic side view of two adjacent capsomers translating along their axis by $x_i$ and $x_j$.

Figure 4

Minimum energy path for the energy (39). White pentagons are detached.