Dynamical formation of empty viral capsids

The basic components of a virus are genetic material and a protein shell, called a capsid, that surrounds and protects the fragile nucleic acids. During the life cycle of a virus, the genetic material is released inside a cell and cellular machinery is hijacked to replicate the viral genome and manufacture new viral proteins. Capsid proteins then assemble with nucleic acid molecules to form new viruses. This process is remarkable because a large number (60 – thousands) of capsid proteins avoid kinetic and thermodynamic traps to assemble rapidly and reliably in many different organimsms and environments. Even more remarkably, in vitro studies show that capsid proteins alone can spontaneously assemble into perfectly formed capsids. Assembly therefore can be directed entirely by interactions between individual proteins. How do these local interactions conspire to form robust large length scale assemblies?

Despite the apparent simplicity of a symmetric virus, modeling the kinetics of capsid assembly poses a great challenge. Assembly times and capsid structures are orders of magnitude larger than the length and time scales that characterize individual subunits. Simulations with atomistic resolution are impractical to study assembly dynamics for one or many capsids. Therefore, we designed coarse-grained models with which to study specific questions about the assembly process. We began with the following question: viral capsid proteins have complex shapes and interact through forces arising from sequences and structures that have evolved over millions of years. What features of these interactions are critical to ensure that system dynamics lead to a free energy minimum (properly formed capsids) rather than metastable disordered states (malformed or incomplete capsids)?

To identify the minimal interactions required for successful assembly, we designed a minimal model for capsid proteins. The model consists of rigid subunits, or "capsomers", with spherically symmetric space filling volumes and directional attractive interactions that represent interactions between complementary interfaces on capsid proteins (see Figure 1). The lowest energy states in the model correspond to "capsids" comprised of multiples of 60 subunits in a shell with icosahedral symmetry. Dynamics are simulated with non-inertial Brownian dynamics, in which particle motions are calculated from Newton's laws with forces arising from subunit-subunit interactions, hydrodynamic drag, and a random buffeting force. An important feature of these simulations is that dynamics are time-reversible and satisfy detailed balance. It is precisely these features of real dynamics that would seem to make assembly into well-defined ordered structures unlikely.

Figure 1 

Figure 1: Description of model subunits. (a) An x-ray crystallography image of a canine parvovirus (CPV) capsid (reproduced from Ref. [1]). (b) A schematic drawing that illustrates how capsid proteins, depicted as trapezoids, are arranged in CPV capsids with icosahedral symmetry. A single schematic protein is outlined in red. (c) Illustration of model subunits used in Ref. [2]. Arrows represent directional attractions that mimic complementary interfaces on capsid proteins. (d) The lowest free energy configuration for the model proteins shown in (c). The size of model subunits have been reduced to aid visibility. For a more detailed discussion, see the section entitled "Relation of model capsids to actual viral capsids" in Ref. [2].

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