The tomato bushy stunt virus is an RNA virus composed of 180 identical coat proteins arranged in icosahedral symmetry. The asymmetric unit of the viral capsid, containing three copies of the coat protein having slightly different conformations, has been crystallized and is shown in Figure . The three conformations of the coat protein are designated A, B, and C, and differ primarily in the orientation of a few surface sidechains. A second major difference is that while all three conformations contain RNA-binding (R), surface (S), and projecting (P) domains, the R domain (residues 1-101) is completely unresolved in the A and B conformations while in the C conformation, residues 67-101 have an ordered structure and are resolved. The full viral coat is shown in Figure , with two spheres representing each protein. The symmetry is more apparent in Figure , where the P domains have been removed and only the S domains are shown. The picture emphasizes the five-fold symmetric axis, but three-fold and two-fold symmetries also exist for the coat. The viral RNA (molecular weight ) is, of course, not icosahedral; it is disordered and does not appear in the crystal structure at all.
In addition to the three proteins, Figure shows the location of the two Ca ions which bind per protein. Each pair of calcium cations binds in a negatively charged pocket at the interface between adjacent S domains in the triad, the pocket being formed by five aspartic acid sidechains contributed by the two proteins. This is shown in more detail in Figure . It is postulated that the interaction between these Asp residues and the Ca ions plays a major role in stabilizing the viral coat. If the Ca ions are removed, the virus expands as the pH is raised above 7. The hydrodynamic radius of the virus can expand by as much as 10%, but there is no loss of mass and the process is reversible. A low-resolution (8 Å) crystal structure was determined for the expanded conformation of the virus and indicated that expansion occurred by relative motions perpendicular to the interfaces where Ca ions bind in the unexpanded conformation. However, no atomic details were available from this low resolution data.
In order to investigate the expansion phenomenon, we carried out molecular dynamics calculations on two different models of the viral coat proteins representing different possible configurations. The model systems include all resolved residues from the asymmetric unit plus counterions, Na and Cl and, perhaps, Ca, for a total of 8138 atoms. Through the use of the transformation matrices in the crystal structure (Brookhaven Protein Database structure 2TBV), coordinates can be generated for the entire viral coat containing 180 proteins and nearly 488,280 atoms. It is not yet practical to simulate a system this large on a standard workstation, so the dynamics were only calculated for the three proteins of the asymmetric unit. However, it is possible to include the electrostatic and van der Waals, i.e., ``nonbonded'' forces contributed by the rest of the viral coat. No standard method for calculating nonbonded forces could be used for a system of this size, but the Cell-Multipole Method (CMM) provides a means for doing such calculations both quickly and accurately. Therefore, we are able to simulate the dynamics of the entire viral coat. The RNA is not represented in the current calculations. Newton-Euler Inverse Mass Operator (NEIMO) Dynamics (see Chapter 2) provide a means of speeding the calculations by allowing us to use internal-coordinate dynamics with timesteps of 2 fs, rather than the 1 fs timesteps required by Cartesian dynamics.