Multiscale Modeling of Virus Structure, Assembly, and Dynamics - Computational Modeling of Biological Systems - page 175

driving capsid formation through theoretical studies [ 19 , 20 , 38 , 44 , 52 - 55 ], structural
analysis [ 56 , 57 ], and in vitro self-assembly experiments of empty capsids using
only purified capsid proteins [ 19 , 58 , 59 ]. Still, a detailed mechanistic understanding
of the capsid self-assembly process is lacking. Despite rapid increases in the
availability of computer power and algorithmic advances, atomically detailed
simulations of the self-assembly process have been difficult due to the large system
sizes and the long timescales involved in the process. As a consequence, to-date
most simulation studies of capsid formation have been performed employing only
simple coarse-grained models that significantly reduce the system size [ 32 , 60 , 61 ].
For example, Hagan and Chandler [ 32 ] modeled capsid proteins or capsomeres as
point particles to simulate the assembly of small shells, Hicks and Henley [ 61 ]used
an elastic model to represent capsid proteins as deformable triangles and Rapaport
simulated the capsid self-assembly of polyhedra structures utilizing trapezoid units
as a building block [ 28 ].
We investigated the spontaneous self-assembly process of different-sized virus
capsids employing a coarse-grained molecular dynamics (MD) simulation ap-
proach. To increase the speed and efficiency of the simulations an extremely fast,
event-driven method called discontinuous molecular dynamics (DMD) was em-
ployed [ 62 - 64 ]. Before performing simulations, we developed a range of geometric
models that capture the geometric shape and energetic details of a coat protein
without any specific built-in self-assembly rules such as nucleation. Interestingly,
our prior two dimensional mathematical modeling studies, as well as, initial
exploratory simulation studies by Rapaport [ 28 ] had predicted that the trapezoidal
shape is a perfect building block to tile a closed icosahedral surface of any capsid
size (see Sect. 3 )[ 40 ]. To test this prediction by way of physical simulations, in our
first generation of coat protein models each protein subunit was represented as a
set of 24 beads arranged in four layers confined in the trapezoidal geometry (see
Fig. 5 a). Using a simplified model that exploits the important role of coat protein
shape, together with the fast DMD method, allowed us to capture the spontaneous
self-assembly of icosahedral capsids of different sizes as well as explore the optimal
temperature and protein concentration required for the spontaneous self-assembly of
capsids.
By performing over a hundred MD simulations at different temperatures and
protein concentrations, we found that the assembly of T D 1 and T D 3 icosahedral
capsids occurs with high fidelity only over a small range of temperatures and protein
concentrations [ 33 , 65 ]. Outside this range, particularly at low temperature or high
protein concentration, large enclosed “monster particles” are produced (Fig. 5 b).
These mis-assemblies are remarkably similar to experimentally observed Turnip
crinkle virus monster particles [ 66 ] or bacteriophage P22 monster particles [ 67 ].
Most importantly, our simulation studies revealed that the capsid assembly dynam-
ics under optimal conditions is a nucleated process [ 58 ] involving monomer addition
in which building blocks (either monomeric, dimeric, or trimeric species) are glued
together in a sequential manner [ 33 ]. It is quite remarkable that our simulations
employing simple models were able to recapitulate the experimental observations
that capsid assembly is a nucleated process [ 19 , 58 , 59 ].