  In this paper, a multiscale virtual particle based elastic network model
(MVP-ENM) is proposed for biomolecular normal mode analysis. The multiscale
virtual particle model is proposed for the discretization of biomolecular
density data in different scales. Essentially, the model works as the
coarse-graining of the biomolecular structure, so that a delicate balance
between biomolecular geometric representation and computational cost can be
achieved. To form "connections" between these multiscale virtual particles, a
new harmonic potential function, which considers the influence from both mass
distributions and distance relations, is adopted between any two virtual
particles. Unlike the previous ENMs that use a constant spring constant, a
particle-dependent spring parameter is used in MVP-ENM. Two independent models,
i.e., multiscale virtual particle based Gaussian network model (MVP-GNM) and
multiscale virtual particle based anisotropic network model (MVP-ANM), are
proposed. Even with a rather coarse grid and a low resolution, the MVP-GNM is
able to predict the Debye-Waller factors (B-factors) with considerable good
accuracy. Similar properties have also been observed in MVP-ANM. More
importantly, in B-factor predictions, the mismatch between the predicted
results and experimental ones is predominantly from higher fluctuation regions.
Further, it is found that MVP-ANM can deliver a very consistent low-frequency
eigenmodes in various scales. This demonstrates the great potential of MVP-ANM
in the deformation analysis of low resolution data. With the multiscale
rigidity function, the MVP-ENM can be applied to biomolecular data represented
in density distribution and atomic coordinates. Further, the great advantage of
my MVP-ENM model in computational cost has been demonstrated by using two
poliovirus virus structures. Finally, the paper ends with a conclusion.
