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In-Depth Information
The harmonic approximation is ubiquitous in physics, and similar models
have been used for calculating elastic properties of bulk polymers and classical
lattice vibrations in crystals (see, for example, Marder, 2000). Proteins, on the
other hand, are small and somewhat flexible, and it was not until Tirion (1996)
demonstrated that a harmonic potential faithfully captures the global dynamics of
proteins that ENMs saw wide use in theoretical investigations of protein
dynamics. Subsequent studies reinforced this observation, bestowing the ENM
with particular relevance to proteins (Cui & Bahar, 2006). It is well established
that a relationship exists between protein structure and protein function. Here we
have a simple network model that enables the calculation of global dynamics
from structure alone, suggesting that protein dynamics is intermediate to
structure and function, and ENMs provide an easily employable conduit between
structure and dynamics.
An attractive feature of ENMs that keeps them in continuous use is that they
provide a wealth of information at low computational cost. Construction of the
EN is a matter of straightforwardly defining and linking nodes provided that
information on structure, or simply on inter-residue contact topology, is
available. The standard technique for determining dynamics or statistical
distributions from an ENM is to conduct a mode decomposition using spectral
graph theory and methods (e.g., Gaussian Network Model (GNM) (Bahar
et al.
,
1997; Bahar
et al.
, 1998) inspired by polymer network theory (Flory, 1976)) or a
normal mode analysis (NMA) with uniform harmonic potentials, both of which
provide analytical solutions to the equations of motion, bypassing the need to
sample conformation space. Although NMA can also be applied to potentials
derived from more detailed force fields, such calculations either require an initial
energy minimization that inevitably distorts the input conformation, or else they
risk producing energetically unstable solutions. ENMs, on the other hand, can
take any conformation as input and guarantee that it resides at a minimum of the
potential and therefore has physical motions. Furthermore, the few parameters
used in ENMs can be easily adjusted as seen fit, giving ENMs uncommon
adaptability. There are, however, some limitations to ENMs as predictive tools.
Although ENMs robustly predict collective global motions, they do not fare as
well in providing reliable descriptions of local motions. Also, the harmonic
approximation requires a potential minimum, limiting the utility of ENMs for
modeling non-equilibrium dynamics. A corollary of this second point is that
only motions in the neighborhood of the global energy minimum can be
accurately predicted by the ENMs, and one must be careful when interpreting the
results from the model not to exceed the limits of the model.
