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Here we will outline the theory behind the ENM and some of its extensions,
and then we will present some recent applications. We will focus on two groups
of proteins, membrane proteins and viral capsids. Membrane proteins form one
of the most ubiquitous classes of proteins, accounting for more than 25% of the
proteins in most genomes (Wallin & von Heijne, 1998). Their functions cover a
wide range of spectrum from transport of metabolites in prokaryotes to regulating
and maintaining intra-cellular communications in eukaryotes by transporting
ions. In mammalians, these proteins are responsible for maintaining the
electrochemical gradients across cell-membrane, which is vital for efficient
functioning of the central nervous system. Malfunctioning of membrane proteins
leads to potentially fatal diseases, such as Alzheimer's, multiple sclereosis and
arrhythmia (Ashcroft, 2000). Membrane proteins indeed constitute a large
fraction of proteins currently targeted by approved drugs. Understanding the
general principles of their structural dynamics and thereby mechanisms of
function is thus essential in the rational design of therapeutics that target
membrane proteins. By way of applications to a number of membrane proteins,
we will illustrate in the present chapter how ENM approaches can provide
insights into gating and/or signal transduction mechanisms.
Viruses constitute another group of proteins that are difficult to examine by
all-atom simulations (due to their sizes of the order of Megadaltons), but are
amenable to ENM analyses. The viral capsids in particular possess solid-like
behavior, and can be well represented by elastic network models and their
material properties. We will show how ENMs can greatly enhance our
understanding of the complex dynamics of viral capsids, and open the way to
simple descriptions in terms of measurable material properties. In summary, both
groups of applications illustrate the utility of ENM approaches in providing
simple descriptions of highly complex structures' dynamics, and gaining insights
into potential mechanisms of biomolecular functions.
7.2. Theory and Assumptions
7.2.1. Statistical mechanical foundations
Potential energy. The elastic network model theory follows the same formalism
that is commonly presented for studying small oscillations (Goldstein, 1953).
Here the physical system is a molecule or molecular assembly consisting of N
constituent particles, where each particle may be an atom, a residue, or some
other structural element acting as a node in the network. The changes in
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