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The energy landscape picture has emerged as a promising approach to answer
this question. Energy landscape, or more precisely potential energy landscape, is the
name commonly given to the graph of the potential energy of interaction between
the microscopic degrees of freedom of the system [3]; the latter is a high-dimensional
surface, but one can also speak of a free energy landscape when only its projection
on a small set of collective variables (with a suitable average over all the other
degrees of freedom) is considered [3]. Before having been applied to biomolecules,
this concept has proven useful in the study of other complex systems, especially of
supercooled liquids and of the glass transition [4]. The basic idea is very simple, yet
powerful: if a system has a rugged, complex energy landscape, with many minima
and valleys separated by barriers of dierent height, its dynamics will experience a
variety of time scales, with oscillations in the valleys and jumps from one valley to
another. Then one can try to link special features of the behavior of the system (i.e.,
the presence of a glass transition, the separation of time scales, and so on) to special
properties of the landscape, like the topography of the basins around minima, the
energy distribution of minima and saddles connecting them and so on. Anyway, a
complex landscape yields a complex dynamics, where the system is very likely to
remain trapped in dierent valleys when the temperature is not so high. This is
consistent with a glassy behavior, but a protein does not show a glassy behavior, it
rather has relatively low frustration. This means that there must be some property
of the landscape such to avoid too much frustration. This property is commonly
referred to as the folding funnel [5]: though locally rugged, the low-energy part of
the energy landscape is supposed to have an overall funnel shape so that most initial
conditions are driven towards the correct native state. The dynamics must then be
such as to make this happen in a reasonably fast and reliable way, i.e., non-native
minima must be eciently connected to the native state so that trapping in the
wrong conguration is unlikely.
However, a direct visualization of the energy landscape is impossible due to its
high dimensionality, and its detailed properties must be inferred indirectly. In the
following, we will describe two strategies to analyze the energy landscape of model
proteins: a local one and a global one. The former strategy, addressed to in Sec. 6.2,
is essentially topological in character and amounts to dene a network (a graph)
whose nodes are the minima of the potential energy and whose edges are the saddles
connecting them. This network has, however, to be properly renormalized in order
to yield signicant results: the renormalization procedure is described in Sec. 6.2.1.
The latter strategy (Sec. 6.3) is instead a geometrical one, and is based on dening
global geometric quantities able to characterize the folding landscape as a whole.
In both cases interesting information about the dierences between the landscapes
of proteinlike systems and those of generic polymers can be obtained.
