Protein flexibility is important for a wide range of biological
phenomena, such as enzymatic reaction and control. In the case of
protein-protein or protein-ligand complex formation, flexibility of the
binding partners provides the origin for their plasticity, enabling them
to conformationally adapt to each other. Equally important as
flexibility per se are changes in the flexibility upon complex
formation. Thus, analyzing flexibility and modeling plasticity of
macromolecules without having to do expensive calculations is of great
importance. Here, flexibility concepts grounded in rigidity theory [1]
are applied and further developed to investigate flexibility changes
upon macromolecular association and to model conformational variability
in macromolecules.
Initially, for validation purposes, the influence of protein-protein
complex formation between H-Ras and the Ras-binding domain of C-Raf1 on
the intrinsic flexibility of both binding partners has been investigated
using molecular dynamics simulations and a network analysis based on
graph theory [1].
Encouragingly, convincing agreement is found, although the computational
time requirement of the network analysis is several orders of magnitude
smaller than for the simulations [2]. Second, we present a method for
rapidly estimating vibrational entropy changes upon macromolecular
complex formation using results from the network analysis. Changes in
the (internal) degrees of freedom of binding partners provide an
entropic contribution that needs to be taken into account when
calculating binding affinities. Currently, normal mode analysis (NMA) is
considered to be the "gold standard" to estimate these changes. However,
NMA is computationally expensive even for macromolecules of about 5000
atoms. Convincingly, for a data set of 10 protein-protein complexes
with widely varying properties, total vibrational entropy changes as
determined by our method correlate well (r2 = 0.84) with those obtained
from NMA, despite only a fraction of computational time required. Third,
we introduce a two-step approach for modeling macromolecular plasticity.
In the first step, the flexibility of the macromolecule is investigated
by a network analysis. Subsequently, applying a block normal mode
analysis, internal motions of flexible regions are modeled using
collective variables, whereas only translational and rotational motions
are allowed for rigid regions ("blocks"). Our method was applied to a
set of protein structures for which conformational changes upon binding
have been observed. Predicted motions agree well with those found in
experiment, both in terms of direction and (relative) magnitude of the
motion.
Finally, an approach for fully-flexible protein-ligand docking will be
presented that is based on an elastic grid representation of interaction
fields inside the binding pocket of potential drug targets.

[1] Jacobs DJ, Rader AJ, Kuhn LA, Thorpe MF. Protein flexibility
predictions using graph theory.
Proteins 2002;44:150-165.
[2] Gohlke, H, Kuhn, LA, Case, DA. Change in protein flexibility upon
complex formation: Analysis
of Ras-Raf using molecular dynamics and a molecular framework approach.
Proteins
2004;56:322-337.
[3] Ahmed, A, Gohlke, H. Multi-scale modeling of macromolecular
conformational changes
combining concepts from rigidity and elastic network theory. Proteins
2006, in press.