Biomedical Engineering Reference
In-Depth Information
concerning the mathematical properties of these constructions in order to arrive at
new metrics, which can in turn serve in interpreting experimental data and proposing
new measurements. To build on Connolly's statement, geometry conditions the
magnitudes of forces, and the models presented in this chapter aim at fostering
our understanding of correlations between structural parameters and biological—
biophysical properties.
The approaches described here are just a beginning in many ways, and can be
extended in different directions. For instance, the analysis of the shelling order of
an interface forms a framework for examining new relations between the interface
structure and the affinity of a protein-protein interaction, or the
ΔΔG
of binding
obtained from alanine scanning, that is more rational than the simple core-rim
model. It is also easy to envisage development of such metrics in the context of
new scoring functions for predictive protein-protein docking, or for discriminating
biological contacts from crystal contacts. Complexes involving proteins and small
molecules such as pharmaceutical agents, or their interaction with nucleic acids
such as DNA were not explored in this chapter, but such systems also provide
opportunities, albeit with geometrical constraints of a different nature.
Still, a concept that we did not approach directly using the techniques deployed
here is the nature of biological macromolecular dynamics. As described in the
introduction, such dynamics underlie virtually all biological interactions, and
complementary geometric and topological concepts should prove instrumental for
investigating them. As we mentioned in the Introduction, a molecule with
n
atoms
enjoys
d
=3
n −
6 conformational degrees of freedom, and a conformational
transition is a path through the
d
-dimensional hyper-surface representing the energy
landscape of the system. Learning the salient features of such landscapes and
inferring thermodynamical and kinetic quantities relies on statistical, geometric
and topological analysis of high-dimensional point clouds, and the evolution of
dynamical systems defined on such landscapes. We anticipate that these and
future developments will shed new light on the deterministic behaviour of macro-
molecular complexes, despite the high dimensionality of the systems, and help us
better discern Nature's strategies.
1.5
Online Resources
1.5.1 Databases
The Protein Databank (PDB)
http://www.rcsb.org
http://www.ebi.ac.uk/pdbe/
http://www.pdbj.org/
The PDB is the reference database for structure of proteins and complexes. The
PDB actually refers to the database of structures itself, and three different interfaces
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