Biomedical Engineering Reference
In-Depth Information
the IPE editor, which encapsulates so-called ipelets, allowing one to run advanced
geometric algorithms from the Computational Geometry Algorithms Library (see
on-line resources
).
1.2
Modeling Atomic Resolution Complexes
1.2.1
Challenges
Formally, binary complexes are the simplest examples of macromolecular interac-
tions. Yet they can be quite challenging, especially when the conformations of the
partners change upon association, which encompasses a great number of biological
systems. Increasingly, atomic level structures of the unbound macromolecular
components of such complexes are available in public data repositories such as
the PDB. A significant number of complex structures exist as well, allowing one to
characterize protein-protein interfaces with the objective of empirically inferring the
rules governing complex formation (e.g., [
32
]). The goals of biophysical modeling
then include being able to understand the structure, energetics and dynamics of a
complex, all in relation to its biological function. In this section we will discuss
the characterization of complex structures but not their prediction (e.g., docking),
although the methods used here may certainly be applied to that end. Geometrical
encoding of the structures and the interface between the components does however
provide means for interpreting dynamic and energetic properties of the complex. We
will see that Voronoı diagrams, Delaunay triangulation and the associated
α
-shape
provide descriptors of molecules that can be correlated to experimental quantities.
1.2.1.1
Experimental Measurements Relevant for Macromolecular
Modeling
Numerous quantitative experimental measures have been developed to describe and
qualify molecular complexes. We present several of these here.
Structural data and its interpretation.
Experimentally-determined protein struc-
tures are stored as PDB entries. Along with details concerning the experimental
setup, the biochemical or biological source of the macromolecule, and the sequences
of the polypeptide chains, the data for each atom is stored. Each atom is associated
with the chain identifier, the residue number and amino acid type, and the atom
name. The
x
,
y
,and
z
values are given in A (0.1 nm) to three decimal places
in order to maintain correct bond lengths and angles, but the actual experimental
precision is much lower. The data also contains the fractional occupancy of each
atom position (alternative positions may be defined from the crystallography), along
with the thermal B-factor (in units of A
2
). The latter quantity describes the region
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