Modeling Macromolecular Complexes: A Journey Across Scales - Modeling in Computational Biology and Biomedicine - page 7

the structure of a complex from the structures of the unbound partners. Docking
methodologies have been developed for such purposes, and an ongoing, open
community experiment (called CAPRI) has been set up in which crystallographers
and NMR groups furnish unreleased structures of complexes as targets for docking
prediction [ 36 ]. Docking, and flexible docking in particular, is a difficult problem,
and its successful resolution will require a detailed understanding of the principles
underlying protein complex formation. The goal of Sect. 1.2 is precisely to con-
tribute to such an understanding.
The second topic is concerned with low-resolution modeling, particularly rele-
vant to the study of protein complexes involving from on the order of 10 to the order
of 100 polypeptide chains. Modeling these complexes is especially challenging due
to their plasticity (their composition may change over time) and their flexibility, and
using complementary data is often compulsory in designing models. These data are
often noisy and ambiguous, and the work presented in Sect. 1.3 aims precisely at
dealing with such uncertainties.
Interestingly, while the questions addressed in these two domains are fundamen-
tally different, the concepts and the constructions used all pertain to the realm of
Vorono¨ıdiagrams.
Public
As just discussed, the goal of this chapter is to show that the more precise the
mathematical models used to investigate macromolecular systems, the sharper the
biological and biophysical conclusions that can be derived. It should thus be of
interest for those designing structural models, as they will find recent geometric and
topological developments. It may also furnish a resource to those wishing to use the
various programs accompanying the contributions described in this chapter as more
than black boxes. Beyond structural biology, this text should also be of interest to a
broad audience in particular in physics and engineering, where simulation methods
involving collections of balls and simplicial complexes are being used. Computers
scientists interested in geometric and topological modeling will find good reasons
to believe that some of the fundamental concepts they have developed over the
past decades are indeed of high interest to the biological community. In particular,
we hope to provide some orientation in a world where mathematically well-posed
questions are not commonplace, and where designing models is actually the central
issue. We also hope to stimulate work, in particular in the realm of curved Voronoı
diagrams and α -shapes, in which a number of algorithmic and complexity questions
are open. Finally, we might hope that students interested in the life sciences in
general will get a feeling for what a protein is, the nature of its complexes, as well
as some ongoing developments concerning the use of geometry to better define their
properties.
We have striven to limit the prerequisites necessary for reading this chapter to a
minimum. In particular, the numerous geometric constructions used are illustrated,
and the reader is invited to reproduce them. This can be facilitated with the help of