Modeling Macromolecular Complexes: A Journey Across Scales - Modeling in Computational Biology and Biomedicine - page 6

Apart from detailed atomic-level simulations, considering the structures of
macromolecules and their complexes in terms of distances, areas, and volumes can
lead to fruitful insights. Our experience with everyday objects underlies numerous
heuristic approaches to measuring such geometric properties of macromolecules and
interpreting them. If these approaches are sometimes less than rigorous, common
sense (or common experience) provides checks and feedback that tend to prevent the
worst sorts of errors. Further, the biochemical results that we wish to interpret are
themselves subject to error. As mentioned in the preceding section, experimentally
observed properties generally represent averages in time and space over a great
number of instances of the macromolecules in question in many somewhat different
conformations. Sample homogeneity can also be a concern. Experimental error
can thus be substantial, typically a factor of 2 or more in protein-protein binding
affinities [ 39 ], and sample variability may trump the theoretical shortcomings of a
particular heuristic.
But we must also go beyond heuristics. The systematic errors that can find
their way into calculated geometric values using simple but inexact approaches
can be substantial [ 14 ]. Further, formal definitions of geometric properties facilitate
generalization, allowing one to obtain new insights by incorporating analyses from
related fields, as in the case of Vorono¨ıdiagrams[ 56 ]. The need for rigorous
algorithms for calculating geometrical properties becomes especially critical when
addressing problems with a higher dimensionality, such as those encountered in
relating different conformations of the macromolecule in the 3 N dimensional
conformational space. Here our day-to-day experience can be misleading, and real
intuition is limited.
At a higher level of abstraction, topology permits describing shapes in a quali-
tative but rigorous manner. In macromolecules, one might wish to identify tunnels
and voids—the former perhaps providing direct access to an active site, the latter
indicating poor packing or trapping solvent or other small molecules. Geometry
provides the quantitative measures that complement such topological descriptions.
These in turn reflect physical interactions, so that the particular observed geometries
and topologies become a fingerprint of the most favourable arrangements of atoms in
biological constructions. In selecting the components of living systems, Biology has
imposed a bias on the physics and chemistry of macromolecules. The approaches
presented in this chapter are aimed at better analyzing and interpreting this bias.

1.1.4 Chapter Overview

Outline

This chapter covers two main topics. The first is concerned with the modeling
of macromolecular complexes at the atomic scale. As mentioned above, the PDB
contains relatively few structures of complexes compared to unbound proteins.
A major goal of biological modeling, known as docking , consists of predicting