Modeling Macromolecular Complexes: A Journey Across Scales - Modeling in Computational Biology and Biomedicine - page 5

interactions. These can be treated using conventional classical mechanics, and
notably the integration of Newton's equations of motion, such as is used for all-atom
molecular dynamics simulations. Such methods require a timestep on the order of
the fastest nuclear vibrations, with a period on the order of 1 fs. Significant time
and computational resources are called for in simulating microsecond (10 9 steps)
processes, but dedicated hardware has allowed in silico folding of small proteins on
the sub-msec scale to be approached [ 62 ].
The corpus of experimental and theoretical results demonstrate unequivocally
that a macromolecule or complex in thermal equilibrium is best represented by
an ensemble of interconverting conformations, in which an individual molecule
at a given instant in time is represented by a single point in a high-dimensional
conformational space. The nature of the energy surface corresponding to this space
is the subject of intensive research, and provides a means of establishing the
probability of occurrence of a given configuration of the system. Experimental
observables reflect the intrinsically statistical quality of the phenomena, in which
a large number of macromolecules, under thermal agitation, repeatedly visit and
revisit favorable regions of the conformational space and only rarely venture
into higher energy zones. The strength (affinity) of a specific interaction between
two macromolecules is typically determined by the properties of three regions in
the configurational space, which regroups the conformational spaces of the two
isolated components and of the complex. Each region is associated with a basin
in the energy surface associated with the stable conformation of the corresponding
macromolecular species. On the other hand, the kinetics, or rate, of the association
depends not only on the character of the stable regions of the space but also of
the accessible paths linking them. The principal pathways describe conformational
changes and different association geometries, and can be approached theoretically
via transition pathway exploration [ 30 ].

1.1.3 Simulation, Geometry, and Insight

Two tempting but false conclusions from this brief exposition must be avoided. The
first is that biological macromolecular systems are so complex that meaningful pre-
dictions must await further theoretical and computational advances. This is clearly
not the case, as many theoretical approaches are directly applicable to biological
systems, and even incomplete theories and limited-timescale simulations have been
capable of producing accurate models and predictions. The second is related to the
first: that simulations alone hold the key to understanding macromolecular behavior.
At some future date such methods, applied blindly, may indeed be capable of
reproducing and reliably predicting the results of certain experimental studies. But
used this way they offer no insight, and we will continue to be faced with the
difficulty of abstracting the principles of the phenomenon under study in order to
go still further.