  EASAL (Efficient Atlasing and Sampling of Assembly Landscapes) is a geometric
method for sampling and computing integrals over the potential energy landscape
of small molecular assemblies. EASAL's efficiency arises from the fact that
small assembly landscapes permit the use of so-called Cayley (inter-atomic
distance based) parameters for geometric representation and sampling of the
assembly configuration space regions; this results in their isolation,
convexification, customized sampling and systematic traversal using a
comprehensive topological roadmap.
  We define custom-designed measurements to investigate and compare various
sampling characteristics of EASAL and the traditional Monte Carlo (MC)
sampling, including (i) sampling speed, (ii) efficiency and accuracy of uniform
grid coverage, (iii) accuracy of weighted coverage at covering low energy
regions, (iv) ability to localize sampling to macrostates, and (v) flexibility
in sampling distributions.
  In particular, we compare the sampling characteristics of EASAL and MC in
sampling the assembly landscape of 2 trans-membrane helices, with short-range
pair-potentials. We demonstrate that EASAL provides a reasonable coverage of
crucial but narrow regions of the energy landscape of low effective dimension,
with much fewer samples and computational resources than MC sampling. Promising
avenues for combining the complementary advantages of the two methods are
discussed.
