  EASAL (efficient atlasing and sampling of assembly landscapes) is a recently
reported geometric method for representing, visualizing, sampling and computing
integrals over the potential energy landscape tailored for small molecular
assemblies. EASAL's efficiency arises from the fact that small assembly
landscapes permit the use of so-called Cayley parameters (inter-atomic
distances) 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, ensuring reasonable coverage of crucial but narrow regions of low
effective dimension.
  However, this alone is inadequate for accurate computation of configurational
entropy and other integrals, required for estimation of both free energy and
kinetics - where it is essential to obtain uniform sampling in appropriate
cartesian or moduli space parameterization. Standard adjustment of Cayley
sampling via the Jacobian of the map between the two parameterizations is
fraught with challenges stemming from an illconditioned Jacobian.
  This paper formalizes and analyzes these challenges to provide modifications
to EASAL that secure the advantages of Cayley sampling while ensuring certain
minimum distance and coverage relationships between sampled configurations - in
Cartesian space. The modified EASAL's performance is compared with the basic
EASAL and the data are presented for Human and Rat Islet Amylin Polypeptide
(HiAPP, PDB-2KJ7 and RiAPP PDB-2KB8) dimerization (the two differ in only 6 out
of 37 residues, but the former aggregates into fibrils, while the latter does
not).
