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because we require full flexibility to investigate local variation, we have limited our general exploration of the minimum to ensembles comprising only a few tens of side chains. each configuration is determined by a set of local parameters, which are ultimately comprised of 84 independent parameters for each residue, plus two more independent translational parameters: a translation of the axis of local symmetry x by a distance l and a rotation of the axis of local symmetry y by an angle t. the minimum over side chain configuration is maximized over t and l, which makes the dimensionality of the space of local minimal configurations equal to 884 + 4 = 888. therefore, given the six lennard-jones potentials and the continuous rotamer parameters associated with the three letters in a dipeptide, the minimum over local configurations of side chains involves 12144 parameters. however, only one third of these are statistically significant at the level of our current calculations; the remaining ones are nonphysical. to remedy the latter problem, we filter out nonphysical states from the minimum by requiring local configurations to be physically acceptable (i.e., to lie in a subset of physical states), thus at most removing one third of the raw minimum.
in addition to the continuous t and l degrees of freedom, it is still possible to maximize the continuous energy over all continuous degrees of freedom. to this end, we divided the degree of freedom into two groups: one with rdihedrals, the three backbone dihedral angles φ, ψ, χ, and the other with rall degrees of freedom with a precision parameter β. however, in all such cases, an optimization over t and l must be performed first. the complexity of calculations has been deliberately kept to a minimum so that we can make this comparison. we chose three amino acids that have a regular rotamer landscape and compared two structures of type i, helical, and type ii, sheet, with the final shapes analyzed along the (rdihedrals + rall ) degrees of freedom. we found no significant difference between the shapes of the final structures obtained in the coarse-grained and traditional treatment. this result is directly due to the width of the sampled deformable space. 3d9ccd7d82