HP-sequence design for lattice proteins - an exact enumeration study on diamond as well as square lattice

We present an exact enumeration algorithm for identifying the {\it native} configuration - a maximally compact self avoiding walk configuration that is also the minimum energy configuration for a given set of contact-energy schemes; the process is implicitly sequence-dependent. In particular, we show that the 25-step native configuration on a diamond lattice consists of two sheet-like structures and is the same for all the contact-energy schemes, ${(-1,0,0);(-7,-3,0); (-7,-3,-1); (-7,-3,1)}$; on a square lattice also, the 24-step native configuration is independent of the energy schemes considered. However, the designing sequence for the diamond lattice walk depends on the energy schemes used whereas that for the square lattice walk does not. We have calculated the temperature-dependent specific heat for these designed sequences and the four energy schemes using the exact density of states. These data show that the energy scheme $(-7,-3,-1)$ is preferable to the other three for both diamond and square lattice because the associated sequences give rise to a sharp low-temperature peak. We have also presented data for shorter (23-, 21- and 17-step) walks on a diamond lattice to show that this algorithm helps identify a unique minimum energy configuration by suitably taking care of the ground-state degeneracy. Interestingly, all these shorter target configurations also show sheet-like secondary structures.Comment: 19 pages, 7 figures (eps), 11 tables (latex files

Can coarse-graining introduce long-range correlations in a symbolic sequence?

We present an exactly solvable mean-field-like theory of correlated ternary sequences which are actually systems with two independent parameters. Depending on the values of these parameters, the variance on the average number of any given symbol shows a linear or a superlinear dependence on the length of the sequence. We have shown that the available phase space of the system is made up a diffusive region surrounded by a superdiffusive region. Motivated by the fact that the diffusive portion of the phase space is larger than that for the binary, we have studied the mapping between these two. We have identified the region of the ternary phase space, particularly the diffusive part, that gets mapped into the superdiffusive regime of the binary. This exact mapping implies that long-range correlation found in a lower dimensional representative sequence may not, in general, correspond to the correlation properties of the original system.Comment: 10 pages including 1 figur