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 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.