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Table 5 Results on stable Z-structures

From: A replica exchange Monte Carlo algorithm for protein folding in the HP model

ID E* PERM t e x p MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabdwgaLjabdIha4jabdchaWbqabaaaleqaaaaa@373A@ REMC pm REMC m
Z-4 -3 -3 (< 1 sec) -3 (< 1 sec) -3 (< 1 sec)
Z-8 -7 -7 (< 1 sec) -7 (< 1 sec) -7 (< 1 sec)
Z-12 -11 -11 (< 1 sec) -11 (< 1 sec) -11 (< 1 sec)
Z-16 -15 -15 (3 sec) -15 (< 1 sec) -15 (< 1 sec)
Z-20 -19 -19 (51 min) -19 (< 1 sec) -19 (< 1 sec)
Z-24 -23 -23 (49 hrs†) -23 (< 1 sec) -23 (< 1 sec)
Z-28 -27 -26 -27 (< 1 sec) -27 (< 1 sec)
Z-32 -31 -29 -31 (< 1 sec) -31 (< 1 sec)
Z-36 -35 -31 -35 (1 sec) -35 (< 1 sec)
Z-40 -39 -34 -39 (2 sec) -39 (1 sec)
  1. The Z-structures proposed in [51] are easy for REMC to fold when compared with PERM. After Z-24, PERM is unable to find the unique optimal conformation in any of the 100 independent runs conducted. When only one folding direction of PERM finds the optimal conformation, we report the mean run-time of that direction, denoting this in the table with a †. When best energies found by PERM t 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabigdaXaqabaaaleqaaaaa@33F5@ and PERM t 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabikdaYaqabaaaleqaaaaa@33F7@ differed (and neither find the optimal solution), the best energy by either is reported and the run-time is omitted. For every instance, 100 independent runs were conducted of 1 CPU hour each. In cases where not every run reached the same energy value after 1 hour, the expected run-time to reach the energy value shown in the table was calculated using the equation detailed by Parkes and Walser [54].