Skip to main content

Table 6 Results on stable L0-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

L0-1

-4

-4 (< 1 sec)

-4 (< 1 sec)

-4 (< 1 sec)

L0-2

-8

-8 (< 1 sec)

-8 (< 1 sec)

-8 (< 1 sec)

L0-3

-12

-12 (< 1 sec)

-12 (< 1 sec)

-12 (< 1 sec)

L0-4

-16

-16 (32 sec)

-16 (7 sec)

-16 (5 sec)

L0-5

-20

-20 (3 hrs†)

-20 (1.1 min)

-20 (55 sec)

L0-6

-24

-23

-24 (16 min)

-24 (13 min)

L0-7

-28

-26 (33 sec)

-28 (3.2 hrs)

-28 (2.5 hrs)

L0-8

-32

-30 (3 min)

-32 (50 hrs)

-32 (16 hrs)

L0-9

-36

-34 (22 min)

-35 (99 hrs)

-35 (100 hrs)

L0-10

-40

-38 (40 min)

-38 (9.6 hrs)

-39 (100 hrs)

  1. The L0-structures proposed in [52] are hard for both REMC and PERM to fold. After L0-5, PERM is unable to find the unique optimal conformation in any of the 100 independent runs conducted. REMC is unable to find the ground-state conformation for L0-9 and L0-10, however, REMC m finds better sub-optimal conformations than PERM in both instances. 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].