Heteropolymer Folding

8 Heteropolymer Folding among the nite T landscape and the one at T = 0. One nds that the structure of the minima does not change much from T = 1 to T = 0, for example. The free energy landscape is quite stable. 16 is a SIMD parallel super-computer. In the tube version, the one we have used here, it has a theoretical speed of 6:5 GGops (and, as we will discuss , reaches an unusually high sustained speed). In its largest version it reaches a theoretical speed of 100 GGops. Why do we need a supercomputer? We want for example to try to understand if properties like the existence of one or few ground states is a generic property of random heteropolymers or just the pattern followed by some realizations of the random system. We want to compute, in essence, a reliable estimate of P() ; (11) where here by P() we indicate the probability distribution of the distances, and with the long bar we indicate the average over the random coupling realizations. We also have to understand if our results do characterize thermal equilibrium or if they are just typical of a transient behavior (due to long correlation times). For doing that we use a quite standard criterion. We simulate two independent copies of the same system, and we compute two diierent estimators of the P(). In the rst one we consider an history distance (i.e. the distance of representatives of the same history at diierent times), while in the second we compute the distances of the two copies at the same time. Only when (and if) these two estimators converge to the same result we can be sure we are looking at an equilibrium phenomenon. The other open question for which we will need a very large statistical sample concerns determining the scaling law of the mass gap (energy diierence of the ground state and the rst excited state) with the chain size. In our parallelization scheme we have one independent realization of random couplings on each processor, and, as we have said, we simulate the evolution of two copies of the system in each coupling set (i.e. in each processor). In our preliminary runs (one week of the 6:5 GGops Ape) we have studied the system at diierent T values (with 16 10 6 full sweeps on 128 30 site systems for each temperature). At …