A modified gambler's ruin model of polyethylene chains in the amorphous region.

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).

The folding mechanism of larger model proteins: role of native structure.

The folding mechanism of a 125-bead heteropolymer model for proteins is investigated with Monte Carlo simulations on a cubic lattice. Sequences that do and do not fold in a reasonable time are compared. The overall folding behavior is found to be more complex than that of models for smaller proteins. Folding begins with a rapid collapse followed by a slow search through the semi-compact globule for a sequence-dependent stable core with about 30 out of 176 native contacts which serves as the transition state for folding to a near-native structure. Efficient search for the core is dependent on structural features of the native state. Sequences that fold have large amounts of stable, cooperative structure that is accessible through short-range initiation sites, such as those in anti-parallel sheets connected by turns. Before folding is completed, the system can encounter a second bottleneck, involving the condensation and rearrangement of surface residues. Overly stable local structure of the surface residues slows this stage of the folding process. The relation of the results from the 125-mer model studies to the folding of real proteins is discussed.