Pull moves are not reversible
"Pull moves" is a popular move set for Monte Carlo or other simulations of lattice models of polymers. The original publication of this move set, Lesh et al. (2003) claimed that the move set is fully reversible, which is an important requirement in all simulations. Since then, many simulations have been performed and published in the literature in the belief that this move set is in fact reversible.
However, we have noticed that some moves in this move set are in fact not reversible. Specifically, those end moves that result in a hook at the end of the chain are irreversible. An example of such a move is shown in the following animation:
In the original conformation, the end of the chain is straight. The applied end pull move creates a conformation having a hook at the end of the chain. This move should be reversible by pulling the chain in the other direction. However, when we do this, the resulting conformation has a bent end instead of a straight end. There is no single move that could restore the original conformation with a straight end.
The problem can be easily solved by excluding all end moves that result in a hook at the end of the chain. Simulations that do not exclude these moves are all flawed.
More details are described in our paper
Györffy D, Závodszky P, Szilágyi A (2012):
"Pull moves" for rectangular lattice polymers are not fully reversible.
IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9(6):1847-1849. (PubMed)