We are considering molecular dynamics and (sequential) membrane systems
from the viewpoint of Markov chain theory. The first step is to understand the structure of
the configuration space, with respect to communicating classes. Instead of a reachability
analysis by traditional methods, we use the explicit monoidal structure of this space with
respect to rule applications. This leads to the notion of precycle, which is an element of
the integer kernel of the stoichiometric matrix. The generators of the set of precycles
can be effectively computed by an incremental algorithm due to Contejean and Devie.
To arrive at a characterization of cycles, we introduce the notion of defect, which is a
set of geometric constraints on a configuration to allow a precycle to be enabled, that
is, be a cycle. An important open problem is the effcient calculation of the defects. We
also discuss aspects of asymptotic behavior and connectivity, as well as give a biological
example, showing the usefulness of the method for model checking.
