Behavioural observations of cell movements with timing aspects

We use membrane systems to define a formalism inspired by cell biology in which mobility and timing are explicitly specified. In order to reason about the behaviours of complex biological systems, we introduce several observational equivalences over mobile membranes with lifetimes. These equivalences based on observations correspond to several combinations of mobility operations that can be performed, timing aspects of the objects involved in mobility and their explicit positions inside membranes. Various relationships between these observational equivalences are proved. Moreover, we use the ambient logic to provide a logical characterization for located observational equivalence.