Summary. This paper continues an investigation into bridging two research areas concerned with natural computing: membrane computing and reaction systems. More specifically, the paper considers a transfer of two assumptions/axioms of reaction systems, nonpermanency and the threshold assumption, into the framework of membrane computing. It is proved that: (1) SN P systems with non-permanency of spikes assumption characterize the semilinear sets of numbers, and (2) symport/antiport P systems with threshold assumption (translated as ω multiplicity of objects) can solve SAT in polynomial time. Also, several open research problems are stated.