Membrane Computing is a chapter of Theoretical Computer Science which is inspired by biochemistry (from the way the living cells process chemicals and energy) and which proposes cell-like computing models of a distributed parallel type.

Basically, in the regions defined by a membrane structure one places multisets of objects which can evolve according to given evolution rules. The rules are used in a maximally parallel manner, nondeterministically choosing them and the objects to which they are applied. The objects (described by symbols from a given alphabet) can interact and can pass (selectively) through membranes, while the membranes can be dissolved or can be divided. By such operations we get transitions from a configuration of a system to another configuration, hence we get computations. A result is associated with a halting computation in the form of the number of objects present in the last configuration within a specified membrane. Several variants of such computing devices (P systems) can compute all recursively enumerable sets of natural numbers. When an enhanced parallelism is provided, by means of membrane division (and, in certain variants where one works with string-objects, by means of object replication), NP-complete problems can be solved in linear time (of course, making use of an exponential space).

No experiment implementing such systems in biochemical media have been done, but there have been several attempts to simulate/implement P systems on usual electronic computers. The domain is rather young, so many problems - both theoretical and "practical" - are still open in spite of the fast mathematical development of the area.