Theoretical and Experimental DNA Computation (Natural ...

66 3 Models of Molecular Computation
well as a classification scheme for reaction rules. Importantly, it also introduces
the membrane construct, which is fundamental to the work described in the
next section.
Psystems
P systems, a variant of the membrane model, were introduced by Gheorge
Păun in [118] (see also [119] for an overview of the entire field). They were
inspired by features of biological membranes found in nature. These membranes
act as barriers and filters, separating the cell into distinct regions and
controlling the passage of molecules between regions. However, although P
systems were inspired by natural membranes, they are not intended to model
them, and so we refrain here from any detailed discussion of their structure
or function.
The membrane structure of a P system is delimited by a skin that separates
the internals of the system from its outside environment. Within the skin lies
a hierarchical arrangement of membranes that define individual regions. An
elementary membrane contains no other membranes, and its region is therefore
defined by the space it encloses. The region defined by a nonelementary
membrane is the space between the membrane and the membranes contained
directly within it. We attach an integer label to each membrane in order to
make it addressable during a computation. Since each region is delimited by
a unique membrane, we use membrane labels to reference the regions they
delimit.
Environment
1
2
3
Regions
Environment
6 7
4
(a)
Skin
5
Environment
Environment
Elementary
membrane
Membranes
1
2 3
4 5
Fig. 3.8. (a) Membrane structure. (b) Tree representation
(b)
6 7
An example membrane structure is depicted in Fig. 3.8a, with its tree representation
in Fig. 3.8b. Note that the skin membrane is represented by the
root node, and that leaf nodes represent elementary membranes.
Each region contains a multiset of objects and a set of rules. Objects are
represented by symbols from a given alphabet V . Rules transform or “evolve”