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The enhanced mobile membranes is a variant of membrane systems which has
been proposed for describing some biological mechanisms of the immune
system. In this paper, we study the computational power of the enhanced
mobile membranes. In particular, we focus on the power of mobility given by
the operations $endo$, $exo$, $fendo$ and $fexo$. The computational
universality is obtained with 12 membranes, while systems with 8 membranes
subsume $ET0L$, and those with 3 membranes are contained in $MAT$.