We improve previously known universality results on enzymatic numerical
P systems (EN P systems, for short) working in all-parallel and one-parallel modes. By
using a
attening technique, we rst show that any EN P system working in one of these
modes can be simulated by an equivalent one-membrane EN P system working in the
same mode. Then we show that linear production functions, each depending upon at most
one variable, su ce to reach universality for both computing modes. As a byproduct, we
propose some small deterministic universal enzymatic numerical P systems