This paper introduces a notion of population P systems as a class of tissue P systems where the links between the cells can be modified by means of a specific set of bond making rules. As well as this, cell division rules which introduce new cells into the system, cell differentiation rules which change the set of rules that can be used inside of a cell, and cell death rules which remove cells from the system are also considered by introducing a particular notion of population P systems with active cells. The paper mainly reports universality results for the following models: (a) population P systems where cells are restricted to communicate only by means of the environment but never forming any bond, (b) population P systems with bond making rules with restricted communication rules, (c) population P systems possessing only the cell differentiation operation, and (d) population P systems equipped with cell division rules and bond making rules.

Membrane computing, Cell bonding, Cell division, Cell differentiation, Turing computability