Substrate inhibition kinetics in assemblages of cells

The collective kinetic behavior of a linear array of cells containing a substrate inhibited enzyme is studied with a model in which each cell is considered a well-stirred compartment surrounded by a semipermeable membrane. At large values of a reaction-permeation modulus, wherein substrate access to interior cells is limited, plots of total reaction rate versus concentration of the external reservoir show sharp projections which correspond to dominant reaction occurring in a pair of symmetrically placed cells. Over prescribed ranges of reservoir concentration, multiple stable steady states can occur, some of which are characterized by asymmetric profiles of concentration and reaction rate across the array. A simple stability criterion is proposed and applied to arrays with arbitrary numbers of cells.