Distributed-in-space product formation in vivo: enzymic kinetics.

Distributed-in-space Michaelis-Menten enzymic conversion of precursor substrate to product within an organ is explored when all formed product is released into the bloodstream. In the nonlinear saturating enzymic case, length-wise precursor concentration profiles are found to vary from a falling exponential to a slowly declining linear profile, with rise in input concentration. The vascular profile for product rises in complimentary fashion; the sum of precursor and product is constant along the length. Symmetric permeability barriers produce stepdowns in precursor concentration from blood to tissue and, for product, converse stepdowns from tissue to blood are produced. Tracer precursor, introduced as an impulse input within this steady state, is converted to product with details of its distribution varying with the number of barriers for precursor. During this conversion, reversible tracer precursor association with enzyme leads to an enzymic space effect perceived as a saturating additional compartment, largest at tracer bulk levels, and decreasing with increase in underlying bulk concentration. While tracer product is not delayed by enzyme association, its outflow profile varies with the amount and location of enzyme, the enzymic rate constants, and the barriers for product between enzyme and the blood.