Increase maximum sustainable yield in gradostat

In this work, we consider a gradostat made up of several chemostats coupled by migrations of substrates and products between them. We seek maximum product synthesis or maximum sustainable yield by optimizing with the dilution rate. The mathematical study of the complete model is carried out by searching equilibrium points and stability. We compare the overall maximal synthesis of the system of coupled chemostats to the sum of the maximal syntheses of isolated chemostats. We show that in the homogeneous case where all the chemostats are identical, the difference between the maximum synthesis of the system of coupled chemostats and the sum of the maximum syntheses of the isolated chemostats or excess yield cannot be positive. We show that the excess yield can be positive only in the heterogeneous case. In these cases, under some conditions, the coupling of chemostats can make it possible to obtain a higher productivity compared to the case of isolated chemostats. We illustrate our theoretical results with numerical simulations with various examples corresponding to slow and fast migrations.