Multi-Enzyme Pathway Optimisation Through Star-Shaped Reachable Sets
Mazurenko, S., Damborsky, J., Prokop, Z.
ADVANCES IN INTELLIGENT SYSTEMS AND COMPUTING 616: 9-17
Fdez-Riverola, F., Mohamad, M. S., Rocha, M., De Paz, J. F., Pinto, T.
This article studies the time evolution of multi-enzyme pathways. The non-linearity of the problem coupled with the infinite dimensionality of the time-dependent input usually results in a rather laborious optimization. Here we discuss how the optimization of the input enzyme concentrations might be efficiently reduced to a calculation of reachable sets. Under some general conditions, the original system has star-shaped reachable sets that can be derived by solving a partial differential equation. This method allows a thorough study and optimization of quite sophisticated enzymatic pathways with non-linear dynamics and possible inhibition. Moreover, optimal control synthesis based on reachable sets can be implemented and was tested on several simulated examples.