Overview
Negative regulators inhibit certain reactions and either lower their reaction rate or stop them altogether.
Our method for pathway inference is the first to address negative regulation.
We incorporate two orders of negative regulation: first order -- where a factory is invalid if it creates any metabolite that negatively regulates a reaction also in the factory, and second order -- where a factory is invalid if any molecule that negatively regulates a reaction in the factory can be created from the sources of the factory.
Odinn only returns factories that are valid under these orders of negative regulation.
First-order negative regulation, where a factory is invalid if it creates any metabolite that negatively regulates a reaction also in the factory, is handled directly as constraints within the MILP.
Second-order negative regulation, where a factory is invalid if any molecule that negatively regulates a reaction in the factory can be created from the active sources of the factory, is handled by iteratively solving a series of MILPs, where constraints are added to exclude invalid factories at each iteration.
Source code
The MILP including negative regulation and documentation on how to exclude factories violating negative regulation are available on GitHub.