Reaction-diffusion model using PDE Toolbox

I am trying to solve the following reaction-diffusion model using the PDE toolbox:

The tricky part is the last term in the first equation in which the product of two functions (L and R) is present. I managed to solve it using 'pdepe' for certain symmetries, but for a general geometry I would need to use 'solvepde', but as far as I know, multiplying two functions to be solved for is not allowed. Is there a way to do it in MATLAB?

[Torsten]

k_on*L*R is a source term and can be put in the "f" in the description of the PDEs that can be solved by the PDE Toolbox.

I think the last two equations for LR and R will cause more problems since they are ODEs, not PDEs (spatial derivatives are missing).