solveLP.lp4

% solve[LP].lp4
% Logic Program in Clingo[LP] - Clingcon ASP format
% Finds fluxes that belongs to the stoichiometric matrix kernel
% Defines an heuristic for them to be enumerated subset minimal

% Domain upper bound for flux values
#const nb=500000.

% Tells clingo that it is okay if the input file does not contain these predicates
reversible(do_not_use, do_not_use).

% Rule A: Since all reactions are irreversible, they must have a nonnegative flux
&dom{0..nb} = flux(R) :- reaction(R).

% Rule B: Two irreversible reactions issued from the splitting of one reversible reaction are mutually exclusive
:- support(R1); support(R2); 1 {reversible(R1, R2); reversible(R2, R1)} 1; reaction(R1); reaction(R2).

	% Note : {a;b} is chosen because relation reversible(X,Y) is symetric
	% This is a precaution in case the relation was only defined one-way

% Rule C : At least one reaction must be used 
:- not support(R) : reaction(R).

% Rule D : For each metabolite, the sum, weighted by the stoichiometry, of fluxes of all reactions is null
&sum{C*flux(R) : stoichiometry(M, R, C), reaction(R)} = 0 :- metabolite(M).

% Compute support
support(R) :- &sum{flux(R)} > 0; reaction(R).

% Support minimization heuristic
#heuristic support(R). [1, false]

% Only show support atoms
#show support/1.