King-Altman method for enzyme kinetics

using Symbolics
using LinearAlgebra # det()

function skip_colrow(mat, i::Int)
    rows = collect(1:size(mat, 1))
    cols = collect(1:size(mat, 2))
    return mat[rows.!=i, cols.!=i]
end

function accumulate_rate!(mat, rate, src::Int, dst::Int)
	mat[dst, src] += rate
	mat[src, src] -= rate
	return mat
end

mat_c1g = let
	@variables a12 a21 a65 a56 a61 a16 a23 a32 a34 a43 a47 a74 a57 a75 a42 a24
	mat = fill(Num(0), 7, 7)
	accumulate_rate!(mat, a12, 1, 2)
	accumulate_rate!(mat, a21, 2, 1)
	accumulate_rate!(mat, a65, 6, 5)
	accumulate_rate!(mat, a56, 5, 6)
	accumulate_rate!(mat, a61, 6, 1)
	accumulate_rate!(mat, a16, 1, 6)
	accumulate_rate!(mat, a23, 2, 3)
	accumulate_rate!(mat, a32, 3, 2)
	accumulate_rate!(mat, a34, 3, 4)
	accumulate_rate!(mat, a43, 4, 3)
	accumulate_rate!(mat, a47, 4, 7)
	accumulate_rate!(mat, a74, 7, 4)
	accumulate_rate!(mat, a57, 5, 7)
	accumulate_rate!(mat, a75, 7, 5)
	accumulate_rate!(mat, a42, 4, 2)
	accumulate_rate!(mat, a24, 2, 4)
end

@time weights_c1g = [(-1)^(7-1) * det(skip_colrow(mat_c1g, i)) |> expand for i in 1:7]

total_weight_c1g = sum(weights_c1g)