using Symbolics
using LinearAlgebra
using LatexifyKing-Altman method for enzyme kinetics
Make a (n-1)x(n-1) matrix by skipping the i-th row and i-th column
function skip_colrow(mat, i::Int)
rows = collect(1:size(mat, 1))
cols = collect(1:size(mat, 2))
return mat[rows.!=i, cols.!=i]
endskip_colrow (generic function with 1 method)Accumulate rates into the transition rate matrix (K matrix)
function accumulate_rate!(mat, rate, src::Int, dst::Int)
mat[dst, src] += rate
mat[src, src] -= rate
return mat
endaccumulate_rate! (generic function with 1 method)SOD McAdam model
From McAdam, 1977
- k1: EA + O2- => EB + O2
- k1: EB + O2- => EA + H2O2
- k3: EB + O2- => EC
- k5: EC => EA
@variables k1 k3 k5 sox
@time sol_sod = let
k12 = k1 * sox
k21 = k1 * sox
k23 = k3 * sox
k31 = k5
mat = fill(Num(0), 3, 3)
accumulate_rate!(mat, k12, 1, 2)
accumulate_rate!(mat, k21, 2, 1)
accumulate_rate!(mat, k23, 2, 3)
accumulate_rate!(mat, k31, 3, 1)
fA = det(skip_colrow(mat, 1))
fB = det(skip_colrow(mat, 2))
fC = det(skip_colrow(mat, 3))
sol_sod = Dict(
:A => fA |> expand,
:B => fB |> expand,
:C => fC |> expand,
:DEN => (fA + fB + fC) |> expand
)
end 6.652386 seconds (14.22 M allocations: 690.311 MiB, 4.03% gc time, 99.88% compilation time)Dict{Symbol, Symbolics.Num} with 4 entries:
:A => k1*k5*sox + k3*k5*sox
:DEN => 2k1*k5*sox + k3*k5*sox + k1*k3*(sox^2)
:B => k1*k5*sox
:C => k1*k3*(sox^2)Superoxide consumption rate
@time vSOD = sox * (k1 * (sol_sod[:A] + sol_sod[:B]) + k3 * sol_sod[:B]) / (sol_sod[:DEN]) |> simplify 23.745200 seconds (38.18 M allocations: 1.817 GiB, 2.35% gc time, 99.92% compilation time: <1% of which was recompilation)\[ \begin{equation} \frac{\left( 2 \mathtt{k1}^{2} \mathtt{k5} + 2 \mathtt{k1} \mathtt{k3} \mathtt{k5} \right) \mathtt{sox}}{2 \mathtt{k1} \mathtt{k5} + \mathtt{k3} \mathtt{k5} + \mathtt{k1} \mathtt{k3} \mathtt{sox}} \end{equation} \]
Complex I simplified Markevich model
Four-state Q-site reaction cycle.
mat_c1q = let
@variables b12 b21 b23 b32 b34 b43 b41 b14
mat = fill(Num(0), 4, 4)
accumulate_rate!(mat, b12, 1, 2)
accumulate_rate!(mat, b21, 2, 1)
accumulate_rate!(mat, b23, 2, 3)
accumulate_rate!(mat, b32, 3, 2)
accumulate_rate!(mat, b34, 3, 4)
accumulate_rate!(mat, b43, 4, 3)
accumulate_rate!(mat, b41, 4, 1)
accumulate_rate!(mat, b14, 1, 4)
end\[ \begin{equation} \left[ \begin{array}{cccc} - \mathtt{b12} - \mathtt{b14} & \mathtt{b21} & 0 & \mathtt{b41} \\ \mathtt{b12} & - \mathtt{b21} - \mathtt{b23} & \mathtt{b32} & 0 \\ 0 & \mathtt{b23} & - \mathtt{b32} - \mathtt{b34} & \mathtt{b43} \\ \mathtt{b14} & 0 & \mathtt{b34} & - \mathtt{b41} - \mathtt{b43} \\ \end{array} \right] \end{equation} \]
@time weights_c1q = [(-1)^(4-1) * det(skip_colrow(mat_c1q, i)) |> expand for i in 1:4] 0.818260 seconds (1.44 M allocations: 70.026 MiB, 99.32% compilation time)\[ \begin{equation} \left[ \begin{array}{c} \mathtt{b21} \mathtt{b32} \mathtt{b41} + \mathtt{b21} \mathtt{b32} \mathtt{b43} + \mathtt{b21} \mathtt{b34} \mathtt{b41} + \mathtt{b23} \mathtt{b34} \mathtt{b41} \\ \mathtt{b12} \mathtt{b32} \mathtt{b41} + \mathtt{b12} \mathtt{b32} \mathtt{b43} + \mathtt{b12} \mathtt{b34} \mathtt{b41} + \mathtt{b14} \mathtt{b32} \mathtt{b43} \\ \mathtt{b12} \mathtt{b23} \mathtt{b41} + \mathtt{b12} \mathtt{b23} \mathtt{b43} + \mathtt{b14} \mathtt{b21} \mathtt{b43} + \mathtt{b14} \mathtt{b23} \mathtt{b43} \\ \mathtt{b12} \mathtt{b23} \mathtt{b34} + \mathtt{b14} \mathtt{b21} \mathtt{b32} + \mathtt{b14} \mathtt{b21} \mathtt{b34} + \mathtt{b14} \mathtt{b23} \mathtt{b34} \\ \end{array} \right] \end{equation} \]
total_weight_c1q = sum(weights_c1q)\[ \begin{equation} \mathtt{b12} \mathtt{b23} \mathtt{b34} + \mathtt{b12} \mathtt{b23} \mathtt{b41} + \mathtt{b12} \mathtt{b23} \mathtt{b43} + \mathtt{b12} \mathtt{b32} \mathtt{b41} + \mathtt{b12} \mathtt{b32} \mathtt{b43} + \mathtt{b12} \mathtt{b34} \mathtt{b41} + \mathtt{b14} \mathtt{b21} \mathtt{b32} + \mathtt{b14} \mathtt{b21} \mathtt{b34} + \mathtt{b14} \mathtt{b21} \mathtt{b43} + \mathtt{b14} \mathtt{b23} \mathtt{b34} + \mathtt{b14} \mathtt{b23} \mathtt{b43} + \mathtt{b14} \mathtt{b32} \mathtt{b43} + \mathtt{b21} \mathtt{b32} \mathtt{b41} + \mathtt{b21} \mathtt{b32} \mathtt{b43} + \mathtt{b21} \mathtt{b34} \mathtt{b41} + \mathtt{b23} \mathtt{b34} \mathtt{b41} \end{equation} \]
Complex I Gauthier model
Based on the Gauthier, 2013 model
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\[ \begin{equation} \left[ \begin{array}{ccccccc} - \mathtt{a12} - \mathtt{a16} & \mathtt{a21} & 0 & 0 & 0 & \mathtt{a61} & 0 \\ \mathtt{a12} & - \mathtt{a21} - \mathtt{a23} - \mathtt{a24} & \mathtt{a32} & \mathtt{a42} & 0 & 0 & 0 \\ 0 & \mathtt{a23} & - \mathtt{a32} - \mathtt{a34} & \mathtt{a43} & 0 & 0 & 0 \\ 0 & \mathtt{a24} & \mathtt{a34} & - \mathtt{a42} - \mathtt{a43} - \mathtt{a47} & 0 & 0 & \mathtt{a74} \\ 0 & 0 & 0 & 0 & - \mathtt{a56} - \mathtt{a57} & \mathtt{a65} & \mathtt{a75} \\ \mathtt{a16} & 0 & 0 & 0 & \mathtt{a56} & - \mathtt{a61} - \mathtt{a65} & 0 \\ 0 & 0 & 0 & \mathtt{a47} & \mathtt{a57} & 0 & - \mathtt{a74} - \mathtt{a75} \\ \end{array} \right] \end{equation} \]
@time weights_c1g = [(-1)^(7-1) * det(skip_colrow(mat_c1g, i)) |> expand for i in 1:7] 0.476795 seconds (840.93 k allocations: 39.818 MiB, 85.28% compilation time)\[ \begin{equation} \left[ \begin{array}{c} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a21} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} \\ \mathtt{a12} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a16} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} \\ \mathtt{a12} \mathtt{a23} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a23} \mathtt{a42} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a23} \mathtt{a43} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a43} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a23} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a23} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a24} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} \\ \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a23} \mathtt{a34} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a24} \mathtt{a32} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a24} \mathtt{a34} \mathtt{a57} \mathtt{a65} \mathtt{a74} \\ \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a65} \mathtt{a75} \\ \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a75} \\ \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a61} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a61} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a57} \mathtt{a61} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a61} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a65} \\ \end{array} \right] \end{equation} \]
Total weight
total_weight_c1g = sum(weights_c1g)\[ \begin{equation} \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a61} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a34} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a23} \mathtt{a42} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a23} \mathtt{a43} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a23} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a61} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a57} \mathtt{a61} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a32} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a61} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a34} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a24} \mathtt{a43} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a24} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a12} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a12} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a12} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a32} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a21} \mathtt{a34} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a21} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a23} \mathtt{a34} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a23} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a23} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a24} \mathtt{a32} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a75} + \mathtt{a16} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a57} \mathtt{a65} + \mathtt{a16} \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a65} \mathtt{a75} + \mathtt{a16} \mathtt{a24} \mathtt{a34} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a24} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a16} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a43} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a21} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a61} \mathtt{a74} + \mathtt{a21} \mathtt{a34} \mathtt{a42} \mathtt{a57} \mathtt{a65} \mathtt{a74} + \mathtt{a21} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a23} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a24} \mathtt{a32} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} + \mathtt{a24} \mathtt{a34} \mathtt{a47} \mathtt{a56} \mathtt{a61} \mathtt{a75} \end{equation} \]
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