This notebook tests the derivation of the Master equation and related functionality in MuMoT.¶

import mumot

mumot.__version__

%%model
$
A -> B : k_1
B -> A : k_2
$

model1 = mumot.parseModel(In[2])

model1.showNoiseEquations()

model1.showNoiseSolutions()

model1.showStoichiometry()

model1.showODEs()

model1.showMasterEquation()

model1.showVanKampenExpansion()

model1.showODEs(method='vanKampen')

model1.showFokkerPlanckEquation()

%%model
$
U -> A : g_1
U -> B : g_2
A -> U : a_1
B -> U : a_2
A + U -> A + A : r_1
B + U -> B + B : r_2
A + B -> A + U : s_1
A + B -> B + U : s_2
$

model2 = mumot.parseModel(In[12])

model2.showNoiseEquations()

model2.showNoiseSolutions()

model2.showODEs()

model2.showStoichiometry()

model2.showMasterEquation()

model2.showVanKampenExpansion()

model2.showODEs(method='vanKampen')

model2.showFokkerPlanckEquation()

model3 = model2.substitute('a_1 = 1/v_1, a_2 = 1/v_2, g_1 = v_1, g_2 = v_2, r_1 = v_1, r_2 = v_2')

model3.showNoiseEquations()

model3.showRates()

model3.showReactants()

model3.showODEs()

model3.showStoichiometry()

model3.showMasterEquation()

model3.showVanKampenExpansion()

model3.showODEs(method='vanKampen')

model3.showFokkerPlanckEquation()

%%model
$
U -> A : g_1
U -> B : g_2
U -> C : g_3
A -> U : a_1
B -> U : a_2
C -> U : a_3
A + U -> A + A : r_1
B + U -> B + B : r_2
C + U -> C + C : r_2
A + B -> A + U : s_1
A + B -> B + U : s_2
A + C -> A + U : s_3
A + C -> C + U : s_4
B + C -> B + U : s_5
B + C -> C + U : s_6
$

model4 = mumot.parseModel(In[44])

model4.showNoiseEquations()

model4.showRates()

model4.showReactants()

model4.showODEs()

model4.showStoichiometry()

model4.showMasterEquation()

model4.showVanKampenExpansion()

model4.showODEs(method='vanKampen')

model4.showFokkerPlanckEquation()

model5 = model4.substitute('s_1 = s, s_2 = s, s_3 = s, s_4 = s, s_5 = s, s_6 = s, U = N-A-B-C')

model5.showRates()

model5.showReactants()

model5.showODEs()

model5.showStoichiometry()

model5.showMasterEquation()

model5.showVanKampenExpansion()

model5.showODEs(method='vanKampen')

model5.showFokkerPlanckEquation()