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Three-state models overview and testing



In this document I follow my introduction of three state models for fitting of series of 1D NMR datasets in IDAP. I will simulate the line shape data with LineShapeKin Simulation and then demonstrate how line shape fitting may be done with IDAP. The user may follow the same protocol to fit real experimental data with these example workflows.




    "Pre-existing equilibrium"  -   U-R model


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    "Induced fit" - U-RL model



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    Equivalent two-site binding -  B-macro model

  GlobalSearch Simplex


log10(K_A1) = 5.58

log10(K_A2)= 4.46

k_2_A1= 6.227387e+02

:k_2_A2 = 9.465268e+00

 w0_RL = 1.479257e+02  

( w0_RL2 = 2.956745e+02  

 FWHH_RL  = 3.011751e+01

 FWHH_RL2  = 2.425213e+01

 ScaleFactor = 3.286271e+02

Total sum of squares (SS) = 1.15811

Worse than simplex

log10(K_A1)= 5.6 

log10(K_A2) = 4.2

k_2_A1= 5.436067e+03

k_2_A2= 1.033124e+01

w0_RL= 1.486588e+02

w0_RL2 = 2.985160e+02

FWHH_RL= 4.800909e+01

FWHH_RL2 = 2.054429e+01

ScaleFactor= 3.409475e+02

Total sum of squares (SS) = 0.889889

  Fitting time: 1100 sec = 20 min Fitting time: 200 sec = 3 min





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Dimerization blocking the binding site  - U-R2 model

Test of the basic U-R2 model "U_R2-model"

Done in Tutorial 6: tutorial_6_testing_new_model

Test of the constrained U-R2 model "U_R2_FWHHconstr-model"


Compare to simulations with LineShapeKin Simulation 

# Unique model identifier
Model_code U_R2

# Model description
Description Slow binding, fast dimerization

# Association constants
Ka_names A B
Ka 1e4 1e3

# Rate constants of REVERSE reactions
k_names A B
k2 5 2000

# Names of NMR-active species
Species_names R RR RL

# Names of NMR unobservable species
NMR_invisible_species_names L

# Chemical shifts of pure species, 1/s
w0 1400 600 1700

# Relaxation rates of pure species, 1/s
R2 90 180 90

# Heat of formation of the species, relative units
# The original species is a standard state with dH=0 !
dH 0 1 -2



Observation: The IDAP model code reproduced the LineShapeKin result.

Fitting with U_R2_FWHHconstr-model







Fitting time: 41 sec


log10(K_A)= 4.1e+00

log10(K_B)= 3.2e+00

k_2_A = 5.7

k_2_B = 3.3e+03

w0_R = 1.4e+03

w0_R2 = 7.110175e+02

FWHH_R_monomer = FWHH_RL = 1.896252e+02

ScaleFactor = 3.524467e+02

Total sum of squares (SS) = 0.00418529
Statistics per dataset:
(1) "IDAP_dataset-1": Priority=1, R^2=0.997, 12% of total SS, Model= "U_R2_FWHHconstr-model"
(2) "IDAP_dataset-2": Priority=1, R^2=0.998, 7.4% of total SS, Model= "U_R2_FWHHconstr-model"
(3) "IDAP_dataset-3": Priority=1, R^2=0.997, 8.8% of total SS, Model= "U_R2_FWHHconstr-model"
(4) "IDAP_dataset-4": Priority=1, R^2=0.997, 7.4% of total SS, Model= "U_R2_FWHHconstr-model"
(5) "IDAP_dataset-5": Priority=1, R^2=0.997, 7.4% of total SS, Model= "U_R2_FWHHconstr-model"
(6) "IDAP_dataset-6": Priority=1, R^2=0.996, 14% of total SS, Model= "U_R2_FWHHconstr-model"
(7) "IDAP_dataset-7": Priority=1, R^2=0.997, 13% of total SS, Model= "U_R2_FWHHconstr-model"
(8) "IDAP_dataset-8": Priority=1, R^2=0.997, 15% of total SS, Model= "U_R2_FWHHconstr-model"
(9) "IDAP_dataset-9": Priority=1, R^2=0.998, 14% of total SS, Model= "U_R2_FWHHconstr-model"


Monte-Carlo run (very slow)


 Implementation of the U_R2_FWHHconstr-model  in IDAP was validated

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