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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.

Contents

• "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

• Dimerization blocking the binding site  - U-R2 model

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    "Pre-existing equilibrium"  -   U-R model

• Location:
  • IDAP/IDAP_Online_Documentation/Tutorials/NMR_line_shapes/Tutorial_8.Overview_and_testing_three_state_model/U_R_model

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• Create 1D datasets using LineShapeKin Simulation. I am creating simulations in two opposite exchange regimes to demonstrate the difference in setting the starting parameters to fits these kinds of data.
  NOTE: make sure your spectral ranges are all in positive values!!!
  
  

  Fast exchange scenario

  • Simulate setup_fast U_R_Af_Bf
    • Result: summary_report
      
      

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  Slow exchange scenario

  • Simulate setup_slow U_R_As_Bs
    • Result: summary_report

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• Fit fast exchange data with IDAP
  • Fast_exchange_Fitting/main_U_R_model_1D.m
    • Inspect the data:
      • run with setup_parameters.Fitting_mode='show-data-only'
      • see output in/ Raw_Data/
      • check the fitting of the first and the last traces
      • make choices on the estimates for frequencies of the three states in terms of percentage of distance between initial and final fast-exchange peaks or absolute frequency values (setup_parameters.line_shape_estimate_mode)

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    • Enter the initial parameters for the model and inspect quality of initial approximation. Try to get as close as possible!
      • run with setup_parameters.Fitting_mode='single-initial-approximation'
      • output in IDAP_dataset.U_R-model.single-initial-approximation.initial_parameters

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    • Run fitting in 'fit-only' mode
      • choose one dataset: setup_parameters.selected_residue_number=1
      • set  setup_parameters.Fitting_mode='single'
      • use 'GlobalSearch' - slow but most robust algorithm
      • output in IDAP_dataset.U_R-model.single.Fit

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    • Determination of error intervals

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    "Induced fit" - U-RL model

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    Equivalent two-site binding -  B-macro model

• Path:
  • IDAP/IDAP_Online_Documentation/Tutorials/NMR_line_shapes/Tutorial_8.Overview_and_testing_three_state_model/B_model

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• simulate:
  • B_coop1.txt
    • Ka_names A1a A1b A2a
      Ka 1e4 1e4 1e4
    • # Rate constants of REVERSE reactions
      k_names A1a A1b A2a A2b
      k2 1000 1000 10 10
    • 
      setup.txt
  • summary_report

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• Fit with IDAP:
  • main_B_macro_model_1D_LR_LB_SF.m

  • Expected parameters	Initial approximation:
    log10(K_A1)= 4   log10(K_A2) = 4 k_2_A1= 1000 k_2_A2= 10 w0_RL= 200 w0_RL2 = 300 FWHH_RL= 10 FWHH_RL2 = 10

	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

CONCLUSIONS:

• The B-macro model works but fitting is difficult, slow and unstable (better algorithm may bring worse result).

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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"

IDAP/IDAP_Online_Documentation/Tutorials/NMR_line_shapes/Tutorial_8.Overview_and_testing_three_state_model/U_R2_FWHHconstr_model

• Matlab code: U_R2_FWHHconstr_testing.m
• HTML report: U_R2_FWHHconstr_testing.html

Compare to simulations with LineShapeKin Simulation 

• simulated_U_R2/
  • make 30 points per trace to simulate realistic data with 5-10 points per peak envelope
  • Make sure not to use zero frequencies in X data!
  • Simulate setup U_R2

# 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

test_fitting/

main_U_R2_FWHHconstr_model_1D.m

Monte-Carlo run (very slow)

Conclusions:

 Implementation of the U_R2_FWHHconstr-model  in IDAP was validated

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