In this module, the two-dimensional line shape models are developed for use with TITAN [1]. TITAN was developed by Chris Waudby and described in [Waudby, C. A., A. Ramos, L. D. Cabrita and J. Christodoulou (2016). "Two-dimensional NMR lineshape analysis." Scientific Reports 6: 8]. You can obtain TITAN from http://www.nmr-titan.com.

The kinetic matrices for these models were developed in Mathematical Models

Contents

Introduction

- Both
**IDAP/code**and**titan/**folders should be on MATLAB path

- IDAP models adapted for TITAN are in
**IDAP/****code/+line_shape_2D_TITAN**.

- The scripts directing line shape simulations and fitting in TITAN are in
**IDAP/code/Control_scripts_archive/TITAN_interface**

- Use of these models is described in Tutorials of 2D NMR line shapes: IDAP_TITAN_model_library

Models

**U-R - conformational selection**

**U-RL - induced fit**

**U-R-RL - combined conformational selection and induced fit**

**U-nR family**(multiple unbound isomers)

**U-1R**

*NOTE: order of species is different than in U-R!*

**U-2R**

**"simple"**These models are simplified by assuming that all isomerization constants from R to R(n*) species are equal and all isomerization constants between starred species are also equal. Equilibrium constants for C transitions are all equal to 1.

**U-3R-simple - example of fully vectorized code (no gain in speed observed!)**

**U-4R-simple**

**U-5R-simple**

**U-nR-RL family**(multiple unbound isomers + induced fit)

**U-1R-RL**- NOT DONE

*NOTE: order of species is different than in U-R-RL!*

- U-2R-RL
<-- decided to do it later, if needed.

**"Simple"**These models are simplified by assuming that all isomerization constants from R to R(n*) species are equal and all isomerization constants between starred species are also equal. Equilibrium constants for C transitions are all equal to 1.

**nU-R-RL family**(multipe binding-competent isomers making multiple encounter complexes but isomerizing into one final state)

**"Simple"**These models are simplified by assuming that all isomerization constants in B1 transitions are equal, in B2 transitions are equal, and all binding constants are equal. This automatically means equilibrium constants in C transitions are equal to unity (identical populations of isomers)

**5U-R-RL-simple****- most recent implementation**

--- Models to be added --------

- U-L
- U-R-L
- U-R-RL-RM

- U-R2
- U-L2
- U-R2L2
- B_R2_R2L2
- B_bidentateL

Developer's notes

- All IDAP models use K_A instead of log10(K_A). Log was used originally in IDAP to allow for a more uniform Monte-Carlo sampling of starting parameters. However, this has not worked well . Use of K_A is aligned with the LineShapeKin Simulation conventions.

- I am setting all concentration units to mol/L. This means that
input values for the Rtotal and Ltotal will have to be scaled when comparing to original TITAN models utilizing TITAN sample data.

- IDAP thermodynamic equation solvers cannot deal with ligand concentration equal to zero. Set the ligand-free point to a very small value: 1e-9 or 1e-6

- The
**TITAN_IDAP_interface**is a class to derive all models for TITAN from.**TITAN_IDAP_interface**adds output of the populations and also checks for the zeros in L concentration array.

- Original TITAN models may be used using IDAP-TITAN control scripts if their parent class is changed to
**TITAN_IDAP_interface**.

- It is possible to include IDAP models to TITAN GUI:

- copy
**setup_binding_model.m**from the**titan/**folder to your working folder.

- insert references to necessary IDAP models in
**bm_list**in**setup_binding_model()**function. Example:

*bm_list = {*

**line_shape_2D_TITAN.U_R_RL**

bmNoExchange

bmTwoState

...

- When you start TITAN in that folder, and it will use your edited
**setup_binding_model.m**instead of the original one from**titan/**.

- copy

**Warning about the units in the original TITAN models**

TITAN operates with all concentrations in **micromoles** per L. This would not have effect on populations as the equilibrium constant is also supplied in micromolar units. However, kinetic matrices are calculated using equilbrium concentration of [L] and that comes out in micromoles from the calculations! This may be a problem in some cases!

PSEUDOFIRST-ORDER RATE CONSTANT IS OK: I checked the two-state model. The kon is derived as koff/Kd. It will be 1000x smaller than it should be. However, when calculating the kab we multiply kon by Lfree, which
is 1000 larger because of the micromolar units. Therefore, there is compensation of effect of the units in the original TITAN models (at least in bmTwoState.m).

- take a model from
**line_shape_2D_TITAN/**with necessary number of states as a template

- Manually insert number of states and number constants in the
**Properties**section

- Insert thermodynamic calculation

- Insert kinetic matrix

- make sure population vector is called
**p0**and transposed to a column.

- Normalize it by
**Rtotal**

- Implement vectorized population calculations for vectorized equilbirium thermodynamic models (check in Mathematical_models/Equilibrium_thermodynamic_models/index.htm)

- Test calculations using HSQC mode vs LineShapeKin Simulation and vs TITAN where possible.

- Current implementation of TITAN (as of 2018) requires re-picking the ROI for fitting every time the user switches the model. However, ROI must be exactly identical in fitting with different models to be able to do hypothesis testing. I need to split extraction of ROI from setting the peak positions.
- Workflow to use
- Define pulse sequence
- Create ROI
- Define model
- Fit