Seitenhistorie

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In this tutorial we will

1. determine learn how to calibrate NOE data to obtain distance restraints,
2. derive a ligand bio-active conformation protein structure with the software CYANA,
3. introduce the NMR² approach for protein-ligand 3D structure elucidation.

To this end we will use the software CYANA, NMR², and excel (or similar)

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Content

• Software
  
• Slides

CYANA Setup 

Please follow the following steps carefully (exact Linux commands are given below; you may copy them to a terminal):

1. Go to your home directory (or data directory)
2. Get the data for the practical from the server (to come data.zip)
3. Unpack the input data for the practical
4. Get the demo version of CYANA for this practical (or here CYANA webpage)
5. Unpack CYANA
6. Go to the downloaded CYANA folder
7. Test whether CYANA can be started by typing, './cyana'
8. If you are a mac user you may need to remove the safety quarantine
9. Setup the CYANA environment variables
10. Go to the newly created directory 'data'
11. Test whether CYANA can be started by typing its name, 'cyana'
12. Exit from CYANA by typing 'q' or 'quit'

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./cyana   

CYANA 3.98.15 (macarm-gfortran)

Copyright (c) 2002-22 Peter Guentert. All rights reserved.
___________________________________________________________________

    Demo license valid for specific sequences until 2024-12-31.

    Library file "/Users/julienorts/Downloads/cyana-3.98.15/lib/cyana.lib" read, 41 residue types.

To be able to execute cyana in any directory, one options is to create an alias. For that,

1. open the ~/.zshrc  (or ~/.bashrc) file
2. add a line with:
   alias cyana='"download path"/cyana-3.98.15/cyana
   (replacing the "download path" with the actual one)
3. source the file in the terminal that you work:
   $ source ~/.zshrc (or ~/.bashrc)
   also newly opened terminal (command line) will have the cyana command available - without the need to execute "source"

Hint: More information on the CYANA commands etc. is in the CYANA 3.0 Reference Manual.

Remark: CYANA is a proprietary software. For any installation problem, contact Peter Güntert, the author of CYANA.

Molecular viewer  

You need also a molecular viewer capable of saving mol2 file

1. Download Chimera (to your personal laptop) from: Chimera
2. Optionally, create also an alias, so that Chimera can be opened from a command line, with a ".pdb" file as an argument. If Chimera was installed into /Applications, the alias for the .zshrc file would look like:
   alias chimera='/Applications/Chimera.app/Contents/MacOS/chimera'

Part 1

Introduction for task 1:

Download the zip file for the workshop: workshopData.zip

Open the simulation_data.xlsx in part1/task1_to_3 directory. These are taken as the experimental data for this task. We will start with the structure calculation of the ligand (drug-like) molecule. From the NOESY spectra, we obtain the cross-relaxation rates using the intensity (volume) of the cross peaks at a known (experimentally set) mixing time.These are directly related to the interatomic distances, which will determine the conformation of the molecule.

Task 1 : Plot the cross peak intensities as  function of the mixing time:

• The NOESY buildup curves. "Intramolecular NOE"
• In the table "Intramolecular NOE", we have the intensity at different mixing times (up to  0.1s) given at the first line.
• Plot those, notice the scale, and shape.

Introduction for task 2:

The NOESY spectrum contain also diagonal cross-peaks. These correspond to the (non-equilibrium Z-) magnetisation decay of the spin-themselves: autorelaxation.

R_ii = ρ_i = b²/d_ij⁶  (J(0) + 3J(ω) + 6J(2ω)) #contribution of one neighbor spin "j" in distance "d".

And the cross-relaxation rate between H-spins "i" and "j" is: 

R_ij = σ_ij = b²/d_ij⁶ (-J(0)  + 6J(2ω)),

where "b" is the dipole-dipole interaction strength, and "J(ω)" is the spectral density at angular frequency "ω".  The spectral density J is the Fourier transformation of the rotational correlation function, and it shows the distribution of frequencies of the molecular rotational motion.

Task2: Plot the diagonal peak intensities as function of the mixing time:

• Notice the scale and shape.

Introduction for task 3:

The initial rate of the NOESY cross-peak, is directly proportional to 1/distance⁶ between the respective spins (protons). The other dependency comes from the rotational correlation time of the molecule, which is dependent on temperature, solvent viscosity, solvation shell of the molecule, shape of the molecule, and in the case of a small molecule partly bound to a larger protein, the effective correlation time is also modulated by this partial bounding - the chemical exchange. Therefore, it is practical to leave these dependencies aside, and calibrate the relation between the NOE buildup rate (cross-relaxation rate) and the interproton distance using a known distance. Fortunately, there are many proton pairs in the molecule with fixed distance, simply due to the covalent structure.

...

a: Identify a suitable pair of protons (H-atoms) and measure their distance.

• Open the the ligand molecule (nutlin.pdb).
  $ chimera nutlin.pdb
• Open the command line: Tools→ General Controls → Command Line and type
• distance @H9,H10
  This will be the reference distance r_Ref.

b: calculate the cross-relaxation rate.

• In a separate column, assuming a linear buildup in time: chose now the first mixing time to get the initial cross-relaxation rate.
• Note that this cross-relaxation rate is not normalized (it is not in [s^-1]), but since we will do the referencing using a know distance, we do not have to normalize.

c:  Calibrate the distances.

For the reference pair of protons. We have now also the reference sigma σ_Ref.
Use the formula
    r_ij = r_Ref * (σ_Ref/σ_ij)^(1/6). [Eq. 1] Vogeli 2014, Eq. 63b
to calculate the other distances between other atoms (in a separate column).

Introduction for task 4:

There is no closed-form formula to calculate the conformation (structure) from a set of distances. The setup starts with defining an energy penalty for every experimental distance not fulfilled by the molecular conformation. These are also called distance restraints. Starting from one chosen conformation, and trying to minimize the structure (using steepest descent or other local method) to fulfill the distances measured by NOE (or any other means) would fail: the structure would end-up in a local minimum. Instead we have to search for a global minimum. A commonly used algorithm for a global minimum is called simulated annealing, where the molecule is heated up such that high energy barriers (due to van-der Waals clashes) can be surpassed. By a subsequent cooling, the imposed distance restraints will drive the molecule towards the conformation with minimal violation of the distance restraints. Many attempts will nevertheless end up in different local minima, and hence, only a subset of resulting conformers, the lowest-energy conformers will be likely to represent the global minimum.

In practice, we have to input the knowledge about the covalent (bonding) structure of the molecule, and the distance restraints. The bonding structure can be as simple as the chain of amino acids, as the standard programs would have libraries of the actual atomic bonding (topology) for those. For an unknown molecule, we have to supply a full topology ourselves. These would be different for different programs.

We will use a program specialized in structure calculation from NMR restraints: CYANA by Prof. Dr. Peter Günter.

CYANA can obtain the bonding topology from a .mol2 molecular structure file, converting it into its own (library) format, a .lib file. This library file will contain information about one molecule, but since biopolymers - proteins contain chain (sequence) of building blocks like amino acid residues of nucleotides, there has to be also information about the sequence of those building blocks. In our case, it contains only one line: the name and the index of our ligand molecule.

We will use a ready mol.lib file in our exercise. Besides of the physical atoms H, there are also pseudoatoms Q created to replace the chemically equivalent H atoms.  We complete the information by a  .seq file with a "sequence" containing only one line : the name and number of the residue (MOL 999).

The other information: the  distance restraints are obtained by CYANA from a separate text file, where the pairs of atoms are identified by three and three columns, and the distance in Ångströms.

...

In our first calculation of a single molecule (residue), obviously only the atomName1 and atomName2 would be different. Further instructions for CYANA are read from the .cya file.

Task 4: Calculate the structure of the ligand molecule.

• In the task4_to_6 directory,
  create a text file using a text editor, the ".upl" file (mol.upl).
  This name is used in the instruction file for CYANA, the CALC.cya file in this exercise.
• To do that, copy the "Intermolecular NOE" table - the first column contains the 6 columns needed for identification of the atom pair.
• The seventh column has to be the distance calculated above.

...

1. ,
2. try how the exchange of the ligand between free and bound state influence the NOESY spectra,
3. derive the structure of protein-ligand complex,
4. try how the incomplete assignment due to chemically identical atoms affect the NOESY simulation.

Lecture slides can be downloaded here: presentation.pdf

Get a copy of the python scripts and of the exercises:

• download exercises.tgz, for example, to your home (~/), and unpack them (in console/terminal, execute:  tar xzvf exercises.tgz).
• download  the pythonScripts.tgz, if you wish to do the calculations yourself (many are somewhat time consuming). 
  • place the python directory, e.g., to the bin folder. In steps: create by mkdir bin, then, if the scripts were in the Downloads folder, use mv  Downloads/python.tgz bin; cd bin; tar xzvf python.tgz, and ensure that the bin/python is in the $PYTHONPATH:
  • in terminal, execute: export PYTHONPATH=$PYTHONPATH:$HOME/bin/python
• be sure to have also these python libraries installed:
  • scipy, numpy, networkx, sympy, matplotlib, ipython
  • (at the moment, one library  of the pythonScripts.tgz is only as a binary, so unfortunately, the exercises may fully work only with python3.11 and 3.12, please contact me if you encounter problems and if you would like to have the scripts working in your environment)

Installing an additional software:

• for visualization of molecules, install vmd https://www.ks.uiuc.edu/Research/vmd/ 
• for structure calculation using NOESY-derived restraints, install cyana http://www.cyana.org/wiki/Main_Page

Introduction for Task 1:

In a real,  experimental situation, we have never complete set of distances between each pair of protons. The NOE crosspeaks are detectable for distances up to around 5 Angstrom. From these, many signal would share the
same frequency in the spectrum, and thus, assignment between signal and atom (atom pair) can be done only within some group, or not at all. Furthermore, the experimentally-derived distances contain various sources of error.
Partly, it is due to random noise, but partly due to incompletely resolved relayed transfer  and partly due to different (local) dynamics influencing the cross-relaxation rate.
Let's start anyway with the unrealistic situation, where we know all the distances within 5.5 A, accurately.

They are written Upper distance Limit files (here PxP.upl) file, which is used by CYANA.

...

About CYANA

There is no closed-form formula to calculate the conformation (structure) from a set of distances. The setup starts with defining an energy penalty for every experimental distance not fulfilled by the molecular conformation. These are also called distance restraints. Starting from one chosen conformation, and trying to minimize the structure (using steepest descent or other local method) to fulfill the distances measured by NOE (or any other means) would fail: the structure would end-up in a local minimum. Instead we have to search for a global minimum. A commonly used algorithm for a global minimum is called simulated annealing, where the molecule is heated up such that high energy barriers (due to van der Waals clashes) can be surpassed. By a subsequent cooling, the imposed distance restraints will drive the molecule towards the conformation with minimal violation of the distance restraints. Many attempts will nevertheless end up in different local minima, and hence, only a subset of resulting conformers, the lowest-energy conformers will be likely to represent the global minimum.

In practice, we have to input the knowledge about the covalent (bonding) structure of the molecule, and the distance restraints. The bonding structure can be as simple as the chain of amino acids, as the standard programs would have libraries of the actual atomic bonding (topology) for those. For an unknown molecule, we have to supply a full topology ourselves. These would be different for different programs.

We will use a program specialized in structure calculation from NMR restraints: CYANA by Prof. Dr. Peter Günter.

CYANA can obtain the bonding topology from a .mol2 molecular structure file, converting it into its own (library) format, a .lib file. This library file will contain information about one molecule, but since biopolymers - proteins contain chain (sequence) of building blocks like amino acid residues of nucleotides, there has to be also information about the sequence of those building blocks. In our case, it contains only one line: the name and the index of our ligand molecule.

Hint: More information on the CYANA commands etc. is in the CYANA 3.0 Reference Manual.

Remark: CYANA is a proprietary software. For any installation problem, contact Peter Güntert, the author of CYANA.

...

Task 1 (030) - structure of protein

• In 000_cyana subfolder, look at the configuration file, CALC.cya..
  • ( execute in terminal/console: cd 030_proteinGetExactDistancesProtein/000_cyana )
  • cat CALC.cya
• Start the calculation by

  cyana CALC.cya

  • The set of structures will be written in demo.pdb
• After the calculation is ready, look at the .owv file (cat demo.ovw)
  See the target functions, its variation.
  See the RMSD - root mean square displacement.
• To view the structure, use

  vmd demo.pdb #the same name will be produced in all trials of this tutorial
  

  In VMD, the default view shows the interatomic bonds as lines.
• Go to Graphics->Representations
  and change the Drawing Method to CPK.
  To see the common representation for proteins, choose NewCartoon as the Drawing method.
  See how alpha-helices, beta-sheets and loops are identified.
• To simulate the NOESY spectrum using a ready protein-ligand structure (final.pdb), in the 030 folder,

  run ./proteinLigandCalcNOESY.py final.pdb (can take 20 min on some architectures, this same command can be used in all examples with protein and/or ligand) obviously doing different tasks but always starting with assembling the relaxation matrix using the given ".pdb" coordinates, and proceeding with simulation of one or several NOESY spectra.
  

Introduction to Task 2

It used to be common to only simply classify the experimental NOE intensities to strong, medium and weak, and assign corresponding distance ranges of around 2 Angstrom for the strongest and 5.5 to the weakest. Here we try to get the actual distances.

031 - structure of protein from approximate distances

Here we use a technique, which would be a starting point for more accurate methods. It uses spectra recorded for different mixing times. As the NOESY spectrum of a protein can take days to record, recording series of them is a large investment. In that the NOE crosspeak volume (intensity) is divided by a geometric mean of the corresponding diagonal volumes. The slope is a better approximation of the crossrelaxation rate than if this "linearization" or "normalization" was not done. In the case of two isolated nuclei, such buildup curve is approximately linear over longer mixing times. We again start with simulation of the NOESY spectrum instead of having an experimental one.

• Check some of the simulated buildups, the buildupsLinearized in the supplied folders.
  • cd ~/exercises/031_getApproximateDistancesProtein/buildupsLinarized
  • open buidupsLin.pdf
• Without further effort, what are the chances to get accurate distances from these?
• Check how many distance restraints we have: 
  • cd ../000_cyana
  • wc -l PxPapp.upl
• Start the structure calculation (cyana CALC.cya), or see the ready demo.pdb and demo.ovw file.

032 - ... continuation

Here we probe three effortless options to obtain a better set of distances. The first comes from an idea, that short distances are much less likely to be affected by relayed transfer (spin diffusion), so we try to keep only those, within 2.5 Angstrom. Furthermore, to be safer, the approximate distances are multiplied by 1.5

• Check how many distances are left.
  • cd ~/exercises/032_getApproximateDistancesProteinOnlyShortX1p5/000_cyana
  • wc -l PxPapp1p5.upl
• Visualize the structure in VMD (vmd demo.pdb), instead of using only one Drawing Method, press Create Rep in Graphical representation. Keep one as Lines and other as NewCartoon.
• (Doublecklick on one of the copy would hide its visibility.)
• What can be problem when using only this short distances?
• Is the result satisfactory?

034 - ... continuation

In the next simple attempt, we multiply all the distances by a constant factor (1.75) and use again those within 5.5A.  Commonly we would expect up to around 10 constraints per aminoacid residue.  In the previous example, it was still around 12800/97 > 100 restraints per residue. Here we try to use, only every 10th restraints.

• Check how many are left, what is the statistics of the structure calculation. 
  
  • cd ~/exercises/034_getApproximateDistancesProteinX1p75Every10th/000_tryCyanaForProtein
  • wc -l PxPapp.upl
• And visualize the structure in vmd.
• Switch again to NewCartoon drawing method.
• What do you think, were these attempts good enough?

Task 3: Adding the exchange

.
We will investigate the effect of exchange of the ligand between the free state in the solution and bound to the protein.

The NOESY spectrum of the ligand  (the intramolecular NOEs) would be formed as a population  average of the bound and free form. In the free form, cross-relaxation rate is commonly negative, whereas in the bound form, it is positive, the same as the protein. Moreover, it is commonly much larger (absolute value).

035 - structure of a ligand

• For the case of 1:10, 1:1 and 1:200 of protein:ligand fractions, in 035, 035...LessOfLigand and 035...MoreOfLigand.
• Check the simulated NOESY spectra (!note that the axes are not chemical shifts but simply atomic indices!)
  • see the file: NOESYZoomLigand.pdf, the right lower corner is the section corresponding to the ligand.
  • cd ~/exercises/035_genLigandDistancesExact
  • open NOESYZoomLigand.pdf
  • what is the sign and intensity of the NOESY crosspeaks of the ligand - indices around 120 to the end? (compared  the part of the protein)
• Check now with lower concentration of the ligand (1:1 ration with protein)
  • cd ~/exercises/035_genLigandDistancesExactLessOfLigand
  • open NOESYZoomLigand.pdf
  • what is not the sign and intensity of the NOESY crosspeaks of the ligand?
• Check with a high concentration of the protein:
  • cd ~/exercises/035_genLigandDistancesExactMoreOfLigand
  • open NOESYZoomLigand.pdf
  • the same question
• Based on these simulated spectra, how would you determine structure of a ligand in the bound state?

038 - effect of the exchange on NOESY spectra (a toy system) 

The exercise above assumed that the exchange rate between free and bound states is large. Here we will look at a toy system of 3 protons representing a protein, and 2 protons representing a ligand, varying the exchange rate and it's effect on the simulated NOESY spectrum. 

• Look at the coordinates (3 and 2 atoms extracted from a protein structure)
  • cd ~/exercises/038_toySystemWeightIntermolecularNoes
  • cat triPepMod.pdb
• Print the content of the file on the screen 

  • cat NOESYwhenDifferentExchangeRates.txt

  • (or you can extract these using: grep -A 5 "NOESY intensities s" outputKex5e*t10)

•  Look at the last column, last two rows, corresponding to the ligand NOE signals and note their intensity for different exchange frequencies - between 5 Hz and 5 MHz
• What would be the consequence of "not so fast" exchange?
  1. for ligand structure calculation
  2. protein structure calculation
  3. protein-ligand distance extraction?
• experiment by modifying the parameters in parametersForKinMatrixDict.json (open in some text editor, such as vim)
• run ./proteinLigandCalcNOESY.py triPepMod.pdb

Assuming the fast exchange, the derive the correct intermolecular distances between the protein and ligand, the extracted cross-relaxation rates have to be scaled by the population of the components (P, L, PL). The formulas are in presentation, whereas the code is used in the end if the python script. You can check it if there is time left.

039 (advanced intermezzo, no exchange!) - effect of pseudoatoms - chemically equivalent atoms

In this exercise, we will test the consequence of chemically equivalent atoms and hence the incomplete assignment of the NOESY spectrum, when deriving the cross-relaxation rates. This will be tested on a toy system with four atoms, of which, the middle two will be treated as 1) separate 2, pseudoatom containing both.

Image Added

• ./pdbSimNoeFrontEnd.py triPep4H.pdb. (or cat pdbSimNoeFrontEnd.out)
• follow the three tasks (printed by the script) to compare. Answer namely,
• how,  in the (simulated) NOESY spectrum, is the crosspeak between the first and last atom  affected by merging the middle ones?
• how is the extracted cross-relaxation rate (again between the first and last atom)  affected by this merging?

You saw that the NOESY crosspeak can be in principle recovered exactly even if the atoms, mediating the relayed magnetization transfer, are merged into a single pseudoatom. 

• See the time-evolution of the cross-peak (first and last atom) as plotted in "relayedThroughHHorQ.pdf". What does it mean?
  • open relayedThroughHHorQ.pdf
• In the script, change the "specIndex" from 10 to 50; now the NOESY will be simulated for tauMixing=2.5s
• rerun the script. Notice the changes in the output.
• see also the new "relayedThroughHHorQ.pdf" file.

What would be needed to recover the full relaxation matrix - mainly the exact cross-relaxation rates exactly? Would be such an effort useful? 

040 - structure of the protein-ligand complex 

In this exercise, we gather together interatomic distances obtained before, separately from protein (030), for ligand (035), and add the protein-ligand distances. In this first attempt,  we have exact distances (assume we are able to obtain them), with the exception of the protein-ligand distances, since here we do not account for the concentration of the P, L and PL as discussed in (038), and hence the intermolecular calibration is incorrect, when using the known distance of protein atom pair. We will see the possible effect in this exercices

• In 000_cyana subdirectory, combine the ".upl" files obtained before like

  • cat PxP* PxL* LxL* > all.upl

• do the structure calculation
  • cd ~/exercises/040_getCommplexUseProteinLigandDistancesWithoutCorrection/000_cyana
  •  cyana CALC.cya or check already the demo.ovw (cat demo.ovw)
• When viewing the complex using VMD, in Graphical representation, you can select the atoms of proteins by typing "protein" and the ligand as "not protein"
• Showing the protein structure as NewCartoon, we may miss a large portion, due to extra atoms - linker needed by CYANA to keep the ligand as a part of the same molecular graph with the protein
• Remove the linker (and other possible pseudoatoms)  by

  • grep -v Q demo.pdb > demoClean.pdb

  • vmd demoClean.pdb

045 - 

Here the populations (concentrations) are take into account correctly, so also the intermolecular distances are calibrated correctly.

• What is the difference WRT 040 ?
• for that, see first the .upl files, only the distances between protein and ligand:
  • cd ~/exercises/045_getProteinLigandDistancesExactAndFixedWeights
  • head PxLrewight.upl ../040_getCommplexUseProteinLigandDistancesWithoutCorrection/PxL.upl
• see then the resulting protein-ligand structure
  • cd 000_cyana
  • remove the Q atoms in demo.pdb as before and see in VMD

...

Prepared by Dr. Jiří Mareš,shaped by discussion with Prof. Julien Orts, Florian Wolf M.Sc. and other members of the research group 

• Navigate to the task4_to_6 directory in the terminal (command line) and start the CYANA:
  $ cyana
• In the cyana prompt, call the instruction in CALC.cya (leaving out the .cya) to perform the structure calculation:
  cyana> CALC

In a little while, the calculation is ready.
We have now the structure file: demo.pdb
and the overview file about the calculation: demo.ovw

• Close CYANA 
  cyana> exit

Introduction for task 5:

From the theoretical introduction about NOE, we know that the existence of cross-peak between two spins does not have to be caused by the direct through-space transfer of magnetisation between them. Instead, magnetisation transfer via a third nucleus can occur. This is called spin diffusion.

Task 5: Interpret overview file (violations ?)

1. Open the overview file in the text editor or a text viewer (less demo.ovw).
   Find the statement "Restraints violated" and identify into which atoms it belong.
2. Look at structure using chimera.
   1. for clarity, select only the first structure:
      select -> chain -> A demo.pdb #0.1
      select -> Invert (all models)
      actions -> Atoms/Bonds -> delete 
3. Explain the violation.
   Is such a problem more likely for atoms separated by short or long distance?
4. Plot normalized buildup curves
   Calculate normalized NOESY buildup curves, by dividing them with the diagonal peaks (for now, use the first table of the diagonal peaks). Plot the buildup curves and comment on their shape. Can you explain the changed shapes?
   Can you see the case(s) with spin diffusion more clearly?

Task 6: Remove spin diffusion and repeat the calculation

1. Copy the calc_ligand_structure into a new one.
   cp -r task4_to_6 task4_to_6_noSD 
2. Open the mol.upl In the text editor, delete the line with the  problematic restraint(s).
3. Repeat the structure calculation in CYANA:
   cyana> CALC

Compare the structures, check the .ovw file. 

Task 7 (optional)

Instead of the first mixing time in  Task 1,

choose the last mixing time and proceed all the way to calculate the structure in CYANA.

Note the differences in extracted distances and in the resulting structures.

Part 2

...

• In the part2 directory, execute
  cyana CALC.cya

Look at the structures using chimera molecular viewer.

Part 3

Task 1: Calculate the structure of the protein-ligand complex.

1. Prepare the intermolecular distance restraints. For that, follow the same steps as in
   Part1, Task 3, but for the Table: "Intermolecular NOE". Use the same same pair of atoms for calibration of the distances.
2. In the part3 directory, place the the distances into intermolecular.upl
3. Copy also the  mol.upl file here from the Part1, Task 4 (part1/task4_to_6).
4. One option is to combine these files:

   cat final_protein.upl mol.upl intermolecular.upl > complex.upl

• calculate the structure:
  cyana CALC.cya
• check the resulting structure using chimera
  for clarity, select only the first structure (as in Task 5)

Note! if using VMD as a molecular viewer, it will refuse to recognize large parts of the secondary structure! Or in other words, the resulting protein-ligand structure has the secondary structure further away from the standard definition.

• Try to explain what can be causing it.
• Check the median of the distance restraints placed into .upl
  It should be around 4.2 Å for intramolecular distances, and 4.4 Å for the intermolecular distances. What do you get?
• Discuss how robust the calculation of the protein-ligand structure is.

Introduction for task 2:

a:

The calibration of the distances from the measured NOE intensities, using a known fixed distance, can be inaccurate due to several reasons. In this exercise, we correct some of them in two steps. First, the NOE intensities will be normalized using the diagonal intensities (their geometric mean) corresponding to the NOE cross-peak. This corrects for

1. different lineshapes (if the peak height and not the peak volumes were taken)
2. differences in the starting Z-magnetisation (beginning of the NOE mixing time) due to incomplete relaxation between the scans
3. differences in the starting Z-magnetisation due coherent transfer through other nuclei, such as in HSQC-NOESY.

This normalization is not final for those peaks stemming from multiplet(s) N₁ x N₂ of equivalent spin groups 1 and 2. In such cases, the average normalized buildup (-->σ_i,j) is obtained by further multiplication by (N₁ x N₂)^^(1/2) /(N₁ x N₂). (See the full formula below.)

b:

The step above  makes the cross-relaxation rates σ_i,j in a correct mutual proportion. The actual values can be still inaccurate due to inaccurate reference distance, r_Ref in Eq. 1, or rather σ_Ref being not correctly proportional to the r_Ref  due to spin diffusion or other effects. It is therefore recommendable to correct the median of the measured distances such that it corresponds to the distances conserved among these organic molecules: around 4.2 Å for intramolecular distances and 4.4 Å for the intermolecular distances. When correcting the derived distances, we include a constant to multiply the distances in order to obtain the desired median.

c: 

There is an important technical detail about how the CYANA handles the sites with multiple spins - such as -CH₃, with three spins with the same chemical shift. These three spins combined into a pseudoatom Q, but, the distance between this atom and another atom is not the average but instead a shorter distance, calculated from the three-fold intensity of the NOE cross-peak. Similarly for cross-peak between two methyl groups, the cross-peak would be 9x larger than expected from one atom, and it will be translated to a very short distance expected by CYANA.

Task 2: Do the  NOE normalization, improve the distance calibration

a:

• Calculate the normalized NOE buildups,  by dividing the original ones by the geometric mean of the diagonal decays and factor due to their possible multiplicity (Q pseudoatoms):
  _NOEij,Norm= NOE_ij/(Decay_i*Decay_j)^^(1/2)  x (N₁ x N₂)^^(1/2) /(N₁ x N₂)
  The tables "diagonal peaks intensities of the ligand (autorelaxation)" are conveniently sorted for this task.

b: 

• calculate the median of the resulting distance using the Eq. 1 as before.
• create a new column, where the distances are multiplied by a factor
  by few trials, find a factor which will make the median of distances near to 4.2 Å

c: 

• find out how many spins from each site contribute to the final crosspeak (NSigma = N1*N2)  contribute to each NOE signal. For cross-peak between two methyl groups, NSigma = 3*3 = 9. The normalisation averaged them such that these distances are approximately the physical ones. Divide those distances by NSigma^(1/6) to obtain shorter distances for cross-peaks originating in multiple spins, as expected by CYANA.

d:

• do points a, b, c for the intermolecular NOE, aiming at 4.4 Å for median of the intermolecular distances.

e:

• create the .upl files from the intramolecular NOEs and for intermolecular NOEs
• combined them with the final_protein.upl as in part4/task1
• redo the calculation in cyana

Part 4

Introduction for task 1

In the previous parts, the protein-ligand complex had a low dissociation constant of 0.1 nM. With the concentrations given, this means, that there is almost no free ligand and no free protein. In this exercise, we assume that the dissociation constant is 500µM, equal to the concentration of the components. The fraction of the free ligand will have much higher mobility, and therefore, the autorelaxation rate will be smaller. The cross-relaxation rate will be also strongly affected, particularly the intermolecular NOE, which will build up only for the fraction staying in the complex. On the other hand, relaxation rate of the protein will remain very similar, with some exceptions near the binding site, but those will not be analyzed here.

Task 1

• In the directory part4/task1,
  open the simulation_data_500uM.xlsx
• looking at the first columns of the buildup curves and the decay curves,
  notice their differences as compared to the excel table of the data from the previous exercises.
• Repeating the instructions in part3/task2, calculate the calibrated intramolecular and intermolecular distances.
• Comment on how much do they differ. 
• Is it possible to determine the conformation of weakly bonding ligand, which is in large excess as compared to the protein? 

NMR² 

NMR² runs via the platform SAMSON.

1. Register and install SAMSON
2. Request the NMR² application

solutions

Further workshop contributors:
Colin Schmoll contributed by providing the simulated data (.xlsx sheets) and plots, Dr. Jiří Mareš assembled part of the text and workshop materials. (https://bionmr.univie.ac.at/people/)

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