NMR Winterschool 2025: Protein-ligand structure determination using NOEs

In this tutorial we will

1. see how to calibrate NOE data to obtain distance restraints,
2. derive a protein structure with the software CYANA,
3. try how the exchange of ligand between free and bound state influence the NOESY spectra,
4. derive structure of  protein-ligand complex.

To this end we will use the software CYANA.

For viewing the molecular structures, we will use VMD.

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'

cd "download path"/cyana-3.98.15 
#optional 
sudo xattr -rd com.apple.quarantine cyanaexe.macarm-gfortran

./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.

Part 1

Introduction for task 1:

In 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, assigment 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 inclompletely resolved relayed transfer  and partly due to different (local) dynamics influencing the cross-relaxation rate.
Let's start anyway with the unreallistic situation, where we know all the distances within 5.5 A, accuratelly.

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

Intermezzo: 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.

Task 1

• Look into the configuration file, CALC.cya, using a text editor/browser.
  The set of structure will be writen in demo.pdb
• Start the calculation by
  cyana CALC.cya
• After the calculation is ready, look at the .owv file.
  See the target functions, its variation.
  See the RMSD - root mean square displacement.
• To view the structure, use
  vmd demo.pdb
  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.

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 Angsrom for the strongest and 5.5 to the weakest.

031
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.

• Check some of the simulated buildups, the buildupsLinearized in the supplied folders.
• Without further effort, what are the chances to get accurate distances from these?
• Check how many distance restraints we have: wc -l PxPapp.upl
• Start the structure calculation, or see the ready demo.pdb and demo.ovw file.

032

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.

• Check how many distances are left.
• Visualize the structure in VMD, intead 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?

033

In the next simple attempt, we multiply all the distances by a constant factor (1.75) and use again those within 5.5A.

• Check how many are left, what is the statistics of the structure calculation. And
• visualize the structure.
• Switch again to NewCartoon drawing method. What happens?

034

Next, we can think that the number of (inaccurate) constraints is simply too large. Commonly we would expect up to
aroound 10 constraints per amimoacid residue.  In the previous example, it was still around 12800/97 > 100 restraints
per residue. Here we try to use, only every 10th restraints.

• See the structure calculation overview. Visualize the structure.
• What do you think, were these attempts good enough?

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).

• Check the simulated NOESY spectra (!note that the axes are not chemical shifts but simply atomic indices!)
• For the case of 1:10, 1:1 and 1:200 of protein:ligand fractions, in 035, 036 and 037.
• What more is not realistic about this simulation?

038 

• We check the effect of the exchange rate on the resulting cross-relaxation rates.
  See e.g. like: tail -n 15 outputKex5e*
• What would be the consequence of "not so fast" exchange?

What is even more important is the population weighting of the intermolecular cross-rates (hence also NOEs)
The "Re weighted" matrix contains includes the correction, whereas the "weight averaged over P, L, PL" does not.

041 

We have exact distances (assume we are able to obtain them), but we ignore the populations, so the intermolecular calibration is wrong.

• Check the PxL.upl
• What are the effects when calculating the protein-ligand complex?
• When viewing the complex, in graphical representation, you can select the atoms of proteins by "proteins" and the ligand as "not protein"

046 

Here the populations are take into account correctly.

• What is the difference WRT 041 ?

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.

Task 3: Calibrate distances from the buildup curves.

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.

ResidueNumber1 residueName1 atomName1 residueNumber2 residueName2 atomName2  distance.

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.

Note that the atom numbers and names have to exactly match the MOL.lib file.
Note also, that the distance has to be in a numerical format using "dot" as a decimal separator  and not a "comma"!

• 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 this short exercise, we will calculate the protein structure using ready distances stored in the final_protein.upl file. We do not need any extra library file, as this time, the sequence file (demoShort.seq) contains only standard
amino acid residues.

• 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/)