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In this tutorial we will

  1. learn how to calibrate NOE data to obtain distance restraints,
  2. derive a protein structure with the software CYANA,
  3. try how the exchange of the ligand between free and bound state influence the NOESY spectra,
  4. derive the structure of protein-ligand complex,
  5. 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:


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.

  • ./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  (https://bionmr.univie.ac.at/people/)


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