In this tutorial we will
Lecture slides can be downloaded here: presentation.pdf
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.
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.
cyana CALC.cya
vmd demo.pdb #the same name will be produced in all trials of this tutorial
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.
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.
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.
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
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.
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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).
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.
cat NOESYwhenDifferentExchangeRates.txt
(or you can extract these using: grep -A 5 "NOESY intensities s" outputKex5e*t10)
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.
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.
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.
What would be needed to recover the full relaxation matrix - mainly the exact cross-relaxation rates exactly? Would be such an effort useful?
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
cat PxP* PxL* LxL* > all.upl
grep -v Q demo.pdb > demoClean.pdb
vmd demoClean.pdb
Here the populations (concentrations) are take into account correctly, so also the intermolecular distances are calibrated correctly.
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/)