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Open the simulation_data.xlsx in part1/task1_to_3 directory. These are for us the experimetal data!We We will start with the structure calculation of our ligand (drug-like) molecule.From From the NOESY spectra, we obtain the cross-relaxation rates using the intensityintensity (volume) of the crosspeaks at a known (experimentally set) mixing time.These are directly related to the interatomic distances, which will determine the conformation of the molecule.
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The NOESY spectrum contain also diagonal crosspeaks. These correspond to the (non-equilibrium Z-) magnetisation decay ofthe of the spin-themselfs: autorelaxation, or in other words, decay with the T1-type (R1-type) relaxation time (rate).
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Rij = σij = b2/dij6 (-J(0) + 6J(2ω)),
where "b" is the dipol-dipol 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, shows the distribution of frequencies of the molecular rotational motion.
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The initial rate of the NOESY crosspeak, is directly proportional to the distance 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.
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In a separate column, assuming a linear buildup in time: chose now
the first mixing time to get the initial cross-relaxation rate.
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In order to calculate the structure (conformation) of the molecule, we need to know the interatomic distances.
This is something what we have already. As these distances come with some inaccuracies, we have to input two distances -
a lower and upper bound in which we believe that the true distance resides.
For practical purpose, we just create two new columns, where the distances derived above are multiplied by factors of
0.8 and 1.2 respectively. In fact, just the upper bound will be enough in our exercises.
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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 aminoacids, 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.
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CYANA can obtain the bonding topology from a .mol2 molecular structure file, converting it into its own (library)
format, a a .lib file. This library file with contain information about one molecule, but since biopolymers - proteins
contain chain (sequence) of building blocks like aminoacid residues of nucleotides, there has to be also information
about the sequence of those building block. In our case it contains only one record: the name of our ligand molecule.
We will use a ready 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 Ånsgrom.
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In our first calculation of a single molecule (residue), obviously only the atomName1 and atomNam2 would be different.Further Further instructions for CYANA are read from the .cya file.
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From the theoretical introduction about NOE, we know that the existence of crosspeak between two spins does not have tobe to be caused by the direct through-space transfer of magnetisation between them.Instead Instead, magnetisation transfer via an third nucleus can occur. This is called spin diffusion.
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- 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. - Look at structure using chimera.
- for clarity, select only the first structure:
select -> chain -> A demo.pdb #0.1
select -> Invert (all models)
actions -> Atoms/Bonds -> delete
- for clarity, select only the first structure:
- Explain the violation.
Is such a problem more likely for atoms short or long apart? - Plot normalized buildup curves
Calculate normalized NOESY buildup curves, by dividing them by 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?
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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
aminoacid residues.
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