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Structural Biochemistry and Bioinformatics
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Laboration

Ranking of a series of non-nucleoside inhibitors to HIV reverse transcriptase.

Background

In order to rank a series of inhibitors we need information of their binding free energies to the target protein. An accurate estimation of the binding free energy of an inhibitor to a protein is a very computer demanding task. Consider two inhibitors L1 and L2 binding to a protein P. We can construct the following thermodynamic cycle:

      DG1        
L1 + P ® L1P      
¯ DGs     ¯ DGb   (1)
L2 + P ® L2P      
      DG2        

DG1 and DG2 are the free energies of binding L1 and L2, respectively, to the protein P. These quantities can be determined experimentally but a direct estimation of them computationally is very difficult. The binding process involves desolvation of the inhibitor, opening of the protein in order to accommodate the inhibitor, docking of the inhibitor to the protein and a final protein closure to its final protein-inhibitor complex. All these motions are quite large scaled and requires a too long simulation time to be practically feasible. However, since the free energy is a state function, it is only depending on its initial and final state and not the path between these states. This implies that when we 'walk around' a closed cycle as above, the free energy difference when the cycle is traversed is zero, i.e:

DG1 + DGb - DG2 - DGs = 0           (2)

which can be rearranged as:

DG2 - DG1 = DGb - DGs           (3)

i.e the relative binding free energies (DG2 - DG1) can also be calculated as DGb - DGs.
The two 'vertical' free energy values, DGb and DGs , are much easier to evaluate and can be performed using varius computational methods. In so called 'full' free energy calculations, L1 is 'mutated' into L2 by a gradual, stepwise transformation of atoms and groups that are unique for L1 into atoms and groups that are unique for L2. The free energy contribution from each step in the transformation is then summed up to give the total values of DGb and DGs, respectively. DGs and DGb are calculated by doing the transformation (or 'perturbation') of L1 ® L2 in solution and when bound to the protein, respectively. Thus, two perturbations have to be performed to get an estimate of the free energy difference DG2 - DG1. Since each step in the gradual transformation also has to be sampled enough to get reasonable statistics, full free energy calculations are very computer demanding. Its use in, for example, ranking a series of inhibitors with respect to their binding free energy as in this study, is therefore limited and only a very few inhibitors (~2) can be treated with this method. To be able to handle a larger set of inhibitors, we have to sacrifice accuracy and simplify the calculations. There are several approaches on how to approximate the calculations, for example, to treat the solvent as a continuum rather than having explicit water in the simulations. Calculations of forces and energies from water molecules takes a great portion of computer time. Another possibility is to skip the intermediate states in the 'full' free energy calculations and only simulate the 'end'-states, i.e. pure L1 and L2 in the solution and bound to the protein. The free energy difference is then approximated simply as the differences in (average) interaction energies between the two simulations.

One TIBO derivative in the non-nucleoside binding pocket of HIV-1 RT.
TIBO is in red and close residues are in green.

In this laboration we will estimate the rank order of 11 TIBO derivatives with respect to their binding free energy to HIV-1 reverse transcriptase (RT). HIV-1 RT is the enzyme in HIV that transcribes the viral RNA into DNA, which is subsequently integrated in the host cell by another enzyme, HIV-1 integrase. The inhibitors to HIV-1 RT can be divided into two classes: 1/ Nucleoside inhibitors which bind to the active site, where the RNA template binds. Examples of such inhibitors are AZT and ddI. 2/ Non-nucleoside inhibitors which bind at another site close to the active, examples are TIBO and nevirapine. The biggest problem with both nucleoside and non-nucleoside inhibitors is that HIV-1 RT quickly mutates so that it becomes resistant to the drug.

A selected set of TIBO derivatives

derivative R1 R2 R3 R4 R5 R6 EC50 (nM)*
9CL 9-Cl S H CH3 H H 33
8H H S H CH3 H H 44
OTIBO H O H CH3 H H 4200
8ME 8-CH3 S H CH3 H H 14
C7ME H S H CH3 H -CH3 (trans) 39
TR7ME H S H CH3 H -CH3 (cis) 790
ETT 8-Cl S H CH3 CH3 H 5.1
4MeT 8-Cl S CH3 H H H  
4ClT 8-Cl S Cl H H H  
HET b S H CH3 H H  
BET c S H CH3 H H  

* EC50 is the concentration that reduces the activity by 50 %. Relative binding free energies can be estimated from the relation:
        DG1 - DG2 = -RT ln [(EC50)1/(EC50)2]

The binding free energy of two ligands to HIV-1 RT will simply be estimated as the difference in inihibitor-protein interaction energies. These interaction energies (Eint) are obtained from the following expression:

Eint = Si,j [ C12(i,j)/rij12 - C6(i,j)/rij6 + qiqj/4pe0errij ]     (4)

where rij is the distance between a protein atom (i) and a ligand atom (j), C12 and C6 are semiempirically determined interaction coefficients between two atoms, qi is the atomic partial charges (determined from quantum mechanics calculations) and e0 and er are the absolute and relative electric constants, respectively. The two first terms correspond to the van der Waal's energy and the last term is the electrostatic energy.
To make the computations faster there are no water molecules present in the 11 protein-inhibitor structures (see below). This probably represents a minor approximation since the TIBO derivatives are buried in a hydrophobic pocket where few water molecules are present. Free energies are energy averages over all possible configurations in the protein-inhibitor complex, whereas we here only consider one configuration, an energy minimized protein-inhibior complex. The TIBO molecules and its surrounding side chains are quite flexible, so an energy average might give a different free energy estimate than from this one configuation. We also have to assume that the different protein-inhibitor complexes have the same solvation free energy. The TIBO derivatives are very similar to each other and we can probably assume that the complexes also are very similar to each other and that they thus have similar solvation energies. The free energies we estimate with the protein-inbitor interaction energies correspond to the free energies of the bound state. We need to correct this value with the solvation free energies of the inhibitors. To easier understand this, consider a modification of an inhibitor that improves the interaction energy with the protein compared to the original inhibitor. If the same inhibitor also improves the solvation free energy, where will be no net improvement of the binding free energy, since the inhibitor leaves the solution and enters the protein upon binding. Therefore, we have to subtract the interaction energies with the solvation free enegies in our approximate estimation of the relative binding free energies. Calculated solvation free energies for the TIBO derivatives are tabulated as follows.

Estimated DGsolv (kcal/mole) of the TIBO derivatives.

TIBO derivative DGsolv
8H -4.18
9CL -4.18
OTIBO -5.00
8ME -3.99
TR7ME -4.30
C7ME -3.89
ETT -3.69
4ClT -4.86
4MeT -3.87
HET -3.43
BET -4.27


Procedure:

Copy all files in the directory /mats/derivates to a directory that you own. This directory contains the .pdb and .mpdb files of the 11 TIBO derivatives in HIV-1 RT. Since this protein is so large (944 amino acids), it has been trunctated, centred around the TIBO derivaties. .pdb is the 'ordinary' Protein Data Bank format, containing the coordinates of all atoms present. .mpdb is an extended variant where also the atomic radii and charges are listed as well. These .mpdb files are needed for the energy calculations which are done for each derivative in two steps. First, with a program 'parm-nonb', a list, 'surf_input.xyz' is created that also contains info about each atom's van der Waal's parameters (eq. 4 above) + some other information that is not needed here.
write
% parm_nonb *.mpdb

where * is replaced with the .mpdb file you want to calculate energies for. In the next step, the program 'ener' uses the file 'surf_input.xyz' to calcuate the protein-inihibtor interaction energies.
write
% ener<ener.in>ener.out
ener.in is a small file that contains info about the dielectric constant er (eq. 4 above) and the residue number of the ligand. 'ener.out' shows the various energies. In addition, a file, 'lig-ener.out', is created, that lists the ligand-protein interaction energies with each and every residue in the protein. This file can be useful when trying to understand why the highest ranked inhibitor is such a good binder. Consider saving it for later inspection.
So, estimate the binding energies for all derivatives, correct them for the different solvation free energies and rank them. Choose '8h' to be the reference derivate to compare against.

Next, use the program 'SwissPBD Viewer' (under NT) and try to explain, based of the structures, why the best ranked inhibitor binds better than, for example '8h'.

HINT: display the two structures simultanuously, only display and label residues that are within 6 A from the inhibitor. Look specially in the region where the inhibitors differ. What residues are surrounding? What kind of residues? polar? charged? non-polar? what is the nature of the added group? When you can point at certain residues that might contribute to an improved binding, check their
energies with the ligand from the 'lig_ener.out' files.

The report should contain the rank order of the inhibitors in a table including their interaction energies. Also, the rank order according to experimental data (where provided) should be included. A structual explanation for the best ranked inhibitor compared to '8h' should be given with examples of some residues than contributes to the stability, including their interaction energies with the inhibitor.


Mats Eriksson, November -98.
Arne Elofsson
Department of Biochemistry,
Arrheniuslaboratoriet
Stockholms Universitet
10691 Stockholm, Sweden
Tel: +46-(0)8/161553
Fax: +46-(0)8/153679
Hem: +46-(0)8/6413158
Email: arne@rune.biokemi.su.se
WWW: /~arne/