1. Molecular dynamics simulations of toxin binding to ion channels Quantitative description protein –ligand interactions is a fundamental problem in molecular biology with applications in pharmacology, medicine, biotechnology, etc. Pharmacological motivation: drug discovery is getting harder using traditional compound libraries. Peptide-ligands from Nature (e.g. toxins) offer an alternative source for drug discovery Computational methods would be very helpful in such studies but their accuracy needs to be improved to tackle large ligands Proof of concept study: Binding of charybdotoxin to KcsA* (shaker) Realistic case study: Binding of ShK toxin to Kv1.1, Kv1.2, and Kv1.3

2. Two main problems in computational studies of protein-ligand interactions 1. Apart from a few cases, the complex structure is not known. Assuming that structures (or homology models) of protein and ligand are known, the complex structure can be determined via docking followed by refinement with MD simulations. 2. Affinity and selectivity of a set of ligands for target proteins need to be determined with chemical accuracy (1 kcal/mol). Binding free energies can be calculated from umbrella sampling MD simulations (standard method). For selectivity, one could use the computationally cheaper free energy perturbation method. The FEP method is especially useful if one is trying to improve selectivity via minor modifications/mutations of a ligand. 2

3. Charybdotoxin binding to KcsA* (shaker mimic) – Complex structure is determined from NMR, so provides a unique test case for MD simulations of peptide binding. – Using HADDOCK for docking followed by refinement via MD simulations reproduces the experimental complex structure. – Binding free energy calculated from the potential of mean force agrees with experimental value within 1 kcal/mol ShK toxin binding to Kv1.1, Kv1.2, and Kv1.3 channels – Kv1.3 is the main target for autoimmune disases – ShK binds to Kv1.3 with pM affinity (but also to Kv1.1) – Need to improve selectivity of ShK for Kv1.3 over Kv1.1 – Some 400 ShK analogues has been developed for this purpose Toxin binding studies to potassium channels

4. Find the initial configuration for the bound complex using a docking algorithm (HADDOCK is recommended ) Refine the initial complex(es) via MD simulations Calculate the potential of mean force for binding of the ligand along a reaction coordinate → binding constants and free energies Determine the key residues involved in the binding Consider mutations of the key residues on the ligand and calculate their binding energies (relative to the wild type) from free energy perturbation in MD simulations Those with higher affinity are candidates for new drug leads Computational program for rational drug design from toxins

5. Structure of the KcsA*- charybdotoxin complex Important pairs: Y78 (ABCD) – K27 D80 (D) – R34 D64, D80 (C) - R25 D64 (B) - K11 K27 is the pore inserting lysine – a common thread in scorpion and other toxins. K11 R34

6. NMR structure ofShK toxin ShK toxin has three disulfide bonds and three other bonds: D5 – K30 K18 – R24 T6 – F27 These bonds confer ShK toxin an extraordinary stability not seen in other toxins

7. Homology model of Kv1.3 Can be obtained from the crystal structure of Kv1.2 (over 90% homology and 1-1 correspondence between residues). Initial model did not work because V  H mutation was not handled correctly. H404 side chains make bonds with the neighbouring D402 and these were broken during the relaxation.

8. Kv1.3-ShK complex Monomers A and CMonomers B and D

9. Pair distances in the Kv1.3-ShK complex (in A) Kv1.3ShK HADDOCKMD aver. Exp. D376–O1(C) R1–N1 5.0 4.5 S378–O(B) H19–N 3.2 3.0 ** Y400–O(ABD) K22–N1 2.9 2.7 ** G401–O(B) S20–OH 2.9 2.7 ** G401–O(A) Y23–OH 3.5 3.5 ** D402–O(A) R11–N2 3.2 3.5 * H404-C(C) F27-C"1 9.7 3.6 * V406–C1(B) M21–C" 9.4 4.7 * D376–O1(C) R29–N1 12.2 10.2 * ** strong, * intermediate ints. (from alanine scanning Raucher, 1998) R24 (**) and T13 and L25 (*) are not seen in the complex (allosteric)

10. RMSD of ShK as a function of umbrella window The RMSD of ShK relative to the NMR structure remains flat throughout

11. Convergence of the PMF for the Kv1.3-ShK complex

12. PMF of ShK for Kv1.1, Kv1.2, and Kv1.3

13. Comparison of binding free energies of ShK to Kv1.x Binding free energies are obtained from the PMF by integrating it along the z-axis. Complex  G well  G b (PMF)  G b (exp) Kv1.1–ShK 18.0 14.3 ± 1.114.7 ± 0.1 Kv1.2–ShK 13.8 10.1 ± 1.111.0 ± 0.1 Kv1.3–ShK 17.8 14.2 ± 1.214.9 ± 0.1 Excellent agreement with experiment for all three channels, which provides an independent test for the accuracy of the complex models.

14. Average pair distance as a function of window position ** ** * ** denotes strong coupling and * intermediate coupling

15. Conclusions Docking methods are useful for providing the initial configurations of the bound complex But their predictions for binding energies are not adequate (it is unlikely that one can optimize a single energy functional which can predict the binding energies for all protein-ligand pairs.) Thus we need to rely on MD simulations for refinement of a protein-ligand complex and accurate calculations of binding free energies. Once a protein-ligand complex is characterized, one can study the effects of mutations on the ligand by performing free energy perturbation calculations. Those with higher affinity relative to the wild-type would offer promising drug leads.