1. QSAR Qualitative Structure-Activity Relationships Can one predict activity (or properties in QSPR) simply on the basis of knowledge of the structure of the molecule? In other, words, if one systematically changes a component, will it have a systematic effect on the activity?

2. Choice of Model Can approach in two directions: Simple to complex model Complex to simple model

3. Simplest Model Linear relationship between x and y Y = mx + b Minimize error by least squares:   (Y i – Y’ i ) 2 =  [Y i – (mX i + b)] 2 Y’ i is predicted value

5. Least Squares

6. Correlation coefficient -1 < r < 1

7. Another test Is the line better than the mean?

8. A circle2 lines

9. One bad pointWrong model

10. Multiple Regression Y = f (X 1, X 2 …X n ) Problems: Choice of model – linear, polynomial, etc. Visualization Interpretation Computationally demanding

11. Variable reduction Principal Component Analysis

12. Principal Component PC 1 = a 1,1 x 1 + a 1,2 x 2 + … + a 1,n x n PC 2 = a 2,1 x 1 + a 2,2 x 2 + … + a 2,n x n Keep only those components that possess largest variation PC are orthogonal to each other

13. Exploring QSAR Pickup the NONLIN program http://www.trinity.edu/sbachrac/drugdesign2007/ Unzip and install it on your computer Read the Read.Me and Nonlin.doc documentation Look at the HeatForm.NLR file with any word processor

14. Running NONLIN Start an MSDOS window Change to directory where the code is Cd /d d:\nonlin Execute the program with data file Nonlin heatForm > output

15. assignment Propose a QSAR scheme to predict the  H f of the alkanes

16. Early Examples Hammett (1930s-1940s)

17. Hammett (cont.) Now suppose have a related series  reflect sensitivity to substituent  reflect sensitivity to different system

18. Hammett (cont.) Linear Free Energy Relationship  G = -2.303RTlog 10 K So  G –  G 0 = -2.303RT  and  G’ –  G’ 0 = -2.303RT  Therefore  G’ –  G’ 0 =  (  G –  G 0 )

19. Free-Wilson Analysis Log 1/C =  a i +  where C=predicted activity, a i = contribution per group, and  =activity of reference

20. Free-Wilson example Log 1/C = -0.30 [m-F] + 0.21 [m-Cl] + 0.43 [m-Br] + 0.58 [m-I] + 0.45 [m-Me] + 0.34 [p-F] + 0.77 [p-Cl] + 1.02 [p-Br] + 1.43 [p-I] + 1.26 [p-Me] + 7.82 activity of analogs Problems include at least two substituent position necessary and only predict new combinations of the substituents used in the analysis.

21. Hansch Analysis Log 1/C = a  + b  + c where  x) = log P RX – log P RH and log P is the water/octanol partition This is also a linear free energy relation

22. Molecular Descriptors Simple rules for describing some aspect of a molecule Structure Property 2D descriptors only use the atoms and connection information of the molecule Internal 3D descriptors use 3D coordinate information about each molecule; however, they are invariant to rotations and translations of the conformation External 3D descriptors also use 3D coordinate information but also require an absolute frame of reference (e.g., molecules docked into the same receptor).

23. Descriptor examples Physical Properties MW log P (ocanol/water partition) bp, mp Dipole moment solubility

24. Descriptor examples Structural descriptors 2D Atom/Bond counts Number non-H atoms Number of rotatable bonds Number of each functional group 2C chains, 3C chains, 4C chains, 5C chains, etc. Rings and their size 3D Number of accessible conformations Surface area

25. Topological Descriptors Weiner Path Index w =  d ij ij>i w = 46

26. Topological Descriptors Randic Index

27. Predict bp of alkanes

28. 3D Molecular Descriptors Potential energy Solvation energy Water accessible surface area Water accessible surface area of all atoms with positive (negative) partial charge

29. Pharmacophore Specification of the spatial arrangement of a small number of atoms or functional groups With the model in hand, search databases for molecules that fit this spatial environment

30. Creating a Pharmacophore

31. 3D Pharmacophore searching With the pharmacophore in hand, search databases containing 3-D structure of molecules for molecules that fit Can rank these “hits” using scoring system described later

32. Pharmacophore Descriptors Number of acidic atoms Number of basic atoms Number of hydrogen bond donor atoms Number of hydrophobic atoms Sum of VDW surface areas of hydrophobic atoms

33. Lipinski’s Rule of 5 potential drug candidates should Have 5 or fewer H-bond donors (expressed as the sum of OHs and NHs) Have a MW <500 LogP less than 5 Have 10 or less H-bond acceptors (expressed as the sum of Ns and Os) Adv. Drug Delivery Rev., 1997, 23, 3

34. Docking Interact a ligand with a receptor Need to do the following A) select appropriate ligands B) select appropriate conformation of receptor C) select appropriate conformations of ligands D) combine the ligand and receptor (docking) E) evaluate these combinations and rank order them

35. Selection of Ligands Want drug-like molecules 250< MW < 500 Lipinski’s rules Search through databases Available Chemicals Directory (ACD) World Drug Index NCI Drug database In-house databases

36. Receptor Conformation Usually Receptor is assumed to be static Get structure from X-ray or NMR experiment Protein Data Bank (http://www.rcsb.org/pdb/) 41385 Structureshttp://www.rcsb.org/pdb/

37. Ligand Conformation Rigid or flexible If rigid, optimize the structure then use it throughout the docking procedure If flexible, can A) create a set of low energy conformations and then use this set as a collection of rigid structures in docking B) optimize structure within active site of receptor, i.e. dock and optimize together

38. Docking Place ligand in appropriate location for interacting with the receptor Methodological problem: 1) No best method for defining shape 2) No general solution for packing irregular objects (the knapsack problem)

39. Docking Algorithmic Components Receptor and Ligand Description (keep in mind relative errors of structures, etc.) Bind the Ligand to Receptor (configuration/conformation search) Geometric search (match ligand and receptor site descriptions) Search for minimum energy - molecular dynamics (MD) or monte carlo (MC) Evaluation of the dock (  G bind ) also called scoring

40. Descriptor Matching Method DOCK program 1) Generate molecular surface for receptor 2) Generate spheres to fill the active site (usually 30-50 spheres) 3) Match sphere centers to the ligand atoms (originally just lowest E conformer, now use multiple conformers, but still rigid) – generates 10K orientations per ligand – Shape-driven! 4) Score the interaction

41. Fragment-Joining Method FlexX, LUDI Place base fragments into microstates of the active site (Fragments can be small molecules like benzene, formaldehyde, formamide, naphthol, etc.) Optimize position of the Base fragment Join fragments with small connecting chains made of CH 2, CO, CONH, etc.

42. Scoring (evaluation of the dock) Want to quickly evaluate the strength of the interaction between ligand and receptor Full free energy computation Expensive Requires excellent force fields Empirical method Fast and cheap Requires fitting to a broad set of ligand/receptor complexes

43. Empirical Scoring Method of Bohm (LUDI, FlexX, etc.)  G bind =  G 0 +  h-bonds  G hb f(  R,  ) +  ion  G ion f(  R,  ) +  G lipo A lipo +  G rot NROT  G 0 reduction in binding energy due to loss of rotation and translation of ligand  G hb contribution from ideal hydrogen bond  G ion contribution from ionic interactions  G lipo contribution from lipophilic interactions  G rot contribution from freezing rotations within ligand These come from empirical fits.

44. Bohm Method (cont.) f(  R,  ) are penalty functions for non-ideal interactions – distances too short/long, angles not linear f (  R,  ) = f1(  R)f2(  ) f1(  R) = 1,  R<0.2 Å f2(  ) = 1,  <30° 1-(  R-0.2)/0.4,  R<0.6 Å 1-(  -30)/50,  <80° 0,  R>0.6 Å 0,  >80°  R is deviation from ideal H... O/N distance of 1.9 Å  is deviation from ideal N/O-H … O/N angle of 180°

45. Bohm Method (cont.) A lipo is the lipophilic contact surface, evaluated by a coarse grid of boxes NROT is the number of rotatable bonds – acyclic sp 3 -sp 3, sp 3 -sp 2 and sp 2 -sp 2. No terminal groups or flexibility of rings incorporated. H.-J. Bohm, J. Comput.-Aided Mol. Des., 1994, 8, 243-256

46. Scoring alternatives Many variations on Bohm scheme Buried Polar term, desolvation term, different forms for the lipophilic term, include metal bonding, etc. Combine scoring functions, i.e. QSAR with scoring functions as variables Use empirical score to select set of hits, then refine with free energy minimization