Applica7ons of 2D Similarity. Outline. Lecture 4: 2D Similarity Applica7ons and 3D Structure. Applica)ons of 2D Similarity.

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1 BIINF 4372 Drug Design 2 Jens Krüger and Philipp Thiel Summer 2014 Lecture 4: 2D Similarity Applica7ons and 3D Structure utline Applica)ons of 2D Similarity Assessing chemical diversity Clustering and selec)on of representa)ve structures 3D Structure Conforma)onal flexibility 3D conformer genera)on Conforma)onal search 2 Applica7ons of 2D Similarity 3 1

2 Diversity Chemical Space: Space spanned by all possible chemical compounds ~ possible organic compounds MW < 500 Da Mul)- dimensional and infinite Important ques)ons concerning chemical space: Which part of the chemical space is covered by a library? How to increase coverage of a compound library? Which of the available libraries is most diverse? How to maintain coverage with a reduced number of compounds? How to choose N compounds from a library, such that diversity becomes maximal? hp://blog.calgarypubliclibrary.com/blogs/movie_maniacs/star_trek_03_1024.jpg 4 Diversity Library Comparison Which library is more diverse? How to measure diversity? Various measures are possible We are interested in methods using 2D similarity 5 Diversity Mean Similarity and Dissimilarity For example Tanimoto- based measures using 2D fingerprints Mean Inter- Molecular Similarity (MIMS): Mean Inter- Molecular Dissimilarity (MIMD): MIMD = 1 MIMS MIMD is a measure of rela7ve diversity, i.e. how strongly the structures differ from each other It is not an absolute measure of the total space covered 6 2

3 Selec7ng Representa7ves Select only one representa)ve structure from each group of very similar compounds: grouping = clustering Selec)ng a representa7ve from each cluster can be achieved e.g. by choosing the compound closest to the cluster centers 7 Clustering Methods Non-hierarchical Hierarchical 8 Clustering Hierarchical Methods Agglomera7ve Each structure forms own cluster Merge clusters un)l only one is leb Divisive All structures form single cluster Divide cluster(s) step by step Examples: Ward s minimum variance Linkage methods (single, complete, average) Examples: MacNaughton- Smith 9 3

4 Clustering Hierarchical Methods: Agglomera>ve Generic Algorithm: 1: Calculate all pairwise similarities 2: While #clusters > 1: 2.1: merge most similar cluster pair 2.2: update similarities (to new cluster) Advantage: Produces very homogeneous clusters (Average linkage, Ward) Disadvantages: Which level for cluster selec)on should be chosen? Computa)onally expensive: space (N²), )me (N 3 ) 10 Clustering Hierarchical Methods: Agglomera>ve Cluster dissimilari)es: Single Linkage Complete Linkage Average Linkage Ward s minimum variance Euclidean distance between centroids 11 Clustering Non- Hierarchical Method: Jarvis- Patrick Generic Algorithm: 1: For each structure s i, compute J nearest neighbors 2: s i and s j are in the same cluster if - s i is under J nearest neighbors of s j and vice versa - K of the J nearest neighbors are shared by s i and s j Advantage: NN Fast implementa)on possible si Disadvantages: Choice of parameters K and J necessary and oben difficult? ben yields heterogeneous clusters NN sj K members in intersection 12 4

5 Clustering Ward Example: Calculate Cluster Tree H 3 C N H HN NH 2 H H 2 C H HN H HN Cl Cl H 3 C N N H 2 N H HS H Cl S Acetaminophen Acetylsalicylic acid Diclofenac Gabapentin Captopril Amphetamin Alprenolol Chlorpromazin Example by David Wild 13 Clustering Ward Example: Cluster Level Selec>on H 3 C 8 N H HN NH 2 H H 2 C H HN H HN Cl Cl H 3 C N N H 2 N H HS H Cl S Acetaminophen Acetylsalicylic acid Diclofenac Gabapentin Captopril Amphetamin Alprenolol Chlorpromazin Example by David Wild 14 Clustering Ward Example: Cluster Level Selec>on Hierarchical methods require a choice of the level where the clusters should be cut off This can be done manually: e.g., define the number of clusters you expect/want There are also numerous automa)c methods that are, however, beyond the scope of this course H 3 C N H HN NH 2 H H 2 C H HN H HN Cl Cl H 3 C N N H 2 N H HS H Cl S Acetaminophen Acetylsalicylic acid Diclofenac Gabapentin Captopril Amphetamin Alprenolol Chlorpromazin Example by David Wild 15 5

6 Summary I Es)ma)on of chemical space diversity (MIMS/MIMD) Chemical space coverage Library comparison Representa)ve selec)on Dissimilarity/similarity measures on 2D fingerprints required for clustering methods Different methodologies used in chemoinforma)cs Hierarchical Non- hierarchical Representa)ve selec)on from clustered data 16 3D Structure 17 utline From Topology to Geometry Conforma)onal Flexibility Molecular Mechanics 3D Structure Genera)on CRINA bstacle: Rings Internal Coordinates Conforma)onal Analysis Conforma)onal Search Methods 18 6

7 Molecule Geometry Mo>va>on Lock- and- Key Principle: A molecule s geometry must fit not it s topology 19 Molecule Geometry Geometry Topology Topologically similar structures oben have different geometries S N NH N H?? 20 Molecule Geometry Conforma>ons Structures of a molecule with idengcal topology, but different geometries are called conforma7ons Certain conforma)ons may be energe7cally more favorable than other conforma)ons Conforma)ons with (locally) minimal energy: ) Conformers In nature we observe conformers with lower energy more oben than those with higher energy ) Boltzmann distribu7on [FJ] p

8 Molecule Geometry Conforma>onal Energy How can we compute which conforma)on is favored? ) Molecular Mechanics (covered in Drug Design 1) + H 3 N N H - 22 Molecular Mechanics Simple Model of a Molecule A molecule M is defined by: 1. A set of N atoms: A = {a i } 2. A set of N atom coordinates r i = (r ix, r iy, r iz ): R = {r i } 3. A set of bonds connec)ng two atoms a i and a j : B = {b ij = {a i, a j }} a 2 a1 b 12 r 2 M = (A, R, B) Because all atoms of a molecule are connected by bonds, the molecular graph of M contains exactly one connected component 23 Molecular Mechanics Simple Model of a Molecule As in every other molecular graph, the model s nodes can be labeled arbitrarily: e.g., with the element, charge, posi)onal constraint, Important proper)es of this simple model: No bonds are formed or broken ) topology is invariable (B = const.) Coordinates may vary and describe the molecule s conforma)on Coordinates r i span the conforma7onal space of the molecule 24 8

9 Molecular Mechanics Modeling Mul>ple Molecules Mul)ple molecule models can be combined in a system ) Molecular graph with mul)ple connected components System 25 Molecular Mechanics Modeling Interac>ons Modeling of molecules requires the accurate modeling of the physical interac)ons ac)ng on the individual atoms Intra- molecular interac)ons (within a molecule) Inter- molecular interac)ons (between molecules) These interac)ons are typically described in terms of energies, i.e., there is an energy func7on E(M) assigning an energy to each conforma)on M of the molecule E(M) depends on the conforma7on (geometry) and the topology of the molecule. 26 Molecular Mechanics Interac>on Types Interac)ons can be grouped into two types: 1. Bonded interac7ons (mediated by bonds) 2. Non- bonded interac7ons (through space) In a system of N atoms, there are typically: (N) bonds and bonded interac)ons (N²) atom pairs and non- bonded interac)ons non-bonded bonded 27 9

10 Molecular Mechanics Force Field Defini)on: A consistent combina7on of several interac7on terms. A force field consists of: 1. An analy7cal descrip7on 2. Parameters for each interac)on 3. Rules describing which parameters have to be applied to which type of atom in a molecule A force field yields for each conforma)on of a molecule An energy The forces ac)ng on each atom 28 Molecular Mechanics Force Field: AMBER AMBER Assisted Model Building with Energy Refinement Developed at UCSF (University of California San Francisco) Five contribu)ons (interac)on terms) Stretches Bends Torsions Van der Waals Electrosta)cs Applicable to both proteins and DNA/RNA Developed for the refinement of X- ray and NMR models There is not one AMBER force field, but a whole family, which are usually referred to by their respec)ve year of publica)on (e.g., AMBER89, AMBER94, AMBER99) 29 Molecular Mechanics Force Field: AMBER 30 10

11 Molecular Mechanics verview of some Force Fields Force Field # atom types vdw ES HB stretch bend cross Applicable to TRIPS MP - P2 P2 - General AMBER MP - P2 P2 - Proteins, DNA CHARMM MP - P2 P2 - Proteins, DNA MM2 71 Exp-6 DP - P3 P6 sb General MM3 155 Exp-6 DP - P4 P6 sb, bb, st General MMFF MP 7-14 P4 P3 sb General DP: Dipole-Dipole MP: Monopole (Coulomb) sb: Stretch/bend bb: Bend/bend st: Stretch/torsion 31 3D Structure Genera7on Energy minimiza)on requires suitable start conforma7on Minimiza)on can produce an excellent conformer structure from a valid start conforma>on Problem: How do we get a good start conforma7on? Approach: Use informa)on about typical bond lengths, angles, and torsions Construct an ini)al 3D model sa)sfying geometric constraints Main obstacle: Rings! 32 3D Structure Genera7on Numerous algorithms in use CNCRD (Rusinko et al., 1988) CRINA (Gasteiger et al., 1990) CNVERTER (Accelrys Inc.) C1CCCCC1 Input Molecule topology (i.e., structural drawing) utput A single reasonable 3D conforma)on CauGon: The geometry produced by such a procedure is typically not op>mal (i.e., not a conformer) 33 11

12 CRINA verview CRINA (from: CoRdINAtes) Decompose structure into: 1. Acyclic parts 2. Large rings (more than 9 atoms) 3. Small/medium rings (up to 9 atoms) Uses tabulated standard bond lengths and bond angles Conforma)ons for small/medium rings are selected from a set of ring templates [GE] p CRINA verview Topology CCC(=)[C@H]1CCC2C3CCC4=CC(=)CC[C@]4(C)C3[C@@H]()C[C@]12C Internal coordinates Fragments Tables: Bond lengths Bond angles Ring templates Acyclic Substructures Large Rings Small/Medium Rings Geometry Geometry ptimization Reassembly & Structure Verification 35 CRINA Fragment Decomposi>on Molecule is decomposed into: H 1. Acyclic parts 2. Ring systems including exocyclic atoms: Small/medium rings (2 < n < 9) Large rings (n > 8) Two rings belong to the same ring system, if they share at least one atom Ring systems are classified into: Rigid systems of small/medium rings H H 3 C Rigid macrocyclic systems Flexible macrocyclic systems 36 12

13 CRINA Acyclic Parts Bond lengths depend on Element and hybridiza)on of incident atoms The bond order cis (Z) Bond angles depend on Element of the central atom Hybridiza)on state trans (E) Tabulated standard values for bond angles and lengths Values derived from experimental data (small molecule X- ray structures) Torsions chosen to maximize distances and reduce steric problems e.g., all- trans preferred over cis isomers 37 Internal Coordinates Assignment of bond lengths and angles is difficult in Cartesian coordinates Problem: Distance/angle changes influence coordinates of all neighboring atoms Independent assignment of distances, angles, torsions not possible Solu7on: ) Internal coordinates Changing the length of the central C- C bond (blue) by changing the coordinates of one of the C atoms also changes the length of the C- H bonds and angles! ) Neighboring coordinates have to be updated (based on topology) aber every change if Cartesian coordinates are used. 38 Internal Coordinates Representa)on by internal coordinates is based on angles, distances, and torsions only Reduces the number of degrees of freedom (DFs) by six: H2 nly internal DFs: no absolute posi7on and orienta7on Loss of three transla)on DFs (posi)on of barycenter) Loss of three rota)onal DFs (overall molecule orienta)on) H1 Molecules with N atoms: 3 N Cartesian coordinates 3 N 6 internal coordinates Example: Water 3 N = 9 Cartesian coordinates 3 N 6 = 3 internal coordinates Distance -H1 Distance -H2 Angle H1--H

14 Internal Coordinates Representa)on as Z- matrix H H H2 H1 Format: one line per atom 1. Atom name 2. Distance to another atom 3. Index (line number) of the correspnding neighbor 4. Angle to another atom 5. Index of the atom for the angle Example: Water 1 st Atom: 2 nd Atom: H1 Distance to atom 1: 0.95 Å 3 rd Atom: H2 Distance to atom 1: 0.95 Å Angle to atoms 1, 2: Internal Coordinates With more than three atoms, we also have to include torsions: Example: 1,2- dichlorethane C1 C Cl H H Cl H H CSD Cambridge Structural Database (CSD) is the largest database for small molecule crystal structures Small molecules = less than 1,000 atoms More than 686,944 structures of small molecules (as of Jan. 2014) From that one can derive standard values for Bond lengths Bond angles Torsion angles Conforma)ons occurring in the CSD are in general globally minimal conforma)ons!

15 CSD Torsion angle analysis of crystallized small molecules (CSD) Histograms indicate preferred values Knowledge can be used to limit conforma)onal search space n-butane [GK] p CSD Adenosine monophosphate (AMP) [GK] p Ring Conforma7ons verview Number of possible ring conforma7ons grows exponen7al in the number of ring atoms: [JG] p.234 Different conforma)ons have different energies Subs7tuents can be destabilizing as well (steric hindrances) R R R R R R R R 45 15

16 Ring Conforma7ons Small/Medium Rings For small and medium rings one can pre- compute low- energy conforma)ons (templates) Rings can be stored as lists of torsion angles Template library contains all known conforma)ons for all sizes of rings and distribu)on of double bonds Conforma)ons are ordered by energy (ring tension) Example: Envelope Planar (less favorable) (30, -30, 30, -30 ) (0, 0, 0, 0 ) 46 Ring Conforma7ons Small/Medium Rings Determine all rings in a molecule (SSSR: Smallest Set of Smallest Rings) Determine most favorable conforma)on For annulated ring systems the templates of the different rings are assembled with a backtracking algorithm [JG] p Ring Conforma7ons Rigid Macrocycles No templates available Superstructure concept (e.g., cage- like) Superstructures describe the topology of the rigid parts Consist of small rings of nodes represen)ng these rigid parts that can be handled with the algorithms for small/medium rings [JG] p.246 Atoms of the rigid substructures are reconstructed in a final step 48 16

17 Ring Conforma7ons Flexible Macrocycles A large number of possible conforma7ons prohibits the use of templates Idea: Search conforma)onal space in a simplified representa)on Based on the observa)on that large rings oben choose regular polygons as their lowest- energy [JG] p.234 Finding such a low- energy conforma)on s)ll remains difficult CRINA produces significant devia)ons from the real crystal structure for flexible macrocycles 49 Ring Conforma7ons Ring System p>miza>on Generated ring systems are op)mized with a simplified molecular mechanics force field: Bends, stretches, and torsions only Thus only intra- molecular terms Minimiza)on is rather quick Simple force field: no non- bonded terms ((N²)) Small number of atoms Convergence is usually reached aber a couple of itera)ons Independent ring systems that are part of the same molecule are op)mized independently 50 CRINA Re- assembly and Valida>on Fragments are reassembled at the bonds they were split Cartesian coordinates are calculated from internal coordinates for all atoms Resul)ng structures are tested for steric clashes Use of a Lennard- Jones poten)al Poten)al clashes are resolved by tes)ng rota)ons around rotatable bonds [C] p

18 CRINA Results FEFZIZ HIYCUN Red: structure generate by CRINA Blue: structure from the CSD 52 CRINA nline 53 CRINA nline nline form allows different input of a structure (e.g., by drawing a structure or as SMILES) Result can be downloaded as PDB Example:

19 3D Structure Genera7on Comparison of Methods Comparison of CRINA with other 3D structure generators (CNCRD, CNVERTER) Comparison of 639 structures from CSD CNCRD 1 CRINA CNVERTER 2 Converted [%] CPU time [s mol -1 ] Heavy-atom RMSD < 0.3 Å [%] Ring atom RMSD < 0.3 Å [%] [JG] p.255 [1] Pearlman R.S., In 3D QSAR in Drug Design, H. Kubinyi (Ed.), ESCM: Leiden, 1993, [2] 55 Conforma7onal Analysis verview 3D structure generators typically yield one conforma)on Drug- like molecules are flexible and can assume a large number of possible conforma)ons Lock- and- key principle: geometry is essen7al!? 56 Conforma7onal Analysis verview Input: An energy func)on (e.g., force field) A reasonable 3D structure (star)ng conforma)on) utput: All conformers Approximate energies for these conformers Problems: How to find minima of the energy func)on? How to find all conformers? 57 19

20 Conforma7onal Analysis Flexibility in Small Molecules Aroma)c rings are rigid Single bonds are rotatable Terminal bonds do not provide DFs Terminal methyl groups are irrelevant Hydrogen atoms are small compared to carbons H H HN Example: Propranolol Seven rotatable bonds 58 Conforma7onal Analysis Conforma>onal Space Poten7al Energy Surface (PES) spanned by molecule torsions Figure: 2 torsions ) 3D surface PES contains minima Minimum energy conforma)ons (conformers) Usually local minima only! Problem: How to find the global minimum? Ques7ons: Can the PES be searched exhaus)vely/systema)cally? Does one have to explore it systema)cally? [AL] p Conforma7onal Analysis Conforma>onal Space Search Two basic approaches: Systema7c search Choose discre)za)on for each torsion Enumerate all possible conforma)ons Requires algorithms for efficient search Success guaranteed for a good discre)za)on Stochas7c search Randomized search of conforma)onal space Smart choice of sampling algorithm (e.g., Monte Carlo methods) No guarantees, but oben more efficient and yielding good results 60 20

21 Conforma7onal Analysis Systema>c Search Possible for a small number of DF only Combinatorial explosion! Example: Molecule with N = 50 atoms Coordinates in a cube with edge length = 10 Å Coordinates discre)zed to 0.2 Å ) 50 discrete posi)ons for each coordinate: 50 3 discrete posi)ons in total ) (50 3 ) 50 ¼ possible conforma7ons For comparison: The whole universe is thought to consist of about elementary par)cles 61 Conforma7onal Analysis Systema>c Search Independent considera)on of all atom coordinates is not meaningful Flexibility is governed by torsions Much smaller number of true DFs Typically < 15 per molecule Few minima along the torsions Thus, coarse discre)za)on sufficient (e.g., 0/120/240 ) Avoids considera)on of physically meaningless conforma)ons H Beispiel: Propranolol 7 Torsionen je 3 Rotationswinkel 3 7 = 2187 Konformere H HN 62 Conforma7onal Analysis Systema>c Search Each torsion may assume only certain values Limit search to the torsion angles and combine them ) all hypothe)cal conformers can be enumerated Choose the most favorable ones (w.r.t. energy func)on) Root Torsion: τ Torsion: τ [AL] p

22 Conforma7onal Analysis Systema>c Search: Rings Rings cause problems Many of the conforma)ons produced by brute- force enumera)on do not sa)sfy ring closure condi7on Majority of ring conforma)ons will be invalid! [JG] p Conforma7onal Analysis Systema>c Search: Rings Use templates for known ring structures Enumera)on for ring atoms not over individual torsions, but ring templates Reduces search space and avoids meaningless conforma)ons As in CRINA, ring templates can be combined if they are sterically compa)ble [JG] p Conforma7onal Analysis Systema>c Search Avoid branches of enumera)on tree that contain clashes If a clash is detected, the induced branch is not considered any further ) Significantly reduce search space! Root [JG] p

23 Conforma7onal Analysis Randomized Methods Evolu7onary Algorithms: Encode torsion angles as ar)ficial chromosomes Gene)c operators: cross- over and mutagon Metropolis- Monte Carlo (MMC): Create random conforma)on Accept conforma)on if MMC criteria are fulfilled Abort if a large enough number of conforma)ons has been produced ben a subsequent clustering of conforma)ons is applied 67 Conforma7onal Analysis Example Conforma)onal sampling of n- butane Energy (kj/mol) Torsion angle τ [GK] p Conforma7onal Analysis Example Conforma)onal sampling of AMP [GK] pp

24 Summary II Three- dimensional structure is important for biological ac)vity Molecules are flexible and can adopt mul)ple conforma)ons Conforma)onal energy can be described by molecular mechanics CRINA can be used to construct a 3D structure from a topology Conforma)onal analysis can then reveal the conforma)onal space that a molecule can span Treatment of rings is non- trivial 70 References Books: [AL] Andrew Leach: Molecular Modelling: Principles and Applica)ons, 2nd ed., Pren)ce Hall, 2001 [LG] Andrew Leach, Valerie Gillet: An Introduc)on to Chemoinforma)cs, Kluwer, 2003 [GE] Johann Gasteiger, Thomas Engel: Chemoinforma)cs. A Textbook, Wiley- VCH, 2003 [GK] Gerhard Klebe: Wirkstoffdesign, Spektrum, 2nd ed., 2009 [JG] Johann Gasteiger (ed.): Handbook of Chemoinforma)cs, Vol. 1, Wiley- VCH, 2003 [FJ] Frank Jensen: Introduc)on to Computa)onal Chemistry, 2nd ed., Wiley,