1. Leiden University. The university to discover. Enhancing Search Space Diversity in Multi-Objective Evolutionary Drug Molecule Design using Niching 1. Leiden Institute of Advanced Computer Science (LIACS) 2. Leiden/Amsterdam Center for Drug Research (LACDR) 3. NuTech Solutions, Inc. A. Aleman 1 A.P. IJzerman 2 E. van der Horst 2 M.T.M Emmerich 1 T. Bäck 1,3 J.W. Kruisselbrink 1 A. Bender 2

2. Leiden University. The university to discover. -Search for molecular structures with specific pharmacological or biological activity that influence the behavior of certain targeted cells -Objectives: Maximization of potency of drug (and minimization of side-effects) -Constraints: Stability, synthesizability, drug-likeness, etc. -A huge search space: 10 20 -10 60 drug-like molecules -Aim: provide the medicinal chemist a set of molecular structures that can be promising candidates for further research Scope: drug design and development

3. Leiden University. The university to discover. Molecule Evolution Fragments extracted from From Drug Databases While not terminate do Generate offspring O from P P t+1 = select from (P U O) Evaluate O Initialize population P 0 -‘Normal’ evolution cycle -Graph based mutation and recombination operators -Deterministic elitistic (μ+λ) parent selection (NSGA-II)

4. Leiden University. The university to discover. Molecule Evolution

5. Leiden University. The university to discover. Fitness Objectives: -activity predictors based on support vector machines: -f 1 : activity predictor based on ECFP6 fingerprints -f 2 : activity predictor based on AlogP2 Estate Counts -f 3 : activity predictor based on MDL Constraints: -a fuzzy constraint score based on Lipinski’s rule of five and bounds on the minimal energy confirmation:

6. Leiden University. The university to discover. Desirability indexes for modeling fuzzy constraints The degree of satisfaction can be measured on a scale between 0 and 1 Constraints can be modeled in the form of desirability values

7. Leiden University. The university to discover. Diversity for Molecule Evolution -A ‘normal’ search yields very similar molecular structures -Aim for a set of diverse candidate structures because: -Vague objective functions may result in finding structures that fail in practice -The chemist desires a set of promising structures rather than only one single solution -Explicit methods are required to enforce diversity in the search space; i.e. niching

8. Leiden University. The university to discover. All molecules are variations of the same theme! Typical output of a ‘normal’ evolutionary search

9. Leiden University. The university to discover. Niching in Multi-Objective EA -Explicitly aim for diversity in the decision space -Different than aiming for diversity in the objective space -Points that lie far apart in the objective space do not necessarily also lie far apart in the decision space

10. Leiden University. The university to discover. Niching-based NSGA-II A Niching-based NSGA-II algorithm as proposed by Shir et al.

11. Leiden University. The university to discover. Dynamic Niche Identification Peak individuals q=3 Individuals that do not belong to niche B.L. Miller, Shaw, M.J.: Genetic algorithms with dynamic niche sharing for multimodal function optimization, Proceedings of IEEE International Conference on EC, May 1996, Pages: 786-791

12. Leiden University. The university to discover. Similarity in Molecular Spaces -Molecules are represented by bitstrings identifying certain structural properties -A ‘1’ at position i denotes the presence of property i in the molecule, and ‘0’ at position i denotes the absence of property i -How to define a similarity measure for the graph-like molecular structures? -Idea: use molecular fingerprints

13. Leiden University. The university to discover. Distance based on fingerprints -The distance between two molecules A and B can be based on the four terms: -a: the number of properties only present in A -b: the number of properties only present in B -c: the number of properties present in both A and B -d: the number of properties not present in A and B -One possible distance measure can be created using the Jaccard coefficient (also known as Tanimoto coefficient): The Jaccard distance fullfills the triangular equation, as opposed to for example the cosine-distance!

14. Leiden University. The university to discover. Triangle inequality

15. Leiden University. The university to discover. Triangle inequality Why do we want to have a dissimilarity (distance) measure that obeys the triangle inequality? If we have very similar molecules, say molecule A is similar to B and molecule A is also similar to C, then we want to be able to say that B is similar to C.

16. Leiden University. The university to discover. Triangle inequality

17. Leiden University. The university to discover. Molecule Evolution with Niching

18. Leiden University. The university to discover. Experiments Aim: Compare the niching-based NSGA-II method with the normal NSGA-II method Two test-cases: -Find ligands for the Neuropeptide Y2 receptor (NPY2) -Find inhibitors for the Lipoxygenase (LOX) Two objectives: -Aggregated fitness score based on activity predictors -Aggregated constraints score function

19. Leiden University. The university to discover. Experimental setup -5 runs for each method on each test-case -1000 generations per runs -Normal NSGA-II: -50 parents -150 offspring -Niching-based NSGA-II: -10 niches -5 parents per niche -150 offspring -niche radius set to 0.85 (empirically set)

20. Leiden University. The university to discover. Average Pareto Fronts NPY2: LOX:

21. Leiden University. The university to discover. Average distance between the individuals in the final populations NPY2: LOX:

22. Leiden University. The university to discover. Output sets of a NPY2 run without and with niching

23. Leiden University. The university to discover. Output sets of a LOX run without and with niching

24. Leiden University. The university to discover. Multi-dimensional Scaling Plots No NichingNiching

25. Leiden University. The university to discover. The chemist’s view on the output Regarding the niching: -The molecules found with the niching method are clearly more diverse than the molecules found by the non- niching approach In general: -The molecules look reasonable overall, but: -Most molecules still possess unstable and/or toxic features that are not easy to synthesize in practice -Similar types of uncommon features seem to appear

26. Leiden University. The university to discover. Conclusions and Outlook Conclusions: -Applying niching using the Jaccard distance based on molecular fingerprints and is a way to enhance search space diversity in molecule evolution -It yields more diverse sets of molecules than a normal evolutionary algorithm for molecule evolution Future research: -Applying these methods on other (more sophisticated) models as well -In vitro testing of selected molecules found using this method -Incorporate more sophisticated measures for testing the synthesizability of candidate molecules

27. Leiden University. The university to discover. Thank you! Alexander Aleman Natural Computing Group LIACS, Universiteit Leiden e-mail: alexander.aleman@gmail.com