Leiden University. The university to discover. Enhancing Search Space Diversity in Multi-Objective...

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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. Aleman1

A.P. IJzerman2

E. van der Horst2

M.T.M Emmerich1

T. Bäck1,3

J.W. Kruisselbrink1

A. Bender2

- 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: 1020-1060 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

Molecule Evolution

Fragments extracted fromFrom Drug Databases

While not terminate do

Generate offspring O from PPt+1= select from (P U O)

Evaluate O

Initialize population P0

- ‘Normal’ evolution cycle- Graph based mutation and

recombination operators- Deterministic elitistic (μ+λ)

parent selection (NSGA-II)

Molecule Evolution

Fitness

Objectives:- activity predictors based on support vector machines:

- f1: activity predictor based on ECFP6 fingerprints- f2: activity predictor based on AlogP2 Estate Counts- f3: activity predictor based on MDL

Constraints:- a fuzzy constraint score based on Lipinski’s rule of five and bounds

on the minimal energy confirmation:

Desirability indexes for modeling fuzzy constraints

The degree of satisfaction can be measured on a scale between 0 and 1Constraints can be modeled in the form of desirability values

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

All molecules are variations of the same theme!

Typical output of a ‘normal’ evolutionary search

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

Niching-based NSGA-II

A Niching-based NSGA-II algorithm as proposed by Shir et al.

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

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

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!

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.

Triangle inequality

Molecule Evolution with Niching

ExperimentsAim:

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

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)

Average Pareto Fronts

Average distance between the individuals in the final populations

Output sets of a NPY2 run without and with niching

Output sets of a LOX run without and with niching

Multi-dimensional Scaling Plots

No Niching Niching

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

Conclusions and OutlookConclusions:- 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

Thank you!

Alexander AlemanNatural Computing GroupLIACS, Universiteit Leidene-mail: alexander.aleman@gmail.com

Leiden University. The university to discover. Enhancing Search Space Diversity in Multi-Objective...

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