Enhancing Search Space Diversity in MultiObjective Evolutionary Drug Molecule Design using Niching

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Enhancing Search Space Diversity in
Multi-Objective Evolutionary Drug Molecule Design
using Niching
M.T.M Emmerich1 T. Bäck1,3
A. Aleman1 A.P. IJzerman2 E. van der Horst2
J.W. Kruisselbrink1 A. Bender2
1. Leiden Institute of Advanced Computer Science
(LIACS) 2. Leiden/Amsterdam Center for Drug
Research (LACDR) 3. NuTech Solutions, Inc.
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Scope drug design and development

• 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

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Molecule Evolution

• Normal evolution cycle
• Graph based mutation and recombination operators
• Deterministic elitistic (µ?) parent selection
  (NSGA-II)

Fragments extracted from From Drug Databases
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Molecule Evolution
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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 Lipinskis rule
  of five and bounds on the minimal energy
  confirmation

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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

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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

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Typical output of a normal evolutionary search
All molecules are variations of the same theme!
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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

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Niching-based NSGA-II
A Niching-based NSGA-II algorithm as proposed by
Shir et al.
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Dynamic Niche Identification
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
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Similarity in Molecular Spaces

• How to define a similarity measure for the
  graph-like molecular structures?
• Idea use molecular fingerprints

• 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

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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!
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Triangle inequality
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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.

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Triangle inequality
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Molecule Evolution with Niching
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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

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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)

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Average Pareto Fronts
NPY2
LOX
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Average distance between the individuals in the
final populations
NPY2
LOX
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Output sets of a NPY2 run without and with niching
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Output sets of a LOX run without and with niching
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Multi-dimensional Scaling Plots

• No Niching Niching

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The chemists 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

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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

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Thank you!
Alexander Aleman Natural Computing Group LIACS,
Universiteit Leiden e-mail alexander.aleman_at_gmail
.com