A Multiobjective Approach to Combinatorial Library Design

1
A Multiobjective Approach to Combinatorial
Library Design

• Val Gillet
• University of Sheffield, UK

2
Outline

• SELECT
• GA based program for combinatorial library design
  
• Combinatorial subset selection in product-space
• Multiobjective optimisation via weighted-sum
  fitness function
• Limitations of a weighted-sum approach
• MoSELECT
• Multiobjective optimisation via MOGA

3
Library Design is a Multiobjective Optimisation
Problem

• Early HTS results disappointing
• Low hit rates
• Hits too lipophilic too flexible high molecular
  weights
• Diverse libraries
• Distance-based/cell-based diversity
• Bioavailability cost ease of synthesis
• Focused/targeted libraries
• Similarity to known active predicted active by
  QSAR model fit to receptor site
• Bioavailability cost,.

4
Product-Based Library Design

• A two-component combinatorial library can be
  represented by a 2D array
• A combinatorial subset can be defined by
  intersecting rows and columns of the array
• Exploring all combinatorial subsets is equivalent
  to testing all permutations of the rows and
  columns of the array

5
Selecting Combinatorial Subsets Using a GA

• Chromosome encoding
• each chromosome represents a combinatorial subset
  as an integer string
• one partition for each reactant pool
• the size of a partition equals the no. of
  reactants required from the corresponding pool
• Crossover, mutation and roulette wheel parent
  selection are used to evolve new potential
  solutions

6
Multiobjective Optimisation in SELECT

• Weighted-sum fitness function
• enumerate the combinatorial library represented
  by a chromosome
• calculate descriptors for molecules in the
  library
• Objectives are scaled and user defined weights
  are applied

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Multiobjective Optimisation in SELECT cont.

• Diversity indices
• distance-based (e.g. sum of pairwise
  dissimilarities and Daylight fingerprints)
• cell-based
• Physical property terms
• minimise the difference between the distribution
  in the library and some reference distribution,
  e.g.
• drug-like profile derived from WDI
• Cost
• minimise the cost of the library

8
Library Enumeration in SELECT

• Virtual library is enumerated upfront
• ADEPT (A Daylight Enumeration and Profiling Tool)
• Identify potential reactants
• Filter out unwanted ones
• Enumerate virtual library
• Reaction Tookit (Reaction transforms MTZ
  language)
• Descriptors are calculated upfront
• Combinatorial subset accessed via fast lookup

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Example Amide Library

• 10K virtual library
• 100 amines 100 carboxylic acids
• 30 x 30 amide subsets
• WDI World Drugs Index
• Reactant-based selection diversity (Diversity
  0.564 )

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WDI
20
15
Percentage of Compounds
10
5
0
0
200
400
600
800
Molecular weight
10
Limitations of a Weighted-Sum Fitness Function

• Definition of fitness function difficult
  especially for different types of objectives
• e.g. molecular weight profile and cost
• Setting of weights is non-intuitive
• Can result in regions of search space being
  obscured especially when objectives are in
  competition
• Difficult to monitor progress since gt1 objective
  to follow simultaneously
• A single solution is found

11
Varying Weights in SELECT

• Objectives are in competition resulting in
  trade-offs
• A family of alternative solutions exist that are
  all equivalent

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Multiobjective Optimisation

• Evolutionary algorithms, e.g., GAs
• operate with a population of individuals
• well suited to search for multiple solutions in
  parallel
• readily adapted to deal with multiobjective
  optimisation
• MOGA MultiObjective Genetic Algorithm
• Fonseca Fleming. IEEE Transactions on Systems,
  Man, and Cybernetics-Part A Systems and Humans,
  28(1), 1998, 26-37.

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MOGA

• Multiple objectives are handled independently
  without summation and without weights
• A hyper-surface is mapped out in the search space
• represents a continuum of solutions where all
  solutions are seen as equivalent
• represents compromises or trade-offs between the
  various objectives
• solutions are called non-dominated, or Pareto
  solutions.
• A family of non-dominated solutions is sought
  rather than a single solution

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Dominance Pareto Ranking
f2

• A non-dominated individual is one where an
  improvement in one objective results in a
  deterioration in one or more of the other
  objectives when compared with the other
  individuals in the population

A
B
f1
15
SELECT
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MoSELECT Search Progress
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Family of Solutions

• Each run of MoSELECT results in a family of
  solutions
• Finding the same coverage of solutions using
  SELECT would require multiple runs using various
  combinations of weights
• One run of MoSELECT takes the same cpu time as
  one run of SELECT

5000 iterations
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Focused Library Aminothiazoles

• a-bromoketones thioureas extracted from ACD
• ADEPT used to
• filter reactants (MW lt 300 RB lt 8)
• enumerate virtual library gt 12850 products (74
  a-bromoketones 170 thioureas)
• MoSELECT used to design 1530 subsets optimised
  on
• Similarity to a target compound (Daylight
  fingerprints)
• Cost (/g)

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MoSELECT Solutions 1
0 iterations
20
MoSELECT Solutions 2
5000 iterations
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Moving to gt 2 ObjectivesParallel Graph
Representation
5000 iterations
0.578
0.582
Diversity
0.586
0.59
0.594
0.58
0.6
0.62
0.64
D
MW
Each objective is scaled using the Max and Min
values achieved when the objective is optimised
independently
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Focused Library Amides

• 100 100 virtual library
• MoSELECT used to design 10 10 subsets
• Objectives
• Similarity to a target
• Sum of similarities using Daylight fps
• Predicted bioavailability
• Each compound rated from 1 to 4
• Sum of ratings
• Hydrogen bond profile
• Rotatable bond profile

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MoSELECT Solutions

• Population size 50
• Iteration 5000
• Niching 30
• Number of solutions 11
• CPU 53s (R12K 360 MHz)

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Conclusions

• Advantages of MoSELECT
• a family of equivalent solutions is obtained in a
  single run with each solution representing one
  combinatorial library
• this is achieved at vastly reduced computational
  cost compared to performing multiple runs of
  SELECT
• no need to determine weights for objectives
• optimisation of different types of objectives is
  readily achieved
• visualisation of the search progress allows
  trade-offs between objectives to be observed
• the user can make an informed choice on which
  solution(s) to explore

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Acknowledgements

• Illy Khatib, Peter Willett Information Studies,
  University of Sheffield
• Peter Fleming Automatic Control and Systems
  Engineering, University of Sheffield
• Darren Green, Andrew Leach GlaxoSmithKline, UK
• Funding by GlaxoSmithKline, UK
• John Bradshaw Daylight
• Daylight for software support