Drug Discovery: Exploring The Utility Of Cluster

Drug Discovery: Exploring the Utility of Cluster Oriented Genetic Algorithms in Virtual Library Design B. Sharma & I. Parmee

M. Whittaker & A. Sedwell

ACDDM Lab (www.ad-comtech.co.uk/ACDDM_Group.htm) University of West of England, Bristol BS16 1QY bhuvan.sharma, [email protected]

Evotec OAI 151 Milton Park Abingdon Oxon, OX14 4SD mark.whittaker, [email protected]

Abstract- In silico combinatorial library design involves the identification of molecules that have a greater probability of exhibiting desired biological activity when subjected to in vitro screening (assaying) against a particular biological target. The paper introduces the integration of cluster-oriented genetic algorithms (COGAs) with such machine-based library design environments. COGAs have a proven capability to identify highperformance regions of complex, continuous design spaces relating to engineering design problems. Modifications to the basic COGA approach are described that allow a transfer of this capability from continuous variable parameter space to the highly discrete spaces described by reactants across reagent libraries. Results relating firstly to the identification of optimal molecules and secondly to the focussing of reagent libraries in terms of high-performance reactants are presented. Single objective optimisation and focussing are initially considered before moving on to multiple objective satisfaction.

carboxylic acids, amines, aldehydes etc. All molecules that contain the key reactive functional group for a reagent would constitute possible reactants across that reagent. In this sense, in a variable parameter space reagent refers to a particular variable parameter (dimension) whereas reactants are the available values / molecules across that dimension.

1 Introduction Drug design and discovery is a systematic, serial process of identification and modification of chemical structure to achieve desired results against biological targets associated with a particular disease. Tradionally, the process involves the development of a biochemical assay for a biological target of interest and the subsequent screening of large numbers of drug-like organic chemical compounds in a high-throughput manner to identify hit compounds. Such hit compounds usually possess weak biological activity that requires improvement by a process of medicinal chemistry optimisation first into a lead series with robust properties and then into a drug candidate that is suitable for evaluation in human clinical trials. This process requires the optimisation of multiple parameters including biological activity, selectivity for the biological target of interest over related proteins, pharmacokinetics, pharmacodynamics and pharmaceutical properties. In modern drug discovery extensive use is being made of in silico techniques to find hit molecules through virtual screening and to then aid their subsequent optimisation. A large compound collection in the form of virtual libraries is described by the reagents required for their synthesis as shown in figure 1. Reagents (inputs to the reaction equation in figure 1) are the chemical reactants required to make a set of molecules. Examples of reagents could be

R1

OH

+

H2N R2

H N

R1

O

R2

O

Carboxylic Acid + Primary Amine ! Secondary Amide Figure 1. Sample reaction scheme The number of possible compounds in a virtual library can be in the order of many millions and this number combinatorially increases with number of included reagents. These libraries may then be subjected to in silico screening to identify compounds (hits) that exhibit activity against the biological target during the subsequent assay. In silico models such as molecular docking, pharmacophore matching, QSAR (Quantitative StructureActivity Relationship), and chemical similarity are utilised as objective functions to identify possible highperformance compounds that have a greater probability of exhibiting desired biological activity during in vitro assaying. The size of the virtual libraries coupled with computational expense relating to most of the objective functions rule out exhaustive search (i.e. complete enumeration of all library members from the corresponding chemical reagents). What is therefore required is a search process that rapidly samples and identifies as many high performance molecules as possible within available time limitations. The development and integration of appropriate search techniques during in-silico screening could significantly enhance the drug discovery process by both improving the hit rates during assaying and reducing drug design cycle times. In collaboration with Evotec OAI, Cluster-oriented Genetic algorithms (COGAs) have been integrated as a potential user-interactive search and exploratory tool with Evotec OAI’s existing drug design software, EVOSeek™. COGA [1] has a proven capability within engineering design environments described by continous variables to

identify regions of high performance (HP) solutions. This can be achieved with no apriori knowledge of the problem space in terms of possible number of local optima and the settings of niche radii, sharing factors etc. The successful transfer of COGA technology to combinatorial chemical space offers significant potential in terms of the ability to identify groupings of HP reactants and hence support the focussing of reagent libraries or the identification of individual HP molecules. This library focussing and optimisation capability is therefore the motivation for the research described in the following sections. This work represents a proof-ofconcept relating to the potential of COGA integration. Section 2 is a brief review of library design literature. Section 3 introduces the COGA methodology. Section 4 describes initial experimentation to determine basic COGA performance Section 5 concentrates upon identufying optimal molecules from a test library whereas Section 6 presents the introduction of a tabu element to the basic COGA to enable focussing of this library. Scaleability issues are investigated in section 7 before moving on to multi-objective satisfaction in section 8.

2 Background A review of drug design approaches and strategies can be found in Tsinopoulos and McCarthy [2]. Computer Aided Drug Design found application in the early 1990s in terms of the modelling of structure-activity relationships (SARs). The introduction of evolutionary computing (EC) techniques to modelling strategies began to emerge a little later. Milne [3] reports of only five published papers employing evolutionary algorithms between 1989 and 1992. However between 1993 and 1997 more than 210 EC-based papers appeared as reviewed in [4,5,6,7]. The first published application of EC to combinatorial library design was by Sheridan et al. [8] utilising a measure of chemical similarity as an objective function. Papers by Singh et al. [9] and Weber et al. [10] however utilised the results from in vitro biological activity to provide a fitness measure for a GA-based search thus providing a proof-ofconcept of the potential of a GA to direct reactant selection for chemical synthesis. Gillet et. al. [11] developed a GA based technique (SELECT) to optimise virtual libraries against a single diversity objective using a distance based diversity matrix. A weighted sum approach for multiple objectives was refined [12] via the introduction of a multi objective genetic algorithm (MoSELECT). Wright et al. [13] developed a different selection scheme in MoSELECT-II for the optimization of library size and configuration. Brown et al. [14], using a GA based approach called GALOPED, also addressed size and configuration whereas Pickett et al. [15] introduced Monte Carlo approaches to achieve similar objectives. There is little comparison between previous work and the aims and objectives of the research described in the paper. Our objective, initially using chemical similarity, is to optimise and focus a library as opposed to Gillet’s objective of generating a diverse library as described in [11]. Whereas we introduce search, optimisation and multi-objective satisfaction in large reagent libraries

other works [8,9,10] have attempted single objective optimisation on significantly smaller libraries, This, plus the absence of suitable benchmark problems, makes comparison of our results with other works very difficult.

3 Cluster Oriented Genetic Algorithms (COGA) Cluster Oriented Genetic Algorithms, initially developed by Parmee in the early 1990s [1], provide the means to identify high-performance (HP) regions of complex conceptual engineering design spaces and enable the extraction of information from such regions [16,17]. COGAs identify HP solution regions through the on-line adaptive filtering of solutions generated by a genetic algorithm. Further work resulted in several variations of COGA and also identified and illustrated the manner in which the COGA approach can be utilised to generate highly relevant design information relating to single and multi-objective problem domains [17,18,19]. COGA comprises two primary components: the diverse search engine which utilises a highly exploratory genetic algorithm to search the design space and the adaptive filter (AF) which extracts solutions from each COGA generation and stores them within a Final Cluster Set (FCS). The AF scales solution fitness in terms of distance from the mean (figure 2) and only solutions that lie above a pre-defned threshold value, Rf, are copied to the FCS. By reducing the severity of Rf, more HP solutions albeit with a lower average fitness can enter the FCS. The user can therefore vary the filter setting in order to identify regions ranging from succinct groupings of very high performance solutions to larger regions of high and lower performance solutions. Design space exploration is enhanced in the underlying search engine via variable mutation regimes [1] or Halton injection sequences [20]. Sufficient HP regional set-cover (in terms of number of solutions) can be achieved to allow significant qualitative and quantitative design information to be extracted. It is not possible within the space available to provide a more detailed description of COGA. However, anyone wishing to replicate the research in this paper can refer to well-documented COGA development in many papers available at http://www.ad-comtech.co.uk/ParmeePublications.htm. The COGA approach was primarily developed for search and exploration across design spaces described by continuous variable parameters which tend to predominate in engineering design. Typical COGA output from continuous design spaces comprises clusters of solutions describing high performance regions. The spread and distribution of these high quality solutions can offer a wealth of information relating to the characteristics of the search space and the complex relationships between variable and objective space as demonstrated in Parmee et. al. [17,19, 21].

3.1 Representation One of the challenges in the research described in the following sections has been to modify the COGA approach in order to ensure a similar utility to that proven in engineering design when searching the discrete combinatorial problem spaces that are an all pervading aspect of drug design. Given the very positive results from the engineering design domain the initial asssumption was that application of COGAs would significantly support the identification of ‘best’ reactants. The chemist could interact with the evolutionary process by varying the adaptive filter to identify either succinct groupings of high-performance molecules or larger collections of lesser performance molecules in terms of any chosen in silico objective function (e.g. QSAR, chemical similarity etc). Binary representation has generally been utilised within the original COGA algorithms. However binary representation for reactants of each reagent revealed a number of potential problems. For instance, directly mapping binary strings onto the integer space comprising the numbered address of each reactant molecule of a reagent grouping results in illegal solutions and / or a degree of redundancy. Problems relating to the crossover of binary strings, the generation of non-feasible solutions and a subsequent requirement for chromosome repair were also inherent.

A test virtual library from the reaction scheme of Figure 1 comprising amines and acids was initially chosen to assess the performance of COGA utilizing Tanimoto Similarity as a simple test objective function. The two reagents each possess 400 reactants creating a search space of 160,000 possible solutions. To allow a true evaluation of COGA performance and proof-of-concept all the product molecules in this virtual library were enumerated and their chemical similarity to a specific drug molecule (methotrexate) calculated. This allows the top 0.5% solutions to be plotted as shown in figure 3 which illustrates a typical distribution of highperformance solutions against which COGA output can be compared. The plot in Figure 3 indicates that: • good solutions can be distributed across the entire range of a virtual library; • reactants producing a high percentage of good solutions can be easily identified. With these results in mind it was intended to determine the potential of the COGA approach in terms of: • optimisation i.e. the identification of a number of very high performance molecules; • focussed library i.e. the identification of high performance reactants that provide a focussed combinatorial compound library the members of which include a significant number of high performance molecules.

Figure 2: The adaptive filter (AF) A straightforward integer encoding was therefore adopted where integer values represent an index of a reactant’s location in the proprietary database. The chromosome in our integer representation scheme has a length (number of genes) equal to the number of dimensions (reagents) of the virtual library. A gene can then take an integer value between one and the maximum number of reactant molecules across that dimension. This number can directly be transposed to the index of that reactant molecule in the chemical database of molecules. The phenotype then is the product molecule of the reaction involving the reactant molecules represented by each gene in the chromosome.

4 Initial Experimentation and Results

Figure 3. Top 0.5% solutions in test library identified by exhaustive search and enumeration

It was initially assumed that appropriate settings of the adaptive filter threshold of COGA would result in the achievement of each of these objectives. High filter settings would provide smaller numbers of HP solutions whereas low settings would identify much larger numbers of high performance solutions with a lower average fitness which would also support the identification of high performance reactants i.e. reactants generally exhibiting high-performance across all possible combinations. Before investigating these initial assumptions both variable mutation COGA (vmCOGA) and Halton injection COGA (hiCOGA) were investigated with the test virtual library from Figure 1 to determine their comparative performance. Performance criteria relates to

Figure 4: Plot of solutions from the FCS of a typical hiCOGA search of the test library

Further experimentation involving variation of the number of Halton injections per generation and variation of the vmCOGA’s mutation regimes further indicated that, in terms of discrete space search, hiCOGA performs better both in terms of the identification of high performance solutions and robustness.

5 Optimisation For the enumerated 400 x 400 amine-acid test library the fitness (chemical similarity against methotrexate) range is between 0.0003 and 0.5812. The identification of small numbers of very high performance molecules can be achieved by appropriate setting of the AF filter.

(a)

(b)

count ( x10^ 3)

Figure 5: Numbers of HP solutions matching the test set for 50 runs of (a) hiCOGA and (b) vmCOGA 4 3.5 3 2.5 2 1.5 1 0.5 0 -1.5

-1

-0.5

0 0.5 1 1.5 2 Rf setting Figure 6a: Variation of solution count in FCS at differing Rf settings 0.56 0.55 0.54 0.53 0.52 0.51 0.5 0.49 0.48 -1.5 -1 -0.5 0 0.5 1 1.5 2 Rf setting avgfitness

each COGA’s ability to identify, within their final clustering sets (FCSs), the greatest number of the enumerated top 0.5% solutions from the exhaustive search. The degree of robustness of each approach was also considered to be a significant criteria. The overall objective of this comparative study was to identify which approach to concentrate further effort on. The top 0.5% of the possible 160,000 solutions of the test virtual library comprised 800 molecules. An adaptive filter setting of 0.9 was initially introduced and a typical plot of the solutions from a hiCOGA’s FCS is shown in figure 4. Similar typical plots from vmCOGA’s FCS have also been generated. The results indicated that both vmCOGA and hiCOGA identify significant numbers of high performance solutions across the library. Fifty runs each of hiCOGA and vmCOGA were executed in each of which a population size of 100 individuals running over 200 generations was utilised. For each run the number of FCS solutions that match those in the top 0.5% of the test library were extracted and are shown in figure 5a and 5b. On average hiCOGA identified ~200 solutions out of the best 800 (top 0.5%), whereas vmCOGA identifed ~150 solutions. It is also evident from the plots that hiCOGA also proved to be more robust with the standard deviation of matching solutions being significantly less than that of the vmCOGA. Robustness is of particular importance in terms of integrating COGA techniques with the in silico drug design processes within Evotec OAI’s EVOseek™ Software.

Figure 6b: Variation of average solution fitness in FCS at differing Rf settings

Figure 6a shows the variation of numbers of HP solutions in the FCS at different filter settings. Figure 6b shows the the average solution fitness within the FCS for different filter settings. The results represent average hiCOGA FCS fitness of 50 runs of 200 generations each at each filter setting with a population size of 100. A typical result from a single 200 generation run of hiCOGA with a filter setting of 2.0 would be an FCS containing circa 45 solutions with an average fitness of 0.56. Dropping the

Figure 7: User interface from EVOseek™ showing top best performing molecules

filter to the previous 0.9 setting results in circa 400 solutions in the FCS with an average fitness of 0.54. This optimisation process has now been integrated with Evotec OAI’s EVOseek™ software with an appropriate user-interface that allows the chemist to explore reagent space via use of different objective functions and the setting of contstraints (e.g. molecular weight, calculated lipophilicity, hydrogen bond donor and acceptor counts). The chemist can request visualisation of a number of the top performing molecules from the optimisation process which are then presented in a tabular form as shown in figure 7. These have been generated from the integrated software on a live (i.e. non-enumerated) library comprising two reagents viz. haloalkane and amine. Fitness was calculated using tanimoto chemical similarity against a molecule known to be present in the library.

6 Generating Focussed Libraries Returning to the plots of the fully enumerated test set (figure 3) of Section 4 and the results from the initial hiCOGA implementation (figure 4); these indicate the existence of high-performance (HP) axes relating to individual reactants. These significantly differ from the typical HP regions identified in continuous design space [16,17,21]. The identification of such axes allows the chemist to develop a focussed library of reactants that provide an enrichment of high performance molecules. Experimentation showed that both hiCOGA and vmCOGA FCS’s contain some HP axes but it is apparent when comparing output to the enumerated test set that many others were not identified. It appears that the explorative nature of the underlying GAs was not sufficient to avoid convergence upon a subset of available HP axes. Further experimentation showed that increasing exploration via increased Halton injection or mutation was not the answer as HP axis identification did not improve and it appeared likely that an appropriate balance between exploration and exploitation does not exist that

will overcome the problem. An alternative search and exploration strategy that rapidly identifies a HP axis but then moves on to discover other axes in unexplored regions of search space was required. One way to achieve this is to introduce some form of memory into the COGA process. In this respect elements of tabu search seemed to offer some utility in formulating a new approach called tabu-COGA (taCOGA). COGA’s FCS is a repository of high fitness solutions an analysis of which during run time could give an indication of the presence of HP axes. After a specified initial number of generations solutions in the FCS can be analysed at each subsequent generation to assess the count of solutions involving specific reactants. A threshold count could be used to identify when a reactant is eligible to be declared as a HP axis. Thereafter, this reactant would become tabu and the search could be directed to other less-visited areas of library space. Some form of replacement strategy is therefore required that, to some extent, re-initialises tabu solutions. Two such strategies have been considered: a) Reactant Replacement (RR): Here the tabu reactant is replaced by another reactant randomly selected from the entire search space. b) Fitness Reassignment (FR): In this approach any solution containing a tabu reactant is assigned a low fitness. The objective of taCOGA is to identify maximum number of true HP axes within a minimum number of generations/ fitness evaluations. With this in mind determining a robust and meaningful threshold count presented a problem. Too low a count and individual HP solutions could falsely render a reactant ‘high-performance’ whereas too high a count could result in very lengthy COGA run times to identify a sufficient number of HP axes. A preliminary experiment utilising hiCOGA with the same test library and filter and injection settings as utilised in the experiments of section 4 was carried out to establish an initial threshold count for taCOGA.

7 Increasing Dimension

Figure 8. Change in HP axes identified with increasing tabu threshold count.

Figure 9a. Number of HP Axes for R1 and R2 identified via RR (Reactant Replacement) strategy. Results given for 50 runs.

Having established a basic working system via the two dimensional enumerated test library, hiCOGA was then integrated with a live library of three reagents (primary amines, aromatic acids, aldehydes) with a total size of 400 x 400 x 400 (64 x 106) reactant combinations. In this case a focussed library approach (i.e. with tabu) again using chemical similarity against methotraxate as a criteria was introduced with a hiCOGA filter setting of 0.9. Resulting plots of FCS solutions projected onto two dimensional hyperplanes are shown in figure 10. The plots show identification of a significant number of high performing reactant axes which can be further investigated by the chemist. A four reagent virtual library comprising aliphatic ketone, isocyanide, primary amine and unsaturated carboxylic acid creating a library of 5297 x 32 x 17510 x 23060 (6.8 x 1013 ) molecules was then introduced. Chemical similarity against a target molecule known to have close analogs in the library, provided an objective for an optimising hiCOGA (i.e. no tabu). Tentative fitness range therefore was between 0.0 and 0.9. The best solution fitness achieved is 0.761 in just 200 generations with a population size of 100 which is considered a promising result considering the size and nature of the search space

8 Multi-objective satisfaction within combinatorial libraries

Figure 9b. Number of HP Axes for R1 and R2 identified via FR (Fitness Reassignment) strategy. Results given for 50 runs.

Average results from 50 runs utilising increasing counts indicated that, for threshold counts below 10, the variation in the number of identified high performance axes was higher than the degree of variation between threshold counts greater than 10 (see figure 8). For this reason a threshold count of 10 was initially adopted for further investigation of the approach. However, further validation in this area is required. A series of experiments then assessed the exploratory potential of the two replacement strategies (RR and FR) with a tabu thereshold count of 10. 50 runs for each strategy were initiated to determine the number of HP axes along each reagent that they could identify. Results are given in figure 9a and 9b.The reactant replacement strategy consistently identifies a greater number of HP axes. It is likely that the immediate reassignment of tabu reactants is more effective than the more gradual replacement of tabu reactants that occurs with fitness reassignment.

Various in silico models can be used as objective functions to ascertain molecule performance against differing criteria. Molecules best satisfying a number of differing criteria have a greter probability of passing the subsequent in vitro tests. In addition to chemical similarity other simple in silico objectives are cLog P, Polar surface area (PSA) and Molar Refractivity. In addition, more sophisticated Quantitative Structure Activity Relationships (QSARs), which correlates the activity of a compound against a particular property (e.g. aqueous solubility, Caco-2 permeability, blood-brainbarrier permeability, hERG channel blockade), with its sructural features can also be used as objective functions. To date chemical similarity, cLog P, and QSAR models for aqueous solubility have been utilised to investigate the utility of the developed taCOGA approach for multiobjective satisfaction. The multi-objective COGA techniques (MOCOGA) developed for searching continuous design spaces [17] should also offer utility in discrete chemical space. The continuous space approach involves running a COGA for each objective with a relatively relaxed filter setting of around 0.5. It has been shown that the resulting identified regions give a very good indication of the degree of conflict between the objectives under investigation [17,19,21]. Mutually inclusive regions of high performance relating to two or more objectives indicate a low degree of conflict whereas mutually exclusive regions indicate high degree of conflict i.e. significantly lower

performance solutions will have to be considered to satisfy all objectives.

similarity resulted in the identification of an average of 30 common HP R1 reactants and running taCOGA on all three objectives identifies an average of 10 common HP R1 reactants. In each case lesser numbers of common R2 reactants were identified.

Figure 11: Number of high performing R1 and R2 axes clusters common to various objectives identified using tabu COGA. Results given for 50 runs.

Figure 10: taCOGA FCS solutions projected on 2 dimensional hyperplanes for a 3 reagent library.

Similarly, in discrete reagent space HP reactant axes that are common to a number of objectives can represent sets of good compromise solutions. In order to identify such common axes an optimisation approach is not appropriate. Initial experimentation utilising the 400x400 enumerated virtual library of section 4 with high Rf filter settings illustrates identification of significantly less number of HP axes. Also, just one common HP solution existed in the FCSs of two selected objectives (aqueous solubility and chemical similarity) from 50 hiCOGA runs with an Rf setting of 0.9. However introducing the taCOGA focussing approach results in the identification of significant numbers high performing reactant axes common to each objective as shown in figure 11. An average of 25 common R1 reactants were identified. Repeating the experiment using cLogP and chemical

It is apparent from these preliminary results that taCOGA offers a great deal of utility when integrated with multiobjective reagent library search. This relates directly to the focussing of libraries in terms of solutions that have a higher probability of high performance regarding several objectives during subsequent in vitro assaying processes. Further analysis of the identified reagents by the chemist and machine-based sampling of HP reactant axes can result in further focussing of the taCOGA sets.

9 Further work An extensive and successful study relating to the satisfaction of molecular constraints to further promote ‘drug likeness’ has been carried out. This has resulted in the introduction of appropriate penalties that further focus the reagent libraries. Unfortunately there is insufficient space to include results from the study in this paper. User-interfaces that present library search results in a succinct manner to the chemist and support userinteraction with the evolutionary search and exploration

processes have been developed and are currently being assessed within Evotec OAI. Further research relating to user-preference and multiobjective satisfaction is currently underway and, now that proof-of-concept has been achieved, further development of the basic techniques described will likely increase performance both in terms of number and fitness of identified solutions and in reduced drug discovery cycletimes. Information emerging from such optimisation and focussing could be utilised to refine in-silico objective functions in the similar manner to the problem redefinition aspects of previous interactive evolutionary design work [16,22]. Further information regarding degree of objective conflict may also be available as has been the case with engineering design applications [17,21]

10 Conclusions A significant utility has been identified via the transfer of basic COGA techniques from the engineering design domain into drug discovery processes. This proof-ofconcept has been achieved via experimental development of hiCOGA to enable successful integration with discrete reagent library focussing and optimisation. A tabuoriented COGA (taCOGA) approach has been successfully developed to support the identification of larger numbers of high-performance reactants. Results are presented from both enumerated reagent libraries and from the integration of COGA with Evotec OAI’s library definition and evaluation sofware. Scaleability aspects have been successfully addressed and the manner in which multi-objective considerations can be taken into account has been illustrated. All results so far indicate a significant potential for the COGA concept providing a firm foundation for complex reagent library search and exploration.

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