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Integrating Everything: the Molecule Selection Toolkit, a System for Compound Prioritization in Drug Discovery David Jesse Cummins, and Michael A Bell J. Med. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.jmedchem.5b01338 • Publication Date (Web): 07 Mar 2016 Downloaded from http://pubs.acs.org on March 9, 2016

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Journal of Medicinal Chemistry is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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Journal of Medicinal Chemistry

Integrating Everything: the Molecule Selection Toolkit, a System for Compound Prioritization in Drug Discovery

David J. Cummins* and Michael A. Bell Eli Lilly and Company, 893 South Delaware Street, Indianapolis, Indiana 46285, United States KEYWORDS: Multi-parameter optimization, MOOP, MPO, Discovery Chemistry, Drug Discovery, Molecular Diversity, Compound Prioritization, Drug Development, Lead Generation.

ABSTRACT

In recent years there have been numerous papers on the topic of multi-attribute optimization in pharmaceutical discovery chemistry, applied to compound prioritization. Many solutions proposed are static in nature – fixed functions are proposed for general purpose use. As needs change, these are modified and proposed as the latest enhancement. Rather than producing one more set of static functions, this work proposes a flexible approach to prioritizing compounds. Most published approaches also lack a design component. This work describes a comprehensive implementation that includes predictive modeling, multi-attribute optimization, and modern statistical design. This gives a complete package for effectively prioritizing compounds for lead generation and lead optimization. The approach described has been used at our company in various stages of discovery since 2001. An adaptable system alleviates the need for different static solutions, each of which inevitably must be updated as the needs of a project change.

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INTRODUCTION This paper describes an integrated system for prioritizing compounds in the context of discovery chemistry projects. The system has its origins in 2001 when we began experimenting with iterative low throughput screening combined with a space-filling design approach, as an alternative to higher throughput screening of molecules in early stage discovery projects. This approach was utilized while testing molecules for potency and selectivity at 15-hydroxyprostaglandin dehydrogenase (15-PGDH). The starting point was a few published documents, and about 30-40 molecules that were tested in our in-house assay. In four rounds of low throughput testing, with 250 molecules per round, the effort progressed from having micromolar inhibitors that were not competitive to finding single digit nanomolar competitive inhibitors of 15-PGDH. To our knowledge, there were no examples of competitive inhibition in the literature. One year later, the same approach was used on a different project, where the target was 11β-hydroxysteroid dehydrogenase type 1 (11bHSD1). In three testing rounds of 500 compounds per round, this method led from double digit micromolar to low nanomolar and selective inhibitors. After these early successes we continued using this new approach, and at the same time began evaluating our traditional way of following up on actives from screening efforts in a formal process referred to as Actives Assessment (AA). We observed that most project teams were taking active molecules and applying filters (potency, molecular weight, etc.) to reduce the set of actives to the most interesting “seed” molecules. Using these as new starting points, molecules in our collection were identified that had not been tested in the screen, but were similar to a seed molecule. This became the expanded set of candidate molecules. At this point, a Cluster Analysis was performed on those “hit expansion” sets of molecules. Cluster Analysis (first coined by Tryon, 1939) includes


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a number of different methods for grouping objects of similar kind into respective categories. In the current context, molecules are divided into groups by an algorithm, and an algorithm is deemed suitable if the groupings are a good approximation of how a chemist would manually separate the molecules into different groups. Readers unfamiliar with Cluster Analysis have a wide range of sources for gaining familiarity; perhaps a good starting point is Bacha et al1. In our Actives Assessment setting, centroids of clusters became interesting molecules for each round of testing (typically 1,000 molecules each round). In reviewing this process, we noted several inefficiencies in the way we were expanding on actives, and we summarized with these three recommendations for actives follow-up: 1. Do not ignore negative information (inactive molecules). Molecules lacking potency give valuable information not to be ignored. 2. Do not use hard filters. This is a brittle approach that can deny one molecule while allowing another with very similar attributes. It leads to lost opportunities. 3. Do not use Cluster Analysis as a design tool. There was a heavy dependency on Cluster Analysis as a way to find representative compounds to explore. This tends to bias too heavily toward molecules merely because they have many close analogs. The third point is especially important at early stages of screening just after medium throughput screening. Often there is a fixed number of molecules to select for follow-up, but many Cluster Analysis algorithms have no control over the number of clusters. If the user needs to select 1,000 molecules, a Cluster Analysis may give an inconvenient number like 2,877, leaving the user to tweak the parameters of the Cluster Analysis over several iterations in search of the 1,000 molecules they need. There are Cluster Analysis algorithms that give control over the number of


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clusters, e.g. Kmeans. These are often not used because the uniformity of the clusters and what chemists consider to be natural groupings of the molecules tends to suffer when a specific number is forced. Tweaking parameters to control the number of clusters is an inappropriate manipulation of an algorithm to accomplish something that is really not natural for it. (If the goal is to analyze an SAR, cluster analysis may be ideal; in this work the focus is on prioritization.) We implemented the new approach to actives follow-up in a system called the Molecule Selection Toolkit (MST). The MST is now generalized for both early and later stages of discovery chemistry project work including Medium Throughput Screening (MTS), Actives Assessment (AA) and Formal Hit Assessment (FHA), Hit to Lead (H2L), Lead Optimization (LO), and Candidate Selection (CS). Components of the system The main components of the MST are: 1. Predictive Modeling (using all information, including inactive molecules). 2. Utility Functions (avoiding hard filters) 3. Weighted Desirability (optimizing many things, not just potency) 4. Biased Spread Design (a powerful design that augments what has been learned) The topic of predictive modeling deserves an in-depth coverage, but is beyond the scope of this paper. Recent advances are built into the MST, but here we will simply say that we use our own implementations of both Random Forest and Support Vector Machines, and for both methods we have adapted good ideas developed by Sheridan2 for rescaling of predictions and for reliability of prediction. Depending on the goal, experimental data may be available for candidate compounds.


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It should be noted that a Multi-Parameter Optimization (MPO) system needs a way to deal with missing values. When experimental data are used, there are often molecules that lack experimental values and an imputation system must be used to fill in those missing values. Often this can be done using the same machine learning methods that would be applied in the case where none of the molecules have experimental data, but there are many other ways to do data imputation, outside the scope of this work. It should also be noted that not all values are of equal reliability. An experimental value from an assay with low noise relative to signal has higher reliability than a measure from a different assay with higher noise. A missing value could be treated as yet another measure with even lower reliability. Importance weighting of various measures can reflect the reliability of the measures as well as their importance to the goals of the project. This paper focuses on the implementation of utility functions and weighted desirability, which form the basis of the MPO component, and Biased Spread Design (BSD), which gives a design component to the way screening efforts are iterated.

MULTI-PARAMETER OPTIMIZATION: A BRIEF REVIEW For more than two decades now, there has been a strong message in pharmaceutical discovery that one must optimize more than just potency. Long gone are the days of sequential design where potency is optimized first, then drugability, and finally safety. Our industry has become a high pressure environment in which one is compelled to address drugability and safety concerns earlier in the process and navigate trade-offs between potency of molecules and other properties. The realization of this goes back to 1997, when the Rule of Five in the design of oral drugs was initially proposed by Lipinski et al3. Although this was not a true multi-parameter optimization (MPO), it


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was one of the earliest publicized attempts at a method to “score” a molecule in a higher dimensional landscape. Soon after that, numerous groups published their own version of “rules” for CNS exposure, or for druglikeness of molecules. Along the way there have also been various ratios proposed, such as various ligand efficiency measures LE4, LLE and LELP5, and the number of specialty ratios is growing. These are specialty measures for optimizing 2-3 aspects of a molecule. For example in our company, potency and size are captured with a ratio called “LEAN,” which is simply IC50 in Molar units divided by the number of heavy atoms. Many of the proposed ratios and “rules” are static, fixed functions, reviewed in Garcia-Sosa et al6. We argue that adding more specialty measures and more rules, or refinements of rules, will give diminishing returns. What is needed in this area is a simple system for prioritizing molecules that is flexible and easily tunable to the current need. We also feel that multi-parameter optimization is not the end, but one step in a process that should include components of predictive modeling and design as well. A significant step beyond the Rule of Five came from another group at Pfizer, who developed a “CNS MPO” that uses six properties of a molecule, chosen to improve not only brain penetration, but also permeability, safety, and clearance7. This is a significant step beyond the Rule of Five because it avoids the use of hard filters. However, it is a fixed set of functions which, as such, lacks flexibility for other purposes. For example, a team optimizing fragments would not be able to use the tool without modifying it to restrict molecular weight, one of its six components, far more than the CNS MPO does. Such a team could develop their own MPO that is adjusted for that purpose. Another team working on a cancer related target might accept higher molecular weight molecules and would need to loosen the limits on molecular weight beyond the CNS MPO. It is easy to foresee the dispensing of many specialized MPO sets ad nauseam. Indeed, a group has already published another paper with a modified set of functions called the “CNS PET MPO”8. One might


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go farther to imagine various target classes: kinases, GPCRs, cell surface receptors, and different therapeutic areas motivating many different variants of an MPO for use in project work. Even the same project team will have different needs a year in the future than at present. Creating and tracking any number of different specialty MPOs (as static functions) is not needed if there is a sufficiently flexible and powerful system to optimize what is needed at the current time. We have developed a system that automatically creates custom functions to optimize any number of endpoints (or properties), on the fly, for use in compound prioritization in discovery chemistry. There are numerous papers on the topic of MPO. Notable for their early contribution, Biswas et al9 proposed a drug likeness score called DLS in 2006. The form of the utility functions constructed was driven by distributions of each property amongst marketed drugs (possibly a disconcerting practice for driving future drug design efforts). Cruz-Monteagudo et al10 proposed, in 2008, a method using Derringer’s desirability for optimizing the potency, safety, and bioavailability of compounds. An even earlier contribution is Gillet et al11 in 2002, which treats diversity as another parameter to be optimized along with various properties, and then uses a genetic algorithm for optimization. A more recent contribution is that of Nissink et al12 in 2013, which develops a uniquely different approach motivated philosophically by Karl Popper’s ideas of falsifiability of hypotheses in science. This approach seems to deal with missing data by reducing the dimensionality of the data for molecules that have missing data, rather than imputing those missing values. Thus, comparisons between two molecules are made in a context whose dimension varies, based on the number of attributes for which both compounds have experimental data. For example, if there were seven properties of interest, then two compounds, call them A and B, may be compared in a 7-dimensional space, while compounds A and C may be compared in a 5dimensional space, if compound C is missing data in two of the endpoints of interest. Thus the


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same compound A is compared to B in a 7-D space, but compared to C in a 5-D space. This seems a most curious approach. For additional review, numerous publications of note include Ekins et al13, Segall et al14, Segall et al15, Debe et al16, and Yusof et al17. What we have implemented is equivalent to a smoothed version of the desirability functions of Derringer18, perhaps more similar to Harrington’s desirability functions19. In this paper we use these terms interchangeably: “utility function,” “desirability,” “score.” These will always refer to a number between 0 and 1 that measures the desirability of a single attribute, or in the weighted aggregation it will be referred to as “overall desirability.” Often in the literature there is a discussion of Pareto Optimality. The references given above, as well as this work, refer to Pareto Optimality as important for an MPO system. A molecule is Pareto optimal if, when examining the aspects being considered, further improvement (say, in the form of a small substituent change) to any one aspect would come at the detriment of one or more other aspects of that molecule. If a molecule cannot be improved in any one aspect without losing ground in one or more other aspects, then that molecule is a Pareto optimal choice. Note that is only defined within a fixed set of solutions, in this case molecules; it is not defined as a claim about all possible solutions.

THE MOLECULE SELECTION TOOLKIT: A HIGH LEVEL OVERVIEW We will cover in more detail the components of the MST, and then show how they are integrated together. Let us begin with the high level architecture of the MST as given in Figure 1. Looking at the figure from left to right, the starting point is the choice of raw endpoints. These may be properties, potency, metabolism, in short any aspect of a molecule that can be expressed as a number. The word “raw” in Figure 1 conveys that the different aspects will have their own units of measurement, for example metabolism may be in units of percentage from 0 to 100, while potency is often in nanomolar units ranging from single digits into the tens of thousands. These


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endpoints represent the optimization opportunities and hurdles that a given team may face at a particular point in time, where in-vitro or in-silico surrogates are used to capture important aspects of molecules. The molecules could be virtual or in an existing collection; either way, predictive modeling is often a heavy component in producing the raw numbers for these inputs. The list of endpoints as shown in Figure 1 is certainly not exhaustive. There are numerous ADME, Toxicological, and related in-vivo endpoints that could be (and often are) included in the inputs. Since each of these may have their own scale of measurement, each endpoint is given a utility function, which converts the raw endpoint to a number between 0 and 1, representing how a molecule is valued in that endpoint. This is covered in more detail in the next section. At this point, there is a set of desirability numbers, each between 0 and 1, and importance weights are assigned to these numbers. As a motivating example, one project team may deem potency to be five times more important than metabolism, while another project team has an over-abundance of potent molecules which all suffer from extreme metabolism, thus for this second team the heavier importance may be placed on metabolism. Yet another team may have a set of anti-targets for which selectivity of the molecules is the biggest challenge. This process is applied to the entire list of endpoints, which often includes 15-20 different properties. A later section discusses how to calibrate the assignment of importance weights. The utility functions are combined into a weighted desirability, using a weighted geometric mean. There are numerous ways to aggregate a group of individual desirabilities into an overall desirability. One could envision a spectrum, with “Min” and “Max” representing extreme ends of the spectrum. Using Min means that the overall desirability is the property that is least desirable, ignoring all other properties. Using Max ignores everything except the property that is most desirable. An arithmetic mean is right in the center of that spectrum, with no bias toward either the best or worst aspect of a molecule. A geometric mean


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is more influenced by the weakest aspects of the molecule than an arithmetic mean, and there are other functions -- hypergeometric, inverse geometric, not defined here -- that lie between arithmetic mean and Max in this spectrum. In any case, having chosen an aggregation method (geometric mean in our case), there is now a single importance weighted desirability number for each molecule, and one could sort the molecules by this number and select from the top of the list. This will likely be suboptimal, because the molecules at the top of the list are often very similar to each other, and effectively represent testing the same hypothesis repeatedly (this varies depending on the diversity and size of the molecule set). A design component is needed in order to maximize the efficiency of sets of molecules chosen for testing. The use of a Biased Spread Design allows one to explore a wider hypothesis space and select a more efficient set of molecules for testing. As will be shown in the Biased Spread Design section, this gives not only molecules that are different from each other, and yet desirable, but it also strategically augments the set of molecules that have previously been tested. Modern design is a critically important step in enriching the information content of molecules selected for testing. After the molecules are tested, the results are processed, any predictive models are evaluated and rebuilt with the new information incorporated, and the learning cycle begins again.

UTILITY FUNCTIONS In reviewing the literature, the reader will see terms such as “utility function,” “desirability,” and “scoring function.” Often in the pharmaceutical discovery chemistry community, these terms are synonymous. Utility functions have their origin in Economics and Finance Theory, and are used to capture preference with respect to a specific good or service. A desirability function is a


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mathematically simplified description of a decision maker's preference. It transforms an objective function to a scale-free desirability value, which measures the decision maker's satisfaction with the objective value. The distinction between preference and desirability is subtle and not important for the use made of this concept here. A utility function can come in many forms. A “filter” is something commonly used in discovery chemistry; this is a utility function that takes on only two values, for whether a molecule “passes” the filter or not. This is simply a step function, for example if one requires a molecule to have a molecular weight (MW) of 350 or less, the result is shown in Figure 2. This seems quite brittle, as a molecule with a MW of 351 is then deemed completely unacceptable, while another molecule whose MW is 349 is completely acceptable. One of the first things we did in restructuring our AA efforts was to recommend against hard filters like this. A more reasonable utility for MW can be constructed by answering the following three questions: 1. Are larger values desirable, or undesirable? 2. What is the smallest value below which two molecules should be considered equivalent, so that any further effort is directed to other aspects to improve? 3. What is the largest value above which two molecules should be considered equivalent, so that any further effort is directed to other aspects to improve? Note that the word “equivalent” in questions 2 and 3 does not imply desirable or undesirable. The answer to question 1 will determine what is desirable and what is undesirable. Once these three questions are answered, it is very easy to compute a smooth utility function. For example, suppose a team is targeting a receptor with a small molecule, and so questions 1-3 are answered as follows: large values of MW are undesirable (Q1), a very good MW is 250 or lower (Q2), and


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a completely unacceptable MW is 400 or higher (Q3). This leads to a utility function that is sigmoidal downward in shape, with a linear portion between 250 and 400, as shown in Figure 3. A value of 1 is a perfect score, while 0 is a reject. The rationale for doing this is two-fold: 1. Setting up to optimize more than one thing requires handling differences of scale. Converting each endpoint to a [0, 1] real number allows combining them all into an overall desirability that is meaningful. 2. Molecules with different MW values will be given the same number if they are all below 250 MW (1) or if they are all above 400 MW (0). This effectively gives leeway for the algorithm to improve other aspects of the molecules rather than working to improve on differences that are not considered important. For example, reducing molecular weight from 800 to 750 would not be considered an improvement if both values are considered unacceptably high by a wide margin. This logic is applied to all properties, not just MW. Many scientists take the log of a potency number. This is actually a special case utility function, but it does not restrict the scale of the result to the [0, 1] interval, and lacks other properties such as the asymptotic behavior of a sigmoidal function. Another example is shown in Figure 4, using potency in nanomolar units. The plot shows that potency below 50 nanomolar is given a perfect score of 1, while potency of 500 nanomolar or higher is given a desirability of zero. Our software automatically generates the function when the user supplies three parameters: in this case, Shape=Down, Lower Limit=50, and Upper Limit=500. The resulting function is shown in Equation [1]. This is expressed as an excel formula, assuming the value is placed in cell A1. Figure 4 shows R code (R programming language: http://www.R-project.org) for generating the plot. =MAX(MIN((1/(1+exp((A1-(500+50)/2) * 10/(500-50) ))) *(1-0.0) + 0.0 ,1),0)

[1]


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Figure 4 uses raw potency in nanomolar units. Log potency can certainly be the input to a utility function, and may well give better results in that it puts the units in terms of orders of magnitude that scientists often think about when comparing compounds. Other companies in the industry are using utility functions. Pfizer’s CNS MPO uses piecewise linear functions. Whether sigmoidal functions or piecewise linear functions are used is a matter of personal preference. We have chosen to use sigmoidal functions to retain the uniformity of drawing from a single family of functions. To illustrate this, Figure 5A shows the Pfizer MPO function for clogP, overlaid with a sigmoidal function that accomplishes a similar effect, but in a smooth fashion. Figure 5B shows a similar comparison for polar surface area, which often motivates a defined range where both low and high extremes are to be avoided. Fretting over utility function forms gives diminishing returns. Whether piecewise linear, sigmoidal, or some other function, the important thing is to use something less brittle than a hard filter. Once each endpoint has been assigned a utility function, there are a number of [0, 1] desirability scores (or “Dscores”) – one for each endpoint of interest -- and one is ready to combine all the endpoints into an overall weighted desirability.

WEIGHTED DESIRABILITY One can accommodate different importance weights to reflect the current priorities of a project. Often at an early stage, priorities are not well established and so an equally weighted desirability can be used. This is commonly the case when building libraries for medium throughput screening. For project work where strengths and weaknesses of each series being investigated are known,


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usually there is a sense that some issues are critically important to solve, others are moderately important, and still other issues are either already solved or not considered much of a threat to the goals of the project. Sometimes an endpoint is just being tracked, without the need to improve that aspect of the molecule, but rather just to keep an eye on it. Suppose for example that there are four endpoints of interest, numbered 1 through 4. They are assigned importance weights a through d. A weighted geometric mean can be used to compute a weighted desirability score as in Equation [2]. 1

𝐷𝑠𝑐𝑜𝑟𝑒 = (𝑢1𝑎 ∗ 𝑢2𝑏 ∗ 𝑢3𝑐 ∗ 𝑢4𝑑 )𝑎+𝑏+𝑐+𝑑

[𝟐]

If, say, 𝑢3 is the utility function for an endpoint that the team simply wants to track, but not use as a criterion for prioritizing molecules, then setting c=0 would accomplish this. The system then computes the endpoint, but it has no effect on how the molecules are prioritized. As has been pointed out numerous times in the literature, a geometric mean finds Pareto optimal solutions. It should be noted that the geometric mean is multiplicative: several numbers, each between 0 and 1, are multiplied in the computation. If any single attribute of a molecule gets a value of 0, then the overall result will be 0, regardless of how the other attributes score. To avoid this, a “shift value” is used in all of our utility functions. In effect, the utility curve bottoms out at 0.10 (our default value) instead of at 0. The shift value can be altered to any number desired and does not affect the shape of the utility function in the location of inflection points. Looking back at Equation [1] the reader will notice a “0.0” in the equation in two places. Changing these to 0.10 achieves the 0.10 shift. Calibrating the importance weights is crucial. Two approaches for this will be described. Both approaches require a set of molecules that have experimental results. One set should be large, say


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hundreds to thousands of molecules if that many are available. Let this be called Set A. Another set should be a more focused, smaller set, which may include 20-50 molecules that are very well understood. Let this be called Set B. Both sets A and B should include some highly desirable molecules, some molecules that are highly undesirable, and some molecules with moderate desirability. An easy first approach is to start with an initial estimate of the importance weights and to compute a Dscore for Set A. Sorting the set by this Dscore, one can observe where a few (usually 2-5) favored molecules fall in the prioritization. Ideally they will be listed in the top 5% of the molecules, and better yet would be in the top 10-20 molecules. (Demanding that they be at the very top of the list runs a risk of “over fitting” to the molecules used to calibrate.) If not, close examination of the molecules that were ranked higher than the favored molecules often suggests one (or both) of two things: 1. The utility function for one or more endpoints was either too “lenient” or too “strict.” A lenient function would accept molecules that the team considers unacceptable, and a strict function would reject molecules that, though not ideal, the team would want to explore. 2. Some aspect of the molecules was given an importance weight that is too low (or high). Increasing (or decreasing) the importance weight for this aspect will cause the favored molecules to “percolate” higher toward the top of the list. It is often very helpful to go through the process of calibrating the weights and utility function shapes in order to see the most favored molecules rise in a prioritized list. Often a team comes to realize that what they thought was most important was actually less important than they realized, and other aspects of molecules were more important than they realized, once they see the concrete impact. This is part of human nature, that one is not able to grasp a complex set of values until the


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impact of them is seen in a concrete way. For an interesting discussion of the impact of abstract versus concrete information on decision making, see Borgida et al20. There is an interface to a tool that is very helpful for getting initial importance weights. This is an approach created by a mathematician in the 1970s, called the Analytical Hierarchy Process (AHP)21. The method uses pairwise comparisons to measure preferences with an ordinal score. By focusing on only two things at a time, it allows the user to focus attention locally while at the same time constructing a post analysis that ranks all the choices. A related paper that also uses the AHP is Petit et al22. The AHP requires constructing a matrix that represents all pairwise preferences, but we have developed an approximation that is far easier to use. Our interface gives an absolute importance line and allows the user to drag and drop labels onto this line. The distance between items on the line is then used to infer pairwise preferences and these in turn are used as input to the AHP algorithm. This makes decision making a very easy matter of dragging and dropping labels visually. Figure 6 shows an example of this, where the relative importances (arbitrarily ordered for illustrative purposes only) are: Toxicity < Properties = Selectivity < ADME < Potency and numbers assigned are used to compute pairwise preferences. Thus Properties is given the same importance as Selectivity. Potency is significantly more important than properties, while ADME is mildly more important than Properties. These numbers become the weights in a geometric mean that gives the overall desirability (Dscore). How “Properties” is defined is not considered at this level; this is handled at a later stage when the user decides which properties will be used (e.g., molecular weight, clogP, PSA, rotatable bonds, pKa, etc) and how they are weighted versus each other. At this initial level these are high level groupings, or aggregations, of aspects of a molecule, tuned to a team’s needs. For example toxicity may involve several specific end points for one team, and a different set for another team, with surrogate measures chosen to estimate each end point. Our approach is


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to compartmentalize the aspects of molecules at a high level and later break down each grouping and within that group also assign importance weights. In most cases, we have used the less tedious first method of calibration, which also uses a larger data set. It is instructive to see well-known reference molecules embedded in a larger set, and to inspect the rankings of the whole set. We described a simple first method to calibrate importance weights. The more difficult method requires a smaller set of 20-50 well understood molecules (described as set B above). This is a team effort. The molecules are laid out in a table, one molecule per row, with the raw endpoints spread out in columns. Now the team must manually prioritize these molecules, considering tradeoffs between the endpoints. Additionally, the structures are hidden and the identifiers are masked. This forces the team to make tough decisions about trade-offs between the endpoints, which at times are conflicting – improving one aspect of a molecule comes at the expense of less desirable values in another aspect. It removes personal biases arising from chemists who may be attached to molecules they have synthesized or designed. For example more potent molecules may have poor solubility or poor permeability, or better selectivity ratios may incidentally increase an unwanted CYP inhibition. Once a consensus prioritization is given for this calibration set of 20-50 molecules, the importance weights can be calibrated to mimic the rankings from this manual prioritization. (This can be done on the log scale using simple linear regression with the manual ranks as the response.) It is usually not possible to exactly replicate the ordering that was manually assigned by the team, but usually the bigger issue to resolve is conflicting orderings from one team member versus another. The discussion needed to resolve these differences of opinions usually adds great value to the project. At this point one may be concerned, and rightly so, about using past data to calibrate a procedure to be used prospectively. Our rationale is this: if we had infinite time and infinite


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resources, we might look at every candidate molecule and exert our expert judgement at a fine level. Since we do not, we take a subset of molecules that we can thoroughly understand, and calibrate an algorithm to mimic what we would do manually (being careful not to overfit). Then we unleash it on the larger set of candidate molecules, we obtain experimental results for those molecules, and we assess and re-calibrate the algorithm. This procedure should reflect the expert judgement of the chemists involved rather than a completely computational approach such as merely looking at the properties in marketed drugs (taken as a surrogate for “desirable” compounds). One may also wonder what should be done in the extreme case where there are no desirable molecules for driving a calibration, such as an orphan disease or target. In that case one can only use a decision tool like the AHP and the expert opinion of team members. A calibration step can (and should) be repeated periodically as experimental data are generated in the project.

BIASED SPREAD DESIGN Spread Design is a greedy, sequential approximation to a modern space-filling design, proposed by Kennard and Stone in 196923. The objective of the method is to find a maximally diverse subset of a larger candidate set of molecules. This is done by finding, at each step in an iterative process, the molecule whose nearest neighbor distance amongst molecules selected thus far is maximized, thus each additional molecule added to the selection set is chosen to maximize a sense of information gained by the addition of that extra molecule. An efficient implementation of this is proposed in Higgs et al24 and a heuristic explanation is given in Cummins25 (both available online). Space-filling designs have origins in spatial problems like sphere packing and oil well drilling. The analogy of oil well drilling is a good way to visualize how this design is used in discovery


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chemistry. Suppose we drill for oil in a particular location, and find none. (Or, if oil is found, similar logic applies.) We may ask where the best place to drill next is. If we drill very close to where we just drilled, we may waste time and money finding the same result. However, if we drill too far away, we may miss something in between. There is a trade-off between the cost of the exploration and the information returned. The cost constraints will impose a limit on how many drilling explorations can be done. This is quite analogous to the discovery chemistry setting, where one can only screen (or synthesize) a finite number of molecules in each round of discovery. Consider Figure 7, and suppose that this is a plot of potential places where we could drill for oil. Now suppose a constraint such that we can only drill in 30 places, so we must pick 30 of the light grey dots in the plot that best represent the space we wish to explore. Some areas of the plot are far denser than other areas (dots very close together), but the density or sparsity of the dots reflect surface topography and not what lies beneath the surface (oil reserves or not). The topography on the surface creates limitations in where we can drill, but the oil reserves beneath the surface are the only thing that really matters. (Tying this analogy back to our industry, there are limitations in our ability to synthesize some molecules but what really matters is designing the best molecules for the target of interest.) A Cluster Analysis would draw the points toward the dense areas (often these would be molecules that are easy to synthesize), but a spread design ignores the density of points and optimizes the spatial exploration alone. On page 868 of Higgs et al24 there is a modification proposed to allow for accommodation of a “demerit.” This is what the MST uses and which we refer to as a bias. Thus, Biased Spread Design in the MST uses a renormalized version of the demerit of Higgs. Continuing with the analogy of oil drilling, if we have information about where oil may be found, the design shown in Figure 8 does not reflect that. Suppose that we had found oil in a prior exploration, and this oil was found in the upper right corner of the plot in Figure


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7. If this were the case, we may no longer consider the Unbiased Spread Design of Figure 8 to give the most informative set of 30 locations to explore. Instead, we may wish to put more emphasis in the area where oil was found, while at the same time also pushing outward from that area to enhance our learning. In the extreme, if we focus only in that area, we might have a design as shown in Figure 9 – this is actually not a design at all. Figure 9 represents the opposite extreme from that of Figure 8. In Figure 8 we have a pure design with no bias; in Figure 9 we have pure bias with no design. A compromise is shown in Figure 10, where we have biased the design points in a direction toward the upper right area in order to enhance success, but we have also pushed outward in order to enhance learning. In Figure 7 and those following, we have maintained an analogy of oil drilling in order to help the reader visualize the concepts. In actuality, the plots come from an active project in our company, and are a two-dimensional projection of the structures of a large set of virtual molecules considered for synthesis and testing. This kind of plot, often called a “structure space plot,” can be achieved using either a Principal Components or Multi-dimensional scaling algorithm, outside the scope of this paper. The projection itself is only used to aid visualization; the algorithm does not use this projection, but rather uses distance between molecules. Details of this distance are discussed in Higgs et al24 and Cummins25; we will simply describe it as either a Mahalanobis Distance or a Tanimoto based distance, depending on what type of analysis is done. For visualization purposes, each dot represents a molecule, and dots close together are molecules that are similar to each other. The dots could be colored by overall desirability, or by structural series or cluster number, if such an analysis is done. We feel that this kind of visualization increases the temptation to attempt a manual selection of molecules, rather than a designed approach, which we advocate and implement with the Biased Spread Design.


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We stress that the bias in Figure 10 is one of many possible trade-offs between desirability of the molecules and pure space-filling design. There is a whole spectrum possible. This point is so important that we risk belaboring it with Figure 11 and Figure 12, which show levels of bias between that of Figure 8 and Figure 10. We have found that the context requires differing levels of Desirability or Design, perhaps roughly summarized as follows: 1. Medium Throughput Screening (MTS) across targets and projects: Unbiased Spread as illustrated in Figure 8. 2. Actives Assessment (AA) following MTS: Small bias as in Figure 11. 3. Hit-to-lead efforts (H2L): Moderate bias as more is known, Figure 12 or Figure 10. 4. Lead optimization: High bias as much is now known, Figure 10 or Figure 9. The Supporting Information, available online at http://pubs.acs.org, shows the interface for the MST, and this includes diagnostic plots that help the user visualize, in a practical way, the tradeoff between Desirability and Design (treating “Design” and “Diversity” as roughly equivalent). One thing that is evident in the figures with Spread Design (biased or not) is that the design points are “pushed” apart from each other. The degree to which they are repelled from each other depends on the amount of Bias used in the design. The outcome is that the top of the rank ordered list will be molecules that are different from each other, to some degree, tunable by the user. Unbiased Spread Design will very quickly find all the unusual molecules in a supplied set. This is often quite useful for “cleaning” a compound set, as often these molecules are undesirable and sometimes their presence was unknown or overlooked (a different purpose than prioritization, but often an important first step).


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There is an additional capability to this analysis, and it is very powerful. One can create a “previously selected” list containing molecules that have already been tested in previous rounds of screening. The design will augment this set of previously tested molecules, to give an optimal design not only amongst the candidate molecules from which a subset is desired, but also in the sense of augmenting what has already been learned in previous testing. Thus one maximizes the information returned from the next round of testing. If the goal is to select molecules for testing in an enzyme assay, then the list of previously selected molecules will be all compounds that have been tested in that enzyme assay. If the goal is for testing in a cell-based assay, or an in-vivo assay, the list will be the corresponding set that have been tested in the same assay. Molecules that have not yet been tested, but are slated for testing, would also be in this list. To illustrate the effect of this, Figure 13 shows an Unbiased Spread with 30 random starting points (asterisks) and 30 Design points (solid boxes). Note that the random selection is largely drawn in to dense areas in the center of the map. With these marked as previously selected, the design points (boxes) augment that set so that the final set of 60 points has the best possible spacefilling properties. The 30 starting points have dashed boundaries overlaid, to help visualize how the design points shy away from areas already covered. The Supporting Information includes an additional example showing the interplay between bias and augmentation. This is shown in Figures S1 through S4 of that document. The dependency on Cluster Analysis that we have seen is so enormous, and the inertia to change so great, that we make three points on the topic of Cluster Analysis versus Spread Design. 1. Spread design has the useful feature that the entire set of molecules is prioritized and gives an optimal set, however far you drill down the prioritized list. Whether 5 molecules are needed, or 5,000, the best design is obtained by drawing off the top of the prioritized list.


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There is no need to control the number by iterating through parameter changes, as often happens with Cluster Analysis. The Spread Design gives a ranking that is in some sense the best set of molecules, regardless of the number of molecules to be selected. 2. Cluster Analysis has no direct way to accommodate the information from molecules already tested in an assay, what we call the list of previously selected molecules. With Spread Design, maximum use is made of all the available data in an augmentation sense. 3. Cluster Analysis is inherently unable to incorporate a bias to give a desirability gradient. The bias introduced in Spread Design is intuitive, easy to implement, and effective. Often in order to achieve this effect, scientists have turned to Leader Analysis (e.g., Spath et al26), which effectively sorts the data by desirability and drills down the list, skipping molecules that are very similar to a molecule higher in the list (the “previously selected” of item 2). Leader Analysis is not a true simultaneous optimization, in that there is no direct management of the trade-off between design and desirability. In contrast, Biased Spread Design chooses each additional design point in a way that optimizes the prioritization as a whole. We note that the Spread algorithm is a greedy approximation, thus it is not strictly the most optimal possible. However, a great deal of experience has shown that it is quite adequate for the context of interest.

PUTTING IT ALL TOGETHER We have evaluated the approach in a number of parallel experiments in real time, in different stages of Lead Generation. These experiments were done in live projects at our company, where the immediate goal was to advance a scaffold to the next milestone, e.g. if a project was in a pre hit-to-lead state, the next milestone would be hit declaration, and if this is achieved, the project


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would then transition to a hit-to-lead stage, where the next milestone would then be a lead declaration. A computational chemist and/or lead project chemist selected molecules for testing, using the standard approaches (taken as a baseline for this experiment) and at the same time the MST was used to optimize potency, selectivity, metabolism and a number of other properties. The same set of properties were the focus for both sides of the experiment. To show results of these studies in all these aspects for each project would consume too much space, and for proprietary reasons we are not able to reveal the targets. We will describe some of the results in terms of the potency hit rates, but similar improvements were seen in metabolism and other aspects for each of these projects. For a CNS target related to cognition in an AA stage (screening follow-up), the standard approach selected a set of molecules that revealed a 5.3% hit rate and the MST selected molecules with a hit rate of 26.3%. If only different scaffolds are counted in the hit rate computation, thus requiring novelty of hits, the hit rates were 5.7% and 32.3%, respectively. This latter comparison shows that novelty of structure was improved in the MST approach, as expected from the design component built into the system (covered in a later section). In a cancer project in an AA stage, the standard approach gave a set of molecules with an active rate of 3.1%, where the MST approach gave a hit rate of 24.7%. There was an interesting situation where the purification process created a number of false positives for many series in the sets tested. The molecules selected using the MST were from a series that did not suffer from this effect, and in fact were the only series that showed a true SAR. Viewing this effect as an additional source of noise, one may interpret this success as the ability of the predictive models to find the “signal” in the noise. Thus, in spite of training models on data that later were shown to have numerous false positives, the true relationship was uncovered and exploited to select molecules that showed confirmed activity. In another cancer project in a similar stage, the MST doubled the hit rate of active molecules. In


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another CNS project related to pain, a hit was defined in two dimensions, as potent at the target of interest and not potent at a specific anti-target. The traditional method gave a hit rate of 2.4% and the MST gave a hit rate of 8.1%. The power of this system has been shown in H2L stages as well, and also in prospective design. In one recent H2L project, a molecule was chosen to represent a scaffold of interest (call this the “seed”). The potency, selectivity, and metabolism were known for this molecule, and the team had a clear understanding of what was needed to move this scaffold to the next milestone, with the need to improve all three of these aspects. This seed was divided into four “domains” and substituent replacements were hypothesized at each area of the molecule. For example, in one area of the molecule, 45 different substituent replacements were hypothesized, each with a view to improving metabolism, or selectivity, etc. A full virtual library was generated with 45 x 13 x 18 x 38 = 400,140 virtual molecules. None of these molecules existed in our collection. There were several potency assays, both enzymatic and cellular, and models were trained on available data from these. There were three anti-targets of interest, and the team was also looking at solubility and metabolism as well as a few other properties. An MST template was created, and a mere 30 compounds were selected from these 400k. These were synthesized and tested in the assays. The potency found was two orders of magnitude greater than the seed in both enzymatic and cellular assays, and over a hundred-fold more selective, with improved metabolism across four different species. Yet these molecules were only 60% similar to the seed. From this set of results the team quickly declared a lead molecule and moved on to the next stage of development. This experiment has been done in a number of prospective design contexts. While not always a dramatic success, when the results were discouraging, the traditional methods also had discouraging results.


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In the Supporting Information, available online, we illustrate the method with a concrete example using a retrospective set of 912 marketed drugs (proprietary concerns require using a set like this, rather than live project data). The set of marketed drugs is dated (prior to 2001) and not comprehensive. For example, it includes Morphine analogs, but not Morphine itself. It also includes (intentionally) drugs taken off the market (e.g., Astemizole). The point of the example is merely to illustrate the mechanics of the MST system. In our first example, we generate a scenario in which we seek compounds that enter the brain and are free of two liabilities: hERG blockade and phospholipidosis (PL). In the second example, we create a scenario in which we are looking for biased mu opiod receptor agonists, in the same set of 912 marketed drugs. Throughout both examples the reader will see useful diagnostics such as scree plots and spread diagnostic plots, and discussion of pitfalls and other issues related to implementation of a comprehensive system such as this. In particular, the examples contain important details about how to manage a balance between Desirability and Diversity, through the use of what we call the “Dweight.” We do reproduce below one of the figures found in that document; Figure 14 gives a schematic of the process from start to finish (same as Figure S21 in the Supporting Information). This, coupled with Figure 1, gives a high level “thumbnail” view of the entire system for prioritizing compounds.

COMMERCIAL SOFTWARE There are numerous commercial software packages for doing visualization, QSAR, and for other individual pieces of an MPO system. There seem to be very few packages that put it all together into one integrated system. One package that puts much of this all together is produced by Optibrium; the package is called StarDrop27. This package has several strengths; it uses utility functions (therein called “scoring functions”) aggregated to an overall desirability. It has predictive


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modeling capabilities, and it has extremely good visualization features. StarDrop also has a diversity component, which uses a genetic algorithm to optimize the trade-off between desirability of the molecules and diversity of the selection. It also accommodates a previously explored set in order to allow the current selection to augment what has already been learned, a capability that we find especially important. The software also offers the user control over the predictive modeling, in the same way that the MST does, by allowing the user to supply scripts that call their own modeling software and inputs. All this power and flexibility does come at a cost. A single license for the packages needed to perform these tasks came at a rather hefty price tag (in our view), plus additional costs for optional add-ons. Aside from StarDrop and our in-house MST system, we are not aware of a software package that uses a space-filling design in combination with predictive modeling to prioritize compounds.

CONCLUSION We have shown a method, and an implementation system, for prioritizing molecules that does not rely on fixed functions or endpoint sets. The method is simple to use in that a few interpretable parameters will define what a team has determined to be desirable for each endpoint. The method allows compartmental thinking about each parameter by itself, constructing meaningful and interpretable desirability functions for each parameter, and then through importance weighting, an overall desirability score. We have presented a modern design method that augments what a team has already learned and efficiently prioritizes the entire set of input molecules so that if K molecules are desired, the top K molecules in that prioritized list will be the most information rich and most desirable set of K molecules for the next round of assay testing. Finally, we described parallel experiments demonstrating the effectiveness of the system. We believe that static MPO


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functions were a good initial step for our industry, but that a flexible system such as this is the next logical step in discovery chemistry.


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FIGURES Figure 1: MST 1,000 Foot Level. This shows a schematic of computing utility functions for each endpoint, combining those into a weighted desirability, and using that as input to a Biased Spread Design. The scatterplot is meant to convey that different iterations of design and testing are done within the same space. The dots and small X’s represent earlier rounds of exploration. The crosses represent the current selection set. The red circle represents the region of structure space that has highest desirability (which may in part be based on predictions). Some crosses are “pushed” outside of that area as a “hedging of our bets” to give an optimal (biased) exploration of the candidate space. The output of the BSD is a prioritization that drives a learning cycle.


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Figure 2: MW Filter as a Step Utility Function. Here a weight of 350 or higher is a failure.

Figure 3: Smooth Sigmoidal Utility for molecular weight.


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Figure 4: Utility Function for Potency, in IC50 nanomolar units. A value of 50 nM or lower is given a perfect score of 1. A value of 500 or higher gets a score of 0. This figure can be generated in R by pasting the following four lines at an R prompt: A1=seq(from=0.01,to=800,length=1000) shift=0.0 ; ll=50 ; ul=500 ; slope=10 U=pmax(pmin( (1/(1+exp((A1-(ul+ll)/2) * slope/(ul-ll) ))) *(1-shift) + shift ,1),0) plot(A1,U,type="l", xlab="IC50_nM")


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Figure 5: Pfizer MPO functions (solid red) and sigmoidal alternative (dashed blue). A: clogP (left panel), B: PSA (right panel). We find that a single family of sigmoidal functions covers all cases needed.


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Figure 6: Importance line input for Analytical Hierarchy Process (AHP). Endpoints can be stacked if their importance is equal: Properties = Selectivity. Taking these absolute importance rankings as input, the interface infers pairwise preferences, gives the user an opportunity to adjust those, performs the AHP computations, and rounds the results to whole numbers, with the lowest importance given a weight of 1. Here the final result will be Toxicity=1, Properties=Selectivity=2, ADME=4, and Potency=8. These weights are now relative and are used directly in the geometric mean: Dscore = (Toxicity1 * Properties2 * Selectivity2 * ADME4 * Potency8)(1/17).


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Figure 7: Two-Dimensional projection of structures of molecules for an active project. One could think of this in the oil drilling analogy as potential places to drill for oil, where cost constraints allow only 30 exploratory drillings, and so the most informative 30 points must be chosen.


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Figure 8: One extreme: Spread Design, unbiased, with 30 design points.

Figure 9: The other extreme versus Figure 8: top 30 molecules with no design component.


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Figure 10: Compromise: Biased Spread Design with a moderate bias toward desirability.

Figure 11: Biased Spread Design with a Very Small Amount of Bias.


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Figure 12: Biased Spread Design with a Small-to-Moderate Level of Bias.


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Figure 13: Unbiased Spread with 30 random starting points (asterisks) and 30 Design points (solid boxes). The random selection is largely drawn in to dense areas in the center of the map. With these marked as previously selected, the design points augment that set so that the final set of 60 points has the best possible space-filling properties. The 30 starting points have dashed boundaries overlaid to help visualize how the design points shy away from areas already covered.


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Figure 14: Schematic of process. A set of compounds is selected; this is the candidate set. Properties and predictive models are chosen to represent the aspects to optimize. Each of these is given a utility function and an importance weight. From these, a weighted desirability is computed (D or Dscore). The compounds, their Dscores (D), and a list of previously selected compounds (P), are the input the Biased Spread Design (BSD). Also input is the importance weight for Desirability (WD). This tells how heavy should be the design component versus the desirability of the molecules. The circular arrows indicate that the user can interact with this by selecting molecules which are ranked high in the output but are not appropriate for the purpose at hand. These molecules are added to the previously selected list (P) and the BSD is run again. The user can iterate as often as desired to refine the prioritization.


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ASSOCIATED CONTENT Supporting Information. SMILES, predicted values, and properties for 912 Marketed Drugs in excel format. Additional figures and technical details in pdf format. Two worked examples also given in pdf format. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *Phone: +1 (317) 771-1035; Email: [email protected], [email protected] Notes The authors declare no competing financial interest. Biography David J. Cummins is a Senior Research Advisor at Eli Lilly Headquarters, Indianapolis, Indiana, U.S. He joined Eli Lilly in 1997, the same year he earned his Ph.D. in Mathematical Statistics from North Carolina State University. Before that he spent five years at GSK, (Glaxo-Wellcome at the time), in Research Triangle Park, North Carolina as a Statistical Research Associate in Drug Discovery Informatics. He is author and coinventor on over 20 patents, book chapters and scientific publications. Michael A. Bell is a Research Scientist at Eli Lilly Headquarters, Indianapolis, Indiana, U.S. In 2001 he earned an MS in Computer Science from University of North Carolina, Chapel Hill. He has supported the Statistical community at Eli Lilly as a Computer Scientist since 2004.


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ACKNOWLEDGMENT We thank Yue Wang Webster and Patty Bragger for early involvement in the graphical user interface. We thank Ian Watson for implementation of Biased Spread Design using molecular fingerprints, and many other useful tools that have been integrated in the software, and also for many productive conversations. We thank Richard E. Higgs for implementation of Biased Spread Design using descriptors, and for the innovation in introducing a bias (penalty) in the Spread Design algorithm. ABBREVIATIONS MOOP, Multi-attribute optimization; MPO, Multi-parameter optimization; Dscore, Desirability Score; BSD, Biased Spread Design; MST, Medium throughput screening; AA, actives assessment; FHA, formal hit assessment; H2L, hit to lead or hit-to-lead; LO, lead optimization; CS, candidate selection; DIPL, drug-induced phospholipidosis; LE, ligand efficiency; LLE, lipophilic ligand efficiency;

15-Hydroxyprosta-glandin

Dehydrogenase,

15-PGDH;

11β-hydroxysteroid

dehydrogenase type 1, 11bHSD1.

REFERENCES (1) Bacha, P.; Brunck, T.; Delany, J. Clustering Methods and their Uses. Daylight Chemical Information Systems Inc. 2007, Web, 24 Feb 2015. (2) Sheridan, R. P. Using Random Forest to Model the Domain Applicability of Another Random Forest Model. J. Chem. Inf. and Modeling 2013, 53, 2837–2850.


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