Predicting Activity Cliffs - Can We Use Machine Learning for Special Cases?

Rajarshi GuhaNIH Center for Translational Therapeutics

August 4, 2011Joint Statistical Meeting, Miami Beach

Outline

• Structure-activity landscapes• Characterization• Prediction

Structure Activity Relationships

• Similar molecules will have similar activities• Small changes in structure will lead to small

changes in activity• One implication is that SAR’s are additive• This is the basis for QSAR modeling

Martin, Y.C. et al., J. Med. Chem., 2002, 45, 4350–4358

Exceptions Are Easy to Find

Tran, J.A. et al., Bioorg. Med. Chem. Lett., 2007, 15, 5166–5176

Ki = 39.0 nM Ki = 1.8 nM

Ki = 10.0 nM Ki = 1.0 nM

Structure Activity Landscapes

• Rugged gorges or rolling hills?– Small structural changes associated with large

activity changes represent steep slopes in the landscape

– But traditionally, QSAR assumes gentle slopes – Machine learning is not very good for special cases

Maggiora, G.M., J. Chem. Inf. Model., 2006, 46, 1535–1535

Characterizing the Landscape

• A cliff can be numerically characterized• Structure Activity Landscape Index (SALI)

• Cliffs are characterized by elements of the matrix with very large values

Guha, R.; Van Drie, J.H., J. Chem. Inf. Model., 2008, 48, 646–658

Visualizing SALI Values

• The SALI graph– Compounds are nodes– Nodes i,j are connected if SALI(i,j) > X– Only display connected nodes

What Can We Do With SALI’s?

• SALI characterizes cliffs & non-cliffs• For a given molecular representation, SALI’s

gives us an idea of thesmoothness of the SAR landscape

• Models try and encodethis landscape

• Use the landscape to guidedescriptor or model selection

Descriptor Space Smoothness

• Edge count of the SALI graph for varying cutoffs• Measures smoothness of the descriptor space• Can reduce this to a single number (AUC)

Feature Selection Using SALI

• Instead of fingerprints, we use molecular descriptors

• SALI denominator now uses Euclidean distance

• 2D & 3D random descriptor sets– None are really good– Too rough, or– Too flat

2D

3D

Measuring Model Quality

• A QSAR model should easily encode the “rolling hills”• A good model captures the most significant cliffs• Can be formalized as

How many of the edge orderings of a SALI graph does the model predict correctly?

• Define S (X ), representing the number of edges correctly predicted for a SALI network at a threshold X

• Repeat for varying X and obtain the SALI curve

SALI Curves

Predicting the Landscape

• Rather than predicting activity directly, we can try to predict the SAR landscape

• Implies that we attempt to directly predict cliffs– Observations are now pairs of molecules

• A more complex problem– Choice of features is trickier– Still face the problem of cliffs as outliers– Somewhat similar to predicting activity differences

Scheiber et al, Statistical Analysis and Data Mining, 2009, 2, 115-122

Motivation

• Predicting activity cliffs corresponds to extending the SAR landscape

• Identify whether a new molecule will perform better or worse compared to the specific molecules in the dataset

• Can be useful for guiding lead optimization, but not necessarily useful for lead hopping

Predicting Cliffs

• Dependent variable are pairwise SALI values, calculated using fingerprints

• Independent variables are molecular descriptors – but considered pairwise– Absolute difference of descriptor pairs, or– Geometric mean of descriptor pairs– …

• Develop a model to correlate pairwise descriptors to pairwise SALI values

A Test Case

• We first consider the Cavalli CoMFA dataset of 30 molecules with pIC50’s

• Evaluate topological and physicochemical descriptors

• Developed random forest models– On the original observed

values (30 obs)– On the SALI values

(435 observations)

Cavalli, A. et al, J Med Chem, 2002, 45, 3844-3853

Double Counting Structures?

• The dependent and independent variables both encode structure.

• But pretty low correlations between individual pairwise descriptors and the SALI values

Model Summaries

• All models explain similar % of variance of their respective datasets

• Using geometric mean as the descriptor aggregation function seems to perform best

• SALI models are more robust due to larger size of the dataset

Original pIC50RMSE = 0.97

SALI, AbsDiffRMSE = 1.10

SALI, GeoMeanRMSE = 1.04

Test Case 2

• Considered the Holloway docking dataset, 32 molecules with pIC50’s and Einter

• Similar strategy as before• Need to transform SALI values • Descriptors show minimal

correlation

Holloway, M.K. et al, J Med Chem, 1995, 38, 305-317

Model Summaries

• The SALI models perform much poorer in terms of % of variance explained

• Descriptor aggregation method does not seem to have much effect

• The SALI models appear to perform decently on the cliffs – but misses the most significant

Original pIC50RMSE = 1.05

SALI, AbsDiffRMSE = 0.48

SALI, GeoMeanRMSE = 0.48

Model Summaries

• With untransformed SALI values, models perform similarly in terms of % of variance explained

• The most significant cliffs correspond to stereoisomers

Original pIC50RMSE = 1.05

SALI, AbsDiffRMSE = 9.76

SALI, GeoMeanRMSE = 10.01

Test Case 3

• 38 adenosine receptor antagonists with reported Ki values; use 35 for training and 3 for testing

• Random forest model on the SALI values performed reasonable well (RMSE = 7.51, R2=0.62)

• Upper end ofSALI rangeis better predicted

Kalla, R.V. et al, J. Med. Chem., 2006, 48, 1984-2008

Test Case 3

• For any given hold out molecule, range of error in SALI prediction is large

• Suggests that some form of domain applicability metric would be useful

• The dataset does not containing really big cliffs

• Generally, performance is poorer for smaller cliffs

Model Caveats

• Models based on SALI values are dependent on their being an SAR in the original activity data

• Scrambling results for these models are poorer than the original models but aren’t as random as expected

Conclusions

• SALI is the first step in characterizing the SAR landscape

• Allows us to directly analyze the landscape, as opposed to individual molecules

• Being able to predict the landscape could serve as a useful way to extend an SAR landscape

Acknowledgements

• John Van Drie• Gerry Maggiora• Mic Lajiness• Jurgen Bajorath