Combi-Chem

4h. Library comparison and augmentation

Introduction

The functionality in the C²·LibCompare module is accessed through the LIBRARY COMPARISON card in the COMBI-CHEM I deck.

• Define Libraries: Define multiple libraries.

• Compare Libraries: Compare library diversity.

• Complement Library: Augment a library based on distance metrics (MaxMin, Product PowerSum, D-Optimal, or the Max MinSpanningTree).

• Holes in Property Space: Find holes in property space in one library and then fill those holes with models from a second library.

Controls in this panel allow you to:

• Assign selected rows to a specific library.

• Add selected rows to a previously defined library.

• Remove selected rows from a previously defined library.

• Select the rows corresponding to a specific library.

• Import a library from a previously saved .tbl file. All rows from the .tbl file are added at the bottom of the study table, matching the descriptors in the .tbl file with the corresponding columns in the study table. You may import only those descriptors (columns) currently present in the study table.

• Clear all library definitions.

• List all the libraries currently defined in the table.

• Show (display the rows) of specific libraries, with an option to display only one specific library.

Comparing library diversity

It is often possible to compare two libraries by qualitative visual inspection of the compounds in property or principal component space. The library comparison functionalities provide a quantitative measurement which should confirm your visual assessments.

Several methods are available for comparing libraries. To access the control panels that give access to this functionality, click the Compare Libraries menu item on the LIBRARY COMPARISON card in the COMBI-CHEM I deck. Then select one of the menu items.

The diversity integral method

1.   Generate a set of random points that sample the property space covered by the two libraries and calculate the distance between each random point and the closest models in library 1 and library 2.

2.   Calculate the sum (integral) over all the minimum distances between random points and library 1 and random points and library 2, normalizing by the number of random points.

3.   The library with the lowest value of this sum is considered to be more diverse (that is, it better samples the property space occupied by the two libraries) by this method.

• The number of random points used to sample the space covered by the libraries.

• The metric used to measure the distance between random points and models in the two libraries, which is given by the equation:

where D_ij is the distance between model i and random point j, the sum is over all the independent variables (properties) k from 1 to N, X_i,k is the value of property k for model i, and X_j,k is the value of property k for random point j.

• For the exponents n and m, common choices are:

  n = 1, m = 1 (street-block metric)

  n = 2, m = 2 (Euclidean distance)

  n = 2, m = 1 (Euclidean distance squared)

The Compare Libraries Similarity control panel gives you a number of options for displaying the data in plot, histogram or table formats as well as an option to select rows in the study table which satisfy certain comparison criteria (i.e., user-specified minimum, average and maximum distances).

The cell-based comparison method

When using the option to compare libraries based on counting empty or occupied cells (see below), a cell is considered occupied by reference or by candidate molecules only if the number of molecules is greater than or equal to a user-specified minimum.

The cell-based library comparison method is accessed from the Compare Libraries/Cell Based menu item on the LIBRARY COMPARISON card in the COMBI-CHEM I deck, which opens the Compare Libraries Cell Based control panel.

Cell-based library comparison can be used with data in BDF files or in the QSAR study table. The space occupied by the two libraries can be binned to obtain a specified number of total cells or a specified number of cells occupied by at least one molecule. The optimum binning algorithm, which tries to divide the properties to create cells with sides as similar as possible, is used in both cases.

The comparison metrics can be calculated in two ways (Compare Libraries Based on popup):

• By taking cells as empty or occupied (with a user-defined minimum number of molecules in a cell to consider it occupied).

• Or by taking into account the actual number of reference and candidate molecules in each cell.

Cell number	Candidate molecules	Reference molecules
1	1	8
2	5	3
3	2	0
4	0	6
5	4	10
6	2	1
7	0	9
8	0	0
9	1	11
10	3	0

Then the comparison metrics using a) empty or occupied cells with a minimum of 1 molecule per cell to consider it occupied, b) empty or occupied cells with a minimum of 3 molecules per cell to consider it occupied, or c) taking into account the actual number of molecules per cell, are:

Metric	a) Empty or occupied (min = 1)	b) Empty or occupied (min = 3)	c) Actual number of molecules in cells
Cells with candidate mols	7	3	7
Cells with reference mols	7	6	7
Cells with candidate and reference mols	5	2	5
Cells with candidate or reference mols	9	7	9
Tanimoto coefficient	0.56	0.29	0.56
Hamming distance	4	5	46
Distance	2.00	2.24	17.89
Percentage overlap	71.43	33.33	71.43
Carbo index	0.71	0.47	0.48
Hodgkin index	0.71	0.44	0.32

You can also use the by Reference Molecules popup to select molecules in the candidate library that occupy cells not occupied by reference molecules (different or new molecules) or select candidate molecules that are in cells already occupied by reference molecules (similar molecules).

Cosine-coefficient diversity and similarity

Cosine-coefficient similarity

The cosine-coefficient similarity metric is used to compare two libraries, computing the diversity of library A (candidate library), the diversity of library B (reference library), and the change in diversity when library A is added to library B. This metric works with numeric descriptors and with 2D fingerprints.

The control panel (Compare Libraries Cosine Coeff Diversity) that enables you to compare libraries using cosine-coefficient similarity with data in the study table and in BDF files is accessed from the Compare Libraries/Cosine Coeff Diversity menu item on the LIBRARY COMPARISON card.

Fingerprints OnBits metrics

In the functionality accessed by selecting the Rgroup Subsetting/Diverse Library menu item on the LIBRARY ANALYSIS card and setting the Diversity Metric (in the Rgroup subsetting Diverse Library control panel) to Fingerprint OnBits, libraries are designed to maximize the number of on bits in the modal 2D and/or 3D fingerprint of the sublibrary.

In the functionality accessed from the Rgroup Subsetting/Focused Library menu item on the LIBRARY ANALYSIS card and setting the Distance Metric (in the Rgroup subsetting Diverse Library control panel) to Fingerprint OnBits, libraries are designed to maximize the number of common bits between the modal fingerprint of the sublibrary and a target fingerprint.

Fingerprint metrics are also available in Library Comparison. To access the Compare Libraries 3D Fingerprints Onbits control panel, select Compare Libraries/3D Fingerprints Onbits from the LIBRARY COMPARISON card.

3D fingerprint focusing

The modal 3D fingerprint of the candidate library is compared with the modal fingerprint of the reference library, reporting the number of on bits in each library, the number of common bits, the number of on bits in the candidate library not present in the reference library, and the number of on bits in the reference library not present in the candidate library. Options in the Compare Libraries 3D Fingerprints Onbits control panel allow you to list the molecules in the candidate library with on bits present in the reference library and to select the top N molecules from the candidate library (the ones with the highest number of common bits).

The option to Create Histogram of New and Common Pharmacophores plots the frequency of new and common on bits when the molecules in the candidate library are compared with the modal 3D fingerprint of the reference library.

Distance-based library augmentation

This functionality is accessed by opening the Complement Library control panel (select the Complement Library menu item on the LIBRARY COMPARISON card in the COMBI-CHEM I deck).

You can control several options:

• Number of diverse molecules to select.

• Library to select from (From Library).

• Library to complement (To Library).

• Diversity function to use.

The stochastic optimization proceeds similar to a distance-based diverse selection, except that a subset of compounds (the library to add to) is not allowed to vary and is maintained as a fixed selection throughout the optimization.

Hole identification and hole filling

The hole identification capabilities are accessed by opening the Find Holes control panel. Do this by selecting the Holes in Property Space/Find Holes menu item on the LIBRARY COMPARISON card in the COMBI-CHEM I deck.

The functionality available includes:

• Number of holes to find.

• Which hole-finding method to use:

  Halfway Positions: The points halfway between every pair of models are calculated, defining holes whenever no other models are found within a distance to the hole center equal to 1/2 the distance between the corresponding pair of models.

  Random Points Search: Random points are used to sample the space covered by the models in a library, measuring the distance to the closest model and keeping track of the largest holes, whose sizes are defined by these minimum distances.

• Starting list of models to take into account: All the models present in the study table or only models from a specific library.

• Whether to include the holes found by this analysis as additional rows (virtual molecules) in the study table, with their corresponding values for the independent variables (descriptors). They can then be visualized using the 3D plot functionality.

Note

After holes are found, they can be filled using the hole-filling functionality. Use the Fill Holes control panel, which is opened by selecting the Holes in Property Space/Fill Holes menu item from the LIBRARY COMPARISON card in the COMBI-CHEM I deck.

• The list of holes to be filled can be set to include all holes in the study table or only a selected set of holes.

• The list of candidate models for hole filling can be set to all the models present in the study table or only models from a specific library. These models are analyzed in terms of their distances to holes that were found.

3D fingerprint hole finding and filling

The modal 3D fingerprint of the candidate library is compared with the modal fingerprint of the reference library, reporting the number of OnBits in each library, the number of common bits, the number of OnBits in the candidate library not present in the reference library, and the number of OnBits in the reference library not present in the candidate library.

Options allow you to list the molecules in the candidate library with OnBits not present in the reference library and to select the top N molecules from the candidate library (the ones with the highest number of new OnBits).

Distance histogram library comparison

Access distance histogram library comparison by selecting Compare Libraries - Similarity from the LIBRARY COMPARISON card.

Options for Library Comparison include:

• Library specification:

  Candidate Library: Library containing candidate compounds.

  Reference Library: Library containing existing collection.

• Output option:

  Similarity Plots: Plot of distances from each candidate compound.

  Similarity Histograms: Histogram distribution of distances from candidate compounds.

  Similarity Table: Table of distances from candidate compounds.

• Selection options:

  Select molecules in Candidate Library: Turn on selection from Candidate Library.

  Minimum Distance: Use minimum distance to Reference Library as criteria for selection.

  Average Distance: Use average distance to Reference Library as criteria for selection.

  Maximum Distance: Use maximum distance to Reference Library as criteria for selection.

  Selection criteria: <= (less than or equal to) OR >= (greater than or equal to)

  Distance specification: Specifies distance threshold to use for selection.

• Distance measurement in comparison:

  Minimum Distance: Calculate distance to closest compound in the reference library.

  Average Distance: Calculate average distance to compounds in the reference library.

  Maximum Distance: Calculate distance to furthest compound in the reference library.

• Plot Options:

  Number of bins for histograms: Binning scheme for distance histogram.

Note

The library comparison scheme proceeds as follows: for every compound in the Candidate Library, distances to all compounds in the Reference Library are investigated. Depending on the distance measurement option, the minimum, maximum or average of these distances is retained. The set of distances obtained can then be plotted individually or as a histogram plot over the distance range. Results can also be analyzed in a Study Table.

Upon completion, the Compare Libraries - Similarity scheme provides several graphs. The default Similarity Plot (left) and Similarity Histogram (right) are shown below:

Analysis of distance histograms

In the analysis of a single minimum distance histogram, those compounds that correspond to the left-hand side of the histogram are those for which there exists at least one close (similar) compound in the reference library. These compounds are therefore redundant with the reference library. The compounds that correspond to the right-hand side of the histogram are those for which there are no close (similar) compounds in the reference library. Those compounds are therefore of interest as potential complements to the reference library. A distance threshold can be set in the selection process so as to isolate those compounds from the rest of the candidate library.

The same procedure may be used to determine whether a subset of a library correctly represents the entire set of compounds. In this case, the entire set should be taken as the candidate library and the subset used as the reference library. The library comparison procedure will check that for every compound in the entire library there is an appropriate representative in the subset.

One key aspect of this methodology is the identification of proper distance thresholds. In other words, how different is different enough? Studies on the validation of descriptors have been conducted by Brown and Martin and have suggested thresholds for use with fingerprint descriptors. A value of 0.85 has been suggested for Tanimoto similarity coefficients corresponding to a Tanimoto distance of 0.15 (1 - 0.85).