Comparison

The distance between two fingerprints is calculated in two steps:

1. Calculate feature distances: Calculate distance for each feature (e.g. distance between pairwise 85 size feature bits). Use L1 norm for discrete features and L2 norm for continuous features (scaled by number of bits per feature).

2. Calculate fingerprint distance: Calculate the weighted sum of all feature distances (sum of feature weights equals 1).

Figure 1: The pairwise kissim fingerprint comparison.

Respective objects performing these calculates are the FeatureDistances and FingerprintDistance objects. Furthermore, such distances can not only be generated between two fingerprints as described above but also in bulk for a set of fingerprints in an all-against-all comparison using the objects FingerprintDistanceGenerator and FeatureDistancesGenerator.

Let’s take a look at the API logic in this table again:

Action	Module	Single calculation	Bulk calculation
Encode structures as fingerprint	encoding	Fingerprint	FingerprintGenerator
Compare fingerprint features (calculate feature distances)	comparison	FeatureDistances	FeatureDistancesGenerator
Compare fingerprints (calculate fingerprint distance)	comparison	FingerprintDistance	FingerprintDistanceGenerator

# Load path to test data
from kissim.dataset.test import PATH as PATH_TEST_DATA

Set up local KLIFS session using the opencadd.databases.klifs module.

from opencadd.databases.klifs import setup_local

KLIFS_LOCAL = setup_local(PATH_TEST_DATA / "KLIFS_download")

Select structure KLIFS IDs

structure_klifs_ids = [109, 118, 12347, 1641, 3833, 9122]

Generate fingerprints

Let’s generate a few fingerprints for the structures in our local KLIFS download using the bulk fingerprint generator FingerprintGenerator.

from kissim.encoding import FingerprintGenerator

fingerprint_generator = FingerprintGenerator.from_structure_klifs_ids(
    structure_klifs_ids=structure_klifs_ids, klifs_session=KLIFS_LOCAL
)
print(f"Number of fingerprints: {len(fingerprint_generator.data.keys())}")

Number of fingerprints: 6

Note: If fingerprint cannot be generated (e.g. because structural data is missing), the structure is skipped.

Compare two fingerprints

Let’s first focus on the comparison between two fingerprints only.

For two fingerprints (Fingerprint objects), we will

1. Calculate the feature distances using FeatureDistances and

2. Calculate based on these feature distances and given feature weights the final fingerprint distance using FingerprintDistance.

Generate feature distances between two fingerprints (FeatureDistances)

• Input: Two Fingerprint objects

• Output: FeatureDistances object

fingerprints = list(fingerprint_generator.data.values())
fingerprint1 = fingerprints[0]
fingerprint2 = fingerprints[1]

from kissim.comparison import FeatureDistances

feature_distances = FeatureDistances.from_fingerprints(fingerprint1, fingerprint2)
print(f"Kinase pair: {feature_distances.kinase_pair_ids}")
print(f"Structure pair: {feature_distances.structure_pair_ids}")
feature_distances.data

Kinase pair: ('ABL2', 'ABL2')
Structure pair: (109, 118)

	feature_type	feature_name	distance	bit_coverage
0	physicochemical	size	0.000000	1.00
1	physicochemical	hbd	0.000000	1.00
2	physicochemical	hba	0.000000	1.00
3	physicochemical	charge	0.000000	1.00
4	physicochemical	aromatic	0.000000	1.00
5	physicochemical	aliphatic	0.000000	1.00
6	physicochemical	sco	0.080000	0.88
7	physicochemical	exposure	0.294118	1.00
8	distances	distance_to_centroid	0.059839	1.00
9	distances	distance_to_hinge_region	0.122168	1.00
10	distances	distance_to_dfg_region	0.105499	1.00
11	distances	distance_to_front_pocket	0.070291	1.00
12	moments	moment1	0.060816	1.00
13	moments	moment2	0.116013	1.00
14	moments	moment3	0.204469	1.00

Generate fingerprint distance between two fingerprints (FingerprintDistance)

• Input: FeatureDistances object and optionally feature weights

• Output: FingerprintDistance object

Use standard feature weights

from kissim.comparison import FingerprintDistance

fingerprint_distance = FingerprintDistance.from_feature_distances(
    feature_distances, feature_weights=None
)
print(f"Fingerprint distance: {fingerprint_distance.distance}")
print(f"Fingerprint bit coverage: {fingerprint_distance.bit_coverage}")

Fingerprint distance: 0.07421423894307076
Fingerprint bit coverage: 0.9919999999999999

Use user-defined feature weights

feature_weights = [0.3 / 8] * 8 + [0.5 / 4] * 4 + [0.2 / 3] * 3
fingerprint_distance = FingerprintDistance.from_feature_distances(
    feature_distances, feature_weights=feature_weights
)
print(f"Fingerprint distance: {fingerprint_distance.distance}")
print(f"Fingerprint bit coverage: {fingerprint_distance.bit_coverage}")

Fingerprint distance: 0.08417398268335104
Fingerprint bit coverage: 0.9954999999999999

Compare all-against-all fingerprints

Let’s now take a look at the bulk distance generators to generate all-against-all comparisons for a set of fingerprints.

For a FingerprintGenerator object, which contains the fingerprints for a set of structures, we will

1. Calculate feature distances for all fingerprint pairs using FeatureDistancesGenerator and

2. Calculate based on these feature distances and given feature weights the final fingerprint distance for all fingerprint pairs using FingerprintDistanceGenerator.

Generate feature distances for all pairwise structures/fingerprints (FeatureDistancesGenerator)

• Input: FingerprintGenerator object

• Output: FeatureDistancesGenerator object

from kissim.comparison import FeatureDistancesGenerator

feature_distances_generator = FeatureDistancesGenerator.from_fingerprint_generator(
    fingerprint_generator
)
feature_distances_generator.data

	structure.1	structure.2	kinase.1	kinase.2	distance.1	distance.2	distance.3	distance.4	distance.5	distance.6	...	bit_coverage.6	bit_coverage.7	bit_coverage.8	bit_coverage.9	bit_coverage.10	bit_coverage.11	bit_coverage.12	bit_coverage.13	bit_coverage.14	bit_coverage.15
0	109	118	ABL2	ABL2	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	...	1.00	0.88	1.00	1.00	1.00	1.00	1.00	1.0	1.0	1.0
1	109	12347	ABL2	BRAF	0.410256	0.397436	0.333333	0.243590	0.141026	0.230769	...	0.92	0.67	0.92	0.92	0.92	0.92	0.92	1.0	1.0	1.0
2	109	1641	ABL2	CHK1	0.388235	0.352941	0.364706	0.247059	0.141176	0.223529	...	1.00	0.86	1.00	1.00	1.00	1.00	1.00	1.0	1.0	1.0
3	109	3833	ABL2	AAK1	0.505882	0.505882	0.411765	0.211765	0.082353	0.270588	...	1.00	0.86	1.00	1.00	1.00	1.00	1.00	1.0	1.0	1.0
4	109	9122	ABL2	ADCK3	0.623529	0.470588	0.435294	0.258824	0.235294	0.305882	...	1.00	0.88	0.98	1.00	1.00	1.00	1.00	1.0	1.0	1.0
5	118	12347	ABL2	BRAF	0.410256	0.397436	0.333333	0.243590	0.141026	0.230769	...	0.92	0.65	0.92	0.92	0.92	0.92	0.92	1.0	1.0	1.0
6	118	1641	ABL2	CHK1	0.388235	0.352941	0.364706	0.247059	0.141176	0.223529	...	1.00	0.84	1.00	1.00	1.00	1.00	1.00	1.0	1.0	1.0
7	118	3833	ABL2	AAK1	0.505882	0.505882	0.411765	0.211765	0.082353	0.270588	...	1.00	0.85	1.00	1.00	1.00	1.00	1.00	1.0	1.0	1.0
8	118	9122	ABL2	ADCK3	0.623529	0.470588	0.435294	0.258824	0.235294	0.305882	...	1.00	0.86	0.98	1.00	1.00	1.00	1.00	1.0	1.0	1.0
9	12347	1641	BRAF	CHK1	0.346154	0.423077	0.346154	0.243590	0.115385	0.217949	...	0.92	0.65	0.92	0.92	0.92	0.92	0.92	1.0	1.0	1.0
10	12347	3833	BRAF	AAK1	0.435897	0.474359	0.333333	0.230769	0.102564	0.230769	...	0.92	0.65	0.92	0.92	0.92	0.92	0.92	1.0	1.0	1.0
11	12347	9122	BRAF	ADCK3	0.576923	0.371795	0.397436	0.256410	0.269231	0.282051	...	0.92	0.68	0.89	0.92	0.92	0.92	0.92	1.0	1.0	1.0
12	1641	3833	CHK1	AAK1	0.352941	0.411765	0.352941	0.200000	0.082353	0.235294	...	1.00	0.84	1.00	1.00	1.00	1.00	1.00	1.0	1.0	1.0
13	1641	9122	CHK1	ADCK3	0.611765	0.494118	0.541176	0.317647	0.282353	0.317647	...	1.00	0.86	0.98	1.00	1.00	1.00	1.00	1.0	1.0	1.0
14	3833	9122	AAK1	ADCK3	0.611765	0.482353	0.494118	0.282353	0.223529	0.341176	...	1.00	0.87	0.98	1.00	1.00	1.00	1.00	1.0	1.0	1.0

15 rows × 34 columns

Generate fingerprint distance for all pairwise structures/fingerprints (FingerprintDistanceGenerator)

• Input: FeatureDistancesGenerator object (or FingerprintGenerator object) and optionally feature weights

• Output: FingerprintDistanceGenerator object

from kissim.comparison import FingerprintDistanceGenerator

fingerprint_distance_generator = FingerprintDistanceGenerator.from_feature_distances_generator(
    feature_distances_generator
)

Note: Fingerprint distances can also be calculated directy from the fingerprints (FingerprintGenerator > FingerprintDistanceGenerator) instead of using the feature distances explicitly as show above (FingerprintGenerator > FeatureDistancesGenerator > FingerprintDistanceGenerator):

fingerprint_distance_generator = FingerprintDistanceGenerator.from_fingerprint_generator(
    fingerprint_generator
)

fingerprint_distance_generator.data.head()

	structure.1	structure.2	kinase.1	kinase.2	distance	bit_coverage
0	109	118	ABL2	ABL2	0.074214	0.992000
1	109	12347	ABL2	BRAF	0.259053	0.919333
2	109	1641	ABL2	CHK1	0.253045	0.990667
3	109	3833	ABL2	AAK1	0.277368	0.990667
4	109	9122	ABL2	ADCK3	0.358882	0.990667

Kinase distance matrix

fingerprint_distance_generator.kinase_distance_matrix(by="minimum")

kinase.2	AAK1	ABL2	ADCK3	BRAF	CHK1
kinase.1
AAK1	0.000000	0.277368	0.303542	0.307277	0.229590
ABL2	0.277368	0.000000	0.358882	0.259053	0.246844
ADCK3	0.303542	0.358882	0.000000	0.376875	0.347142
BRAF	0.307277	0.259053	0.376875	0.000000	0.303330
CHK1	0.229590	0.246844	0.347142	0.303330	0.000000

Show on diagonal experimental values for structure pairs representing each kinase pair (as opposed to simply setting the diagonal to 0 by default).

fingerprint_distance_generator.kinase_distance_matrix(by="minimum", fill_diagonal=False)

kinase.2	AAK1	ABL2	ADCK3	BRAF	CHK1
kinase.1
AAK1	NaN	0.277368	0.303542	0.307277	0.229590
ABL2	0.277368	0.074214	0.358882	0.259053	0.246844
ADCK3	0.303542	0.358882	NaN	0.376875	0.347142
BRAF	0.307277	0.259053	0.376875	NaN	0.303330
CHK1	0.229590	0.246844	0.347142	0.303330	NaN

More structure-kinase mapping methods are available, e.g. maximum or mean. Additionally, the number of structure pairs per kinase pair can be fetched.

fingerprint_distance_generator.kinase_distance_matrix(by="size")

kinase.2	AAK1	ABL2	ADCK3	BRAF	CHK1
kinase.1
AAK1	0	2	1	1	1
ABL2	2	1	2	2	2
ADCK3	1	2	0	1	1
BRAF	1	2	1	0	1
CHK1	1	2	1	1	0

fingerprint_distance_generator.kinase_distance_matrix(by="std")

kinase.2	AAK1	ABL2	ADCK3	BRAF	CHK1
kinase.1
AAK1	0.000	0.004	NaN	NaN	NaN
ABL2	0.004	0.000	0.001	0.01	0.004
ADCK3	NaN	0.001	0.000	NaN	NaN
BRAF	NaN	0.010	NaN	0.00	NaN
CHK1	NaN	0.004	NaN	NaN	0.000

The kinase distance matrix can also be filtered for kinase pairs with a user-defined bit coverage.

fingerprint_distance_generator.kinase_distance_matrix(by="minimum", coverage_min=0.99)

kinase.2	AAK1	ABL2	ADCK3	CHK1
kinase.1
AAK1	0.000000	0.277368	NaN	NaN
ABL2	0.277368	0.000000	0.358882	0.253045
ADCK3	NaN	0.358882	0.000000	NaN
CHK1	NaN	0.253045	NaN	0.000000

If you are interested in more information about selected structure pairs (in case of methods minimum and maximum), please use the following method:

fingerprint_distance_generator.kinase_distances(by="minimum").head()

		index	structure.1	structure.2	distance	bit_coverage
kinase.1	kinase.2
ABL2	ABL2	0	109	118	0.074214	0.992000
	BRAF	1	109	12347	0.259053	0.919333
	CHK1	6	118	1641	0.246844	0.989333
	AAK1	3	109	3833	0.277368	0.990667
	ADCK3	4	109	9122	0.358882	0.990667

Structure distance matrix

fingerprint_distance_generator.structure_distance_matrix()

structure.2	109	118	1641	3833	9122	12347
structure.1
109	0.000000	0.074214	0.253045	0.277368	0.358882	0.259053
118	0.074214	0.000000	0.246844	0.282949	0.360833	0.273133
1641	0.253045	0.246844	0.000000	0.229590	0.347142	0.303330
3833	0.277368	0.282949	0.229590	0.000000	0.303542	0.307277
9122	0.358882	0.360833	0.347142	0.303542	0.000000	0.376875
12347	0.259053	0.273133	0.303330	0.307277	0.376875	0.000000

The structure distance matrix can also be filtered for structure pairs with a user-defined bit coverage.

fingerprint_distance_generator.structure_distance_matrix(coverage_min=0.99)

structure.2	109	118	1641	3833	9122
structure.1
109	0.000000	0.074214	0.253045	0.277368	0.358882
118	0.074214	0.000000	NaN	NaN	NaN
1641	0.253045	NaN	0.000000	NaN	NaN
3833	0.277368	NaN	NaN	0.000000	NaN
9122	0.358882	NaN	NaN	NaN	0.000000