EC-BLAST: a tool to automatically search and compare enzyme reactions, SA Rahman, SM Cuesta, N Furnham, GL Holliday, JM Thornton; Nature methods 11 (2), 171-174
EC-BLAST: a tool to automatically search and compare enzyme reactions, SA Rahman, SM Cuesta, N Furnham, GL Holliday, JM Thornton; Nature methods 11 (2), 171-174
Shortest Path (SP) has been used in many aspects of graph traversing. The idea is to minimise the cost (number of edges to be traversed or the cost on the edge) of traveling between a source and destination. This is one of the most optimal ways of finding a path in the graph where you can generate a combination of paths using random walk.
Interestingly, generation of path based hashed fingerprint is very common in the area of chemo-informatics. The basic idea is to find all paths of a certain length from the source atom (fragments) in a molecule and convert it into a hashed fingerprint. This works very well with smaller or sparsed graphs, although in a few cases the run time may increase exponentially with the size of the graph (connectivity). The Chemistry Development Kit (CDK) has one such effective path based hashed fingerprint generator (Fingerprinter.java). This module in the CDK has generated a lot of interest from the user community. Recently, Nina Nikolova – Jeliazkova posted an interesting set of molecules were the path search in the fingerprint was hit by combinatorial explosion!
Note: The behaviour of the path finding algorithm is compromised once the depth of the path search is more than 6 (the recommended depth is 8). Hence for these set of molecules one may not be able to find the fingerprints.
Here are the exemplar molecules where the present CDK hashed fingerprint is subdued.
I have modified the existing CDK fingerprinter to report the shortest path rather than all paths. This overcomes the problem of combinatory explosion and runtime is no longer exponential as compared to previous case.
Here is the runtime and the density of the FP (number of bit occupied) as calculated by the SP based FP. One can deduce the runtime and density by half if the FP is only based either on weighted or unweighted bonds. In the modified SP based FP, I have used both weighted and unweighted bonds to give better consensus FP (more in my next blog!).
Here is the code.
a) Presently the fingerprint accounts for only one shortest path between a source and the sink atom (discriminates between aromatic, ring and aliphatic paths). Hence, I had to canonicalize the atoms in the graph container such that if two molecules are similar then the returned SP path is same. A natural extension would be to report k-shortest path but this maybe as good as CDK default fingerprinter (in terms of the runtime).
b) For spare graph and smaller graphs it might be as fast as the previous implementation, and it will perform better on complex graphs.
Edited: 6th August 2012
Here is a test case based on the ring systems (aromatic and non aromatic) and aliphatic molecules.
Updated: 29th Aug 2012
Thanks to Egon for his suggestions to use SP2 hybridization instead of aromaticity checker. In my case I have to use CDK aromaticity detection as SP2 concept may not work.
I have clustered 11 molecules based on their fingerprint similarity scores using the
a) CDK default finprinter,
b) SP based Fingerprinter and
c) CDK Hybridization Fingerprinter
The clustered results are as shown below.
The Hybridization based fingerprinter is the fastest one (in the non-complex cases), followed by the SP fingerprinter and improved CDK fingerprinter. In terms of the sensitivity and specificity, SP fingerprinter is the best and in complex cases its by far the fast one!
I will leave it to the readers to choose their favorite fingerprinter.
Kindly leave your comments and suggestions!
Edited: 4th Nov, 10:20 AM
In my previous post, I discussed the impact of the hashcode and random number generators on a hashed fingerprint. They play a major role in the uniform distribution of the bits in a fixed length array and the occurrence of the bit clashes. In order to prove the concept, I have prepared a test case of 1200 molecules and preformed a substructure search using the default CDK Fingerprinter class and its improved Fingerprinter class version (with the Apache math librarys HashCodeBuilder() method and Mersenne Twister random number generator).
Each molecule was searched against other molecules in the dataset including itself. This was done at an interval of 200 data points. The gold standard was the substructure search results from the SMSD.
As expected the improved version of the Fingerprinter class outperformed the present CDK Fingerprinter class. The number of false positives (FP) were reduced by 35-40% (due to minimal bit clashes) thereby increasing the accuracy of the results, while the true positives remained unchanged. This also made an overall positive impact on the speed of the search results!
The raw results and the Fingerprinter code is available via my github account https://github.com/asad/CDKHashFingerPrint.
The present code can further be optimised for lowering the number of false positives.
Thus a better hashcode and random number generator leads to an improved hashed fingerprint.
Atom typing, bitset, circular fingerprints, Fingerprints, hashCode(), hashed fingerprints, hashing, Java, Mersenne Twister, molecular signatures, Random(), rings, RNG's, Similarity, SMARTS, stereo, subfingerprints, substructure
Fingerprints have been widely used in various fields to find similar features. Now for those of you who are using their detective instincts and aiming for DNA fingerprint or biological fingerprints, I might disappoint you in the later half of my post. Fingerprints are typically used to avoid cumbersome data comparison by using shorter “bit” string. My focus will be on the molecular fingerprints which have been used by chemo/bio informatician for finding similar molecular structures i.e. finding a needle in a hay stack! Theoretically, if you know the prerequisite features of “should have and not have” in the target molecules, then you can use a set of predefined keys to generate fingerprints. For examples PubChem fingerprint, MACCS keys etc. are based on certain substructure/SMARTS keys which are expected to be found or skipped in your target. On the other hand when we play with unknowns both at the level of query and target then one of the fastest ways to go for the kill is hashed fingerprints. Typically, in a hashed fingerprint a set of patterns are generated by gathering atom environment information or subgraph information or both. The generated patterns are then transformed into hash codes (a fixed size message digest) using hashing algorithm in computer science. These hash codes can then transformed into bit strings using random number generation of a defined length (size of the fingerprint). The presence and the absence of a pattern is marked as “1” and “0” respectively.
Let’s play with some real-time examples to understand the depth of the above mentioned statements. Now we need to generate some patterns from molecules and store them as fingerprints. In order to analyse the quality of the fingerprints we will open the black box by keeping track of the generated pattern types. This will help us to quantify the patterns involved in the bitset clashes. The circular fingerprint or molecular signatures can be used to generate patterns of various diameter/height for a molecule. By increasing the diameter/height, we can enrich the patterns/information about the molecules. However, this will also increase the overhead of balancing the fingerprint size and reducing the bit clashes.
Stage 1: Generate patterns using molecular signatures of heights 0 to 3 for every atom in the molecule. An example is illustrated in the figure below.
Stage 2: Transform these patterns as SMARTS/SMILES/Signatures and generate hash code for each pattern using your favourite algorithm.
Stage 3: Once we have the hash codes for these patterns then using random number generator, convert these hash codes into bit set bucket with a fixed range (eg. 1024).
I have used the CDK to generate molecular signatures (σ) of various heights (0 to 3) for 5000 mols. These signatures were transformed into canonical SMILES and hash code was generated using Java Apache math library HashCodeBuilder() method (better than default java hashCode() due to the flexibility). Well, you could use any method you like as long as equal objects produce same hash code and unequal objects produce distinct hash codes. Some of the most common hash code generation algorithms are MD5, SHA, PJW (Peter Weinberger’s hash) etc. The choice is made on the basis of data distribution (balance between random generation vs pattern in generation) and hashing function efficiency (should be very quick, stable and deterministic).
Now the tricky part is the conversion of hash codes into a fingerprint. I have used the famous Mersenne Twister random number generator. This yields better results than default java Random() method in terms of minimising the bit clashes and maximizing the bit set resolution.
Here are few statistical measure regarding the patterns generated and encoded into fingerprint bitsets.
|Statistical Measure (5000 mols)||Height 0||Height 1||Height 2||Height 3|
|Unique Pattern Count (UPC)||53||426||4083||14448|
|Average number of patterns/fingerprint||3.09 +/- 1.04||10.34 +/- 5.82||15.16 +/- 10.01||17.01 +/- 13.07|
|Median number of patterns/fingerprint||3||9||13||13|
|Max. number of patterns/fingerprint||7||35||64||89|
In order to understand the resolution of the fingerprints with respect to the bit clash and size of the fingerprints, I generated fingerprints of various sizes (ranging from 128 to 8192 bits). The fingerprint size 1024 bits seems like a good bet for signatures of height up to 2 (as marked in the graph below), while 4096 stands good for signature of height 3 (more than 95% bitsets are used and lesser % of bits clash).
From the above figure, it is clear that one of the key improvements which can be made in the hashed fingerprints is to divide it into sub-fingerprints. Then each sub-fingerprint can be populated with certain chemical/subgraph property of the molecule. Say in the case of molecular fingerprint of size 1024 bitset, one can divide the fingerprints into two sub-fingerprints –
a) One of 256 bits for storing labelled atom types and,
b) The second, of 768 bits for graph/topological information.
The hash code from the atom typed section is the depiction of concatenated labelled string of the CDK atom types + presence of atom in a ring system + stereo for each atom in a molecule (you could choose your own physiochemical labelling schema). The signatures/graph section can be populated with signatures/circular fingerprints of height/diameter 2. The Sub-fingerprints are easy to achieve and store with the above mentioned process due to the flexibility of generating hash codes within a range. The idea is to get the best of both the worlds i.e. physiochemical properties and subgraph patterns.
The quality of the hashed fingerprint depends a lot on the patterns generated (UPC), size of the bitsets, hashing function and random number generator. Next step for me would to cluster these similarity matrices or perform Leave One Out test on the dataset to check the specificity and sensitivity of the model.
Further reading and reference therein will give you more insight into the story:
How can I run SMSD using Java Thread….is SMSD thread safe?
The short answer is “YES” you can.
Here is a snippet to demonstrate that SMSD is thread safe.
The latest version of the SMSD is not also thread safe but it also comes with optimised matchers (bond and atom).
For, example you could demand it to respect the ring matching (restrict) while finding MCS.
Thus an MCS between a query SMILES “ONC1=CC=CC=C1” and target SMILES “O1C=CC=CN1C1=CC=CC=C1”.
a) without ring matcher is “ONC1=CC=CC=C1”
b) with ring matcher is “C1=CC=CC=C1”
This might be useful for few SMSD users.
Updated on : 28th July 2011
A chemically valid atom typing leads to better chemistry and consistent outputs from any chemo-informatics toolkit. In my previous post, I had highlighted the performance of the CDK atom typing on the KEGG dataset and the pressing need to improve it. Mr. Nimish Gopal (from IIT Roorkee, India) has taken up this herculean task to fix the missing CDK atom types (reported in the KEGG molecules) as part of his summer internship in Prof. Thornton’s group at the EMBL-EBI. Since I am deeply involved with this project, I thought it would be fruitful for the community to know about the progress we have made in this direction.
Aim: The aim of this project was to enrich the atom typing model in the CDK.
Assumption: A valid atom typing will lead to an accurate explicit hydrogen count.
Conclusion: We have successfully added around
90 missing 124 missing/curated atom types in the CDK. They range from metals to salts, etc. You can find the atom type enriched CDK on my github CDK branch named as atomtype.
Model: We have performed cross validation using Chemaxon as gold standard. The KEGG molecules were used as test cases. Each KEGG mol file was read by the CDK; hydrogens were stripped and two cloned copies were generated. Explicit hydrogens were added using the CDK and Chemaxon on the respective copies of the cloned molecules. The explicit hydrogen count was recored and if they were empirically same then a subgraph Isomorphism search was performed on them (in order to make sure the hydrogens were placed correctly).
Result: 15499 KEGG molecules were tested and only 5 of them disagreed between the CDK and Chemaxon explicit hydrogen adder results. From the graphs its clear that the improved and enriched atom typing in the CDK outperforms the present CDK atom typing model. The new enriched atom typing model based CDK hydrogen adder also concurs with the Chemaxon hydrogen adder results.
The failed cases are of ambiguous nature (C11065, C13932, C18368, C18380, C18384) and both softwares have different approach to handle such cases. The Chemaxon adds hydrogens to each atom in a molecules which is perceived correctly and skips ones (sets an error flag) which are not defined correctly. Whereas, CDK adds hydrogens to each atom in a molecule but exits (throws exception) as soon as it finds an untyped atom. Theoretically, they should end up giving same results but technically they differ.
The good news is that now CDK is able to atom type all the valid molecules from the KEGG database (June 2011 release). I am sure that there are few missing atom types which might crop up with some other small molecule databases ( e.g. ChEBI or PubChem etc.).
Atom typing is an important and integral part of any chemoinformatics software. Most of the calculations, and more importantly the assignment of implicit/explicit hydrogen(s) depend on this. Thanks to Egon, Rajarshi and others, the CDK has improved a lot over the years.
I (with Nimish a summer intern) did a quick test on the KEGG molecules (before KEGG becomes a paid service on 30th June, which is a pity…..!).
The good news is that only 1.37% molecules failed the “Atom Typing” test, as compared to last year (the failure rate was approximately 10%, mostly phosphates). Most of the failed atoms are metals (Cl,N,S,Fe,Mn,Zn,Cu, etc).
Here are the raw results: https://gist.github.com/1016328
Wish list: I hope the CDK developers or chemists can fix these too!
Kindly comment and leave your suggestions.
Lately, an interesting question was posed to me.
How can I join two molecules?
Well for many of us this might be a regular exercise on a chemical editor but this is a little trickier to program. So mathematically, we are aiming for a union between two molecules. The union between two molecules can be defined as (A ∪ B) = n(A) + n(B) – (A ∩ B), where A is a query molecule and B is the target molecule. The intersection (A ∩ B) can be obtained by finding isomorphism between two molecules. The joining part is a little challenging as not all combination(s) might be chemically valid. So we need to find combination(s) which are unique and unsaturated!
java -jar Union.jar "OOC1=CC=CC=C1" "c1ccc(cc1)c2ccccc2"
------------- Combination 1-------------------- Query SMILES OOC1=CC=CC=C1, count 8 Target SMILES c1ccc(cc1)c2ccccc2, count 12 Union SMILES OOc1ccccc1c2ccccc2, count 14 ------------- Combination 2-------------------- Query SMILES OOC1=CC=CC=C1, count 8 Target SMILES c1ccc(cc1)c2ccccc2, count 12 Union SMILES OOc1cccc(c1)c2ccccc2, count 14 ------------- Combination 3-------------------- Query SMILES OOC1=CC=CC=C1, count 8 Target SMILES c1ccc(cc1)c2ccccc2, count 12 Union SMILES OOc1ccc(cc1)c2ccccc2, count 14
Here are some interesting results as they highlight the run time between three flavours of substructure search algorithms. I have chosen, a) UIT (Universal Isomorphism Tester) as implemented in the CDK (Chemistry Development Kit); b) VF2 as implemented in the SMSD (I have further optimised it); and c) VF2 as ported from ChemKit. The former two implementations (i.e. a and b) are optimised for substructure search whereas the later implementation (i.e. c) is optimised for the graph automorphism search (further extension would be good/ideal).
While benchmarking the substructure search, I realised that the CDK AtomContainer takes ample amount of time for methods such as getConnectedAtomsList(atom) or getConnectedAtomsCount(atom). Hence, I ended up refactoring the AtomContainer to store the adjacency map of atoms and bonds. This will speed up the above mentioned methods and the benchmark results will bring out the actual differences in the run time. Please find the updated AtomContainer here (there is scope for further optimisation).
Now let’s focus on the results from the benchmark 🙂
The comparative study/benchmark results between the three algorithms revealed some very interesting characteristics.
1) ChemKit version of the VF2 is very fast as it just looks for graph automorphisms (light green bars on the graph).
2) CDK UIT seems to perform better on graphs with atom count <= 19.
3) VF2 implementation in the SMSD performs better on graphs with atom count > 19 and yes this implementation is better off in the worst case (i.e. if no hits were reported, e.g.: first bar with 11 atoms).
Further permutation based tests will reveal more intricacies, artefacts and the innate nature of these algorithms and implementation. If you are interested in these implementations and test cases please feel free to refer to the benchmark code on the github.
Update (16 March 2011): VF2 implementation from the Chemkit now calculates substructure isomorphism. Thanks to Kyle Lutz for his feedback. The new runtime of the VF2 chemkit implementation looks as good as the one in the SMSD except that the rejection of a solution (in case of mismatch) is faster in the SMSD version of the VF2 whereas matching is faster in the former. Rest of the facts regarding size and runtime mentioned in the graph above still hold good. Below is the updated graph.
Update (17 March 2011): Further optimisation of the ChemKit ported VF2 implementation makes is fastest (reporting the matches and rejection of solution; refer to the benchmark code on the github).
Updated (17 March 2010): Gilleain and myself were able to code an ultrafast VF2 algorithm for Isomorphism substructure search (permutation bug is resolved). The code is ported or re-factored from Chemkit and I have further optimised the code at our end. The previous VF2 code in the SMSD is more MCS oriented which was a big compromise in terms of speed while performing a substructure search. I have mentioned these issues in a previous blog. The whole idea of a substructure search is to answer a boolean question i.e. is A a subgraph/substructure of B ? If the answer is true then matching atoms are reported. On the other hand MCS where it’s about reporting the commonality between A and B.
Below is the benchmark graph which speaks about the performance (30 queries were subjected to 15030 targets, same as my previous benchmark test cases) of the VF2.
As is apparent from the benchmark graph, VF2 takes less than 10-20% of the total time (in most cases) for performing substructure searches (results are sorted in ascending order of the query atom count). So as for now we have an implementation which at last outperforms UIT (CDK code) in terms of speed for automorphic graphs. The performance of the VF2 improves as the query atom count (graph size) increases. We might need a few changes in the CDK AtomContainer class itself to further improve the speed/performance but this will involve further discussions with CDK developers.