1. Toxicity vs CHEMICAL space

2. Can we predict toxicity of a chemical compound?
To predict toxicity of a compound a, we assume there exists Another compound B with
known toxicity
Similar properties with A
Based on the similarity between a and b, we expect
Toxicity of A = toxicity of b + small difference
The result depends on the definition of similarity
there are many similarity coefficients
Structure-based similarity searches (SAR, QsAR)
usually tiny change of chemical is based on trivial assumptions
In general, failed to give small difference
Regarded as a non-smooth trend ( for example in toxicity)
known as non-smooth chemical space but no rule where to put
how do we know right position of the chemical in the space
Mendeleev solved positioning of the chemical elements

3. An example to position chemicals: How to position chemical?
reymond & awale (2012) proposed 42-dimensional space to position all known and unknown small molecules (chemicals)
Every chemical is assigned with 42-integer valued molecular quantum numbers (MQN)
positioned in 42-dimensional grid on R42 (can assume it a bin in R42)
conducted principal component analysis (PCA)
To extract most relevant dimensions (in the form of principal components, PC)
To Represent projections of the chemical space in a PC-plane,
For most databases, more than 70% of variance of MQN-space is covered by PC1, PC2 and PC3
MQN-Maps derived from projections in the PC-planes – an overview of their chemical space
MQN-space was inline with already defined groups with a proper direction
Groups of related bioactive compounds often cluster together on MQN-maps
MQN-similarity does not select for substructure similarity -> can reveal non-trivial relationship between actives

4. A figure from Nguyen et al (2009)
does position matter?
A figure from Nguyen et al (2009)

5. A drawback of MQN-space
MQN-space (1billion COMPOUNDS): known/synthesized, <0.01%
unknown/generated, >99.9%
ZINC database (21M) GDB-11 database (26.4M)
no. of compounds
no. of MQN-bins
no. of single occupied MQN-bins
no. of compounds in most occupied MQN-bin
no. of shared MQN-bins
no. of compounds in shared MQN-bins

6. A need to improve MQN-space
Do compounds in shared MQN-bins have same or similar biological activity (for example toxicity)?
If yes, MQN-space perfectly works – but probably not (with probability)
If no,
need to distinguish between 2 compounds in a bin
Re-position them in the mqn-space without disturbing other chemical’s position
Using structural similarity

7. OUR PROPOSAL Each compound in a bin in mqn-space has 42 neighbours
For simplicity, suppose we have 2 compounds in a particular bin
We know 1 compound will definitely stay at grid but the other (X) must shift
we know all its 42 neighbours will definitely stay at their grid
we will compute structure-based distance (SD) of X from all 42 neighbours
For example, using soergel distance based on 2d structural similarity (0<SD<1)
Choose minimum SD direction, and shift X into this direction with the shift length SD

8. Thank you! Further directions: Defining fixed points
Checking consistencies with existing mathematical spaces (e.g. R42)