Compound Combination Modelling

Richard Lewis

Bender Group Meeting



  • What is Compound Combination Modelling, and how can it help?

  • Compound combination data
  • Visualization
  • Modelling

Introduction to CCM

  • Compound combinations are 'mixtures' of two or more constituent compounds.

  • The properties of the combination tend to often be non-linearly dependent on the properties of the constituent compounds

  • This deviation of a biological response from additive is a phenomenon known as synergy.

Combinations in the real world

  • Medicinal (both western and traditional)

  • Toxicity considerations for industrial products and intermediates

  • Pesticides

  • Flavourings and perfumes

There are many reasons to study combinations:

Combinations are much more common and relevant to the real world than purified single agents commonly considered in chemistry.

Experimental Compound Combination Data

Number of Compounds in a Combination

The relevant combinations in Nature tend to be tens of compounds.

For example, TCM remedies combine many herbs together, each of which have multiple active compounds in.

This is very complicated to study, and datasets have tended to focus very much on pairwise interaction.

Combination Experimental Design

Drug vs All

All vs All

One compound combined with a library

Compounds in a library combined together

Most useful for exploring synergy in general

Most useful for finding partners for an already identified compound

Many different compounds

Fewer compounds

Experimental Combination Data

There are two main techniques for assessing the activity and synergy of combinations of compounds.

  • 'Point' measurements
  • Surface measurements

Point Measurements

  • The dose-response curve for each individual agent is measured.
  • An appropriate concentration from the curve (such as the IC50) is selected for each compound.
  • Compounds are mixed together at the particular concentration.
  • Assuming the compounds act independently (are additive), the expected fractional response is given by Bliss Additivity:
R_c / R_0 = 1 - (1 - R_a / R_0) (1 - R_b / R_0)
  • For mixtures of compounds at IC50 concentrations, this is 0.75.
  • The deviation from this, the excess over Bliss, is given as a measure of synergy.
B = R_{c, exp}/R_0 - R_{c, pred}/R_0
  • The excess over bliss is positive for synergistic combinations.

Surface Measurements

  • The dose-response curve for each individual agent is measured.
  • An appropriate concentration interval (covering as much  of the response range as possible) is selected, usually on a per compound basis, in which several concentration points are chosen.
  • A combination of two compounds are tested by mixing the concentration points for each compound in a mesh grid, to yield a surface.

Metrics from surfaces

  • Bliss Independence

  • Deviation from Gaddum's Non Interaction model (Highest Single agent model

  • Maximal distance from additive line

  • Area methods

Surface vs Point Measurements



More measurements required

Fewer Measurements required

Replicates less costly

Replicates more costly

Survey different dose ratios

Only look at one dose ratio

The shape of the surface may encode information

No extra information encoded

Visualisation of Compound Combination Datasets

Visualization Techniques

Any plots need to visualise the compounds and their interactions.

In the literature, there have been two main approaches:

  • Heatmaps
  • Networks

Reasonably straightforward for drug vs all, as there is a 1:1 ratio of compounds to interactions.

More difficult for all vs all datasets: the number of combinations is proportional to the square of the compounds


  • Compounds are positioned on edges

  • Combinations are patches in the heat map

  • The colour of the patches indicates the degree of synergy of the combination.

  • Can order the compounds according to properties

  • Examples for the malaria database.

Structural Space

Physicochemical Space

Protein Target Space


  • Nodes are compounds.

  • Edges are combinations.

  • Degree of synergy indicated by thickness/colour of the edges.

  • Node positioning can be done using a layout algorithm dependent of the edge weights.

Synergy Maps

Lewis et. al. Synergy Maps: exploring compound combinations using network-based visualisation J.Chem.Inf. 2015 (submitted)


Modelling Compound Combination Data

General vs Specific

  • Drug vs All and All vs All datasets are structured to suggest two different paradigms of model building.

  • All vs All pairwise data suggests a general model of the synergy between two given compounds

S_{C_i,C_j} = f_\theta(C_i, C_j)
  • Drug vs All however suggests a more simple model, as one compound is kept constant, so the model can be simplified to the familiar QSAR problem:

S_{C_i,C_j} = f_\theta(C_i, C_j) = f_{\theta,C_j}(C_i)

Drug vs All Modelling

A drug vs all dataset of the anticancer drug Ibrutinib in combination with a diverse screening library of 465 compounds, tested against DLBCL cells.

Using the predicted target log-probabilities from PIDGIN as compound features for the MIPE compounds, and negative log Gamma as an output, a Leave One Out cross validation was performed with Random Forest Regressor models.


  • r2 value is ~0.05
  • Didn't really work!
  • The data very noisy - might need to do better filtering.
  • The label, pGamma, may not be the best indicator of synergy
  • The features are not descriptive enough.


Next Steps

  • Discretise the continuous space to transform to a classification problem

  • Filter the data to remove bad surfaces

  • Try out new synergy metrics

  • Try removing additive data from the training set

  • Use more detailed features, such as fusion fingerprints

Thanks for listening, any questions?

Dr. Andreas Bender

CCM 'task force'

All the Bender Group

Dr. Rajarshi Guha


EPSRC and Department of Chemistry for funding

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