Continuous Representation of Molecules Using Graph Variational Autoencoder

Abstract

In order to continuously represent molecules, we propose a generative model in the form of a VAE which is operating on the 2D-graph structure of molecules. A side predictor is employed to prune the latent space and help the decoder in generating meaningful adjacency tensor of molecules. Other than the potential applicability in drug design and property prediction, we show the superior performance of this technique in comparison to other similar methods based on the SMILES representation of the molecules with RNN based encoder and decoder.

Keywords

• Adjacency tensor

Introduction

Using machine learning to predict molecular structure properties is a challenging problem [ 7, 3 ]. While the governing equations (e.g. Schrodinger equation) are difficult and computationally expensive to solve, the fact that an underlying model exists is appealing for machine learning techniques. However, this problem is difficult from a technical point of view. The space of molecules is discrete and non-numerical. Thus, “how to best represent molecules and atoms for machine learning problems?” is still a question.

Despite having numerous ways to represent molecules such as methods introduced in [ 18, 1 ], all the representations are suffering from a few shortcomings, such as 1) discrete representation, 2) lengthy representation, 3) non-injective mapping, and 4) non-machine readable representation.

Here, we proposed a new method that borrows the main idea from [ 5 ] and [ 12 ] and overcomes all the aforementioned shortcomings. Our method which takes the graphical structure of the molecule as the inputs consists of a variational framework with a side predictor to better prune the structure of the latent space. Then an inner product decoder transfers the samples of latent space into meaningful adjacency tensors. To compare with the main benchmark which is a textbased encoding of molecules [ 9 ] we performed two experiments on the QM9 dataset [ 16, 15 ] and ZINC [ 11 ]. Both experiments show the success of this method. Although this Copyright c 2020, for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CCBY 4.0).

Node-feature matrix Adjacency tensor

Side target GCN Encoder GCN Encoder

Side predictor

Pooling work is presenting preliminary results of Graph VAE, further experiments and comparisons are left to future work.

Method

Molecules and Graphs A molecule can be represented by an undirected graph G = (V; E; R), with nodes (atoms) vi 2 V and labeled edges (bonds) (vi; e; vj ) 2 E where r 2 R is an edge type. Since we focus on small molecules with four bond types, R is equal to 4. An n by d node-feature matrix H is also carrying more information about each node. These two tensors, together, represent a molecular structure. Variational Autoencodes To help ensure that points in the latent space correspond to valid realistic molecules, and to minimize the dead areas of the latent space, we chose to use a variational autoencoder (VAE). To further ensure that the outputs of the decoder are corresponding valid molecules we employed the open-source cheminformatics suite RDKit30 to validate the chemical structures of output molecules in terms of atomic valence. All invalid outputs are discarded. It is necessary to mention that the ordering of the nodes assumed to be unchanged.

VAE and Side Prediction To better learn the graph structure of the molecules, the encoder part of the VAE consists of GCN layers. The same method as [ 17 ] has been employed to perform relational update which can be formulated as: hl+1 = i (X

X where Nri denotes the set of nodes connected to node i through the edge type r 2 R. Since we are focusing on small molecules, we applied three layers of GCN in our encoder model to gather information from 3-hop neighbors of each atom. The structure of encoder consists of two, three-layer GCNs for both mean and the covariance. GCNs of the encoder share the filters of the first two layers. Here we can formulate the encoding and sampling scheme as follows: q(ZjH; A) =

N Y qi(zijH; A); 1 qi(zijH; A) = N (zijGCN ; GCN )

The GCN and similarly GCN are: GCN (H; A) = A^ (A^ (A^H W0)W1)W2, where the A^ is the normalized adjacency tensor, Wi is the filter parameter of each layer, and is the activation function [2]. Finally, as suggested in [ 12 ] we use the simplest form of the decoder which can be seen as graph deconvolution network. The output of the encoder is simply the inner product between latent variable:

N N p(AjZ) = Y Y p(Aij jzi; zj );

1 1 p(Aij = 1jzi; zj ) = (ziT zj )

For the side prediction part, we employ a simple regression model in the form of a multilayer perceptron (MLP) to the network that predicts the properties from the latent space representation. The input of the side predictor is a vector obtained through a pooling mechanism of the latent representation as follows:

N

G(H (L)) = X sof tmax(hiL:Wp) Where WP is the pooling weight matrix and H (L) is the output of the GCN .

Finally, the autoencoder is trained jointly on the reconstruction task and a property prediction task; The joint loss function is the summation of the two losses, as follows: i=1 L = ELBO + negative log likelihood = Eq(ZjH;A)

KL(q(ZjH; A)jjp(Z)) + M SE(sidenetwork)

Experiments

We performed two experiments to show the usefulness of continuous representation. In the first experiment, we focus on the prediction of property and the generation of the valid molecules. In the second experiment, we use this continuous representation to propose a new metric for measuring the molecular similarity.

Nicotine

Ecstasy Amphetamine

Caffeine

Aspirin Using a subset of QM9 dataset [ 15 ] as the training set, we extract 48,000 molecules covering a broad range of molecules. Each molecule in the training set is chosen to have up to 20 atoms. The training objective on the side predictor was set to be one of the Solubility, Druglikeliness, and Synthesizability. We employ the continuous representation of molecules using each network to predict the other two unseen properties. The performance of each model plus the percentages of validly generated molecules are summarized in Table 1. In order to check the validity of the outcome, we only check for the validity of the atomic valence. As it is shown in Table 1 the accuracy of each property is comparable to the state of the art property predictions mentioned in [ 8 ]. Although Graph VAE is not outperforming the predictions based on [ 8 ], it shows that using a property as a heuristic to prune the latent space, can help with predicting other molecule properties.

Molecular Similarity Measure Numerous similarity or distance measures have been used widely to calculate the similarity or dissimilarity between two samples. Since metrics are focusing more on 2dimensional representation rather than 3-dimensional structure, our model as a “2D structure-aware representation” is an accurate metric for the similarity measure. Normalized Euclidean distance between the latent representation of two molecules after pooling operation is the metric we define to capture the similarity. Here we compare three wellknown similarity measures with our technique and also to the methods introduced in [ 9 ]. This method which is using the SMILES representation of the molecules as the input employs a VAE with a side predictor. Both encoder and decoder parts of the VAE are based on RRN and sequence to sequence model. Although all the graphical information of the molecule is encoded within the SMILES representation, inferring the graphical structure (e.g., adjacency tensor) from the SMILES string is an exhausting process that is based on several rules. Despite the numerous techniques built upon using the SMILES representation of the molecules [ 6, 10, 4, 14, 13 ], it has been shown that it is more efficient to take advantage of the graph structures and employ GCNs to process molecular structures. Here, we chose Aspirin as a sample drug and compare its similarity with four different drugs with four different similarity measures. We compare the performances of our technique with [ 9 ], which is using a similar approach but operating on text representation of molecules. Our experiment shows that graph-based hidden representation is carrying more information than only text. Table 2 is summarizing the result of the similarity measure experiment.

As it is shown in table 2, our metric is very well aligned with all other well-known metrics which is another proof for the applicability of our model.

Experiment Details

GVAE consists of two GCNs for the encoder, a pooling mechanism, and a multi-layer perceptron for the side prediction. Both GCNs are three-layer networks with filter matrices W0; W1, and W2 of 32*32, 32*32m and 32*16 respectively. The pooling weight matrix Wp is of size 1*64 which outputs a vector of length 64 to represent the whole molecule. A two-layer MLP with 32 and 1 hidden units is employed to perform the regression task.

In Table 2, we use our own implementation of the SMILES VAE. Both GVA and SMILES VAE are trained using a dataset of 70,000 molecules which are randomly selected from ZINC.

In Table 2, all measures except the continuous representations are calculated with the same fingerprinting algorithm. It identifies and hashes topological paths (e.g. along with bonds) in the molecule and then uses them to set bits in a fingerprint of length 2048. The set of parameters used by the algorithm is - minimum path size: 1 bond - maximum path size: 7 bonds - number of bits set per hash: 2 - target on-bit density 0.3.

Conclusion

We proposed a generative model through which we can find continuous representation for molecules. As shown in the experiments section, this technique can be used in different chemoinformatics tasks such as drug design, drug discovery and property prediction. As future work, one can think of attention based graph convolutions and more complicated decoders. These two extensions can be studied in future works.

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