# Projecting Molecules into Synthesizable Chemical Spaces

Shitong Luo  Wenhao Gao  Zuofan Wu  Jian Peng  Connor W. Coley  Jianzhu Ma

###### Abstract

Discovering new drug molecules is a pivotal yet challenging process due to the
near-infinitely large chemical space and notorious demands on time and
resources. Numerous generative models have recently been introduced to
accelerate the drug discovery process, but their progression to experimental
validation remains limited, largely due to a lack of consideration for
synthetic accessibility in practical settings. In this work, we introduce a
novel framework that is capable of generating new chemical structures while
ensuring synthetic accessibility. Specifically, we introduce a postfix
notation of synthetic pathways to represent molecules in chemical space. Then,
we design a transformer-based model to translate molecular graphs into postfix
notations of synthesis. We highlight the model’s ability to: (a) perform
bottom-up synthesis planning more accurately, (b) generate structurally
similar, synthesizable analogs for unsynthesizable molecules proposed by
generative models with their properties preserved, and (c) explore the local
synthesizable chemical space around hit molecules.

chemical space, synthesizability, molecular generation

##  1 Introduction

Designing novel drug molecules, a process that aims to identify molecular
structures with desired properties, is known to be notoriously complex, time-
and resource-consuming (Wouters et al., 2020). Methods that could accelerate
the discovery process are thus of significant interest in medicinal science
and the pharmaceutical industry. Historically, two principal computational
methodologies have been employed in drug design: virtual screening (Shoichet,
2004) and de novo design (Hartenfeller & Schneider, 2011). Virtual screening
involves predicting properties for a predefined set of molecules, known as
virtual libraries, and identifying the most promising candidates for
subsequent validation. These libraries are usually commercial catalogs (make-
on-demand compounds) from chemical vendors (Lyu et al., 2019) and generally
consist of molecules with assured synthesizability (Enamine, 2023). However,
screening large numbers of molecules is a time-intensive process. Moreover,
even libraries on the scale of billions present only a tiny fraction of the
theoretical chemical space (Figure 1a), which is nearly infinite in the number
of potential synthesizable small molecules (Bohacek et al., 1996). This means
that many potentially valuable molecules might not be included in these
libraries. Additionally, as the size of the library increases, so does the
cost of screening, which in turn limits the effectiveness and efficiency of
virtual screening in the drug discovery process.

De novo molecular design methods, unlike virtual screening, dynamically create
molecules tailored to specific objectives like protein binding and
bioactivity. Early methods of this kind typically adopt combinatorial
optimization (Venkatasubramanian et al., 1995; Jensen, 2019; Brown et al.,
2019), while recently, neural network enhanced optimization (You et al., 2018;
Fu et al., 2021) and generative modeling (Gómez-Bombarelli et al., 2018; Jin
et al., 2018) have become popular. These methods aren’t constrained by the
limitations of virtual libraries, enabling the efficient exploration of novel
chemical entities (see Figure 1c). However, a notable defect with most
existing generative models is their tendency to propose synthetically
infeasible molecules (Figure 1c) (Gao & Coley, 2020), a concern particularly
pronounced in structure-based drug design, an area of increasing interest
(Bohacek et al., 1996; Luo et al., 2021; Fu et al., 2022). This issue stems
from the inherent ignorance of synthetic accessibility in formulations of most
existing generative algorithms, in which molecules are constructed using
SMILES strings or atoms and motifs as fundamental units (Gao et al., 2022).
This often leads to chemical structures that fall outside synthesizable
chemical spaces, posing practical challenges in the experimental validation as
well as production of such designs.

Incorporating synthesizability as an additional optimization criterion is a
common strategy, yet it introduces complex challenges. Synthesizability is
difficult to define precisely due to its sensitivity to subtle structural
differences, reaction selectivity, and building block availability inherent in
chemical reactions (Gao & Coley, 2020). While notable efforts have been made
to estimate synthetic accessibility (Ertl & Schuffenhauer, 2009; Thakkar et
al., 2021; Voršilák et al., 2020), reliable quantification of synthetic
accessibility is still a far goal. A more effective strategy involves
constraining the design process to only consider molecules that are
synthesizable, ensuring that algorithms focus exclusively on viable
structures. Based on this idea, several models have been introduced (Bradshaw
et al., 2019, 2020; Gao et al., 2021; Swanson et al., 2023), though these
models have notable limitations, such as poor coverage of synthesizable
chemical space or inefficiency in optimizing the properties, as further
discussed in Section 2.

To address the recognized challenges, we introduce a framework that learns to
“project” molecules into synthesizable chemical spaces (Figure 1d). Given
molecules without synthesizability guarantee, our model is able to “fix” them
by identifying synthesizable analogs that are structurally similar, thus
preserving the structural factors that contributed to the desired properties
(Janela & Bajorath, 2022). We represent molecules by a scalable linear
representation for synthetic pathways based on postfix notations. By
generating synthetic pathways in the form of postfix notations rather than
molecular graphs or strings, we can ensure the designed molecules are
derivable from purchasable chemical building blocks and expert-defined
chemical reaction rules, thereby guaranteeing the synthesizability of
resulting molecules. We adopt the transformer architecture (Vaswani et al.,
2017), with an encoder for molecular graphs and a decoder to generate postfix
notations of synthesis.

We validate the effectiveness of the model by showcasing its ability to
generate synthesizable analogs that are structurally and functionally similar
to input unsynthesizable molecules. Furthermore, the model demonstrates its
proficiency in navigating the local synthesizable chemical space, proving
invaluable for the expansion and exploration of potential hit molecules. The
main contributions of our work can be summarized as follows:

  * •

We propose a novel linear representation for synthesis pathways based on
postfix notations. This also provides a uniform and generalizable
representation for all experimental procedures.

  * •

We present a novel and robust algorithm tailored for synthesizable molecular
design. Specifically, our model can project unsynthesizable molecules from
existing generative models to synthesizable chemical space to obtain a
structural analog with desired properties such as binding and bioactivity
preserved, as well as explore local chemical space for hit expansion.

  * •

We demonstrate strong empirical performance in evaluations of bottom-up
synthesis planning and analog design, outperforming prior methods.

##  2 Related Work

Figure 1:  Illustration of (a) virtual screening algorithms, (b) combinatorial
optimization algorithms, (c) de novo generative models, and (d) projection to
synthesizable chemical space. Each dot represents a chemical structure, and
the gray curve represents a synthesizable chemical space.

We divide the synthesizable molecular design methods into combinatorial
optimization algorithms, reinforcement learning, and autoencoders. We
acknowledge and emphasize that the boundaries between these categories are not
clear-cut and many intersections exist. This classification is primarily for
the sake of clarity in our discussion.

Combinatorial optimization algorithms use a set of chemical building blocks
and reaction templates to make the chemical space combinatorial, and then
apply combinatorial optimization algorithms, such as genetic algorithms (Gao
et al., 2021), Monte Carlo tree search (Swanson et al., 2023), and Bayesian
optimization (Korovina et al., 2020), to search for desired molecules (Figure
1b). Early representative work before the advent of molecular deep learning
includes SYNOPSIS (Vinkers et al., 2003) and DOGS (Hartenfeller et al., 2012),
which perform virtual reactions to generate candidate molecules and select
candidates according to scoring functions. In recent years, advances in deep
learning for chemical reactions (Coley et al., 2019a; Schwaller et al., 2019)
have inspired methods such as MoleculeChef (Bradshaw et al., 2019), ChemBO
(Korovina et al., 2020), and DoGs (Bradshaw et al., 2020) that use neural
networks to predict reaction outcomes in a “template-free” manner.

Reinforcement learning approaches, exemplified by PGFS (Gottipati et al.,
2020) and REACTOR (Horwood & Noutahi, 2020), formulate the forward synthesis
process as Markov decision processes and train agents to explore the chemical
space under the guidance of reward functions that quantify desired properties.
The agent is provided with a set of reactants and reaction templates and
learns to synthesize desirable molecules with them. As the agent is aware of
the objective, its search process is directed and expected to be more
efficient.

Autoencoder-based methods, represented by MoleculeChef (Bradshaw et al., 2019)
and DoGs (Bradshaw et al., 2020), leverage the autoencoder architecture to
model synthetic pathways in a generative manner. MoleculeChef is one of the
earliest neural models of this kind. Instead of synthetic paths, it tries to
encode and decode a bag of starting reactants from purchasable building
blocks. Following an enumeration of the one-step synthetic pathways, the
“best” molecule from the products is chosen as the output. DoGs represents
synthetic pathways as directed acyclic graphs and serializes the graph
construction process as a sequence of actions that includes node addition,
reactant selection, and node connection. DoGs use recurrent neural networks to
generate action sequences from latent codes, enabling de novo molecular
generation by drawing samples from the latent space. SynNet (Gao et al., 2021)
can also be seen as this kind, in which the molecular fingerprinting algorithm
is the encoder, and neural networks are used as a decoder to generate
synthetic paths.

Limitations: While the synthesizable molecular design methods have advanced
significantly, they are still in the proof-of-concept stage and far from
mature. The efficiency of combinatorial optimization often falls short, as
these algorithms edit molecules locally, thus being inefficient to explore the
vast chemical space. Reinforcement learning techniques depend heavily on
querying oracle functions, which can hinder their practical application.
MoleculeChef (Bradshaw et al., 2019) primarily explores one-step pathways due
to the computational impracticality of enumerating an exponentially growing
number of candidates. Models like PGFS (Gottipati et al., 2020) and REACTOR
(Horwood & Noutahi, 2020) are limited to generating only linear synthetic
pathways. In addition, the capacity of these models to generalize and
construct complex synthetic paths is yet to be convincingly demonstrated.
Models such as DoGs (Bradshaw et al., 2020) and SynNet (Gao et al., 2021),
theoretically capable of encompassing a complete chemical space, have not been
empirically validated for their ability to adapt to novel, unseen chemicals.
Additionally, these models are generally less adept at generating convergent
pathways or more intricate molecular structures, indicating a need for further
refinement in their design and functionality.

Figure 2:  Top: Simulation of the synthetic plan
$R_{2}(R_{1}(B_{1},B_{2}),B_{3})$ with a memory stack to store intermediate
molecules. In the first two steps, building blocks $B_{1}$ and $B_{2}$ are
pushed onto the stack. In the third step, $B_{1}$ and $B_{2}$ are popped from
the stack and used as input for reaction $R_{1}$, leading the intermediate
reaction product $I$, which is then added back onto the stack. Subsequently,
in the fourth step, building block $B_{3}$ is pushed onto the stack. Finally,
reaction $R_{2}$ is applied to $I$ and $B_{3}$, leading to the final product
$Y$. Bottom: The postfix notation of the synthetic pathway is
$[B_{1},B_{2},R_{1},B_{3},R_{2}]$. Each symbol in the notation corresponds to
one step in the synthesis.

##  3 Method

###  3.1 Preliminaries

#### Chemical space

A chemical space ${\mathcal{C}}$ is a set of molecules generated by a finite
set of building block molecules ${\mathcal{B}}=\\{B_{1},B_{2},\ldots
B_{N}\\}\subseteq{\mathcal{C}}$ and a set of reaction rules
${\mathcal{R}}=\\{R_{1},R_{2},\ldots R_{M}\\}$. Formally, a reaction rule maps
reactants to a reaction product. For example, a reaction rule $R$ with two
reactants can be denoted by:

$\displaystyle R:$
$\displaystyle{\mathcal{X}}_{1}\times{\mathcal{X}}_{2}\rightarrow{\mathcal{C}}$
(1) $\displaystyle(X_{1},X_{2})\mapsto Y,$

where ${\mathcal{X}}_{1}$ and ${\mathcal{X}}_{2}$ are sets of molecules to
which reaction $R$ can be applied, and $Y$ is the main reaction product. The
chemical space is generated by starting from the building blocks and
iteratively applying the reactions to every possible combination of molecules.
There are some cases where a reaction has multiple possible main products. For
ease of discussion, we assume that reactions produce only one main product in
this section, though the actual implementation of our model supports multiple
products.

Every molecule in the chemical space is a product of a synthetic process,
which involves applying reaction rules to building blocks and intermediate
molecules to build a complex molecule. For example,
$R_{2}(R_{1}(B_{1},B_{2}),B_{3})$ denotes a process in which we first apply
reaction $R_{1}$ to building blocks $B_{1}$ and $B_{2}$, and then apply
reaction $R_{2}$ to building block $B_{3}$ and the product of
$R_{1}(B_{1},B_{2})$.

#### Postfix notation of synthesis

We formalize the synthetic process as a sequence of function call instructions
with a memory stack to store arguments and intermediate results. The
instruction sequence contains two types of operations: pushing a building
block molecule onto the stack and applying a reaction. The reaction operation
first pops the required number of molecules at the top of the stack, then
computes the reaction product which will be pushed back onto the stack. The
two operations can be denoted by the building block and the reaction
associated with them, leading to the postfix notation of the synthetic
process.

Following the above example, the instruction sequence for
$R_{2}(R_{1}(B_{1},B_{2}),B_{3})$ is: (1) push $B_{1}$; (2) push $B_{2}$; (3)
apply $R_{1}$; (4) push $B_{3}$; (5) apply $R_{2}$, which can be simplified as
the postfix notation: $[B_{1},B_{2},R_{1},B_{3},R_{2}]$ (Figure 2).

The synthetic process can be parsed to an abstract syntax tree (AST), which is
equivalent to the synthetic tree used in previous work and the postfix
notation is a post-order traversal sequence of the AST. Although it has
connections with previous methods, the proposed postfix notation has multiple
advantages. First, the postfix notation is capable of representing branched
synthesis pathways, where reactions can be applied to more than one
intermediate deposited in the stack. In contrast, previous methods (Gottipati
et al., 2020; Horwood & Noutahi, 2020) are limited to linear synthetic
pathways, where intermediates can only react with building blocks. In
addition, the postfix notation is a simple representation comprising only
building blocks and reactions, whereas previous synthetic tree-based
representations require extra symbols, such as node addition and edge
addition, to construct a synthetic plan. Lastly, the postfix notation allows
reactions with multiple (more than two) molecule inputs, while the previous
representation (Gao et al., 2021) is incompatible with such complex reaction
rules. Therefore, the postfix notation can be immediately applied to chemical
spaces that include reactions with reagent specification or with multiple
reactants, showing the potential for more complex settings in future work.

#### Problem definition

We formulate the task of this work, projecting molecules into the chemical
space, as generating a postfix notation of synthesis from the input molecular
graph, so that the postfix notation denotes a molecule in the chemical space
that is identical or structurally similar to the input molecule.

Figure 3:  (a) Overall architecture of the network. A graph transformer
encodes the input molecular graph into atom embeddings. A transformer decoder
autoregressively decodes the postfix notation, with atom embeddings as the
context. (b) Architecture of the prediction network. First, a classifier
predicts the token type from the token embedding. If the predicted token type
is [BB] (building block), the token embedding is used to predict the building
block fingerprint to retrieve building blocks. If the token type is [RXN]
(reaction), the token embedding is used to predict the type of reaction.
Otherwise, [END] marks the end of the postfix notation.

###  3.2 Model

The model consists of two components: a graph transformer encoder network that
encodes the molecular graph and a transformer decoder network that
autoregressively generates postfix notations.

#### Molecular graph encoder

A molecule is represented by a graph with a set of atoms and bonds. The graph
encoder network first converts each atom into initial embeddings according to
the atomic number. Then a stack of graph transformer layers (Ying et al.,
2021), which take edges into account by adding a bond type-dependent learnable
bias term to the query-key product matrix, performs multi-head self-attention
on the atoms. Finally, the output per-atom embeddings are used for decoding.

#### Postfix notation decoder

A postfix notation of synthesis is a sequence that contains four types of
tokens: building block tokens, reaction tokens, a start token [START], and an
end token [END]. A building block token is attached with the fingerprint of
the building block molecule, denoted by [BB,${\bm{p}}$], where
${\bm{p}}\in\\{0,1\\}^{256}$ is the Morgan fingerprint of length 256 and
radius 2 (Morgan, 1965). Building block tokens are converted into embeddings
by an MLP. A reaction token is the index $r$ of the reaction denoted by
[RXN,$r$]. The reaction tokens and the start token are converted into
embeddings by looking up from the embedding table. Sinusoidal positional
encodings (Vaswani et al., 2017) that indicate the order of tokens are added
to the embeddings. In summary, the initial embedding of the $i$-th token
$T_{i}$ is defined as:

${\bm{h}}_{i}^{(0)}=\operatorname{PE}(i)+\begin{cases}{\bm{e}}_{\text{start}},&\operatorname{type}(T_{i})=\texttt{START}\\\
\operatorname{MLP}_{\text{fp}}({\bm{p}}_{i}),&\operatorname{type}(T_{i})=\texttt{BB}\\\
\operatorname{Embed}_{\text{rxn}}(r_{i}),&\operatorname{type}(T_{i})=\texttt{RXN}\end{cases}.$
(2)

Next, a stack of standard transformer layers (Vaswani et al., 2017) takes the
sequence embeddings along with the molecular graph embeddings as input, and
then predicts the next token using the embeddings from the last layer
${\bm{h}}_{i}$ for each position of the sequence. The prediction network first
predicts the type of the next token:

$\operatorname{type}(\hat{T}_{i+1})\sim\operatorname{softmax}(\operatorname{MLP}_{\text{type}}({\bm{h}}_{i})),$
(3)

where possible token types include BB, RXN, and END. If the next token is
predicted to be a reaction token BB, the fingerprint will be predicted and the
building block will be retrieved via nearest-neighbor search:

$\displaystyle\hat{{\bm{p}}}_{i+1}$
$\displaystyle=\operatorname{sigmoid}(\operatorname{MLP}_{\text{fp-
pred}}({\bm{h}}_{i})),$ (4) $\displaystyle\hat{B}_{i+1}$
$\displaystyle=\operatorname{Nearest-
Neighbor}(\hat{{\bm{p}}}_{i+1},\\{B_{1},\ldots B_{N}\\}),$ (5)

where $\\{B_{1},\ldots B_{N}\\}$ is the building block set of the chemical
space. The fingerprint of the retrieved $\hat{B}_{i+1}$ is used to replace the
predicted fingerprint as input to the model before predicting the next token.
The nearest-neighbor search could produce multiple building block candidates,
enabling the generation of diverse pathways. If the next token is predicted to
be a reaction token, the reaction type will be predicted by:

$\hat{r}_{i+1}\sim\operatorname{softmax}(\operatorname{MLP}_{\text{rxn}}({\bm{h}}_{i})).$
(6)

Similarly, the sampled reaction template $\hat{r}_{i+1}$ is used as input to
the decoder to predict the next token.

###  3.3 Training

We sample synthetic pathways from the chemical space and convert product
molecules into graphs to create (postfix notation, graph) pairs for training.
The synthesis sampling algorithm iteratively selects building blocks and
applicable reactions at random to generate valid operation sequences as
described in Algorithm 1 in Appendix. Synthetic pathways are generated on-the-
fly at each training step.

We use the standard technique to train transformer decoders in parallel
(Vaswani et al., 2017) — feeding the complete sequence into the decoder,
offseting the output embeddings by one position, and applying causal masking.

The training loss consists of three terms corresponding to the three
prediction heads. The first term is a cross entropy loss for token type:

$L_{\text{type}}=\frac{1}{\ell}\sum_{i=0}^{\ell-1}\operatorname{CE}\left(\operatorname{type}(\hat{T}_{i+1}),\operatorname{type}(T_{i+1})\right),$
(7)

where $\ell$ is the length of the sequence. The second term is a loss function
for building block fingerprints:

$\displaystyle L_{\text{bb}}$
$\displaystyle=\frac{1}{n}\sum_{i=0}^{\ell-1}{\mathbb{I}}\left(\operatorname{type}(T_{i+1})=\texttt{BB}\right)\cdot$
(8)
$\displaystyle\qquad\qquad\qquad\sum_{j=0}^{255}\operatorname{BCE}\left(\hat{{\bm{p}}}_{i+1}[j],{\bm{p}}_{i+1}[j]\right),$

where ${\mathbb{I}}$ is the indicator function, BCE is the binary cross
entropy loss function, and
$n=\sum_{i=0}^{\ell-1}{\mathbb{I}}\left(\operatorname{type}(T_{i+1})=\texttt{BB}\right)$
is the number of BB tokens in the sequence. The last term is a cross entropy
loss for reaction type:

$L_{\text{rxn}}=\frac{1}{m}\sum_{i=0}^{\ell-1}{\mathbb{I}}\left(\operatorname{type}(T_{i+1})=\texttt{RXN}\right)\cdot\operatorname{CE}\left(\hat{r}_{i+1},r_{i+1}\right).$
(9)

The final loss function is the sum of the three terms:
$L=L_{\text{type}}+L_{\text{bb}}+L_{\text{rxn}}$.

Table 1:  The proposed method achieves higher success rate, reconstruction
rate, and similarity scores in comparison to the baseline model, indicating
that our model can find synthetic pathways for synthesizable molecules more
accurately.

Dataset Method Success% Recons.% Sim.(Morgan) Sim.(Scaffold) Sim.(Gobbi) Test
Set SynNet 84.1% 10.7% 0.4575 0.5109 0.3465 Proposed 97.5% 28.4% 0.7167 0.7791
0.7273 ChEMBL SynNet 85.0% 5.4% 0.4270 0.4174 0.2678 Proposed 98.8% 13.3%
0.5978 0.5869 0.5570

###  3.4 Inference

At inference time, we create an empty stack and generate tokens one by one.
When the generated token is a building block token, we look up the building
block molecule according to the predicted fingerprint and push the building
block onto the stack. When the generated token is a reaction token, we first
pop molecules from the stack according to the number of required reactants,
then use RDKit to predict the product according to the reaction template, and
finally push the product onto the stack. If the number of molecules on the
stack is less than the required number or if the reaction is not applicable to
the molecules, the inference process will be aborted. Finally, an end token
[END] terminates the process and the molecule at the top of the stack will be
taken as the final product. The product molecule is considered to be a
projection of the input molecular graph in the chemical space. We select the
final product molecules according to properties of interest, such as
similarity and docking scores.

###  3.5 Experiment Setup

#### Reaction templates

We use the SynNet reaction template set (Gao et al., 2021) curated by the
authors from two publicly available template sets (Hartenfeller et al., 2012;
Button et al., 2019). The template set contains 91 reaction templates encoded
in SMARTS string format (Daylight Chemical Information Systems, Inc., 2023),
of which 13 are uni-molecular reactions and 78 are bi-molecular reactions.

#### Building blocks

We use the building blocks in the Enamine US Stock catalog retrieved in
October 2023 (Enamine, 2023). For building blocks that include more than one
molecule (e.g., salts, hydrates), we keep the largest molecule and drop the
remaining ones. Building blocks that fail the RDKit sanitization check or do
not match any reaction template are removed. Duplicate building blocks are
also removed. The pre-processing procedure leads to the final building block
set containing 211,220 molecules.

#### Similarity scores

To evaluate the similarity between the input molecule and the output molecule,
we use the Tanimoto similarity score on three different fingerprints: (1)
Morgan fingerprint of length 4096 and radius 2 (Morgan, 1965), (2) Morgan
fingerprint of Murcko scaffold, and (3) Gobbi pharmacophore fingerprint (Gobbi
& Poppinger, 1998). The three similarity scores indicate chemical similarities
in three different aspects: overall structure, scaffold structure, and
pharmacophore property, respectively, and are all normalized to $[0,1]$.

#### Code and data

The code and data of this project are available at
https://github.com/luost26/ChemProjector.

##  4 Results

Figure 4: Examples of projecting molecules generated by Pocket2Mol to
synthesizable analogs. The projection improves the Vina score and proposes
synthesis pathways. The docking poses remain similar.

In this section, we first examine the model’s capability of finding synthesis
pathways for molecules that are known to be synthesizable, and explore the
generalization ability of the models (Section 4.1). Then, we study the
application of the model in three drug design settings: structure-based drug
design (Section 4.2), goal-directed generation (Section 4.3), and hit
expansion (Section 4.4).

###  4.1 Generalization in Bottom-Up Synthesis Planning

We first validate our model’s ability in bottom-up synthesis planning,
particularly in proposing synthetic pathways for novel molecular structures.
To assess this capability with unseen molecules, we employed the following
testing approach. First, we clustered building blocks into 128 groups using
K-means algorithm based on their fingerprints, reserving one cluster
exclusively for testing while using the remaining 127 for training. This
approach generated a test set of 1,000 molecules from the reserved building
block to evaluate our model’s generalization. During testing, we allow the
model to access the reserved building blocks. In addition, we include another
challenging benchmark: 1,000 molecules from the ChEMBL database (Release
33)(Gaulton et al., 2012), reported to be predominantly “unreachable” in
previous work (Gao et al., 2021). This not only tested our model against
complex, unseen molecular structures but also set a strenuous standard for
assessing its generalizability.

We evaluate the model using the following metrics: (1) success rate: the
percentage of valid postfix notations; (2) reconstruction rate: the percentage
of proposed synthetic pathways that lead to products identical to input
molecules; (3) average similarities. The similarity score is set to 0 for
failed cases. We compare our model with the baseline model SynNet (Gao et al.,
2021).

Our model produces valid synthetic pathways for most test cases and thus
achieves a high success rate (Table 1). Most notably, 29.3% of the test
molecules and 13.4% of the ChEMBL molecules have been successfully
reconstructed. Furthermore, the similarity scores of the proposed model are
significantly higher than the baseline model. The result demonstrates that our
model exhibits generalizability to unseen molecules.

Table 2: Similarity scores between molecules generated by Pocket2Mol and their
analogs.

Sim. Sim. Sim. (Morgan) (Scaffold) (Gobbi) ADRB2 0.5804 0.6362 0.4409 ALDH1
0.3875 0.3399 0.3034 ESR1_ago 0.4066 0.3520 0.2990 ESR1_ant 0.4965 0.4919
0.4122 FEN1 0.4180 0.4090 0.3369 GBA 0.3140 0.2572 0.2460 IDH1 0.3830 0.3423
0.3178 KAT2A 0.5028 0.4831 0.4378 MAPK1 0.4274 0.3942 0.3886 MTORC1 0.4565
0.4193 0.3820 OPRK1 0.5125 0.5428 0.4312 PKM2 0.4558 0.4315 0.3818 PPARG
0.4992 0.4884 0.4416 TP53 0.5566 0.5386 0.4617 VDR 0.4355 0.3857 0.3615

Table 3: The analogs slightly improve Vina scores, suggesting the binding is
likely to be preserved.

Vina (kcal/mol) Target Ref. Gen. Analog ($\downarrow$) $\Delta$ ($\downarrow$)
ADRB2 -8.24 -8.70 -9.09 -0.38 ALDH1 -8.49 -9.10 -9.00 0.10 ESR1_ago -8.28
-9.46 -9.36 0.09 ESR1_ant -7.62 -9.77 -9.77 0.00 FEN1 -6.32 -6.54 -6.60 -0.06
GBA -8.14 -6.96 -7.69 -0.73 IDH1 -9.19 -9.50 -9.56 -0.07 KAT2A -7.18 -8.07
-8.18 -0.11 MAPK1 -8.63 -8.61 -8.98 -0.37 MTORC1 -9.64 -10.17 -10.20 -0.04
OPRK1 -8.83 -8.36 -8.77 -0.40 PKM2 -9.23 -9.45 -10.09 -0.65 PPARG -7.16 -8.47
-8.53 -0.06 TP53 -6.13 -7.11 -7.47 -0.36 VDR -8.81 -10.51 -10.46 0.05

Table 4: In general, the molecules generated by goal-directed generative
models do not show significant similarity to their analogs. The projection
typically results in a drop in the objective scores. Nonetheless, the maximum
scores of the analogs on 6 targets decrease by an amount of less than 0.1,
indicating that the properties are still preserved for some molecules.

Sim. Sim. Sim. Avg(Objective) Max(Objective) Property Morgan Scaffold Gobbi
Gen. Analog $\Delta$ Gen. Analog $\Delta$ Amlodipine MPO 0.4593 0.3098 0.3855
0.8110 0.4824 -0.3286 0.8895 0.8793 -0.0102 Deco Hop 0.5499 0.8273 0.7173
0.9768 0.7296 -0.2472 0.9992 0.9652 -0.0340 Fexofenadine MPO 0.4510 0.4589
0.3431 0.9316 0.4321 -0.4995 1.0000 0.8999 -0.1001 Osimertinib MPO 0.4339
0.3956 0.5620 0.9030 0.5424 -0.3606 0.9508 0.9326 -0.0182 Perindopril MPO
0.3175 0.2605 0.3181 0.7169 0.3552 -0.3617 0.7850 0.7011 -0.0839 Ranolazine
MPO 0.4145 0.4648 0.5029 0.8889 0.5652 -0.3237 0.9103 0.8377 -0.0726 Scaffold
Hop 0.5092 0.7499 0.6125 0.9558 0.5283 -0.4275 1.0000 0.8993 -0.1007
Sitagliptin MPO 0.2536 0.2230 0.2427 0.6527 0.0158 -0.6369 0.8437 0.4909
-0.3528 Valsartan SMARTS 0.3500 0.3558 0.2572 0.8191 0.0036 -0.8155 0.9861
0.4776 -0.5085 Zaleplon MPO 0.5328 0.5653 0.5429 0.6379 0.2502 -0.3877 0.7151
0.7122 -0.0029

###  4.2 Projecting Molecules Generated by Structure-Based Drug Design Models

Generative models for structure-based drug design (SBDD) build molecules to
fit a protein pocket structure (Luo et al., 2021). SBDD models often produce
chemically invalid structures, because they operate in the 3D space with a few
chemical constraints (Harris et al., 2023). As a remedy, we apply our model to
molecules proposed by the SBDD models to find valid and synthesizable analogs.

We use Pocket2Mol (Peng et al., 2022) to generate molecules for targets in the
LIT-PCBA dataset (Tran-Nguyen et al., 2020). The LIT-PCBA dataset contains 15
protein targets, each of which has at least one X-ray structure that can be
used to run Pocket2Mol to generate molecules. For each target, we select 300
generated molecules based on the sum of QED and SA scores. Then, we apply our
model to generate 5 analogs for each molecule and select best one according to
Vina scores (Eberhardt et al., 2021). The estimated binding energy in kcal/mol
shows slight improvement for the majority of targets (Table 3), suggesting
that the top-1 synthesizable analogs of each molecule could maintain binding.
Figure 4 presents two examples in which the synthesizable analogs improve
predicted binding. Figure 6 and 7 in the appendix present more examples.

###  4.3 Projecting Molecules Generated by Goal-Directed Generative Models

Goal-directed generative models are pivotal in molecular design, yet their
practicality is often hampered by the synthesizability of the produced
molecules. This issue was highlighted by Gao & Coley, who, utilizing three
algorithms on the GuacaMol benchmark suite’s multi-property objectives (Brown
et al., 2019), revealed that around 70% of the molecules generated were
considered unsynthesizable by the ASKCOS retrosynthesis analysis tool (Coley
et al., 2019b).

We applied our model to these molecules which were labeled as
“unsynthesizable” by ASKCOS. The analogs show limited structural similarity
with an average Morgan fingerprint similarity score of 0.43 (Table 4). This
divergence in structure is primarily due to the non-synthesizability of the
original molecules, making it hard to compose a similar analog using the
provided building blocks and reactions of the chemical space. The property
scores achieved by the original unsynthesizable molecules are affected by the
structural discrepancies, as indicated by the drop in average objective score.
However, for most of the targets, there still exists at least one analog that
mostly retains the original property as shown by the maximum objective scores.

In conclusion, the projection generally leads to synthesizable analogs that
are sub-optimal in terms of the oracle property scores. These sub-optimal
analogs share some common structural factors with the original molecules,
hopefully making them good starting points for combinatorial optimization
within the chemical space (Gao et al., 2021; Swanson et al., 2023).

Figure 5: The distribution of JNK3 oracle scores and similarity of analogs
generated by expanding the hit molecule.

###  4.4 Projecting Molecules to Explore Local Chemical Space for Hit
Expansion

Our model’s capabilities also extend to hit expansion in drug discovery,
offering a strategic approach to identifying structurally similar,
synthesizable analogs of hit molecules (Keserű & Makara, 2006; Levin et al.,
2023).

We showcase our model’s hit expansion capability by designing inhibitors for
c-Jun N-terminal Kinases-3 (JNK3), following the setting of Levin et al..
Based on the oracle function provided by Li et al., our goal is to identify
high-scoring, synthesizable molecules similar to a specified hit molecule with
a JNK3 score of 0.68. We generated 500 analogs for the hit, resulting in a
diverse array of analogs with different JNK3 scores and structural
similarities, as depicted in Figure 5. Remarkably, 21 analogs outperformed the
original hit in JNK3 score while maintaining an average Tanimoto similarity of
0.67. Additionally, these analogs present distinct synthetic pathways,
different from traditional synthesis planning and building block exchange
strategies (Levin et al., 2023), underlining our model’s capability to cover
broader chemical space (Figure 8 in the appendix).

##  5 Conclusion

In this work, we introduce a method that projects molecules proposed by
generative models into synthesizable chemical space. The method is composed of
a novel postfix notation-based representation of synthesis and a transformer-
based encoder-decoder network. We study the application of the method in
structure-based drug design, goal-directed molecular generation, and hit
expansion. The results demonstrate that the model can effectively convert the
generated molecules into synthesizable analogs while maintaining the desired
properties. As opposed to previous methods that rely on combinatorial
optimization or virtual screening, the proposed approach enables efficient
exploration of the chemical space by utilizing the flexibility of generative
models while respecting synthetic feasibility, further unlocking the potential
of machine learning in molecular design.

## Acknowledgement

J.M. acknowledges the support through the National Key Research and
Development Program of China grant 2022YFF1203100. W.G. is supported by the
Google Ph.D. Fellowship and Office of Naval Research under grant number
N00014-21-1-2195. C.W.C. thanks the AI2050 program at Schmidt Futures (grant
G-22-64475) for financial support.

## Impact Statement

This paper presents work whose goal is to advance the generative modeling of
molecular structures. There are many potential societal consequences of our
work, none of which we feel must be specifically highlighted here.

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##  Appendix A Implementation

###  A.1 Training Data

The algorithm for the construction of (postfix notation, molecular graph)
pairs is described below:

Algorithm 1 Construct a (postfix notation, molecular graph) pair for training

Input: $m_{r}$, maximum number of reactions

Input: $m_{a}$, maximum number of atoms

Input: ${\mathcal{F}}:M\mapsto\\{R\\}$, a function that returns available
reactions for molecule $M$. When $M=\texttt{null}$, it returns all the
reactions ${\mathcal{R}}$.

Global: ${\mathcal{H}}:R\mapsto\\{M\\}$, a hash map that stores eligible
molecules for each reaction.

Initialize:  $S\leftarrow[]$ (empty stack)

Initialize:  $P\leftarrow[]$ (empty postfix notation)

while $\operatorname{CountReactions}(P)<m_{r}$ and
$\operatorname{CountAtoms}(\operatorname{top}(S))<m_{a}$ do

Let $R\sim{\mathcal{R}}(\operatorname{top}(S))$ (randomly choose a reaction)

Let $\\{B_{i}:1\leq
i\leq(\operatorname{NumReactants}(R)-\operatorname{len}(S))\\}\sim{\mathcal{H}}(R)$
(randomly choose reactants for $R$)

for $1\leq i\leq(\operatorname{NumReactants}(R)-\operatorname{len}(S))$ do

Push $B_{i}$ onto $S$

Append $B_{i}$ to $P$

end for

Pop $\operatorname{NumReactants}(R)$ elements from $S$ to Call $R$; Then Push
the product $Y$ onto $S$.

Append $R$ to $P$

end while

Return $P$, $\operatorname{top}(S)$ (postfix notation and its product
molecular graph)

###  A.2 Parameters

The molecular graph encoder consists of 8 graph transformer layers, each of
which has 8 attention heads, and the dimension of the input and output
features is 512. The postfix notation decoder is a stack of 8 transformer
decoder layers. Each has 8 attention heads, and the dimension of the input and
output features is also 512. In the nearest-neighbor search, each building
block molecule is indexed by the Morgan fingerprint (Morgan, 1965) of length
256 and radius 2. We use the AdamW optimizer (Loshchilov & Hutter, 2017) to
train the network with a learning rate of 3e-4 and a batch size of 256 for
500,000 iterations. During the construction of synthesis for training, we
limit the maximum number of reactions to 5 and the maximum number of atoms to
80. At inference time, we set the maximum sequence length to 16. If the end
token is not generated within the limit, the process will be considered
unsuccessful.

##  Appendix B Additional Results

###  B.1 Stricter Test Split for Bottom-Up Synthesis Planning

To test the model’s generalization more strictly, we construct a refined
subset of the test set described in Section 4.1. Specifically, for each
building block in the test set, we identify its most similar counterpart in
the training set and calculate the maximum training set similarity
accordingly. Building blocks with a maximum training set similarity greater
than 0.6 are then removed, resulting in a refined set of test building blocks.
We use this refined building block set to generate 1,000 molecules to test our
model and SynNet, and the results are presented below.

Method Success% Recons.% Sim.(Morgan) Sim.(Scaffold) Sim.(Gobbi) SynNet 84.0%
10.0% 0.4552 0.6012 0.3348 Proposed 95.8% 17.0% 0.5921 0.7239 0.6110

Despite the stricter partition affecting the performance of both models, our
model demonstrates superior generalization. Particularly noteworthy is the
higher scaffold similarity, indicating that our model better preserves the
scaffold of unseen molecules.

###  B.2 Baseline for Goal-Directed Generation

We present below a comparison between our model and the baseline model SynNet
in the goal-directed generation setting. Our model outperforms the baseline in
7 out of 10 objectives in both similarity and property scores. Additionally,
our model’s performance is on par with the baseline in the remaining 3
objectives.

Sim. Morgan Sim. Scaffold Sim. Gobbi Avg(Obj) Max(Obj) Property SynNet Ours
SynNet Ours SynNet Ours SynNet Ours SynNet Ours Amlodipine MPO 0.3732 0.4593
0.2333 0.3098 0.2787 0.3855 0.3358 0.4824 0.8605 0.8793 Deco Hop 0.4854 0.5499
0.5385 0.8273 0.5535 0.7173 0.6434 0.7296 0.9474 0.9652 Fexofenadine MPO
0.4308 0.4510 0.3942 0.4589 0.2983 0.3431 0.3501 0.4321 0.7928 0.8999
Osimertinib MPO 0.2375 0.4339 0.1740 0.3956 0.2494 0.5620 0.4827 0.5424 0.8613
0.9326 Perindopril MPO 0.3184 0.3175 0.2402 0.2605 0.2900 0.3181 0.2214 0.3552
0.6789 0.7011 Ranolazine MPO 0.3528 0.4145 0.2972 0.4648 0.2895 0.5029 0.3628
0.5652 0.8451 0.8377 Scaffold Hop 0.3694 0.5092 0.4965 0.7499 0.5082 0.6125
0.4593 0.5283 0.5299 0.8993 Sitagliptin MPO 0.3309 0.2536 0.2852 0.2230 0.2711
0.2427 0.0302 0.0158 0.4648 0.4909 Valsartan SMARTS 0.3742 0.3500 0.3805
0.3558 0.2771 0.2572 0.0074 0.0036 0.6034 0.4776 Zaleplon MPO 0.5141 0.5328
0.4884 0.5653 0.4856 0.5429 0.1477 0.2502 0.5548 0.7122

###  B.3 Baseline for Hit Expansion

In hit expansion, the objective is to identify similar molecules within the
local chemical space. Given that random molecular edits may not guarantee
synthesizability, we adopt querying a chemical database as the baseline
method. Specifically, we search PubChem (Kim et al., 2023) using the hit
molecule and retrieve the most similar 500 molecules based on fingerprint
similarity. Only 7 out of the retrieved molecules surpass the hit in JNK3
score, with an average similarity score of 0.67. This result underscores the
efficiency of our model in identifying relevant synthesizable compounds within
the chemical space.

###  B.4 Molecules Generated by Pocket2Mol and Analogs

Figure 6: Molecules generated by Pocket2Mol and their analogs (1/2).

Figure 7: Molecules generated by Pocket2Mol and their analogs (2/2).

###  B.5 Synthetic Pathways in Hit Expansion

Figure 8: Distinct synthetic pathways of the analogs in hit expansion.