A Deep Generative Model for Molecule Optimization via One Fragment Modification

Related Work

• Prior molecule generators include RL-based GCPN (You et al.9), flow-based GraphAF (Shi et al.12) and MoFlow (Zang and Wang13), and VAE-based JT-VAE (Jin et al.8), JTNN (Jin et al.14), and HierG2G (Jin et al.15).Source: Related Work · p. 2
• Existing generative methods typically encode entire molecular graphs and generate whole molecules from empty or randomly selected structures.Source: Related Work · p. 2
• Unlike these methods, Modof encodes the difference between molecules before and after optimization, simplifying learning and generation while retaining major molecular scaffolds.Source: Related Work · p. 2

• Penalized logP (plogP) combines Crippen logP, synthetic accessibility, and ring size; higher plogP indicates higher lipid-phase concentration with potentially good synthetic accessibility and simple rings.Crippen logP is used as a scalable estimate of experimental logP; the passage reports a correlation of r2=0.918 with experimental logP.Source: Problem Definition · p. 2
• Modof can optimize properties other than plogP, and can also optimize multiple properties simultaneously.The paper discusses these extensions in Sections S11 and S12, respectively.Source: Problem Definition · p. 2
• Optimization transforms molecule Mx into My while requiring sim(Mx, My) ≥ δ and a better value for the property of interest.For the default property, the improvement condition is plogP(My) > plogP(Mx).Source: Problem Definition · p. 2

Data

• 55,686 molecule pairs (104,708 unique molecules) formed the training set after filtering Jin’s 75K-pair training dataset for pairs with one disconnection site.The extracted set was 26% smaller than Jin’s; Jin’s validation set was used for tuning and the test set contained 800 molecules.Source: Data · p. 2

Training Data Generation

• Training instances paired similar molecules differing in property and in only one fragment at one disconnection site, identified through optimal graph edit paths between junction-tree representations.Pairs satisfying the similarity and property constraints were retained; high-similarity pairs, such as those above 0.6, were likely to have one disconnection site.Source: Training Data Generation · p. 3

Molecule Similarity Calculation

• Molecule similarity was measured with the Tanimoto coefficient on 2,048-dimensional binary Morgan fingerprints with radius 2.Source: Training Data Generation · p. 3

Baseline Methods

• The comparison included JT-VAE, GCPN, JTNN, HierG2G, GraphAF, and MoFlow as molecule-optimization baselines.Source: Baseline Methods · p. 3

Overall Comparison on plogP Optimization

• With δ=0, Modof-pipe improves plogP by 7.61±2.30 (81.2% over GCPN’s 4.20±1.28), while Modof-pipem reaches 9.37±2.04 (123.1% over GCPN).At δ=0.2, 0.4 and 0.6, Modof-pipe achieves plogP improvements of 6.23±1.77, 5.00±1.53 and 2.72±1.68, respectively—51.2%, 25.6% and 9.2% over the best baselines; Modof-pipem achieves 7.58±1.65, 5.89±1.57 and 3.14±1.77, with 84.0%, 48.0% and 26.1% improvement. Results use the exact benchmark test set; the authors note that some baselines used different test sets or trained or fine-tuned on test molecules.Source: Table 1 · p. 3, Overall Comparison on plogP Optimization · pp. 3–4
• Modof uses at least 40% fewer parameters and 26% less training data while outperforming or matching state-of-the-art baselines.The paper reports this comparison in its model-complexity analysis.Source: Overall Comparison on plogP Optimization · p. 4

Case Study

• Training fragments average 2.85 atoms when removed and 7.55 atoms when attached, indicating optimization typically removes small fragments and adds larger ones.Source: Case Study · p. 4
• Iterative single-fragment edits trade property gains against synthetic accessibility, while the example retains the molecule’s major scaffold.The example removes a hydroxyl group and adds 2-chlorophenyl, then replaces methyl with trifluoromethyl; the reported similarities across iterations are 0.630, 0.506, 0.421 and 0.4111. The authors describe the learned modifications as end-to-end, without imposing chemical rules or templates a priori.Source: Case Study · pp. 4–5

Performance on DRD2 and QED Optimization

• At δ=0.4, Modof-pipem significantly outperforms or matches baselines on DRD2 and QED optimization using either benchmark success metrics or training-data-based criteria.The examples show QED improving through fragment edits that reduce aromatic rings and hydrogen-bond acceptors; the paper also reports an example where DRD2 and QED scores both rise over optimization iterations.Source: Table 2 · p. 5, Performance on DRD2 and QED Optimization · pp. 5–6

Molecule Optimization using Simulated Properties

• Simulated or predicted properties enable large-scale training, but inaccurate predictions can produce inaccurate optimization and harm downstream drug-development tasks.The paper notes DRD2 prediction accuracy of 98% and argues that continued improvement of property simulations and generative models could advance in silico drug development.Source: Molecule Optimization using Simulated… · p. 6

Synthesizability and Retrosynthesis

• Improving synthesis accessibility does not ensure generated molecules are synthesizable, motivating future optimization with explicit feasible retrosynthesis paths.The authors envision a framework for synthesizable molecules with preferable properties, supported by substantial training data, domain knowledge, and human experts.Source: Synthesizability and Retrosynthesis · p. 6

In vitro Validation

• In vitro testing and pharmaceutical-industry collaboration are needed to translate computational methods into impact; prioritizing a small feasible set could enable practical validation.Large-scale in vitro validation remains a challenging future direction.Source: In vitro Validation · pp. 6–7

Other Issues in Computational Molecule Optimization

• Modof-pipe uses local greedy optimization, while broader computational molecule optimization must address multiple properties, target-specific goals, and other application domains.In its greedy iterations, molecules that do not improve are not passed through further Modof iterations.Source: Other Issues in Computational Molecule… · p. 7

Conclusions

• Modof learns pre- and post-optimization differences and modifies one disconnection site at a time, achieving significantly better or similar performance with a much less complex model.Its modifications currently occur at molecule peripheries; the authors are investigating internal-region modification and integration of domain knowledge to improve explainability.Source: Conclusions · p. 7

Molecular Difference Encoder

• Modof encodes molecular differences with message passing over molecular graphs and junction trees, producing a latent representation of fragments to remove and attach at a shared disconnection site.The encoder separately represents the removal and addition differences, then samples and concatenates their latent vectors.Source: Molecular Difference Encoder… · p. 8, Step 2. Node Embedding over Junction… · p. 8, Step 3. Difference Embedding (DE) · p. 9

Molecular Difference Decoder

• The decoder predicts a disconnection site, removes selected neighboring fragments to form an intermediate scaffold, then sequentially attaches new fragments by predicting child connections, node types, and attachment points.When attachment configurations are ambiguous, it predicts attachment atoms at both the parent and child; valence checks restrict candidates to chemically legitimate attachment points.Source: Molecular Difference Decoder… · p. 9, Step 2. Removal Fragment Prediction… · p. 9, Step 3. Intermediate Representation… · p. 9

Implementation

• For plogP optimization, Modof caps optimized molecules at 38 atoms, samples 20 latent-space decodings per input, and selects the best-property molecule satisfying the similarity constraint.The size cap is intended to prevent trivially increasing plogP by increasing molecule size.Source: Step 4. New Fragment Attachment (NFA) · p. 10, Sampling Schemes · p. 10

Modof Pipelines

• Modof-pipe applies identical Modof models sequentially, continuing only when each output meets similarity and property constraints; Modof-pipem instead produces multiple optimized molecules per input.The iterative approach is described as easier to control for desired similarities and properties, and to optimize fragments that are far apart.Source: Modof Pipelines · p. 10

Model Training

• During training, Modof uses teacher forcing and optimizes a variational autoencoder objective combining reconstruction likelihood with KL divergence, using AMSGRAD.The probabilistic decoder models the likelihood of the target molecule given the input and latent embedding, with a standard normal prior.Source: Model Training · p. 11

S1 Additional Related Work

• Podda et al. [16] break molecules into reaction-based fragments, encode them as SMILES, and use a VAE to decode and reassemble complete molecules.Source: S1 Additional Related Work · p. 14
• Modof samples a latent “difference” distribution at test time to generate multiple diverse optimized molecules, unlike T&S polish, which generates one per input.The cited work argues that generative models should support multiple diverse optimizations for each input molecule [14].Source: S1 Additional Related Work · p. 14
• Modof learns which scaffold to retain from test molecules and completes it with fragments, unlike Lim et al.’s method, which uses training-derived cyclic scaffolds and adds side-chain atoms.The authors state that they could not compare directly with T&S polish because its code was unavailable and its experimental setting differed [17].Source: S1 Additional Related Work · p. 14

S2 Modof-pipem Protocol

• At each of up to five iterations, Modof-pipem samples 20 outputs per input, forwards up to five similarity-compliant molecules with the best properties, then returns up to 20 unique, unforwarded outputs with the best properties.It stops early if an iteration produces no molecules; forwarded molecules may lack improved properties, and only outputs satisfying the similarity constraint are eligible for forwarding.Source: S2 Modof-pipem Protocol · p. 14

S3 Data Used in plogP Optimization Experiments

• Table S1 presents statistics for the data used in the plogP optimization experiments.Source: S3 Data Used in plogP Optimization… · p. 14

S3.1 Training Data Representativeness

• Cluster distributions for Modof training data, {Mx}trn, and {My}trn resembled ZINC, with paired tests showing no significant differences (p-values close to 1.0).The analysis used 56 clusters; conclusions were unchanged with 100 or 200 clusters.Source: Figure S1 · p. 15, S3.1 Training Data Representativeness · p. 15
• Modof training pairs were selected from ZINC under the constraint that paired molecules differ structurally at only one disconnection site.The paper identifies training-data representativeness as relevant to generalization across ZINC chemical space.Source: S3.1 Training Data Representativeness · p. 15
• The analysis clustered 324,949 molecules using 2,048-dimensional Morgan fingerprints and Tanimoto similarity, grouping training-pair molecules by property and the remaining ZINC molecules.CLUTO formed 50 clusters and six disconnected components in the nearest-neighbor graphs.Source: S3.1 Training Data Representativeness · p. 15

S4 Graph Edit Path Identification for Training Data Generation

• Graph edit paths use node and edge addition or deletion, without substitutions, and are identified with DF-GED in NetworkX [25, 57].Disconnection sites are matched nodes adjacent to nodes that are removed or newly added.Source: S4 Graph Edit Path Identification for… · p. 15

S5 Disconnection Site Analysis in plogP Training Data

• 74.4% of molecule pairs with similarity above 0.6 have one disconnection site, 21.1% have two, supporting one-fragment-at-a-time optimization for most cases.Modof-pipe and Modof-pipem can handle multiple sites through multiple one-fragment optimizations.Source: S5 Disconnection Site Analysis in… · p. 16, Figure S2 · p. 16
• On average, more nodes are attached than removed at disconnection sites, indicating that optimized molecules with better plogP become larger.The analysis uses junction-tree node counts in Jin’s benchmark dataset [15].Source: S5 Disconnection Site Analysis in… · p. 16

S6 Discussion on Parameter Settings in plogP Optimization

• GraphAF samples 200 candidates per test molecule, versus 20 for JTNN, HierG2G, and Modof; T&S polish samples once, so comparing its output with baseline best outputs is fairer.These differing candidate-pool sizes make it unclear whether GraphAF’s performance reflects optimization quality or more sampling.Source: S6 Discussion on Parameter Settings in… · p. 16

S7 Molecule Similarity Calculation

• A binary-fingerprint Tanimoto similarity of 0.644 contrasted with a substructure-count similarity of 0.393 for two molecules that looked sufficiently different.This illustrates how binary Morgan fingerprints may overestimate molecular similarity.Source: S7 Molecule Similarity Calculation · p. 16
• Because aromatic rings can contribute to large plogP values, binary-fingerprint overestimation could permit adding many rings while satisfying similarity constraints, yielding very large, less drug-like molecules.28The authors propose using substructure-count fingerprints or limiting optimized molecule size to avoid this outcome.Source: S7 Molecule Similarity Calculation · p. 16
• Modof uses the same binary Morgan fingerprints as the baselines and constrains optimized molecules to at most 38 atoms, the maximum molecule size in ZINC.Source: S7 Molecule Similarity Calculation · p. 16

S8.1 Discussion on plogP Test Sets

• GraphAF and MoFlow’s published results are not comparable with other baselines because they used a different, easier test set; this section evaluates both on the benchmark test set.The benchmark contains 800 ZINC test-set molecules with the lowest plogP values, whereas their test sets selected 800 lowest-plogP molecules from the entire ZINC dataset.Source: S8.1 Discussion on plogP Test Sets · pp. 16, 18
• On the benchmark test data, GraphAF and MoFlow do not outperform GCPN, JTNN, Hier2G2, or Modof.GraphAF was fine-tuned on 10K molecules that do not overlap with the benchmark test set; MoFlow used its authors’ trained model, with optimization performed at test time via gradient-ascent search in latent space.Source: S8.1 Discussion on plogP Test Sets · p. 18

Discussion on Reinforcement Learning Settings

• GCPN, MolDQN, and GraphAF used 800 test molecules for training or fine-tuning, risking environment overfitting, memorized optimization paths, and poor generalization to new molecules.Prior studies on environment overfitting29,30 recommend that reinforcement learning use an isolated test set completely disjoint from training data.Source: S8.2 Discussion on Reinforcement… · p. 18
• GraphAF fine-tuned on 10K non-overlapping ZINC molecules did not outperform other baselines on isolated benchmark test molecules.The sampled molecules had a property range similar to the test molecules ([-11.0, -0.5]).Source: S8.2 Discussion on Reinforcement… · p. 18

S9.1 Overall Pipeline Performance

• At δ=0.0, 84.88% of molecules passed through three iterations, and overall property improvement p±std reached 7.61±2.30 after iteration 5.Per-iteration gains slowed later; higher similarity thresholds reduced the number of molecules continuing and the improvement per iteration.Source: S9.1 Overall Pipeline Performance · p. 18

S9.2 Molecule Similarity Comparison

• Modof-pipe’s optimized molecules had low pairwise similarity around 0.14–0.18, while their average similarity to all training molecules remained small.Similarity to the top-10 nearest training molecules decreased with further optimization, while optimized molecules became slightly more similar to one another.Source: S9.2 Molecule Similarity Comparison · p. 18

S9.3 Optimized Molecule Size Analysis

• At δ=0.4, plogP mean rose from -2.75 to 2.25, logP from -1.40 to 2.85, and SA score from -1.30 to -0.64 after Modof-pipe optimization.The passage also reports improvement in the combined SA and cycle scores, indicating that the optimization learned to favor more synthesizable molecules.Source: Figure S4 · p. 19, S9.4 Improvement on Different… · pp. 19–20

S9.5 Chemical Transformation via Modof-pipe Optimization

• Among 800 test molecules optimized at δ=0.4, 24.38% changed ZINC clusters, versus about 9.20% of training inputs paired with a different-cluster output.Test and optimized molecules had broadly similar cluster distributions, suggesting optimization was not concentrated in one chemical subspace.Source: Figure S5 · p. 19, S9.5 Chemical Transformation via… · pp. 20–21

S9.6 Comparison on Retaining Molecule Scaffolds

• Modof-pipe and Modof-pipem modify molecule peripheries while retaining major scaffolds, unlike baselines that make very small changes or sometimes alter the scaffold substantially.In the two examples, both Modof variants achieved substantial plogP improvement.Source: S9.6 Comparison on Retaining Molecule… · p. 21

S9.7 Model Complexity Comparison

• At δ=0.4, Modof has 1.89M parameters, compared with 3.74M for JTNN and 6.8M for HierG2G, while achieving comparable or better results.Across constraints, the paper reports at least 40% fewer parameters and 26% less training data than the best baselines. In plogP training data, removed fragments averaged 2.85 atoms and attached fragments 7.55 atoms.Source: S9.7 Model Complexity Comparison · p. 21, S10 Fragment and Molecule Size… · p. 22

S11.3 Evaluation Metrics

• For DRD2 and QED, training used 125,469 and 92,045 single-disconnection molecule pairs, respectively; evaluation groups optimized molecules by property and similarity criteria.The three groups were OM, OM-pic (meeting benchmark property-improvement criteria), and OM-trn (matching training-data improvement criteria); the test sets contained 1,000 DRD2 and 800 QED molecules.Source: S11.1 Training Data Generation for… · p. 22, S11.3 Evaluation Metrics · pp. 23–24

S11.4 Experimental Results

• Modof-pipem achieves the highest DRD2 optimization success rates in the OM, OM-pic, and OM-trn groups at similarity constraints δ=0.4, 0.5, and 0.6.The benchmark contains 1,000 molecules, and each evaluated optimized molecule satisfies its corresponding similarity constraint.Source: Table S7 · p. 24, Experimental Results on Optimizing DRD2 · p. 24
• In DRD2 optimization, Modof-pipem achieved a 99.10% success rate in OM versus 91.5% for HierG2G(m), and led success rates across tested constraints in OM, OM-pic, and OM-trn.For QED, it led success rates across the same groups and constraints except OM-pic at δ=0.4 and 0.6, where it ranked second.Source: Experimental Results on Optimizing DRD2 · p. 25, Experimental Results on Optimizing QED · p. 25

S12.1 Training Data Generation for Multi-Property Optimization

• Multi-property training used 14,230 pairs and 800 test molecules with DRD2(M) < 0.5 and QED(M) < 0.6; 16.75% of training Mx molecules had fragments removed without new fragments attached.The task modifies molecules to improve both DRD2 and QED; the authors suggest the removal-only pattern may reflect smaller molecules having better QED.Source: S12.1 Training Data Generation for… · p. 26, Fragment and Molecule Size Analysis… · p. 26, S12 Experimental Results on… · p. 26

S12.4 Experimental Results

• At similarity δ=0.4, Modof-pipe and Modof-pipem achieved 24.62% and 38.88% success rates for molecules meeting both DRD2 and QED thresholds, versus 14.50% for HierG2G(m).The reported improvements over HierG2G(m) were 69.79% and 168.14%, respectively; both Modof methods also outperformed the baselines at δ=0.5 and 0.6.Source: Table S11 · p. 27, S12.4 Experimental Results · p. 27

S13.1 Local Greedy Optimization

• Modof-pipe’s local greedy strategy stops when a step yields no property improvement, potentially missing later gains; Modof-pipem mitigates this by advancing top candidates even without improvement.About 4% of molecules at δ=0.4 stop before completing five iterations.Source: S13.1 Local Greedy Optimization · p. 28

S13.2 Multi-Property Optimization

• Simultaneously optimizing multiple drug properties is difficult because combined objectives can be biased, the optimization is combinatorial, and concurrent-property training data may be limited.Sequential single-property optimization can also be suboptimal because later changes may alter an earlier property.Source: S13.2 Multi-Property Optimization · p. 28

S13.3 Target-Specific Molecule Optimization

• Modof performs well on DRD2 but is not readily adapted to protein-target information, such as binding-pocket structures, which may be scarce in training data.The authors identify incorporating target information and modifying functional groups and 3D structures accordingly as challenges for target-specific optimization.Source: S13.3 Target-Specific Molecule… · pp. 28–29

S13.4 Optimization in Other Areas

• Modof could extend beyond drug development to optimize measured compound or substance properties, including solar-cell band gaps, melting or boiling points, and battery solubility.The proposed adaptation replaces molecular properties and measurements in the loss function with those for the target application.Source: S13.4 Optimization in Other Areas · p. 29

S14 Algorithms of Modof

• The algorithms encode molecular differences, remove non-scaffold fragments, attach new fragments breadth-first, and iteratively optimize under similarity constraints.Modof-pipem advances up to m unique best candidates per iteration and returns the best b molecules among decoded candidates.Source: S14 Algorithms of Modof · p. 29
• The excerpt ends an `if` block and two nested loops, but does not show what operations they contain.The supplied lines are a fragment of the algorithm pseudocode.Source: S14 Algorithms of Modof · p. 31