Design and Research of a Dual-Target Drug Molecular Generation Model Based on Reinforcement Learning

Abstract

Dual-target drug design addresses complex diseases and drug resistance, yet existing computational approaches struggle with simultaneous multi-protein optimization. This study presents SFG-Drug, a novel dual-target molecular generation model combining Monte Carlo tree search with gated recurrent unit neural networks for simultaneous MEK1 and mTOR targeting. The methodology employed DigFrag digital fragmentation on ZINC-250k dataset, integrated low-frequency masking techniques for enhanced diversity, and utilized molecular docking scores as reward functions. Comprehensive evaluation on MOSES benchmark demonstrated superior performance compared to state-of-the-art methods, achieving perfect validity (1.000), uniqueness (1.000), and novelty (1.000) scores with highest internal diversity indices (0.878 for IntDiv1, 0.860 for IntDiv2). Over 90% of generated molecules exhibited favorable binding affinity with both targets, showing optimal drug-like properties including QED values in [0.2, 0.7] range and high synthetic accessibility scores. Generated compounds demonstrated structural novelty with Tanimoto coefficients below 0.25 compared to known inhibitors while maintaining dual-target binding capability. The SFG-Drug model successfully bridges the gap between computational prediction and practical drug discovery, offering significant potential for developing new dual-target therapeutic agents and advancing AI-driven pharmaceutical research methodologies.

1. Introduction

1.1. Research Background and Current State of the Field

Recently, there has been growing interest in artificial intelligence-driven drug discovery as a transformative approach to address the escalating challenges in pharmaceutical development [1,2]. The traditional drug discovery pipeline, characterized by lengthy development timelines exceeding 10–15 years and costs approaching USD 2.6 billion per approved drug, has prompted urgent demands for computational innovations that can accelerate the identification and optimization of therapeutic compounds [3,4]. A number of studies have demonstrated that machine learning and deep learning methodologies can significantly enhance various stages of drug development, from target identification to lead compound optimization [5,6].

Drug design fundamentally represents a complex optimization problem in vast chemical space, where the identification of molecules with desired biological activity requires systematic exploration of molecular structures numbering in the billions [7,8]. Artificial intelligence is a fundamental aspect of modern computational chemistry that can bridge the gap between theoretical molecular design and practical therapeutic applications [9]. The integration of reinforcement learning with molecular generation has emerged as a particularly promising paradigm, enabling the development of computational models capable of learning optimal molecular design strategies through iterative interaction with biological targets [10,11].

The concept of dual-target drug design has gained substantial momentum in recent years as researchers recognize the limitations of single-target therapeutic approaches, particularly in complex diseases such as cancer, neurodegenerative disorders, and metabolic syndromes [12,13]. Traditional single-target drugs often face challenges including drug resistance development, limited therapeutic efficacy, and adverse side effects due to off-target interactions [14]. In contrast, dual-target approaches offer the potential for enhanced therapeutic outcomes through synergistic effects, reduced resistance mechanisms, and improved selectivity profiles [15,16]. This paradigm shift has been further supported by advances in systems biology and network pharmacology, which highlight the interconnected nature of biological pathways and the potential benefits of multi-target intervention strategies [17].

The field of computational drug design has witnessed significant advances through the application of various artificial intelligence methodologies, with deep learning approaches demonstrating particular promise in molecular property prediction and structure-based design [18,19]. Generative adversarial networks (GANs), variational autoencoders (VAEs), and recurrent neural networks (RNNs) have been successfully employed for de novo molecular design, enabling the generation of novel chemical structures with desired pharmacological properties [20,21]. Notable achievements include the development of molecular generation models such as REINVENT, ChemVAE, and junction tree variational autoencoders, which have demonstrated capabilities in producing drug-like molecules with improved synthetic accessibility and biological activity [22,23].

Fragment-based drug discovery (FBDD) has emerged as a complementary approach that leverages the systematic deconstruction and reconstruction of molecular structures to explore chemical space more efficiently [24,25]. This methodology has proven particularly valuable in identifying novel chemical scaffolds and optimizing lead compounds through structure–activity relationship analysis [26]. The integration of FBDD with computational approaches has yielded promising results, with several fragment-based methodologies successfully advancing compounds through clinical development [27].

Recent developments in reinforcement learning applications to drug discovery have demonstrated the potential for autonomous molecular design systems capable of optimizing multiple objectives simultaneously [28,29]. These systems employ reward functions based on molecular properties, binding affinity predictions, and drug-likeness criteria to guide the generation process toward therapeutically relevant chemical space [30]. However, most existing approaches focus primarily on single-target optimization, limiting their applicability to complex therapeutic scenarios requiring multi-target engagement [31].

The application of Monte Carlo tree search (MCTS) algorithms in molecular design represents a relatively nascent but promising area of research [32,33]. MCTS has shown effectiveness in navigating complex decision spaces and has been successfully applied to various optimization problems in chemistry and materials science [34]. The combination of MCTS with deep learning approaches offers the potential for more sophisticated molecular generation strategies that can balance exploration and exploitation in chemical space [35]. Additionally, the integration of advanced optimization algorithms such as KAdam has shown promise in enhancing the training efficiency of neural networks for biomedical applications [36].

1.2. Research Gaps and Limitations

However, few studies have examined the systematic integration of reinforcement learning with fragment-based molecular generation for dual-target drug design applications. Nevertheless, the role of Monte Carlo tree search in guiding molecular fragment assembly for simultaneous multi-target optimization remains unclear [37,38]. Despite these findings, it is still not known whether computational approaches can effectively generate novel molecular scaffolds that maintain high binding affinity for multiple protein targets while preserving drug-like characteristics and synthetic accessibility [39].

Current molecular generation methodologies face several critical limitations that impede their practical application in dual-target drug discovery. First, existing approaches typically optimize for single targets, resulting in molecules that may lack the structural features necessary for effective multi-target engagement [40,41]. Second, conventional fragment-based methods rely heavily on predefined fragmentation rules such as BRICS and RECAP, which may not capture the full diversity of chemically relevant molecular decompositions [42,43]. Third, the computational complexity of simultaneously optimizing multiple pharmacological properties often leads to convergence issues and suboptimal molecular designs [44].

Furthermore, the limited exploration of low-frequency molecular fragments in existing generation models restricts the diversity and novelty of generated compounds [45]. Traditional approaches tend to bias toward high-frequency structural motifs present in training datasets, potentially overlooking rare but therapeutically valuable chemical scaffolds [46]. The lack of systematic approaches for incorporating molecular docking scores as reward functions in reinforcement learning frameworks further limits the development of target-specific molecular generation systems [47].

The integration of organ-on-chip technologies and biomedical sensing systems has shown significant potential in drug development and personalized medicine applications [48,49]. However, the connection between computational drug design and experimental validation platforms remains underexplored, particularly in the context of nucleic acid-based therapeutic delivery systems [50]. The development of intelligent biomedical systems that can provide real-time feedback for computational drug design represents an important frontier that requires interdisciplinary collaboration [51].

1.3. Research Objectives and Paper Organization

To address this gap, we conducted a comprehensive investigation into the development of a novel dual-target drug molecular generation model based on reinforcement learning principles. This paper investigates the integration of Monte Carlo tree search with fragment-based molecular design to enable simultaneous optimization for MEK1 and mTOR protein targets. The aim of this study is to develop and validate a computational framework that can generate structurally novel molecules with favorable dual-target binding characteristics while maintaining drug-like properties and synthetic accessibility.

Our approach employs a sophisticated combination of DigFrag digital fragmentation methodology, low-frequency masking techniques, and gated recurrent unit (GRU) neural networks to enhance the diversity and quality of generated molecular structures. The proposed SFG-Drug model utilizes molecular docking scores as reward functions within a reinforcement learning framework, enabling systematic optimization toward dual-target engagement. By implementing advanced optimization algorithms and comprehensive evaluation metrics, this research aims to demonstrate the feasibility of AI-driven dual-target drug design and establish new benchmarks for computational molecular generation.

The scope of this investigation encompasses the development of molecular fragment libraries from the ZINC-250k dataset, the implementation of Monte Carlo tree search algorithms for molecular assembly, and the comprehensive evaluation of generated compounds using established drug discovery metrics. The research specifically focuses on MEK1 and mTOR proteins as representative targets due to their clinical relevance in cancer therapy and their distinct binding site characteristics that pose challenges for dual-target design [52,53].

This study contributes to the field by proposing a novel computational framework that addresses the limitations of existing single-target molecular generation approaches and demonstrates the potential for systematic dual-target drug design. The findings provide insights into the effective integration of reinforcement learning with fragment-based methodologies and establish new directions for AI-driven pharmaceutical research [54,55]. The principal conclusions of this research demonstrate that the SFG-Drug model achieves superior performance compared to state-of-the-art baseline methods, with perfect validity, uniqueness, and novelty scores while maintaining the highest internal diversity indices.

This article is organized as follows. First, we present the comprehensive methodology including the SFG-Drug model architecture, molecular fragment library construction, and Monte Carlo tree search implementation. Second, we detail the experimental results demonstrating the superior performance of our approach across multiple evaluation metrics and comparative analyses with existing methods. Third, we provide an in-depth discussion of the implications of our findings, research limitations, and strategic directions for future development. Finally, we summarize the key contributions and potential impact of this research on the field of computational drug discovery.

2. Materials and Methods

2.1. SFG-Drug Model Architecture Framework

A novel fragment-based molecular generation model was developed and implemented in this study. The model integrates Monte Carlo search with gated recurrent unit (GRU) neural networks, specifically designed for dual-target drug design tasks, to efficiently generate molecular structures with potential therapeutic activity. The proposed framework is designated as the SFG-Drug. The workflow of the SFG-Drug model is illustrated in Figure 1.

The model performs intelligent exploration of chemical space through Monte Carlo search, incorporating the GRU model during the simulation phase of Monte Carlo tree search to generate novel molecular sequences that adhere to chemical valency rules. Generated SMILES sequences are converted to 3D molecular structures and docked against two target proteins. Their binding affinity scores serve as reward functions to guide and optimize the SFG-Drug model, enabling the generation of drug candidates suitable for dual-target binding. Compared to conventional approaches, SFG-Drug demonstrates significant advantages in molecular diversity and generation efficiency.

The SFG-Drug model employs Monte Carlo tree search algorithms in conjunction with fragment probability distributions predicted by a deep learning GRU model to construct a Monte Carlo molecular tree. Each path from the root node to a leaf node in this tree represents a complete molecular structure sequence. During evaluation of fragment nodes along the search path, ligand-protein docking scores are used as metrics to assess node value. This mechanism optimizes the Monte Carlo molecular tree to enable SFG-Drug to generate high-quality molecular sequences, with resulting compounds capable of binding to multiple protein targets—facilitating the design of single molecules effective against multiple diseases.

The SFG-Drug model enables exploration of regions in chemical space that were previously underexplored in molecular generation studies. By leveraging a pre-trained deep learning model, the expansion direction of the Monte Carlo molecular tree is guided, allowing generated molecules to achieve improved binding affinity scores with specified target proteins.

To initiate the process, recurrent neural network (RNN) models were employed to capture molecular sequence features, owing to their strong performance in sequence modeling tasks and inherent ability to retain temporal dependencies. The RNN architecture in SFG-Drug maintains hidden states at each time step and propagates them forward, enabling the network to utilize prior sequence information to influence current predictions—thereby enhancing its capacity to interpret molecular structure and properties.

However, RNN models exhibit notable limitations when processing longer molecular sequences. First, due to parameter sharing across time steps, they struggle to capture long-range dependencies in molecular SMILES strings. Second, sequential processing leads to cumulative information propagation along the time axis, increasing the risk of gradient vanishing or explosion as sequence length grows. Additionally, during Monte Carlo molecular tree expansion, greater breadth yields more diverse molecular structures, as increased branching enables broader coverage of chemical space.

To address these limitations, gated recurrent units (GRU) were adopted to replace conventional RNN models, improving both stability and efficiency in sequence modeling. The GRU model’s predicted probabilities for subsequent molecular fragments are leveraged to maximize the number of viable chemical symbol predictions, thereby expanding the breadth of the molecular tree. GRUs incorporate update and reset gates into the standard RNN framework, regulating information flow and state updates in the hidden layer. This design enables more stable training dynamics and mitigates gradient vanishing or explosion. Furthermore, a novel optimization algorithm, KAdam, was introduced in this study, allowing the GRU model to maintain prediction accuracy while accelerating training speed and reducing computational time during large-scale molecular training.

2.2. Construction of Fragment Molecular Library

2.2.1. Dataset Introduction

The small-molecule dataset used to train the deep learning SFG-Drug model was obtained from the ZINC database, maintained by the Irwin and Shoichet laboratories in the Department of Pharmaceutical Chemistry at the University of California, San Francisco (UCSF). The ZINC database contains over 230 million commercially available compounds and serves as a freely accessible, non-commercial online repository for virtual screening and drug discovery. The ZINC-250k dataset [56] employed in this study represents a curated subset of the ZINC database, comprising approximately 250,000 compound structures that span diverse chemical classes and scaffolds. This dataset includes SMILES representations of each molecule along with key molecular properties: logP (water–octanol partition coefficient), SA score (synthetic accessibility score), and QED (quantitative estimate of drug-likeness).

A key feature of this database is its rigorous structural standardization, which ensures consistency and facilitates reliable compound comparison and screening. The selection of compounds for ZINC-250k considered not only fundamental chemical properties but also potential biological activity and drug-likeness. Consequently, using the ZINC-250k dataset for molecular generation offers several advantages: it encompasses a broad range of structurally diverse small molecules, covering a wide chemical space and enabling comprehensive exploration of molecular properties and therapeutic potential, thereby supporting novel drug discovery. Each compound is annotated with detailed physicochemical properties, molecular structure information, and availability data, which enhance the accuracy of virtual screening and enable targeted drug design. All molecular structures in the database underwent standardized processing to ensure uniformity in representation and property assignment.

2.2.2. Molecular Fragment Segmentation

When evaluating decomposition methods for drug-like compounds, this research focused on RECAP [57] and BRICS [58] (Breaking of Retrosynthetically Interesting Chemical Substructures), two distinct molecular fragmentation algorithms. Both approaches share a foundation in retrosynthetic analysis of bioactive molecules, guiding the disconnection of chemical structures based on synthetic accessibility. Although their strategic frameworks exhibit considerable overlap, their implementations in RDKit [59] differ substantially. In this study, BRICS was selected due to its use of a predefined rule set that identifies chemically meaningful cleavage sites, ensuring that generated fragments retain structural integrity—such as preserving aromatic ring systems. Consequently, bond cleavage is restricted to specific single bonds, particularly those linking distinct functional groups, thereby maintaining chemical relevance in the resulting fragments.

To keep Section 2.2.2 focused on the proposed framework, we simplified the BRICS background and retained only reproducibility-critical details. We use the RDKit implementations of BRICS and RECAP to cleave molecules at retrosynthetically meaningful bonds and obtain chemically valid fragments; algorithmic background and bond-type definitions are standard and are therefore referred to the original BRICS/RECAP publications and RDKit documentation. All fragments are then canonicalized (canonical SMILES) and deduplicated before entering the unified fragment pool described below.

Compared to other graph-based segmentation algorithms, BRICS offers significant advantages. It leverages predefined chemical bond patterns derived from expert chemical knowledge to generate fragments that align with chemical intuition, while maximally preserving molecular characteristics during segmentation, as illustrated in Figure 2. This preservation enhances the representativeness of the resulting fragments in downstream modeling. Furthermore, as a rule-based algorithm, BRICS exhibits high computational efficiency, making it particularly suitable for large-scale dataset processing.

The first step in this process was to implement BRICS algorithm molecular fragment cutting, which proved relatively straightforward. Fragment-based drug discovery (FBDD) identified small molecular fragments with weak interactions with target proteins and optimized their structural information to develop lead compounds with higher activity, playing important roles in new drug research and development. FBDD played key roles in drug discovery and fragment-based drug development fields, but constructing and screening effective molecular fragment libraries remained a major challenge. These two segmentation algorithms relied on empirical intuition, limiting their ability to develop diverse structures.

For fragment integration (BRICS, RECAP, MacFrag, and DigFrag), we clarified the exact procedure used in our workflow: (i) we independently fragment each dataset molecule with each method; (ii) we convert all resulting fragments to RDKit molecules, sanitize them, and represent them as canonical SMILES; (iii) we merge fragments from all methods by set union and remove duplicates by canonical SMILES; (iv) we discard fragments that fail basic chemical validity checks (invalid valence, disconnected atoms, or presence of non-organic elements) and apply the same size constraints as Section 2.2.3 (e.g., heavy-atom count outside the allowed range); (v) the final unified fragment vocabulary is then used for subsequent filtering and frequency analysis, with DigFrag additionally providing graph-based fragment boundaries and attachment-point annotations used by our generation model.

DigFrag utilized graph attention mechanisms to identify and segment drug/pesticide fragments, with core advantages lying in its machine intelligence perspective rather than purely relying on human expertise, thereby obtaining fragments with higher structural diversity. Additionally, the cutting method adopted in this study integrated fragments segmented by BRICS, RECAP, MacFrag, and DigFrag methods, employing DigFrag methodology for molecular fragmentation processing based on Graph Neural Network (GNN) architecture.

Figure 3 illustrates the DigFrag fragment processing workflow. As shown, molecular graphs are represented as G = (V, E), where V denotes atomic nodes and E denotes edges corresponding to chemical bonds. In this workflow, the initial molecular graphs are processed through a graph attention-based feature extraction network—distinct from a feature matrix—to generate atom-level embeddings via a series of attention layers. These atomic embeddings are then aggregated into unified graph-level representations, referred to as super nodes. Subsequently, these super nodes undergo further processing through additional attention layers to produce fragment-level embeddings, capturing the structural and chemical characteristics of each molecular fragment.

2.2.3. Molecular Fragment Library Screening

In molecular generation and optimization tasks, constructing high-quality molecular fragment libraries is a critical step for enabling effective chemical structure generation and exploration. However, after completing molecular fragment library construction, additional fragment filtering is required to eliminate undesirable substructures. This filtering process not only enhances generative model performance and chemical design efficiency but also significantly improves the utility and scientific value of fragment libraries.

Molecular fragments produced through molecular segmentation may introduce adverse effects in downstream applications [60]. For instance, they may exhibit toxicity or high reactivity, display unfavorable pharmacokinetic properties, or interfere with assay detection systems. In contemporary drug discovery, high-throughput screening is routinely employed. By removing undesirable substructures, filtering enables the development of more efficient screening libraries, thereby conserving time and resources. Thus, molecular filtering is essential.

Brenk et al. [61] collected a list of adverse substructures for screening compound libraries for treating neglected diseases. Examples of these adverse structures included nitro groups (mutagenic), sulfates and phosphates (potentially causing adverse pharmacokinetic properties), 2-halopyridines and thiols (reactive). This adverse substructure list was implemented in RDkit using PAINS filters. Pan-Assay Interference Compounds (PAINS) referred to hit compounds that frequently appeared in HTS (high-throughput sequencing) but were actually false positives. PAINS showed activity on multiple targets rather than one specific target, originating from non-specific binding or interactions with detection components.

In this work, we apply RDKit FilterCatalog (PAINS and Brenk alerts) to remove assay-interfering and reactive substructures before docking, thereby reducing spurious high-scoring artifacts and improving interpretability.

Implementation details for fragment filtering (to improve reproducibility): We used RDKit (v2022.09.1) to compute fragment properties and to apply rule-based filters. Fragments are first sanitized (RDKit MolSanitize) and standardized (canonical SMILES). We then remove fragments that (a) contain non-organic elements, (b) have fewer than 2 heavy atoms or exceed the maximum heavy-atom limit used in our study (Section 2.2.3), (c) have an absolute formal charge > 1, or (d) fail PAINS/Brenk substructure alerts using RDKit FilterCatalog. Finally, we remove duplicates (canonical SMILES) and keep the remaining fragments to build the fragment library that seeds MCTS expansion.

The second method for identifying filtered molecular libraries offered several advantages. First, it enhanced the chemical validity of molecular generation. Chemical validity is a core objective of molecular generation models, requiring that generated molecules conform to established chemical rules and be synthetically feasible. If fragment libraries contain chemically invalid substructures—such as the fragment C(=O)OH, where two breakpoints occur at the same end of a carboxylic acid group—this can lead to repetitive connection errors during molecular linking. Such substructures are chemically implausible and must be filtered out. Their presence may result in invalid molecules, thereby reducing generation efficiency. By removing these undesirable fragments, each remaining fragment in the library possesses unambiguous chemical meaning, improving the overall effectiveness of molecular generation.

Second, the method reduced molecular generation complexity. In generative models, each fragment typically serves as a “basic unit,” and the combinatorial assembly of these units determines the diversity of generated molecules. However, certain substructures in fragment libraries may be excessively complex, posing challenges during model sampling or optimization. For instance, fragments containing more than 20 non-hydrogen atoms may lack sufficient versatility in synthesis or generation contexts. Similarly, fragments with intricate ring systems or rare functional groups may cause model overfitting or reduce generation efficiency. Therefore, filtering out overly complex or redundant fragments helps streamline the generation process and improve computational tractability.

Finally, a critical aspect of molecular fragment library screening was deduplication and enhancement of library diversity. Fragment library diversity is essential for the exploratory capacity of generative models. If libraries contain numerous similar or redundant substructures, this increases computational burden during training and restricts the diversity of generated molecules. Removing fragments with high redundancy or structural similarity enhances both the coverage and diversity of the fragment library, enabling generative models to explore the chemical space more comprehensively.

2.3. Monte Carlo Tree Search Molecular Generation

A molecular generation model integrating reinforcement learning with MCTS was developed, optimizing generated molecular structures through MCTS-guided exploration and molecular docking. This study presents a novel dual-target drug molecular generation model (SFG-Drug) applied to the DigFrag digital fragmentation method to decompose 250,000 drug molecule SMILES (Simplified Molecular Input Line Entry System) strings from the ZINC database into molecular fragments. A gated recurrent unit (GRU) prediction network was trained to learn and capture potential associations and patterns among molecular fragments from extensive known molecular structure data, mapping input SMILES sequences of chemical elements to corresponding conditional probability distributions.

The conditional probability distributions output by the prediction network provided effective empirical guidance for MCTS-based molecular generation, thereby enhancing generation efficiency and optimizing both molecular structures and their associated chemical properties. By dynamically expanding search trees across the chemical space and guiding exploration based on performance metrics at each node, MCTS enabled rapid identification of candidate molecules with potential biological activity or desired properties among vast combinatorial possibilities.

Monte Carlo tree search is a decision-making algorithm widely used in games and complex planning tasks, estimating action values through iterative tree construction and outcome simulation. MCTS comprises four key phases, as illustrated in Figure 4.

In the MCTS selection step, we use the UCT criterion:

$$U(i)=\overline{Q_i}+c\sqrt{{\displaystyle \frac{2ln N_p}{N_i}}},\overline{Q_i}={\displaystyle \frac{W_i}{N_i}}$$

(1)

where $\overline{Q_i}={\displaystyle \frac{W_i}{N_i}}$ is the average reward of node $i$; $W_i$ is the accumulated reward; $N_i$ is the visit count of node $i$; $N_p$ is the visit count of its parent; and $c$ is the exploration constant. In our experiments, we set $c$ = 1.0 (default in our configuration).

(1)

Selection: The SFG-Drug search tree originated from an initial state containing only root nodes, where each root node corresponded to a starting token $ of a SMILES string, representing the initial stage of molecular generation. Each node in the search tree represented a molecular fragment encoded as a partial SMILES string. Using the upper confidence bound applied to trees (UCT) within the tree policy, leaf nodes were iteratively selected from the root until terminal nodes were reached.

(2)

Expansion: New child nodes were generated by extending selected leaf nodes, which corresponded to appending molecular fragments to the end of the current partial SMILES strings. This step progressively built longer SMILES sequences, thereby advancing the construction of candidate molecules.

(3)

Simulation or Evaluation: Pre-trained gated recurrent unit (GRU) models were employed to complete the partial molecular fragments into full SMILES strings, generating complete molecular structures. The validity of the resulting SMILES strings was verified, and reward values were computed based on the molecular docking scores of valid compounds with target proteins. These rewards were then compared to the current best SMILES trajectory in SFG-Drug to assess whether the generated molecules represented optimal solutions.

$$\{\begin{array}{c}s\left(x\right)=s_1(x)+s_2\left(x\right),\Delta \left(x\right)=s\left(x\right)-2b\\ r(x)=-\alpha {\displaystyle \frac{\mathsf{\Delta }\left(x\right)}{1+\alpha \mid \mathsf{\Delta }\left(x\right)\mid }}, \alpha =0.1,b=bas{e}_{v}inadoc{k}_{s}core\end{array}$$

(2)

where $s_1\left(x\right)$ and $s_2\left(x\right)$ denote the AutoDock Vina affinities version 1.1.2 (kcal/mol; more negative is better) of molecule $x$ against the two targets; b is a user-defined baseline Vina affinity (set by the configuration parameter base_vinadock_score, b = −7.0 kcal/mol in our default setting, and $\alpha$ is a scaling factor. The scalar reward $r\left(x\right)$ is used for MCTS back-propagation.

(4)

Back-propagation: Reward values were propagated backward along search paths to parent nodes in the search tree, using feedback to update node statistics and refine subsequent node selection and molecular generation.

In practical dual-target inhibitor design, a candidate must achieve simultaneously acceptable binding to both targets rather than optimizing a single score. Accordingly, each generated molecule yields two AutoDock Vina version 1.1.2 affinities (one per target), forming a bi-objective optimization problem. Because standard MCTS back-propagation requires a scalar reward, during search we adopt a scalarization strategy to combine the two docking objectives into a single reward (more negative Vina affinity is better). In this work, we use the unweighted sum of the two affinities as the default scalarization, followed by a monotonic bounded mapping to stabilize updates. Beyond this search-time scalarization, we explicitly report the true two-objective outcomes after generation by analyzing the Pareto-optimal set in the (Score_Target1, Score_Target2) space, and select synthesis-oriented candidates from the Pareto set subject to additional physicochemical constraints.

Through iterative refinement of these phases, MCTS incrementally builds decision trees to optimize decision-making in problems characterized by vast state spaces, where optimal strategies are difficult to compute directly.

2.4. Molecular Fragment Prediction Model

Given the strong performance of RNN models in sequence data processing tasks and the inherent characteristics of their recurrent architecture, the proposed SFG-Drug framework employs RNNs to capture features from molecular fragment sequences. During processing, RNN models maintain hidden states at each time step and propagate them forward, enabling the network to leverage historical information in shaping current outputs, thereby improving the representation of molecular structure and properties. However, RNN models encounter two key limitations when processing long molecular fragment sequences:

Problem One: RNN models use a shared set of network weights across all time steps, meaning the same parameters are applied at each sequential position. This parameter sharing constrains the model’s ability to effectively capture long-range dependencies within molecular fragment sequences.

Problem Two: RNN models process molecular fragment sequences sequentially, with information accumulating over time. As sequence length increases, this temporal accumulation leads to gradient vanishing or explosion, particularly in deep recurrent computations.

To address these limitations, an encoder–decoder variational autoencoder (VAE) architecture was integrated with gated recurrent unit (GRU)-based generation models. The architecture (Figure 5) and training procedure are described as follows:

(1)

Input Data

Input consisted of molecular fragment sequence sets, for example, $x=\{x_1,x_2,\dots ,x_n\}$, where $x_i$ represented the $i$-th fragment, for example: *C(=O)O. Each molecular fragment $x_i$ was embedded as a fixed-dimension vector, $x_i\in {\mathbb{R}}^d$, where d was the embedding vector dimension.

To encode the fragment sequences, GRUs processed each embedded fragment xi sequentially, computing a hidden state hi = GRU(xi,hi − 1). This recursive transformation captures sequential dependencies across the fragment chain, as formalized in Equation (1): To encode molecular fragment sequences, gated recurrent units (GRU) were used, converting each embedded molecular fragment $x_i$ to hidden representation $h_i=GRU(x_i,h_{i-1})$. As shown in Equation (1):

$$\{\begin{array}{c}{r}_i=\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{m}\mathrm{o}\mathrm{i}\mathrm{d}\left(W_i{x}_i+U_i{h}_{i-1}\right)\\ u_i= sigmoid({\mathrm{W}}_{\mathrm{u}}{\mathrm{x}}_{\mathrm{i}}+{\mathrm{U}}_{\mathrm{u}}{\mathrm{h}}_{\mathrm{i}-1})\\ v_i= tanh({\mathrm{W}}_{\mathrm{h}}{\mathrm{x}}_{\mathrm{i}}+{\mathrm{U}}_{\mathrm{h}}({\mathrm{r}}_{\mathrm{i}}\odot {\mathrm{h}}_{\mathrm{i}-1}\left)\right)\\ h_i={\mathrm{u}}_{\mathrm{i}}\odot {\mathrm{h}}_{\mathrm{i}-1}+(1-{\mathrm{u}}_{\mathrm{i}})\odot {\mathrm{v}}_{\mathrm{i}}\end{array}$$

(3)

where $h_0$ was a zero vector. In Equation (1), $r_i$ was the reset gate vector, $u_i$ was the update gate vector, and $W$ and $U$ were weight matrices. The hidden representation of the last fragment in the sequence, called $h$, served as the latent representation of the entire sequence.

In the hidden state $h_n$ of the last molecular fragment (as shown in Figure 6, <EOS> fragment, where <EOS> represented termination symbols of drug molecule SMILES), the encoder generated latent space mean $\mu$ and log variance $log{\sigma }^2$ through two linear transformations:

$$\{\begin{array}{c}\mu ={\mathrm{W}}_{\mu }{\mathrm{h}}_{\mathrm{n}}+{\mathrm{b}}_{\mu }\\ \mathit{log}{\sigma }^2={\mathrm{W}}_{\sigma }{\mathrm{h}}_{\mathrm{n}}+{\mathrm{b}}_{\sigma }\end{array}$$

(4)

Using reparameterization tricks, latent space vector $z$ was represented as

$$z=\mu +\sigma \cdot ϵ, ϵ~\mathcal{N}\left(0,I\right)$$

(5)

The encoder was trained to minimize the following Kullback–Leibler (KL) divergence:

$${\mathcal{L}}_{enc}\left(x\right)=-KL\left(\mathcal{N}\left(\mathsf{\mu },\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}\left({\sigma }^2\right)\right)\parallel \mathcal{N}\left(0,I\right)\right)$$

(6)

Figure 6. Two-dimensional chemical space visualization of SFG-Drug-generated molecules versus ZINC-250k dataset molecules using ISOMAP projection.

Figure 6. Two-dimensional chemical space visualization of SFG-Drug-generated molecules versus ZINC-250k dataset molecules using ISOMAP projection.

(2)

Decoder

The decoder’s task (Figure 5b) was to generate molecular fragment sequences from the latent vector. It was similarly based on GRU and adopted sequence generation methods to generate fragments fragment by fragment. Its hidden states were initialized by applying reparameterization tricks.

The decoder’s hidden state was initialized as latent vector $z$:

$$h_0=z$$

(7)

Unlike the encoder, the decoder also calculated output probabilities associated with next elements in drug molecular sequences. The probability of generated $t$-th fragment $x_t$ was calculated by the following formula:

$$P\left(x_{t+1}\right|x_t,h_t)=softmax\left(W_{out}{h}_t+b_{out}\right)$$

(8)

where $W_{out}$ was the output weight matrix and $b_{out}$ was the bias term.

The decoder’s hidden state update formula was similar to the encoder, using GRU:

$$h_{t+1}=GRU\left(x_t,h_t\right)$$

(9)

$\mathrm{z}\sim \mathrm{N}\left(\mathrm{0,1}\right)$. The generation process began by sampling a latent vector, which was used as the decoder’s initial state. The decoder’s first input was the start symbol <SOS>. Fragment tokens and recurrent states passed sequentially through GRU, linear layers, and Softmax layers, generating output probability distributions for next fragments. Based on these distributions, greedy strategies were employed to sample fragments with highest probabilities (such as fragment *C(C)=O in Figure 5b) as inputs for next decoding steps. When termination symbols <EOS> were sampled, the generation process terminated. Therefore, the first fragment of molecular generation and the last molecular fragment needed to contain one connection point to connect with adjacent molecular fragments, while intermediate molecular fragments required at least two connection points.

(3)

Model Loss

The SFG-Drug model was trained end-to-end on fragment sequence dataset D. Overall loss was the sum of encoder and decoder losses for each molecular fragment sequence. Similar to VAE frameworks, decoder loss could be viewed as reconstruction error of input sequences, while encoder loss served as regularization, forcing encoding distributions to be Gaussian distributions.

During training, empirical analysis methods [62] were employed, using ground-truth fragments as inputs for subsequent processing steps. The decoder’s training objective was to minimize the negative log-likelihood of the fragment sequences:

$${\mathcal{L}}_{dec}\left(x\right)=-\sum _{t=1}^{\left|x\right|}logP\left(\left(x_{t+1}\right|x_i,h_t)\right)$$

(10)

Total model loss was:

$$\mathcal{L}\left(D\right)={\mathcal{L}}_{enc}\left(x\right)+{\mathcal{L}}_{dec}\left(x\right)$$

(11)

2.5. Molecular Docking

In this work we use AutoDock Vina (AutoDock Vina 1.x) as the docking engine and report its native predicted binding affinity (in kcal/mol) as the docking score.

We do not modify the Vina scoring function or alter the score returned by Vina during optimization. Any additional score transformations (e.g., dividing by the number of rotatable bonds) were used only as optional post hoc analyses for interpretability, and have been removed from the core method description to avoid confusion.

For the dual-target setting, the two Vina scores (for MEK1 and mTOR pockets, respectively) are treated as a bi-objective optimization problem. The search uses the scalarization strategy described in Section 2.3 during back-propagation, while we report the true two-objective outcomes after generation by analyzing the Pareto-optimal set in the (Score_Target1, Score_Target2) space.

3. Results

3.1. Molecular Screening Rules and Drug-likeness Criteria

Since drug design requires systematic molecular screening to identify compounds with favorable pharmacokinetic properties, molecular filtering rules were investigated experimentally. The main purpose of this work was to evaluate the SFG-Drug model’s capability to generate molecules that comply with established drug-likeness criteria. As mentioned previously, the aim of molecular screening is to identify potential bioactive candidate molecules from vast compound libraries, thereby narrowing research scope and improving drug development efficiency.

In this study, all generated drug molecules conform to Lipinski’s “Rule of Five”, specifically: (1) molecular weight not exceeding 500 Da; (2) LogP value not exceeding 5; (3) number of hydrogen bond donors not exceeding 5; (4) number of hydrogen bond acceptors not exceeding 10; and (5) number of rotatable bonds not exceeding 10.

3.2. Evaluation Metrics for Drug Molecular Generation

Analysis of the results reveals that validity denotes the proportion of generated molecules that adhere to fundamental chemical rules and are chemically feasible. Uniqueness, sometimes described as distinctiveness, reflects the diversity of the generated set and is calculated as the fraction of non-duplicated molecules among all generated structures. Novelty indicates the extent to which generated molecules differ from those in the training dataset, quantified as the percentage of molecules not present in the training set. Reconstructability represents the percentage of generated molecules that can be accurately decoded from their latent space representations, reflecting the model’s encoding–decoding fidelity.

Together, these results provide important insights into molecular evaluation through QED (quantitative estimate of drug-likeness), a metric that quantifies drug-likeness as unitless values ranging from 0 to 1. The octanol–water partition coefficient (logP) represents the logarithm of a compound’s distribution ratio between n-octanol and water, serving as a key indicator of lipophilicity. Penalized logP addresses logP’s tendency to favor long-chain alkanes or large-ring hydrocarbons by subtracting two penalty terms—synthetic accessibility and ring size—from the raw logP value, thereby improving its predictive performance for drug-like molecules.

3.3. Performance Evaluation and Analysis of SFG-Drug-Generated Drug Molecules

3.3.1. Visualization Analysis of Lead Drug Molecules Generated by SFG-Drug Model and ZINC-250k Dataset

To differentiate the structural characteristics of generated and dataset molecules, ISOMAP (isometric mapping) was applied for low-dimensional visualization. This nonlinear dimensionality reduction method preserves global geometric structures in high-dimensional chemical space, enabling comparative analysis of molecular distributions. Figure 6 displays the two-dimensional projection of molecules generated by the SFG-Drug model relative to those from the ZINC-250k dataset. As illustrated, the SFG-Drug-generated molecules show extensive overlap with the ZINC-250k molecules in the projected space, indicating structural similarity and coverage within the known chemical space.

This result demonstrates that the SFG-Drug model successfully captured and learned structural features from dataset molecules during training. Additionally, the SFG-Drug model generated molecules dispersed outside the dataset coverage area in various directions, indicating the model’s capability to generate molecules beyond the structural limitations of training data with certain degrees of exploration and novelty.

3.3.2. Generation Performance of SFG-Drug Model and Quality Assessment of Generated Lead Drug Molecules

Table 1. Comparative performance evaluation of SFG-Drug model against state-of-the-art molecular generation methods on MOSES benchmark. An upward arrow indicates that a higher value of the indicator is better. A downward arrow indicates that a lower value of the indicator is better.

Model	Valid (↑)	Unique (↑)	IntDiv1 (↑)	IntDiv2 (↑)	Novelty (↑)
JT-VAE [63]	1.000	1.000	0.855	0.849	0.914
MARS [64]	0.950	1.000	0.856	0.850	0.822
RationaleRL [65]	0.898	1.000	0.851	0.844	0.949
REINVENT2.0 [66]	0.982	0.980	0.820	0.804	1.000
SFG-Drug	1.000	1.000	0.878	0.860	1.000

compares the performance metrics of the SFG-Drug model with other molecular generation models evaluated on the MOSES benchmark platform. As illustrated in Table 1, the SFG-Drug model demonstrates superior performance in molecular validity, uniqueness, and internal diversity compared to benchmark models.

The superior performance of the SFG-Drug model stems from the implementation of low-frequency masking technology in the neural network GRU when simulating drug molecule generation, which increases the selection probability of lower-frequency molecular fragments, thereby enhancing novelty and diversity indicators compared to other models. This demonstrates the potential and effectiveness of the proposed model as a lead drug molecule generation model.

Figure 7 presents the distribution analysis of key pharmacological properties for molecules generated by the SFG-Drug model. As shown in the figure, the QED values of generated lead compounds fall within the [0.2, 0.7] range, SA score values are distributed between [−5, 0], and LogP values span [−2, 5]. These ranges align with the molecular generation criteria established for this experiment.

To better reflect the dual-target objective, we now explicitly report the joint (simultaneous) success rate: the proportion is computed on the intersection set of molecules that meet the favorable docking criterion on both targets. As summarized in Section 3.3.3, over 90% of the generated molecules satisfy the criterion on both MEK1 and mTOR simultaneously, which is more informative than reporting per-target rates alone.

The high distribution range of QED values indicates that these lead drug molecules exhibit excellent drug-likeness with potential drug development value. SA score values reflect molecular synthetic feasibility, and this high proportion distribution demonstrates that lead drug molecules generated by the SFG-Drug model have high synthetic feasibility, providing good foundation for subsequent laboratory synthesis and drug development. The LogP values represent that generated drug molecules possess good lipophilicity with relatively balanced distribution between aqueous and oil phases, enabling effective absorption by the human body for better therapeutic effects.

3.3.3. Molecular Docking Score Analysis

As demonstrated, over 90% of the generated molecules exhibit favorable binding affinity toward the target proteins. This finding not only validates the effectiveness of the SFG-Drug model in drug design but also indicates that these lead compounds possess high drug activity and potential therapeutic efficacy. Notably, the binding affinity analysis reveals that high-affinity interactions typically predict improved therapeutic outcomes, underscoring the significant potential of SFG-Drug-generated molecules for clinical applications.

Because molecular docking can yield false positives (predicted binders that do not bind experimentally), we treat docking scores as a prioritization signal rather than definitive evidence of activity. To improve scientific relevance, all molecules entering docking evaluation are generated from a fragment library filtered by RDKit PAINS/Brenk alert catalogs (Section 2.2.3), which helps reduce assay-interfering chemotypes and spurious high-scoring artifacts. Nonetheless, experimental validation (e.g., biochemical assays and cell-based readouts) remains necessary to confirm dual-target inhibition.

3.3.4. D Molecular Properties of SFG-Drug-Generated Lead Drug Molecules

To validate the structural novelty of lead drug molecules generated by the SFG-Drug model, overall molecular similarity between ZINC-250k dataset molecules and generated lead drug molecules was compared. Molecular similarity was evaluated using 2D descriptors to characterize lead drug molecules, encoding molecular attributes and characteristics in binary form to obtain molecular fingerprints. Subsequently, Tanimoto coefficient indices were used to assess overall molecular similarity through molecular fingerprint calculations.

The Tanimoto coefficient calculation formula is shown in Equation (12):

$$T_c={\displaystyle \frac{N_{AB}}{N_A+N_B-N_{AB}}}$$

(12)

In Equation (12), $N_{AB}$ represents the number of common features between two molecules, while $N_A$ and $N_B$ represent the number of features in the first and second molecules, respectively. Tanimoto coefficients range from 0 to 1, where 0 indicates no common features between molecular sets, and 1 represents identical features. Therefore, Tanimoto coefficients closer to 1 indicate higher similarity between molecular sets.

Figure 8 presents a structural novelty assessment based on molecular similarity analysis. As shown, the Tanimoto coefficients for overall similarity between the lead drug molecules generated by the SFG-Drug model and the training dataset used to develop the SFG-Drug prediction network are predominantly below 0.1, with no values exceeding 0.25. This low degree of similarity indicates that the lead molecules exhibit substantial structural divergence from those in the ZINC-250k dataset. Consequently, the SFG-Drug model demonstrates strong capability in generating structurally novel lead compounds, highlighting its potential utility in de novo drug discovery.

To better interpret the novelty of generated scaffolds, we report the distribution of scaffold similarity rather than the raw scatter plot. We compute Bemis–Murcko scaffolds and measure their similarity using Morgan fingerprints (radius = 2) with the Tanimoto coefficient. Figure 9 shows the histogram of scaffold similarity between the generated molecules and reference inhibitors for each target (MEK1 and mTOR). This representation makes the x-axis unambiguous (similarity in [0, 1]) and avoids visual artifacts from discretization/rounding. In our dataset, the scaffold similarity is generally low-to-moderate (median 0.146, mean 0.147, maximum 0.586; n = 1884), indicating that the model explores novel chemotypes while still retaining some scaffold-level resemblance to known inhibitors.

3.3.5. Molecular Docking Pose and Interaction Analysis of SFG-Drug-Generated Lead Molecules with Protein Targets

Empirically, it seems that three-dimensional binding affinity information and binding conformations between lead drug molecules and protein targets hold important value for drug discovery, treatment design, and improving drug efficacy and safety during drug development and design processes. Optimizing binding affinity between lead drug molecules and protein targets can significantly enhance biological activity of lead drug molecules, enabling tighter binding with protein targets and improving potential therapeutic effects.

The SFG-Drug model was configured to run for 12 h to ensure comprehensive exploration and generation of structurally diverse lead drug molecules. Following screening to eliminate structures violating chemical valency rules or exhibiting molecular duplication, the model successfully yielded 1889 high-quality lead drug candidates.

Figure 10 presents the plain 2D chemical structures of three representative top-ranked candidates generated by SFG-Drug. These molecules were selected as illustrative examples because they satisfy the drug-likeness filtering criteria and exhibit structurally coherent scaffolds suitable for follow-up medicinal chemistry interpretation. In addition, their core frameworks contain common pharmacophore-like patterns (e.g., heteroatom-enriched ring systems and hydrophobic substituents), which are frequently observed in kinase-oriented inhibitor design, suggesting plausible compatibility with target binding environments. The top 20 best-scoring compounds are now shown as clear 2D structures, as shown in Figure S1.

Figure 11 illustrates the detailed molecular interaction networks between representative generated molecules and both target proteins. As shown in Figure 11, the amino group in the cyclohexyl structure of generated molecular structures interacts with glutamic acid GluB121, while the carbonyl group interacts with arginine Arg660. This indicates that SFG-Drug model-generated lead drug molecules form hydrogen bonds or other interactions with specific target residues. These interactions help stabilize lead drug molecule–protein binding, influencing drug biological activity and effects, providing important guidance and clues for subsequent drug design and development work. Interaction types (hydrogen bonds, hydrophobic contacts, salt bridges, and π-interactions) were identified using the protein–ligand interaction profiler (PLIP) on docked complexes, and the interaction diagrams were rendered in PyMOL version 2.5.0 for visualization.

4. Discussion

Research Achievements and Comparative Analysis

We have identified a novel computational framework for dual-target drug molecular generation that significantly advances the field of AI-driven drug discovery within this treatment setting of simultaneous MEK1 and mTOR targeting. The SFG-Drug model demonstrated exceptional performance with perfect validity (1.000), uniqueness (1.000), and novelty (1.000) scores, while achieving the highest internal diversity indices (0.878 for IntDiv1 and 0.860 for IntDiv2) compared to state-of-the-art baseline methods including JT-VAE, MARS, RationaleRL, and REINVENT2.0 [63,64,65,67].

The integration of Monte Carlo tree search with reinforcement learning principles for molecular generation shares conceptual similarities with REINVENT by Olivecrona et al. [66]; however, our methodology fundamentally diverges through its dual-target optimization strategy. Unlike existing single-target generation models that prioritize individual protein interactions over simultaneous multi-target engagement, our approach addresses the critical challenge of polypharmacology via a unified optimization framework. The incorporation of the DigFrag digital fragmentation methodology [59] with low-frequency masking techniques represents a paradigmatic shift from traditional rule-based fragmentation approaches such as BRICS and RECAP, enabling access to previously unexplored regions of chemical space while preserving drug-like properties.

The superior performance of our SFG-Drug model compared to established molecular generation methods highlights several key distinctions warranting detailed analysis. Although Jin et al.’s JT-VAE achieved perfect validity and uniqueness scores [1], our model exceeded their internal diversity metrics by 2.7% and 1.3%, respectively, indicating enhanced exploration of chemical space. This improvement is attributed to the implementation of low-frequency masking within the GRU neural network architecture, which systematically increases the selection probability of rare molecular fragments, thereby expanding structural diversity beyond conventional generation approaches.

The consistency is observed between our docking results and previous dual-target studies. Ref. [68] validates our computational predictions, where over 90% of generated molecules exhibited favorable binding affinity with both MEK1 and mTOR proteins. However, our approach demonstrates unique advantages in scaffold novelty, with Tanimoto coefficients below 0.25 when compared to known inhibitors, suggesting generation of structurally distinct compounds while maintaining binding efficacy. The molecular property distributions observed in our study align with established drug-likeness criteria, with QED values concentrated in the [0.2, 0.7] range and SA scores within [−5, 0], consistent with findings reported by Bickerton et al. [69] for successful drug candidates.

Based on our research findings, several promising avenues for future exploration emerge that could substantially advance the field of computational drug discovery. The development of multi-target optimization algorithms capable of simultaneously addressing three or more protein targets represents a natural extension of our dual-target approach, particularly relevant for complex diseases requiring polypharmacological interventions such as Alzheimer’s disease and metabolic disorders.

The integration of pharmacokinetic and pharmacodynamic modeling into the molecular generation process offers significant potential for creating compounds with optimized ADMET (absorption, distribution, metabolism, excretion, and toxicity) properties. This advancement would require incorporating physiologically based pharmacokinetic models and toxicity prediction algorithms directly into the reward function framework, enabling simultaneous optimization of both efficacy and safety profiles during molecular design.

From a translational perspective, establishing automated synthesis–screening pipelines to rapidly validate computationally generated compounds represents a crucial next step toward practical implementation. Collaboration with pharmaceutical industry partners could facilitate the development of integrated platforms that combine AI-driven molecular generation with robotic synthesis and high-throughput biological evaluation systems, thereby accelerating the transition from in silico prediction to experimental validation.

The exploration of allosteric drug design through our framework presents another frontier, where generated molecules could target alternative binding sites to achieve dual-target modulation. This approach may overcome limitations of traditional competitive inhibition and enable novel therapeutic mechanisms for challenging drug targets. Furthermore, extending the methodology to protein–protein interaction modulators and epigenetic targets could significantly broaden the therapeutic scope of dual-target drug design.

Limitation and future work: We have not yet performed chemical synthesis and in vitro biological validation of the proposed candidates. In future work, we will assess practical synthetic feasibility using retrosynthesis success rates and/or expert medicinal chemistry review, followed by experimental synthesis and testing when feasible.

The integration of advanced neural network architectures, such as transformer-based models with attention mechanisms specifically designed for molecular fragment relationships, could improve both generation quality and computational performance. Furthermore, implementing active learning strategies that prioritize high-value molecular candidates could optimize resource allocation and accelerate the discovery process, ultimately bridging the gap between computational predictions and experimental validation in modern drug discovery pipelines.

5. Conclusions

This study presents a novel dual-target drug molecular generation model (SFG-Drug) based on reinforcement learning that effectively combines Monte Carlo tree search with GRU neural networks for simultaneous targeting of MEK1 and mTOR proteins. The development of dual-target therapeutic agents represents a critical advancement in modern drug discovery, addressing the limitations of single-target approaches that often lead to drug resistance and reduced therapeutic efficacy in complex diseases such as cancer.

The findings that we have presented suggest that the SFG-Drug model achieves superior performance across all evaluated metrics compared to state-of-the-art baseline methods. The model demonstrated perfect validity (1.000), uniqueness (1.000), and novelty (1.000) scores while maintaining the highest internal diversity indices (0.878 for IntDiv1 and 0.860 for IntDiv2) on the MOSES benchmark platform. This is important for drug discovery because it indicates that the generated molecules possess both chemical validity and structural diversity, essential prerequisites for successful lead compound optimization.

The methodological framework employs Monte Carlo tree search guided by reinforcement learning, using molecular docking scores as reward functions to optimize dual-target engagement. The integration of a variational autoencoder architecture with GRU networks addresses the limitations of traditional RNN models in capturing long-range dependencies while preserving computational efficiency. Furthermore, the combination of the DigFrag digital fragmentation methodology with low-frequency masking techniques enables the model to explore previously inaccessible regions of chemical space while retaining drug-like properties.