Molecular Graph Research Articles

MGT: Machine Learning Accelerates Performance Prediction of Alloy Catalytic Materials.

The application of deep learning technology in the field of materials science provides a new method for predicting the adsorption energy of high-performance alloy catalysts in hydrogen evolution reactions and material discovery. The activity and selectivity of catalytic materials are mainly influenced by the properties and positions of active sites and adsorption sites. However, current deep learning models have not sufficiently focused on the importance of active atoms and adsorbates, instead placing more emphasis on the overall structure of the catalytic materials. In this paper, the overall molecular graph and a masked graph, which ignores fixed atoms, are separately input into the Masked Graph Transformer (MGT) network to enhance the model's ability to recognize key sites in catalytic reactions. Second, we introduce a nonlinear message-passing mechanism to improve the dot-product attention in the Transformer and capture the directional information on the relative positions of nodes by integrating molecular geometric information through deep tensor products. Subsequently, we constructed the NLMP-TransNet framework, which combines MPNN and Transformer and optimizes the model's learning and prediction capabilities through weight sharing and residual connections. The MGT achieves an error rate of 0.5447 eV on the small data set OC20-Ni, surpassing existing technologies. Ablation studies confirm the necessity of focusing on site features for accurate adsorption energy prediction. Code is available at https://github.com/KristinSun/OCP-MGT.git.

On the multiplicative sum Zagreb index of molecular graphs

Abstract Multiplicative sum Zagreb index is a modified version of the famous Zagreb indices. For a graph G G , the multiplicative sum Zagreb index is defined as Π 1 * ( G ) = ∏ u v ∈ E ( G ) ( d G ( u ) + d G ( v ) ) {\Pi }_{1}^{* }\left(G)={\prod }_{uv\in E\left(G)}\left({d}_{G}\left(u)+{d}_{G}\left(v)) , where E ( G ) E\left(G) is the edge set of G G and d G ( u ) {d}_{G}\left(u) stands for the degree of vertex u u in G G . In this article, we determine the extremal multiplicative sum Zagreb indices among all n n -vertex molecular trees, molecular unicyclic graphs, molecular bicyclic graphs and molecular tricyclic graphs.

CGPDTA: An Explainable Transfer Learning-Based Predictor With Molecule Substructure Graph for Drug-Target Binding Affinity.

Identifying interactions between drugs and targets is crucial for drug discovery and development. Nevertheless, the determination of drug-target binding affinities (DTAs) through traditional experimental methods is a time-consuming process. Conventional approaches to predicting drug-target interactions (DTIs) frequently prove inadequate due to an insufficient representation of drugs and targets, resulting in ineffective feature capture and questionable interpretability of results. To address these challenges, we introduce CGPDTA, a novel deep learning framework empowered by transfer learning, designed explicitly for the accurate prediction of DTAs. CGPDTA leverages the complementarity of drug-drug and protein-protein interaction knowledge through advanced drug and protein language models. It further enhances predictive capability and interpretability by incorporating molecular substructure graphs and protein pocket sequences to represent local features of drugs and targets effectively. Our findings demonstrate that CGPDTA not only outperforms existing methods in accuracy but also provides meaningful insights into the predictive process, marking a significant advancement in the field of drug discovery.

FormulationBCS: A Machine Learning Platform Based on Diverse Molecular Representations for Biopharmaceutical Classification System (BCS) Class Prediction.

The Biopharmaceutics Classification System (BCS) has facilitated biowaivers and played a significant role in enhancing drug regulation and development efficiency. However, the productivity of measuring the key discriminative properties of BCS, solubility and permeability, still requires improvement, limiting high-throughput applications of BCS, which is essential for evaluating drug candidate developability and guiding formulation decisions in the early stages of drug development. In recent years, advancements in machine learning (ML) and molecular characterization have revealed the potential of quantitative structure-performance relationships (QSPR) for rapid and accurate in silico BCS classification. The present study aims to develop a web platform for high-throughput BCS classification based on high-performance ML models. Initially, four data sets of BCS-related molecular properties: log S, log P, log D, and log Papp were curated. Subsequently, 6 ML algorithms or deep learning frameworks were employed to construct models, with diverse molecular representations ranging from one-dimensional molecular fingerprints, descriptors, and molecular graphs to three-dimensional molecular spatial coordinates. By comparing different combinations of molecular representations and learning algorithms, LightGBM exhibited excellent performance in solubility prediction, with an R2 of 0.84; AttentiveFP outperformed others in permeability prediction, with R2 values of 0.96 and 0.76 for log P and log D, respectively; and XGBoost was the most accurate for log Papp prediction, with an R2 of 0.71. When externally validated on a marketed drug BCS category data set, the best-performing models achieved classification accuracies of over 77 and 73% for solubility and permeability, respectively. Finally, the well-trained models were embedded into the first ML-based BCS class prediction web platform (x f), enabling pharmaceutical scientists to quickly determine the BCS category of candidate drugs, which will aid in the high-throughput BCS assessment for candidate drugs during the preformulation stage, thereby promoting reduced risk and enhanced efficiency in drug development and regulation.

MolGraph: a Python package for the implementation of molecular graphs and graph neural networks with TensorFlow and Keras.

Molecular machine learning (ML) has proven important for tackling various molecular problems, such as predicting molecular properties based on molecular descriptors or fingerprints. Since relatively recently, graph neural network (GNN) algorithms have been implemented for molecular ML, showing comparable or superior performance to descriptor or fingerprint-based approaches. Although various tools and packages exist to apply GNNs in molecular ML, a new GNN package, named MolGraph, was developed in this work with the motivation to create GNN model pipelines highly compatible with the TensorFlow and Keras application programming interface (API). MolGraph also implements amodule to accommodate the generation of small molecular graphs, which can be passed to a GNN algorithm to solve a molecular ML problem. To validate the GNNs, benchmarking was conducted using the datasets from MoleculeNet, as well as three chromatographic retention time datasets. The benchmarking results demonstrate that the GNNs performed in line with expectations. Additionally, the GNNs proved useful for molecular identification and improved interpretability of chromatographic retention time data. MolGraph is available at https://github.com/akensert/molgraph . Installation, tutorials and implementation details can be found at https://molgraph.readthedocs.io/en/latest/ .

An Effective and Robust Approach Based on Malatya Centrality Algorithm for Interpreting Cheminformatics Graphs Using Maximum Clique

Cheminformatics graphs are derived by transforming the atomic nodes and bonds of chemical compounds into graph structures and are used to analyze the chemical and structural properties of molecules. In this study, an effective and robust approach based on the Malatya Centrality Algorithm is proposed for identifying the maximum clique in cheminformatics graphs. The proposed method transforms cheminformatics graphs by taking their complement and calculates the Malatya centrality values for these graphs. Using these values, the minimum independent set is identified in the complemented graph, which corresponds to the set of nodes forming the maximum clique in the original graph. The study demonstrates, through tests on various cheminformatics graphs, including enzyme and molecular graphs, that maximum clique and chromatic number values provide significant insights into the structural properties of these graphs. Notably, the maximum clique value was often calculated as 2 for bipartite graphs. Additionally, it was observed that enzyme graphs exhibit maximum clique and chromatic number values that are optimal or near-optimal, with some graphs possessing perfect graph properties. The proposed approach offers an effective and robust solution for structural analysis in cheminformatics graphs.

How Good are Current Pocket-Based 3D Generative Models?: The Benchmark Set and Evaluation of Protein Pocket-Based 3D Molecular Generative Models.

The development of a three-dimensional (3D) molecular generative model based on protein pockets has recently attracted a lot of attention. This type of model aims to achieve the simultaneous generation of molecular graphs and 3D binding conformation under the constraint of protein binding. Various pocket-based generative models have been proposed; however, currently, there is a lack of systematic and objective evaluation metrics for these models. To address this issue, a comprehensive benchmark data set, named POKMOL-3D, is proposed to evaluate protein pocket-based 3D molecular generative models. It includes 32 protein targets together with their known active compounds as a test set to evaluate the versatility of generation models to mimic the real-world scenario. Additionally, a series of two-dimensional (2D) and 3D evaluation metrics with some newly created ones was integrated to assess the quality of generated molecular structures and their binding conformations. It is expected that this work can enhance our comprehension of the effectiveness and weakness of current 3D generative models and stimulate the discussion on challenges and useful guidance for developing the next wave of molecular generative models.

Discovery of novel VEGFR2 inhibitors against non-small cell lung cancer based on fingerprint-enhanced graph attention convolutional network

Despite the proven inhibitory effects of drugs targeting vascular endothelial growth factor receptor 2 (VEGFR2) on solid tumors, including non-small cell lung cancer (NSCLC), the development of anti-NSCLC drugs solely targeting VEGFR2 still faces risks such as off-target effects and limited efficacy. This study aims to develop a novel fingerprint-enhanced graph attention convolutional network (FnGATGCN) model for predicting the activity of anti-NSCLC drugs. Employing a multimodal fusion strategy, the model integrates a feature extraction layer that comprises molecular graph feature extraction and molecular fingerprint feature extraction. The performance evaluation results indicate that the model exhibits high accuracy and stability in predicting activity. Moreover, we explored the relationship between molecular features and biological activity through visualization analysis, thus improving the interpretability of the approach. Utilizing this model, we screened the ZINC database and conducted high-precision molecular docking, leading to the identification of 11 potential active molecules. Subsequently, molecular dynamics simulations and free energy calculations were performed. The results demonstrate that all 11 aforementioned molecules can stably bind to VEGFR2 under dynamic conditions. Among the short-listed compounds, the top six exhibited satisfactory inhibitory activity against VEGFR2 and A549 cells. Especially, compound Z-3 displayed VEGFR2 inhibitory with IC50 values of 0.88 μM, and anti-proliferative activity against A549 cells with IC50 values of 4.23 ± 0.45 μM. This approach combines the advantages of target-based and phenotype-based screening, facilitating the rapid and efficient identification of candidate compounds with dual activity against VEGFR2 and A549 cell lines. It provides new insights and methods for the development of anti-NSCLC drugs. Furthermore, further biological activity tests revealed that Z1-Z3 and Z6 manifested relatively strong antiproliferative activities against NCI-H23 and NCI-H460, and relatively low toxicity towards GES-1. The hit compounds were promising candidates for the further development of novel VEGFR2 inhibitors against NSCLC.

Multimodal Fused Deep Learning for Drug Property Prediction: Integrating Chemical Language and Molecular Graph

Accurately predicting molecular properties is a challenging but essential task in drug discovery. Recently, many mono-modal deep learning methods have been successfully applied to molecular property prediction. However, mono-modal learning is inherently limited as it relies solely on a single modality of molecular representation, which restricts a comprehensive understanding of drug molecules. To overcome the limitations, we propose a multimodal fused deep learning (MMFDL) model to leverage information from different molecular representations. Specifically, we construct a triple-modal learning model by employing Transformer-Encoder, BiGRU, and graph convolutional network (GCN) to process three modalities of information from chemical language and molecular graph: SMILES-encoded vectors, ECFP fingerprints, and molecular graphs, respectively. We evaluate the proposed triple-modal model using five fusion approaches on six molecule datasets including Delaney, Llinas2020, Lipophilicity, SAMPL, BACE, and pKa from DataWarrior. The results show that the MMFDL model achieves the highest Pearson coefficients, and stable distribution of Pearson coefficients in a random splitting test, outperforming mono-modal models in accuracy and reliability. Furthermore, we validate the generalization ability of our model in the prediction of binding constants for protein-ligand complex molecules and assess the resilience capability against noise. Through analysis of feature distributions in chemical space and the assigned contribution of each modal model, we demonstrate that the MMFDL model shows the ability to acquire complementary information by using proper models and suitable fusion approaches. By leveraging diverse sources of bioinformatics information, multimodal deep learning models hold the potential for successful drug discovery.

TEMPERATURE INDICES OF WELL KNOWN DENDRIMER NETWORKS

Chemical graph theory is a branch of graph theory. In this field, molecules are modeled using graph theory and a mathematical approach is obtained. Thus, predictions can be made about the physical, chemical and bioactivity properties of molecules. In this study, temperature indices depending on the vertex degree are considered. Temperature indices of Polyamidoamine (PAMAM) dendrimers, Porphyrin core dendrimers are obtained and the results are compared numerically using the MATLAB program.

Advanced AI-Driven Prediction of Pregnancy-Related Adverse Drug Reactions.

Ensuring drug safety during pregnancy is critical due to the potential risks to both the mother and fetus. However, the exclusion of pregnant women from clinical trials complicates the assessment of adverse drug reactions (ADRs) in this population. This study aimed to develop and validate risk prediction models for pregnancy-related ADRs of drugs using advanced Machine Learning (ML) and Deep Learning (DL) techniques, leveraging real-world data from the FDA Adverse Event Reporting System. We explored three methods─Information Component, Reporting Odds Ratio, and 95% confidence interval of ROR─for classifying drugs into high-risk and low-risk categories. DL models, including Directed Message Passing Neural Networks (DMPNN), Graph Neural Networks, and Graph Convolutional Networks, were developed and compared to traditional ML models like Random Forest, Support Vector Machines, and XGBoost. Among these, the DMPNN model, which integrated molecular graph information and molecular descriptors, exhibited the highest predictive performance, particularly at the preferred term level. The model was validated against external data sets from SIDER and DailyMed, demonstrating strong generalizability. Additionally, the model was applied to assess the risk of 22 oral hypoglycemic drugs, and potential substructure alerts for pregnancy-related ADRs were identified. These findings suggest that the DMPNN model is a valuable tool for predicting ADRs in pregnant women, offering significant advancement in drug safety assessment and providing crucial insights for safer medication use during pregnancy.

Group graph: a molecular graph representation with enhanced performance, efficiency and interpretability

The exploration of chemical space holds promise for developing influential chemical entities. Molecular representations, which reflect features of molecular structure in silico, assist in navigating chemical space appropriately. Unlike atom-level molecular representations, such as SMILES and atom graph, which can sometimes lead to confusing interpretations about chemical substructures, substructure-level molecular representations encode important substructures into molecular features; they not only provide more information for predicting molecular properties and drug‒drug interactions but also help to interpret the correlations between molecular properties and substructures. However, it remains challenging to represent the entire molecular structure both intactly and simply with substructure-level molecular representations. In this study, we developed a novel substructure-level molecular representation and named it a group graph. The group graph offers three advantages: (a) the substructure of the group graph reflects the diversity and consistency of different molecular datasets; (b) the group graph retains molecular structural features with minimal information loss because the graph isomorphism network (GIN) of the group graph performs well in molecular properties and drug‒drug interactions prediction, showing higher accuracy and efficiency than the model of other molecular graphs, even without any pretraining; and (c) the molecular property may change when the substructure is substituted with another of differing importance in group graph, facilitating the detection of activity cliffs. In addition, we successfully predicted structural modifications to improve blood‒brain barrier permeability (BBBP) via the GIN of group graph. Therefore, the group graph takes advantages for simultaneously representing molecular local characteristics and global features.Scientific contribution The group graph, as a substructure-level molecular representation, has the ability to retain molecular structural features with minimal information loss. As a result, it shows superior performance in predicting molecular properties and drug‒drug interactions with enhanced efficiency and interpretability.

GT-NMR: a novel graph transformer-based approach for accurate prediction of NMR chemical shifts

In this work, inspired by the graph transformer, we presented an improved protocol, termed GT-NMR, which integrates 2D molecular graph representation with Transformer architecture, for accurate yet efficient prediction of NMR chemical shifts. The effectiveness of the GT-NMR was thoroughly examined with the standard nmrshiftdb2 dataset, 37 natural products and structural elucidation of 11 pairs of natural products. Systematical analysis affirms that GT-NMR outperforms traditional graph-based methods in all aspects, achieving state-of-the-art performance, with the mean absolute error of 0.158 and 1.189 ppm in predicting 1H and 13C NMR chemical shifts, respectively, for the standard nmrshiftdb2 dataset. Further scrutiny of its practical applications indicates that GT-NMR's efficacy is closely tied to molecular complexity, as quantified by the size-normalized spatial score (nSPS). For relatively simple molecules (nSPS < = 27.71), GT-NMR performs comparably to the best density functional while its effectiveness significantly diminishes with complex molecules characterized by higher nSPS values (nSPS > = 38.42). This trend is consistent across other graph-based NMR chemical shift prediction methods as well. Therefore, while employing GT-NMR or other graph-based methods for the rapid and routine prediction of NMR chemical shifts, it is advisable to utilize nSPS to assess their suitability. The source codes and trained model of GT-NMR are publicly available at GitHub.Scientific contributionGT-NMR, which combines the 2D molecular graph representation with the Transformer architecture, was implemented for the first time to predict atom-level NMR chemical shifts, achieving state-of-the-art performance. More importantly, the reliability of the GT-NMR and graph-based methods was assessed for the first time in terms of molecular complexity, as quantified by the size-normalized spacial score (nSPS). Systematical scrutiny demonstrated that GT-NMR offer a valuable way for routine application in structural screening and elucidation of relatively simple molecules.

AABBA Graph Kernel: Atom-Atom, Bond-Bond, and Bond-Atom Autocorrelations for Machine Learning.

Graphs are one of the most natural and powerful representations available for molecules; natural because they have an intuitive correspondence to skeletal formulas, the language used by chemists worldwide, and powerful, because they are highly expressive both globally (molecular topology) and locally (atom and bond properties). Graph kernels are used to transform molecular graphs into fixed-length vectors, which, based on their capacity of measuring similarity, can be used as fingerprints for machine learning (ML). To date, graph kernels have mostly focused on the atomic nodes of the graph. In this work, we developed a graph kernel based on atom-atom, bond-bond, and bond-atom (AABBA) autocorrelations. The resulting vector representations were tested on regression ML tasks on a data set of transition metal complexes; a benchmark motivated by the higher complexity of these compounds relative to organic molecules. In particular, we tested different flavors of the AABBA kernel in the prediction of the energy barriers and bond distances of the Vaska's complex data set (Friederich et al., Chem. Sci., 2020, 11, 4584). For a variety of ML models, including neural networks, gradient boosting machines, and Gaussian processes, we showed that AABBA outperforms the baseline including only atom-atom autocorrelations. Dimensionality reduction studies also showed that the bond-bond and bond-atom autocorrelations yield many of the most relevant features. We believe that the AABBA graph kernel can accelerate the exploration of large chemical spaces and inspire novel molecular representations in which both atomic and bond properties play an important role.

Conformalized Graph Learning for Molecular ADMET Property Prediction and Reliable Uncertainty Quantification.

Drug discovery and development is a complex and costly process, with a substantial portion of the expense dedicated to characterizing the absorption, distribution, metabolism, excretion, and toxicity (ADMET) properties of new drug candidates. While the advent of deep learning and molecular graph neural networks (GNNs) has significantly enhanced in silico ADMET prediction capabilities, reliably quantifying prediction uncertainty remains a critical challenge. The performance of GNNs is influenced by both the volume and the quality of the data. Hence, determining the reliability and extent of a prediction is as crucial as achieving accurate predictions, especially for out-of-domain (OoD) compounds. This paper introduces a novel GNN model called conformalized fusion regression (CFR). CFR combined a GNN model with a joint mean-quantile regression loss and an ensemble-based conformal prediction (CP) method. Through rigorous evaluation across various ADMET tasks, we demonstrate that our framework provides accurate predictions, reliable probability calibration, and high-quality prediction intervals, outperforming existing uncertainty quantification methods.

Accurate and transferable drug-target interaction prediction with DrugLAMP.

Accurate prediction of drug-target interactions (DTIs), especially for novel targets or drugs, is crucial for accelerating drug discovery. Recent advances in pretrained language models (PLMs) and multi-modal learning present new opportunities to enhance DTI prediction by leveraging vast unlabeled molecular data and integrating complementary information from multiple modalities. We introduce DrugLAMP (PLM-assisted multi-modal prediction), a PLM-based multi-modal framework for accurate and transferable DTI prediction. DrugLAMP integrates molecular graph and protein sequence features extracted by PLMs and traditional feature extractors. We introduce two novel multi-modal fusion modules: (i) pocket-guided co-attention (PGCA), which uses protein pocket information to guide the attention mechanism on drug features, and (ii) paired multi-modal attention (PMMA), which enables effective cross-modal interactions between drug and protein features. These modules work together to enhance the model's ability to capture complex drug-protein interactions. Moreover, the contrastive compound-protein pre-training (2C2P) module enhances the model's generalization to real-world scenarios by aligning features across modalities and conditions. Comprehensive experiments demonstrate DrugLAMP's state-of-the-art performance on both standard benchmarks and challenging settings simulating real-world drug discovery, where test drugs/targets are unseen during training. Visualizations of attention maps and application to predict cryptic pockets and drug side effects further showcase DrugLAMP's strong interpretability and generalizability. Ablation studies confirm the contributions of the proposed modules. Source code and datasets are freely available at https://github.com/Lzcstan/DrugLAMP. All data originate from public sources.

Molecular Complexity-Inspired Synthetic Strategies toward the Calyciphylline A-Type Daphniphyllum Alkaloids Himalensine A and Daphenylline.

In this report, we detail two distinct synthetic approaches to calyciphylline A-type Daphniphyllum alkaloids himalensine A and daphenylline, which are inspired by our analysis of the structural complexity of these compounds. Using MolComplex, a Python-based web application that we have developed, we quantified the structural complexity of all possible precursors resulting from one-bond retrosynthetic disconnections. This led to the identification of transannular bonds as especially simplifying to the molecular graph, and, based on this analysis, we pursued a total synthesis of himalensine A from macrocyclic intermediates with planned late-stage transannular ring formations. Despite initial setbacks in accessing an originally designed macrocycle, targeting a simplified macrocycle ultimately enabled investigation of this intermediate's unique transannular reactivity. Given the lack of success to access himalensine A based solely on molecular graph analysis, we revised our approach to the related alkaloid, daphenylline. Herein, we also provide the details of the various synthetic challenges that we encountered and overcame en route to a total synthesis of daphenylline. First, optimization of a Rh-mediated intramolecular Buchner/6π-electrocyclic ring-opening sequence enabled construction of the pentacyclic core. We then describe various attempts to install a key quaternary methyl group and, ultimately, our solution to leverage a [2 + 2] photocycloaddition/bond cleavage sequence to achieve this elusive goal. Finally, a late-stage Friedel-Crafts cyclization and deoxygenation facilitated the 11-step total synthesis, which was made formally enantioselective by a Rh-mediated dihydropyridone conjugate arylation. Complexity analysis of the daphenylline synthesis highlights how complexity-building/C-C cleavage combinations can be uniquely effective in achieving synthetic outcomes.

CPIScore: A Deep Learning Approach for Rapid Scoring and Interpretation of Protein-Ligand Binding Interactions.

Protein-ligand binding affinity prediction is a crucial and challenging task in the field of drug discovery. However, traditional simulation-based computational approaches are often prohibitively time-consuming, limiting their practical utility. In this study, we introduce a novel deep learning method, CPIScore, which leverages the capabilities of Transformer and Graph Convolutional Networks (GCN) to enhance the prediction of protein-ligand binding affinity. CPIScore utilizes the Transformer architecture to capture comprehensive global contexts of protein and ligand sequences, while the GCN component effectively extracts local features from small molecular graphs. Our results demonstrate that CPIScore surpasses both traditional machine learning and other deep learning models in accuracy, achieving a Pearson's r of 0.74 on our test set. Furthermore, CPIScore has been validated across multiple targets, proving its ability to discern inhibitors from a diverse compound library with high enrichment rates. Notably, when applied to a generated focused library of compounds, CPIScore successfully identified six potent small-molecule inhibitors of ATR, which were tested experimentally and four small molecules exhibited inhibitory activity below ten nanomoles. These results highlight CPIScore's potential to significantly streamline and enhance the efficiency of drug discovery processes.

Extremizing antiregular graphs by modifying total σ-irregularity

The total σ-irregularity is given by σt(G)=∑{u,v}⊆V(G)(dG(u)−dG(v))2, where dG(z) indicates the degree of a vertex z within the graph G. It is known that the graphs maximizing σt-irregularity are split graphs with only a few distinct degrees. Since one might typically expect that graphs with as many distinct degrees as possible achieve maximum irregularity measures, we modify this invariant to σtf(n)(G)=∑{u,v}⊆V(G)|dG(u)−dG(v)|f(n), where n=|V(G)| and f(n)>0. We study under what conditions the above modification obtains its maximum for antiregular graphs. We consider general graphs, trees, and chemical graphs, and accompany our results with a few problems and conjectures.

The Minimal Molecular Tree for the Exponential Randić Index

Topological indices are numerical parameters that provide a way to quantify the structural features of molecules using their graph representations. In chemical graph theory, these indices have been effectively employed to predict various physico-chemical properties of molecules. Among these, the Randić index stands out as a classical and widely used molecular descriptor in chemistry and pharmacology. The Randić index R(G) for a given graph G is defined as R(G)=∑vivj∈E(G)1d(vi)d(vj), where d(vi) represents the degree of vertex vi and E(G) is the set of edges in the graph G. Given the Randić index’s strong discrimination ability in describing molecular structures, a variant known as the exponential Randić index was recently introduced. The exponential Randić index ER(G) for a graph G is defined as ER(G)=∑vivj∈E(G)e1d(vi)d(vj). This paper further explores and fully characterizes the minimal molecular trees in relation to the exponential Randić index. Moreover, the chemical relevance of the exponential Randić index is also investigated.