Quantitative Structure-property Relationship Models Research Articles

Chemometric modeling of pharmaceuticals for partitioning between sludge and aqueous phase during the wastewater treatment process.

Computational techniques, such as quantitative structure-property relationships (QSPRs), can play a significant role in exploring the important chemical features essential for the degree of sorption or sludge/water partition coefficient (Kd) towards sewage sludge of wastewater treatment process to evaluate the environmental consequence and risk of pharmaceuticals. The current research work aims to construct a predictive QSPR model for the sorption of 148 diverse active pharmaceutical ingredients (APIs) in sewage sludge during wastewater treatment. For the development of the model, we employed easily computable 2D descriptors as independent variables. The model has been developed following the Organization for Economic Cooperation and Development's (OECD) guidelines. It has undergone internal and external validation using a variety of methodologies, as well as been tested for its applicability domain. A measure of hydrophobicity, i.e., MLOGP2, showed the most promising contribution in modeling the sorption coefficient of APIs. Among other parameters, the number of tertiary aromatic amines, the presence of electronegative atoms like N, O, and Cl, the size of a molecule, the number of aromatic hydroxyl groups, the presence of substituted aromatic nitrogen atoms and alkyl-substituted tertiary carbon atoms were also found to be influential for the regulation of solid water partition coefficient of APIs during the wastewater treatment process. The statistical validity tests performed on the developed partial least squares (PLS) model showed that it is statistically evident, robust, and predictive (R2Train = 0.750, Q2LOO = 0.683, Q2F1 = 0.655, Q2F2 (or R2Test) = 0.651). In addition, the predictivity of the constructed model was further inspected by using the "prediction reliability indicator" tool for 14 external APIs.

Prediction of critical micelle concentration for per- and polyfluoroalkyl substances

ABSTRACT In this study, we focus on the development of Quantitative Structure-Property Relationship (QSPR) models to predict the critical micelle concentration (CMC) for per- and polyfluoroalkyl substances (PFASs). Experimental CMC values for both fluorinated and non-fluorinated compounds were meticulously compiled from existing literature sources. Our approach involved constructing two distinct types of models based on Support Vector Machine (SVM) algorithms applied to the dataset. Type (I) models were trained exclusively on CMC values for fluorinated compounds, while Type (II) models were developed utilizing the entire dataset, incorporating both fluorinated and non-fluorinated compounds. Comparative analyses were conducted against reference data, as well as between the two model types. Encouragingly, both types of models exhibited robust predictive capabilities and demonstrated high reliability. Subsequently, the model having the broadest applicability domain was selected to complement the existing experimental data, thereby enhancing our understanding of PFAS behaviour.

Decoding Nonsteroidal Anti-inflammatory Drugs with Sombor Invariants: A Quantum Leap in QSPR Modeling

We investigate the Sombor indices for a diverse group of nonsteroidal anti-inflammatory drugs (NSAIDs) to understand their molecular architecture and physicochemical properties. By utilizing quantitative structure-property relationship (QSPR) modeling, we establish mathematical models linking Sombor indices to key pharmacodynamic and toxicological parameters. Our study sheds light on how the molecular composition of NSAIDs influences their drug profiles and biological behavior, offering valuable insights for drug development and safety assessment.

Optimization of Monte Carlo Method-Based QSPR modeling for lipophilicity in radiopharmaceuticals

Radiopharmaceuticals have emerged as essential tools in modern medicine, playing a pivotal role in disease diagnosis and treatment. This paper explores the application of Quantitative Structure-Property Relationships (QSPR) for predicting logP of a dataset comprising 121 molecules. Utilizing a hybrid optimal descriptor that combines SMILES and the hydrogen suppressed graph, QSPR models are constructed. The QSPR model established in splits 2, 6, and 8, demonstrating the highest R2 values for the validation set (0.8859, 0.8816, and 0.8144, respectively), is identified as the leading model. Moreover, these leading models provide insights into the promoters influencing the increase and decrease of logP.

Development of quantum machine learning to evaluate the corrosion inhibition capability of pyrimidine compounds

This investigation employs a quantum neural network (QNN) synergistically integrated with a quantitative structure-property relationship (QSPR) model for the comprehensive evaluation of corrosion inhibition efficiency (CIE) in pyrimidine compounds. The QNN, exhibiting superior performance over conventional methodologies, attains commendable predictive precision, as evidenced by metrics: R2 = 0.981, RMSE = 0.53, MAE = 0.43, and MAD = 0.42. The prognosticated CIE values for the synthesized derivatives (P1, P2, P3) are 91.17, 98.69, and 99.21, respectively. This pioneering approach holds promise for a transformative impact on both the manufacturing and evaluation procedures associated with novel anti-corrosion materials.

Comparative analysis of temperature-based graphical indices for correlating the total π-electron energy of benzenoid hydrocarbons

In a graph [Formula: see text], the temperature [Formula: see text] of a vertex [Formula: see text] is defined as [Formula: see text], where n is the order of G and [Formula: see text] is the valency/degree of x. A topological/graphical index [Formula: see text] is a map [Formula: see text], where ∑ (respectively, [Formula: see text]) is the set of simple connected graphs (respectively, real numbers). Graphical indices are employed in quantitative structure-property relationship (QSPR) modeling to predict physicochemical/thermodynamic/biological characteristics of a compound. A temperature-based graphical index of a chemical graph G is defined as [Formula: see text], where [Formula: see text] is a symmetric 2-variable map. In this paper, we introduce two new novel temperature-based indices named as the reduced reciprocal product-connectivity temperature ([Formula: see text]) index and the geometric-arithmetic temperature ([Formula: see text]) index. The predictive potential of these indices has been investigated by employing them in structure-property modeling of the total [Formula: see text]-electronic energy [Formula: see text] of benzenoid hydrocarbons. In order to validate the statistical inference, the lower 30 BHs have been opted as test molecules as their experimental data for [Formula: see text] is also publicly available. First, we employ a computer-based computational method to compute temperature indices of 30 lower BHs. Certain QPSR models are proposed by utilizing the experimental data of [Formula: see text] for the BHs. Our statistical analysis suggests that the most efficient regression models are, in fact, linear. Our statistical analysis asserts that both [Formula: see text] and [Formula: see text] outperformed all the existing temperature indices for correlating [Formula: see text] for the BHs. The results suggest their further employability in QSPR modeling. Importantly, our research contributes toward countering proliferation of graphical indices.

Solubility evaluation of palm-based Mono-diacylglycerols (MDAGs) in food grade solvent (hexane, ethanol, acetone, water) using QSPR model approach

Mono-diacylglycerols (MDAGs) are emulsifiers widely used in the food industry. MDAGs based on refined bleached deodorized palm stearin (RBDPS) have not been widely developed. MDAGs have been synthesized using glicerolysis between RBDPS and glycerols. Due to their low solubility in food-grade solvents (hexane, ethanol, acetone, and water), it has been difficult to purify or fractionate MDAGs only by a simple method. This research attempted to develop a model of MDAGs solubility in food-grade solvents and understand the parameters that influence the solubility of MDAGs in food-grade solvents. The process used a combination of experimental data collection and quantitative structure–property relationship (QSPR) models. The QSPR model for MDAGs solubility in a single and binary solvent demonstrated that the descriptors of Δ dipole moment (Δµ), E HOMO, E LUMO, electronic energy, gap energy HOMO-LUMO (ΔE1, ΔE2) softness (S), electrophilicity index (ω), and electron transfer (ΔN) have a significant impact in determining the solubility of MDAGs. Both the single and the binary solvents solubility models can give satisfactory prediction results: the square of the correlation coefficient (R2pred) was 0.933 and 0.948, and the root-mean-square error (RMSE) was 0.075 and 0.031, respectively, for the whole data set. In addition, this paper provided a new and effective method for predicting the solubility of MDAGs in single and binary food-grade solvent systems.

Advancing material property prediction: using physics-informed machine learning models for viscosity

In materials science, accurately computing properties like viscosity, melting point, and glass transition temperatures solely through physics-based models is challenging. Data-driven machine learning (ML) also poses challenges in constructing ML models, especially in the material science domain where data is limited. To address this, we integrate physics-informed descriptors from molecular dynamics (MD) simulations to enhance the accuracy and interpretability of ML models. Our current study focuses on accurately predicting viscosity in liquid systems using MD descriptors. In this work, we curated a comprehensive dataset of over 4000 small organic molecules’ viscosities from scientific literature, publications, and online databases. This dataset enabled us to develop quantitative structure–property relationships (QSPR) consisting of descriptor-based and graph neural network models to predict temperature-dependent viscosities for a wide range of viscosities. The QSPR models reveal that including MD descriptors improves the prediction of experimental viscosities, particularly at the small data set scale of fewer than a thousand data points. Furthermore, feature importance tools reveal that intermolecular interactions captured by MD descriptors are most important for viscosity predictions. Finally, the QSPR models can accurately capture the inverse relationship between viscosity and temperature for six battery-relevant solvents, some of which were not included in the original data set. Our research highlights the effectiveness of incorporating MD descriptors into QSPR models, which leads to improved accuracy for properties that are difficult to predict when using physics-based models alone or when limited data is available.Graphical

QSPR for the prediction of critical micelle concentration of different classes of surfactants using machine learning algorithms

The determination of the critical micelle concentration (CMC) is a crucial factor when evaluating surfactants, making it an essential tool in studying the properties of surfactants in various industrial fields. In this present research, we assembled a comprehensive set of 593 different classes of surfactants including, anionic, cationic, nonionic, zwitterionic, and Gemini surfactants to establish a link between their molecular structure and the negative logarithmic value of critical micelle concentration (pCMC) utilizing quantitative structure-property relationship (QSPR) methodologies. Statistical analysis revealed that a set of 14 significant Mordred descriptors (SlogP, GATS6d, nAcid, GATS8dv, GATS4dv, PEOE_VSA11, GATS8d, ATS0p, GATS1d, MATS5p, GATS3d, NdssC, GATS6dv and EState_VSA4), along with temperature, served as appropriate inputs. Different machine learning methods, such as multiple linear regression (MLR), random forest regression (RFR), artificial neural network (ANN), and support vector regression (SVM), were employed in this study to build QSPR models. According to the statistical coefficients of QSPR models, SVR with Dragonfly hyperparameter optimization (SVR-DA) was the most accurate in predicting pCMC values, achieving (R2 = 0.9740, Q2 = 0.9739, r‾m2 = 0.9627, and Δrm2 = 0.0244) for the entire dataset.

Prediction of Corrosion Inhibition Efficiency Based on Machine Learning for Pyrimidine Compounds: A Comparative Study of Linear and Non-linear Algorithms

The corrosion of materials poses a significant challenge in various industries, leading to substantial economic impacts. In this context, pyrimidine compounds emerge as promising, non-toxic, cost-effective, and versatile corrosion inhibitors. However, conventional methods for identifying such inhibitors are typically time-consuming, expensive, and labor-intensive. Addressing this challenge, our study leverages machine learning (ML) to predict pyrimidine compounds corrosion inhibition efficiency (CIE). Using a quantitative structure-property relationship (QSPR) model, we compared 14 linear and 12 non-linear ML algorithms to identify the most accurate predictor of CIE. The bagging regressor model demonstrated superior performance, achieving a root mean square error (RMSE) of 5.38, a mean square error (MSE) of 28.93, a mean absolute error (MAE) of 4.23, and a mean absolute percentage error (MAPE) of 0.05 in predicting the CIE values for pyrimidine compounds. This research marks a significant advancement in corrosion science, offering a novel and efficient ML-based approach as an alternative to traditional experimental methods. It shows that machine learning can quickly and accurately determine how well organic chemical inhibitors like pyrimidine stop material corrosion. This method gives the industry a new perspective and a workable solution to a problem that has existed for a long time.
 Keywords: machine learning, corrosion inhibition, pyrimidine, QSPR model, predictive analysis

QSPR modeling for the prediction of partitioning of VOCs and SVOCs to indoor fabrics: Integrating environmental factors

Porous fabrics have a significant impact on indoor air quality by adsorbing and emitting chemical substances, such as volatile organic compounds (VOCs) and semi-volatile organic compounds (SVOCs). Understanding the partition behavior between organic compound molecules and indoor fabrics is crucial for assessing their environmental fate and associated human exposure. The physicochemical properties of fabrics and compounds are fundamental in determining the free energy of partitioning. Moreover, environmental factors like temperature and humidity critically affect the partition process by modifying the thermal and moisture conditions of the fabric. However, existing methods for determining the fabric-air partition coefficient are limited to specific fabric-chemical combinations and lack a comprehensive consideration of indoor environmental factors. In this study, large amounts of experimental data on fabric-air partition coefficients (Kfa) of (S)VOCs were collected for silk, polyester, and cotton fabrics. Key molecular descriptors were identified, integrating the influences of physicochemical properties, temperature, and humidity. Subsequently, two typical quantitative structure-property relationship (QSPR) models were developed to correlate the Kfa values with the molecular descriptors. The fitting performance, robustness, and predictive ability of the two QSPR models were evaluated through statistical analysis and internal/external validation. This research provides insights for the high-throughput prediction of the environmental behaviors of indoor organic compounds.

Environmental impact of PFAS: Filling data gaps using theoretical quantum chemistry and QSPR modeling

Per- and polyfluorinated alkyl substances (PFAS), known for their widespread environmental presence and slow degradation, pose significant concerns. Of the approximately 10,000 known PFAS, only a few have undergone comprehensive testing, resulting in limited experimental data. In this study, we employed a combination of physics-based methods and data-driven models to address gaps in PFAS bioaccumulation potential. Using the COnductor-like Screening MOdel for Realistic Solvents (COSMO-RS) method, we predicted n-octanol/water partition coefficients (logKOW), crucial for PFAS bioaccumulation. Our developed Quantitative Structure-Property Relationship (QSPR) model exhibited high accuracy (R2 = 0.95, RMSEC = 0.75) and strong predictive ability (Q2LOO = 0.93, RMSECV = 0.83). Leveraging the extensive NORMAN, we predicted logKOW for over 4,000 compounds, identifying 244 outliers out of 4519. Further categorizing the database into eight Organisation for Economic Co-operation and Development (OECD) categories, we confirmed fluorine atoms role in enhanced bioaccumulation. Utilizing predicted logKOW, water solubility logSW, and vapor pressure logVP values, we calculated additional physicochemical properties that are responsible for the transport and dispersion of PFAS in the environment. Parameters such as Henry’s Law (kH), air–water partition coefficient (KAW), octanol–air coefficient (KOA), and soil adsorption coefficient (KOC) exhibited favorable correlations with literature data (R2 > 0.66). Our study successfully filled data gaps, contributing to the understanding of ubiquitous PFAS in the environment and estimating missing physicochemical data for these compounds.

Predicting protein retention in ion-exchange chromatography using an open source QSPR workflow.

Protein-based biopharmaceuticals require high purity before final formulation to ensure product safety, making process development time consuming. Implementation of computational approaches at the initial stages of process development offers a significant reduction in development efforts. By preselecting process conditions, experimental screening can be limited to only a subset. One such computational selection approach is the application of Quantitative Structure Property Relationship (QSPR) models that describe the properties exploited during purification. This work presents a novel open-source Python tool capable of extracting a range of features from protein 3D models on a local computer allowing total transparency of the calculations. As open-source tool, it also impacts initial investments in constructing a QSPR workflow for protein property prediction for third parties, making it widely applicable within the field of bioprocess development. The focus of current calculated molecular features is projection onto the protein surface by constructing surface grid representations. Linear regression models were trained with the calculated features to predict chromatographic retention times/volumes. Model validation shows a high accuracy for anion and cation exchange chromatography data (cross-validated R2 of 0.87 and 0.95). Hence, these models demonstrate the potential of the use of QSPR to accelerate process design.

A chirality-sensitive approach to predict chemical transfer across the human placental barrier

The placenta is a membrane that separates the fetus from the maternal circulation, and in addition to protecting the fetus, plays a key role in fetal growth and development. With increasing drug use in pregnancy, it is imperative that reliable models of estimating placental permeability and safety be established. In vitro methods and animal models such as rodent placenta are limited in application since the species-specific nature of the placenta prevents meaningful extrapolations to humans. In this regard, in silico approaches such as quantitative structure-property relationships (QSPRs) are useful alternatives. However, despite evidence that drug transport across the placenta is stereoselective (i.e., governed by the spatial arrangement of the atoms in a molecule), many QSPR models for placental transfer have been built using 2D descriptors that do not account for chirality and stereochemistry. In this study, we apply a chirality-sensitive and proven QSPR methodology titled “EigenValue ANalySis” (EVANS) to build QSPR models for placental transfer. We deploy EVANS along with robust machine learning algorithms to build (i) regression models on a dataset of environmental chemicals (dataset PD I) followed by (ii) classification models on a set of drug-like compounds (dataset PD II). The best models were found to achieve state-of-the-art performance, with the support vector machine algorithm returning rtrain2=0.85,rtest2=0.75 for PD I, and the logistic regression algorithm giving accuracy 0.88 and F1 score 0.93 for PD II. The best models were interpreted with the Shapley Additive Explanations paradigm, and it was found that autocorrelation descriptors are crucial for modelling placental permeability. In conclusion, we demonstrate the need of a chirality-sensitive approach for modelling placental transfer of chemicals, and present two predictive QSPR models that may reliably be used for prediction of placental transfer.

Decoding crystallization behavior of aluminoborosilicate glasses: From structural descriptors to Quantitative Structure – Property Relationship (QSPR) based predictive models

Successful decoding of structural descriptors controlling the crystallization in multicomponent functional glasses can pave the way for the transition from the trial-and-error approach and empirical modeling for glass/glass-ceramic composition design toward more rational and scientifically rigorous Quantitative Structure-Property Relationship (QSPR) based models. However, due to the compositional and structural complexity of multicomponent glasses and the longer time and length scales associated with nucleation, the development and validation of QSPR models are still in it's infancy. The work presented in the article is an attempt to leap forward in this pursuit by combining the strengths of experimental and computational materials science to decode the chemo-structural drivers that promote or suppress nucleation and crystal growth in alkali/alkaline-earth aluminoborosilicate glasses leading to the development of a QSPR-based model (powered by MD simulations). The results reveal the following two descriptors that govern the nucleation and crystallization of a particular aluminosilicate phase in the functional glasses: (1) degree of mixing between the SiO4 and AlO4 units, i.e., Si–O–Al linkages, and (2) difference/similarity between the short-to-intermediate range ordering in the glass structure to that of the structure of corresponding crystalline phase. Based on the established composition–structure–crystallization behavior relationships, a cluster analysis based QSPR model has been developed (and tested) to predict the propensity of nepheline (and anorthite) crystallization in the investigated glasses. The model has been tested on several compositions from the present and previous studies and has successfully predicted the crystallization propensity of all glass compositions, even in cases where previous empirical and semi-empirical models were unsuccessful.

Quantitative structure-property relationship modelling on autoignition temperature: evaluation and comparative analysis

ABSTRACT The autoignition temperature (AIT) serves as a crucial indicator for assessing the potential hazards associated with a chemical substance. In order to gain deeper insights into model performance and facilitate the establishment of effective methodological practices for AIT predictions, this study conducts a benchmark investigation on Quantitative Structure-Property Relationship (QSPR) modelling for AIT. As novelties of this work, three significant advancements are implemented in the AIT modelling process, including explicit consideration of data quality, utilization of state-of-the-art feature engineering workflows, and the innovative application of graph-based deep learning techniques, which are employed for the first time in AIT prediction. Specifically, three traditional QSPR models (multi-linear regression, support vector regression, and artificial neural networks) are evaluated, alongside the assessment of a deep-learning model employing message passing neural network architecture supplemented by graph-data augmentation techniques.

Application of machine learning-based read-across structure-property relationship (RASPR) as a new tool for predictive modelling: Prediction of power conversion efficiency (PCE) for selected classes of organic dyes in dye-sensitized solar cells (DSSCs).

The application of various in-silico-based approaches for the prediction of various properties of materials has been an effective alternative to experimental methods. Recently, the concepts of Quantitative structure-property relationship (QSPR) and read-across (RA) methods were merged to develop a new emerging chemoinformatic tool: read-across structure-property relationship (RASPR). The RASPR method can be applicable to both large and small datasets as it uses various similarity and error-based measures. It has also been observed that RASPR models tend to have an increased external predictivity compared to the corresponding QSPR models. In this study, we have modeled the power conversion efficiency (PCE) of organic dyes used in dye-sensitized solar cells (DSSCs) by using the quantitative RASPR (q-RASPR) method. We have used relatively larger classes of organic dyes-Phenothiazines (n=207), Porphyrins (n=281), and Triphenylamines (n=229) for the modelling purpose. We have divided each of the datasets into training and test sets in 3 different combinations, and with the training sets we have developed three different QSPR models with structural and physicochemical descriptors and validated them with the corresponding test sets. These corresponding modeled descriptors were used to calculate the RASPR descriptors using a Java-based tool RASAR Descriptor Calculator v2.0 (https://sites.google.com/jadavpuruniversity.in/dtc-lab-software/home), and then data fusion was performed by pooling the previously selected structural and physicochemical descriptors with the calculated RASPR descriptors. Further feature selection algorithm was employed to develop the final RASPR PLS models. Here, we also developed different machine learning (ML) models with the descriptors selected in the QSPR PLS and RASPR PLS models, and it was found that models with RASPR descriptors superseded in external predictivity the models with only structural and physicochemical descriptors: RMSEP reduced for phenothiazines from 1.16-1.25 to 1.07-1.18, for porphyrins from 1.60-1.79 to 1.45-1.53, for triphenylamines from 1.27-1.54 to 1.20-1.47.

Adapting Deep Learning QSPR Models to Specific Drug Discovery Projects.

Medicinal chemistry and drug design efforts can be assisted by machine learning (ML) models that relate the molecular structure to compound properties. Such quantitative structure-property relationship models are generally trained on large data sets that include diverse chemical series (global models). In the pharmaceutical industry, these ML global models are available across discovery projects as an "out-of-the-box" solution to assist in drug design, synthesis prioritization, and experiment selection. However, drug discovery projects typically focus on confined parts of the chemical space (e.g., chemical series), where global models might not be applicable. Local ML models are sometimes generated to focus on specific projects or series. Herein, ML-based global models, local models, and hybrid global-local strategies were benchmarked. Analyses were done for more than 300 drug discovery projects at Novartis and ten absorption, distribution, metabolism, and excretion (ADME) assays. In this work, hybrid global-local strategies based on transfer learning approaches were proposed to leverage both historical ADME data (global) and project-specific data (local) to adapt model predictions. Fine-tuning a pretrained global ML model (used for weights' initialization, WI) was the top-performing method. Average improvements of mean absolute errors across all assays were 16% and 27% compared with global and local models, respectively. Interestingly, when the effect of training set size was analyzed, WI fine-tuning was found to be successful even in low-data scenarios (e.g., ∼10 molecules per project). Taken together, this work highlights the potential of domain adaptation in the field of molecular property predictions to refine existing pretrained models on a new compound data distribution.

The study of regression model based on CoM-polynomial in blood cancer drug properties

A topological index (TI) is a real number that determined the structure of a graph. Topological indices (TIs) serves mathematical descriptors that aid in predicting and understanding the physicochemical properties and structure-activity relationships of chemical compounds, thus facilitating drug design and discovery processes. TIs utilizes to forecast the effectiveness of cancer treatment by providing details on the molecules of the medications and their associated properties. In order to create safe and effective treatments, it is crucial to employ TIs to accurately predict the toxicity and side effects of medications. In this paper, we have considered the physical and biological properties of some blood cancer treatment medications through degree based Banhatti topological indices from the M-polynomial by using derivations. The drugs are Palbociclib, Ivosidenib, Glasdegib, Gilteritinib, and Daunorubicin and the TI's are given in Table 1. Subsequently, a linear regression technique is employed to establish a quantitative structure-property relationship (QSPR) model for predicting various parameters such as molecular weight, complexity, molar volume, boiling point (BP), and flash point (FP). Results indicate that topological indices have potential as a drug discovery and development tool in the fight against cancer.

Prioritizing Asthma Treatment Drugs through Multicriteria Decision Making.

Asthma is a medical condition characterized by inflammation, narrowing, and swelling of a person's airways, leading to increased mucus production and difficulties in breathing. Topological indices are instrumental in assessing the physical and chemical attributes of these asthma drugs. As resistance to current treatments continues to emerge and undesirable side effects are linked to certain medications, the search for novel and enhanced drugs becomes a top priority. In this study, the examination of 19 distinct asthma medications was focused. In this study, quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) modeling, in combination with multicriteria decision-making (MCDM) technique VIKOR (VIekriterijumsko KOmpromisno Rangiranje) were employed on asthma drugs, to achieve the most favorable rankings for each asthma drug, taking into account their distinct properties. The topological indices employed for QSPR modeling were Randic index, reciprocal Randic index, Zagreb indices, hyper-Zagreb index, harmonic index, geometric arithmetic index, and forgotten index.