Structural Descriptors Research Articles

Exploring a novel approach for computing topological descriptors of graphene structure using neighborhood multiple M-polynomial

Exploring a novel approach for computing topological descriptors of graphene structure using neighborhood multiple M-polynomial

On the Exponential Atom-Bond Connectivity Index of Graphs

Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, the literature has introduced the exponential vertex-degree-based topological index. The exponential atom-bond connectivity index is defined as follows: eABC=eABC(Υ)=∑vivj∈E(Υ)edi+dj−2didj, where di is the degree of the vertex vi in Υ. In this paper, we prove that the double star DSn−3,1 is the second maximal graph with respect to the eABC index of trees of order n. We give an upper bound on eABC of unicyclic graphs of order n and characterize the maximal graphs. The graph K1∨(P3∪(n−4)K1) gives the maximal graph with respect to the eABC index of bicyclic graphs of order n. We present several relations between eABC(Υ) and ABC(Υ) of graph Υ. Finally, we provide a conclusion summarizing our findings and discuss potential directions for future research.

Quantitative Structure–Activity Relationship (QSAR) Modeling of Chiral CCR2 Antagonists with a Multidimensional Space of Novel Chirality Descriptors

The development of chirality descriptors for quantitative chirality structure–activity relationship (QCSAR) modeling has always attracted attention, owing to the importance of chiral molecules in pharmaceutical, agriculture, food, and fragrance industries, and environmental toxicology. The utility of a multidimensional space of novel relative chirality indices (RCIs) in the QCSAR modeling of twenty CCR2 antagonists is reported upon in this paper. The numerical characterization of chirality by the RCI approach gives a large pool of chirality descriptors with different degrees of mutual correlation (the correlation coefficient among the computed descriptors varied from 0.02 to 0.99). In the present study, the final data set contains 198 chirality descriptors for each of the twenty CCR2 antagonist molecules, providing a multidimensional space for modeling. The data reduction using principal component analysis resulted in the extraction of eight principal components (PCs). The linear regression using the principal component scores (PCSs) resulted in a three-predictor prediction model with good statistics: R2 = 0.823; Adj R2 = 0.790. The regression models were rebuilt using the chirality descriptors (RCIs) that are most correlated with each of the scores (PCSs) of the three principal components. The R2 value for the regression models with three RCIs as the predictors is 0.742 and the five-fold cross validation, Rcv2, is 0.839. The new chirality descriptors, namely, the RCIs calculated using a different weighting scheme, provide a multidimensional space of chirality descriptors for a set of chiral molecules, and such a multidimensional chirality space is a powerful tool to build quantitative chiral structure–activity relationship (QCSAR) models.

On some neighborhood degree-based structure descriptors and their applications to graphene

On some neighborhood degree-based structure descriptors and their applications to graphene

Toward mitigating the impact of non-bulk defects on describing water structure in salt aqueous solutions: Characterizing solution density with a network-based structural indicator.

Structural indicators, also known as structural descriptors, including order parameters, have been proposed to quantify the structural properties of water to account for its anomalous behaviors. However, these indicators, mainly designed for bulk water, are not naturally transferrable to the vicinity of ions due to disruptions in the immediate neighboring space and a resulting loss of feature completeness. To address these non-bulk defects, we introduced a structural indicator that draws on the concept of clique number from graph theory and the criterion in agglomerative clustering, denoted as the average cluster number. This structural indicator aims to discern intrinsic structural characteristics within the water molecules regardless of the ions occupying the neighboring space, without requiring additional corrections. From molecular dynamics simulation results for neat water and salt aqueous solutions utilizing the TIP4P/2005 water model and the Madrid-2019 force field, we characterized the variations in densities with temperature using this network-based indicator, thereby demonstrating its practical utility. The findings suggest that at lower temperatures, the addition of ions disrupts the intrinsic structure of water molecules, with this effect diminishing as the temperature rises. Cations with larger charge density tend to induce stronger disruptions. This study highlights the importance of mitigating the impact of non-bulk defects before applying the indicators to analyze water's intrinsic structural properties in solutions. By doing so, the relationship between changes in water structure and solution behaviors can be more accurately assessed.

Robust Method for Property Prediction via Artificial Neural Networks: Incorporating Key Structural Features for Carbon Dioxide-Ionic Liquid Mixtures.

This study addresses a critical gap in the existing literature on carbon dioxide and ionic liquid (IL) mixtures, where fragmented and incomplete data, particularly for flow properties, hinder practical applications. Therefore, this work aimed to establish a robust and efficient method for predicting the density of the CO2-IL mixtures across diverse operating conditions and IL families using novel validation techniques. Both linear and symbolic regression models provided relevant insights but failed to accurately capture the IL-CO2 interactions in a mixture that determine the molar volume of CO2 at infinite dilution when solubilized by a given IL. Therefore, more mathematically flexible artificial neural networks (ANN) were trained based on three different sets of features: (1) IL critical properties, (2) IL structural descriptors, and (3) a selective combination of (1) and (2). While all models showed relative deviations consistently below 3% for the testing data, combining critical and structural data significantly improved accuracy (R2 = 0.986, testing data set). A postprocessing outlier-handling method enhanced model performance, removing a minimal fraction (below 0.2%) of unphysical data points. Furthermore, molecular dynamics simulations validated the robust generalization of all ANN models, with the combined model exhibiting remarkable accuracy over operating conditions outside the training ranges for ILs in the training set and even for ILs that are not included in this data set. This computational approach provides a significantly faster and broader alternative to other thermodynamical tools, establishing a solid method for future machine learning (ML)-based property prediction augmented by external validation from cross-comparison tests and statistical thermodynamics models.

Closed-Loop Chemical Recycling of a Biobased Poly(oxanorbornene-fused γ-butyrolactone).

New polymers, properly designed for end-of-life and efficiently formed from renewable carbon, are key to the transition to a more sustainable circular plastics economy. Ring-opening polymerization (ROP) of bicyclic lactones is a promising method for the production of intrinsically recyclable polyesters, but most lactone monomers lack an efficient synthesis route from biobased starting materials, even though this is essential to sustainably account for material loss during the life cycle. Herein, we present the exceptionally rapid and controlled polymerization of a fully biobased tricyclic oxanorbornene-fused γ-butyrolactone monomer (M1). Polyester P(M1) was formed in low dispersity (D̵ = 1.2-1.3) and controllable molecular weight up to Mn = 76.8 kg mol-1 and exhibits a high glass transition temperature (Tg = 120 °C). The orthogonal olefin and lactone functionalities offer access to a wide range of promising materials, as showcased by postpolymerization modification by hydrogenation of the olefin, which increased polymer thermal stability by over 100 °C. Next to rapid hydrolytic degradation and solvolysis, the poly(oxanorbornene-fused γ-butyrolactone) could be cleanly chemically recycled back to the monomer (CRM), in line with its favorable ceiling temperature (Tc) of 73 °C. The density functional theory (DFT)-computed ΔH° of ring-opening with methanol of γ-butyrolactone-based monomers provided a model to predict Tc, and the DFT-computed and X-ray crystal structure-derived structural parameters of M1, hydrogenated analogue M1-H2, and regioisomer M2 offered insights into the structural descriptors that cause the high polymerizability of M1, which is key to establishing structure-property relations.

DeepAIPs-Pred: Predicting Anti-Inflammatory Peptides Using Local Evolutionary Transformation Images and Structural Embedding-Based Optimal Descriptors with Self-Normalized BiTCNs.

Inflammation is a biological response to harmful stimuli, playing a crucial role in facilitating tissue repair by eradicating pathogenic microorganisms. However, when inflammation becomes chronic, it leads to numerous serious disorders, particularly in autoimmune diseases. Anti-inflammatory peptides (AIPs) have emerged as promising therapeutic agents due to their high specificity, potency, and low toxicity. However, identifying AIPs using traditional in vivo methods is time-consuming and expensive. Recent advancements in computational-based intelligent models for peptides have offered a cost-effective alternative for identifying various inflammatory diseases, owing to their selectivity toward targeted cells with low side effects. In this paper, we propose a novel computational model, namely, DeepAIPs-Pred, for the accurate prediction of AIP sequences. The training samples are represented using LBP-PSSM- and LBP-SMR-based evolutionary image transformation methods. Additionally, to capture contextual semantic features, we employed attention-based ProtBERT-BFD embedding and QLC for structural features. Furthermore, differential evolution (DE)-based weighted feature integration is utilized to produce a multiview feature vector. The SMOTE-Tomek Links are introduced to address the class imbalance problem, and a two-layer feature selection technique is proposed to reduce and select the optimal features. Finally, the novel self-normalized bidirectional temporal convolutional networks (SnBiTCN) are trained using optimal features, achieving a significant predictive accuracy of 94.92% and an AUC of 0.97. The generalization of our proposed model is validated using two independent datasets, demonstrating higher performance with the improvement of ∼2 and ∼10% of accuracies than the existing state-of-the-art model using Ind-I and Ind-II, respectively. The efficacy and reliability of DeepAIPs-Pred highlight its potential as a valuable and promising tool for drug development and research academia.

Deep learning assisting construction of heat transfer constitutive relationships for porous media

Predicting heat transfer in porous materials is challenging due to their complex microstructure, and traditional experimental and theoretical methods often fall short. To address this, we present a machine learning-based approach using a single Descriptor-to-Property Network (D2P-Net) to identify the relationships between the effective thermal conductivity (ETC) of porous media with the structural descriptors. The D2P-Net, an ensemble of decision trees, uses eleven structural descriptors, such as porosity, pore size, and connectivity, derived from four distinct types of three-dimensional porous structures. These structures are computationally generated, and their ETC is computed using the Lattice Boltzmann Method (LBM) to create a robust dataset for training. The model is trained using mean squared error (MSE) employed as the loss function, and achieves an R2 value of 0.994 and a root mean square error (RMSE) of 0.229, indicating high predictive accuracy. Additionally, SHapley Additive exPlanations (SHAP) values are employed to analyze the importance of each structural descriptor, offering valuable insights into their contributions to ETC predictions. This approach provides a reliable and interpretable method for understanding and optimizing the thermal properties of porous materials, with potential applications in areas requiring efficient thermal management, such as hypersonic vehicles.

EpiTCR-KDA: Knowledge Distillation model on Dihedral Angles for TCR-peptide prediction

Abstract Motivation The prediction of the T-cell receptor (TCR) and antigen bindings is crucial for advancements in immunotherapy. However, most current TCR-peptide interaction predictors struggle to perform well on unseen data. This limitation may stem from the conventional use of TCR and/or peptide sequences as input, which may not adequately capture their structural characteristics. Therefore, incorporating the structural information of TCRs and peptides into the prediction model is necessary to improve its generalizability. Results We developed epiTCR-KDA, a new predictor of TCR-peptide binding that utilizes the dihedral angles between the residues of the peptide and the TCR as a structural descriptor. This structural information was integrated into a knowledge distillation model to enhance its generalizability. epiTCR-KDA demonstrated competitive prediction performance, with an AUC of 1.00 for seen data and AUC of 0.91 for unseen data. On public datasets, epiTCR-KDA consistently outperformed other predictors, maintaining a median AUC of 0.93. Further analysis of epiTCR-KDA revealed that the cosine similarity of the dihedral angle vectors between the unseen testing data and training data is crucial for its stable performance. In conclusion, our epiTCR-KDA model represents a significant step forward in developing a highly effective pipeline for antigen-based immunotherapy. Availability and implementation epiTCR-KDA is available on GitHub (https://github.com/ddiem-ri-4D/epiTCR-KDA). Supplementary information Supplementary data are available at Bioinformatics Advances online.

Molecular identification via molecular fingerprint extraction from atomic force microscopy images

Non–Contact Atomic Force Microscopy with CO–functionalized metal tips (referred to as HR-AFM) provides access to the internal structure of individual molecules adsorbed on a surface with totally unprecedented resolution. Previous works have shown that deep learning (DL) models can retrieve the chemical and structural information encoded in a 3D stack of constant-height HR–AFM images, leading to molecular identification. In this work, we overcome their limitations by using a well-established description of the molecular structure in terms of topological fingerprints, the 1024–bit Extended Connectivity Chemical Fingerprints of radius 2 (ECFP4), that were developed for substructure and similarity searching. ECFPs provide local structural information of the molecule, each bit correlating with a particular substructure within the molecule. Our DL model is able to extract this optimized structural descriptor from the 3D HR–AFM stacks and use it, through virtual screening, to identify molecules from their predicted ECFP4 with a retrieval accuracy on theoretical images of 95.4%. Furthermore, this approach, unlike previous DL models, assigns a confidence score, the Tanimoto similarity, to each of the candidate molecules, thus providing information on the reliability of the identification. By construction, the number of times a certain substructure is present in the molecule is lost during the hashing process, necessary to make them useful for machine learning applications. We show that it is possible to complement the fingerprint-based virtual screening with global information provided by another DL model that predicts from the same HR–AFM stacks the chemical formula, boosting the identification accuracy up to a 97.6%. Finally, we perform a limited test with experimental images, obtaining promising results towards the application of this pipeline under real conditions.Scientific contributionPrevious works on molecular identification from AFM images used chemical descriptors that were intuitive for humans but sub–optimal for neural networks. We propose a novel method to extract the ECFP4 from AFM images and identify the molecule via a virtual screening, beating previous state-of-the-art models.

Search for Stable Structures of Adsorbed Molecules on Material Surfaces by Bayesian Optimization

Titanium dioxide (TiO2) is one of the most technologically promising oxides with a broad range of catalytic and photocatalytic activities, and first-principles simulations of molecular adsorption onto TiO2 surface have been extensively performed. Our group experimentally reported that the formation of an amorphous structure on the TiO2 surface enhances its catalytic activity, and is investigating the origin of high activity for amorphous surface. From the theoretical point of view, searching for stable adsorption sites on an amorphous surface model based on first-principles calculations need much high computational cost due to many adsorption sites in a large supercell. In this study, to efficiently explore stable adsorption sites on an amorphous surface, we applied Bayesian optimization, a global search method for black-box optimization, and found the most stable adsorption site of a water molecule.First-principles calculations are performed with SIESTA code [1] with localized basis, using the generalized gradient approximation (GGA) for the exchange-correlation energy functional. The amorphous surface models of TiO2 are generated by quenching a (101) surface model of anatase-type TiO2 crystal containing 162 atoms with first-principles molecular dynamics simulation. Fig. 1 shows one of TiO2 surface models.The adsorption energy of a molecule adsorbate is defined asEads=Etot (surf+mol)-(Etot surf+Etot mol )Etot (surf+mol) is the total energy of the surface with a molecule adsorbate, Etot surf is the total energy of the clean surface, and Etot mol is the energy of a molecular in a vacuum.Bayesian optimization is adopted for searching the lowest energy site with fixing TiO2 surface configurations. A Gaussian kernel and an Expected Improvement (EI) for the acquisition function are used.Absorption energies were calculated on mesh points in the six-dimension space of the atomic positions of the oxygen (x, y, z) and rotational angles. First, we performed Bayesian optimization in the six-dimension space of the position and the angle, but this did not work well due to the discontinuity of the potential surface. Thus, we performed Bayesian optimization in the structural-descriptor space. We adopted the smooth overlap of atomic positions (SOAP) and the radial distribution function (RDF) as structural descriptors. The lowest energy sites were much efficiently found in the descriptor space, and we achieved high search efficiency. Figure 1

Enhancing Discovery and Understanding of Atomically Dispersed Single Atom Catalysts for CO2 Reduction Reaction with Density Functional Theory and Machine Learning

Atomically dispersed M-N-C catalysts are a promising class of materials for efficiently reducing CO2 to valuable feedstock chemicals such as carbon monoxide and ethylene. However, for such catalysts to achieve commercial viability it is necessary to optimize several properties in tandem such as activity towards the CO2 reduction reaction, Faradaic efficiency towards selected products, and in situ stability. This complex multi-objective optimization problem cannot be effectively tackled with costly trial-and-error experimentation alone. Therefore, computational modeling is necessary to accelerate fundamental understanding and to aid in identifying viable active sites in silico before preparation of down-selected candidate materials is attempted in the laboratory. Density functional theory (DFT) can be utilized to model catalytic surfaces and obtain useful electrochemical properties (e.g., free energies of reaction), but an advanced framework is necessary to effectively explore the large chemical space of possible permutations of different transition metals, proximity of metal centers, defects, and other structural considerations. Furthermore, machine learning may be leveraged to accelerate materials understanding and discovery for CO2RR beyond what is feasible for DFT alone.In this talk, we will discuss our library-based approach for understanding structure-to-function relationships in these materials and identifying novel active sites. This library is built using our high-throughput DFT framework to calculate different properties (e.g., adsorption energies) for a large number of active sites. The structures of the active sites are combinatorically generated based on permutations of transition metals, defects, and other structural considerations. Our automated framework combines DFT and cheminformatics tools to autonomously run DFT calculations as well as to collect, process, and store the results of our simulations and to evaluate different structural descriptors. We will also discuss considerations made for incorporating solvation and electrification effects in a robust manner into our framework.This library is then used as the basis for the development of machine learning models, which learn to map from descriptor-based structural representations of these surfaces (e.g., metal center, type of defect) to target properties, thereby accelerating understanding of structure to function relationships for M-N-C materials. Game theoretical methods are used to provide model interpretability and insight for how individual structural properties contribute to properties of interest, such as activity or overpotential. We discuss the use of our trained model, capable of screening millions of unique chemistries, in discovering novel M-N-C active sites with optimized properties. By thus combining DFT and machine learning, we aim both to provide fundamental understanding of CO2 reduction activity and durability and to discover new viable active sites. Examples of our modeling strategies applied to direct air capture of CO2 utilizing similar workflows will also be discussed.

Multiple New Families of Fast Oxygen Interstitial Conductor Discovered by High-Throughput Computational Screening

Discovery and design of highly efficient oxygen-active materials that react with, absorb, and transport oxygen is essential for the development of improved fuel cells, electrolyzers and related applications.Currently, the predominant families of oxygen-active materials used in commercial fuel cell and electrolyzer devices are perovskites and fluorites, which diffuse oxygen via a vacancy mechanism and only have adequate oxygen diffusivity and surface exchange at high temperatures (e.g., ~800 ˚C), impeding their use at lower temperatures desirable for more cost-effective and long-lasting device operation. The development of alternative electrolyte/electrode materials with high oxygen ionic conductivity at low temperatures (e.g., room temperature to 400 °C) is of great interest. Interstitial oxygen ion conductors typically have significantlylower migration barriers than even state-of-the-art vacancy-mediated oxygen conductors, which can provide orders of magnitude kinetic enhancement at low temperatures, but have received far less attention than vacancy-mediated conductors. In our recent work, we combined physically-motivated structure and property descriptors, ab initio simulations, and experiments to demonstrate an approach to discover new fast interstitial oxygen conductors. We first conducted a comprehensive high-throughput screening of the 34k oxide materials from the Materials Project database utilizing a set of screening criteria including the geometric free space, thermodynamic stability, synthesizability, redox-active elements, and presence of short diffusion pathways. This screening winnowed the field of 34k oxides down to just 345 oxides, an approximate 99% reduction in the search space considered. For this reduced set of promising materials, ab initio simulations were performed to calculate the interstitial oxygen formation energy and migration energy. We identified multiple new promising structural classes, including but not limited to double molybdates A2TM2(MoO4)3 (A=alkali metal, TM=transition metal), perrierite/chevkinite RE4TM5Si4O22 (RE=rare earth, TM=transition metal), and germinates RE1TM2Ge4O12 (RE= rare earth, TM=transition metal), and have demonstrated the exceptional performance of one example material, La4Mn5Si4O22+ 𝜹 (LMS) with experimental validation. The discovery of a new high-performing interstitial oxygen conductor from the experimental study of just one system, as well as the prediction of multiple families of promising interstitial ion conductors, suggests that many more materials exhibiting fast interstitial oxygen kinetics remain to be found.In this work, we performed detailed studies on the oxygen interstitial diffusion behavior in ZrMn2Ge4O12 (ZMG) and CeMn2Ge4O12 (CMG), as two representive compounds belong to germanate family. Oxygen ion mobility in ZMG and CMG (in the presence of 2% oxygen interstitials) is examined through ab initio molecular dynamics (AIMD) simulations and the associated migration barrier is studied by Climbing Image Nudged Elastic Band (CI-NEB) method. Our results reveal that the oxygen interstitials diffuse through an interstitial-mediated (interstitialcy) mechanism, with the energy barriers of approximately 0.33 eV for ZMG and 0.54 eV for CMG. To validate the fast oxygen conduction, we synthesized ZMGthrough the solid-state reaction and measured both the experimental total and ionic conductivities. Our experimental activation energy barrier aligns closely with the computational prediction, but the measured conductivities were lower. Further analyses of the microstructure, secondary phases, and impurity phases in the synthesized ZMG are essential to fully understand and leverage the fast oxygen diffusion capabilities in ZMG as indicated by our ab initio studies.

Improved prediction of post-translational modification crosstalk within proteins using DeepPCT.

Post-translational modification (PTM) crosstalk events play critical roles in biological processes. Several machine learning methods have been developed to identify PTM crosstalk within proteins, but the accuracy is still far from satisfactory. Recent breakthroughs in deep learning and protein structure prediction could provide a potential solution to this issue. We proposed DeepPCT, a deep learning algorithm to identify PTM crosstalk using AlphaFold2-based structures. In this algorithm, one deep learning classifier was constructed for sequence-based prediction by combining the residue and residue pair embeddings with cross-attention techniques, while the other classifier was established for structure-based prediction by integrating the structural embedding and a graph neural network. Meanwhile, a machine learning classifier was developed using novel structural descriptors and a random forest model to complement the structural deep learning classifier. By integrating the three classifiers, DeepPCT outperformed existing algorithms in different evaluation scenarios and showed better generalizability on new data owing to its less distance dependency. Datasets, codes, and models of DeepPCT are freely accessible at https://github.com/hzau-liulab/DeepPCT/.

Insight into the Mechanism of Machine Learning Models for Predicting Ionic Liquids Toxicity Based on Molecular Structure Descriptors

Insight into the Mechanism of Machine Learning Models for Predicting Ionic Liquids Toxicity Based on Molecular Structure Descriptors

Investigations on symbol regression for improving the prediction accuracy of gas-metal adsorption energies in machine learning

Adsorption energy plays a crucial role in surface catalytic reactions and influences the performance of the catalysts. Machine learning offers a novel approach for the computation of adsorption energy. The selection of a crystal plane is critical for the calculation of the adsorption energy, with current research focusing on low-index crystal planes. The prediction of catalytic performance is challenging because of the complexity arising from the surface reactions occurring on multiple crystal planes. However, this challenge can be resolved by introducing effective descriptors and utilizing advanced machine learning methods. This study collected data from various sources, such as databases, literature, and Density Functional Theory calculations, and utilized machine learning to predict the adsorption energies of prevalent adsorbates on multiple crystal planes of several platinum group metals in catalytic reactions. New structural descriptors were developed by leveraging the expertise of material researchers, and feature engineering techniques were employed to improve the predictive accuracy of the machine learning model. To prevent data loss and detect potential regularities, new features are created using symbolic regression. The introduction of these new features significantly enhanced the model's performance, increasing R2 from 0.885 to 0.921, and providing innovative concepts for future catalyst design.

Optimizing structure-property models of three general graphical indices for thermodynamic properties of benzenoid hydrocarbons

Cheminformatics is an interdisciplinary field that combines principles of chemistry, computer science, and information technology to process, store, analyze, and interpret chemical data. One area of cheminformatics is quantitative structure–property relationship (QSPR) modeling which is a computational approach that correlates the structural attributes of chemical compounds with their physical, chemical, or biological properties to predict the behavior and characteristics of new or untested compounds. Structure descriptors deliver contemporary mathematical tools required for QSPR modeling. One of a significant class of such descriptors is graph-based descriptors known as graphical descriptors. A degree-based graphical descriptor/invariant of a υ-vertex graph Ω=(VΩ,EΩ) has a general structure GDd=∑ij∈EΩπdegxi,degxj, where π is bivariate symmetric map, and degxi is the degree of vertex xi∈VΩ. For α∈R∖{0}, if π=(degxi×degxj)α (resp. π=(degxi+degxj)α, then GDd is called the general product-connectivity PCα (resp. sum-connectivity SCα) index of Ω. Moreover, the general Sombor index SOα has the structure π=(degxi2×degxj2)α. By choosing the heat capacity ΔH and the entropy E as representatives of thermodynamic properties, we in this paper find optimal value(s) of α which deliver the strongest potential of the predictors GDd∈{PCα,SCα,SOα} for predicting ΔH and E of benzenoid hydrocarbons. In order to achieve this, we employ tools such as discrete optimization and multivariate regression analysis. This, in turn, study completely solves two open problems proposed in the literature.

An Approach to Growth Mechanics Based on the Analytical Mechanics of Nonholonomic Systems

Motivated by the convenience, in some biomechanical problems, of interpreting the mass balance law of a growing medium as a nonholonomic constraint on the time rate of a structural descriptor known as growth tensor, we employ some results of analytical mechanics to show that such constraint can be studied variationally. Our purpose is to move a step forward in the formulation of a field theory of the mechanics of volumetric growth by defining a Lagrangian function that incorporates the nonholonomic constraint of the mass balance. The knowledge of such Lagrangian function permits, on the one hand, to deduce the dynamic equations of a growing medium as the result of a variational procedure known as Hamilton–Suslov Principle (clearly, up to non-potential generalized forces that are accounted for by extending this procedure), and, on the other hand, to study the symmetries and conservation laws that pertain to a given growth problem. While this second issue is not investigated in this work, we focus on the first one, and we show that the Euler–Lagrange equations of the considered growing medium, which describe both its motion and the evolution of the growth tensor, can be obtained by reformulating a variational method developed by other authors. We discuss the main features of this method in the context of growth mechanics, and we show how our procedure is able to improve them.

Prediction of melting and solid phase transitions temperatures and enthalpies for triacylglycerols using artificial neural networks

Triacylglycerols (TAG) are the main components of vegetable oils and any attempt to simulate vegetable oils processes will demand knowledge of their properties. However, experimental values are scarce, considering that several TAG in their pure forms are unavailable or too expensive for experimental measurements. On the other hand, correlating physical properties with TAG molecular structure is not simple. TAG is a molecule composed of 3 fatty acids (FA) esterified to a glycerol (GL) backbone, making properties dependent on carbon number (CN) of each FA, number of unsaturations (UN) of each FA, and position of the FA in the GL backbone. Few models are available in literature for prediction of TAG melting properties, with a special attention to melting temperature (Tfus) and enthalpy (ΔHfus) and solid-solid transition properties of the TAG polymorphic forms. Wesdorp's, Moorthy's et al. and Zeberg-Mikkelsen and Stenby's works present models based on the Group-Contribution theory nowadays used, despite some flaws, particularly considering the polymorphic transitions. Therefore, this work was aimed at evaluating Artificial Neural Network (ANN) models for prediction of TAG's Tfus and ΔHfus (β-form) as well as temperature and enthalpy transitions of molecule polymorphic forms (α and β’). Database was composed of temperature and enthalpy experimental data from literature. For each TAG, 7 input data were provided: total CN, as well as CN and UN at sn-1, 2 and 3 TAG position. The Multilayer Perceptron Feed Forward (MPL) model was used, and the topology was evaluated for number of hidden layers (HL), number of neurons (NN) and activation function at each hidden layer, and convergence algorithm. Number of HL and NN was screened by using a Central Composite Rotatable Design (CCRD). Models were further evaluated by Explainable Artificial Intelligence (XAI) and feature evaluation strategies. Architectures showed a significant higher accuracy for calculation and prediction of TAG's melting properties of the 3 polymorphic forms, with R2 higher to 0.91 for all databases when compared to literatures’ models (excepted for the prediction of the melting temperature of the β form, where Wesdorp's model presented a better predictive ability, despite great similarity). Good results were probably related to the well-defined physicochemical relationship between input (molecular structure descriptors) and output (melting properties), that could be described by XAI evaluation. This is an important advantage considering the improvement of the performance of process and products design including TAG molecules.