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The study of protein folding is attractive to scientists from various natural sciences, including physicists/biophysicists [1]. One of them is M. Karplus, Nobel laureate 2013, who modelled protein folding and unfolding of 33 proteins using models selected from 24 generated sequence-based features/descriptors [2]. Protein folding rates correlate with protein length (the total number of amino acids in a protein), the content of secondary structures in the protein, the absolute and relative mean distance of contact order between amino acids, etc. [3]. We have defined and introduced several new sequence-based attributes/features suitable for modelling the folding rates of proteins, such as the features related to the secondary structure of proteins (segments of alpha or beta secondary structure) and the average distance of amino acids. Models were also developed with different combinations of the above features. Improved models have been developed to predict the folding rates of proteins and all features are not dependent on the 3D structure of the protein. References: [1] D.N. Ivankov, A.V. Finkelstein, Biomolecules 10, 250 (2020) [2] A. R. Dinner, S. S. So, M. Karplus, Advan. Chem. Phys. 120, 1 (2002) [3] H. Zhou, Y. Zhou, Biophys. J. 82, 458 (2002)

Protein folding is a very important problem in life sciences that has been studied experimentally, but also through modelling (theoretical and simulation analyses).[1] It is assumed that all the information that determines the protein folding process and the protein folding rate is contained in the primary structure of the proteins (i.e. in the sequence of the amino acids). Modelling the protein folding constants kf (s-1), which are equal to 1 / (time required for protein folding), is a size-dependent problem, which means that ln (kf) depends on the length of the protein sequence. Here we have defined and calculated new descriptors (features) that take into account mutual arrangements of hydrophobic amino acids in the primary structure such as the average distance between amino acids. These attributes were found to have better agreement (correlation) with protein folding rates in three protein sets than protein length, relative contact order distance or other parameters calculated from the protein's primary sequence or its three-dimensional structure.

When developing structure-property molecular models, it is desirable to pay attention to their simplicity and to include only informative variables (descriptors) in the models, i.e. those that contain useful and interpretable structural information. Moreover, almost every dataset used for model development contains some information that is redundant. Therefore, the protocol we use to validate the quality of the model is extremely important. One of the parts of the model validation procedures is the estimation and evaluation of the random accuracy resulting from the complexity (i.e. monotonicity) of the input data and the model quality, the background of which is mainly represented by the number of parameters optimised in the model. The complexity of the dichotomous variables representing the molecular descriptors and the property of the molecules to be modelled, as well as the values predicted by the model, will be assessed by estimating the number of possible permutations (permutation entropy) of values of a variable. Formulas were derived for new statistical measures that can be used to assess the quality and complexity of classification models and variables. In addition, formulae were derived for calculating the minimum and maximum possible accuracy/agreement of the model and for the average random accuracy/agreement. If we consider the case where predicted and experimental variables have identical distributions, we can obtain expressions for measuring the monotonicity of a variable. Recent results from this area of research will be presented and illustrated with examples of models developed to predict the structure of membrane proteins, the toxicity of organic compounds and the folding rates of proteins.

Understanding the protein folding process is considered one of the most critical issues in structural biophysics of proteins. The problem of modelling the protein folding rate is essential for finding the underlying factors that are predominantly responsible for the protein folding process and has been intensively researched for the past 25 years [1]. The main structural descriptors that determine the rate of protein folding were the length of the protein sequence, secondary structure content of the protein, and the mean contact order distance between amino acids. In the reproduction of results from the literature and in the process of defining own descriptors that are important for protein folding rate, we noticed inconsistency and scattering of experimental data in literature databases and those available online. This paper compared the uniformity of experimental data such as protein lengths, amino acid sequence, and protein folding rate constants in databases and the most important models from the literature and those available as network web servers [2], and analyse their influence on the accuracy of models for prediction of protein folding rates.

Topological indices, so-called degree-based topological indices, are defined as the sum (over all bonds/edges) of the contributions of valences of atoms/vertices forming chemical bonds in the molecular structure represented by a graph. They are a large family of molecular descriptors used in QSAR/QSPR (Quantitative Structure-Activity/Property Relationship) modelling. The development of new degree-based topological indices and the analysis of their mathematical properties belong to the field of mathematics (mathematical chemistry), while their chemical interpretation and application takes place in the field of chemical modelling, with applications in biology, pharmacy, toxicology or environmental protection. Among the degree-based topological indices, the Zagreb indices M1 and M2, introduced 50 years ago by Gutman and Trinajstić [1], stand out together with the Randić connectivity index [2]. They have recently attracted more and more attention and became the basis and motivation for the introduction of numerous new degree-based indices [3]. The application and suitability of these new topological descriptors for chemical modelling will be explained in terms of their (1) chemical-structural interpretation and (2) correlation with the chemical properties of molecules. To assess the statistical significance of the obtained relationships, more advanced validation methods used in the validation of models in chemistry, such as cross-validation and external predictivity, were used. The final results, based on more rigorous validation procedures, favour the original variants of the Zagreb indices and those based on the sum of the valences of the atoms. These results differ from those in the literature, which are based only on fit validation procedures. References [1] I. Gutman ; N. Trinajstić, Chem. Phys. Lett., 17 (1972) 535-538. [2] M. Randić, J. Am. Chem. Soc. 97 (1975) 6606–6615. [3] I. Gutman, Croat. Chem. Acta. 86 (2013) 351–361.

In the development of structure-property relationship models and multivariate models in general, there is a tendency to include as few structural variables (molecular descriptors) as possible in the final optimised models. Due to the ubiquitous digitisation of data and molecular fingerprints, molecular descriptors are increasingly binary variables with values of 1 or 0. Even the experimental properties of chemical compounds are expressed in binary values - e.g. toxic (1) or non-toxic (0). We have performed the calculation and simulation of the correspondence between the two binary variables in paired and unpaired sorting cases. These two experiments provide us with the maximum (in the paired sorting case) and minimum possible correspondence (unpaired sorting) of these variables. Theoretically, we have derived formulae for calculating the maximum and minimum agreement between two variables where x-values (first variable) and y-values (second variable) belong to class 1. The difference between the minimum and maximum values reflects the information content or monotonicity between the two variables. If we consider the case x = y, we obtain expressions that measure the monotonicity of a variable with x values in class 1 and (N - x) values in class 0. If the number of elements in class 1 and class 0 is expressed by the values of the error matrix corresponding to a binary classification (TP - true positive, TN - true negative, FN - false negative, FP - false positive ; x = TP + FN, N - x = TN + FP), we obtain general expressions for calculating the maximum and minimum values of any variable measuring the agreement, correlation or error between two classification variables. In addition to being used to evaluate the monotonicity of variables, the results obtained are also used to evaluate the quality of binary classification models.

There is enormous public interest in the EU, but also the interest of the pharmaceutical industry in the possibility of finding significant factors that would make it possible to distinguish between approved drugs and drugs that have been withdrawn after several years of use. The EU responded to this interest by funding a large AI4EU project, which launched calls for proposals to develop various artificial intelligence (AI)-based computing solutions.[1] Among them was the task to develop a predictive AI solution based on the deep neural network method to distinguish drugs from withdrawn drugs based on their structure.[2] In this presentation, the process of defining the problem and creating a dataset will be elaborated, as well as related issues such as the different status of the same drug in different countries or regions, or the problem of cleaning datasets, as many drugs are not pure compounds but complexes. We have calculated comprehensive sets of molecular structure descriptors for the final sets of approved and withdrawn drugs. The analysis of the importance/usefulness of each structure-based molecular descriptor (including those related to ADMETox properties of drugs) in discriminating between approved and withdrawn drugs will be presented. As expected, the classification accuracy of the multivariate models based on descriptors is not high. Nevertheless, it is comparable to (or sometimes better than) more complex models and significantly higher than the accuracy achieved by random guessing (random model). REFERENCES [1] The AI4EU Call for Solutions Seeking Companies to Solve AI Challenges, https://internationaldataspaces.org/the-ai4eu-call-for-solutions-seeking-companies-to-solve-aichallenges/ (assessed on April 15, 2022) [2] The AI-on-demand platform, https://www.ai4europe.eu/ and https://www.ai4media.eu/projectoverview/ (assessed on April 15, 2022)

Despite decades of intensive search for compounds that modulate the activity of particular protein targets, a large proportion of the human kinome remains as yet undrugged. Effective approaches are therefore required to map the massive space of unexplored compound-kinase interactions for novel and potent activities. Here, we carry out a crowdsourced benchmarking of predictive algorithms for kinase inhibitor potencies across multiple kinase families tested on unpublished bioactivity data. We find the top-performing predictions are based on various models, including kernel learning, gradient boosting and deep learning, and their ensemble leads to a predictive accuracy exceeding that of single-dose kinase activity assays. We design experiments based on the model predictions and identify unexpected activities even for under-studied kinases, thereby accelerating experimental mapping efforts. The open-source prediction algorithms together with the bioactivities between 95 compounds and 295 kinases provide a resource for benchmarking prediction algorithms and for extending the druggable kinome. The IDG-DREAM Challenge carried out crowdsourced benchmarking of predictive algorithms for kinase inhibitor activities on unpublished data. This study provides a resource to compare emerging algorithms and prioritize new kinase activities to accelerate drug discovery and repurposing efforts.

Protein folding is a very important problem in the biosciences that is studied experimentally but also by modelling (theoretical and simulation analyses) [1]. Undoubtedly, all information related to folding is contained in the primary structure of proteins - in the sequence of amino acids. For the past 20 years, attempts have been made to model the dependences of the protein folding constants kf (s-1), which are equal to 1 / (time needed for protein folding). It was observed in the very beginning that this is a size-dependent problem, which means that ln(kf) significantly depends on the length of the protein sequence, i.e. on the number of amino acid residues in the protein chain. Then, the dependence on the number of amino acids that take on the correct secondary structure of alpha or beta, on the topology of the 3D structure, was also observed [2]. As better predictors of protein folding constants, new structural parameters based on the total number of amino acids in regular secondary structures in the protein chain were obtained [3]. Furthermore, the parameters that calculate the permutation entropy of the secondary structure of the protein also show good agreement with the protein folding constants.

Recently, a new accuracy parameter was introduced for binary classification models, that can be used for estimating the (real) model contribution which is over the level of random accuracy [1, 2]. The randomization of the Y variable is used as a standard procedure in the model quality analysis in general, but particularly in the modelling of relationships between the structure and property/activity (QSP(A)R) of chemical compounds. A good result of randomization analyses for a model is when its actual accuracy, estimated by a selected statistical measure (parameter) of model quality, is significantly higher than the accuracy obtained by the best-randomized model. In binary classification models, both the experimental variable Y and corresponding model variable Y’ (estimated/predicted by the model) have values of 0 or 1 (inactive/active). The values of each statistical measure (parameters, metrics) of such a model, derived from the comparison of experimental (Y) and model (Y’) variables, can be expressed by four numbers forming a confusion matrix/table. These are TP (true positive) and TN (true negative) representing the total number of correct classification (when the same values are in variables Y and Y’), and FN (false negative) and FP (false positive) that are incorrect predictions. By performing permutation analysis of the values of model variable Y’ keeping variable Y in the original order, we defined the characteristic values of the statistical measure (metric, parameter) as the border values (i.e. minimal and maximal) and the most probable (random) value. We derived the formulae for estimating the characteristic values of accuracy parameter (metric) measuring the percent of correct classification. Also, the usefulness of derived parameters will be illustrated in the analysis of the quality of balanced and non- balanced QSP(A)R models and confirmed by simulation results. Further, the possibility of application of the developed methodology in estimating the complexity of binary classification variables and models will be elaborated and generalized to multi-class problems.

Previous approaches implemented on drug-kinase binding affinity benchmark datasets show poor performance on rigorous test scenarios with unseen small compounds or protein kinase targets - thus limiting their real-world application. We represent methodology which relies on an ensemble approach, XGBoost trained on fingerprint based and protein kinase domain sequence-based similarity features - and graph convolutional networks (GCN) as more advanced representation learning predictive methodology. To assess the uncertainty surrounding model predictions, we defined a structure-based applicability domain with a focus on density of compound space in the training set.

In plant biochemistry and physiology, coumarins are known as antioxidants, enzyme inhibitors and precursors of toxic substances. Nuclear magnetic resonance (NMR) spectra are primary sources of molecular structural data. NMR provides detailed information about the local environment of the atom which can be used to determine the atomic connectivity, stereochemistry, and molecular conformation. For many years the molecular structure has been determined by NMR spectroscopy and chemical shifts are determined manually with the help of computer programs. However, recent progress in computational chemistry and chemo/bioinformatics opened the possibility for the prediction of chemical shifts (especially those of 1H and 13C nuclei) of new chemicals. We analyzed the accuracy of three available chemoinformatics methods developed for the prediction of 1H and 13C chemical shifts based on deep neural networks CASCADE [1], an older prediction method based on classical neural networks NMRshiftDB [2, 3], and group-contribution method in ChemDraw [4]. The mean absolute errors (MAEs) in the prediction of NMR shifts of four newly synthesized coumarins [5] by CASCADE, NMRshiftDB and ChemDraw are (respectively) 0.39, 0.65 and 0.32 ppm for 1H, and 1.5, 6.5 and 2.3 ppm for 13C atoms, shoving relatively big differences between these prediction methods.

Antioxidants play an important role in preserving human health in the fight against cell damage caused by free radicals [1]. Different types of honey and from different geographical origins show different polyphenol content. The aim of this study was to determine the total polyphenol content (TPC) in 96 honey samples from different countries of Central and Eastern Europe (Croatia, Serbia, Bosnia and Herzegovina, Hungary, Slovenia and Italy) by a spectrophotometric method with Folin Ciocalteu reagent [2]. If we analyze the measurements of the same types of honey (e.g. acacia or chestnut) from a number of literature sources, large differences in the values of total phenols are observed, which cannot be attributed only to seasonal or geographical variations. Our previous studies gave the TPC values from 1164.99 mg/kg to 212.9 mg/kg for the dominant uni- and multi-floral honey. In an attempt to decipher the reasons for these excessive differences, we analyzed the impact of sample ageing and seasonal and geographic variations. However, some differences are too large, and the cause seems to be the inconsistency of the calculation of the measurement units. Namely, some authors state that they modified method [1, 2], but do not state in detail which part they modified. Our experience to date shows that the authors took different amounts of honey for analysis and some used a gallic acid for calibration curve in the range of 0–200 μg/mL and some of 0–400 μg/mL. For these reasons, we would suggest a more strict standardisation of the total polyphenol content measurements.

Molecular modelling is an ever-increasing and very important research sub-field in chemistry, drug design, life and environmental sciences in transferring and archiving the chemical knowledge into the digital form. The final developed model is a mathematical equation, or nowadays often computational method available for the use as a web server or computer program. Some of the models like Quantitative Structure-Activity Relationships (QSARs) found application in environmental protection by regulatory agencies both in the US and in the EU. QSARs are methods for estimating properties of a chemical from its molecular structure and have the potential to provide information on hazards of chemicals while reducing time, monetary cost and animal testing. [1] The development of a QSAR model starts with a large set of reliable chemical structures and experimental data. If the data set is larger, and if the experimental data were measured with higher accuracy, then the developed model and conclusions based on it will be more significant. For many modern chemical models, it is not easy to give a clear interpretation, and also, they often suffer from overfitting. Moreover, proper validation of the expected accuracy of models in an application on a new data set is not an easy task. OECD initiated in 1990 a project devoted to the evaluation of the predictive power of the QSAR models development of regulatory procedures for the use of QSARs to predict the toxicity of chemicals.[1] Improvement of models and modelling procedure in the strong connection of chemistry, mathematical statistics, and computer science will help to enter into the digital chemistry era with more significant models and chemical information. The IUPAC activities in the standardization of digital form of chemical data, information and databases, in an increase of the size and quality of database of chemical relevance, and (together with OECD) in the standardization of validation parameters and modelling procedures could strongly support the development of QSARs and molecular modelling.