Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks

In this paper, we present and compare four methods to enforce Dirichlet boundary conditions in Physics-Informed Neural Networks (PINNs) and Variational Physics-Informed Neural Networks (VPINNs). Such conditions are usually imposed by adding penalization terms in the loss function and properly choosing the corresponding scaling coefficients; however, in practice, this requires an expensive tuning phase. We show through several numerical tests that modifying the output of the neural network to exactly match the prescribed values leads to more efficient and accurate solvers. The best results are achieved by exactly enforcing the Dirichlet boundary conditions by means of an approximate distance function. We also show that variationally imposing the Dirichlet boundary conditions via Nitsche's method leads to suboptimal solvers.

Effects of treated industrial wastewaters and temperatures on growth and enzymatic activities of duckweed (Lemna minor L.)

The efficacy of the removal of contaminants from wastewater depends on physico-chemical properties of pollutants and the efficiency of treatment plant. Sometimes, low amounts of toxic compounds can be still present in the treated sewage. In this work we considered the effects of contaminant residues in treated wastewaters and of temperatures on Lemna minor L. Treated effluent waters were collected, analyzed and used as duckweed growth medium. In order to better understand the effects of micropollutants and seasonal variation, the plants were grown under ambient conditions for seven days in summer and winter. Relative growth rate, pigments and phenolic compounds concentrations were determined, as well as the activities of catalase (CAT), ascorbate peroxidase (APX), guaiacol peroxidase (G-POD) and polyphenol oxidase (PPO). The pollutant concentrations varied in the two seasons, depending on the industrial and municipal activities and efficiency of treatments. Treated waters contained heavy metals, nitrogenous and phosphorus compounds, surfactants and hydrocarbons. Compared to the control, duckweed growth of treated plants decreased by 25% in summer, while in the winter due to the lower temperatures and the presence of pollutants was completely impeded. The amounts of photosynthetic pigments of treated plants were not significantly affected in the summer, while they were higher than the control in the winter when the effluent had a high nitrogen amount. High CAT activity was registered in both seasons. Treated plants had significantly lower APX activity in the summer (53%) and winter (59%) respect to the controls. The observed inhibition of the peroxidase activities in the exposed plants, confirms the controversy existing in the literature about the variability of enzymatic response in stress condition.

Determination of lactoferrin and immunoglobulin g in animal milks by new immunosensors

Two different immunosensors, recently developed for the determination of antibacterial proteins (lactoferrin and immunoglobulin G) in buffalo milk and in other commercial animal milks samples, were used in the present study. The aim was to propose these immunosensor methods for routine control of important diet products, such as cow and goat milks, and in particular buffalo milk. To this end we employed two different kinds of immunosensors: one for the analysis of immunoglobulin G (IgG), the other was a new amperometric immunosensor for lactoferrin analysis. Lactoferrin and IgG immunosensors were also used for the determination of lactoferrin and immunoglobulin G in buffalo milk on different days of lactation.

Binary classification models for endocrine disrupter effects mediated through the estrogen receptor

Endocrine disrupters (EDs) form an interesting field of application attracting great attention in the recent years. They represent a number of exogenous substances interfering with the function of the endocrine system, including the interfering with developmental processes. In particular EDs are mentioned as substances requiring a more detailed control and specific authorization within REACH, the new European legislation on chemicals, together with other groups of chemicals of particular concern. QSAR represents a challenging method to approach data gap which is foreseen by REACH. The aim of this study was to provide an insight into the use of QSAR models to address ED effects mediated through the estrogen receptor (ER). New predictive models were derived to assess estrogenicity for a very large and heterogeneous dataset of chemical compounds. QSAR binary classifiers were developed based on different data mining techniques such as classification trees, decision forest, fuzzy logic, neural networks and support vector machines. The focus was given to multiple endpoints to better characterize the effects of EDs evaluating both binding (RBA) and transcriptional activity (RA). A possible combination of the models was also explored. A very good accuracy was reached for both RA and RBA models (higher than 80%).

Ecotoxicity prediction by adaptive fuzzy partitioning: comparing descriptors computed on 2D and 3D structures

Classification models were established on four endpoints, i.e. trout, daphnia, quail and bee, including from 100 to 300 pesticides subdivided into 3 toxicity classes. For each species, five separate sets of molecular descriptors, computed by several software, were compared, including parameters related to 2D or 3D structures. The most relevant descriptors were selected with help of a procedure based on genetic algorithms. Then, structure-activity relationships were built by Adaptive Fuzzy Partition (AFP), a recursive partitioning method derived from Fuzzy Logic concepts.Globally, satisfactory results were obtained for each animal species. The best cross-validation and test set scores reached values of about 70-75%. More important, the relationships derived from the descriptors calculated from 2D structures were superior or similar to those computed from 3D structures. These results underline that the long computational time employed to compute 3D descriptors is often useless to improve the prediction ability of the ecotoxicity models. Finally, the differences in the prediction ability between the different software used were quite reduced and show the possibility to use different descriptor packages for obtaining similar satisfactory models.

Database mining applied to central nervous system (CNS) activity

A data set of 389 compounds, active in the central nervous system (CNS) and divided into eight classes according to the receptor type, was extracted from the RBI database and analyzed by Self-Organizing Maps (SOM), also known as Kohonen Artificial Neural Networks. This method gives a 2D representation of the distribution of the compounds in the hyperspace derived from their molecular descriptors. As SOM belongs to the category of unsupervised techniques, it has to be combined with another method in order to generate classification models with predictive ability. The fuzzy clustering (FC) approach seems to be particularly suitable to delineate clusters in a rational way from SOM and to get an automatic objective map interpretation. Maps derived by SOM showed specific regions associated with a unique receptor type and zones in which two or more activity classes are nested. Then, the modeling ability of the proposed SOM/FC Hybrid System tools applied simultaneously to eight activity classes was validated after dividing the 389 compounds into a training set and a test set, including 259 and 130 molecules, respectively. The proper experimental activity class, among the eight possible ones, was predicted simultaneously and correctly for 81% of the test set compounds.

Protein-based alignment in 3D QSAR of 26 indole inhibitors of human pancreatic phospholipase A2

An automated docking procedure was applied on a series of 26 reversible and competitive indole inhibitors of human pancreatic phospholipase A2 (hp-PLA2). X-ray data of this enzyme are not available and the structure was then reconstructed exploiting its protein sequence and the crystallographic data of a bovine pancreatic source. The docking data were used to build a three-dimensional quantitative structure-activity relationship (3D QSAR) model, established using the comparative molecular field analysis (CoMFA) method. This model, joined to the previous one developed for the indole inhibitors of human non-pancreatic secretory phospholipase A2 (hnps-PLA2), an enzyme involved in inflammation processes, will allow for the selection of new strong anti-inflammatory drugs with negligible side effects, at least at the level of hp-PLA2.

A molecular modeling and 3D QSAR study of a large series of indole inhibitors of human non-pancreatic secretory phospholipase A2

Automated docking allowing protein-based alignment was performed for a series of 188 indole inhibitors of the human non-pancreatic secretory phospholipase A2 (hnps-PLA2). All the substituted indoles were docked to the crystal structure of hnps-PLA2 and a three-dimensional QSAR model was then established using the CoMFA method. The set of 188 compounds was divided into two subsets, the first one constituting the training set (126 compounds), while the second constituted the test set (62 compounds). The established CoMFA model derived from the training set was then applied to the test set. A good correlation between predicted and experimental activity data allows to validate the 3D QSAR model. A second and global 3D QSAR including all the compounds was established, allowing the creation of the hnps-PLA2 pharmacophore.

Hybrid systems for virtual screening: interest of fuzzy clustering applied to olfaction

Kohonen neural networks, also known as Self Organizing Map (SOM), offer a useful 2D representation of the compound distribution inside a large chemical database. This distribution results from the compound organization in a molecular diversity hyperspace derived from a large set of molecular descriptors. Fuzzy techniques based on the "concept of partial truth" reveal to be also a valuable tool for the direct exploitation of chemical databases or SOM. In such cases a fuzzy clustering algorithm is used. In this paper, a complete hybrid system, combining SOM and fuzzy clustering, is applied. As example, a series of olfactory compounds was selected. The complexity of such information is that a same compound may exhibit different odors. It is shown how fuzzy logic helps to have a better understanding of the organization of the compounds. These hybrid systems, using simultaneously SOM and fuzzy clustering, are foreseen as powerful tools for "virtual pre-screening".

Interaction of Ca2+ and Na+ ions with polygalacturonate chains: a molecular dynamics study

Partially esterified polygalacturonic acid is the main component of pectin in higher plants. The carboxylic groups and their methyl esters markedly affect the ability of the pectin molecules to bind oppositely charged ions and to form gels. In order to make a contribution to the understanding of the mechanisms which regulate the ionic transfer at the soil-root interface and in the apoplast, we report the results of a set of molecular dynamics experiments in which the interactions of four fully deprotonated fragments of polygalacturonic acid, each counting 12 units, 300 water molecules and 48 or 24 Na+ and Ca2+ ions were studied. We observed the formation of Ca2+ bridges between the polygalacturonate chains. The forces driving the aggregation processes are characterized by the formation of strong coulombic interactions between the metal ions and the carboxylate groups. The results are consistent with experiment evidence of the formation of Ca-polygalacturonate organized gels. The Ca-polygalacturonate complex exhibits a lower energy compared to that of Na-polygalacturonate. The ratio of the Na+ and Ca2+ diffusion coefficients agree well with experimental reports.

A molecular modelling study of the interaction between beta-cyclodextrin and the organophosphorothioate pesticide parathion

The interaction between parathion and beta-cyclodextrin was investigated by Molecular Dynamics. Several in vacuo trajectories were calculated for the system imposing a 1:1 stoichiometry. The influence of the solvent and temperature was considered. The results account for the formation of adducts which are stable at room temperature and involve mainly the nitrophenoxy group of the guest molecules which interacts with the hydrophobic cavity of the host by van der Waals forces.

A molecular dynamics study of the inclusion of mono- and disubstituted benzenes in beta-cyclodextrin

The interaction between beta-cyclodextrin and five mono- and disubstituted benzenes in water was investigated by means of molecular dynamics. The trajectories were calculated for each system, imposing a 1:1 host-guest stoichiometry with 512 water molecules. Periodic boundary conditions were adopted. The results account for the formation of stable adducts and the predicted geometry agrees with experimental circular dichroism data.