Combinatorial k-means clustering as a machine learning tool applied to diabetes mellitus type 2

A new original procedure based on k-means clustering is designed to find the most appropriate clinical variables able to efficiently separate into groups similar patients diagnosed with diabetes mellitus type 2 (DMT2) and underlying diseases (arterial hypertonia (AH), ischemic heart disease (CHD), diabetic polyneuropathy (DPNP), and diabetic microangiopathy (DMA)). Clustering is a machine learning tool for discovering structures in datasets. Clustering has been proven to be efficient for pattern recognition based on clinical records. The considered combinatorial k-means procedure explores all possible k-means clustering with a determined number of descriptors and groups. The predetermined conditions for the partitioning were as follows: every single group of patients included patients with DMT2 and one of the underlying diseases; each subgroup formed in such a way was subject to partitioning into three patterns (good health status, medium health status, and degenerated health status); optimal descriptors for each disease and groups. The selection of the best clustering is obtained through the parameter called global variance, defined as the sum of all variance values of all clinical variables of all the clusters. The best clinical parameters are found by minimizing this global variance. This methodology has to identify a set of variables that are assumed to separate each underlying disease efficiently in three different subgroups of patients. The hierarchical clustering obtained for these four underlying diseases could be used to build groups of patients with correlated clinical data. The proposed methodology gives surmised results from complex data based on a relationship with the health status of the group and draws a picture of the prediction rate of the ongoing health status

Calculating the partition coefficients of organic solvents in octanol/water and octanol/air

Partition coefficients define how a solute is distributed between two immiscible phases at equilibrium. The experimental estimation of partition coefficients in a complex system can be an expensive, difficult, and time-consuming process. Here a computational strategy to predict the distributions of a set of solutes in two relevant phase equilibria is presented. The octanol/water and octanol/air partition coefficients are predicted for a group of polar solvents using density functional theory (DFT) calculations in combination with a solvation model based on density (SMD) and are in excellent agreement with experimental data. Thus, the use of quantum-chemical calculations to predict partition coefficients from free energies should be a valuable alternative for unknown solvents. The obtained results indicate that the SMD continuum model in conjunction with any of the three DFT functionals (B3LYP, M06-2X, and M11) agrees with the observed experimental values. The ighest correlation to experimental data for the octanol/water partition coefficients was reached by the M11 functional; for the octanol/air partition coefficient, the M06-2X functional yielded the best performance. To the best of our knowledge, this is the first computational approach for the rediction of octanol/air partition coefficients by DFT calculations, which has remarkable accuracy and precision

Multivariate analysis for the classification of copper lead and copper zinc glasses

The similarity patterns in the physicochemical properties of copper-lead and copper-zinc borate glasses were identified by means of finding similarity within the objects of study using multivariate statistical analysis. As exploratory methods of multivariate analysis, cluster analysis, principal components analysis, and two-way clustering were applied for a set of copper-lead and copper-zinc borate glasses. Specific correlations among the physicochemical properties of copper glasses were interpreted. In particular, the effect of Pb and Zn doping metal ion in copper glasses in the structural and mechanical properties is identified. Interestingly, the degree of lead content determines two kinds of glasses with specific physicochemical properties

On the use of the discrete constant pH molecular dynamics to describe the conformational space of peptides

Solvent pH is an important property that defines the protonation state of the amino acids and, therefore, modulates the interactions and the conformational space of the biochemical systems. Generally, this thermodynamic variable is poorly considered in Molecular Dynamics (MD) simulations. Fortunately, this lack has been overcome by means of the Constant pH Molecular Dynamics (CPHMD) methods in the recent decades. Several studies have reported promising results from these approaches that include pH in simulations but focus on the prediction of the effective pKa of the amino acids. In this work, we want to shed some light on the CPHMD method and its implementation in the AMBER suitcase from a conformational point of view. To achieve this goal, we performed CPHMD and conventional MD (CMD) simulations of six protonatable amino acids in a blocked tripeptide structure to compare the conformational sampling and energy distributions of both methods. The results reveal strengths and weaknesses of the CPHMD method in the implementation of AMBER18 version. The change of the protonation state according to the chemical environment is presumably an improvement in the accuracy of the simulations. However, the simulations of the deprotonated forms are not consistent, which is related to an inaccurate assignment of the partial charges of the backbone atoms in the CPHMD residues. Therefore, we recommend the CPHMD methods of AMBER program but pointing out the need to compare structural properties with experimental data to bring reliability to the conformational sampling of the simulations

Unravelling Constant pH Molecular Dynamics in Oligopeptides with Explicit Solvation

An accurate description of the protonation state of amino acids is essential to correctly simulate the conformational space and the mechanisms of action of proteins or other biochemical systems. The pH and the electrochemical environments are decisive factors to define the effective pKa of amino acids and, therefore, the protonation state. However, they are poorly considered in Molecular Dynamics (MD) simulations. To deal with this problem, constant pH Molecular Dynamics (cpHMD) methods have been developed in recent decades, demonstrating a great ability to consider the effective pKa of amino acids within complex structures. Nonetheless, there are very few studies that assess the effect of these approaches in the conformational sampling. In a previous work of our research group, we detected strengths and weaknesses of the discrete cpHMD method implemented in AMBER when simulating capped tripeptides in implicit solvent. Now, we progressed this assessment by including explicit solvation in these peptides. To analyze more in depth the scope of the reported limitations, we also carried out simulations of oligopeptides with distinct positions of the titratable amino acids. Our study showed that the explicit solvation model does not improve the previously noted weaknesses and, furthermore, the separation of the titratable amino acids in oligopeptides can minimize them, thus providing guidelines to improve the conformational sampling in the cpHMD simulations

Effect of charge regulation and conformational equilibria in the 2 stretching properties of weak polyelectrolytes

Weak polyelectrolytes can modulate their charge in response to external perturbations, such as changes in the pH, ionic strength (I), or electrostatic interactions with other charged species, a phenomenon known as charge regulation (CR). On the other hand, it is well established that CR is highly coupled with the conformational degrees of freedom. In this paper, the influence of CR in the stretching properties of weak polyelectrolytes is analyzed, and the possibility of CR induced by mechanical stretching is explored. With this aim, we make use of a minimal model, which captures the fundamental aspects present in the stretching of a flexible weak linear polyelectrolyte: internal angle rotation, bond stretching, bond bending, and proton binding, which is the paradigmatic mechanism of CR. The angle rotation is described by using the rotational isomeric state approximation, while for protonation, the site binding model is assumed. Mechanical stretching is studied by performing semi-grand canonical Monte Carlo simulations at different pH and ionic strength conditions. The simulations simultaneously provide both conformational (bond state probabilities, persistence length lP, and chain elongation) and protonation properties (degree of protonation θ and the effective protonation constant Kc). The obtained force−extension curves suggest that the pH value and the ionic strength I have a significant effect on polyelectrolyte stretching. Three different force regimes can be observed. For large forces (F > 100 pN for typical force constants), the force−extension curve is almost independent of the pH and I. For low forces, the persistence length lP is force-independent, although it strongly increases with the pH value. Under this regime, linear and Pincus scaling behaviors are observed. Finally, in the intermediate-force regime, both rotational and protonation degrees of freedom are mechanically activated, and the picture becomes more complicated. It is found that lP increases with F and, under certain conditions, a significant increase of θ with F is observed, indicating that CR could in principle be induced by means of mechanical stretching. This fact can be explained by analyzing the coupling between θ and the probability of a bond to be in the gauche state P(g). P(g) decreases with F as the bonds adopt the trans conformation so that the electrostatic repulsion is reduced and θ increases. Finally, the intricate interplay between short-range and long-range interactions is analyzed, leading to apparently contradictory behaviors (P(g) and lp simultaneously decrease with I), which can only be explained by CR and the presence of complex spatial correlations

Applying discriminant and cluster analysis to separate allergenic from non-allergenic proteins

As a result of increased healthcare requirements and the introduction of genetically modified foods, the problem of allergies is becoming a growing health problem. The concept of allergies has prompted the use of new methods such as genomics and proteomics to uncover the nature of allergies. In the present study, a selection of 1400 food proteins was analysed by PLS-DA (Partial Least Square-based Discriminant Analysis) after suitable transformation of structural parameters into uniform vectors. Then, the resulting strings of different length were converted into vectors with equal length by Auto and Cross-Covariance (ACC) analysis. Hierarchical and non-hierarchical (K-means) Cluster Analysis (CA) was also performed in order to reach a certain level of separation within a small training set of plant proteins (16 allergenic and 16 non-allergenic) using a new three-dimensional descriptor based on surface protein properties in combination with amino acid hydrophobicity scales. The novelty of the approach in protein differentiation into allergenic and non-allergenic classes is described in the article. The general goal of the present study was to show the effectiveness of a traditional chemometric method for classification (PLS-DA) and the options of Cluster Analysis (CA) to separate by multivariate statistical methods allergenic from non-allergenic proteins

Insight into Electric field-induced rupture mechanism of water-in-toluene emulsion films from a model system

This paper presents a model, which we have designed to get insight into the development of electro- induced instability of a thin toluene emulsion film in contact with the saline aqueous phase. Molecular dynamics (MD) simulations demonstrate the role of charge accumulation in the toluene-film rupture induced by a DC electric field. Two ensembles¿NVT and NPT ¿are used to determine the critical value of the external field at which the film ruptures, the charge distribution and capacitance of the thin film, number densities, and the film structure. The rupture mechanism as seen from this model is the following: in both NVT and NPT ensembles, condenser plates, where the charge density is maximal, are situated at the very border between the bulk aqueous (water) phase and the mixed layer. No ion penetration is observed within the toluene core, thus leaving all the distribution of charges within the mixed zone and the bulk phase that could be attributed to the formation of hydration shells. When the critical electric field is reached within a certain time after the field application, electric discharge occurs indicating the beginning of the rupturing process. The MD simulations indicate that the NPT ensemble predicts a value of the critical field that is closer to the experimental finding. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.498316

Dealing with long-range interactions in the determination of polyelectrolyte ionization properties. Extension of the transfer matrix formalism to the full range of ionic strengths

The ionization state of charged macromolecules in solution is usually determined by the extent of the binding processes. These processes are very sensitive to the ionic strength of the medium, which are of long-range nature. The ionization properties of weak polyelectrolytes can be described by means of Ising-type models, which is only feasible when long-range interactions are neglected. Here, this formalism is extended to include long-range interactions by introducing a modified free energy involving only effective short-range interaction parameters. These parameters can be systematically calculated by using the Gibbs-Bogoliubov variational principle. The technique is illustrated with the calculation of titration curves of homogeneous and heterogeneous polyelectrolytes in a wide range of ionic strengths. The correction of the site protonation free energy (first order correction) is enough to obtain an excellent agreement between theory and Monte Carlo simulations. Corrections to other cluster parameters (higher order corrections) are also implemented. In general, the correction to a particular parameter represents the average change in the long-range energy when a new interaction is created in the polyelectrolyte. The method presented here represents an improvement in the description of the ionization state of polyelectrolytes that can be relevant in a wide range of areas.represents the average change in the long range energy when a new interaction (of the type described by the cluster parameter), is created in the polyelectrolyte. The method presented here represents an improvement in the description of the ionization state of charged macromolecules that can be relevant in a wide range of areas such as biochemistry, environmental chemistry, materials science, etc

Unveiling the Effect of Low pH on the SARS-CoV-2 Main Protease by Molecular Dynamics Simulations

(1) Background: Main Protease (Mpro) is an attractive therapeutic target that acts in the replication and transcription of the SARS-CoV-2 coronavirus. Mpro is rich in residues exposed to protonation/deprotonation changes which could affect its enzymatic function. This work aimed to explore the effect of the protonation/deprotonation states of Mpro at different pHs using computa- tional techniques. (2) Methods: The different distribution charges were obtained in all the evaluated pHs by the Semi-Grand Canonical Monte Carlo (SGCMC) method. A set of Molecular Dynamics (MD) simulations was performed to consider the different protonation/deprotonation during 250 ns, verifying the structural stability of Mpro at different pHs. (3) Results: The present findings demon- strate that active site residues and residues that allow Mpro dimerisation was not affected by pH changes. However, Mpro substrate-binding residues were altered at low pHs, allowing the increased pocket volume. Additionally, the results of the solvent distribution around Sγ, Hγ, Nδ1 and Hδ1 atoms of the catalytic residues Cys145 and His41 showed a low and high-water affinity at acidic pH, respectively. It which could be crucial in the catalytic mechanism of SARS-CoV-2 Mpro at low pHs. Moreover, we analysed the docking interactions of PF-00835231 from Pfizer in the preclinical phase, which shows excellent affinity with the Mpro at different pHs. (4) Conclusion: Overall, these findings indicate that SARS-CoV-2 Mpro is highly stable at acidic pH conditions, and this inhibitor could have a desirable function at this condition