Canonical versus grand canonical occupation numbers for simple systems

An ideal gas ofN indistinguishable particles is described by a canonical ensemble (c.e.) and also by a grand canonical ensemble (g.c.e.) which hasN as themean total number of particles, the temperature and volume being the same in both cases. Exact mean occupation numbersn _j(N) are found if the system has only two states 1 and 2 of energiesE ₂E ₁. This should apply to quantum wells and similar simple systems. For systems which have captured one particle, the theory gives the simplest answers, and one find a maximum discrepancy of 17% between the two ensembles for the fermion case. It occurs whenE ₂–E ₁53 meV at room temperature. ForN=1 the mean occupation number for the c.e. is identical for fermions and for bosons, being in both cases given byn ₂(1)={exp[(E ₂-E ₁)/kT]+1}^-1,n ₁(1)=1-n ₂(1) For largeN one reverts to the usual situation and the discrepancy between the ensembles becomes small.     

In silico models for the prediction of dose-dependent human hepatotoxicity

The liver is extremely vulnerable to the effects of xenobiotics due to its critical role in metabolism. Drug-induced hepatotoxicity may involve any number of different liver injuries, some of which lead to organ failure and, ultimately, patient death. Understandably, liver toxicity is one of the most important dose-limiting considerations in the drug development cycle, yet there remains a serious shortage of methods to predict hepatotoxicity from chemical structure. We discuss our latest findings in this area and present a new, fully general in silico model which is able to predict the occurrence of dose-dependent human hepatotoxicity with greater than 80% accuracy. Utilizing an ensemble recursive partitioning approach, the model classifies compounds as toxic or non-toxic and provides a confidence level to indicate which predictions are most likely to be correct. Only 2D structural information is required and predictions can be made quite rapidly, so this approach is entirely appropriate for data mining applications and for profiling large synthetic and/or virtual libraries.     

Field-Template,QSAR, Ensemble Molecular Docking,and 3D-RISM Solvation Studies Expose Potential of FDA-Approved Marine Drugs as SARS-CoVID-2 Main Protease Inhibitors

Currently, SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) has infected people among all countries and is a pandemic as declared by the World Health Organization (WHO). SARS-CoVID-2 main protease is one of the therapeutic drug targets that has been shown to reduce virus replication, and its high-resolution 3D structures in complex with inhibitors have been solved. Previously, we had demonstrated the potential of natural compounds such as serine protease inhibitors eventually leading us to hypothesize that FDA-approved marine drugs have the potential to inhibit the biological activity of SARS-CoV-2 main protease. Initially, field-template and structure–activity atlas models were constructed to understand and explain the molecular features responsible for SARS-CoVID-2 main protease inhibitors, which revealed that Eribulin Mesylate, Plitidepsin, and Trabectedin possess similar characteristics related to SARS-CoVID-2 main protease inhibitors. Later, protein–ligand interactions are studied using ensemble molecular-docking simulations that revealed that marine drugs bind at the active site of the main protease. The three-dimensional reference interaction site model (3D-RISM) studies show that marine drugs displace water molecules at the active site, and interactions observed are favorable. These computational studies eventually paved an interest in further in vitro studies. Finally, these findings are new and indeed provide insights into the role of FDA-approved marine drugs, which are already in clinical use for cancer treatment as a potential alternative to prevent and treat infected people with SARS-CoV-2.     

Synergizing Off-Target Predictions for In Silico Insights of CENH3 Knockout in Cannabis through CRISPR/Cas

The clustered regularly interspaced short palindromic repeats (CRISPR)/Cas-mediated genome editing system has recently been used for haploid production in plants. Haploid induction using the CRISPR/Cas system represents an attractive approach in cannabis, an economically important industrial, recreational, and medicinal plant. However, the CRISPR system requires the design of precise (on-target) single-guide RNA (sgRNA). Therefore, it is essential to predict off-target activity of the designed sgRNAs to avoid unexpected outcomes. The current study is aimed to assess the predictive ability of three machine learning (ML) algorithms (radial basis function (RBF), support vector machine (SVM), and random forest (RF)) alongside the ensemble-bagging (E-B) strategy by synergizing MIT and cutting frequency determination (CFD) scores to predict sgRNA off-target activity through in silico targeting a histone H3-like centromeric protein, HTR12, in cannabis. The RF algorithm exhibited the highest precision, recall, and F-measure compared to all the tested individual algorithms with values of 0.61, 0.64, and 0.62, respectively. We then used the RF algorithm as a meta-classifier for the E-B method, which led to an increased precision with an F-measure of 0.62 and 0.66, respectively. The E-B algorithm had the highest area under the precision recall curves (AUC-PRC; 0.74) and area under the receiver operating characteristic (ROC) curves (AUC-ROC; 0.71), displaying the success of using E-B as one of the common ensemble strategies. This study constitutes a foundational resource of utilizing ML models to predict gRNA off-target activities in cannabis.     

Crystal and molecular structures of two modifications of a chelate compound of Pb[(<Emphasis Type="Italic">iso</Emphasis>-C<Subscript>4</Subscript>H<Subscript>9</Subscript>)<Subscript>2</Subscript>PS<Subscript>2</Subscript>]<Subscript>2</Subscript>

A chelate compound Pb[(iso-C₄H₉)₂PS₂]² is synthesized. Using X-ray diffraction data, the crystal structures of two modifications of this compound are determined (X8 APEX diffractometer, MoK _α radiation, 14169 F _hkl , R = 0.0480 for the low temperature α-form and 6261 F _hkl , R = 0.0387 for the β-form studied at ambient temperature). The crystals are triclinic: a = 11.047(2) Å, b = 14.486(3) Å, c = 32.048(6) Å; α = 91.30(3)°, β = 99.73(3)°, γ = 101.61(3)°, V = 4942.9(17) ų, Z = 8, ρ_calc = 1.682 g/cm³ (α-modification) and a = 11.2124(5) Å, b = 14.6989(7) Å, c = 17.1644(6) Å; α = 109.393(1)°, β = 94.989(2)°, γ = 101.649(1)°, V = 2576.83(19) ų, Z = 4, ρ_calc = 1.613 g/cm³ (β-modification), space group \(P\bar 1\) for both polymorphs. The structures are molecular, coordination cores of PbS₄ are tetragonal pyramids with Pb atoms in the vertices and S atoms in the base. In both structures intermolecular Pb...S contacts yield supramolecular ensembles comprising by four molecules, where PbS₄₊₂ cores form planar aggregates of edge-sharing octahedra. The ensembles are joined by weak intermolecular S...S interactions resulting in the development of polymeric chains along the a axis.     

Prediction of adsorption of small molecules in porous materials based on ab initio force field method

Computational prediction of adsorption of small molecules in porous materials has great impact on the basic and applied research in chemical engineering and material sciences. In this work,we report an approach based on grand canonical ensemble Monte Carlo(GCMC) simulations and ab initio force fields. We calculated the adsorption curves of ammonia in ZSM-5 zeolite and hydrogen in MOF-5(a metal-organic-framework material). The predictions agree well with experimental data. Because the predictions are based on the first principle force fields,this approach can be used for the adsorption prediction of new molecules or materials without experimental data as guidance.     

Prediction of adsorption of small molecules in porous materials based on <Emphasis Type="Italic">ab initio</Emphasis> force field method

Computational prediction of adsorption of small molecules in porous materials has great impact on the basic and applied research in chemical engineering and material sciences. In this work, we report an approach based on grand canonical ensemble Monte Carlo (GCMC) simulations and ab initio force fields. We calculated the adsorption curves of ammonia in ZSM-5 zeolite and hydrogen in MOF-5 (a metal-organic-framework material). The predictions agree well with experimental data. Because the predictions are based on the first principle force fields, this approach can be used for the adsorption prediction of new molecules or materials without experimental data as guidance. Supported by the National “973” Program (Grant No. 2007CB209701, 2003CB615804)     

The average stress tensor in systems with interacting particles

The derivation of an expression of the macroscopic stress tensor in terms of microscopic variables in systems of finite interacting particles is discussed from different points of view. It is shown that in volume averaging the introduction of a fictitious “interaction stress field”T ^I with special boundary conditions on the boundary of the averaging volume is needed. In ensemble averaging similar results are obtained by using a multipole expansion of the local stress and force fields. In the appropriate limiting cases, the obtained results are shown to be consistent with the results of kinetic theories of polymer solutions. Paper, presented at the First Conference of European Rheologists at Graz, April 14 – 16, 1982.     

Coulomb excitation of double giant dipole resonances

We implement the Brink–Axel hypothesis for the excitation of the double giant dipole resonance (DGDR): the background states which couple to the one-phonon giant dipole resonance are themselves capable of dipole absorption. These states (and the ones which couple to the two-phonon resonance) are described in terms of the gaussian orthogonal ensemble of random matrices. We use second-order time-dependent perturbation theory and calculate analytically the ensemble-averaged cross section for excitation of the DGDR. Numerical calculations illuminate the mechanism and the dependence of the cross section on the various parameters of the theory, and are specifically performed for the reaction ²⁰⁸Pb + ²⁰⁸Pb at a projectile energy of 640 MeV/nucleon. We show that the contribution of the background states to the excitation of the DGDR is significant. We find that the width of the DGDR, the energy-integrated cross section and the ratio of this quantity over the energy-integrated cross section for the single giant dipole resonance, all agree with experiment within experimental errors. We compare our approach with that of Carlson et al. who have used a similar physical picture.     

Density Profiles in a Classical Coulomb Fluid Near a Dielectric Wall. II. Weak-Coupling Systematic Expansions

In the framework of the grand-canonical ensemble of statistical mechanics, we give an exact diagrammatic representation of the density profiles in a classical multicomponent plasma near a dielectric wall. By a reorganization of Mayer diagrams for the fugacity expansions of the densities, we exhibit how the long-range of both the self-energy and pair interaction are exponentially screened at large distances from the wall. However, the self-energy due to Coulomb interaction with images still diverges in the vicinity of the dielectric wall and the variation of the density is drastically different at short or large distances from the wall. This variation is involved in the inhomogeneous Debye–Hückel equation obeyed by the screened pair potential. Then the main difficulty lies in the determination of the latter potential at every distance. We solve this problem by devising a systematic expansion with respect to the ratio of the fundamental length scales involved in the two coulombic effects at stake. (The application of this method to a plasma confined between two ideally conducting plates and to a quantum plasma will be presented elsewhere). As a result we derive the exact analytical perturbative expressions for the density profiles up to first order in the coupling between charges. The mean-field approach displayed in Paper I is then justified.