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We revisit the numerical solutions of vibrational eigenstates of weakly bound homonuclear and heteronuclear noble gas pairs by applying a Fortran program based on the Numerov method. The harmonic, Lennard-Jones (LJ), Morse, Tang-Toennies (TT), and Improved Lennard-Jones (ILJ) potential models have been implemented to represent the potential energy curves (PECs). The obtained vibrational energies spectrum was tested on the experimental data and accurate ab initio calculations at CCSD(T)/CBS level. The vibrational eigenvalues and eigenfunctions can be reproduced accurately within the ILJ potential model. Moreover, considering the calculated lifetime of van der Waals (vdW) complexes, the implementation of ILJ rather than standard LJ potential model has a significant impact on the systems dynamics by providing more representative atomic trajectories when the function is incorporated in force fields for molecular dynamics (MD) simulations. Overall, the ILJ function is the best suited potential model for the representation of vibrational motions and the determination of vibrational energy levels of weakly bound systems, both at equilibrium and non-equilibrium conditions.

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The formation of mesoporous gold sponges by explosive decomposition of 'knallgold' (also known as 'fulminating' gold) is studied. Proof-of-principle experiments are conducted and then the phenomena are further investigated using 'toy physics' molecular dynamics simulations. The simulations invoked various ratios of a volatile Lennard-Jones element G and a noble metal element N. In both experiment and simulation the morphology of the resulting sponge is found to depend on the stoichiometry of the starting material. As the mole fraction of G (χG) is increased from 0.5 to close to 1.0 in the simulations, the morphology of the sponges changes from closed to open, with a corresponding increase in the average mean curvature from 0 to +0.12 inverse Lennard-Jones length (L) units. The average Gaussian curvature of the simulated sponges is always negative, with the minimum value of 0.05 L-2 being found for χG≈0.65. In broad agreement with experiment, sponge formation in the simulations is bounded by stoichiometry; no sponges form if χG is <0.52, for χG between 0.52 and 0.70 the sponge is characterized by vermicular cavities whereas classic bicontinuous fibrous sponges form for 0.70<χG<0.85 and, finally, discrete particles result if χG>0.85.

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This study employs a combination of mathematical derivation and optimization technique to investigate the adsorption of drug molecules on nanocarriers. Specifically, the chemotherapy drugs, fluorouracil, proflavine, and methylene blue, are non-covalently bonded with either a flat graphene sheet or a spherical C 60 fullerene. Mathematical expressions for the interaction energy between an atom and graphene, as well as between an atom and C 60 fullerene, are derived. Subsequently, a discrete summation is evaluated for all atoms on the drug molecule utilizing the U-NSGA-III algorithm. The stable configurations' three-dimensional architectures are presented, accompanied by numerical values for crucial parameters. The results indicate that the nanocarrier's structure effectively accommodates the atoms on the drug's carbon planes. The three drug types' molecules disperse across the graphene surface, whereas only fluorouracil spreads on the C 60 surface; proflavine and methylene blue stack vertically to form a layer. Furthermore, all atomic positions of equilibrium configurations for all systems are obtained. This hybrid method, integrating analytical expressions and an optimization process, significantly reduces computational time, representing an initial step in studying the binding of drug molecules on nanocarriers.

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We present a new method for approximating two-body interatomic potentials from existing ab initio data based on representing the unknown function as an analytic continued fraction. In this study, our method was first inspired by a representation of the unknown potential as a Dirichlet polynomial, i.e., the partial sum of some terms of a Dirichlet series. Our method allows for a close and computationally efficient approximation of the ab initio data for the noble gases Xenon (Xe), Krypton (Kr), Argon (Ar), and Neon (Ne), which are proportional to r - 6 and to a very simple d e p t h = 1 truncated continued fraction with integer coefficients and depending on n - r only, where n is a natural number (with n = 13 for Xe, n = 16 for Kr, n = 17 for Ar, and n = 27 for Neon). For Helium (He), the data is well approximated with a function having only one variable n - r with n = 31 and a truncated continued fraction with d e p t h = 2 (i.e., the third convergent of the expansion). Also, for He, we have found an interesting d e p t h = 0 result, a Dirichlet polynomial of the form k 1 6 - r + k 2 48 - r + k 3 72 - r (with k 1 , k 2 , k 3 all integers), which provides a surprisingly good fit, not only in the attractive but also in the repulsive region. We also discuss lessons learned while facing the surprisingly challenging non-linear optimisation tasks in fitting these approximations and opportunities for parallelisation.

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Complex networks is a growing discipline aimed at understanding large interacting systems. One of its goals is to establish a relation between the interactions of a system and the networks structure that emerges. Taking a Lennard-Jones particle system as an example, we show that when interactions are governed by a potential, the notion of structure given by the physical arrangement of the interacting particles can be interpreted as a binary approximation to the interaction potential. This approximation simplifies the calculation of the partition function of the system and allows to study the stability of the interaction structure. We compare simulated results with those from the approximated partition function and show how the network and system perspective complement each other. With this, we draw a direct connection between the interactions of a molecular system and the network structure it forms and assess the degree to which it describes the system. We conclude by discussing the advantages and limitations of this method for weighted networks, as well as how this concept might be extended to more general systems.

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BACKGROUND: The COVID-19 pandemic has led to significant loss of life and economic disruption worldwide. Currently, there are limited effective treatments available for this disease. SARS-CoV-2 RNA-dependent RNA polymerase (SARS-CoV-2 RdRp) has been identified as a potential target for drug development against COVID-19. Natural products have been shown to possess antiviral properties, making them a promising source for developing drugs against SARS-CoV-2. OBJECTIVES: The objective of this study is to identify the most effective natural inhibitors of SARS-CoV-2 RdRp among a set of 4924 African natural products using a multi-phase in silico approach. METHODS: The study utilized remdesivir (RTP), the co-crystallized ligand of RdRp, as a starting point to select compounds that have the most similar chemical structures among the examined set of compounds. Molecular fingerprints and structure similarity studies were carried out in the first part of the study. The second part of the study included molecular docking against SARS-CoV-2 RdRp (PDB ID: 7BV2) and Molecular Dynamics (MD) simulations including the calculation of RMSD, RMSF, Rg, SASA, hydrogen bonding, and PLIP. Moreover, the calculations of Molecular mechanics with generalised Born and surface area solvation (MM-GBSA) Lennard-Jones and Columbic electrostatic interaction energies have been conducted. Additionally, in silico ADMET and toxicity studies were performed to examine the drug likeness degrees of the selected compounds. RESULTS: Eight compounds were identified as the most effective natural inhibitors of SARS-CoV-2 RdRp. These compounds are kaempferol 3-galactoside, kaempferol 3-O-ß-D-glucopyranoside, mangiferin methyl ether, luteolin 7-O-ß-D-glucopyranoside, quercetin-O-ß-D-3-glucopyranoside, 1-methoxy-3-indolylmethyl glucosinolate, naringenin, and asphodelin A 4'-O-ß-D-glucopyranoside. CONCLUSION: The results of this study provide valuable information for the development of natural product-based drugs against COVID-19. However, the elected compounds should be further studied in vitro and in vivo to confirm their efficacy in treating COVID-19.

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The objective of this paper is to design a fast and efficient immune algorithm for solving various optimization problems. The immune algorithm (IA), which simulates the principle of the biological immune system, is one of the nature-inspired algorithms and its many advantages have been revealed. Although IA has shown its superiority over the traditional algorithms in many fields, it still suffers from the drawbacks of slow convergence and local minima trapping problems due to its inherent stochastic search property. Many efforts have been done to improve the search performance of immune algorithms, such as adaptive parameter setting and population diversity maintenance. In this paper, an improved immune algorithm (IIA) which utilizes a parallel mutation mechanism (PM) is proposed to solve the Lennard-Jones potential problem (LJPP). In IIA, three distinct mutation operators involving cauchy mutation (CM), gaussian mutation (GM) and lateral mutation (LM) are conditionally selected to be implemented. It is expected that IIA can effectively balance the exploration and exploitation of the search and thus speed up the convergence. To illustrate its validity, IIA is tested on a two-dimension function and some benchmark functions. Then IIA is applied to solve the LJPP to exhibit its applicability to the real-world problems. Experimental results demonstrate the effectiveness of IIA in terms of the convergence speed and the solution quality.

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Using the Lennard-Jones potential, we determine analytical expressions for van der Waals interaction energies between a point and a rectangular prism-shaped pore, writing them in terms of standard elementary functions. The parameter values for a new ferric ion sensor are used to compare these calculations with the cylindrical pore approximation for the interactions between an ion and a metal organic framework (MOF) pore. The results using the prismatic pore approximation predict the same qualitative outcomes as a cylindrical pore approximation. However, the prismatic approximation predicts lower magnitudes for both the interaction potential energy minimum and the force maximum, since the average distance from the centre-line to the surface of the prism is greater. We suggest that in some circumstances it is sufficient to use the simpler cylindrical approximation, provided that the cylinder radius is chosen so that the cross-sectional area is equal to the area of the prism pore opening. However, atoms at the nodes should remain approximated by semi-infinite lines. We also determine the interaction between a second ferric ion and a blocked MOF pore; as expected, the second ferric ion experiences a force away from the pore, implying that approaching ferric ions can only occupy vacant MOF pores.

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Umbrella Sampling Molecular Dynamics has been used to determine transition energies for different guest molecules through hydroquinone ß-clathrate nanochannels, as well as their temperature trend. This clathrate has been shown to successfully enclathrate different types of small gases with remarkable selectivity, and thus it has been proposed as a potential gas separation and storage medium. Most of these potential guest gases can be successfully modeled as single Lennard-Jones spheres. Then, to obtain a general view of diffusion probabilities for different potential guest molecules, a comparative study for different virtual guest molecules described by different Lennard-Jones parameters has been performed. A regular temperature trend has been obtained for the transition energies for the molecular model characteristic parameter range explored. Finally, to locate the transition energy values of real gases within the space of phases explored, calculations have been repeated for molecular models of different noble gases and H2. The correlation results presented allow a wide interpolation ability for determining the transition energies of potential guest molecules stored or diffusing through the nanochannels of the studied clathrate structure.

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Hydration free energies of small molecules are commonly used as benchmarks for solvation models. However, errors in predicting hydration free energies are partially due to the force fields used and not just the solvation model. To address this, we have used the 3D reference interaction site model (3D-RISM) of molecular solvation and existing benchmark explicit solvent calculations with a simple element count correction (ECC) to identify problems with the non-bond parameters in the general AMBER force field (GAFF). 3D-RISM was used to calculate hydration free energies of all 642 molecules in the FreeSolv database, and a partial molar volume correction (PMVC), ECC, and their combination (PMVECC) were applied to the results. The PMVECC produced a mean unsigned error of 1.01±0.04kcal/mol and root mean squared error of 1.44±0.07kcal/mol, better than the benchmark explicit solvent calculations from FreeSolv, and required less than 15 s of computing time per molecule on a single CPU core. Importantly, parameters for PMVECC showed systematic errors for molecules containing Cl, Br, I, and P. Applying ECC to the explicit solvent hydration free energies found the same systematic errors. The results strongly suggest that some small adjustments to the Lennard-Jones parameters for GAFF will lead to improved hydration free energy calculations for all solvent models.

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We illustrate three methods for calculating the binodals of phase-separated condensates from molecular simulations. Because molecular simulations can only be carried out for small system sizes, correction for finite sizes may be required for making direct comparison between calculated results and experimental data. We first summarize the three methods and then present detailed implementation of each method on a Lennard-Jones fluid. In the first method, chemical potentials are calculated over a range of particle densities in canonical-ensemble simulations; the densities of the dilute and dense phases at the given temperature are then found by a Maxwell equal-area construction. In Gibbs-ensemble Monte Carlo, the exchange between separated dilute and dense phases is simulated to obtain their densities. Lastly, slab-geometry molecular dynamics simulations model the dilute and dense phases in coexistence and yield not only their densities but also their interfacial tension. The three types of simulations are carried out for a range of system sizes, and the results are scaled to generate the binodals corrected for finite system sizes. Size-corrected interfacial tension is also produced from slab-geometry molecular dynamics simulations.

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As was found in our previous works, when Nafion swells in water, polymer fibers unwind into the bulk of the surrounding liquid. This effect is controlled by the content of deuterium in water. Here, we present the results of studying the dynamics of methylene blue (MB) adsorption on the Nafion surface for MB solutions based on natural water (deuterium content is 157 ppm, the unwinding effect occurs) and based on deuterium-depleted water (DDW; deuterium content is 3 ppm, there is no unwinding). In addition, we studied the dynamics of water desorption during drying of the Nafion polymer membrane after soaking in MB solution based on natural water and DDW. It turned out that in the case of natural water, the rate of MB adsorption and water desorption is higher than in the case of DDW. It also turned out that the amount of MB adsorbed on the membrane in the case of natural water is greater than in the case of DDW. Finally, it was found that the desorption of water during drying is accompanied by a rearrangement of the absorption spectrum of Nafion. This rearrangement occurs earlier in the case of DDW. Thus, by infinitesimal changes in the deuterium content (from 3 to 157 ppm) in an aqueous solution, in which a polymer membrane swells, we can control the dynamics of adsorption and desorption processes. A qualitative model, which connects the observed effects with the slowing down of diffusion processes inside the layer of unwound fibers, is proposed.

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In the last years, a few experiments in the fields of biological and soft matter physics in colloidal suspensions have reported "normal diffusion" with a Laplacian probability distribution in the particle's displacements (i.e., Brownian yet non-Gaussian diffusion). To model this behavior, different stochastic and microscopic models have been proposed, with the former introducing new random elements that incorporate our lack of information about the media and the latter describing a limited number of interesting physical scenarios. This incentivizes the search of a more thorough understanding of how the media interacts with itself and with the particle being diffused in Brownian yet non-Gaussian diffusion. For this reason, a comprehensive mathematical model to explain Brownian yet non-Gaussian diffusion that includes weak molecular interactions is proposed in this paper. Based on the theory of interfaces by De Gennes and Langevin dynamics, it is shown that long-range interactions in a weakly interacting fluid at shorter time scales leads to a Laplacian probability distribution in the radial particle's displacements. Further, it is shown that a phase separation can explain a high diffusivity and causes this Laplacian distribution to evolve towards a Gaussian via a transition probability in the interval of time as it was observed in experiments. To verify these model predictions, the experimental data of the Brownian motion of colloidal beads on phospholipid bilayer by Wang et al. are used and compared with the results of the theory. This comparison suggests that the proposed model is able to explain qualitatively and quantitatively the Brownian yet non-Gaussian diffusion.

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Carbon nanomaterials have received increasing attention in drug-delivery applications because of their distinct properties and structures, including large surface areas, high conductivity, low solubility in aqueous media, unique chemical functionalities, and stability at the nano-scale size. Particularly, they have been used as nano-carriers and mediators for anticancer drugs such as Cisplatin, Camptothecin, and Doxorubicin. Cancer has become the most challenging disease because it requires sophisticated therapy, and it is classified as one of the top killers according to the World Health Organization records. The aim of the current work is to study and investigate the mechanism of combination between single-walled carbon nanotubes (SWCNTs) and fullerene derivatives (CN-[OH]ß) as mediators, and anticancer agents for photodynamic therapy directly to destroy the infected cells without damaging the normal ones. Here, we obtain a bio-medical model to determine the efficiency of the usefulness of Doxorubicin (DOX) as an antitumor agent conjugated with SWCNTs with variant radii r and fullerene derivative (CN-[OH]ß). The two sub-models are obtained mathematically to evaluate the potential energy arising from the DOX-SWCNT and DOX-(CN-[OH]ß) interactions. DOX modelled as two-connected spheres, small and large, each interacting with different SWCNTs (variant radii r) and fullerene derivatives CN-[OH]ß, formed based on the number of carbon atoms (N) and the number of hydroxide molecules (OH) (ß), respectively. Based on our obtained results, we find that the most favorable carbon nanomaterial is the SWCNT (r = 15.27 Å), followed by fullerene derivatives CN-(OH)22, CN-(OH)20, and CN-(OH)24, with minimum energies of -38.27, -33.72, -32.95, and -29.11 kcal/mol.

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An atomic-scale mechanism of T Cell Receptor (TCR) mechanosensing of peptides in the binding groove of the peptide-major histocompatibility complex (pMHC) may inform the design of novel TCRs for immunotherapies. Using steered molecular dynamics simulations, our study demonstrates that mutations to peptides in the binding groove of the pMHC - which are known to discretely alter the T cell response to an antigen - alter the MHC conformation at equilibrium. This subsequently impacts the overall strength (duration and length) of the TCR-pMHC bond under constant load. Moreover, physiochemical features of the TCR-pMHC dynamic bond strength, such as hydrogen bonds and Lennard-Jones contacts, correlate with the immunogenic response elicited by the specific peptide in the MHC groove. Thus, formation of transient TCR-pMHC bonds is characteristic of immunogenic peptides, and steered molecular dynamics simulations can be used in the overall design strategy of TCRs for immunotherapies.

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The reaction between the cyano radical CN and cyanoacetylene molecule HC3N is of great interest in different astronomical fields, from star-forming regions to planetary atmospheres. In this work, we present a new synergistic theoretical approach for the derivation of the rate coefficient for gas phase neutral-neutral reactions. Statistic RRKM calculations on the Potential Energy Surface are coupled with a semiempirical analysis of the initial bimolecular interaction. The value of the rate coefficient for the HC3N + CN → H + NCCCCN reaction obtained with this method is compared with previous theoretical and experimental investigations, showing strengths and weaknesses of the new presented approach.

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We use atomistic as well as coarse-grained molecular dynamics simulations to study the conformation of a single poly(3-hexylthiopene) chain as a function of temperature. We find that mainly bundle and toroid structures appear with bundles becoming more abundant for decreasing temperatures. We compare an atomistic and a Martini-based coarse-grained model which we find in very good agreement. We further illustrate how the temperature dependence of P3HT can be connected to that of simple Lennard-Jones model polymers in a vacuum. Upon adding solvent (THF) we observe the occurrence of a prominent swelling of the molecular size at a temperature of about 220 K. This swelling is in close agreement with the interpretation of recent spectroscopic experiments which allows us to explain the experimental observations by an increased frequency of bundle structures.

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A model is proposed to calculate the melting points of nanoparticles based on the Lennard-Jones (L-J) potential function. The effects of the size, the shape, and the atomic volume and surface packing of the nanoparticles are considered in the model. The model, based on the L-J potential function for spherical nanoparticles, agrees with the experimental values of gold (Au) and lead (Pb) nanoparticles. The model, based on the L-J potential function, is consistent with Qi and Wang's model that predicts the Gibbs-Thompson relation. Moreover, the model based on the non-integer L-J potential function can be used to predict the melting points Tm of nanoparticles.

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Two-dimensional nanomaterials, such as graphene and hexagonal boron nitride nanosheets, have attracted tremendous interest in the research community and as a starting point for the development of nanotechnology. Using classical applied mathematical modeling, we derive explicit analytical expressions to determine the binding energies of noble metals, including copper, silver, gold, platinum and iridium (Cu, Ag, Au, Pt and Ir) atoms, on graphene and hexagonal boron nitride nanosheets. We adopt the 6-12 Lennard-Jones potential function, together with the continuous approach, to determine the preferred minimum energy position of an offset metal atom above the surface of the graphene and hexagonal boron nitride nanosheets. The main results of this study are analytical expressions of the interaction energies, which we then utilize to report the mechanism of adsorption of the metal atoms on graphene and hexagonal boron nitride surfaces. The results show that the minimum binding energy occured when Cu, Ag, Au, Pt and Ir were set at perpendicular distances in the region from 3.302 Å to 3.683 Å above the nanosheet surface, which correspond to adsorption energies in the region ranging from 0.842 to 2.978 (kcal/mol). Our results might assist in providing information on the interaction energies between the metal atoms and the two-dimensional nanomaterials.

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In this work, simulations of friction at the atomic level were performed to evaluate the influence of inclusions coming from metallic nanoadditives in the friction pair. The simple 2D model was applied considering appropriate values of Lennard-Jones potential parameters for given sets of interacting atoms. The real sliding pairs were replaced by effective equivalents consisting of several atoms. The calculations were based on the pseudo-static approximation. The simplicity of the model enabled to repeat the fast calculations in a very wide range of local pressures and for several types of atomic tribopairs. The performed simulations demonstrated a strong dependence of the coefficient of friction (COF) on the atomic environment of the atoms constituting a tribopair. It was confirmed theoretically that the Mo-Fe pair is characterized by lower atomic COF than Fe-Fe, Cu-Fe, and Ag-Fe pairs. This points to the great applicational potential of metallic molybdenum coating applications in tribological systems. Moreover, it was demonstrated that, although Cu-Cu and Ag-Ag pairs are characterized by relatively high COF, they lower the friction as inclusions in Fe surfaces.