Interaction Potential Parameters Research Articles

Revealing miRNAs patterns by employing matrix representations and energy analysis

MicroRNAs (miRNAs) are small, non-coding RNA molecules that regulate gene expression. Despite their relatively short length (about 21 nucleotides), they can regulate thousands of transcripts within a cell. Due to their low complementarity to targets, studying their activity and binding region preferences (3′UTR, 5′UTR, or CDS) is challenging. In this paper, we analyzed a set of human miRNAs to uncover their general patterns. We began with a sequence logo to verify conservation at specific positions. To discover long-range correlations, we employed chaos game representation (CGR) and genomatrix, methods that enable both graphical and analytical analysis of sequence sets and are well-established in bioinformatics. Our results showed that miRNAs exhibit strongly non-random and characteristic patterns. To incorporate physicochemical properties into the analysis, we applied the electron-ion interaction potential (EIIP) parameter. An important part of our study was to validate the division of miRNAs into two parts—seed and puzzle. The seed region is responsible for target binding, while the puzzle region likely interacts with the RISC complex. We estimated duplex binding energy within the 3′UTR, 5′UTR, and CDS regions using the miRanda tool. Based on the median energy distribution, we divided the miRNAs into two subsets, reflecting different patterns in chaos game representation. Interestingly, one subset displayed significant similarity to conserved and highly confidential miRNAs. Our results confirm the low complementarity of miRNA/mRNA interactions and support the functional division of miRNA structure. Additionally, we present findings related to the localization of transcript target sites, which form the basis for further analyses.

Global ranking of the sensitivity of interaction potential contributions within classical molecular dynamics force fields

Uncertainty quantification (UQ) is rapidly becoming a sine qua non for all forms of computational science out of which actionable outcomes are anticipated. Much of the microscopic world of atoms and molecules has remained immune to these developments but due to the fundamental problems of reproducibility and reliability, it is essential that practitioners pay attention to the issues concerned. Here a UQ study is undertaken of classical molecular dynamics with a particular focus on uncertainties in the high-dimensional force-field parameters, which affect key quantities of interest, including material properties and binding free energy predictions in drug discovery and personalized medicine. Using scalable UQ methods based on active subspaces that invoke machine learning and Gaussian processes, the sensitivity of the input parameters is ranked. Our analyses reveal that the prediction uncertainty is dominated by a small number of the hundreds of interaction potential parameters within the force fields employed. This ranking highlights what forms of interaction control the prediction uncertainty and enables systematic improvements to be made in future optimizations of such parameters.

On the Physical Meaning of the Parameters of Intermolecular Interaction Potentials in the Asymptotic Line Wing Theory

On the Physical Meaning of the Parameters of Intermolecular Interaction Potentials in the Asymptotic Line Wing Theory

Solitonic rogue and modulated wave patterns in the monoatomic chain with anharmonic potential

Modulation instability and rogue wave structures have been investigated in this work. This study is an extension of the work in Abbagari (2023), where a nonlinear Schrödinger equation with higher-order dispersion is derived to show only the development of the modulated waves bounded to bright soliton as a nonlinear exhibition of modulation instability. Here, the coupled nonlinear Schrödinger equation is derived by using the multi-scale scheme. An overview of the analytical calculations of the perturbed plane wave is carried out to show the effects of the nonlinear chain parameters on the modulation instability growth rate and bandwidths. The interest of this study lies equally in the nonlinear modes of excitation, where solitonic waves are generated under certain conditions in lower and upper frequency bands. On the other hand, relevant results have been developed to show the features of the type I and type II rogue waves of the Manakov system. Such investigations are obtained under the variation of the interaction potential parameters and the free parameter of the similarity method. Via a numerical simulation, rogue wave structures have been generated as a consequence of the long-time evolution of the perturbed plane wave. At a specific time of propagation, another localized object has been obtained to show the Akhmediev breathers and Kuznetsov-Ma solitons clusters under a strong perturbed wave number. These results have opened up new features, and many applications could follow in the future.

Force Field for Calculation of the Vapor-Liquid Phase Equilibrium of trans-Decalin

Based on the TraPPE force field, previously unknown values of the parameters of the intermolecular interaction potential of trans-decalin were determined. Parametrization was carried out using experimental data on saturated vapor pressure and density at atmospheric pressure. The found parameters make it possible to adequately describe the boiling and condensation lines of trans-decalin and also predict the critical values of pressure, density, and temperature with satisfactory accuracy. Calculations of vapor-liquid phase equilibrium conditions for a binary CO2—trans-decalin mixture in supercritical conditions for CO2 were carried out. When quantitatively comparing the calculated values with experimental data, an underestimation of pressure at a temperature of 345.4 K by 30% is observed, which decreases to 5% for temperatures up to 525 K.

Anomalous diffusion, gigahertz, and terahertz spectroscopy of aliphatic ketones.

The experimental results of the complex dielectric permittivity of aliphatic ketones in dilute solutions of inert solvent cyclohexane in the gigahertz (GHz) and terahertz (THz) frequencies of the electromagnetic spectrum are examined in terms of the theory of inertial anomalous diffusion of polar molecules, considered as an assembly of molecules with interacting dipolar groups, in polar liquids. The theory is based on the generalization of the Debye rotational diffusion model of dielectric relaxation of polar molecules. The model comprises two interacting dipolar groups-one lighter and the other heavier; each has a finite moment of inertia and each experiences a finite friction with an extensive range of damping or drag coefficient and the dipole moment ratio of the two groups. The lighter group refers to the reference molecule, whereas the heavier group simulates the neighboring molecules, and the two groups interact with each other via the dipole-dipole interaction potential. The resulting approximate expression contains terms in both the Rocard form and the Сole-Сole form. The experimental data on aliphatic ketones are shown to fit extremely well with the theory, and parameters of the fit offer physical significance. An agreement of the plot of the experimental data on dielectric loss versus frequency to the formulas derived from the model offers a mathematical basis of the semiempirical equations used in the literature to fit the experimental data. Experimental results of the dielectric loss of neat polar liquid acetone in GHz and THz, as an example, are shown to fit the theory; however, the interaction potential parameter compared to its dilute solution counterpart is significantly increased, reflecting the increase in the dipole-dipole interaction energy.

Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-informed Deep Generative Models

We propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple "snapshots". Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots. By training a physics-informed generative model that generates "fake" sample paths, we aim to fit the observed particle ensemble distributions with a curve in the probability measure space, which is induced from the inferred particle dynamics. We employ different metrics to quantify the differences between distributions, e.g., the sliced Wasserstein distances and the adversarial losses in generative adversarial networks (GANs). We refer to this method as generative "ensemble-regression" (GER), in analogy to the classic "point-regression", where we infer the dynamics by performing regression in the Euclidean space. We illustrate the GER by learning the drift and diffusion terms of particle ensembles governed by SODEs with Brownian motions and Levy processes up to 100 dimensions. We also discuss how to treat cases with noisy or truncated observations. Apart from systems consisting of independent particles, we also tackle nonlocal interacting particle systems with unknown interaction potential parameters by constructing a physics-informed loss function. Finally, we investigate scenarios of paired observations and discuss how to reduce the dimensionality in such cases by proving a convergence theorem that provides theoretical support.

Five-Site Model for Brownian Dynamics Simulations of a Molecular Walker in Three Dimensions.

Motor proteins play an important role in many biological processes and have inspired the development of synthetic analogues. Molecular walkers, such as kinesin, dynein, and myosin V, fulfill a diverse set of functions including transporting cargo along tracks, pulling molecules through membranes, and deforming fibers. The complexity of molecular motors and their environment makes it difficult to model the detailed dynamics of molecular walkers over long time scales. In this work, we present a simple, three-dimensional model for a molecular walker on a bead-spring substrate. The walker is represented by five spherically symmetric particles that interact through common intermolecular potentials and can be simulated efficiently in Brownian dynamics simulations. The movement of motor protein walkers entails energy conversion through ATP hydrolysis while artificial motors typically rely on a local conversion of energy supplied through external fields. We model energy conversion through rate equations for mechanochemical states that couple positional and chemical degrees of freedom and determine the walker conformation through interaction potential parameters. We perform Brownian dynamics simulations for two scenarios: In the first, the model walker transports cargo by walking on a substrate whose ends are fixed. In the second, a tethered motor pulls a mobile substrate chain against a variable force. We measure relative displacements and determine the effects of cargo size and retarding force on the efficiency of the walker. We find that, while the efficiency of our model walker is less than for the biological system, our simulations reproduce trends observed in single-molecule experiments on kinesin. In addition, the model and simulation method presented here can be readily adapted to biological and synthetic systems with multiple walkers.

Particle shape tunes fragility in hard polyhedron glass-formers.

We demonstrate that fragility, a technologically relevant characteristic of glass formation, depends on particle shape for glass-formers comprised of hard polyhedral particles. We find that hard polyhedron glass-formers become stronger (less fragile) as particle shape becomes increasingly tetrahedral. We correlate fragility with local structure, and show that stronger systems display a stronger preference for a pairwise face-to-face motif that frustrates global periodic ordering and gives rise in most systems studied to bond angle distributions that are peaked around the ideal tetrahedral bond angle. We demonstrate through mean-field-like simulations of explicit particle pairs and surrounding baths of "ghost" particles that the prevalence of this pairwise configuration can be explained via free volume exchange and emergent entropic force arguments. Our study provides a clear and direct link between the local geometry of fluid structure and the properties of glass formation, independent of interaction potential or other non-geometric tuning parameters. We ultimately demonstrate that the engineering of fragility in colloidal systems via slight changes to particle shape is possible.

Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data

This paper concerns the parameter estimation problem for the quadratic potential energy in interacting particle systems from continuous-time and single-trajectory data. Even though such dynamical systems are high-dimensional, we show that the vanilla maximum likelihood estimator (without regularization) is able to estimate the interaction potential parameter with optimal rate of convergence simultaneously in mean-field limit and in long-time dynamics. This to some extend avoids the curse-of-dimensionality for estimating large dynamical systems under symmetry of the particle interaction.

Quantitative determination of the interaction potential between two surfaces using frequency-modulated atomic force microscopy.

The interaction potential between two surfaces determines the adhesive and repulsive forces between them. It also determines interfacial properties, such as adhesion and friction, and is a key input into mechanics models and atomistic simulations of contacts. We have developed a novel methodology to experimentally determine interaction potential parameters, given a particular potential form, using frequency-modulated atomic force microscopy (AFM). Furthermore, this technique can be extended to the experimental verification of potential forms for any given material pair. Specifically, interaction forces are determined between an AFM tip apex and a nominally flat substrate using dynamic force spectroscopy measurements in an ultrahigh vacuum (UHV) environment. The tip geometry, which is initially unknown and potentially irregularly shaped, is determined using transmission electron microscopy (TEM) imaging. It is then used to generate theoretical interaction force–displacement relations, which are then compared to experimental results. The method is demonstrated here using a silicon AFM probe with its native oxide and a diamond sample. Assuming the 6-12 Lennard-Jones potential form, best-fit values for the work of adhesion (Wadh) and range of adhesion (z0) parameters were determined to be 80 ± 20 mJ/m2 and 0.6 ± 0.2 nm, respectively. Furthermore, the shape of the experimentally extracted force curves was shown to deviate from that calculated using the 6-12 Lennard-Jones potential, having weaker attraction at larger tip–sample separation distances and weaker repulsion at smaller tip–sample separation distances. This methodology represents the first experimental technique in which material interaction potential parameters were verified over a range of tip–sample separation distances for a tip apex of arbitrary geometry.

A computational study of the behavior of colloidal gel networks at low volume fraction

Colloidal gel networks appear in different scientific and industrial applications because of their unique properties. Molecular dynamics simulations could reveal the relation between molecular level and macroscopic properties of these systems. Nevertheless, the predictions of numerical simulations might depend on the specific form and parameters of interaction potentials. In this paper, a new effective interaction potential is used for characterizing the mechanical behavior of low volume fraction colloidal gels under large shear deformation. The findings are compared with those obtained from other available forms of interaction potentials in order to determine gel characteristics that are interaction potential independent. Furthermore, the macroscopic stress–strain behavior is discussed in terms of the behavior of different terms of the proposed interaction potential. The correlation between the stretch of interparticle bonds and their alignment in the direction of the maximum principal stress is also computed in order to provide microscopic explanations for the initial strain softening behavior. It is concluded that, in addition to topology, local mechanical interactions between colloidal particles are important in defining the mechanical response of soft gels.

Speed dependence of friction on single-layer and bulk MoS2 measured by atomic force microscopy

We perform atomic force microscopy (AFM) experiments on mechanically exfoliated, single-layer and bulk molybdenum disulfide (MoS2) in order to probe friction forces as a function of sliding speed. The results of the experiments demonstrate that (i) friction forces increase logarithmically with respect to sliding speed, (ii) there is no correlation between the speed dependence of friction and the number of layers of MoS2, and (iii) changes in the speed dependence of friction can be attributed to changes in the physical characteristics of the AFM probe, manifesting in the form of varying contact stiffness and tip-sample interaction potential parameters in the thermally activated Prandtl–Tomlinson model. Our study contributes to the formation of a mechanistic understanding of the speed dependence of nanoscale friction on two-dimensional materials.

Stochastic simulation of transport processes in liquids

The subject of this paper is molecular stochastic modeling the transport processes in liquids. The proposed method and the corresponding algorithm are an alternative to the molecular dynamics method. However, unlike the latter the system of Newtonian equations is not solved for modeling the phase trajectories of the system studied. The phase trajectories of the molecular system are simulated stochastically. For this purpose, the database of the intermolecular forces acting on each molecule of the system during the considered time interval has been created. The distribution function of these forces has been built. It was shown that this distribution function can be approximated by certain analytic function. The dependency of the parameters of this function on the liquid temperature and parameters of the intermolecular interaction potential (the Lennard-Jones interaction potential is used) is determined. Using this distribution function the force acting on each molecule at given time is determined. After that the coordinates and velocity of all molecules of the system are calculated. As a result, the full information about the phase variables of the molecular system is obtained. All macroscopic characteristics of the system (temperature, pressure, transport coefficients etc.) are calculated by means of the methods of nonequilibrium statistical mechanics. The transport coefficients are calculated using fluctuation-dissipation theorems that relate transport coefficients to the evolution of the corresponding correlation functions. The algorithm was tested on the calculation of the viscosity of several simple liquids.

Properties of Yukawa Crystals and Liquid under Phase Equilibrium Conditions

The equilibrium properties of a system of particles whose interaction is described by the Yukawa potential are studied. Liquids and crystals with bcc and fcc lattices near the melting line are considered. The latent heat of melting for crystals and the density change during the phase transition are calculated. We analyze the temperature dependences of the thermodynamic quantities near the melting line and calculate the thermal expansion coefficient and the heat capacity at constant pressure. We show that the state of a Yukawa system cannot be uniquely defined by a pair of dimensionless quantities, the temperature and the pressure, which use the interaction potential parameters (the product of the charges and the screening length) as scales. In particular, the position of the melting line is ambiguously determined on a two-parameter phase diagram constructed in dimensionless quantities.

Mathematical modelling of pore formation in polymers using supercritical fluid media in the Ornstein-Zernike approximation

The paper studies the process of pore formation using supercritical fluid media. A mathematical model of pore formation in polymers in the process of supercritical carbon dioxide decompression has been developed, taking into account fluctuations in the Ornstein-Zernike approximation based on Patel-Teja cubic equation. Calculations and comparison with experimental data are given on the example of pore formation in polystyrene, which showed satisfactory agreement of the theory with experiment. Parameters of the Lennard-Jones pair interaction potential for carbon dioxide in the carbon dioxide-polystyrene system were obtained. The diffusion coefficient of supercritical carbon dioxide in a polymer takes on a different value than the coefficient of self-diffusion of pure carbon dioxide under the same thermodynamic conditions due to a change in the Lenard-Jones potential profile in a polymeric medium. The obtained values of the parameters of the Lennard-Jones equation, namely, the parameters of the intermolecular interaction potential and the maximum value of the attraction energy, make it possible to adequately estimate the value of the diffusion coefficient under given thermodynamic conditions.

Dynamic Interaction of Nitrogen Atoms with the Surface of an Aluminum Crystal

A possibility of reconstructing the ion-atom dynamic interaction potential from the dependence of the rainbow scattering angle of nitrogen atoms under the conditions of grazing incidence on the surface of an aluminum crystal on the total kinetic energy of the accelerated atomic particles is demonstrated. The parameters of the dynamic interaction potential are determined within the energy range from 10 to 70 keV using the best possible fit between the calculated dependence of the rainbow scattering angle on the energy of the particles incident on the aluminum crystal surface along the crystallographic directions and the available experimental data.

Designing active particles for colloidal microstructure manipulation via strain field alchemy.

Defects in a crystal can exert forces on each other via strain field interactions. Here we explore the strain-field-mediated interaction between an anisotropic interstitial probe particle and dislocation microstructures in a colloidal crystal composed of particles interacting via steep repulsive isotropic potentials. We optimize the interaction between probe particle and dislocation with the anisotropic shape of the probe as a free parameter. Such alchemical optimization is typically carried out upon the explicitly defined interaction potential parameters; instead, we optimize the strain field of the probe and then map back to particle shape. We distinguish this tactic from other alchemical methods as 'strain alchemy'. We report several findings: (1) a robust mapping exists between strain field calculation methods (the method of eigenstrains) and strains produced by an anisotropic interstitial, (2) optimization of strain field interactions in the strain domain permits rapid evaluation of candidate shapes for interstitials, (3) interstitial mobility barriers can be estimated from the strain field, and (4) strongly interacting and highly mobile interstitial particles can be found that are capable of driving dislocation glide with applied force. Active particle-induced dislocation glide is examined for the cases of edge dislocation arrays and extrinsic dislocation loops. For edge dislocations, particle geometries of alternating large and small diameter segments were found to interact most strongly. For dislocation loops, interstitials with a single small radius segment surrounded by large radius segments are best.

Long-range dispersion C6 coefficient for SF6 dimer: Experimental and theoretical study.

The long-range dispersion C6 coefficient for the SF6 dimer is experimentally measured using a technique that uses the expansion of a supersonic pulse jet into a vacuum. A dynamic model of the jet enables us to correlate the position of the maximal peak in the time-of-flight spectrum with the initial conditions of the experiment and the parameters of the intermolecular interaction potential. Due to the low temperature of the jet target, the C6 coefficient can be extracted directly from the experimental results. Theoretical calculation of the C6 dispersion coefficient is also performed by using linearly approximated explicitly correlated coupled-cluster singles and doubles (CCSD(F12)) method with the subsequent utilization of the Casimir-Polder formula. Good agreement of experimental and theoretical results confirms the reliability of results.

Potential cluster calculations for the astrophysical S-factor and reaction rate of the radiative 3He(4He,γ)7Be capture

In the frame of modified potential cluster model based on the classification of orbital states by Young diagrams and revised interaction potential parameters for the bound states of 7Be in 3He4He cluster model with forbidden states the astrophysical S-factor for the radiative capture reaction has been calculated from the 10 keV. Obtained results S(23 keV) = 0.561 keV b reproduce the latest experimental data at 23 keV. Calculated and parametrized reaction rate is compared to some results known in the range of temperatures from 0.05 to 5 T9.