Molecular Interaction Potential Research Articles

Function evaluation of the molecular scattering angle in multicomponent gaseous medium

The molecular interaction potential (2(n+3),6) for the multicomponent gaseous medium is proposed. To compute the values of a function of scattering angle, an asymptotic analysis is performed that permits the explicit expressions for this function to be obtained. The trajectories of molecules described on a set of real and complex numbers are first considered.

A multiscale view of therapeutic protein aggregation: a colloid science perspective.

The formation of aggregates in protein-based pharmaceuticals is a major issue that can compromise drug safety and drug efficacy. With a view to improving protein stability, considerable effort is put forth to unravel the fundamental mechanisms underlying the aggregation process. However, therapeutic protein aggregation is a complex multistep phenomenon that involves time and length scales spanning several orders of magnitude, and strategies addressing protein aggregation inhibition are currently still largely empirical in practice. Here, we review how key concepts developed in the frame of colloid science can be applied to gain knowledge on the kinetics and thermodynamics of therapeutic protein aggregation across different length scales. In particular, we discuss the use of coarse-grained molecular interaction potentials to quantify protein colloidal stability. We then show how population balance equations simulations can provide insights into the mechanisms of aggregate formation at the mesoscale, and we highlight the strength of the concept of fractal scaling to quantify irregular aggregate morphologies. Finally, we correlate the macroscopic rheological properties of protein solutions with the occupied volume fraction and the aggregate structure. Overall, this work illustrates the power and limitations of colloidal approaches in the multiscale description of the aggregation of therapeutic proteins.

Quantitative analysis of molecular interaction potentials of ionic liquid anions using multi-functionalized stationary phases in HPLC.

The molecular interaction potentials, including S (dipolarity/polarizability), A (hydrogen bonding acidity), and B (hydrogen bonding basicity), of anions are experimentally determined using multi-functionalized stationary phases in high-performance liquid chromatography (HPLC) systems. We employ three different multi-functionalized stationary phase columns (Obelisc R, Obelisc N, and Acclaim Trinity-P1) combined with two ingredients, namely, acetonitrile (ACN) and methanol (MeOH). These conditions can cause neutral, cationic, and anionic compounds to be retained. By using the retention characteristics of calibration compounds, including cations, anions, and neutral compounds, system parameters including the ionic interaction terms (zc Zc , za Za ) are evaluated using multiple linear regression, resulting in a standard deviation (SD) of 0.090-0.158 log units. Based on the system parameters and retention characteristics of the anions of interest, their molecular interaction potentials are characterized on the same scale for neutral and cationic molecules. Furthermore, to verify the determined molecular interaction potentials, we predict anion hydrophobicity. The results show that the determined S, A, and B, together with the computable descriptors E (excess molar refraction) and V (McGowan volume), can predict anion hydrophobicity with R(2) =0.982 and SD=0.167 (dimensionless).

Bayesian approach to inverse statistical mechanics.

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

State-resolved diffraction oscillations imaged for inelastic collisions of NO radicals with He, Ne and Ar

Just as light scattering from an object results in diffraction patterns, the quantum mechanical nature of molecules can lead to the diffraction of matter waves during molecular collisions. This behaviour manifests itself as rapid oscillatory structures in measured differential cross-sections, and such observable features are sensitive probes of molecular interaction potentials. However, these structures have proved challenging to resolve experimentally. Here, we use a Stark decelerator to form a beam of state-selected and velocity-controlled NO radicals and measure state-to-state differential cross-sections for inelastic collisions of NO with He, Ne and Ar atoms using velocity map imaging. The monochromatic velocity distribution of the NO beam produced scattering images with unprecedented sharpness and angular resolution, thereby fully resolving quantum diffraction oscillations. We found excellent agreement with quantum close-coupling scattering calculations for these benchmark systems.

Collective Variable Approaches for Single Molecule Flexible Fitting and Enhanced Sampling

It is now well established that proteins and nucleic acids undergo local and global conformational fluctuations to perform a variety of cellular functions such as signal transduction, transport, and catalysis.1 Many experimental techniques such as X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy, small-angle X-ray scattering (SAXS), and single-particle electron microscopy (EM) have indeed provided structural evidence at different resolutions to support the view of multiple functional states of biomolecules. Yet it remains difficult to characterize the vast conformational repertoire of biomolecules via experimental methods alone. Therefore, biophysical theory, modeling, and simulation techniques rooted in statistical mechanics are often useful for a detailed molecular understanding of biomolecular structures.2−5 Despite the limitations of molecular mechanics interaction potentials, computational methods can now be combined with low-resolution structural data to generate experimentally consistent conformational ensembles as well as to probe underlying mechanistic questions. Analyses of structural data for different functional states of biomolecules have revealed large-scale conformational rearrangements on the scales of entire domains. This means that a large group of atoms collectively move in a concerted way to facilitate functional movements. Traditionally, one relatively less expensive computational method to analyze collective motions in proteins has been to carry out normal-mode analysis (NMA) of equilibrium structures, because low-frequency modes are typically indicative of high-amplitude/large-scale motions.6−8 Such global and collective modes are robust, independent of sequence detail, and are intrinsically accessible to each biomolecule because they are encoded in their global shape.9−13 Given that the total number of degrees-of-freedom (DOF) in biomolecules is very large, NMA provides an efficient way to describe biomolecular dynamics in a reduced number of variables. As was originally pointed out by Hayward and Go,6 this reduction in dimensionality has led to the concept of an important subspace of variables, “collective variables (CVs)”, that are well-suited to characterize the dynamics of biomolecules. Interestingly, the concept of CVs as reaction coordinates has been recently extended to atomistic molecular dynamics (MD) simulations,14 which has significantly increased their capability in capturing long time-scale motions. This is chiefly possible because sampling in these CVs can be carried out more extensively in comparison to all possible DOF. Such methods are typically referred to as enhanced sampling techniques because they increase the likelihood of observation of a rare biomolecular event. The range of studies in which NMA and MD simulations have played a central role is immense, and it is not possible to do justice to all such studies in this focused Review. However, we refer the reader to pertinent comprehensive literature on those subjects along the way. Therefore, we have limited the scope of this Review to some specific applications of NMA, and enhanced sampling via temperature-acceleration in the context of flexible fitting to low-resolution EM data on macromolecular complexes. Particularly, we concentrate on two methods in this Review: (a) normal mode flexible fitting (NMFF)15,16 for structural refinement into EM maps; and (b) temperature-accelerated molecular dynamics (TAMD)17,18 for conformational exploration and flexible fitting. We first discuss theoretical underpinnings of all-atom and coarse-grained NMA of protein structures, which is followed by highlights of various successful applications. The theory and applications of NMA for flexible fitting of protein structures into EM maps are described thereafter. This is immediately followed by a discussion of the importance of enhanced sampling in biomolecular simulations, and how dynamics in these systems can be explored by evolving CVs via temperature acceleration, for example. Specifically, we discuss in detail various aspects of TAMD. During these discussions, we further highlight a few of the many cases where NMA and TAMD have alleviated difficulties faced by other methods in understanding large-scale functional excursions in biomolecules. This Review concludes with a brief overview and future outlook for these methods.

Estimation of Interaction Potentials through the Configurational Temperature Formalism.

Molecular interaction potentials are difficult to measure experimentally and hard to compute from first principles, especially for large systems such as proteins. It is therefore desirable to estimate the potential energy that underlies a thermodynamic ensemble from simulated or experimentally determined configurations. This inverse problem of statistical mechanics is challenging because the various potential energy terms can exhibit subtle indirect and correlated effects on the resulting ensemble. A direct approach would try to adapt the force field parameters such that the given configurations are highly probable in the resulting ensemble. But this would require a full simulation of the system whenever a parameter changes. We introduce an extension of the configurational temperature formalism that allows us to circumvent these difficulties and efficiently estimate interaction potentials from molecular configurations. We illustrate the approach for various systems including fluids and a coarse-grained protein model.

In silico modelling for predicting the cationic hydrophobicity and cytotoxicity of ionic liquids towards the Leukemia rat cell line, Vibrio fischeri and Scenedesmus vacuolatus based on molecular interaction potentials of ions

In this study we present prediction models for estimating in silico the cationic hydrophobicity and the cytotoxicity (log [1/EC50]) of ionic liquids (ILs) towards the Leukemia rat cell line (IPC-81), the marine bacterium Vibrio fischeri and the limnic green algae Scenedesmus vacuolatus using linear free energy relationship (LFER) descriptors computed by COSMO calculations. The LFER descriptors used for the prediction model (i.e. excess molar refraction (E), dipolarity/polarizability (S), hydrogen-bonding acidity (A), hydrogen-bonding basicity (B) and McGowan volume (V)) were calculated using sub-descriptors (sig2, sig3, HBD3, HBA4, MR, and volume) derived from COSMO–RS, COSMO and OBPROP. With the combination of two solute descriptors (B, V) of the cation we were able to predict cationic hydrophobicity values (log ko ) with r 2 = 0.987 and standard error (SE) = 0.139 log units. By using the calculated log k o values, we were able to deduce a linear toxicity prediction model. In the second prediction study for the cytotoxicity of ILs, analysis of descriptor sensitivity helped us to determine that the McGowan volume (V) terms of the cation was the most important predictor of cytotoxicity and to simplify prediction models for cytotoxicity of ILs towards the IPC-81 (r 2 of 0.778, SE of 0.450 log units), Vibrio fischeri (r 2 of 0.762, SE of 0.529 log units) and Scenedesmus vacuolatus (r 2 of 0.776, SE of 0.825 log units). The robustness and predictivity of the two models for IPC-81 and Vibrio fischeri were checked by comparing the calculated SE and r 2 (coefficient of determination) values of the test set.

Modelling carbon dioxide molecule interacting with aquaglyceroporin and aquaporin-1 channels

Aquaporin (AQP) is a family of membrane proteins that enable water and small individual molecules to permeate cell membranes. Examples of these protein channels are aquaglyceroporin and aquaporin-1 (AQP1). Here, we investigate the permeability of carbon dioxide \((\hbox {CO}_2)\) through both aquglyceroporin and AQP1 channels and explain their selectivity mechanisms. We provide a mathematical model which determines the molecular interaction potential between carbon dioxide molecule and an AQP channel. We evaluate this interaction using two approaches, namely discrete-continuum and completed discrete approaches. Both calculations agree well and our results indicate the acceptance of \((\hbox {CO}_2)\) molecule into these channels which is in good agreement with other recent studies.

An ab initio approach to understanding the specific ion effect

Although there is a consensus that large, polarizable anions will adsorb to the air-water interface, the precise interactions that give rise to surface enhancement are still being debated. Previously, we have demonstrated that there is a significant dependence on the choice of molecular interaction potential for I-adsorption at the air-water interface. Specifically, density functional theory (DFT) based interaction potentials lead to significantly less adsorption than empirical interaction potentials that include polarization. We have also demonstrated that DFT based interaction potentials can accurately capture the structure of the first solvation shell of both simple and polyatomic anions as compared to multi-edge X-ray absorption fine structure (XAFS) experiments. We utilize DFT to examine the local hydration structure of SCN- and IO3- that exhibit both chaotropic and kosmotropic characteristics. We compare and contrast the solvation structure of the polyatomic anions with the series of halide anions. A picture emerges where we can correlate local solvation structure to the ions' position in the Hofmeister series.

Stress-induced activation of decomposition of organic explosives: a simple way to understand

We provide a very simply way to understand the stress-induced activation of decomposition of organic explosives by taking the simplest explosive molecule nitromethane (NM) as a prototype and constraining one or two NM molecules in a shell to represent the condensed phrase of NM against the stress caused by tension and compression, sliding and rotational shear, and imperfection. The results show that the stress loaded on NM molecule can always reduce the barriers of its decomposition. We think the origin of this stress-induced activation is due to the increased repulsive intra- and/or inter- molecular interaction potentials in explosives resulted from the stress, whose release is positive to accelerate the decomposition. Besides, by these models, we can understand that the explosives in gaseous state are easier to analyze than those in condensed state and the voids in condensed explosives make them more sensitive to external stimuli relative to the perfect crystals.

Determination of LFER Descriptors of 30 Cations of Ionic Liquids—Progress in Understanding Their Molecular Interaction Potentials

In order to understand molecular interaction potentials of 30 cations of ionic liquids (ILs), the well-known linear free energy relationship concept (LFER) was applied. The LFER descriptors for the excess molar refractivity and the molar volume were calculated in silico and for hydrogen-bonding acidity and basicity, and the polarizability/dipolarity of IL cations were experimentally determined through high performance liquid chromatography (HPLC) measurements. For the study, three different columns (RP-select B, Cyan, and Diol) and buffered mobile phases, based on two organic solvents acetonitrile (ACN) and methanol (MeOH), were selectively combined to the HPLC separation systems RP-select B-ACN, RP-select B-MeOH, Cyan-MeOH, Diol-ACN, and Diol-MeOH. By measuring the retention factors of 45 neutral calibration compounds and calculating LFER descriptors of three cations in the HPLC systems, the system parameters, including an ionic z coefficient, were determined. Conversely, the LFER descriptors of 30 ionic liquid cations were determined, based on the parameters of five systems and their retention factors in the HPLC systems. The results showed that the type of head group, alkyl chain length and further substituents of the cation have a significant influence on the dipolarity/polarizability and the hydrogen-bonding acidity, and functionalized groups (hydroxyl, ether, and dimethylamino) lead to hydrogen-bonding basicity of the cation. The characterization of cationic LFER descriptors opens up the chance for a more quantitative understanding of molecular interaction potentials and physicochemical properties of ILs.

Theoretical Study on Cooperativity Effects between Anion–π and Halogen‐Bonding Interactions

This article analyzes the interplay between lone pair-π (lp-π) or anion-π interactions and halogen-bonding interactions. Interesting cooperativity effects are observed when lp/anion-π and halogen-bonding interactions coexist in the same complex, and they are found even in systems in which the distance between the anion and halogen-bond donor molecule is longer than 9 Å. These effects are studied theoretically in terms of energetic and geometric features of the complexes, which are computed by ab initio methods. Bader's theory of "atoms in molecules" is used to characterize the interactions and to analyze their strengthening or weakening depending upon the variation of charge density at critical points. The physical nature of the interactions and cooperativity effects are studied by means of molecular interaction potential with polarization partition scheme. By taking advantage of all aforementioned computational methods, the present study examines how these interactions mutually influence each other. Additionally, experimental evidence for such interactions is obtained from the Cambridge Structural Database (CSD).

Thinking in Terms of Structure-Activity-Relationships (T-SAR): A Tool to Better Understand Nanofiltration Membranes.

A frontier to be conquered in the field of membrane technology is related to the very limited scientific base for the rational and task-specific design of membranes. This is especially true for nanofiltration membranes with properties that are based on several solute-membrane interaction mechanisms. “Thinking in terms of Structure-Activity-Relationships” (T-SAR) is a methodology which applies a systematic analysis of a chemical entity based on its structural formula. However, the analysis become more complex with increasing size of the molecules considered. In this study, T-SAR was combined with classical membrane characterization methods, resulting in a new methodology which allowed us not only to explain membrane characteristics, but also provides evidence for the importance of the chemical structure for separation performance. We demonstrate an application of the combined approach and its potential to discover stereochemistry, molecular interaction potentials, and reactivity of two FilmTec nanofiltration membranes (NF-90 and NF-270). Based on these results, it was possible to predict both properties and performance in the recovery of hydrophobic ionic liquids from aqueous solution.

A molecular model of water based on the lattice gas model

A lattice gas model is used to describe the vapor-liquid state of water molecules. The orientationally directed interaction of the water molecules via their tetrahedral structure and dipole-dipole interaction are considered in the theory, along with the Lennard-Jones contributions to the potential of molecular interaction, which stabilize the system with dipole interaction. We studied how the radius of the molecular interaction potential affects the equilibrium characteristics of the system (the phase separation curves of the vapor-liquid system, and the relationship between the fluid density and the chemical potential value).

Lattice Boltzmann method for Lennard-Jones fluids based on the gradient theory of interfaces

In the present study we propose a lattice Boltzmann equation (LBE) model derived from density gradient expansions of the discrete BBGKY evolution equations. The model is based on the mechanical approach of the gradient theory of interfaces. The basic input is the radial distribution function, which is related exclusively to the molecular interaction potential, rather than semiempirical equations of state used in previous LBE models. This function can be provided from independent molecular simulations or from approximate theories. Evidently the accuracy of the interaction potential, and thus the radial distribution function, reflects on the accuracy of the thermodynamic properties and consistency of the derived LBE model. We have applied the proposed model to obtain equilibrium bulk and interfacial properties of a Lennard-Jones fluid at different temperatures, T, close to critical, T(c). The results demonstrate that the LBE model is in excellent agreement with gradient theory as well as with independent literature results based on different molecular simulation approaches. Hence the proposed LBE model can recover accurately bulk and interfacial thermodynamics for a Lennard Jones fluid at T/T(c)>0.9.

Carbon nanotube oscillators for applications as nanothermometers

Nanostructures such as carbon nanotubes have a broad range of potential applications such as nanomotors, nano-oscillators and electromechanical nanothermometers, and a proper understanding of the molecular interaction between nanostructures is fundamentally important for these applications. In this paper, we determine the molecular interaction potential of interacting carbon nanotubes for two configurations. The first is a shuttle configuration involving a short outer tube sliding on a fixed inner tube, and the second involves a telescopic configuration for which an inner tube moves both in the region between two outer tubes and through the tubes themselves. For the first configuration we examine two cases of semi-infinite and finite inner carbon nanotubes. We employ the continuum approximation and the 6–12 Lennard-Jones potential for non-bonded molecules to determine the molecular interaction potential and the resulting van der Waals force, and we evaluate the resulting surface integrals numerically. We also investigate the acceptance condition and suction energy for the first configuration. Our results show that for the shuttle configuration with a semi-infinite inner tube, the suction energy is maximum when the difference between the outer and inner tubes radii is approximately 3.4 Å, which is the ideal inter-wall spacing between graphene sheets. For the finite inner tube, the potential energy is dependent on both the inner and outer tube lengths as well as on the inter-wall spacing. In terms of the oscillating frequency, the critical issue is the length of the moving outer tube, and the shorter the length, the higher the frequency. Further, for the telescopic configuration with two semi-infinite outer nanotubes of different radii, we find that the interaction energy also depends on the difference of the tube radii. For two outer nanotubes of equal radii we observe that the shorter the distance between the two outer nanotubes, the higher the magnitude of the interaction potential around the origin.

Safe stress assessment in the strength concept by Zhurkov

The paper proposes an assessment method for safe stress in the kinetic concept of strength based on the warm-up drift technique in the model of a steady state with a broken bond. The authors added molecular interaction potential with a second potential energy minimum that corresponds to an excited molecule with broken bonds with its neighbors. The quasi-homogenous fracture model with using macro-values of a continuum has yielded that safe stress for metals and salts equals 10–20 % of their temporal tensile strength.

Multiscale modelling and simulation of the deformation and adhesion of a single gecko seta

A 3D multiscale model is presented which describes the adhesion and deformation of a gecko seta. The multiscale approach combines three models at different length scales: at the top level, on the order of several micrometers, a nonlinear finite element beam model is chosen to capture the branched microstructure of the gecko seta. At the intermediate level, on the order of several nanometers, a second finite element model is used to capture the detailed behaviour of the seta tips, the so-called spatulae. At the lowest level, on the order of a few angstroms, a molecular interaction potential is used to describe the van der Waals adhesion forces between spatulae and substrate. Coarse-graining techiques are used to bridge the scale between the model levels. To illustrate and validate the proposed gecko seta model, numerical pull-off simulations are shown and compared to experimental data from the literature.

Predicting Drug–Drug Interactions: An FDA Perspective

Pharmacokinetic drug interactions can lead to serious adverse events, and the evaluation of a new molecular entity's drug-drug interaction potential is an integral part of drug development and regulatory review prior to its market approval. Alteration of enzyme and/or transporter activities involved in the absorption, distribution, metabolism, or excretion of a new molecular entity by other concomitant drugs may lead to a change in exposure leading to altered response (safety or efficacy). Over the years, various in vitro methodologies have been developed to predict drug interaction potential in vivo. In vitro study has become a critical first step in the assessment of drug interactions. Well-executed in vitro studies can be used as a screening tool for the need for further in vivo assessment and can provide the basis for the design of subsequent in vivo drug interaction studies. Besides in vitro experiments, in silico modeling and simulation may also assist in the prediction of drug interactions. The recent FDA draft drug interaction guidance highlighted the in vitro models and criteria that may be used to guide further in vivo drug interaction studies and to construct informative labeling. This report summarizes critical elements in the in vitro evaluation of drug interaction potential during drug development and uses a case study to highlight the impact of in vitro information on drug labeling.