Bond Angle Potentials Research Articles

A Comparative Analysis of Force Fields of Drug-Like Molecules: Omeprazole, Favipiravir and Amoxicillin by using Bonded and Non-Bonded Potential Distributions

This research aims to compare and analyze the force field parameters of drug-like compounds generated by the online servers CGenFF, SwissParam, and LigParGen. CHARMM27, OPLS-AA, and CHARMM36 force fields of amoxicillin, favipiravir, and omeprazole have been examined by bonded and non-bonded energy distributions of the potential function. The local terms of the force field function are bond length, bond angle, and dihedral potentials, while the non-local terms are van der Waals and pairwise electrostatic interactions. The parabolic curves of bond length potential appear to internally bend because of the larger values of force constants. The bond length and angle energies are lowest at reference values for each of the corresponding atom pairs in the molecules. The higher values of the bending force constant positively deflect the sinusoidal curve from the equilibrium position according to the dihedral angle energy distribution. The Lennard-Jones interaction exhibits the same repellent nature at closer ranges and the same attracting nature at farther ranges whereas a mildly differentiated interaction is seen at the intermediate state as a result of changing well-depth parameters. Depending on the size of the optimized partial charges, it is discovered in electrostatic interaction that the distributions of end-to-end lengths of identical atom pairs are more exponentially skewed from one another. The main cause of inconsistency in the results of MD simulations for the same protein-ligand system is due to the shifted topology and parameters.

A nonlinear molecular mechanics model for graphene subjected to large in-plane deformations

In this paper we present a fully nonlinear stick-and-spring model for graphene subjected to in-plane deformations. The constitutive behaviors of sticks and springs are defined, respectively, by the modified Morse potential and a nonlinear bond angle potential. The equilibrium equations of the representative cell are written considering large displacements of the nodes (atoms) and the stability of the solutions is assessed using an energy criterion. The solutions for the uniaxial load cases along armchair and zigzag directions show that graphene is isotropic for small deformations, while it exhibits anisotropy when subjected to large deformations. Moreover, graphene shows a negative Poisson’s ratio after a critical value of deformation. In the case of equibiaxial load, multiple solutions of the equilibrium are found and graphene can experience asymmetric deformations despite the symmetry of the external loads. The nonlinear formulation of the equilibrium is then linearized by introducing the hypothesis of small displacements. The expressions of Young’s modulus and Poisson’s ratio are derived.

Theoretical studies (DFT) on hydrogen bonded liquid crystal derived from 4-amino and 4-dodecyloxy benzoic acids

Hydrogen bonded liquid crystal (HBLC) complex was obtained from the combination of 4-Amino benzoic acid (ABA) and mesogenic 4-(Dodecyloxy) benzoic acid (12OBA). The HBLC molecular structure was optimized by B3LYP/6-311G basis set (d, p). The O-H⋯O bond angle, bond length and electrostatic potential (ESP) had been studied by DFT. The natural bonding orbital (NBO) reveals the intermolecular charge transfers within the molecules, and the monomer I, monomer II and dimer O-H⋯O intermolecular stabilization energy were analysed. Further, the band gap energy for monomer I (4.275 eV), monomer II (4.559 eV) and dimer (4.745 eV) were calculated by Homo-Lumo. Mulliken analysis shows the clear evidence of the charge distribution between the molecules. Thermochemistry properties, O-H⋯O binding energy, collision diameter and chemical parameters were also computed by Gaussian 16 programme. Computational studies were performed to identify the nature of HBLC complex and its possible applications in the field of optoelectronics.

Constant velocity pulling and unfolding of thyroid hormone receptor by steered molecular dynamics

Unfolding pathways of T3 liganded thyroid hormone receptor (THRT3) can be studied by using the protocols of steered molecular dynamics (SMD). Theory of constant velocity pulling has been implemented to the structure of THRT3 in a neutral water-ion solution equilibrated up to 20 ns. The globular form of THRT3 is completely unfolded extending N-C termini from 38 Å to 876 Å at a constant speed of 0.1 Å/ps by means of 8.5 ns long SMD simulations. The peak force measured in the intermediate conformations is related to a burst of backbone H-bonds among a-helices and b-hairpins. With decrease in H-bonds, electrostatic energy increases by losing gradually the secondary structure and separating a and b-strands in solution. The force at the end (t > 8.5 ns) increases steeply with the large increase in bond-angle and bond-length potentials when the system becomes completely unfolded. The hydrophobic ligand binding domain (LBD) of THR-b with load bearing H-bonds protects T3 from water attack. Even after complete unfolding of THR-b LBD, the position of T3 is not deviated more than 2.5 Å and a large number of water molecules remain in the surrounding of this domain area. This is a strong evidence for the mechanochemical stability of a receptor protein’s LBD towards hormone activated gene expressions followed by ligand binding and dissociation.
 BIBECHANA 17 (2020) 50-57

Phase behavior of flexible and semiflexible polymers in solvents of varying quality.

The interplay of nematic order and phase separation in solutions of semiflexible polymers in solvents of variable quality is investigated by density functional theory (DFT) and molecular dynamics (MD) simulations. We studied coarse-grained models, with a bond-angle potential to control chain stiffness, for chain lengths comparable to the persistence length of the chains. We varied both the density of the monomeric units and the effective temperature that controls the quality of the implicit solvent. For very stiff chains, only a single transition from an isotropic fluid to a nematic is found, with a phase diagram of "swan-neck" topology. For less stiff chains, however, also unmixing between isotropic fluids of different concentration, ending in a critical point, occurs for temperatures above a triple point. The associated critical behavior is examined in the MD simulations and found compatible with Ising universality. Apart from this critical behavior, DFT calculations agree qualitatively with the MD simulations.

Nematic order in solutions of semiflexible polymers: Hairpins, elastic constants, and the nematic-smectic transition.

Coarse-grained models of lyotropic solutions of semiflexible polymers are studied by both molecular dynamics simulations and density functional theory calculations, using an implicit solvent bead-spring model with a bond-angle potential. We systematically vary the monomer density, persistence length, and contour length over a wide range and explore the full range from the isotropic-nematic transition to the nematic-smectic transition. In the nematic regime, we span the entire regime from rigid-rod like polymers to thin wormlike chains, confined in effective straight tubes caused by the collective nematic effective ordering field. We show that the distribution of bond angles relative to the director is well described by a Gaussian, irrespective of whether the chains are rod-like or rather flexible. However, the related concept of "deflection length" is shown to make sense only in the latter case for rather dilute solutions since otherwise the deflection length is of the order of about two bond lengths only. When the solution is semi-dilute, a substantial renormalization of the persistence length occurs, while this effect is absent in the isotropic phase even at rather high monomer densities. The effective radii of the "tubes" confining the chains in the related description of orientational ordering are significantly larger than the distances between neighboring chains, providing evidence for a pronounced collective character of orientational fluctuations. Hairpins can be identified close to the isotropic-nematic transition, and their probability of occurrence agrees qualitatively with the Vroege-Odijk theory. The corresponding theoretical predictions for the elastic constants, however, are not in good agreement with the simulations. We attribute the shortcomings of the theories to their neglect of the coupling between local density and orientational fluctuations. Finally, we detected for this model a transition to a smectic phase for reduced monomer densities near 0.7.

Sequence-Dependent Three Interaction Site Model for Single- and Double-Stranded DNA.

We develop a robust coarse-grained model for single- and double-stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data Bank. Some of the parameters in the stacking interactions were calculated using a learning procedure, which ensured that the experimentally measured melting temperatures of dimers are faithfully reproduced. Without any further adjustments, the calculations based on the TIS model reproduce the experimentally measured salt and sequence-dependence of the size of single-stranded DNA (ssDNA), as well as the persistence lengths of poly(dA) and poly(dT) chains. Interestingly, upon application of mechanical force, the extension of poly(dA) exhibits a plateau, which we trace to the formation of stacked helical domains. In contrast, the force-extension curve (FEC) of poly(dT) is entropic in origin and could be described by a standard polymer model. We also show that the persistence length of double-stranded DNA, formed from two complementary ssDNAs, is consistent with the prediction based on the worm-like chain. The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. Our model predicts the melting temperatures of DNA hairpins with excellent accuracy, and we are able to recover the experimentally known sequence-specific trends. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting profiles of dimers, attests to the transferability and robustness of the TIS model for ssDNA and dsDNA.

Adsorption and structure formation of semiflexible polymers on spherical surfaces

Rigid spheres with a short-range attractive potential are taken as a coarse-grained model of vesicles, which contain a solution of semiflexible polymers in their interior. Assuming good solvent conditions with an implicit description of the solvent, effective monomers experience bond-length and bond-angle potentials as well as excluded-volume interaction. Due to the attractive vesicle surface, phase separation occurs between a thin shell of adsorbed monomers at the surface and a rather dilute, and therefore, disordered polymer solution in the sphere interior. While at a planar attractive surface the wormlike chains would exhibit liquid crystalline (nematic and smectic) order, the curvature of the sphere frustrates this order, causing the existence of defects in the orientational order. In the dense monolayer of surface-attached polymers, the stiff chains acquire a curvature corresponding to banana-like shapes for rather small contour length, causing a local nematic order of biaxial type. These orderings are compared to related phenomena in spheres densely filled with semiflexible polymers. We complement the results obtained by Molecuar Dynamics simulations by corresponding Density Functional Theory calculations.

Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles

The conformations of semiflexible polymers in two dimensions confined in a strip of width D are studied by computer simulations, investigating two different models for the mechanism by which chain stiffness is realized. One model (studied by molecular dynamics) is a bead-spring model in the continuum, where stiffness is controlled by a bond angle potential allowing for arbitrary bond angles. The other model (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles (0° and ±90°) are possible, and the bond angle potential then controls the density of kinks along the chain contour. The first model is a crude description of DNA-like biopolymers, while the second model (roughly) describes synthetic polymers like alkane chains. It is first demonstrated that in the bulk the crossover from rods to self-avoiding walks for both models is very similar, when one studies average chain linear dimensions, transverse fluctuations, etc., despite their differences in local conformations. However, in quasi-one-dimensional confinement two significant differences between both models occur: (i) The persistence length (extracted from the average cosine of the bond angle) gets renormalized for the lattice model when D gets less than the bulk persistence length, while in the continuum model it stays unchanged. (ii) The monomer density near the repulsive walls for semiflexible polymers is compatible with a power law predicted for the Kratky-Porod model in the case of the bead-spring model, while for the lattice case it tends to a nonzero constant across the strip. However, for the density of chain ends, such a constant behavior seems to occur for both models, unlike the power law observed for flexible polymers. In the regime where the bulk persistence length ℓp is comparable to D, hairpin conformations are detected, and the chain linear dimensions are discussed in terms of a crossover from the Daoud/De Gennes "string of blobs"-picture to the flexible rod picture when D decreases and/or the chain stiffness increases. Introducing a suitable further coarse-graining of the chain contours of the continuum model, direct estimates for the deflection length and its distribution could be obtained.

Consistent model reduction of polymer chains in solution in dissipative particle dynamics: Model description

We introduce a framework for model reduction of polymer chain models for dissipative particle dynamics (DPD) simulations, where the properties governing the phase equilibria such as the characteristic size of the chain, compressibility, density, and temperature are preserved. The proposed methodology reduces the number of degrees of freedom required in traditional DPD representations to model equilibrium properties of systems with complex molecules (e.g., linear polymers). Based on geometrical considerations we explicitly account for the correlation between beads in fine-grained DPD models and consistently represent the effect of these correlations in a reduced model, in a practical and simple fashion via power laws and the consistent scaling of the simulation parameters. In order to satisfy the geometrical constraints in the reduced model we introduce bond–angle potentials that account for the changes in the chain free energy after the model reduction. Following this coarse-graining process we represent high molecular weight DPD chains (i.e., ≥200 beads per chain) with a significant reduction in the number of particles required (i.e., ≥20 times the original system). We show that our methodology has potential applications modeling systems of high molecular weight molecules at large scales, such as diblock copolymer and DNA.

Structure and rheology of star polymers in confined geometries: a mesoscopic simulation study.

Mesoscopic simulations of star polymer melts adsorbed onto solid surfaces are performed using the dissipative particle dynamics (DPD) method. A set of parameters is developed to study the low functionality star polymers under shear. The use of a new bond-angle potential between the arms of the star creates more rigid chains and discriminates between different functionalities at equilibrium, but still allows the polymers to deform appropriately under shear. The rheology of the polymer melts is studied by calculating the kinetic friction and viscosity and there is good agreement with experimental properties of these systems. The study is completed with predictive simulations of star polymer solutions in an athermal solvent.

Computational study of the intramolecular proton transfer reactions of dipicolinic acid (pyridine-2,6-dicarboxylic acid) and its dimers

The intramolecular proton transfer (IPT) reaction and dimerization processes of dipicolinic acid (DPA) have been investigated using density functional theory (DFT) at the B3LYP/6-31G++(d) basis set level. The influence of the solvent on the zwitterion -to- neutral transition of DPA was examined using the continuum model (CPCM) with different dielectric constants (ε=4.9, CHCl3; ε=7.42, THF; ε=32.63, CH3OH; ε=78.39, H2O). The intramolecular proton transfer reaction occurs more readily in the gas phase than solution. Results also show that the stability of DPA dimers in the gas phase is directly affected by the hydrogen bond angle and electrostatic potential (ESP) value in the dimer structure.

Conformation and segmental mobility of a diluted single polymer chain simulated with bond fluctuation model

The conformation of a single long polymer chain has been modelled using the Bond Fluctuation Model. The interaction between non-bonded segments has been introduced in the model by means of a Lennard-Jones potential while two energy potentials depending on bond length and bond angle took into account intramolecular interactions. The effect on chain configuration of varying bond angle potential, which tends to extend the polymer chain, was studied. The chain was allowed to equilibrate at high temperature, adopting a random coil conformation. When the system was subjected to a cooling ramp, its energy and dynamically accessible volume decreased but the system maintained the liquid conditions up to a temperature range in which the glass transition yielded a glassy coil with very restricted but not null segmental mobility. The remaining mobility in the glassy state, as well as its conformation, characterised through correlation functions, also depended significantly on the strength of bond angle potential. Further isothermal annealing yielded very compact structures, always amorphous with particular shapes depending on annealing temperature.

Semicrystalline ordering in polymeric systems simulated by Bond Fluctuation Model

Arresting of segmental mobility in polymer systems on cooling from the melt was simulated by means of the Bond Fluctuation Model. In order to represent the behaviour of the system, three potentials were included: a Lennard–Jones potential, a bond length potential and a bond angle potential. The effect of the bond angle and bond length potential combination is to stretch the chains, while the Lennard–Jones potential leads to a lack of free volume which appears when temperature decreases. So, when a cooling ramp is applied, depending on the balance of these potentials, the system shows a transition in which molecules densely pack or, on the contrary, remains amorphous. Therefore, the choice in the weighting of these three potentials is a key point to simulate a physical system by using the Bond Fluctuation Model.

A coarse-graining procedure for polymer melts applied to 1,4-polybutadiene

We present a coarse-graining procedure for homopolymer melts mapping intra- as well as inter-molecular interactions from a chemically realistic united atom description to a bead-spring type molecular model. On the coarse-grained level the repeat units interact through bond-length and bond angle potentials and a non-bonded Lennard-Jones type interaction. The latter one is of the 7,4 form and softer than the typically employed 12,6 interactions. The coarse-graining of the intramolecular interactions follows well developed procedures, however, we point out in which way the non-bonded intramolecular interactions in the chemically realistic model should be treated. The parameters of the non-bonded interaction on the coarse level are determined by matching the zero pressure isobar of the chemically realistic model of a 1,4-polybutadiene melt. For the coarse-grained model we perform melt simulations at several temperatures and compare structural and dynamic properties with the behavior of the chemically realistic model.

The dependence of nanostructures on the molecule rigidity of A2(B4)2-type miktoarm block copolymer

Using the dissipative particle dynamics simulation technique, we have studied the influence of the molecule rigidity on the nanostructures of the A2(B4)2-type miktoarm block copolymers. A typical spherical micellar ordered structure is obtained for a coil-coil miktoarm block copolymer in melt. By introducing a bond angle potential in our model to enhance the molecule rigidity systematically, we find, respectively, a hexagonal cylindrical structure and a parallel ellipsoid in lamellae structure which is discovered for the first time.

The Victor/FRST Function for Model Quality Estimation

Scoring functions are widely used in the final step of model selection in protein structure prediction. This is of interest both for comparative modeling targets, where it is important to select the best model among a set of many good, "correct" ones, as well as for other (fold recognition or novel fold) targets, where the set may contain many incorrect models. A novel combination of four knowledge-based potentials recognizing different features of native protein structures is introduced and tested. The pairwise, solvation, hydrogen bond, and torsion angle potentials contain largely orthogonal information. Of these, the torsion angle potential is found to show the strongest correlation with model quality. Combining these features with a linear weighting function, it was possible to construct a robust energy function capable of discriminating native-like structures on several benchmarking sets. In a recent blind test (CAFASP-4 MQAP), the scoring function ranked consistently well and was able to reliably distinguish the correct template from an ensemble of high quality decoys in 52 of 70 cases (33 of 34 for comparative modeling). An executable version of the Victor/FRST function for Linux PCs is available for download from the URL http://protein.cribi.unipd.it/frst/.

Calculation of the entropy and free energy from monte carlo simulations of a peptide stretched by an external force.

Hypothetical scanning Monte Carlo (HSMC) is a method for calculating the absolute entropy, S, and free energy, F, from a trajectory generated by any simulation technique. HSMC was applied initially to fluids (argon and water) and later to peptides and self-avoiding walks on a lattice. In this paper we make a step further and apply it to a model of decaglycine (at T = 300 K) in vacuum with constant bond lengths where external stretching forces are exerted at the end points; the changes in S and F are calculated as the forces are increased. The molecule is placed initially in a helical structure, which is changed to an extended structure after a short simulation time due to the exerted forces. This study has relevance to problems in polymers (e.g., rubber elasticity) and to the analysis of experiments where individual molecules are stretched by atomic force microscopy (AFM), for example. The results for S and F are accurate and are significantly better than those obtained by the quasi-harmonic approximation and the local states method. However, the molecule is quite stiff due to the strong bond angle potentials and the extensions are small even for relatively large forces. Correspondingly, as the force is increased the decrease in the entropy is relatively small while the potential energy is enhanced significantly. Still, differences, TDeltaS, for different forces are obtained with very good accuracy of approximately 0.2 kcal/mol.

Molecular dynamics modeling of polymer crystallization; from simple polymers to helical ones

Crystallization of helical polymers is a very big challenge for molecular simulation. It involves many significant issues, such as folding in biomolecules and molecular recognition during crystal growth. Though direct molecular simulations of the process still involve very difficult problems, we here report our recent efforts toward better understanding of the crystallization in helical polymers. We begin with a brief review of our former studies on simple polyethylene-like polymers, and then we introduce several helical polymer models which are systematically made more complicated. We have already reported that a simple polyethylene-like polymer crystallizes very fast into chain folded lamellae from the melt. A slight modification of this simple polymer model by introducing proper bond angle and dihedral angle potentials gives one of the present models of the helical polymer. This helical polymer model is devised to be relatively rigid but mobile, to show easy helix-reversals, and to have a definite preference for gauche bonds. We find that this highly mobile helical polymer shows quick chain folded crystallization and forms approximate 4/1 helical structure. The intra- and the intermolecular order grow quite simultaneously suggesting highly cooperative nature of the phenomena. Further elaboration of the helical model, giving pendant side groups and higher energy barrier to the helix reversals, leads us to a realistic united atom model of iPP. The conventional and the multi-canonical Monte Carlo simulations are applied to find probable modes of chain folding and the ground state conformations. Though a very short chain readily forms a regular 3/1 helix of alternating trans and gauche bonds, much longer chains of 30- and 50-propylene units are not found to have energetic ground states in the regularly folded conformations.

Bond-Angle-Potential-Dependent Dissipative Particle Dynamics Simulation and Lipid Inverted Phase

A bond-angle-potential-related dissipative particle dynamics (DPD) simulation method was established for the first time to simulate the inverted phase of a lipid. We observed that the correct elastic properties of the membrane in the DPD model can be reproduced by introducing a proper bond angle potential. Using this modified model, we succeed for the first time in producing spherical micellar, rodlike micellar, disklike micellar, and three types of inverted phases and phase sequences with different architecture. The results are in excellent agreement with the experiments and theory. The model can be applied for the simulation of biomembrane fusion and other dynamical processes associated with lipid phase behavior.