Equilibrium Lengths Research Articles

Nucleation limits the lengths of actin filaments assembled by formin

Formins stimulate actin polymerization by promoting both filament nucleation and elongation. Because nucleation and elongation draw upon a common pool of actin monomers, the rate at which each reaction proceeds influences the other. This interdependent mechanism determines the number of filaments assembled over the course of a polymerization reaction, as well as their equilibrium lengths. In this study, we used kinetic modeling and in vitro polymerization reactions to dissect the contributions of filament nucleation and elongation to the process of formin-mediated actin assembly. We found that the rates of nucleation and elongation evolve over the course of a polymerization reaction. The period over which each process occurs is a key determinant of the total number of filaments that are assembled, as well as their average lengths at equilibrium. Inclusion of formin in polymerization reactions speeds filament nucleation, thus increasing the number and shortening the lengths of filaments that are assembled over the course of the reaction. Modulation of the elongation rate produces modest changes in the equilibrium lengths of formin-bound filaments. However, the dependence of filament length on the elongation rate is limited by the number of filament ends generated via formin’s nucleation activity. Sustained elongation of small numbers of formin-bound filaments, therefore, requires inhibition of nucleation via monomer sequestration and a low concentration of activated formin. Our results underscore the mechanistic advantage for keeping formin’s nucleation efficiency relatively low in cells, where unregulated actin assembly would produce deleterious effects on cytoskeletal dynamics. Under these conditions, differences in the elongation rates mediated by formin isoforms are most likely to impact the kinetics of actin assembly.

Modification and Validation of the DREIDING Force Field for Molecular Liquid Simulations (DREIDING-UT)

In this study, we modified Lennard-Jones (LJ) parameters and point-charge parameters of the DREIDING force field (the modified force-field model is named DREIDING-UT). While the original LJ parameters of DREIDING were derived through an analytical formula to reproduce the potential depths and the equilibrium lengths of the Buckingham potentials of DREIDING/X6, the modified LJ parameters were derived through the least square fitting of the Buckingham potentials. Because the Gasteiger-Marsili (GM) charges of the original DREIDING underestimated electrostatic interactions, we replaced it with the restrained electrostatic potential (RESP) charges calculated from the ab initio wavefunctions, taking the dynamic electron correlation and solvation effects into account. To confirm how the modified force field works, we conducted molecular dynamics (MD) simulations of typical liquids. It was found that the densities and self-diffusion coefficients of the DREIDING-UT model agreed with the experimental ones much better than those of the original model.

Microcrack under internal pressure at dislocation defect

By solving the problem of the theory of elasticity for a boundary dislocation with a cavity on its continuation, a stress-strain state in a solid crystalline body is determined. The correlation for calculating the energy of a body with a dislocation crack under pressure is obtained. The geometric parameters of a crack-like dislocation cavity are calculated. The values of equilibrium and non-equilibrium crack lengths are established on this basis. Also the value of the critical pressure at which the dislocation crack start begins is received. Stress intensity factors for the dislocation crack are obtained and calculated. Physical essence of fracture toughness is established using stress intensity factors.

Wave Ripple Development on Mixed Clay‐Sand Substrates: Effects of Clay Winnowing and Armoring

AbstractBased on bed form experiments in a large‐scale flume, we demonstrate that the rate of development of wave ripples on a mixed sand‐clay bed under regular waves is significantly lower than on a pure‐sand bed, even at clay fractions as low as 4.2%, and that this rate of development decreases exponentially from 4.2% to 7.4% clay. These experiments also showed that, despite the slow growth of the bed forms in the mixed sand‐clay, the equilibrium length and height of the wave ripples were independent of the initial bed clay fraction. Given that the ripple crests were composed of pure sand at the end of all the experiments that started with well‐mixed sand‐clay, it is inferred that the clay was removed from the bed during the development of the wave ripples through winnowing into the water column, and possibly also by sieving into the subsurface, where the final clay fractions were found to be higher than the initial clay fractions. These clay removal processes are interpreted to have facilitated the wave ripples to reach equilibrium lengths and heights that are similar to those in pure sand. Clay‐carrying pore flow initiated by pressure gradients between the wave ripple troughs and crests might also have contributed to the accumulation of clay in the sediment below the wave ripples. The formation of the clay‐enriched “armoring” layer in the substrate is likely to further reduce erosion rates and could influence the dispersion of nutrients and pollutants in coastal seas.

АДСОРБЦІЙНІ ВЛАСТИВОСТІ КОМПОЗИТУ ПОЛІПІРОЛ - ШПІНЕЛЬ NiCo2O4

To interpret the experimentally established fact of the reduction of molecular oxygen on the surface of the multilayered polypyrrole/spinel (NiCo2O4) composite using quantum chemical calculations. The adsorption of oxygen molecules on surfaces of polypyrrole/spinel (NiCo2O4) composite is studied using ab initio embedded cluster calculations. The total energies of the molecular cluster of the composition Ni2Co4O22C8N2H28 and the adsorption complexes Ni2Co4O22C8N2H28-O2, Ni2Co4O22C12N2H28-O2H-, Ni2Co4O22C12N2H28-2OH, Ni2Co4O22C12N2H28-H2O2H2 were calculated. The electron density distribution between the power centers, bonds and atomic orbitals were determinate. In addition, the equilibrium lengths of adsorption bonds and adsorption energy of oxygen were clarified. It was shown for the first time that in polypyrrole/spinel (NiCo2O4) composite oxygen can be reduced by four electronic mechanisms. Practical significance. The obtained results can be used in experimental studies of catalytic activity of polypyrrole/spinel (NiCo2O4) composite and other composite materials based on transition metal oxides and electrically conductive polymers.

One-electron densities of freely rotating Wigner molecules

A formalism enabling computation of the one-particle density of a freely rotating assembly of identical particles that vibrate about their equilibrium positions with amplitudes much smaller than their average distances is presented. It produces densities as finite sums of products of angular and radial functions, the length of the expansion being determined by the interplay between the point-group and permutational symmetries of the system in question. Obtaining from a convolution of the rotational and bosonic components of the parent wavefunction, the angular functions are state-dependent. On the other hand, the radial functions are Gaussians with maxima located at the equilibrium lengths of the position vectors of individual particles and exponents depending on the scalar products of these vectors and the eigenvectors of the corresponding Hessian as well as the respective eigenvalues. Although the new formalism is particularly useful for studies of the Wigner molecules formed by electrons subject to weak confining potentials, it is readily adaptable to species (such as ʻballiums’ and Coulomb crystals) composed of identical particles with arbitrary spin statistics and permutational symmetry. Several examples of applications of the present approach to the harmonium atoms within the strong-correlation regime are given.

Dimers of heavy p-elements of groups IV–VI: Electronic, vibrational, and magnetic properties

Equilibrium lengths and binding energies, vibrational frequencies, width of the HOMO–LUMO gap, and the magnetic anisotropy energies for one- and two-component dimers of heavy p elements of Groups IV (Sn, Pb), V (Sb, Bi), and VI (Se, Te) with a pronounced relativistic effect have been calculated with the use of the formalism of the density functional theory. It has been shown that it is necessary to take into account the spin–orbit coupling, which significantly affects the energy parameters of clusters. The analysis of the data obtained has revealed that the Pb–Te, Pb–Se, Sn–Te, and Sn–Se dimers have the widest gap at the Fermi level and the lowest reactivity. The magnetic anisotropy energy has been calculated for all single- and doublecomponent dimers and the direction of the easy magnetization axis has been determined.

Computer-Aided Molecular Design of a Histone Deacetylase (HDAC) Inhibitor, N-Hydroxy-N-Phenyloctanediamide (Vorinostat)

Vorinostat, (N-hydroxy-N-phenyloctanediamide) is in a class of medications called histone deacetylase (HDAC) inhibitors. It is a good chemotherapeutic agent for treating cutaneous T-cell lymphoma (CTCL, a type of cancer) in patients whose disease has not improved, has gotten worse, or has come back after taking other medications. Conformational analysis and geometry optimization of vorinostat was performed according to the Hartree-Fock (HF) calculation method by ArgusLab 4.0.1 software. Molecular mechanics calculations were based on specific interactions within the molecule. These interactions included stretching or compressing of bond beyond their equilibrium lengths and angles, torsional effects of twisting about single bonds, the Vander Waals attractions or repulsions of atoms that came close together, and the electrostatic interactions between partial charges in vorinostat due to polar bonds. The steric energy for vorinostat was calculated to be 0.030859 a.u. (19.364457 kcal/mol). It was concluded that the lowest energy and most stable conformation of vorinostat was 19.36445736 kcal/mol). The most energetically favourable conformation of vorinostat was found to have a heat of formation of 115441.244100 kcal/mol. The self-consistent field (SCF) energy was calculated by geometry convergence function using RHF/AM1 method in ArgusLab software. The most feasible position for vorinostat to act as histone deacetylase (HDAC) inhibitor was found to be-116.682947 au (−73219.720900 kcal/mol).

How the credit assignment problems in motor control could be solved after the cerebellum predicts increases in error.

We present a cerebellar architecture with two main characteristics. The first one is that complex spikes respond to increases in sensory errors. The second one is that cerebellar modules associate particular contexts where errors have increased in the past with corrective commands that stop the increase in error. We analyze our architecture formally and computationally for the case of reaching in a 3D environment. In the case of motor control, we show that there are synergies of this architecture with the Equilibrium-Point hypothesis, leading to novel ways to solve the motor error and distal learning problems. In particular, the presence of desired equilibrium lengths for muscles provides a way to know when the error is increasing, and which corrections to apply. In the context of Threshold Control Theory and Perceptual Control Theory we show how to extend our model so it implements anticipative corrections in cascade control systems that span from muscle contractions to cognitive operations.

In Silico Geometry Optimization, Excited-State Properties of (2E)-N-Hydroxy-3-[3-(Phenylsulfamoyl) Phenyl] prop-2-Enamide (Belinostat) and its Molecular Docking Studies with Ebola Virus Glycoprotein

The histone deacetylase inhibitor (2E)-N-hydroxy-3-[3-(phenylsulfamoyl)phenyl]prop-2-enamide (belinostat) is a drug designed for the treatment of hematological malignancies and solid tumors. Geometry optimization of (2E)-N-hydroxy-3-[3-(phenylsulfamoyl)phenyl]prop-2-enamide (belinostat) using Argus lab software was performed. Molecular mechanics calculations were based on specific interactions within the molecule. These interactions included stretching or compressing of bond beyond their equilibrium lengths and angles. The excited states of belinostat were created. The final self-consistent field (SCF) energy was found to be be 126.3659168682 au (−79295.8815 kcal/mol). This is the average interaction between a given belinostat particle and other belinostat particles of a quantum-mechanical system consisting of many particles. The most energetically favourable conformation of belinostat was found to have a heat of formation of 581.1137 kcal/mol via PM3 (NDDO) RHF SCF Type. The steric energy calculated for belinostat was 0.64665673 a.u.(405.78359283 kcal/mol). Molecular docking result revealed the binding free energy. The global binding energy value-28.87 Kcal/mole was ranked first because it had the least energy. The most feasible position for belinostat to inhibit ebola virus glycoprotein was predicted to be-28.87 kcal/mol.

Quantum Chemical Studies of Anti-Cancer Chemotherapy Drug 4-Amino1-[(2R, 3R, 4S, 5S)-3, 4, 5-Trihydroxytetrahydrofuran-2-yl]-1, 3, 5-Triazin2(1H)-one (Azacitidine)

4-amino-1-[(2R, 3R, 4S, 5S)-3, 4, 5-trihydroxytetrahydrofuran-2-yl]-1, 3, 5-triazin-2(1H)-one (azacitidine) is an anticancer chemotherapy drug mainly used in the treatment of myelodysplastic syndrome (MDS). Azacitidine is a chemical analogue of the cytosine, a nucleoside found in DNA and RNA. Conformational analysis and geometry optimization of azacitidine was performed according to the Hartree-Fock (HF) calculation method by Argus Lab 4.0.1 software. Molecular mechanics calculations were based on specific interactions within the molecule. These interactions included stretching or compressing of bond beyond their equilibrium lengths and angles, torsional effects of twisting about single bonds, the Vander Waals attractions or repulsions of atoms that came close together, and the electrostatic interactions between partial charges azacitidine due to polar bonds. Surface created to visualize ground state properties as well as excited state properties such as orbital, electron densities, electrostatic potential (ESP) spin densities. The generated grid data were used to make molecular orbital surface, visualized the molecular orbital, electrostatic potential map and electron density surface. The steric energy for azacitidine was calculated to be 0.12162642 a.u.(76.32179805 kcal/mol). It was concluded that the lowest energy and most stable conformation of azacitidine was 0.12162642 a.u.(76.32179805 kcal/mol) The most energetically favourable conformation of azacitidine was found to have a heat of formation of 157.6452 kcal/mol. The self-consistent field (SCF) energy was calculated by geometry convergence function using RHF/PM3 method in ArgusLab software. The most feasible position for azacitidine to induce antineoplastic activity in the receptor was found to be-110.6126839099 au (−69410.5697 kcal/mol)

Conformation Analysis and Self-Consistent Field Energy of Immune Response Modifier, 1-(2-methylpropyl)-1H-imidazo[4, 5]quinolin-4-amine (Imiquimod)

1-(2-methylpropyl)-1H-imidazo[4, 5]quinolin-4-amine (imiquimod) is an immune response modifier and is used to treat genital warts, superficial basal cell carcinoma, and actinic keratosis. Conformational analysis and geometry optimization of imiquimiod was performed according to the Hartree-Fock (HF) calculation method by Argus Lab 4.0.1 software. Molecular mechanics calculations were based on specific interactions within the molecule. These interactions included stretching or compressing of bond beyond their equilibrium lengths and angles, torsional effects of twisting about single bonds, the Van der Waals attractions or repulsions of atoms that came close together, and the electrostatic interactions between partial charges in imiquimod due to polar bonds. The steric energy for imiquimiod was calculated to be 59.09 kcal/mol. It was concluded that the lowest energy and most stable conformation of imiquimiod was 59.09 kcal/mol. The most energetically favourable conformation of imiquimiod was found to have a heat of formation of 908.38 kcal/mol. The self-consistent field (SCF) energy was calculated by geometry convergence function using Argus Lab software. The most feasible position for the drug to interact with the receptor was found to be-95.99 au (−60240.26 kcal/mol).

Elastic instability of bilayer graphene using atomistic finite element

In-plane elastic instability of bilayer graphene sheets is investigated using atomistic finite element approaches. The equivalent homogenised properties of graphene sheet are expressed in terms of the thickness, equilibrium lengths and force-field models used to represent the C–C bonds of the graphene lattice. The covalent bonds are represented as structural beams with stretching, bending, torsional and shear deformation, and the strain energies associated to affine deformation mechanisms. The overall mechanical properties and geometric configurations of the nano-structures represented as truss assemblies are then calculated minimising the total potential energy associated to the loading, thickness and average equilibrium lengths of the bonds. Different boundary conditions and aspect ratios are considered for both bilayer and single-layer graphene sheets. The bilayer graphene sheets are found to be offering remarkably higher buckling strengths as compared to single-layer sheets.

Dynamics of mechanical waves in periodic graphene nanoribbon assemblies

We simulate the natural frequencies and the acoustic wave propagation characteristics of graphene nanoribbons (GNRs) of the type (8,0) and (0,8) using an equivalent atomistic-continuum FE model previously developed by some of the authors, where the C-C bonds thickness and average equilibrium lengths during the dynamic loading are identified through the minimisation of the system Hamiltonian. A molecular mechanics model based on the UFF potential is used to benchmark the hybrid FE models developed. The acoustic wave dispersion characteristics of the GNRs are simulated using a Floquet-based wave technique used to predict the pass-stop bands of periodic mechanical structures. We show that the thickness and equilibrium lengths do depend on the specific vibration and dispersion mode considered, and that they are in general different from the classical constant values used in open literature (0.34 nm for thickness and 0.142 nm for equilibrium length). We also show the dependence of the wave dispersion characteristics versus the aspect ratio and edge configurations of the nanoribbons, with widening band-gaps that depend on the chirality of the configurations. The thickness, average equilibrium length and edge type have to be taken into account when nanoribbons are used to design nano-oscillators and novel types of mass sensors based on periodic arrangements of nanostructures.PACS 62.23.Kn · 62.25.Fg · 62.25.Jk

Thickness and in-plane elasticity of graphane

The thickness and in-plane mechanical properties (Youngʼs, shear modulus, Poissonʼs ratios) of fully hydrogenated graphene (graphane) sheets are predicted using a molecular mechanics approach. The equilibrium lengths and bond angles distortions used for the graphane models are obtained from Density Functional Theory (DFT) simulations. Our models compare well with existing data on the uniaxial properties of graphane and graphene sheets from first principle and Molecular Dynamics (MD) simulations, highlight a special orthotropic mechanical behaviour for graphane, and identify thickness and shear stiffness values which are peculiar of hydrogenated graphene.

Reaction dynamics in the formidable gap

One of the least understood and least exploited aspects of nanoscience is dynamic coupling between directional translation at mesoscales (lengths above ~50 nm) and changes in local chemical bonding (lengths below ~1 nm). A major cause is the traditional dominance of two distinct and seemingly incompatible models for describing dynamics at the two scales: continuum mechanics based on the balance of forces, i.e., mechanical equilibrium (lengths above ~50 nm) and activated escape from an energy well, i.e., chemical equilibrium (below ~1 nm). These models yield meaningful results within their respective dimensional limits but leave processes in between in the gray area of conceptual ambiguity and technical intractability. Such processes underlie phenomena as diverse as catastrophic failure of strained materials, operation of motor polymers, behavior of polymer flows, and mechanosensing. Chemomechanics integrates the two conventional dynamic models into a single internally consistent, scale-independent framework that is essential for a quantitative understanding and the efficient exploitation of dynamic coupling across the “formidable gap” at ~1–50 nm. Chemomechanics holds promise (1) to facilitate significantly the design of new stress-responsive and actuating polymers, including those optimized specifically for the propulsion of autonomous nanomechanical devices and for use in micro- and nanoscale stress sensors; and (2) to yield general predictive molecular relationships between chemical composition, structure, and mechanical properties of polymers both at the single-chain and bulk levels. Theoretical and experimental studies of dynamic coupling across the formidable gap have traditionally been carried out within soft-matter physics. As far as I am aware, my group was the first to approach the problem from a chemist’s perspective. Below, I summarize the state-of-the-art of chemical understanding of processes in the formidable gap from both theoretical and experimental perspectives.

Still states of bistable lattices, compatibility, and phase transition

We study a two-dimensional triangular lattice made of bistable rods. Each rod has two equilibrium lengths, and thus its energy has two equal minima. A rod undergoes a phase transition when its elongation exceeds a critical value. The lattice is subject to a homogeneous strain and is periodic with a sufficiently large period. The effective strain of a periodic element is defined. After phase transitions, the lattice rods are in two different states and lattice strain is inhomogeneous, the Cauchy–Born rule is not applicable. We show that the lattice has a number of deformed still states that carry no stresses. These states densely cover a neutral region in the space of entries of effective strains. In this region, the minimal energy of the periodic lattice is asymptotically close to zero. When the period goes to infinity, the effective energy of such lattices has the “flat bottom” which we explicitly describe. The compatibility of the partially transited lattice is studied. We derive compatibility conditions for lattices and demonstrate a family of compatible lattices (strips) that densely covers the flat bottom region. Under an additional assumption of the small difference of two equilibrium lengths, we demonstrate that the still structures continuously vary with the effective strain and prove a linear dependence of the average strain on the concentration of transited rods.

Tin(II) Phthalocyaninate and Tin(IV) bis-Phthaloc Yaninate: A Quantum Chemical Study

The structural parameters of tin(II) phthalocyaninate PcSn and tin(IV) bis-phthalocyaninate Pc2Sn as well as of their cations are determined by B3LYP/SDD and PBE0/SDD quantum chemical methods. The PcSn molecule is characterized by C4v symmetry, and SnN bond lengths are 2.307/2.299 A (B3LYP/PBE0). The Sn nucleus is by 1.11 A (B3LYP, PBE0, single crystal X-ray diffraction analysis) higher than the plane of four neighboring nitrogen nuclei. The “hindered” configuration (D4d symmetry) with a high (27–30 kcal/mole) internal rotation barrier corresponds to the Pc2Sn energy minimum. The calculated equilibrium lengths of eight equivalent SnN bonds of 2.366/2.347 (B3LYP/PBE0) are similar to the average SnN bond length of 2.347 A (single crystal X-ray diffraction). Vertical and adiabatic ionization potentials are calculated: Iv 6.40/6.48 eV, IA 6.38/6.45 eV for PcSn and Iv 5.63/5.66 eV, IA 5.60/5.63 eV for Pc2Sn.

Generation of disclination dipoles and nanoscopic cracks in deformed nanoceramic materials

The processes of generation of disclination dipoles and nanoscopic cracks (nanocracks) in deformed nanoceramic materials are investigated theoretically. It is demonstrated that disclination dipoles are formed at grain boundaries in the course of grain-boundary sliding. The geometric features of the generation of disclination dipoles are analyzed. The conditions under which the nucleation of nanocracks in the vicinity of the disclination dipoles is energetically favorable are calculated for the nanoceramic materials α-Al2O3 (corundum) and 3C-SiC (the cubic phase of silicon carbide). The equilibrium lengths of these nanocracks are also calculated. It is shown that the equilibrium lengths of nanocracks can be comparable to the grain size. As a consequence, these nanocracks can coalesce, thus eventually resulting in the brittle fracture of nanoceramic materials.

Scaling Behavior and Equilibrium Lengths of Knotted Polymers

We use numerical simulations to investigate how the chain length and topology of freely fluctuating knotted polymer rings affect their various spatial characteristics such as the radius of the smallest sphere enclosing momentary configurations of simulated polymer chains. We describe how the average value of a characteristic changes with the chain size and how this change depends on the topology of the modeled polymers. Although the scaling profiles of a spatial characteristic for distinct knot types do not intersect (at least, in the range of our data), the profiles for nontrivial knots intersect the corresponding profile obtained for phantom polymers, i.e., those that are free to explore all available topological states. For each knot type, this point of intersection defines its equilibrium length with respect to the spatial characteristic. At this chain length, a polymer forming a given knot type will not tend to increase or decrease, on average, the value of the spatial characteristic when the polymer is released from its topological constraint. We show interrelations between equilibrium lengths defined with respect to spatial characteristics of different character and observe that they are related to the lengths of ideal geometric configurations of the corresponding knot types.