Elastic properties, Young's modulus determination and structural stability of the tropocollagen molecule: a computational study by steered molecular dynamics

The aim of this report is to investigate at microscopic level the elastic properties of a tropocollagen-like molecule submitted to linear traction along its longitudinal axis. For this purpose, we performed steered molecular dynamics (SMD) simulations for a wide range of spring constants in order to test the molecular response based on a two-spring model connected in series. An elastic behavior was observed in an elongation range of 2.5-4% of the molecular length, estimating an "effective molecular elastic constant" of 1.02+/-0.20 kcal/mol A2 in this region. Accordingly, a Young's modulus for the tropocollagen molecule of Y=4.8+/-1.0 GPa was calculated. The complex hydrogen bond network was traced along molecular dynamics (MD) and SMD simulations revealing a rearrangement of these interactions preserving the integrity of the molecular structure when submitted to traction. No evidence of the significant role attributed to water bridges for structural stability was detected, on the contrary facts pointed out that the hydrogen bond network might be the responsible.     

Influence of resin cement rigidity on the stress distribution of resin-bonded fixed partial dentures

The mechanical properties of the adhesive cement used in resin-bonded fixed partial dentures (RBFPD) can modify the clinical performance of the rehabilitation. The goal of this study was to evaluate the influence of the elastic modulus of different cements on the stress distribution in RBFPD using finite element analysis. For that an anterior 3-unit prosthesis was modeled based in a stereolithography file. The model was meshed with tetrahedral elements and materials considered isotropic, linearly elastic and homogeneous. The force applied to the palatal area of the lateral incisor (pontic) at 45° was 100?N. The cements used presented 7 different elastic modulus (E): 2, 6, 10, 14, 18, 22 or 26?GPa. The total deformation, von-Mises stress and maximum principal stress criteria were used to calculate the results. The lower tensile stress occurred in the cement layer with E?=?2?GPa [25.6 (canine) and 16.32?MPa (incisor)]. For the prosthesis, the model with the lower tensile stress [287 (canine) and 248?MPa (incisor)] occurred when the cement presented E?=?26?GPa.

In this way, the stress concentration may have its magnitude modified depending on the stiffness of the cement. Since more flexible cements concentrate less tensile stress in its structure, but allow an increased displacement of the prosthesis, which is friable and rigid and ends up concentrating more tensile stress at its connector. In that way the clinician should avoid the use of adhesive cement with lower elastic modulus due to it increases the stress concentration in the ceramic.     

REACH Coarse-Grained Simulation of a Cellulose Fiber

A molecular level understanding of the structure, dynamics and mechanics of cellulose fibers can aid in understanding the recalcitrance of biomass to hydrolysis in cellulosic biofuel production. Here, a residue-scale REACH (Realistic Extension Algorithm via Covariance Hessian) coarse-grained force field was derived from all-atom molecular dynamics (MD) simulations of the crystalline Iβ cellulose fibril. REACH maps the atomistic covariance matrix onto coarse-grained elastic force constants. The REACH force field was found to reproduce the positional fluctuations and low-frequency vibrational spectra from the all-atom model, allowing elastic properties of the cellulose fibril to be characterized using the coarse-grained force field with a speedup of >20 relative to atomistic MD on systems of the same size. The calculated longitudinal/transversal Young's modulus and the velocity of sound are in agreement with experiment. The persistence length of a 36-chain cellulose microcrystal was estimated to be ～380 μm. Finally, the normal-mode analysis with the REACH force field suggests that intrinsic dynamics might facilitate the deconstruction of the cellulose fibril from the hydrophobic surface.     

Ab initio predictions of structural and elastic properties of struvite: contribution to urinary stone research

In the present work, we carried out density functional calculations of struvite – the main component of the so-called infectious urinary stones – to study its structural and elastic properties. Using a local density approximation and a generalised gradient approximation, we calculated the equilibrium structural parameters and elastic constants C _ijkl . At present, there is no experimental data for these elastic constants C _ijkl for comparison. Besides the elastic constants, we also present the calculated macroscopic mechanical parameters, namely the bulk modulus (K), the shear modulus (G) and Young's modulus (E). The values of these moduli are found to be in good agreement with available experimental data. Our results imply that the mechanical stability of struvite is limited by the shear modulus, G. The study also explores the energy-band structure to understand the obtained values of the elastic constants.     

Computation of elastic constants of solids using molecular simulation: comparison of constant volume and constant pressure ensemble methods

We compute the elastic stiffness tensor of fcc argon at 60 K and 1 bar using molecular simulation tools. Three different methods are investigated: explicit deformations of the simulation box, strain fluctuations at constant pressure and stress fluctuations at constant volume. Statistical ensemble sampling is done using molecular dynamics and Monte Carlo simulations. We observe a good agreement between the different methods and sampling algorithms excepted with molecular dynamics simulations in the (NpT) ensemble. There, we notice a strong dependence of the computed elastic constants with the barostat parameter, whereas molecular dynamics simulations in the (NVT) ensemble are not affected by the thermostat parameter.     

Determination of Young's modulus for nanofibrillated cellulose multilayer thin films using buckling mechanics

The Young's modulus of multilayer films containing nanofibrillated cellulose (NFC) and polyethyleneimine (PEI) was determined using the strain-induced elastic buckling instability for mechanical measurements (SIEBIMM) technique. (1) Multilayer films were built up on polydimethylsiloxane substrates using electrostatic layer-by-layer assembly. At 50% relative humidity, SIEBIMM gave a constant Young's modulus of 1.5 ± 0.2 GPa for 35-75 nm thick films. Conversely, in vacuum, the Young's modulus was 10 times larger, at 17.2 ± 1.2 GPa. A slight decrease in buckling wavelength with increasing strain was observed by scanning electron microscopy with in situ compression, and above 10% strain, extensive cracking parallel to the compressive direction occurred. We conclude that whereas PEI acts as a "glue" to hold multiple layers of NFC together, it prevents full development of hydrogen bonding and specific fibril-fibril interactions, and at high humidity, its hygroscopic nature decreases the elastic modulus when compared with pure NFC films.     

Supermolecular structure of cellulose/amylose blends prepared from aqueous NaOH solutions and effects of amylose on structural formation of cellulose from its solution

We previously proposed a mechanism for the structural formation of cellulose from its solution using a molecular dynamics (MD) simulation and suggested that the initial structure from its solution plays a critical role in determining its final structure. Structural changes in the van der Waals-associated cellulose molecular sheet as the initial structure were examined by MD simulation; the molecular sheet was found to be disordered due to maltohexaoses as an amylose model in terms of the hydrogen bonding system of cellulose. The structure and properties of cellulose/amylose blends prepared from an aqueous NaOH solution were examined experimentally by wide-angle X-ray diffraction and dynamic viscoelasticity measurements. The crystallinity of cellulose in the cellulose/amylose blend films was lower than that of cellulose film. The diffraction peaks of the cellulose/amylose blends were slightly shifted; specifically, () was shifted to a higher angle, and (1 1 0) and (0 2 0) were shifted to lower angles. These experimental results probably resulted from the disordered molecular sheet, as revealed by MD simulations.     

First principles investigation of pressure dependent stability,phonon, Debye temperature,physical, mechanical and thermodynamic properties of Rh3Al intermetallic compound

ABSTRACT

Pressure dependence of stability, phonon, Debye temperature, physical, mechanical and thermodynamic properties of Rh₃Al intermetallic compound were investigated by first-principles The calculated cohesive energy (E_c), formation enthalpy (ΔH) show that Rh₃Al is a thermodynamically stable compound. Properties related to the phonons of Rh₃Al were also obtained. In addition, the transverse sound velocity (ν_s), longitudinal sound velocity (ν_l), average sound velocity (ν_m) and Debye temperature (Θ_D) of Rh₃Al were calculated by using the VRH method along with pressure range from 0 to 60?GPa. The values of lattice parameters, bulk modulus and its first-order pressure derivative are consistent well with other works. The band structure indicates that Rh₃Al compound exhibits a metallic character. Moreover, the total density of states, partial density of states, Mulliken charges and electron density difference have been analysed to explain the physical properties. Based on the stress–strain approach and the Born stability criteria, the mechanical properties were evaluated by elastic constants (C_ij), other modulus (B, E, G), (B/G) ratio, Poisson’s ratio (ν), the anisotropic index (A), hardness (H) and compressibility (K) for this intermetallic compound. Finally, the thermodynamic properties, including enthalpy, free energy, entropy and heat capacity are discussed range from 0 to 1000?K.     

Combining AFM and Acoustic Probes to Reveal Changes in the Elastic Stiffness Tensor of Living Cells

Knowledge of how the elastic stiffness of a cell affects its communication with its environment is of fundamental importance for the understanding of tissue integrity in health and disease. For stiffness measurements, it has been customary to quote a single parameter quantity, e.g., Young’s modulus, rather than the minimum of two terms of the stiffness tensor required by elasticity theory. In this study, we use two independent methods (acoustic microscopy and atomic force microscopy nanoindentation) to characterize the elastic properties of a cell and thus determine two independent elastic constants. This allows us to explore in detail how the mechanical properties of cells change in response to signaling pathways that are known to regulate the cell’s cytoskeleton. In particular, we demonstrate that altering the tensioning of actin filaments in NIH3T3 cells has a strong influence on the cell''s shear modulus but leaves its bulk modulus unchanged. In contrast, altering the polymerization state of actin filaments influences bulk and shear modulus in a similar manner. In addition, we can use the data to directly determine the Poisson ratio of a cell and show that in all cases studied, it is less than, but very close to, 0.5 in value.     

Combining AFM and Acoustic Probes to Reveal Changes in the Elastic Stiffness Tensor of Living Cells

Knowledge of how the elastic stiffness of a cell affects its communication with its environment is of fundamental importance for the understanding of tissue integrity in health and disease. For stiffness measurements, it has been customary to quote a single parameter quantity, e.g., Young’s modulus, rather than the minimum of two terms of the stiffness tensor required by elasticity theory. In this study, we use two independent methods (acoustic microscopy and atomic force microscopy nanoindentation) to characterize the elastic properties of a cell and thus determine two independent elastic constants. This allows us to explore in detail how the mechanical properties of cells change in response to signaling pathways that are known to regulate the cell’s cytoskeleton. In particular, we demonstrate that altering the tensioning of actin filaments in NIH3T3 cells has a strong influence on the cell's shear modulus but leaves its bulk modulus unchanged. In contrast, altering the polymerization state of actin filaments influences bulk and shear modulus in a similar manner. In addition, we can use the data to directly determine the Poisson ratio of a cell and show that in all cases studied, it is less than, but very close to, 0.5 in value.     

Structural phase transition of BeTe: an ab initio molecular dynamics study

Beryllium telluride (BeTe) with cubic zinc-blende (ZB) structure was studied using ab initio constant pressure method under high pressure. The ab initio molecular dynamics (MD) approach for constant pressure was studied and it was found that the first order phase transition occurs from the ZB structure to the nickel arsenide (NiAs) structure. It has been shown that the MD simulation predicts the transition pressure P _T more than the value obtained by the static enthalpy and experimental data. The structural pathway reveals MD simulation such as cubic → tetragonal → orthorhombic → monoclinic → orthorhombic → hexagonal, leading the ZB to NiAs phase. The phase transformation is accompanied by a 10% volume drop and at 80 GPa is likely to be around 35 GPa in the experiment. In the present study, our obtained values can be compared with the experimental and theoretical results.

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Graphical abstract The energy-volume relation and ZB phase for the BeTe

     

Nanomechanical and structural properties of native cellulose under compressive stress

Cellulose is an important biopolymer with applications ranging from its use as an additive in pharmaceutical products to the development of novel smart materials. This wide applicability arises in part from its interesting mechanical properties. Here we report on the use of high pressure X-ray diffraction and Raman spectroscopy in a diamond anvil cell to determine the bulk and local elastic moduli of native cellulose. The modulus values obtained are 20 GPa for the bulk modulus and 200-355 and 15 GPa for the crystalline parts and the overall elastic (Young's) modulus, respectively. These values are consistent with those calculated from tensile measurements. Above 8 GPa, the packing of the cellulose chains within the fibers undergoes significant structural distortion, whereas the chains themselves remain largely unaffected by compression.     

Structure of a self-assembled single nanotube of cyclo[(-d-Ala-l-Ala)4-]

Diameter and wall thickness of self-assembled peptide nanotube of cyclo[(-d-Ala-l-Ala)₄-] were characterised by molecular simulation. In order to verify the existence of peptide nanotube of cyclo[(-d-Ala-l-Ala)₄-], cyclo[(-d-Ala-l-Ala)₄-] was firstly synthesised through Fmoc solid-phase synthesis method and then self-assembled in trifluoroacetic acid. Based on the results of experiment, the single nanotube structure was further characterised by molecular dynamics (MD) employing the COMPASS force field. The results indicate that cyclo[(-d-Ala-l-Ala)₄-] is self-assembled into nanotube bundles of about 0.5 μm in diameter and 10 μm in length; the inner and outer diameter of the single nanotube is 8.5 and 15.9 Å, respectively, and the nanotube wall thickness is 3.3 Å.     

The new program OPAL for molecular dynamics simulations and energy refinements of biological macromolecules

Summary A new program for molecular dynamics (MD) simulation and energy refinement of biological macromolecules, OPAL, is introduced. Combined with the supporting program TRAJEC for the analysis of MD trajectories, OPAL affords high efficiency and flexibility for work with diferent force fields, and offers a user-friendly interface and extensive trajectory analysis capabilities. Salient features are computational speeds of up to 1.5 GFlops on vector supercomputers such as the NEC SX-3, ellipsoidal boundaries to reduce the system size for studies in explicit solvents, and natural treatment of the hydrostatic pressure. Practical applications of OPAL are illustrated with MD simulations of pure water, energy minimization of the NMR structure of the mixed disulfide of a mutant E. coli glutaredoxin with glutathione in different solvent models, and MD simulations of a small protein, pheromone Er-2, using either instantaneous or time-averaged NMR restraints, or no restraints.Abbreviations D diffusion constant in cm²/s - Er-2 pheromone 2 from Euplotes raikovi - GFlop one billion floating point operations per second - Grx(C14S)-SG mixed disulfide between a mutant E. coli glutaredoxin, with Cys¹⁴ replaced by Ser, and glutathione - MD molecular dynamics - NOE nuclear Overhauser enhancement - rmsd root-mean-square deviation - density in g/cm³     

Roles of electrostatic interaction and dispersion in CH···CH,CH···π, and π···π ethylene dimers

The structural, mechanical, electronic, and optical properties of orthorhombic Bi₂S₃ and Bi₂Se₃ compounds have been investigated by means of first principles calculations. The calculated lattice parameters and internal coordinates are in very good agreement with the experimental findings. The elastic constants are obtained, then the secondary results such as bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, anisotropy factor, and Debye temperature of polycrystalline aggregates are derived, and the relevant mechanical properties are also discussed. Furthermore, the band structures and optical properties such as real and imaginary parts of dielectric functions, energy-loss function, the effective number of valance electrons, and the effective optical dielectric constant have been computed. We also calculated some nonlinearities for Bi₂S₃ and Bi₂Se₃ (tensors of elasto-optical coefficients) under pressure.

Computational simulation study on the anion recognition properties of functionalized tetraphenyl porphyrins

Dedicated bond force constant and bulk modulus of C _n fullerenes (n = 20, 28, 36, 50, 60) are computed using density functional theory (DFT). DFT predicts bond force constants of 611, 648, 675, 686, and 691 N/m, for C₂₀, C₂₈, C₃₆, C₅₀, and C₆₀, respectively, indicating that the bond force constant increases for larger fullerenes. The bulk modulus predicted by DFT increases with decreased fullerene diameter, from 0.874 TPa for C₆₀ to 1.830 TPa for C₂₀. The bond force constants predicted by DFT are then used as an input for finite element analysis (FEA) of the fullerenes, considered as spatial frames in structural models where the bond stiffness is represented by the DFT-computed bond force constant. In agreement with DFT, FEA predicts that smaller fullerenes are stiffer, and underestimates the bulk modulus with respect to DFT. The difference between the FEA and DFT predictions of the bulk modulus decreases as the size of the fullerene increases, from 20.9 % difference for C₂₀ to only 4 % difference for C₆₀. Thus, it is concluded that knowing the appropriate bond force constant, FEA can be used as a plausible approximation to model the elastic behavior of small fullerenes.

     

Optimum temperature policy for batch reactors performing biochemical reactions in the presence of enzyme deactivation

A necessary condition is found for the optimum temperature policy which leads to the minimum reaction time for a given final conversion of substrate in a well stirred, enzymatic batch reactor performing an enzyme-catalyzed reaction following Michaelis-Menten kinetics in the presence of first order enzyme decay. The reasoning, which is based on Euler's classical approach to variational calculus, is relevant for the predesign steps because it indicates in a simple fashion which temperature program should be followed in order to obtain the maximum advantage of existing enzyme using the type of reactor usually elected by technologists in the fine biochemistry field. In order to highlight the relevance and applicability of the work reported here, the case of optimality under isothermal operating conditions is considered and a practical example is worked out.List of Symbols C _E mol.m^–3 concentration of active enzyme - C _E ^* dimensionless counterpart of C_E - C _E,0 mol.m^–3 initial concentration of active enzyme - C _E,b mol.m^–3 final concentration of active enzyme - C _E,opt ^* optimal dimensionless counterpart of C_E - C _smol.m^–3 concentration of substrate - C _S ^Emphasis>/* dimensionless counterpart of C_S - C _S,0mol.m^–3 initial concentration of substrate - C _S,bmol.m^–3 final concentration of substrate - E enzyme in active form - E ₃ ^* dimensionless counterpart of E_a,3 - E _a,1J.mol^–1 activation energy associated with k₁ - E _a,3J.mol^–1 activation energy associated with k₃ - E _d enzyme in deactivated form - ES enzyme/substrate complex - k ₁ s^–1 kinetic constant associated with the enzyme-catalyzed transformation of substrate - k _1,0 s^–1 preexponential factor associated with k₁ - k ₂ mol^–1.m³s^–1 kinetic constant associated with the binding of substrate to the enzyme - k _–2 s^–1 kinetic constant associated with the dissociation of the enzyme/substrate complex - K _2,0 mol.m^–3 constant value of K₂ - K _2,0 ^* dimensionless counterpart of K_2,0 - k ₃ s^–1 kinetic constant associated with the deactivation of enzyme - k _3,0 s^–1 preexponential factor associated with k₃ - k _3,0 ^* dimensionless counterpart of k_3,0 - P product - R J.K^–1.mol^–1 ideal gas constant - S substrate - t s time since start-up of reaction - T K absolute temperature - T ^* dimensionless absolute temperature - T _i,opt ^* optimal dimensionless isothermal temperature of operation - T _opt ^* optimal dimensionless temperature of operation - t _b s time of a batch - t _b ^* dimensionless counterpart of t_b - t _b,min ^* minimum value of the dimensionless counterpart of t_b Greek Symbols dimensionless counterpart of C_E,0 - dimensionless counterpart of C_E,b - dummmy variable of integration - dummy variable of integration - auxiliary dimensionless variable - ^* dimensionless variation of k₁ with temperature - _i ^* dimensionless value of k₁ under isothermal conditions - _opt ^* optimal dimensionless variation of k₁ with temperature     

Elastic energy storage in β-sheets with application to F<Subscript>1</Subscript>-ATPase

We present a methodology for obtaining the elastic properties of protein motifs. We combine the use of interpolated structures (IS), molecular dynamics (MD) and collective coordinates to deduce the elastic properties of the -sheet in F₁ ATPase. We find that about 3.5 kcal/mol (6 k_BT at room temperature) of elastic energy is stored in the -sheet as the -subunit undergoes its hinge bending motion, in good agreement with the finite element model of Wang and Oster [Nature (1998) 396:279–282]. The technique should be useful for -sheets in other proteins and aid in the construction of phenomenological models for molecular motors that are computationally prohibitive for MD alone.