Calculation of the standard molal thermodynamic properties of aqueous biomolecules at elevated temperatures and pressures II. Unfolded proteins

Equations of state for completely unfolded proteins have been generated from group additivity algorithms and the revised Helgeson-Kirkham-Flowers (HKF) equations of state to compute the standard molal thermodynamic properties of these molecules at elevated temperatures and pressures. The requisite equations of state parameters were computed from those of groups retrieved by regression of experimental calorimetric and densimetric data reported in the literature. This approach permits calculation of the standard molal thermodynamic properties as a function of temperature and pressure for any completely unfolded protein for which the amino acid sequence is known. Calculations of this kind have been carried out for 11 thermophilic proteins. The thermodynamic properties reported below can be combined with those for protein unfolding to compute the corresponding properties of completely folded (i.e. native) proteins.     

Thermodynamics, mechanical and electrical properties of biomembranes

A set of thermodynamic fundamental equations has been derived, including chemical potentials of immobile components of a biomembrane. The results obtained are compatible with those known in the theory of shells, but the approach developed is more general. The influence of an outer electric field on the isotropic tension of a biomembrane has been discussed. The thermodynamic relations derived are used for the treatment of intracellular pressure changes recently observed by Terakawa (1985, J. Physiol. 369, 229) in the squid giant axon at potential variations.     

Computational investigation of pressure profiles in lipid bilayers with embedded proteins

The distribution of surface tension within a lipid bilayer, also referred to as the lateral pressure profile, has been the subject of theoretical scrutiny recently due to its potential to radically alter the function of biomedically important membrane proteins. Experimental measurements of the pressure profile are still hard to come by, leaving first-principles all-atom calculations of the profile as an important investigative tool. We describe and validate an efficient implementation of pressure profile calculations in the molecular dynamics package NAMD, capable of distinguishing between internal, bonded and nonbonded contributions as well as those of selected atom groups. The new implementation can also be used in conjunction with Ewald summation for long-range electrostatics, improving the accuracy and reproducibility of the calculated profiles. We then describe results of the calculation of a pressure profile for a simple protein–lipid system consisting of melittin embedded in a DMPC bilayer. While the lateral pressure in the protein–lipid system is nearly the same as that of the bilayer alone, partitioning of the lateral pressure by atom type revealed substantial perturbation of the pressure profile and surface tension in an asymmetric manner.     

Application of kinetic Monte Carlo method to the vapour–liquid equilibria of associating fluids and their mixtures

Canonical kinetic Monte Carlo (C-kMC) simulations have been carried out to assess their feasibility and potential for calculating the vapour–liquid equilibria of various pure components with increasingly strong electrostatic interactions (carbon dioxide, methanol, ammonia and water) over a wide range of temperatures and for methanol/water mixtures at 298 K. The simulation results show that C-kMC is successful as a method for studying phase equilibria and thermodynamic properties. For all the examples investigated, the performance of the C-kMC method is at least as good as that of the conventional Monte Carlo (MC) methods and is efficient at low temperature where these fail. It also provides a route that is superior to the Widom method for the calculation of chemical potential. We recommend this method for this purpose and as an alternative to conventional MC for simulations of strongly associating fluids and at low temperatures.     

Measurement of the circumferential mechanical properties of the umbilical vein: experimental and numerical analyses

Coronary artery disease is responsible for almost 30% of all deaths worldwide. The saphenous vein and umbilical vein (UV) are the most common veins using for treatment as a coronary artery bypass graft (CABG). The mechanical properties of UV belonging to its long-term patency for CABG are very important. However, there is a lack of knowledge on the linear elastic and nonlinear hyperelastic mechanical properties of the UV. In this study, three stress definitions (second Piola–Kichhoff stress, engineering stress and true stress) and four strain definitions (Almansi–Hamel strain, Green–St Venant strain, engineering strain and true strain) are used to determine the elastic modulus, maximum stress and strain of eight human UVs under circumferential loading. The nonlinear mechanical behaviour of the UV is computationally investigated using Mooney–Rivlin hyperelastic model. A numerical finite element analysis is also carried out to simulate the constitutive modelling versus its numerical results. The results show that the Almansi–Hamel strain definition overestimates the elastic modulus while Green–St Venant strain definition underestimates the elastic modulus at different stress definitions. The true stress–true strain definition, which gives more accurate measurements of the tissue's response using the instantaneous values, reveals the Young's modulus and maximum stress of 2.18 and 6.01 MPa, respectively. The Mooney–Rivlin material model is well represented by the nonlinear mechanical behaviour of the UV. The findings of this study could have implications not only for understanding the extension and rupture mechanism of UV but also for interventions and surgeries, including balloon angioplasty, bypass and stenting.     

Distribution of mechanical stress in the Escherichia coli cell envelope

The cell envelope in Gram-negative bacteria comprises two distinct membranes with a cell wall between them. There has been a growing interest in understanding the mechanical adaptation of this cell envelope to the osmotic pressure (or turgor pressure), which is generated by the difference in the concentration of solutes between the cytoplasm and the external environment. However, it remains unexplored how the cell wall, the inner membrane (IM), and the outer membrane (OM) effectively protect the cell from this pressure by bearing the resulting surface tension, thus preventing the formation of inner membrane bulges, abnormal cell morphology, spheroplasts and cell lysis. In this study, we have used molecular dynamics (MD) simulations combined with experiments to resolve how and to what extent models of the IM, OM, and cell wall respond to changes in surface tension. We calculated the area compressibility modulus of all three components in simulations from tension-area isotherms. Experiments on monolayers mimicking individual leaflets of the IM and OM were also used to characterize their compressibility. While the membranes become softer as they expand, the cell wall exhibits significant strain stiffening at moderate to high tensions. We integrate these results into a model of the cell envelope in which the OM and cell wall share the tension at low turgor pressure (0.3 atm) but the tension in the cell wall dominates at high values (>1 atm).     

Modeling DNA Thermodynamics under Torsional Stress

Negatively twisted DNA is essential to many biological functions. Due to torsional stress, duplex DNA can have local, sequence-dependent structural defects. In this work, a thermodynamic model of DNA was built to qualitatively predict the local sequence-dependent mechanical instabilities under torsional stress. The results were compared to both simulation of a coarse-grained model and experiment results. By using the Kirkwood superposition approximation, we built an analytical model to represent the free energy difference ΔW of a hydrogen-bonded basepair between the B-form helical state and the basepair opened (or locally melted) state, within a given sequence under torsional stress. We showed that ΔW can be well approximated by two-body interactions with its nearest-sequence-neighbor basepairs plus a free energy correction due to long-range correlations. This model is capable of rapidly predicting the position and thermodynamics of local defects in a given sequence. The result qualitatively matches with an in vitro experiment for a long DNA sequence (>4000 basepairs). The 12 parameters used in this model can be further quantitatively refined when more experimental data are available.     

Modeling DNA Thermodynamics under Torsional Stress

Negatively twisted DNA is essential to many biological functions. Due to torsional stress, duplex DNA can have local, sequence-dependent structural defects. In this work, a thermodynamic model of DNA was built to qualitatively predict the local sequence-dependent mechanical instabilities under torsional stress. The results were compared to both simulation of a coarse-grained model and experiment results. By using the Kirkwood superposition approximation, we built an analytical model to represent the free energy difference ΔW of a hydrogen-bonded basepair between the B-form helical state and the basepair opened (or locally melted) state, within a given sequence under torsional stress. We showed that ΔW can be well approximated by two-body interactions with its nearest-sequence-neighbor basepairs plus a free energy correction due to long-range correlations. This model is capable of rapidly predicting the position and thermodynamics of local defects in a given sequence. The result qualitatively matches with an in vitro experiment for a long DNA sequence (>4000 basepairs). The 12 parameters used in this model can be further quantitatively refined when more experimental data are available.     

Molecular structure,vibrational spectroscopic,NBO and HOMO–LUMO studies of 2-amino 6-bromo 3-formylchromone

A systematic quantum mechanical study of the possible conformations and vibrational spectra of 2-amino 6-bromo 3-formylchromone has been reported. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities and activities of Raman scattering were calculated by Hartree–Fock and density functional theory employing Becke's three-parameter (local, non-local and HF) hybrid exchange functionals with Lee–Yang–Parr co-relational (B3LYP) functionals using 6-311++G(d,p) basis set with complete relaxation in the potential energy surface. The calculated wavenumbers after proper scaling show a very good agreement with the observed values. The electrostatic potential mapped onto isodensity surface has been obtained. The natural bond orbital analysis has been carried out in order to study the intra-molecular bonding, interactions among bonds and delocalisation of unpaired electrons. The highest occupied molecular orbital–lowest unoccupied molecular orbital studies have been conducted in order to determine the way the molecule interacts with other species.     

Oscillatory tension differentially modulates matrix metabolism and cytoskeletal organization in chondrocytes and fibrochondrocytes

Several modes of mechanical stimulation, including compression, shear, and hydrostatic pressure, have been shown to modulate chondrocyte matrix synthesis, but the effects of mechanical tension have not been widely explored. Since articular cartilage is primarily loaded in compression, tension is not generally viewed as a major contributor to the stress state of healthy tissue. However, injury or attempted repair may cause tension to become more significant. Additionally, fibrocartilaginous tissues experience significant tensile stresses in their normal mechanical environment. In this study we investigated mechanical tension as a means to modulate matrix synthesis and cytoskeletal organization in bovine articular chondrocytes and meniscal fibrochondrocytes (MFCs) in a three-dimensional fibrin construct culture system. Oscillatory tension was applied to constructs at 1.0 Hz and 0–10% displacement variation using a custom device. For nearly all conditions and both cell types, oscillatory tension inhibited matrix synthesis as indicated by ³H-proline and ³⁵S-sulfate incorporation. Additionally, oscillatory tension significantly increased proliferation by chondrocytes but not MFCs. Confocal imaging revealed that all cells initially displayed a rounded morphology, but over time MFCs spontaneously developed a three-dimensional, stellate morphology with numerous projections containing organized cytoskeletal filaments. Interestingly, while unloaded chondrocytes remained rounded, chondrocytes subjected to oscillatory tension developed a similar stellate morphology. Both the biochemical and morphological results of this study have important implications for successfully developing cartilage and fibrocartilage tissue replacements and repair strategies.     

Molecular simulation of volume of mixing,Helmholtz free energy of mixing and entropy of mixing in bulk fluid mixtures

We describe a kinetic Monte Carlo molecular simulation procedure to calculate the Helmholtz free energy, the entropy and the chemical potentials of all components in a bulk fluid mixture. This allows us to derive the excess properties (volume, free energy and entropy) resulting from the mixing of homogeneous fluids of pure components at constant temperature and pressure. We have chosen neon–xenon mixtures to illustrate our method because of the large difference in collision diameter and well-depth of the interaction energy. When xenon is predominant in the mixture, the volume of mixing is larger. The excess entropy of mixing correlates with the volume of mixing, since a positive excess volume enables more configurations (more possible molecular distributions). The excess thermodynamic quantities as functions of the total density were found to be insensitive to temperature. To investigate the effects of the molecular parameters, we also studied argon–nitrogen and argon–krypton mixtures. The effect of the difference in molecular parameters is in the order: argon–nitrogen < argon–krypton < neon–xenon. A large difference in the well-depth of the interaction energies results in an increase in the excess thermodynamic variables, which is in agreement with the literature McDonald IR. NpT-ensemble Monte Carlo calculations for binary liquid mixtures. Mol Phys. 1972;23(1):41–58; Singer JVL, Singer K. Monte Carlo calculation of thermodynamic properties of binary mixtures of Lennard-Jones (12-6) liquids. Mol Phys. 1972;24(2):357–390.     

Theoretical modeling of the interaction between alveoli during inflation and deflation in normal and diseased lungs

Alveolar recruitment is a central strategy in the ventilation of patients with acute lung injury and other lung diseases associated with alveolar collapse and atelectasis. However, biomechanical insights into the opening and collapse of individual alveoli are still limited. A better understanding of alveolar recruitment and the interaction between alveoli in intact and injured lungs is of crucial relevance for the evaluation of the potential efficacy of ventilation strategies. We simulated human alveolar biomechanics in normal and injured lungs. We used a basic simulation model for the biomechanical behavior of virtual single alveoli to compute parameterized pressure–volume curves. Based on these curves, we analyzed the interaction and stability in a system composed of two alveoli. We introduced different values for surface tension and tissue properties to simulate different forms of lung injury. The data obtained predict that alveoli with identical properties can coexist with both different volumes and with equal volumes depending on the pressure. Alveoli in injured lungs with increased surface tension will collapse at normal breathing pressures. However, recruitment maneuvers and positive endexpiratory pressure can stabilize those alveoli, but coexisting unaffected alveoli might be overdistended. In injured alveoli with reduced compliance collapse is less likely, alveoli are expected to remain open, but with a smaller volume. Expanding them to normal size would overdistend coexisting unaffected alveoli. The present simulation model yields novel insights into the interaction between alveoli and may thus increase our understanding of the prospects of recruitment maneuvers in different forms of lung injury.     

Cell Surface Deformation during an Action Potential

The excitation of many cells and tissues is associated with cell mechanical changes. The evidence presented herein corroborates that single cells deform during an action potential. It is demonstrated that excitation of plant cells (Chara braunii internodes) is accompanied by out-of-plane displacements of the cell surface in the micrometer range (～1–10 μm). The onset of cellular deformation coincides with the depolarization phase of the action potential. The mechanical pulse: 1) propagates with the same velocity as the electrical pulse (within experimental accuracy, ～10 mm s^?1), 2) is reversible, 3) in most cases is of biphasic nature (109 out of 152 experiments), and 4) is presumably independent of actin-myosin-motility. The existence of transient mechanical changes in the cell cortex is confirmed by micropipette aspiration experiments. A theoretical analysis demonstrates that this observation can be explained by a reversible change in the mechanical properties of the cell surface (transmembrane pressure, surface tension, and bending rigidity). Taken together, these findings contribute to the ongoing debate about the physical nature of cellular excitability.     

Functional modes and residue flexibility control the anisotropic response of guanylate kinase to mechanical stress

The coupling between the mechanical properties of enzymes and their biological activity is a well-established feature that has been the object of numerous experimental and theoretical works. In particular, recent experiments show that enzymatic function can be modulated anisotropically by mechanical stress. We study such phenomena using a method for investigating local flexibility on the residue scale that combines a reduced protein representation with Brownian dynamics simulations. We performed calculations on the enzyme guanylate kinase to study its mechanical response when submitted to anisotropic deformations. The resulting modifications of the protein's rigidity profile can be related to the changes in substrate binding affinity observed experimentally. Further analysis of the principal components of motion of the trajectories shows how the application of a mechanical constraint on the protein can disrupt its dynamics, thus leading to a decrease of the enzyme's catalytic rate. Eventually, a systematic probe of the protein surface led to the prediction of potential hotspots where the application of an external constraint would produce a large functional response both from the mechanical and dynamical points of view. Such enzyme-engineering approaches open the possibility to tune catalytic function by varying selected external forces.     

Comparison of three local frame definitions for the kinematic analysis of the fingers and the wrist

Because the hand is a complex poly-articular limb, numerous methods have been proposed to investigate its kinematics therefore complicating the comparison between studies and the methodological choices. With the objective of overcoming such issues, the present study compared the effect of three local frame definitions on local axis orientations and joint angles of the fingers and the wrist. Three local frames were implemented for each segment. The “Reference” frames were aligned with global axes during a static neutral posture. The “Landmark” frames were computed using palpated bony landmarks. The “Functional” frames included a flexion–extension axis estimated during functional movements. These definitions were compared with regard to the deviations between obtained local segment axes and the evolution of joint (Cardan) angles during two test motions. Each definition resulted in specific local frame orientations with deviations of 15° in average for a given local axis. Interestingly, these deviations produced only slight differences (below 7°) regarding flexion–extension Cardan angles indicating that there is no preferred method when only interested in finger flexion–extension movements. In this case, the Reference method was the easiest to implement, but did not provide physiological results for the thumb. Using the Functional frames reduced the kinematic cross-talk on the secondary and tertiary Cardan angles by up to 20° indicating that the Functional definition is useful when investigating complex three-dimensional movements. Globally, the Landmark definition provides valuable results and, contrary to the other definitions, is applicable for finger deformities or compromised joint rotations.     

A Molecular Dynamics Simulation Study of Nanomechanical Properties of Asymmetric Lipid Bilayer

A very important part of the living cells of biological systems is the lipid membrane. The mechanical properties of this membrane play an important role in biophysical studies. Investigation as to how the insertion of additional phospholipids in one leaflet of a bilayer affects the physical properties of the obtained asymmetric lipid membrane is of recent practical interest. In this work a coarse-grained molecular dynamics simulation was carried out in order to compute the pressure tensor, the lateral pressure, the surface tension and the first moment of lateral pressure in each leaflet of such a bilayer. Our simulations indicate that adding more phospholipids into one monolayer results in asymmetrical changes in the lateral pressure of the individual bilayer leaflets. Interestingly, it has been observed that a change in phospholipid density in one leaflet affects the physical properties of unperturbed leaflet as well. The asymmetric behavior of the physical properties of the two leaflets as a result of a change in the contribution of the various intermolecular forces in the presence of additional phospholipids may be expressed formally.     

Monte Carlo and Poisson–Boltzmann calculations of the fraction of counterions bound to DNA

The counterion density and the condensation region around DNA have been examined as functions of both ion size and added-salt concentration using Metropolis Monte Carlo (MC) and Poisson–Boltzmann (PB) methods. Two different definitions of the “bound” and “free” components of the electrolyte ion atmosphere were used to compare these approaches. First, calculation of the ion density in different spatial regions around the polyelectrolyte molecule indicates, in agreement with previous work, that the PB equation does not predict an invariance of the surface concentration of counterions as electrolyte is added to the system. Further, the PB equation underestimates the counterion concentration at the DNA surface, compared to the MC results, the difference being greatest in the grooves, where ionic concentrations are highest. If counterions within a fixed radius of the helical axis are considered to be bound, then the fraction of polyelectrolyte charge neutralized by counterions would be predicted to increase as the bulk electrolyte concentration increases. A second categorization—one in which monovalent cations in regions where the average electrostatic potential is ledd than ?kT are considered to be bound—provides an informative basis for comparison of MC and PB with each other and with counterion-condensation theory. By this criterion, PB calculations on the B from of DNA indicate that the amount of bound counterion charge per phosphate group is about .67 and is independent of salt concentration. A particularly provocative observatiob is that when this binding criterion is used, MC calculations quantitatively reproduce the bound fraction predicated by counterion-condensation theory for all-atom models of B-DNA and A-DNA as well as for charged cylindera of varying lineat charge densities. For example, for B-DNA and A-DNA, the fractions of phosphate groups neutralized by 2 Å hard sphere counterions are 0.768 and .817, respectively. For theoretical studies, the rediys enclosing the region in which the electrostatic potential is calculated studies, the radius enclosing the region in which the electrostatic potential is calculated to be less than ?kT is advocated s a more suitable binding or condensation radius that enclosing the fraction of counterions given by (1 – ξ^?1). A comparsion of radii calculated using both of these definitions is presented. © 1994 John Wiley & Sons, Inc.     

Finite-size effects of Kirkwood–Buff integrals from molecular simulations

The modelling of thermodynamic properties of liquids from local density fluctuations is relevant to many chemical and biological processes. The Kirkwood–Buff (KB) theory connects the microscopic structure of isotropic liquids with macroscopic properties such as partial derivatives of activity coefficients, partial molar volumes and compressibilities. Originally, KB integrals were formulated for open and infinite systems which are difficult to access with standard Molecular Dynamics (MD) simulations. Recently, KB integrals for finite and open systems were formulated (J Phys Chem Lett. 2013;4:235). From the scaling of KB integrals for finite subvolumes, embedded in larger reservoirs, with the inverse of the size of these subvolumes, estimates for KB integrals in the thermodynamic limit are obtained. Two system size effects are observed in MD simulations: (1) effects due to the size of the simulation box and the size of the finite subvolume embedded in the simulation box, and (2) effects due to computing radial distribution functions (RDF) from a closed and finite system. In this study, we investigate the two effects in detail by computing KB integrals using the following methods: (1) Monte Carlo simulations of finite subvolumes of a liquid with an analytic RDF and (2) MD simulations of a WCA mixture for various simulation box sizes, but at the same thermodynamic state. We investigate the effect of the size of the simulation box and quantify the differences compared to KB integrals computed in the thermodynamic limit. We demonstrate that calculations of KB integrals should not be extended beyond half the size of the simulation box. For finite-size effects related to the RDF, we find that the Van der Vegt correction (J Chem Theory Comput. 2013;9:1347) yields the most accurate results.