Statistical geometry of lattice chain polymers with voids of defined shapes: sampling with strong constraints

Proteins contain many voids, which are unfilled spaces enclosed in the interior. A few of them have shapes compatible to ligands and substrates and are important for protein functions. An important general question is how the need for maintaining functional voids is influenced by, and affects other aspects of proteins structures and properties (e.g., protein folding stability, kinetic accessibility, and evolution selection pressure). In this paper, we examine in detail the effects of maintaining voids of different shapes and sizes using two-dimensional lattice models. We study the propensity for conformations to form a void of specific shape, which is related to the entropic cost of void maintenance. We also study the location that voids of a specific shape and size tend to form, and the influence of compactness on the formation of such voids. As enumeration is infeasible for long chain polymer, a key development in this work is the design of a novel sequential Monte Carlo strategy for generating large number of sample conformations under very constraining restrictions. Our method is validated by comparing results obtained from sampling and from enumeration for short polymer chains. We succeeded in accurate estimation of entropic cost of void maintenance, with and without an increasing number of restrictive conditions, such as loops forming the wall of void with fixed length, with additionally fixed starting position in the sequence. Additionally, we have identified the key structural properties of voids that are important in determining the entropic cost of void formation. We have further developed a parametric model to predict quantitatively void entropy. Our model is highly effective, and these results indicate that voids representing functional sites can be used as an improved model for studying the evolution of protein functions and how protein function relates to protein stability.     

Monte Carlo simulations on the effect of substrate geometry on adsorption and compression

Canonical Monte Carlo simulations were used to study the adsorption and compression of fluid layers on model substrates with cubic, (111) fcc, and graphite geometries. The effect of the relative size of the fluid and substrate molecules on adsorption was considered for strong molecule-surface interactions. In the case of monolayer formation, it was found that the surface geometry and the size of the adsorbate molecules had a significant effect on the structure of the adsorbed layer. These structures varied from well-ordered, commensurate layers to liquid-like structures. Lateral compression was observed for certain fluid to substrate molecule sizes. For the interactions studied in this work, it was found that maximum lateral compression occurred on the cubic surface when adsorbate molecules had a diameter approximately 15% larger than the substrate diameter. In the case of multilayer formation, it was found that second and higher adsorbed layers could compress into the adsorbed layers below them. For cubic substrates, the interlayer compression was predicted analytically with reasonable accuracy, with maximum interlayer compression found for fluid diameters approximately 90% the size of substrate molecule diameters.     

Study of the interaction between progesterone and beta-cyclodextrin by electrochemical techniques and steered molecular dynamics

The interaction of progesterone with beta-cyclodextrin (beta-CD) was studied by differential pulse polarography. The aim of the present work was to study the effect of beta-CD on the electrochemical behavior of progesterone in aqueous solution and also to analyze the molecular interactions involved in formation of the inclusion complex. The complex with stoichiometry of 1:1 was thermodynamically characterized. In addition, steered molecular dynamics (SMD) was used to investigate the energetic properties of formation of the inclusion complex along four different pathways (reaction coordinates), considering two possible orientations. From multiple trajectories along these pathways, the potentials of mean force for formation of the beta-CD progesterone inclusion complex were calculated. The energy analysis was in good agreement with the experimental results. In the beta-CD progesterone inclusion complex, a large portion of the steroid skeleton is included in the beta-CD cavity. The lowest energy was found when the D-ring of the guest molecule is located near the secondary hydroxyls of the beta-CD cavity. In the most probable orientation, one intermolecular hydrogen bond is formed between the O of the C-20 keto group of the progesterone and a secondary hydroxyl of the beta-CD.     

Propagation, beam geometry, and detection distortions of peak shapes in two-dimensional Fourier transform spectra

Using a solution of Maxwell's equations in the three-dimensional frequency domain, femtosecond two-dimensional Fourier transform (2DFT) spectra that include distortions due to phase matching, absorption, dispersion, and noncollinear excitation and detection of the signal are calculated for Bloch, Kubo, and Brownian oscillator relaxation models. For sample solutions longer than a wavelength, the resonant propagation distortions are larger than resonant local field distortions by a factor of approximately L/lambda, where L is the sample thickness and lambda is the optical wavelength. For the square boxcars geometry, the phase-matching distortion is usually least important, and depends on the dimensionless parameter, L sin(2)(beta)Deltaomega/(nc), where beta is the half angle between beams, n is the refractive index, c is the speed of light, and Deltaomega is the width of the spectrum. Directional filtering distortions depend on the dimensionless parameter, [(Deltaomega)w(0) sin(beta)/c](2), where w(0) is the beam waist at the focus. Qualitatively, the directional filter discriminates against off diagonal amplitude. Resonant absorption and dispersion can distort 2D spectra by 10% (20%) at a peak optical density of 0.1 (0.2). Complicated distortions of the 2DFT peak shape due to absorption and dispersion can be corrected to within 10% (15%) by simple operations that require knowledge only of the linear optical properties of the sample and the distorted two-dimensional spectrum measured at a peak optical density of up to 0.5 (1).     

A monte carlo lattice study of living polymers in a confined geometry

We investigate the changes in the average chain length of a solution of semi-flexible living polymers between two hard repulsive walls as the width of the slit, D, is varied. Two different Monte Carlo models, that of the ‘slithering snake’ and of the ‘independent monomer states’ are employed in order to simulate a polydisperse system of chain molecules confined in a gap which is either closed (with fixed total density), or open and in contact with an external reservoir. It appears that the mean chain length L in a state of equilibrium polymerization depends essentially on the geometry constraints for sufficiently small D. We find that in the case of an open slit the mean length L(D) decreases with D → 0 for flexible chains whereas it grows if the chains are sufficiently stiff. As the width of a closed gap D is decreased, in a three-dimensional gap L(D) gradually decreases for absolutely flexible chains whereas for semi-rigid chains it goes through a minimum at D = 2 and then grows again for D = 1. In two dimensions, in a closed strip the average chain length L(D) for both flexible and rigid macromolecules goes through a sharp minimum and then grows steeply in compliance with a predicted divergence for semi-rigid polymers as D → 0. We attribute the observed discrepancies of our numeric experiments with some recent analytic predictions to the ordering effect of container walls on the polymer solution when chain stiffness and excluded volume interactions are taken into account.     

Comparison of experimental and calculated peak shapes for three cylindrical geometry FAIMS prototypes of differing electrode diameters

High-field asymmetric waveform ion mobility spectrometry (FAIMS) separates ions at atmospheric pressure and room temperature based on the difference of the mobility of ions in strong electric fields and weak electric fields. This field-dependent mobility of an ion is reflected in the compensation voltage (CV) at which the ion is transmitted through FAIMS, at a given asymmetric waveform dispersion voltage (DV). Experimental CV, relative peak ion intensity, and peak width data were compared for three FAIMS prototypes with concentric cylindrical electrodes having inner/outer electrode radii of: (1) 0.4/0.6 cm, (2) 0.8/1.0 cm, and (3) 1.2/1.4 cm. The annular analyzer space was 0.2 cm wide in each case. A finite-difference numerical computation method is described for evaluation of peak shapes and widths in a CV spectrum collected using cylindrical geometry FAIMS devices. Simulation of the radial distribution of the ion density in the FAIMS analyzer is based upon calculation of diffusion, electric fields, and the electric fields introduced by coulombic ion-ion repulsion. Excellent agreement between experimental and calculated peak shapes were obtained for electrodes of wide diameter and for ions transmitted at low CV.     

Flat polymer ribbons and other shapes by electrospinning

In addition to round nanofibers, electrospinning a polymer solution can produce thin fibers with a variety of cross‐sectional shapes. Branched fibers, flat ribbons, ribbons with other shapes, and fibers that were split longitudinally from larger fibers were observed. The transverse dimensions of these asymmetric fibers were typically 1 or 2 μm, measured in the widest direction. A correlation of the branches and bends, observed in high‐frame‐rate videography of the electrified jets of polymer solutions from which the ribbons and branched fibers were produced, suggest that these phenomena occur at scales ranging from around 1 mm to 1 μm. The observation of fibers with these cross‐sectional shapes from a number of different kinds of polymers and solvents indicates that fluid mechanical effects, electrical charge carried with the jet, and evaporation of the solvent all contributed to the formation of the fibers. The influence of a skin on the jets of polymer solutions accounts for a number of the observations. The observed shapes can be used as guides for the extension of mathematical or computer‐generated models for the electrospinning process. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2598–2606, 2001     

Optimized geometry,electronic structure and Ag adsorption property of nanosheet graphene with different symmetry shapes: a theoretical investigation

Optimized geometries and electronic structures of three different symmetry shapes of nanosheet graphenes with armchair and zig-zag edges were generated by using the generalized gradient approximation/Perdew–Burke–Ernzerhof (GGA/PBE) method of density function theory (DFT) with the double-zeta polarized (DZP) basis set. Based on the results, the calculated HOMO–LUMO energy gap (Eg = LUMO–HOMO) with different symmetry shapes, and nanosheet size for with zig-zag and armchair edges were also presented. Because the p _π orbital was widely localized over the sheet surface, the calculated E _g decreased with increasing the sheet size. Further, the quantum mechanics calculation was used to investigate the adsorption property of the Ag atom adsorbed to the nanosheet graphene (expressed by C₉₀H₃₀) surface. The calculations show that the Ag atom binds to the bridge site (B site) of triangular nanosheet graphene (C₉₀H₃₀) as it is the most stable adsorption site compared with others, and since it has higher formation energy (ΔE) with shorter distance between the Ag atom and the graphene surface. Above all, calculations suggest that the Ag-adsorbed nanosheet graphene is a good option as an adsorbent in environmental research.     

Exploring the free-energy landscapes of biological systems with steered molecular dynamics

We perform steered molecular dynamics (SMD) simulations and use the Brownian dynamics fluctuation-dissipation-theorem (BD-FDT) to accurately compute the free-energy profiles for several biophysical processes of fundamental importance: hydration of methane and cations, binding of benzene to T4-lysozyme L99A mutant, and permeation of water through aquaglyceroporin. For each system, the center-of-mass of the small molecule (methane, ion, benzene, and water, respectively) is steered (pulled) at a given speed over a period of time, during which the system transitions from one macroscopic state/conformation (State A) to another one (State B). The mechanical work of pulling the system is measured during the process, sampling a forward pulling path. Then the reverse pulling is conducted to sample a reverse path from B back to A. Sampling a small number of forward and reverse paths, we are able to accurately compute the free-energy profiles for all the afore-listed systems that represent various important aspects of biological physics. The numerical results are in excellent agreement with the experimental data and/or other computational studies available in the literature.     

How charging corannulene with one and two electrons affects its geometry and aggregation with sodium and potassium cations

Bowl-shaped mono- and dianions are prepared by reduction of corannulene (C(20)H(10), 1) with sodium and potassium metals in the presence of [18]crown-6 ether. Single-crystal X-ray diffraction studies of two sodium salts, [Na(THF)(2)([18]crown-6)](+)[1(-)] (2a) and [Na([18]crown-6)](+)[1(-)] (2b), reveal the presence of naked corannulene monoanions 1(-) in both cases. In contrast, the potassium adduct, [K([18]crown-6)](+)[1(-)] (3), shows an η(2)-binding of the K(+) ion to the convex face of 1(-). For the first time, corannulene dianions have been isolated as salts with sodium, [Na(2)([18]crown-6)](2+)[1(2-)] (4a) and [Na(THF)(2)([18]crown-6)](+)[Na([18]crown-6)](+)[1(2-)] (4b), and potassium counterions, [K([18]crown-6)](2)(+)[1(2-)] (5). Their structural characterization reveals geometry perturbations upon addition of two electrons to a bowl-shaped polyarene. It also demonstrates η(5)- or η(6)-binding of metals to the curved carbon surface of 1(2-), depending on the crystallization conditions. Both mono- and doubly-charged corannulene bowls show the preferential exo binding of Na(+) and K(+) ions in all investigated compounds. Various types of C-H···π interactions are found in the crystals of 2-5. The UV/Vis, ESR, and (1)H NMR spectroscopic studies of 2-5 indicate different coordination environment of corannulene anions in solution, depending on the metal ion.     

Cluster-cluster aggregation controlled by the number of intercluster connections: kinetics of aggregation and cluster mass frequency

The aggregation of colloids in the presence of hydrodynamic forces was investigated, employing a numerical model that took into account the masses of the individual clusters and the number of intercluster connections established when two clusters stuck together. The number of possible connections was determined by analyzing all the possible nonoverlapping configurations of stuck clusters. This operation was done for a couple of clusters of various masses, taking into account the assembly of clusters of even and uneven masses. The formulation of the constraints established a certain hierarchy in the sticking on a basis compatible with the irregular fracture model of Horwatt and co-workers. As a result, the permanent sticking of large clusters required the formation of a large number of connections, whereas that of small clusters might be realized even with a small number of connections. Thus, the aggregation started with the features of the standard reaction-limited process and this cluster growth became progressively inhibited as a result of the prevailing effects of the connection constraints. The cluster-mass frequency showed the emergence at least of a second population whose bell-shaped mass distribution was superimposed on the monotonically decreasing distribution resulting from the reaction-limited aggregation process. The results of the numerical study were confronted with those previously obtained in the aggregation of hydrated polystyrene latex particles dispersed in 1 M sodium chloride solution. The two striking features--the aggregate growth kinetics and the mass distribution function--were common to the computer-generated clusters and the latex aggregates.     

Inhibition effect of {surfactant–substrate} aggregation on the rate of oxidation of reducing sugars by alkaline hexacyanoferrate(III)

The effect of cationic (cetyltrimethylammonium bromide, CTAB), anionic (sodium lauryl sulfate, NaLS), and nonionic (Brij‐35) surfactants on the rate of oxidation of some reducing sugars (xylose, glucose, and fructose) by alkaline hexacyanoferrate(III) has been studied in the temperature range from 35 to 50°C. The rate of oxidation is strongly inhibited in the presence of surfactant. The inhibition effect of surfactant on the rate of reaction has been observed below critical micelle concentration (CMC) of CTAB. In case of NaLS and Brij‐35, the inhibition effect was above CMC, at which the surfactant abruptly associates to form micelle. The kinetic data have been accounted for by the combination of surfactant molecule(s) with a substrate molecule in case of CTAB and distribution of substrate into micellar and aqueous pseudophase in case of NaLS and Brij‐35. The binding parameters (binding constants, partition coefficients, and free‐energy transfer from water to micelle) in case of NaLS and Brij‐35 have been evaluated with the help of Menger and Portnoy model reported for micellar inhibition. © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 595–604, 2007     

A topographically optimized substrate with well-ordered lattice micropatterns for enhancing the osteogenic differentiation of murine mesenchymal stem cells

Although recently a growing number of reports demonstrate that topography or geometry of the substrate also plays an important role in the fate of the stem cells, most of these studies are usually completed by a few distinct patterns such as simple lines, posts, etc. As a result, there is a lack of quantitative analysis of the relationship between topographical variation and the differentiation of stem cells. Here, the effectiveness of topography variation is studied systematically in several microengineered substrates on osteogenic differentiation. It is found that the effectiveness of the osteogenic differentiation has a peak around 3 μm in the interval length of micropatterns.     

Mechanically untying a protein slipknot: multiple pathways revealed by force spectroscopy and steered molecular dynamics simulations

Protein structure is highly diverse when considering a wide range of protein types, helping to give rise to the multitude of functions that proteins perform. In particular, certain proteins are known to adopt a knotted or slipknotted fold. How such proteins undergo mechanical unfolding was investigated utilizing a combination of single molecule atomic force microscopy (AFM), protein engineering, and steered molecular dynamics (SMD) simulations to show the mechanical unfolding mechanism of the slipknotted protein AFV3-109. Our results reveal that the mechanical unfolding of AFV3-109 can proceed via multiple parallel unfolding pathways that all cause the protein slipknot to untie and the polypeptide chain to completely extend. These distinct unfolding pathways proceed via either a two- or three-state unfolding process involving the formation of a well-defined, stable intermediate state. SMD simulations predict the same contour length increments for different unfolding pathways as single molecule AFM results, thus providing a plausible molecular mechanism for the mechanical unfolding of AFV3-109. These SMD simulations also reveal that two-state unfolding is initiated from both the N- and C-termini, while three-state unfolding is initiated only from the C-terminus. In both pathways, the protein slipknot was untied during unfolding, and no tightened slipknot conformation was observed. Detailed analysis revealed that interactions between key structural elements lock the knotting loop in place, preventing it from shrinking and the formation of a tightened slipknot conformation. Our results demonstrate the bifurcation of the mechanical unfolding pathway of AFV3-109 and point to the generality of a kinetic partitioning mechanism for protein folding/unfolding.