Contribution of nonlocal interactions to DNA elasticity

A nonlocal harmonic elastic rod model is proposed to describe the elastic behavior of short DNA molecules. We show that the nonlocal interactions contribute to effective bending energy of the molecule and affect its apparent persistence length. It is also shown that the anomalous behavior which has been observed in all-atom molecular dynamic simulations [A. K. Mazur, Biophys. J. 134, 4507 (2006)] can be a consequence of both nonlocal interactions between DNA base pairs and the intrinsic curvature of DNA.     

Dynamics of magnesium-bicarbonate interactions

The complexation kinetics of Mg²⁺ with CO ₃ ⁼ and HCO ₃ ^? has been studied in methanol and water by means of the stopped-flow and temperature-jump methods. Kinetic parameters were obtained in methanol by coupling the magnesium-carbonato reactions with the metal-ion indicator Murexide. Relatively high stability constants were found in methanol (K=1.0×10⁵ liters-mole^?1 for Mg²⁺-Murexide,K=7.0×10⁴ liters-mole^?1 for Mg²⁺?HCO ₃ ^? , andK=2.0×10⁵ for Mg²⁺?CO ₃ ⁼ liters-mole^?1). The corresponding, observed formation rate constants were determined to be $$\begin{gathered} k_f = 4.0 \times 10^6 M^{ - 1} - sec^{ - 1} (Mg^{2 + } - Murexide) \hfill \\ k_f = 5.0 \times 10^5 M^{ - 1} - sec^{ - 1} (Mg^{2 + } - HCO_3^ - ) \hfill \\ k_f = 6.8 \times 10^5 M^{ - 1} - sec^{ - 1} (Mg^{2 + } - CO_3^ = ) \hfill \\ \end{gathered} $$ The relaxation times were found to be much shorter (τ≈5–20 μsec) in aqueous solutions, primarily due to the relatively high dissociation rate constants. The data could be interpreted on the basis of a coupled reaction scheme in which the protolytic equilibria are established relatively rapidly, followed by a single relaxation process due to the formation of MgHCO ₃ ⁺ and MgCO₃ between pH 8.7 and 9.3. The observed formation rate constants were determined to be $$\begin{gathered} k_f = 5.0 \times 10^5 M^{ - 1} - sec^{ - 1} (Mg^{2 + } - HCO_3^ - ) \hfill \\ k_f = 1.5 \times 10^6 M^{ - 1} - sec^{ - 1} (Mg^{2 + } - CO_3^ = ) \hfill \\ \end{gathered} $$ These results, in conjunction with NMR solvent exchange rate constants, are analyzed in terms of a dissociative (S _N1) mechanism for the rate of complex formation. The significance of these kinetic parameters in understanding the excess sound absorption in seawater is discussed.     

Dynamics of a single copolymer chain

The dynamics of a single copolymer chain in a solution containing identical chains is studied. The intermediate scattering function is calculated, and two different modes are identified and analyzed as a function of wave vector q. The first mode is characteristic of the copolymer system and leads to a peculiar constant relaxation frequency as q goes to zero. The second mode represents the diffusion of the chain in the solution.     

Confinement and viscoelastic effects on chain closure dynamics

Chemical reactions inside cells are typically subject to the effects both of the cell's confining surfaces and of the viscoelastic behavior of its contents. In this paper, we show how the outcome of one particular reaction of relevance to cellular biochemistry--the diffusion-limited cyclization of long chain polymers--is influenced by such confinement and crowding effects. More specifically, starting from the Rouse model of polymer dynamics, and invoking the Wilemski-Fixman approximation, we determine the scaling relationship between the mean closure time t(c) of a flexible chain (no excluded volume or hydrodynamic interactions) and the length N of its contour under the following separate conditions: (a) confinement of the chain to a sphere of radius d and (b) modulation of its dynamics by colored Gaussian noise. Among other results, we find that in case (a) when d is much smaller than the size of the chain, t(c) ~ Nd(2), and that in case (b), t(c) ~ N(2/(2-2H)), H being a number between 1/2 and 1 that characterizes the decay of the noise correlations. H is not known a priori, but values of about 0.7 have been used in the successful characterization of protein conformational dynamics. At this value of H (selected for purposes of illustration), t(c) ~ N(3.4), the high scaling exponent reflecting the slow relaxation of the chain in a viscoelastic medium.     

Perturbation theory with an approximate perturbation: The effect of charge overlap on interatomic interactions

The evaluation of interatomic interactions at large separations (R) typically involves neglecting electron exchange, treating the Coulomb interaction between atoms as a perturbation, neglecting third- and higher-order energy contributions, and approximating the Coulomb interaction by a short expansion in spherical harmonics and, usually, powers of R^?1. This last approximation, using an approximate perturbing Hamiltonian to evaluate a second-order perturbed energy, is examined here; error bounds and a simple correction are introduced. Three illustrative applications to the H? H⁺ interaction are given: the error incurred by truncating the spherical-harmonic expansion is bounded, the R^?1 expansion is corrected for the overlap of the “atomic” charge distributions, and the R^?1 expansion is analyzed to see why it works as well as it does.     

The virial theorem for non-coulombic interactions and scaled approximate wave functions

The virial theorem for various not necessarily homogeneous potential functions V(r) is derived. It is proved in a transparent way that approximate wave functions at optimal scale satisfy the general virial theorem for any radial potential V(r). The proposed method for improving a variational wave function which by the scaling procedure obeys the virial theorem is tested in the case of some simple screened coulomb potentials.

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Zusammenfassung Das Virialtheorem für verschiedene, nicht unbedingt homogene Potentialfunktionen V(r) wird abgeleitet. Es wird gezeigt, da\ eine NÄherungsfunktion mit optimalem Skalenparameter auch das allgemeine Virialtheorem für beliebige Radialpotentiale V(r) erfüllt. Die Methode der Streckung des Grundgebietes (scaling) dient zur Verbesserung von NÄherungsfunktionen, was am Beispiel einiger abgeschirmter Coulomb-Potentiale demonstriert wird.

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Résumé Le théorème du viriel pour quelques fonctions de potentiel V(r) non nécessairement homogènes est dérivé du théorème général. Il est prouvé d'une manière intuitive que des fonctions d'onde approchées, à l'échelle optimum, satisfont le théorème du viriel général pour tous les potentiels radiaux V(r). La méthode proposée pour améliorer une fonction d'onde variationnelle, qui obéit au théorème du viriel, est essayée dans le cas de quelques simples potentiels coulombiens écrantés.

     

Dynamics of interactions involving deformable drops: hydrodynamic dimpling under attractive and repulsive electrical double layer interactions

A model developed previously to analyze force measurements between two deformable droplets in the atomic force microscope [Langmuir 2005, 21, 2912-2922] is used to model the drainage of an aqueous film between a mica plate and a deformable mercury drop for both repulsive and attractive electrical double-layer interactions between the mica and the mercury. The predictions of the model are compared with previously published data [Faraday Discuss. 2003, 123, 193-206] on the evolution of the aqueous film whose thickness has been measured with subnanometer precision. Excellent agreement is found between theoretical results and experimental data. This supports the assumptions made in the model which include no-slip boundary conditions at both interfaces. Furthermore, the successful fit attests to the utility of the model as a tool to explore details of the drainage mechanisms of nanometer-thick films in which fluid flow, surface deformations, and colloidal forces are all involved. One interesting result is that the model can predict the time at which the aqueous film collapses when attractive mica-mercury forces are present without the need to invoke capillary waves or other local instabilities of the mercury/electrolyte interface.     

Dynamics in the presence of attractive patchy interactions

We report extensive Monte Carlo and event-driven molecular dynamics simulations of a liquid composed of particles interacting via hard-sphere interactions complemented by four tetrahedrally coordinated short-range attractive ("sticky") spots, a model introduced several years ago by Kolafa and Nezbeda (Kolafa, J.; Nezbeda, I. Mol. Phys. 1987, 87, 161). To access the dynamic properties of the model, we introduce and implement a new event-driven molecular dynamics algorithm suited to study the evolution of hard bodies interacting, beside the repulsive hard-core, with a short-ranged interpatch square well potential. We evaluate the thermodynamic properties of the model in deep supercooled states, where the bond network is fully developed, providing evidence of density anomalies. Different from models of spherically symmetric interacting particles, the liquid can be supercooled without encountering the gas-liquid spinodal in a wide region of packing fractions phi. Around an optimal phi, a stable fully connected tetrahedral network of bonds develops. By analyzing the dynamics of the model we find evidence of anomalous behavior: around the optimal packing, dynamics accelerate on both increasing and decreasing phi. We locate the shape of the isodiffusivity lines in the (phi - T) plane and establish the shape of the dynamic arrest line in the phase diagram of the model. Results are discussed in connection with colloidal dispersions of sticky particles and gel-forming proteins and their ability to form dynamically arrested states.     

An approximate method for calculating depletion and structural interactions between colloidal particles

An approximate method is evaluated for calculating the second virial coefficient in a dilute macromolecular solution bounded by two interfaces. The approximation is essentially the superposition of the coefficients calculated independently for each surface. To test this approach, the depletion interaction between two particles in a solution of nonadsorbing, spherical macromolecules is calculated in systems with either hard-wall or long-range electrostatic interactions. In all systems tested, the interparticle interaction energy calculated with the approximation is found to be in good agreement with that calculated using the exact approach (e.g., error less than 2% at the smallest separations). The primary advantage of this approximation is a significant reduction in the computation time required for calculating the depletion interaction, especially in charged systems. The paper also shows that the expressions for predicting the depletion interaction in purely hard-sphere systems can be used in dilute ionic systems, provided the appropriate effective macromolecule size is used. For the attractive depletion interaction, this effective size is determined by the range of the particle-macromolecule interaction (as opposed to the macromolecule-macromolecule interaction).     

Car-Parrinello treatment for an approximate density-functional theory method

The authors formulate a Car-Parrinello treatment for the density-functional-based tight-binding method with and without self-consistent charge corrections. This method avoids the numerical solution of the secular equations, the principal drawback for large systems if the linear combination of atomic orbital ansatz is used. The formalism is applicable to finite systems and for supercells using periodic boundary conditions within the Gamma-point approximation. They show that the methodology allows the application of modern computational techniques such as sparse matrix storage and massive parallelization in a straightforward way. All present bottlenecks concerning computer time and consumption of memory and memory bandwidth can be removed. They illustrate the performance of the method by direct comparison with Born-Oppenheimer molecular dynamics calculations. Water molecules, benzene, the C(60) fullerene, and liquid water have been selected as benchmark systems.     

Dynamics of the nitroxide side chain in spin-labeled proteins

The dynamics of the tether linking methanethiosulfonate (MTSSL) spin probes to alpha-helices has been investigated with the purpose of rationalizing its effects on ESR line shapes. Torsional profiles for the chain bonds have been calculated ab initio, and steric interactions with the alpha-helix and the neighboring residues have been introduced at the excluded-volume level. As a consequence of the restrictions deriving from chain geometry and local constraints, a limited number of allowed conformers has been identified that undergo torsional oscillations and conformational jumps. Torsional fluctuations are described as damped oscillations, while transition rates between conformers are calculated according to the Langer multidimensional extension of the Kramers theory. The time scale and amplitude of the different motions are compared; the major role played by rotations of the outermost bonds of the side chain emerges, along with the effects of substituents in the pyrroline ring on the conformer distribution and dynamics. The extent and symmetry of magnetic tensor averaging produced by the side chain motions are estimated, the implications for the ESR spectra of spin-labeled proteins are discussed, and suggestions for the introduction of realistic features of the spin probe dynamics into the line shape simulation are presented.     

Influence of short-range interactions on the shape of an unperturbed polymer chain: polyethylene

The average instantaneous shape of an unperturbed polyethylene chain is studied with a Monte Carlo technique. Different short-range interactions in the polyethylene chain are considered. The shape is evaluated as the ratio 〈L〉:〈L〉:〈L〉, where L₁≤L₂≤L₃ are the orthogonal components in the system of principal axes of gyration. Differences are found for different interactions in short- and medium-length chains, while for long chains all ratios converge to a common limit, which is about 1:2.7:12.0 for polyethylene chains.     

Thermodynamic treatment of ligand-receptor interactions

This work reports the development of a physico-chemical model for ligand-receptor interactions. It considers receptors having groups of different binding sites in equilibrium and far from equilibrium where each of these may have multiple occupancies. The obtained results under appropriate simplifications give the well known Scatchard, Hill and Adair relations and provide a very interesting tool for studying receptor-ligand phenomena and for determining the related parameters and interaction energies.     

Amino acid side chain interactions in the presence of salts

The effects of salt on the intermolecular interactions between polar/charged amino acids are investigated through molecular dynamics simulations. The mean forces and associated potentials are calculated for NaCl salt in the 0-2 M concentration range at 298 K. It is found that the addition of salt may stabilize or destabilize the interactions, depending on the nature of the interacting molecules. The degree of (de)stabilization is quantified, and the origin of the salt-dependent modulation is discussed based upon an analysis of solvent density profiles. To gain insight into the molecular origin of the salt modulation, spatial distribution functions (sdf's) are calculated, revealing a high degree of solvent structuredness in all cases. The peaks in the sdf's are consistent with long-range hydrogen-bonding networks connecting the solute hydrophilic groups, and that contribute to their intermolecular solvent-induced forces. The restructuring of water around the solutes as they dissociate from close contact is analyzed. This analysis offers clues on how the solvent structure modulates the effective intermolecular interactions in complex solutes. This modulation results from a critical balance between bulk electrostatic forces and those exerted by (i) the water molecules in the structured region between the monomers, which is disrupted by ions that transiently enter the hydration shells, and (ii) the ions in the hydration shells in direct interactions with the solutes. The implications of these findings in protein/ligand (noncovalent) association/dissociation mechanisms are briefly discussed.     

Performance of a rigid rod statistical mechanical treatment to predict monolayer ordering: a study of chain interactions and comparison with molecular dynamics simulation

A statistical mechanical model that treats hydrocarbon self-assembled monolayer (SAM) chains as rigid rods is examined to interrogate the mechanisms involved in monolayer ordering. The statistical mechanical predictions are compared to fully atomistic molecular dynamics simulations of SAMs with different packing densities. The monolayer chain order is examined as a function of surface coverage, chain-surface interactions, and chain–chain interactions. Reasonable interaction potentials are deduced from ab initio electronic structure calculations of small model systems. It is found that the chain-surface interaction is the most important parameter in formation of flat-lying monolayer phases, while formation of standing phase monolayers is driven most importantly by increased density of molecules at the surface. A brief discussion of the utility and validity of the rigid rod treatment is given in light of the molecular dynamics results.     

Dynamics imaging of lipid phases and lipid-marker interactions in model biomembranes

Biomembranes are complex systems that regulate numerous biological processes. Lipid phases that constitute these membranes influence their properties and transport characteristics. Here, we demonstrate the potential of short-range dynamics imaging (excited-state lifetime, rotational diffusion, and order parameter) as a sensitive probe of lipid phases in giant unilamellar vesicles (GUVs). Liquid-disordered and gel phases were labeled with Bodipy-PC at room temperature. Two-photon fluorescence lifetime imaging microscopy of single-phase GUVs reveals more heterogeneity in fluorescence lifetimes of Bodipy in the gel phase (DPPC: 3.8+/-0.6 ns) as compared with the fluid phase (DOPC: 5.2+/-0.2 ns). The phase-specificity of excited-state lifetime of Bodipy-PC is attributed to the stacking of ordered lipid molecules that possibly enhances homo-FRET. Fluorescence polarization anisotropy imaging also reveals distinctive molecular order that is phase specific. The results are compared with DiI-C12-labeled fluid GUVs to investigate the sensitivity of our fluorescence dynamics assay to different lipid-marker interactions. Our results provide a molecular perspective of lipid phase dynamics and the nature of their microenvironments that will ultimately help our understanding of the structure-function relationship of biomembranes in vivo. Furthermore, these ultrafast excited-state dynamics will be used for molecular dynamics simulation of lipid-lipid, lipid-marker and lipid-protein interactions.     

A breathing wormlike chain model on DNA denaturation and bubble: effects of stacking interactions

DNA stably exists as a double-stranded structure due to hydrogen-bonding and stacking interactions between bases. The stacking interactions are strengthened when DNA is paired, which results in great enhancement of bending rigidity. We study the effects of this stacking-induced stiffness difference on DNA denaturation and bubble formations. To this end, we model double-stranded DNA as a duplex of two semiflexible chains whose persistence length varies depending on the base-pair distance. Using this model, we perform the Langevin dynamics simulation to examine the characteristics of the denaturation transition and the statistics of the bubbles. We find that the inclusion of the stacking interactions causes the denaturation transition to be much sharper than otherwise. At physiological temperature, the stacking interactions prohibit the initiation of bubble formation but promote bubbles, once grown, to retain the large size.     

Origin of nonlocal interactions in adsorption of polar molecules on Si(001)-2 x 1

Using density functional theory slab calculations, we have investigated (i) the origin of nonlocal interactions occurring in the adsorption of small polar molecules (H2O,NH3,CH3OH,CH3NH2) on the clean Si(001)-2 x 1 surface and (ii) the nonlocal effects on two-dimensional arrangement of adsorbates. Our results show the adsorption properties are significantly altered in the presence of adsorbates on an adjacent dimer along a row. We have identified that the coverage dependent behavior arises from a combination of (i) surface polarization change, (ii) adsorbate-induced charge delocalization, (iii) adsorbate-adsorbate repulsion, and (iv) hydrogen bonding. The nucleophilic-electrophilic molecular adsorption involves charge delocalization to neighboring dimers along a row, which in turn undermines molecular adsorption on the neighboring dimers. Nonlocal effects associated with polar interactions with neighboring dimers and adsorbates vary with adsorption system. While such polar interactions are unimportant in CH3OH adsorption, hydrogen bonding and adsorbate-adsorbate repulsion play an important role in determining the adsorption structures of H2O and NH3CH3NH2, respectively. In addition, the electrostatic attraction with the buckled-up Si atoms of adjacent dimers contributes to stabilization of H2O, NH3, and CH3NH2 adsorption. We also discuss kinetic effects on two-dimensional ordering of adsorbates, in conjunction with surface phase transition and adsorption-dissociation rates.     

Monte Carlo simulation of miscibility of polymer blends with repulsive interactions: effect of chain structure

The effects of the chain structure and the intramolecular interaction energy of an A/B copolymer on the miscibility of the binary blends of the copolymer and homopolymer C have been studied by means of a Monte Carlo simulation. In the system, the interactions between segments A, B and C are more repulsive than those between themselves. In order to study the effect of the chain structure of the A/B copolymer on the miscibility, the alternating, random and block copolymers were introduced in the simulations, respectively. The simulation results show that the miscibility of the binary blends strongly depends on the intramolecular interaction energy () between segments A and B within the A/B copolymers. The higher the repulsive interaction energy, the more miscible the A/B copolymer and homopolymer C are. For the diblock copolymer/homopolymer blends, they tend to form micro phase domains. However, the phase domains become so small that the blend can be considered as a homogeneous phase for the alternating copolymer/homopolymer blends. Furthermore, the investigation of the average end-to-end distance () in different systems indicates that the copolymer chains tend to coil with the decrease of whereas the of the homopolymer chains depends on the chain structure of the copolymers. As for the system containing the alternating or the random copolymers, the homopolymer chains also tend to coil with the decrease of . However, for the systems including the block copolymers, there is a slight difference in the of the homopolymer chains with the variation of .