On binding of DNA-bending proteins to DNA minicircles

We present a theoretical study of binding of DNA-bending proteins to circular DNA, using computer simulations of the wormlike chain model of DNA. We find that the binding affinity is affected by the bending elasticity and the conformational entropy of the polymer and that while protein adsorption is identical on open and closed long DNA molecules, there is significant enhancement of binding on DNA minicircles, compared to their linear counterparts. We also find that the ratio of the radii of gyration of open and closed chains depends on protein concentration for short DNA molecules. Experimental tests of our predictions are proposed.     

Kinetics of interior loop formation in semiflexible chains

Loop formation between monomers in the interior of semiflexible chains describes elementary events in biomolecular folding and DNA bending. We calculate analytically the interior distance distribution function for semiflexible chains using a mean field approach. Using the potential of mean force derived from the distance distribution function we present a simple expression for the kinetics of interior looping by adopting Kramers theory. For the parameters, that are appropriate for DNA, the theoretical predictions in comparison with the case are in excellent agreement with explicit Brownian dynamics simulations of wormlike chain (WLC) model. The interior looping times (tauIC) can be greatly altered in the cases when the stiffness of the loop differs from that of the dangling ends. If the dangling end is stiffer than the loop then tauIC increases for the case of the WLC with uniform persistence length. In contrast, attachment of flexible dangling ends enhances rate of interior loop formation. The theory also shows that if the monomers are charged and interact via screened Coulomb potential then both the cyclization (tauc) and interior looping (tauIC) times greatly increase at low ionic concentration. Because both tauc and tauIC are determined essentially by the effective persistence length [lp(R)] we computed lp(R) by varying the range of the repulsive interaction between the monomers. For short range interactions lp(R) nearly coincides with the bare persistence length which is determined largely by the backbone chain connectivity. This finding rationalizes the efficacy of describing a number of experimental observations (response of biopolymers to force and cyclization kinetics) in biomolecules using WLC model with an effective persistence length.     

Brownian dynamics simulation of the diffusion of rods and wormlike chains in a gel modeled as a cubic lattice: application to DNA

The translational diffusion constant of a particle, D, in a congested medium or a gel can be written as the product of two terms that account for long-range hydrodynamic interaction between the gel or congested medium and the particle, DEM, and a short-range "steric" term, S. For particles of arbitrary shape, DEM has been examined previously within the framework of the effective medium, EM, model (S. Allison et al., J. Phys. Chem. B 2008, 112, 5858-5866). In the present work, we examine S for rod- and wormlike chain models of duplex DNA in the size range of 100 to over 2000 base pairs. The gel is modeled explicitly as a cubic lattice, and Brownian dynamics simulation is used to examine S for a wide range of rod/wormlike chain and gel parameters. For wormlike chains with P = 50 nm, an empirical formula is derived for S that should be valid over a wide range of wormlike chain/gel parameters. For duplex DNA in the size of several hundred to several thousand base pairs in an agarose gel of 2% or less, fair agreement between modeling and experiment is obtained. However, modeling overestimates the length dependence of D observed experimentally. Finally, the reduction of D of DNA (100 to over 1000 base pairs in length) in cytoplasm relative to water can be accounted for quite well using the effective medium plus steric correction approach.     

A new reverse wormlike micellar system: mixtures of bile salt and lecithin in organic liquids

We report a new route for forming reverse wormlike micelles (i.e., long, flexible micellar chains) in nonpolar organic liquids such as cyclohexane and n-decane. This route involves the addition of a bile salt (e.g., sodium deoxycholate) in trace amounts to solutions of the phospholipid lecithin. Previous recipes for reverse wormlike micelles have usually required the addition of water to induce reverse micellar growth; here, we show that bile salts, due to their unique "facially amphiphilic" structure, can play a role analogous to that of water and promote the longitudinal aggregation of lecithin molecules into reverse micellar chains. The formation of transient entangled networks of these reverse micelles transforms low-viscosity lecithin organosols into strongly viscoelastic fluids. The zero-shear viscosity increases by more than 5 orders of magnitude, and it is the molar ratio of bile salt to lecithin that controls the viscosity enhancement. The growth of reverse wormlike micelles is also confirmed by small-angle neutron scattering (SANS) experiments on these fluids.     

Nematic Homopolymers: From Segmented to Wormlike Chains

We present a density functional approach to orientational ordering in homopolymeric systems. The polymers are modeled as chains of identical rodlike segments connected via a simple generic bending potential. The segments are impenetrable to each other, and it is their mutual excluded volume that drives the transition from the orientationally disordered isotropic phase to the orientationally ordered nematic fluid. These excluded volume effects are accounted for within the so‐called Onsager approximation at the chain–chain level and in an independent pairwise overlap approximation at the segment–segment level. The Khokhlov and Semenov formalism for nematic wormlike polymers is shown to be an exact limiting case of our treatment. The ordering transition is studied analytically by using a linear stability analysis of the isotropic phase yielding the properties of the system at the isotropic‐nematic (I–N) bifurcation point. Using a numerical scheme, the equilibrium distribution functions in the nematic phase are calculated, and the location of the thermodynamic I–N transition is determined. For stiff bending potentials, chains with a relatively small number of segments are found to behave like wormlike chains, and we determine the regime of model parameters for which this identification holds.     

Distribution functions and dynamical properties of stiff macromolecules

An analytically tractable model for chain molecules with bending stiffness is presented and the dynamical properties of such chains are investigated. The partition function is derived via the maximum entropy principle taking into account the chain connectivity as well as the bending restrictions in form of constraints. We demonstrate that second moments agree exactly with those known from the Kratky-Porod wormlike chain. Moreover, various distribution functions are calculated. In particular, the static structure factor is shown to be proportional to 1/q at large scattering vectors q. The equations of motion for a chain in a melt as well as in dilute solution are presented. In the latter case the hydrodynamic interaction is taken into account via the Rotne-Prager tensor. The dynamical equations are solved by a normal mode analysis. In the limit of a flexible chain the model reproduces the well-known Rouse and Zimm dynamics, respectively, on large length scales, whereas in the rod limit the eigenfunctions correspond to bending motion only. In addition, the coherent and incoherent dynamic structure factor is discussed. For melts we show that at large scattering vectors the incoherent dynamic structure factor is a universal function of only the combination q^8/3tp^1/3, where 1/(2p) is the persistence length of the macromolecules. The comparison of the theoretical results with quasielastic neutron and light scattering experiments of various polymers in solution and melt exhibits good agreement. Our investigations show that local stiffness strongly influences the dynamics of macromolecules on small length scales even for long and flexible chains.     

Configurational entropy of polyethylene and other linear polymers

The configurational entropy of the polyethylene chain at the melting points calculated in two ways. In both calculations, tetrahedral angles and discrete trans and gauche arrangements of all bonds are assumed, and trans bonds are assumed more stable than gauche by energy U₁. First, calculations are made on chains of up to N = 18 bonds, disallowing all configurations having overlapping atoms, and the result is extrapolated to large N. Second, a calculation is made directly for long chains, with overlaps excluded only over every short chain segment. The results are in almost exact agreement, suggesting that the second method can be safely used with other molecules. The calculated configurational entropy is in line with that suggested by the entropy of fusion, assuming the chains to acquire a configurational freedom in the melt which approaches that of independent chains.     

Quantitative single-molecule conformational distributions: a case study with poly-(L-proline)

Precise measurement of the potential of mean force is necessary for a fundamental understanding of the dynamics and chemical reactivity of a biological macromolecule. The unique advantage provided by the recently developed constant-information approach to analyzing time-dependent single-molecule fluorescence measurements was used with maximum entropy deconvolution to create a procedure for the accurate determination of molecular conformational distributions, and analytical expressions for the errors in these distributions were derived. This new method was applied to a derivatized poly(L-proline) series, P(n)CG3K(biotin) (n = 8, 12, 15, 18, and 24), using a modular, server-based single-molecule spectrometer that is capable of registering photon arrival times with a continuous-wave excitation source. To account for potential influence from the microscopic environment, factors that were calibrated and corrected molecule by molecule include background, cross-talk, and detection efficiency. For each single poly(L-proline) molecule, sharply peaked F?rster type resonance energy transfer (FRET) efficiency and distance distributions were recovered, indicating a static end-to-end distance on the time scale of measurement. The experimental distances were compared with models of varying rigidity. The results suggest that the 23 angstroms persistence length wormlike chain model derived from experiments with high molecular weight poly(L-proline) is applicable to short chains as well.     

Synthesis of Defective Phospholipids

Phospholipids have been synthesized that possess a normal 16-carbon chain plus a "defective" chain only 8 or 12 carbons long and terminated with methoxyl, hydroxyl, or carboxyl groups. In addition, dimeric phospholipids have been prepared in which two phospholipid units are joined at position-1 with chains of 22 or 32 carbons while unconnected chains at position-2 are, once again, short and functionalized. These phospholipids are potentially useful for constructing membranes that contain cavities or irregularities and, therefore, are capable of serving as self-assembled host systems in which drugs and other guest molecules are retained and, perhaps, eventually released.     

Elastic Properties of Semi-Flexible Chains and Networks

Summary: Elastic properties of noncharged polymers of stiffness ranging from flexible to rigid chains are determined from Monte Carlo simulations. The discrete wormlike chain (WLC) model with self-interacting units is applied to chains of intermediate lengths. Elastic free energy and the force-extension profiles of chains of variable stiffness are computed in an isometric ensemble. Occurrence of a plateau on the force-extension curves at intermediate chain stiffness is noted. Qualitative differences are found between force profiles from simulations and from the standard (ideal) WLC model. The single-chain data on influence of bending stiffness were employed in the three-chain model of networks. Stress-strain relations for networks show a highly nonlinear behavior with the marked strain-stiffening effect.     

Density functional theory of adsorption of mixtures of charged chain particles and spherical counterions

We propose a microscopic density functional theory to describe nonuniform ionic fluids composed of chain molecules with charged "heads" and spherical counterions. The chain molecules are modeled as freely jointed chains of hard spheres, the counterions are oppositely charged spheres of the same diameter as all segments of chain molecules. The theory is based on the approach of Yu and Wu [J. Chem. Phys. 117, 2368 (2002)] of adsorption of chain molecules and on theory of adsorption of electrolytes [O. Pizio, A. Patrykiejew, and S. Sokolowski, J. Chem. Phys. 121, 11957 (2004)]. As an application of the proposed formalism we investigate the structure and adsorption of fluids containing segments of different length in a slitlike pore.     

Equilibrium and dynamical properties of gaussian stiff chain molecules

We present a novel analytically tractable model for stiff chain molecules. The equilibrium distribution function of the chain is derived using the maximum-entropy principle. For that purpose, we first formulate a discrete chain model, where the connections of the points and the restriction on bending are taken into account via constraints. We then perform the limit to a continuous chain and show that the mean-square end-to-end distance and the radius of gyration of the continuous chain are identical with the same quantities of the Kratky-Porod wormlike chain. The dynamics of our chain is investigated in dilute solution without hydrodynamic interactions. The linear dynamical equation is solved by a normal mode analysis. We discuss the dependence of the relaxation times on the single parameter of the model, the persistence length. For small persistence lengths we obtain the well known relaxation times of the Rouse model. In the stiff-chain limit, we find the pure bending relaxation times and, in addition, the rotational relaxation time.     

Emergence of multiple tori structures in a single polyelectrolyte chain

We investigated the collapsed structure of a weakly charged wormlike chain under a moderate concentration of 1:1 electrolyte solution. By assuming a torus as a grand state, we found that the size of a torus is determined by the balance between surface energy and electrostatic energy, which leads to a finite torus thickness almost independent of the chain contour length. Owing to this unique characteristic, a long charged wormlike chain forms multiple tori structure as a collapsed product, which is never seen with a neutral wormlike chain. These features were confirmed by a Monte Carlo simulation.     

Analysis of the conformation of wormlike chains by combination of small-angle x-ray and small-angle neutron scattering

An analysis of the conformation of a wormlike polymer by small-angle scattering is presented. By a combined investigation of small-angle X-ray and of small-angle neutron scattering the effect of the finite size of the repeating units can be eliminated. The procedure suggested herein therefore allows to obtain the scattering function for a respective infinitely thin chain. The latter quantity is compared to current models of the scattering function of wormlike chains.     

Numerical Simulation of the Distribution Function and Free Energy of a Single Wormlike Polymer Confined between Hard Walls

We focus on the distribution and free energy of a wormlike polymer confined between two parallel hard walls.The variation in the distribution and free energy of the wormlike chain as the spacing between the walls decreases(or as the total contour length of the wormlike chain increases or as the persistence length of the chain increases)is simulated.The main reason for these changes is a degradation of the long wormlike chain into a Gaussian long chain under weak confinement.     

V-shaped crystalline structures of di-n-alkyl esters of phosphoric acid

We prepared crystals of di-n-alkyl esters of phosphoric acid with chain lengths of n = 10, 12, 14, 16, and 18. These were characterized by single-crystal X-ray analysis and differential scanning calorimetry (DSC). It was found that the alkyl chains are in an extended all-trans conformation and aligned close to perpendicular, forming V-shaped molecules. This is in strong contrast to the typical arrangement of the alkyl chains of phospholipids where the two alkyl chains are arranged parallel in the same direction (e.g., tuning fork configuration in bilayers). Additionally, it was found that the arrangement of the V-shaped molecules of the di-n-alkyl esters in neighboring stacks of the lamellar crystals is antiparallel for short chain lengths (n = 10 and 12) and parallel for the longer (n = 14 and 16). DSC reveals that the melting of the crystals increases systematically with increasing chain lengths from 48 to 82 degrees C. The contribution of each methylene group to the melting enthalpy (70-133 kJ/mol) is independent of the chain length (3.9 kJ per mol CH2).     

Understanding the growth rates of polymer cocrystallization in the binary mixtures of different chain lengths

Polymer materials often contain a polydispersity of molecular lengths. We studied the linear growth rates of polymer lamellar crystals in the binary mixtures of different chain lengths by means of dynamic Monte Carlo simulations. Both chain lengths were chosen large enough to perform chain folding upon crystal growth but not very large to avoid the effect of chain entanglement in the bulk phase. We found that the crystal growth rates exhibit a linear dependence upon the compositions of mixtures. This linear relation implies that the overall crystal growth rates are integrated by the separate contributions of variable-length single polymers, supporting the model of intramolecular crystal nucleation. In each event of crystal growth of single polymers, long chains yield more crystallinity than short chains. This high efficiency explains higher crystal growth rates of long chains than that of short chains, and the explanation is quite different from the traditional view on the basis of their different melting points. In addition, with a partial release of sliding diffusion for crystal thickening, a new dependence of crystal growth rates occurs near the dilute end of long-chain compositions at high temperatures, which can be attributed to the preference of integer-number chain folding at the crystal growth front. The preferred fold lengths may vary with chain lengths and thus influence the crystal growth rates.     

Monte Carlo simulation of the structure of mono- and bidisperse polyethylene nanocomposites

The structure of bidisperse polyethylene(PE) nanocomposite mixtures of 50:50(by mole) of long and short chains of C160H322/C80H162 and C160H322/C40H82 filled with spherical nanoparticles were investigated by a coarse-grained, on lattice Monte Carlo method using rotational isomeric state theory for short-range and Lennard-Jones for long-range energetic interactions. Simulations were performed to evaluate the effect of wall-to-wall distance between fillers(D), polymer-filler interaction(w) and polydispersity(number of short chains in the mixture) on the behavior of the long PE chains. The results indicate that long chain conformation statistics remain Gaussian regardless of the effects of confinement, interaction strength and polydispersity. The various long PE subchain structures(bridges, dangling ends, trains, and loops) are influenced strongly by confinement whereas monomer-filler interaction and polydispersity did not have any impact. In addition, the average number of subchain segments per filler in bidisperse PE nanocomposites decreased by about 50% compared to the nanocomposite system with monodisperse PE chains. The presence of short PE chains in the polymer matrix leads to a reduction of the repeat unit density of long PE chains at the interface suggesting that the interface is preferentially populated by short chains.