The effect of hydrodynamic interactions on the dynamics of DNA translocation through pores

In this work, we investigate the effect of hydrodynamic interactions on the dynamics of DNA translocation through micropores. We simulate DNA as a bead-spring chain and use a lattice Boltzmann method to simulate the flow field that arises from the motion of the molecule. We investigate the free-draining entrance of DNA to the pore by diffusion and find that, consistent with experiments, molecules have a higher probability of entering the pore from one end. We then consider the electric-field driven translocation of 21-210 microm DNA with and without hydrodynamic interactions. Consistent with experiments, we study translocation events that are much shorter than the relaxation time of DNA. We find that the effect of hydrodynamic interactions on this process is to cause different regions of a molecule, other than the ones pulled by voltage or chain connectivity into the pore, to move toward the pore. We quantify this effect and show that it is smaller than the difference in the translocation dynamics of chains that arises from different initial configurations of the molecules. A power-law scaling of translocation time with chain length is observed, with exponents of 1.28+/-0.03 and 1.31+/-0.03 in simulations with and without hydrodynamic interactions, respectively. Our results are in good agreement with recent translocation experiments conducted in small pores and show that, for the regime considered in this work, hydrodynamic interactions play a minor role in the relation of the translocation time to chain length. For fast translocation processes, the effect of hydrodynamic interactions is local and the main factor determining the dynamics of DNA is the initial configuration of the molecules.     

Polymer translocation in solid-state nanopores: dependence of scaling behavior on pore dimensions and applied voltage

We investigate unforced and forced translocation of a Rouse polymer (in the absence of hydrodynamic interactions) through a silicon nitride nanopore by three-dimensional Langevin dynamics simulations, as a function of pore dimensions and applied voltage. Our nanopore model consists of an atomistically detailed nanopore constructed using the crystal structure of β-Si(3)N(4). We also use realistic parameters in our simulation models rather than traditional dimensionless quantities. When the polymer length is much larger than the pore length, we find the translocation time versus chain length scales as τ ～ N(2+ν) for the unforced case and as τ ～ N((1+2ν)/(1+ν)) for the forced case. Our results agree with theoretical predictions which indicate that memory effects and tension on the polymer chain play an important role during the translocation process. We also find that the scaling exponents are highly dependent on the applied voltage (force). When the length of the polymer is on the order of the length of the pore, we do not find a continuous scaling law, but rather scaling exponents that increase as the length of the polymer increases. Finally, we investigate the scaling behavior of translocation time versus applied voltage for different polymer and pore lengths. For long pores, we obtain the theoretical scaling law of τ ～ 1/V(α), where α ? 1 for all voltages and polymer lengths. For short pores, we find that α decreases for very large voltages and/or small polymer lengths, indicating that the value of α = 1 is not universal. The results of our simulations are discussed in the context of experimental measurements made under different conditions and with differing pore geometries.     

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength E, length of the chain N, and length of the pore L on forced translocation. As our main result, we find a crossover scaling for the translocation time tau with the chain length from tau approximately N2nu for relatively short polymers to tau approximately N1+nu for longer chains, where nu is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains v approximately N-nu, which crosses over to v approximately N(-1) for long polymers. The reason for this is that with increasing N there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which R parallel, the radius of gyration Rg along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large N, however, the asymptotic scaling tau approximately N1+nu is recovered. In this regime, tau is almost independent of L. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for R parallel approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.     

Kinetics of protein adsorption by nanoporous carbons with different pore size

Kinetics of bovine serum albumin and ovalbumin adsorption by nanoporous carbons with different main pore sizes (1.6, 5, 7.8 and 28 nm) was studied. Experimental kinetics curves were well described by multi-exponential equation with different number of exponents (from 1 to 4). Protein adsorption kinetics showed significant dependence on pore size of carbonaceous adsorbent. Correlation between pore size distribution and amount of protein adsorbed revealed threshold pore size 7.3 nm for BSA and 6.8 nm for OVA, which are close to hydrodynamic diameter of protein molecules. The fastest and the highest adsorption of proteins were observed in carbons having developed porosity with pore sizes larger than 15 nm.     

Translocation of polymers with folded configurations across nanopores

The transport of polymers with folded configurations across membrane pores is investigated theoretically by analyzing simple discrete stochastic models. The translocation dynamics is viewed as a sequence of two events: motion of the folded segment through the channel followed by the linear part of the polymer. The transition rates vary for the folded and linear segments because of different interactions between the polymer molecule and the pore. It is shown that the translocation time depends nonmonotonously on the length of the folded segment for short polymers and weak external fields, while it becomes monotonous for long molecules and large fields. Also, there is a critical interaction between the polymers and the pore that separates two dynamic regimes. For stronger interactions, the folded polymer moves slower, while for weaker interactions, the linear chain translocation is the fastest. In addition, our calculations show that the folding does not change the translocation scaling properties of the polymer. These phenomena can be explained by the interplay between translocation distances and transition rates for the folded and linear segments of the polymer. Our theoretical results are applied for analysis of experimental translocations through solid-state nanopores.     

Precise measurement of the self-diffusion coefficient for poly(ethylene glycol) in aqueous solution using uniform oligomers

Uniform poly(ethylene glycol) (PEG) oligomers, with a degree of polymerization n=1-40, were separated by preparative supercritical fluid chromatography from commercial monodispersed samples. Diffusion coefficients, D, for separated uniform PEG oligomers were measured in dilute solutions of deuterium oxide (D(2)O) at 30 degrees C, using pulsed-field gradient nuclear magnetic resonance. The measured D for each molecular weight was extrapolated to infinite dilution. Diffusion coefficients obtained at infinite dilution follow the scaling behavior of Zimm-type diffusion, even in the lower molecular weight range. Molecular-dynamics simulations for PEG in H(2)O also showed this scaling behavior, and reproduced close hydrodynamic interactions between PEG and water. These findings suggest that diffusion of PEG in water is dominated by hydrodynamic interaction over a wide molecular weight range, including at low molecular weights around 1000.     

Polymer translocation through a nanopore: a two-dimensional Monte Carlo study

We investigate the problem of polymer translocation through a nanopore in the absence of an external driving force. To this end, we use the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. To overcome the entropic barrier without artificial restrictions, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau required for the polymer to completely exit the pore on either end. We find numerically that tau scales with the chain length N as tau approximately N(1+2nu), where nu is the Flory exponent. This is the same scaling as predicted for the translocation time of a polymer which passes through the nanopore in one direction only. We examine the interplay between the pore length L and the radius of gyration R(g). For LR(g), we find tau approximately N. In addition, we numerically find the scaling function describing crossover between short and long pores. We also show that tau has a minimum as a function of L for longer chains when the radius of gyration along the pore direction R( parallel) approximately L. Finally, we demonstrate that the stiffness of the polymer does not change the scaling behavior of translocation dynamics for single-segment dynamics.     

Hydrodynamic Radius Characterization of a Vinyl-Type Polynorbornene by Size-Exclusion Chromatography with a Static and Dynamic Laser Light Scattering Detector

Both absolute molecular weight and molecular sizes (radius of gyration and hydrodynamic radius) of a vinyl-type polynorbornene eluting from size-exclusion chromatography columns were determined by combined with a static and dynamic laser light scattering detector. The hydrodynamic radius of polymer fraction eluting from size-exclusion chromatography columns was obtained from dynamic laser light scattering measurements at only a single angle of 90° by introducing a correction factor. According to the scaling relationship between molecular sizes and molecular weight and the ratio between radius of gyration and hydrodynamic radius, the vinyl-type polynorbornene took a random coil conformation in 1,2,4-trichlorobenzene at 150 °C.     

Equilibrium conformational dynamics of a polymer in a solvent

Molecular dynamics simulations were used to study the conformational dynamics of a bead-spring model polymer in an explicit solvent under good solvent conditions. The dynamics of the polymer chain were investigated using an analysis of the time autocorrelation functions of the Rouse coordinates of the polymer chain. We have investigated the variation of the correlation functions with polymer chain length N, solvent density rho, and system size. The measured initial decay rates gamma(p) of the correlation functions were compared with the predictions from a theory of polymer dynamics which uses the Oseen tensor to describe hydrodynamic interactions between monomers. Over the range of chain lengths considered (N = 30-60 monomers), the predicted scaling of gamma(p) proportional to N(-3nu) was observed at high rho, where nu is the polymer scaling exponent. The predicted gamma(p) are generally higher than the measured values. This discrepancy increases with decreasing rho, as a result in the breakdown in the conditions required for the Oseen approximation. The agreement between theory and simulation at high rho improves considerably if the theoretical expression for gamma(p) is modified to avoid sum-to-integral approximations, and if the values of (R(p)2), which are used in the theory, are taken directly from the simulation rather than being calculated using approximate scaling relations. The observed finite-size scaling of gamma(p) is not quantitatively consistent with the theoretical predictions.     

Unexpected relaxation dynamics of a self-avoiding polymer in cylindrical confinement

We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation time of the chain, tau, with the chain length N and pore diameter D. An earlier scaling analysis based on the de Gennes blob picture led to tau approximately N(2)D(13). Our numerical effort that combines molecular dynamics and Monte Carlo simulations, however, consistently produces different tau results for N up to 2000. We argue that the previous scaling prediction is only asymptotically valid in the limit N"D(53)"1, which is currently inaccessible to computer simulations and, more interestingly, is also difficult to reach in experiments. Our results are thus relevant for the interpretation of recent experiments with DNA in nano- and microchannels.     

Numerical and theoretical study on the mechanism of biopolymer translocation process through a nano-pore

We conducted a numerical study on the translocation of a biopolymer from the cis side to the trans side of a membrane through a synthetic nano-pore driven by an external electric field in the presence of hydrodynamic interactions (HIs). The motion of the polymer is simulated by 3D Langevin dynamics technique using a worm-like chain model of N identical beads, while HI between the polymer and fluid are incorporated by the lattice Boltzmann equation. The translocation process is induced by electrophoretic force, which sequentially straightens out the folds of the initial random configuration of the polymer chain on the cis side. Our simulation results on translocation time and velocity are in good quantitative agreement with the corresponding experimental ones when the surface charge on the nano-pore and the HI effect are considered explicitly. We found that the translocation velocity of each bead inside the nano-pore mainly depends upon the length of the straightened portion of the polymer in forced motion near the pore. We confirmed this by a theoretical formula. After performing simulations with different pore lengths, we observed that translocation velocity mainly depends upon the applied potential difference rather than upon the electric field inside the nano-pore.     

Diffusion of Nanoparticles in Semidilute Polymer Solutions: A Multiparticle Collision Dynamics Study

The diffusion of nanoparticles immersed in semidilute polymer solutions is investigated by a hybrid mesoscopic multiparticle collision dynamics method. Effects of polymer concentration and hydrodynamic interactions among polymer monomers are focused. Extensive simulations show that the dependence of diffusion coefficient D on the polymer concentration c agrees with Phillies equation D-exp (-αc^δ) with a scaling exponent δ≈0.97 which coincides with the experimental one in literature. For increasing nanoparticle size, the scaling prefactor α increases monotonically while the scaling exponent always keeps fixed. Moreover, we also study the diffusion of nanoparticle without hydrodynamic interactions and find that mobility of the nanoparticle slows down, and the scaling exponent is obviously different from the one in experiments, implying that hydrodynamic interactions play a crucial role in the diffusion of a nanoparticle in semidilute polymer solutions.     

Dynamic self-assembly in ensembles of camphor boats

Millimeter-sized gel particles loaded with camphor and floating at the interface between water and air generate convective flows around them. These flows give rise to repulsive interparticle interactions, and mediate dynamic self-assembly of nonequilibrium particle formations. When the numbers of particles, N, are small, particle motions are uncorrelated. When, however, N exceeds a threshold value, particles organize into ordered lattices. The nature of hydrodynamic forces underlying these effects and the dynamics of the self-assembling system are modeled numerically using Navier-Stokes equations as well as analytically using scaling arguments.     

Gel permeation chromatography: Effect of pore-size distribution

The pore-size distributions of various grades of porous glass were determined by gas desorption and mercury porosimeter measurements. This allowed the calculation of elution volumes as a function of pore diameters. The coil sizes of polystyrenes in toluene were obtained for a series of molecular weights from hydrodynamic theory and matched with pore diameters. In this manner, expected calibration curves for gel permeation chromatography could be calculated. Good agreement was found with experimental data.     

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.     

Hydrodynamic modeling of diffusion tensor properties of flexible molecules

We present a computationally efficient implementation of hydrodynamic modeling for the evaluation of diffusion tensors of molecules with internal degrees of freedom, adapted to take into account information from linear scaling computations of solvent accessible surfaces implemented in the framework of last generation continuum solvent models. Torsional angles are taken also explicitly into account, while retaining correct hydrodynamic interactions. A comparison with literature data is presented to prove the effectiveness of the approach for a wide range of molecular dimensions and solvent environments.     

Polymer translocation through a nanopore. II. Excluded volume effect

Following our previous study of a Gaussian chain translocation, we have investigated the transport of a self-avoiding chain from one sphere to another sphere through a narrow pore, using the self-consistent field theory formalism. The free energy landscape for polymer translocation is significantly modified by excluded volume interactions among monomers. The free energy barrier for the placement of one of the chain ends at the pore depends on the chain length N nonmonotonically, in contrast to the N-independence for Gaussian chains. This results in a nonmonotonic dependence of the average arrival time [tau0] on N for self-avoiding chains. When the polymer chain is partitioned between the donor and recipient spheres, a local free energy minimum develops, depending on the strength w of the excluded volume interaction and the relative sizes of the donor and recipient spheres. If the sizes of spheres are comparable, the average translocation time tau (the average time taken by the polymer, after the arrival at the pore, to convert from the donor to the recipient) increases with an increase in w for a fixed N value. On the other hand, for the highly asymmetric sizes of the donor and recipient spheres, tau decreases with an increase in w. As in the case of Gaussian chains, tau depends nonmonotonically on the pore length.     

Sedimentation of concentrated monodisperse colloidal suspensions: role of collective particle interaction forces

The sedimentation velocities and concentration profiles of low-charge, monodisperse hydroxylate latex particle suspensions were investigated experimentally as a function of the particle concentration to study the effects of the collective particle interactions on suspension stability. We used the Kossel diffraction technique to measure the particle concentration profile and sedimentation rate. We conducted the sedimentation experiments using three different particle sizes. Collective hydrodynamic interactions dominate the particle-particle interactions at particle concentrations up to 6.5 vol%. However, at higher particle concentrations, additional collective particle-particle interactions resulting from the self-depletion attraction cause particle aggregation inside the suspension. The collective particle-particle interaction forces play a much more important role when relatively small particles (500 nm in diameter or less) are used. We developed a theoretical model based on the statistical particle dynamics simulation method to examine the role of the collective particle interactions in concentrated suspensions in the colloidal microstructure formation and sedimentation rates. The theoretical results agree with the experimentally-measured values of the settling velocities and concentration profiles.     

Structures and Properties of Supported Polyimide/SnO2 Hybrid Membranes

A series of polyimide/SnO2 hybrid membranes supported on TiO2/kieselguhr-mullite were prepared from polyimide with a large amount of carboxyl and SnO2 sol via a sol-gel process. The SnO2 phase chemically linked with the polyimide through the pendant carboxyl along the polyimide. The hybrid membranes were highly homogeneous, and when the SnO2 contents reached 15wt% the SnO2 phase was observed as particles with a diameter of 5 nm dispersed in the hybrid membranes . The cross-linking between the SnO2 phase and polyimide effectively enhanced the glass temperature of the hybrid films. With the increasing of the SnO2 contents, the pore sizes of the membranes decreased, and their pore sizes were mainly focused on 3.8, 3.1, 2.8 and 2.4 nm. The hybrid membranes showed higher permeability for H2, CO2, CO and H2O when compared to the pure polyimide. The separation factors of the polyimide/SnO2 hybrid membranes with 15wt% SnO2 content for H2/N2, CO2/N2, CO/N2 and H2O/N2 were 54.1, 30.2, 35.9 and 40.1, respectively.     

Connection between the virial equation of state and physical clusters in a low density vapor

We carry out Monte Carlo simulations of physical Lennard-Jones and water clusters and show that the number of physical clusters in vapor is directly related to the virial equation of state. This relation holds at temperatures clearly below the critical temperatures, in other words, as long as the cluster-cluster interactions can be neglected--a typical assumption used in theories of nucleation. Above a certain threshold cluster size depending on temperature and interaction potential, the change in cluster work of formation can be calculated analytically with the recently proposed scaling law. The breakdown of the scaling law below the threshold sizes is accurately modeled with the low order virial coefficients. Our results indicate that high order virial coefficients can be analytically calculated from the lower order coefficients when the scaling law for cluster work of formation is valid. The scaling law also allows the calculation of the surface tension and equilibrium vapor density with computationally efficient simulations of physical clusters. Our calculated values are in good agreement with those obtained with other methods. We also present our results for the curvature dependent surface tension of water clusters.