Tomáš Bleha

Chain Extension of DNA Confined in Channels

The mechanism of DNA elongation in nanochannels was explored by Monte Carlo simulations as a function of the channel dimension D, DNA length, and stiffness. Simulations were based on the bead-spring model, representing double-stranded DNA chains of moderate length at a high salt concentration. As a rule, the channel-induced elongation profiles of R( parallel) vs D from the simulations were in qualitative agreement with those from microfluidic measurements of DNA. The longitudinal chain elongation in narrow channels was found to be correctly predicted by the Odijk relation for the deflection regime. The scaling relation of R( parallel) vs D(-1), based on the statistics of ideal-chain blobs, was used to explain the simulation data at the intermediate channel widths. Contrary to the blob-theory presumption, the nonlinear dependence of DNA elongation R( parallel) on the chain length N was observed in simulations at moderate confinement. It was suggested that discrepancies found between the simulations and the blob theory arose from the formation of various DNA hairpin structures within channels.

Steric exclusion/adsorption compensation in partitioning of polymers into micropores in good solvents

Abstract Partitioning equilibrium between bulk and slit-like pores in dilute solution was studied by Monte Carlo (MC) simulations on a cubic lattice in the presence of attractive, polymer–pore interaction. Athermal chains with excluded volume of variable lengths were generated in a direct simulation of the equilibrium partition coefficient K . The results show that by the variation of the polymer–pore adsorption energy, ϵ , three modes of liquid chromatography of polymers in good solvents can be reproduced. In contrast to ideal chains, the compensation point where K =1, relevant to critical chromatography, was found to be a function of the chain length. The attraction energy in the compensation point ϵ c is independent of the slit width and can be identified with the critical energy of adsorption as well as with the adsorption theta point in infinite chains. The counterbalance of steric exclusion (the depletion layer) and wall attraction (the enrichment layer) at the compensation point was confirmed by a flat concentration profile across the pore. The distribution functions of the chain end-to-end distances perpendicular and parallel to slit walls were calculated. It was inferred that in wide pores corresponding to size exclusion chromatography the partitioning proceeds by the coil orientation, and, additionally, that the critical chromatography operates in the regime of weakly adsorbed chains characterized by a diffuse adsorption layer.

Persistence Lengths and Structure Factors of Wormlike Polymers under Confinement

The behavior of semiflexible chains modeling wormlike polymers such as DNA and actin in confined spaces was explored by coarse-grained Monte Carlo simulations. The persistence length P, mean end-to-end distance R2, mean radius of gyration Rg2, and the size ratio R2/Rg2 were computed for chains in slits, cylinders, and spheres. It was found that the intrinsic persistence length of a free chain undergoes on confinement substantial alteration into the apparent persistence length. The qualitative differences were found in trends of the apparent persistence lengths between slits and cylinders on one side and spheres on the other side. The quantities P, R2, Rg2, and R2/Rg2 display similar dependences upon squeezing the chains in nanopores. The above quantities change nonmonotonically with confinement in slits and cylinders, whereas they drop smoothly with decreasing radius of a sphere. For elongation of a chain in a cylinder, two regimes corresponding to strong and moderate confinements were found and compared to experiments and predictions of the blob and Odijk theories. In a spherical cavity, the toroidal chain structure with a hole in the center was detected under strong confinements. The scattering form factor S(q) computed for semiflexible confined chains revealed three regimes of behavior in a slit and a cylinder that matched up well with the scaling theory. The complex form of the function S(q) computed for a sphere was interpreted as a sign of the toroidal structure. A reasonable agreement was found between the simulations and measurements of DNA and actin filaments, confined in nano- and microfluidic channels and spherical droplets, pertaining to the changes of the persistence lengths, chain elongation, and toroidal structure formation.

Estimation of thermodynamic quality of the solvent from the concentration effect in gel permeation chromatography of polymers

Abstract Dependences of the elution volume, Ve, on the concentration of the injected polystyrene (PS), c, in gel chromatography with inorganic carriers were studied in various single and binary eluents. It was found that the dependence of Ve on c is approximately linear in the region of low concentrations and its slope depends on the thermodynamic quality of the eluent. This relationship is more pronounced for higher molecular weights. Correlation for the slope k with the limiting viscosity numbers [η] proposed earlier in the literature is not valid for thermodynamically poor eluents; however, a correlation was found for all the eluents employed between k and the product A2M, where A2 is the second virial coefficient of polymer in solution. This supports the interpretation of the concentration effect in gel chromatography of polymers as a consequence of the decreasing effective hydrodynamic volume of coils with increasing concentration. The link between the empirically found correlation of k with A2M and the existing theory of the concentration effect in g.p.c. was examined. Comparison of the virial coefficients determined from the slope k for PS in various eluents with the literature data showed that gel chromatography could yield a rapid estimate of the value A2. As has been shown by an analysis of the concentration effect on the distribution coefficient K the concentration effect leads to the formation of a non-linear isotherm and to the asymmetrical peak shapes. In the range of very low concentrations, deviations from the linear dependence of Ve on c can be expected as a result of both the sorption effect and the thermodynamic partition of the solute.

Effect of confinement on properties of stiff biological macromolecules

The behaviour of semiflexible chains, modelling biopolymers such as DNA and actin in confined spaces, was investigated by means of Monte Carlo simulations. Simulations, based on the coarse-grained worm-like chain (WLC) model, assumed confinement length-scales comparable to those used in micro- and nanofluidic devices. The end-to-end chain elongation R was determined as a function of the channel dimensions and chain bending rigidity. Three regions of chain elongation R, identified in simulations in a cylinder and a slit, were described by current theoretical concepts. In harmony with the measurements of confined DNA, an abrupt transition between the blob region at moderate confinement and the deflection region at strong cylindrical confinement was found. The conditions for hairpin formation were elucidated as a trade-off between confinement and chain stiffness. The intrinsic persistence length of unconfined polymers was calculated by four methods that provided practically identical results. However, in confined geometries only the rigorous and WLC methods predicted the dependence of apparent persistence length P on confinement in a qualitatively correct way. It was found that the simple exponential function, suitable for the description of orientation correlations in free chains is, in confined systems, limited only to short distances along the chain contour and, thus, the apparent persistence length determined by this method just reproduces the intrinsic value of P. The orientation correlations from simulations were compared with analytical predictions in the deflection regime under strong confinement and with the measurements of actin filaments.

Concentration dependence of chain dimensions and its role in gel chromatography

Abstract A theoretical model has been developed for the concentration effect in gel chromatography, i.e. the dependence of the elution volume Ve on the concentration of injected polymer c. On the basis of the theoretical relations of Yamakawa and Eizner for coil shrinkage with increasing concentration in the range of dilute polymer solutions, relations predicting the extent of the concentration effect have been derived. A comparison of the calculated and experimental data for polystyrene in tetrahydrofuran and toluene has shown that both theories slightly underestimate the extent of the concentration effect but qualitatively correctly describe its dependence on molecular mass M and on thermodynamic quality of an eluent given by the product A2M, where A2 is the second virial coefficient of the polymer-eluent system. The proposed model explains the recently established correlation between the slope of the concentration dependence of Ve and the thermodynamic quality of the eluent and theoretically accounts for the method for estimating the coefficient A2 from gel chromatographic measurements. The possibility of using the measurements of concentration effects for examining the reliability of the theoretical relations for coil shrinkage with concentration in dilute polymer solution as well as for eventual semiempirical modification of these relations is examined.

Monte-Carlo calculations of equilibrium partitioning of flexible chains into pores

Abstract The partition coefficient K of flexible coils distributed between bulk solution and a cubic pore was calculated by the Monte-Carlo method on a simple cubic lattice. Self-avoiding walks up to 100 steps have been generated with the variable intersegmental energy simulating coils in solvents of various thermodynamical quality. The coefficient K decreases rapidly from 1 in large pores to negligible values at λ over 0.8, where λ is the ratio of the characteristic dimensions of the coil and pore. The partition curve is only slightly affected by solvent quality. The marked change of coil statistics with solvent is observed in the region of large confinement of coils by pores for λ > 1. This does not seem to be properly reflected by the scaling theory. However, the local ‘conformational’ structure of chains is not influenced by pore constraints. Implications of results for the static and dynamic measurements of partition equilibrium and for transport properties of macromolecules in porous media are discussed.

Weak-to-strong penetration transition of macromolecules into a slit in theta solvent

Partitioning of polymer chains in the theta solution with a confined space of a slit was studied in a wide range of concentrations by using lattice Monte Carlo simulations. The slit width was equal to or greater than the radius of gyration of the theta chains. In the low concentration limit, the partitioning of the theta chains was indistinguishable from that of athermal chains compared at the same chain dimension. At higher concentrations but below the overlap concentration in the solution surrounding the slit, the partition coefficient was nearly independent of the concentration. With a further increase in the concentration, the partition coefficient increased toward unity, as the motional unit in the solution changed from a single chain to the concentration blob of the semidilute theta solution and the blob size decreased with an increasing concentration. The increase in the partition coefficient occurred, however, at concentrations much higher than those for the athermal solutions that showed a simila...

Gel permeation chromatography with mixed eluents: Polymer solution as mobile phase

Abstract The GPC elution behaviour of a polymer was studied when a solution of another polymer in a liquid was used as an eluent. In ternary systems containing two polymers, GPC results are influenced by the thermodynamics of polymer incompatibility. The incompatibility manifests itself both in the slope of the dependence of elution volume upon the concentration of injected polymer and in the shift of elution volumes extrapolated to zero concentration. Experimental data for systems containing poly(styrene) and poly(methyl methacrylate) have been accounted for qualitatively by theoretical views on coil shrinkage resulting from polymer incompatibility. The concentration effects of the injected polymer and the polymer in the mobile phase on elution volume are compared; further parameters affecting the separation in the systems with polymer solution as eluent are discussed.

Concentration dependence of the global and anisotropic dimensions of confined macromolecules

The chain dimension of nondilute polymer solutions confined to a slit of the width D were studied using lattice simulations. It was found that the chain compression induced in good solvents by the concentration O in confined and unconfined theta solutions. At intermediate slit widths, a region was noted where coils are squeezed along all three axes. This region is manifested as a channel on a three-dimensional surface (D,O) in both good and theta solvents. The coil anisotropy, given by the ratio of the parallel and perpendicular components of the chain dimensions R / , reaches high values at strong confinements, where coils form quasi-two-dimensional pancakes. The concentration-induced reduction of the global chain dimensions in good solvents is almost fully transmitted the parallel component . The computed effects of concentration and confinement were compared with the predictions of mean-field and scaling theories, and implications of the results to ultrathin films and layered nanocomposites were discussed. In addition, the distribution functions of the components of the end-to-end distance R perpendicular and parallel to the plates, W(R x ) and W(R y ), were calculated. The function W(R x ) combined with the concentration profile O(x) along the pore provided details of the chain structure close to walls. A marked difference in the pace of the filling up of the depletion layer was noticed between chains in theta and good solvents. From the distribution function W(R x ) and W(r y ), the highly anisotropic force-elongation relations imply the deformation of chains in confined solutions and ultrathin bulk films.