Peter Cifra

Channel confinement of flexible and semiflexible macromolecules

We compare in detail the channel confinement of flexible and semiflexible chains over a broad range of confinements and chain lengths using molecular simulations. Flexible and semiflexible chains differ over the regimes involved under confinement. For the stiff chain we confirm a transition between strong and weak confinement at the tube diameter approximately equal to the chain persistence length. Deviations from the predicted behavior for confined semiflexible macromolecules in the tubelike channel under the weak confinement are explained by a tendency of chains toward ideal chain behavior. There are several indicators of this ideality based on the shape of chain extension R-confinement D curves, on the scaling of R with the chain length, on the structure factor of coil in the range of individual blobs in the channel, on ambiguity in introduction of excluded volume for confined stiff chains in theoretical treatments as well as on the reported experimental observation.

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.

Weak-to-strong confinement transition of semi-flexible macromolecules in slit and in channel

We compare confinement of stiff macromolecule in channel and in slit. Whereas in the channel a distinct and established transition exists, we elucidate here an ongoing controversy reported from previous experiment and simulation on existence of such transition in the slit. Our extensive molecular simulations in both geometries show only a very weak conformational crossover between moderate and strong confinements in slit in the same range of confinements where the distinct transition in channel is observed. In contrast to situation in channels relatively stable hairpin-like structures are not indicated around this weak transition in the slit. Observed difference from the prediction on behavior in blob regime under moderate confinement is explained by a crossover between dimensionalities in the slit and the extent of ideal conformation statistics to which the stiffer chains are prone. The strong confinement regime of stiff chain in slit characterized here has not been interpreted yet and it differs from the respective saturation-like Odijk regime in the channel.

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.

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.

Effective stiffening of DNA due to nematic ordering causes DNA molecules packed in phage capsids to preferentially form torus knots

Observation that DNA molecules in bacteriophage capsids preferentially form torus type of knots provided a sensitive gauge to evaluate various models of DNA arrangement in phage heads. Only models resulting in a preponderance of torus knots could be considered as close to reality. Recent studies revealed that experimentally observed enrichment of torus knots can be qualitatively reproduced in numerical simulations that include a potential inducing nematic arrangement of tightly packed DNA molecules within phage capsids. Here, we investigate what aspects of the nematic arrangement are crucial for inducing formation of torus knots. Our results indicate that the effective stiffening of DNA by the nematic arrangement not only promotes knotting in general but is also the decisive factor in promoting formation of DNA torus knots in phage capsids.

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.

Partitioning of polymer chains in solution with a square channel: lattice Monte Carlo simulations

Abstract Cubic lattice Monte Carlo simulation studies were conducted to examine the effect of confinement on dilute and non-dilute solutions of polymer chains in a channel with a square cross section. In dilute solutions, the partition coefficient K c with channels of different widths d followed the scaling-law prediction, and was close to the square of the partition coefficient K s with a slit of the same d . The chain with its bulk radius of gyration greater than ∼ d /2 adopted a conformation extending along the channel and, with a decreasing channel width, the chain ends were forced to face outside. The chain conformation in broader channels was a compressed random coil. The K c increased with an increasing polymer concentration φ E in the exterior solution equilibrated with the channel. In a weak confinement, K c closely followed K s 2 of the same φ E and d . The chains contracted at higher concentrations as they did in the bulk solutions. In a strong confinement, K c was smaller than K s 2 at the same φ E in the semidilute regime, and, at higher concentrations, sharply increased to the value close to K s 2 .

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...