Polymer Translocation through a Nanopore: DPD Study

Polymer Translocation and Nanopore Sequencing: A Review of Advances and Challenges

Various biological processes involve the translocation of macromolecules across nanopores; these pores are basically protein channels embedded in membranes. Understanding the mechanism of translocation is crucial to a range of technological applications, including DNA sequencing, single molecule detection, and controlled drug delivery. In this spirit, numerous efforts have been made to develop polymer translocation-based sequencing devices, these efforts include findings and insights from theoretical modeling, simulations, and experimental studies. As much as the past and ongoing studies have added to the knowledge, the practical realization of low-cost, high-throughput sequencing devices, however, has still not been realized. There are challenges, the foremost of which is controlling the speed of translocation at the single monomer level, which remain to be addressed in order to use polymer translocation-based methods for sensing applications. In this article, we review the recent studies aimed at developing control over the dynamics of polymer translocation through nanopores.

Dissipative particle dynamics simulations in colloid and Interface science: a review

Dissipative particle dynamics (DPD) is one of the most efficient mesoscale coarse-grained methodologies for modeling soft matter systems. Here, we comprehensively review the progress in theoretical formulations, parametrization strategies, and applications of DPD over the last two decades. DPD bridges the gap between the microscopic atomistic and macroscopic continuum length and time scales. Numerous efforts have been performed to improve the computational efficiency and to develop advanced versions and modifications of the original DPD framework. The progress in the parametrization techniques that can reproduce the engineering properties of experimental systems attracted a lot of interest from the industrial community longing to use DPD to characterize, help design and optimize the practical products. While there are still areas for improvements, DPD has been efficiently applied to numerous colloidal and interfacial phenomena involving phase separations, self-assembly, and transport in polymeric, surfactant, nanoparticle, and biomolecules systems.

Translocation of a Polyelectrolyte through a Nanopore in the Presence of Trivalent Counterions: A Comparison with the Cases in Monovalent and Divalent Salt Solutions

A polyelectrolyte threading through a nanopore in a trivalent salt solution is investigated by means of molecular dynamics simulations under a reflective wall boundary. By varying the chain length N and the strength E of the driving electric field applied inside the pore, the translocation time is carefully calculated to get rid of the bouncing effect because of the boundary. The results are analyzed under the scaling form ⟨τ⟩ ∼ N ^α E ^-δ and four driving force regimes; namely, the unbiased, the weakly driven, the strongly driven trumpet, and the strongly driven isoflux regime, are distinguished. The exponents are calculated in each regime and compared with the cases in the monovalent and divalent salt solutions. Owing to strong condensation of counter ions, the changes of the exponents in the force regimes are found to be nontrivial. A large increase in translocation time can be, however, achieved as the driving field is weak. The variations of the chain size, the ion condensation, and the effective chain charge show that the process is proceeded in a quasi-equilibrium way in the unbiased regime and deviated to exhibit strong nonequilibrium characteristics as E increases. Several astonishing scaling behaviors of the waiting time function, the translocation velocity, and the diffusion properties are discovered in the study. The results provide deep insights into the phenomena of polyelectrolyte translocation in various salt solutions at different driving forces.

Investigation of Magneto Hydro-Dynamics Effects on a Polymer Chain Transfer in Micro-Channel Using Dissipative Particle Dynamics Method

In this paper, the effect of Magneto Hydro-Dynamics (MHD) on a polymer chain in the micro channel is studied by employing the Dissipative Particle Dynamics simulation (DPD) method. First, in a simple symmetric micro-channel, the results are evaluated and validated for different values of Hartmann (Ha) Number. The difference between the simulation and analytical solution is below 10%. Then, two types of polymer chain including short and long polymer chain are examined in the channel and the effective parameters such as Ha number, the harmony bond coefficient or spring constant (K), and the length of the polymer chain (N) are studied in the MHD flow. It is shown that by increasing harmony bond constant to 10 times with Ha = 20, the reduction of about 80% in radius of gyration squared, and half in polymer length compared to Ha = 1 would occur for both test cases. For short and long length of polymer, proper transfer of a polymer chain through MHD particles flow is observed with less perturbations (80%) and faster polymer transfer in the symmetric micro-channel.

Translocation of Star Polyelectrolytes through a Nanopore

The electric field driven translocation of charged star polymers through a cylindrical nanopore has been studied using dissipative particle dynamics simulations. The critical field strength required to induce translocation depends on both the number of arms and the number of beads per arm. It may therefore be possible to separate star polyelectrolytes of different arm lengths using electric field driven translocation through a nanopore. The average translocation time exhibits nonmonotonic variation with the number of arms for good solvent conditions. During translocation, a star polymer with many arms is stretched along the pore axis to a lesser extent as compared to its linear counterpart. Unlike a linear chain that shows tension propagation with large tensions for bonds about to enter the pore, a star has the tensest bonds closest to the branch point whose connectivity to multiple arms raises difficulty for its entry and passage.

Effects of solvent quality and non-equilibrium conformations on polymer translocation

The conformation and its relaxation of a single polymer depend on solvent quality in a polymer solution: a polymer collapses into a globule in a poor solvent, while the polymer swells in a good solvent. When one translocates a polymer through a narrow pore, a drastic conformational change occurs such that the kinetics of the translocation is expected to depend on the solvent quality. However, the effects of solvent quality on the translocation kinetics have been controversial. In this study, we employ a coarse-grained model for a polymer and perform Langevin dynamics simulations for the driven translocation of a polymer in various types of solvents. We estimate the free energy of polymer translocation using steered molecular dynamics simulations and Jarzynski's equality and find that the free energy barrier for the translocation increases as the solvent quality becomes poorer. The conformational entropy contributes most to the free energy barrier of the translocation in a good solvent, while a balance between entropy and energy matters in a poor solvent. Interestingly, contrary to what is expected from the free energy profile, the translocation kinetics is a non-monotonic function of the solvent quality. We find that for any type of solvent, the polymer conformation stays far away from the equilibrium conformation during translocation due to an external force and tension propagation. However, the degree of tension propagation differs depending on the solvent quality as well as the magnitude of the external force: the tension propagation is more significant in a good solvent than in a poor solvent. We illustrate that such differences in tension propagation and non-equilibrium conformations between good and poor solvents are responsible for the complicated non-monotonic effects of solvent quality on the translocation kinetics.

Translocation of Charged Polymers through a Nanopore in Monovalent and Divalent Salt Solutions: A Scaling Study Exploring over the Entire Driving Force Regimes

Langevin dynamics simulations are performed to study polyelectrolytes driven through a nanopore in monovalent and divalent salt solutions. The driving electric field E is applied inside the pore, and the strength is varied to cover the four characteristic force regimes depicted by a rederived scaling theory, namely the unbiased (UB) regime, the weakly-driven (WD) regime, the strongly-driven trumpet (SD(T)) regime and the strongly-driven isoflux (SD(I)) regime. By changing the chain length N, the mean translocation time is studied under the scaling form 〈 τ 〉 ∼ N α E - δ . The exponents α and δ are calculated in each force regime for the two studied salt cases. Both of them are found to vary with E and N and, hence, are not universal in the parameter's space. We further investigate the diffusion behavior of translocation. The subdiffusion exponent γ p is extracted. The three essential exponents ν s , q, z p are then obtained from the simulations. Together with γ p , the validness of the scaling theory is verified. Through a comparison with experiments, the location of a usual experimental condition on the scaling plot is pinpointed.

Electrostatic interactions in dissipative particle dynamics-Ewald-like formalism, error analysis, and pressure computation

An accurate time evolution of charged species having exponentially smeared out charge density (Slater type charge distribution) in dissipative particle dynamic (DPD) simulations necessitates the optimal choice of the Ewald splitting parameter (α), charge smearing length (λ), and real space cutoff (c) when the Ewald summation or its variant such as particle-particle particle-mesh or particle-mesh Ewald is employed for long range electrostatics. The present article offers the error estimates in the electrostatic energy and the force as a function of α and β(1/λ) on account of spherical truncation c in real space. These error estimate formulae are validated by our DPD simulation results. We also give here an Ewald-like derivation for electrostatic energy and force for the Slater type charge density. A quick estimate of the electrostatic pressure without the use of the tedious expression which involves three dimensional Fourier transforms is also presented, and its range of validity is discussed. The basis for the proposed formula for pressure is the fact that the minimum-image truncation in many cases allows one to compute the thermodynamic quantities with reasonable accuracy.

Suspended particle transport through constriction channel with Brownian motion

It is well known that translocation events of a polymer or rod through pores or narrower parts of micro- and nanochannels have a stochastic nature due to the Brownian motion. However, it is not clear whether the objects of interest need to have a larger size than the entrance to exhibit the deviation from the dynamics of the surrounding fluid. We show by numerical analysis that the particle injection into the narrower part of the channel is affected by thermal fluctuation, where the particles have spherical symmetry and are smaller than the height of the constriction. The Péclet number (Pe) is the order parameter that governs the phenomena, which clarifies the spatio-temporal significance of Brownian motion compared to hydrodynamics. Furthermore, we find that there exists an optimal condition of Pe to attain the highest flow rate of particles relative to the dispersant fluid flow. Our finding is important in science and technology from nanopore DNA sequencers and lab-on-a-chip devices to filtration by porous materials and chromatography.

Driven polymer translocation in good and bad solvent: Effects of hydrodynamics and tension propagation

We investigate the driven polymer translocation through a nanometer-scale pore in the presence and absence of hydrodynamics both in good and bad solvent. We present our results on tension propagating along the polymer segment on the cis side that is measured for the first time using our method that works also in the presence of hydrodynamics. For simulations we use stochastic rotation dynamics, also called multiparticle collision dynamics. We find that in the good solvent the tension propagates very similarly whether hydrodynamics is included or not. Only the tensed segment is by a constant factor shorter in the presence of hydrodynamics. The shorter tensed segment and the hydrodynamic interactions contribute to a smaller friction for the translocating polymer when hydrodynamics is included, which shows as smaller waiting times and a smaller exponent in the scaling of the translocation time with the polymer length. In the bad solvent hydrodynamics has a minimal effect on polymer translocation, in contrast to the good solvent, where it speeds up translocation. We find that under bad-solvent conditions tension does not spread appreciably along the polymer. Consequently, translocation time does not scale with the polymer length. By measuring the effective friction in a setup where a polymer in free solvent is pulled by a constant force at the end, we find that hydrodynamics does speed up collective polymer motion in the bad solvent even more effectively than in the good solvent. However, hydrodynamics has a negligible effect on the motion of individual monomers within the highly correlated globular conformation on the cis side and hence on the entire driven translocation under bad-solvent conditions.

Polyelectrolyte Threading through a Nanopore

Threading charged polymers through a nanopore, driven by electric fields E, is investigated by means of Langevin dynamics simulations. The mean translocation time 〈 τ 〉 is shown to follow a scaling law Nα, and the exponent α increases monotonically from 1.16 (4) to 1.40 (3) with E. The result is double-checked by the calculation of mean square displacement of translocation coordinate, which asserts a scaling behavior tβ (for t near τ) with β complying with the relation αβ = 2. At a fixed chain length N, 〈τ〉 displayed a reciprocal scaling behavior E-1 in the weak and also in the strong fields, connected by a transition E-1.64(5) in the intermediate fields. The variations of the radius of gyration of chain and the positions of chain end are monitored during a translocation process; far-from-equilibrium behaviors are observed when the driving field is strong. A strong field can strip off the condensed ions on the chain when it passes the pore. The total charges of condensed ions are hence decreased. The studies for the probability and density distributions reveal that the monomers in the trans-region are gathered near the wall and form a pancake-like density profile with a hump cloud over it in the strong fields, due to fast translocation.

Modeling Aggregation of Ionic Surfactants Using a Smeared Charge Approximation in Dissipative Particle Dynamics Simulations

Using dissipative particle dynamics (DPD) simulations, we explore the specifics of micellization in the solutions of anionic and cationic surfactants and their mixtures. Anionic surfactant sodium dodecyl sulfate (SDS) and cationic surfactant cetyltrimethylammonium bromide (CTAB) are chosen as characteristic examples. Coarse-grained models of the surfactants are constructed and parameterized using a combination of atomistic molecular simulation and infinite dilution activity coefficient calibration. Electrostatic interactions of charged beads are treated using a smeared charge approximation: the surfactant heads and dissociated counterions are modeled as beads with charges distributed around the bead center in an implicit dielectric medium. The proposed models semiquantitatively describe self-assembly in solutions of SDS and CTAB at various surfactant concentrations and molarities of added electrolyte. In particular, the model predicts a decline in the free surfactant concentration with the increase of the total surfactant loading, as well as characteristic aggregation transitions in single-component surfactant solutions caused by the addition of salt. The calculated values of the critical micelle concentration reasonably agree with experimental observations. Modeling of catanionic SDS-CTAB mixtures show consecutive transitions to worm-like micelles and then to vesicles caused by the addition of CTAB to micellar solution of SDS.

Self-assembled polymersomes formed by symmetric, asymmetric and side-chain-tethered coil-rod-coil triblock copolymers

Self-assembly behaviors of coil-rod-coil copolymers in selective solvents are explored by dissipative particle dynamics. The morphological phase diagram as a function of rod length and coil length shows five distinct types of aggregates, including spherical micelles, worm-like micelles, disk-like aggregates, honeycomb structures, and polymersomes. Small polymersomes are formed at rather poor alignment associated with monolayered rod domains. Some of the rods are even lying perpendicular to the radial direction. For symmetric copolymers (CmRxCm), the condition of vesicle formation is restricted to short coil and rod lengths. To favor the formation of CRC-polymersomes, two architecture modifications are adopted. One is to increase the coil length asymmetrically to be CmRxCn, where n > m. The other one is to tether a T-block onto the middle of the rod-block as Cm(RxTy)Cm copolymers. For those CRC-polymersomes, structural, transport, and mechanical properties of the vesicular membrane are determined, including membrane thickness, area density of coil blocks, order parameter, solvent permeability, frequency of flip-flop, membrane tension, and stretching and bending moduli. The influences of the coil length (n) and tethered block length (y) on membrane properties are examined. Finally, the mechanism of membrane fusion between CRC-polymersomes is investigated. The fusion process involves four stages and in the contact region the rods lying perpendicular to the radial direction of the polymersome play the key role. The encounter of two vesicles may result in a fused, hemifused, or non-fused polymersome. The final fate is determined by the competition between membrane tension and the steric barrier of the coil corona. The fusion outcome may change if the tension is altered by manipulating the lumen pressure.