Modeling the separation of macromolecules: A review of current computer simulation methods

Lock-key microfluidics: simulating nematic colloid advection along wavy-walled channels

Liquid crystalline media mediate interactions between suspended particles and confining geometries, which not only has potential to guide patterning and bottom-up colloidal assembly, but can also control colloidal migration in microfluidic devices. However, simulating such dynamics is challenging because nemato-elasticity, diffusivity and hydrodynamic interactions must all be accounted for within complex boundaries. We model the advection of colloids dispersed in flowing and fluctuating nematic fluids confined within 2D wavy channels. A lock-key mechanism between homeotropic colloids and troughs is found to be stronger for planar anchoring on the wavy walls compared to homeotropic anchoring on the wavy walls due to the relative location of the colloid-associated defects. Sufficiently large amplitudes result in stick-slip trajectories and even permanent locking of colloids in place. These results demonstrate that wavy walls not only have potential to direct colloids to specific docking sites but also to control site-specific resting duration and intermittent elution.

Dimension and Flexibility of Polystyrenesulfonate Chains in Methanol-Water

The influence of the relative permittivity of the solvent medium on the single-chain dimension and flexibility of sodium polystyrenesulfonate chains has been investigated in mixed solvent media of methanol and water using viscosity experiments. Particular attention has been paid to explore the effect of the added low-molar-mass electrolyte. The root-mean-square (rms) radii of gyration of the chains in the unperturbed state have been calculated by applying the Flory model, while the intrinsic persistence lengths by the Benoit-Doty equation on the basis of the Kratky-Porod worm-like chain model. Estimation of the expansion factors for the rms radius of gyration, and the electrostatic persistence length helps evaluate the rms radii of gyration and the total persistence length of polystyrenesulfonate chains in the presence of varying amount of the supporting electrolyte. The polyion chains are highly extended at low ionic strengths but exhibit coil-like behavior with small persistence lengths when an excess of the supporting electrolyte is added in all the methanol-water mixtures investigated. Specifically, in the investigated solvent media, the polystyrenesulfonate chains have been found to shrink by ∼63-65% in the θ-state from their expanded conformation in the presence of 0.0001 mol L-1 NaCl. The chain dimensions pass through a maximum as the medium becomes richer in methanol, which could be explained by the formation and breakup of internal rings involving the polyion chain and water and/or methanol molecules. The intrinsic persistence length of sodium polystyrenesulfonate in a methanol-water mixture containing 0.1 mole fraction of methanol is ca. 1.3 times that in a medium with 0.3 mole fraction of methanol, indicating that flexibility of the polyion depends appreciably on the relative permittivity of the medium.

Effects of Sequence Composition, Patterning and Hydrodynamics on the Conformation and Dynamics of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs) perform diverse functions in cellular organization, transport and signaling. Unlike the well-defined structures of the classical natively folded proteins, IDPs and IDRs dynamically span large conformational and structural ensembles. This dynamic disorder impedes the study of the relationship between the amino acid sequences of the IDPs and their spatial structures and dynamics, with different experimental techniques often offering seemingly contradictory results. Although experimental and theoretical evidence indicates that some IDP properties can be understood based on their average biophysical properties and amino acid composition, other aspects of IDP function are dictated by the specifics of the amino acid sequence. We investigate the effects of several key variables on the dimensions and the dynamics of IDPs using coarse-grained polymer models. We focus on the sequence "patchiness" informed by the sequence and biophysical properties of different classes of IDPs-and in particular FG nucleoporins of the nuclear pore complex (NPC). We show that the sequence composition and patterning are well reflected in the global conformational variables such as the radius of gyration and hydrodynamic radius, while the end-to-end distance and dynamics are highly sequence-specific. We find that in good solvent conditions highly heterogeneous sequences of IDPs can be well mapped onto averaged minimal polymer models for the purpose of prediction of the IDPs dimensions and dynamic relaxation times. The coarse-grained simulations are in a good agreement with the results of atomistic MD. We discuss the implications of these results for the interpretation of the recent experimental measurements, and for the further applications of mesoscopic models of FG nucleoporins and IDPs more broadly.

DPD Modelling of the Self- and Co-Assembly of Polymers and Polyelectrolytes in Aqueous Media: Impact on Polymer Science

This review article is addressed to a broad community of polymer scientists. We outline and analyse the fundamentals of the dissipative particle dynamics (DPD) simulation method from the point of view of polymer physics and review the articles on polymer systems published in approximately the last two decades, focusing on their impact on macromolecular science. Special attention is devoted to polymer and polyelectrolyte self- and co-assembly and self-organisation and to the problems connected with the implementation of explicit electrostatics in DPD numerical machinery. Critical analysis of the results of a number of successful DPD studies of complex polymer systems published recently documents the importance and suitability of this coarse-grained method for studying polymer systems.

Driven Transport of Dilute Polymer Solutions through Porous Media Comprising Interconnected Cavities

Driven transport of dilute polymer solutions through porous media has been simulated using a recently proposed novel dissipative particle dynamics method satisfying the no-penetration and no-slip boundary conditions. The porous media is an array of overlapping spherical cavities arranged in a simple cubic lattice. Simulations were performed for linear, ring, and star polymers with 12 arms for two cases with the external force acting on (I) both polymer and solvent beads to model a pressure-driven flow; (II) polymer beads only, similar to electrophoresis. When the external force is in the direction of a principal axis, the extent of change in the polymers’ conformation and their alignment with the driving force is more significant for case I. These effects are most pronounced for linear chains, followed by rings and stars at the same molecular weight. Moreover, the polymer mean velocity is affected by its molecular weight and architecture as well as the direction and strength of the imposed force.

Computer modeling of polymer stars in variable solvent conditions: a comparison of MD simulations, self-consistent field (SCF) modeling and novel hybrid Monte Carlo SCF approach

Computer-aided modeling is a systematic approach to grasp the physics of macromolecules, but it remains essential to know when to trust the results and when not. For a polymer star, we consider three approaches: (i) Molecular Dynamics (MD) simulations and implementing a coarse-grained model, (ii) the self-consistent field approach based on a mean-field approximation and implementing the lattice model due to Scheutjens and Fleer (SF-SCF) and (iii) novel hybrid Monte Carlo self-consistent field (MC-SCF) method, which combines a coarse-grained model driven by a Monte Carlo method and a mean-field representation driven by SF-SCF. We compare the performance of these approaches under a wide range of solvent qualities. The MD approach is formally the most exact but suffers from reasonable convergence. The mean-field approach works similarly in all solvent qualities but is quantitatively least accurate. The MC-SCF hybrid allows us to combine the benefits of the simulation route and the effective performance of SCF. We consider the center-to-end distance R_ce, the radius of gyration R_g² of the star and the polymer density profiles φ(r) of polymer-segments in it. All three methods show a good qualitative agreement one to another. The MC-SCF method is in good agreement with the scaling predictions in the whole range of solvent quality values showing that it grasps the essential physics while remaining computationally in bounds.

Direct printing of functional 3D objects using polymerization-induced phase separation

3D printing has enabled materials, geometries and functional properties to be combined in unique ways otherwise unattainable via traditional manufacturing techniques, yet its adoption as a mainstream manufacturing platform for functional objects is hindered by the physical challenges in printing multiple materials. Vat polymerization offers a polymer chemistry-based approach to generating smart objects, in which phase separation is used to control the spatial positioning of materials and thus at once, achieve desirable morphological and functional properties of final 3D printed objects. This study demonstrates how the spatial distribution of different material phases can be modulated by controlling the kinetics of gelation, cross-linking density and material diffusivity through the judicious selection of photoresin components. A continuum of morphologies, ranging from functional coatings, gradients and composites are generated, enabling the fabrication of 3D piezoresistive sensors, 5G antennas and antimicrobial objects and thus illustrating a promising way forward in the integration of dissimilar materials in 3D printing of smart or functional parts.

Capture of rod-like molecules by a nanopore: Defining an "orientational capture radius"

Both the translational diffusion coefficient D and the electrophoretic mobility μ of a short rod-like molecule (such as dsDNA) that is being pulled toward a nanopore by an electric field should depend on its orientation. Since a charged rod-like molecule tends to orient in the presence of an inhomogeneous electric field, D and μ will change as the molecule approaches the nanopore, and this will impact the capture process. We present a simplified study of this problem using theoretical arguments and Langevin dynamics simulations. In particular, we introduce a new orientational capture radius, which we compare to the capture radius for the equivalent point-like particle, and we discuss the different physical regimes of orientation during capture and the impact of initial orientations on the capture time.

Theoretical and Computational Insight into Solvent and Specific Ion Effects for Polyelectrolytes: The Importance of Local Molecular Interactions

Polyelectrolytes in solution show a broad plethora of interesting effects. In this short review article, we focus on recent theoretical and computational findings regarding specific ion and solvent effects and their impact on the polyelectrolyte behavior. In contrast to standard mean field descriptions, the properties of polyelectrolytes are significantly influenced by crucial interactions with the solvent, co-solvent and ion species. The corresponding experimental and simulation results reveal a significant deviation from theoretical predictions, which also highlights the importance of charge transfer, dispersion and polarization interactions in combination with solvation mechanisms. We discuss recent theoretical and computational findings in addition to novel approaches which help broaden the applicability of simple mean field theories.

Nano for the Public: An Exploranation Perspective

Public understanding of contemporary scientific issues is critical for the future of society. Public spaces, such as science centers, can impact the communication of science by providing active knowledge-building experiences of scientific phenomena. In contributing to this vision, we have previously developed an interactive visualization as part of a public exhibition about nano. We reflect on how the immersive design and features of the exhibit contribute as a tool for science communication in light of the emerging paradigm of exploranation, and offer some forward-looking perspectives about what this notion has to offer the domain.

Analysis Method of the Ion Current-Time Waveform Obtained from Low Aspect Ratio Solid-state Nanopores

Low aspect ratio nanopores are expected to be applied to the detection of viruses and bacteria because of their high spatial resolution. Multiphysics simulations have revealed that the ion current-time waveform obtained from low aspect ratio nanopores contains information on not only the volume of viruses and bacteria, but also the structure, surface charge, and flow dynamics. Analysis using machine learning extracts information about these analytes from the ion current-time waveform. The combination of low aspect ratio nanopores, multiphysics simulation, and machine learning has made it possible to distinguish different types of viruses and bacteria with high accuracy.

Flow-Driven Translocation of a Diblock Copolymer through a Nanopore

Using a hybrid molecular dynamic and lattice Boltzmann simulation method, we investigate the flow-driven translocation of a diblock copolymer which is composed of a hydrophilic block and a hydrophobic block through a nanopore. Our results illustrate the nontrivial translocation dynamics of diblock copolymers. We find that the increase in the number of hydrophobic segments requires a larger critical flow rate and a reduced translocation time, which implies that the separation of diblock copolymers with different fractions of hydrophobic segments can be achieved by adjusting the flow rate. Our work deepens the understanding of copolymer translocation through a nanopore and provides an insight into designing related microscaled separation devices.

Entropic Trapping of DNA with a Nanofiltered Nanopore

Elucidating the kinetics of DNA passage through a solid-state nanopore is a fertile field of research, and mechanisms for controlling capture, passage, and trapping of biopolymers are likely to find numerous technological applications. Here we present a nanofiltered nanopore device, which forms an entropic cage for DNA following first passage through the nanopore, trapping the translocated DNA and permitting recapture for subsequent reanalysis and investigation of kinetics of passage under confinement. We characterize the trapping properties of this nanodevice by driving individual DNA polymers into the nanoscale gap separating the nanofilter and the pore, forming an entropic cage similar to a "two pores in series" device, leaving polymers to diffuse in the cage for various time lengths, and attempting to recapture the same molecule. We show that the cage results in effectively permanent trapping when the radius of gyration of the target polymer is significantly larger than the radii of the pores in the nanofilter. We also compare translocation dynamics as a function of translocation direction in order to study the effects of confinement on DNA just prior to translocation, providing further insight into the nanopore translocation process. This nanofiltered nanopore device realizes simple fabrication of a femtoliter nanoreactor in which to study fundamental biophysics and biomolecular reactions on the single-molecule level. The device provides an electrically-permeable single-molecule trap with a higher entropic barrier to escape than previous attempts to fabricate similar structures.

Modeling Gel Swelling Equilibrium in the Mean Field: From Explicit to Poisson-Boltzmann Models

We develop a double mean-field theory for charged macrogels immersed in electrolyte solutions in the spirit of the cell model approach. We first demonstrate that the equilibrium sampling of a single explicit coarse-grained charged polymer in a cell yields accurate predictions of the swelling equilibrium if the geometry is suitably chosen and all pressure contributions have been incorporated accurately. We then replace the explicit flexible chain by a suitably modeled penetrable charged rod that allows us to compute all pressure terms within the Poisson-Boltzmann approximation. This model, albeit computationally cheap, yields excellent predictions of swelling equilibria under varying chain length, polymer charge fraction, and external reservoir salt concentrations when compared to coarse-grained molecular dynamics simulations of charged macrogels. We present an extension of the model to the experimentally relevant cases of pH-sensitive gels.

Simulation study on the migration of diblock copolymers in periodically patterned slits

The forced migration of diblock copolymers (A_NAB_NB) in periodically patterned slits was investigated by using Langevin dynamics simulation. The lower surface of the slit consists of stripe α and stripe β distributed in alternating sequence, while the upper one is formed only by stripe β. The interaction between block A and stripe α is strongly attractive, while all other interactions are purely repulsive. Simulation results show that the migration of the diblock copolymer is remarkably dependent on the driving force and there is a transition region at moderate driving force. The transition driving force f_t, where the transition region occurs, decreases monotonously with increasing length of block B (N_B) but is independent of the polymer length and the periodic length of the slit, which is interpreted from the free energy landscape of diblock copolymer migration. The results also show that periodic slits could be used to separate diblock polymers with different N_B by tuning the external driving force.

Conformation and Dynamics of Long-Chain End-Tethered Polymers in Microchannels

Polyelectrolytes constitute an important group of materials, used for such different purposes as the stabilization of emulsions and suspensions or oil recovery. They are also studied and utilized in the field of microfluidics. With respect to the latter, a part of the interest in polyelectrolytes inside microchannels stems from genetic analysis, considering that deoxyribonucleic acid (DNA) molecules are polyelectrolytes. This review summarizes the single-molecule experimental and molecular dynamics simulation-based studies of end-tethered polyelectrolytes, especially addressing their relaxation dynamics and deformation characteristics under various external forces in micro-confined environments. In most of these studies, DNA is considered as a model polyelectrolyte. Apart from summarizing the results obtained in that area, the most important experimental and simulation techniques are explained.

Influence of weak groups on polyelectrolyte mobilities

The ionization of dissociable groups in weak polyelectrolytes does not occur in a homogenous fashion. Monomer connectivity imposes constraints on the localization of the dissociated (charged) monomers that affect the local electric potential. As a result, the mean bare charge along a weak polyelectrolyte can vary depending on the proximity to topological features (e.g. presence of crosslinks or dangling ends). Using reaction-ensemble Monte-Carlo simulations we calculate the dissociation inhomogeneities for a few selected PE configurations, linear, rod-like, flexible four-arm star, and a star with stiff arms. An ensemble preaverage is used to obtain the annealed bare charge profile for these different polymer configurations. Using molecular dynamics simulations within a Lattice-Boltzman fluid, we investigate how the electrophoretic mobility is affected by the bare charge inhomogeneities arising from the annealed weak polyelectrolytes. Surprisingly, the mobility obtained for the situations corresponding to the predicted charge profile for annealed weak polyelectrolytes are not significantly different than the mobility obtained when all the monomers have an identical charge (under the constraint that the total polyelectrolyte bare charge is the same). This is also true for the stiff rod-like variants where conformational changes induced from the localization of the monomer charges are negligible. In salty solutions, we find that counterions are affected by the electric potential modulations induced by the topological features. Since the counterions crowd in regions where the electric potential caused by the dissociated monomers is highest, they wash-out the bare charge inhomogeneities and contribute to a more uniform effective backbone charge.

Anomalous packing and dynamics of a polymer chain confined in a static porous environment

Polymers in confined porous environments are ubiquitous throughout biology, physics, materials science, and engineering. Several experiments have suggested that in some porous environments, chain dynamics can become extremely slow. While phenomenological explanations exist, the exact mechanisms for these slow dynamics have not been fully characterized. In this work, we initiate a joint simulation-theory study to investigate chain packing and dynamics in a static porous environment. The main theoretical concept is the free energy of the chain partitioning into several chambers of the porous environment. Both the theoretical results and Langevin dynamics simulations show that chain packing in each of the chambers is predominantly independent of chain length; it is determined by the maximal packing of segments in each chamber. Dynamically, short chains (compared to the chamber size) become trapped in a single chamber and dynamics become extremely slow, characteristic of an Ogston sieving-like behavior. For longer chains, on the other hand, a hierarchy of slow dynamics is observed due to entropic trapping, characterized by sub-diffusive behavior and a temporary plateau in the mean square displacement. Due to the slow nature of the dynamics, the inevitable long-time diffusive behavior of the chains is not captured by our simulations. Theoretically, the slow dynamics are understood in terms of a free energy barrier required to thread the chain from one chamber to the next. There is overall qualitative and quantitative agreement between simulations and theory. This work provides foundations for a better understanding of how chain dynamics are affected by porous environments.

Morphology of depletant-induced erythrocyte aggregates

Red blood cells suspended in quiescent plasma tend to aggregate into multicellular assemblages, including linearly stacked columnar rouleaux, which can reversibly form more complex clusters or branching networks. While these aggregates play an essential role in establishing hemorheological and pathological properties, the biophysics behind their self-assembly into dynamic mesoscopic structures remains under-explored. We employ coarse-grained molecular simulations to model low-hematocrit erythrocytes subject to short-range implicit depletion forces, and demonstrate not only that depletion interactions are sufficient to account for a sudden dispersion-aggregate transition, but also that the volume fraction of depletant macromolecules controls small aggregate morphology. We observe a sudden transition from a dispersion to a linear column rouleau, followed by a slow emergence of disorderly amorphous clusters of many short rouleaux at larger volume fractions. This work demonstrates how discocyte topology and short-range, non-specific, physical interactions are sufficient to self-assemble erythrocytes into various aggregate structures, with markedly different morphologies and biomedical consequences.

Reducing the variance in the translocation times by prestretching the polymer

Langevin dynamics simulations of polymer translocation are performed where the polymer is stretched via two opposing forces applied on the first and last monomer before and during translocation. In this setup, polymer translocation is achieved by imposing a bias between the two pulling forces such that there is net displacement towards the trans side. Under the influence of stretching forces, the elongated polymer ensemble contains less variations in conformations compared to an unstretched ensemble. Simulations demonstrate that this reduced spread in initial conformations yields a reduced variation in translocation times relative to the mean translocation time. This effect is explored for different ratios of the amplitude of thermal fluctuations to driving forces to control for the relative influence of the thermal path sampled by the polymer. Since the variance in translocation times is due to contributions coming from sampling both thermal noise and initial conformations, our simulations offer independent control over the two main sources of noise and allow us to shed light on how they both contribute to translocation dynamics. Simulation parameter space corresponding to experimentally relevant conditions is highlighted and shown to correspond to a significant decrease in the spread of translocation times, thus indicating that stretching DNA prior to translocation could assist nanopore-based sequencing and sizing applications.

DNA Translocations through Nanopores under Nanoscale Preconfinement

To reduce unwanted variation in the passage speed of DNA through solid-state nanopores, we demonstrate nanoscale preconfinement of translocating molecules using an ultrathin nanoporous silicon nitride membrane separated from a single sensing nanopore by a nanoscale cavity. We present comprehensive experimental and simulation results demonstrating that the presence of an integrated nanofilter within nanoscale distances of the sensing pore eliminates the dependence of molecular passage time distributions on pore size, revealing a global minimum in the coefficient of variation of the passage time. These results provide experimental verification that the inter- and intramolecular passage time variation depends on the conformational entropy of each molecule prior to translocation. Furthermore, we show that the observed consistently narrower passage time distributions enables a more reliable DNA length separation independent of pore size and stability. We also demonstrate that the composite nanofilter/nanopore devices can be configured to suppress the frequency of folded translocations, ensuring single-file passage of captured DNA molecules. By greatly increasing the rate at which usable data can be collected, these unique attributes will offer significant practical advantages to many solid-state nanopore-based sensing schemes, including sequencing, genomic mapping, and barcoded target detection.

Hemoglobin-driven iron-directed assembly of gold nanoparticles

The ability to form complex 3D architectures using nanoparticles (NPs) as the building blocks and complex macromolecules that direct these assemblies remains a challenging objective for nanotechnology. Here we report results in which the partial substitution of classical Turkevich citrate-capped gold NPs by a novel, heteroaromatic ligand (L) results in NPs able to form coordination-driven assemblies mediated by free or protein-bound iron ions. The morphology of these assemblies can be tuned depending on the source of iron. To prove the concept, classical citrate and novel NPs were reacted with iron-containing protein hemoglobin (Hb). To diminish the influence of possible electrostatic interactions of native Hb and gold NPs, the reaction was performed at the isoelectric point of Hb. Moreover, thiol groups of Hb were protected with p-quinone to exclude thiol–gold bond formation. As expected, citrate-capped gold NPs are well dispersed in functionalized Hb, while L-functionalized NPs form assemblies. The blue shift of the Soret band of the functionalized Hb, when reacted with novel NPs, unambiguously confirms the coordination of a NP-anchored heteroaromatic ligand with the heme moiety of Hb. Coarse-grained molecular dynamics of this system were performed to gain information about aggregation dynamics and kinetics of iron- and hemoglobin-templated assemblies of L–NPs. A multi-scale simulation approach was employed to extend this model to longer time scales. The application of this model towards novel coordination-based assemblies can become a powerful tool for the development of new nanomaterials.

The ability to form complex 3D architectures using nanoparticles as the building blocks and complex macromolecules that direct these assemblies remains a challenging objective for nanotechnology.

Computer Simulations of Static and Dynamical Properties of Weak Polyelectrolyte Nanogels in Salty Solutions

We investigate the chemical equilibria of weak polyelectrolyte nanogels with reaction ensemble Monte Carlo simulations. With this method, the chemical identity of the nanogel monomers can change between neutral or charged following the acid-base equilibrium reaction HA ⇌ A- + H⁺. We investigate the effect of changing the chemical equilibria by modifying the dissociation constant K a . These simulations allow for the extraction of static properties like swelling equilibria and the way in which charge-both monomer and ionic-is distributed inside the nanogel. Our findings reveal that, depending on the value of K a , added salt can either increase or decrease the gel size. Using the calculated mean-charge configurations of the nanogel from the reaction ensemble simulation as a quenched input to coupled lattice-Boltzmann molecular dynamics simulations, we investigate dynamical nanogel properties such as the electrophoretic mobility μ and the diffusion coefficient D.

Electrokinetic Lattice Boltzmann Solver Coupled to Molecular Dynamics: Application to Polymer Translocation

We have developed a theoretical and computational approach to deal with systems that involve a disparate range of spatiotemporal scales, such as those composed of colloidal particles or polymers moving in a fluidic molecular environment. Our approach is based on a multiscale modeling that combines the slow dynamics of the large particles with the fast dynamics of the solvent into a unique framework. The former is numerically solved via Molecular Dynamics and the latter via a multicomponent Lattice Boltzmann. The two techniques are coupled together to allow for a seamless exchange of information between the descriptions. Being based on a kinetic multicomponent description of the fluid species, the scheme is flexible in modeling charge flow within complex geometries and ranging from large to vanishing salt concentration. The details of the scheme are presented and the method is applied to the problem of translocation of a charged polymer through a nanopores. Lastly, we discuss the advantages and complexities of the approach.

Flow-induced polymer separation through a nanopore: effects of solvent quality

Using a hybrid simulation method that combines a lattice-Boltzmann approach for the flow and a molecular dynamics model for the polymer, we investigated the effect of solvent quality on the flow-induced polymer translocation through a nanopore. We demonstrate the nontrivial dependence of the translocation dynamics of polymers on the solvent quality, i.e., the enhancement in the polymer insolubility increases the critical velocity flux and shortens the translocation time. Accordingly, we propose a new strategy to separate polymers with different solubilities via their translocations in the nanopore by adjusting the velocity flux of the flow, which appears to be promising for the design of micro-scaled polymer separation devices.

Sorting polymers by size via an array of viscous posts

DNA fragments can be sorted according to size by forcing them through an array of nanoposts. Whereas previous studies have explored solid nanoposts, this work examines nanoposts constructed out of viscous inclusions. Langevin dynamics simulations are used to study the dynamics of polymers driven through arrays of these viscous nanoposts for a range of post viscosities. The results are compared to the solid post case. Increasing post viscosity causes a decrease in the mobility of polymers traversing the array. In the limit of high post viscosity, the mobility becomes lower than in the solid post arrays, rather than converging to it. Analysis of the distributions of event times also shows that the viscous case is fundamentally different from the solid post case. The decrease in mobility in the viscous case arises from slowing down the polymer as it interacts with or even moves through the nanoposts, whereas the solid post case exhibits wrapping and unwrapping dynamics, yielding escape-like statistics. This work suggests that it may be possible to use viscous inclusions within nanofluidic and microfluidic devices to sort biomolecules with high resolution.

Modeling and Simulating the Dynamics of Type IV Pili Extension of Pseudomonas aeruginosa

Bacteria such as Pseudomonas aeruginosa use type IV pili to move across surfaces. The pili extend, attach to the surface, and then retract to move the bacteria forward. In this article, a coarse-grained model of pilus extension and attachment is developed. Simulations performed at biologically relevant conditions indicate that pilus extension is a quasistatic process such that the pili are able to relax via thermal fluctuations as it is being built and extended. Results are generated for pili with different rigidities ranging from very flexible to very stiff. It is shown that very flexible pili do not extend very far and thus would limit the bacteria to short jumps forward while stiff pili enable much greater displacements. Feasible mechanisms of attachment to the surface are also found to vary greatly between flexible and stiff pili. While it is not always the tip of flexible pili that first makes contact with the substrate, it is likely to be a part of the pili that is close to the tip. Conversely, stiff pili are much more likely to make contact with the substrate via the tip, but if not then the part of the pilus that attaches can be quite far from the tip. These results thus give insight to help resolve current discrepancies in the literature regarding pilus stiffness and the location of adhesins on pili.

Nonmonotonic DNA-length-dependent mobility in pluronic gels

Two-dimensional electrophoresis was used to analyze the mobility of DNA fragments in micellar gels of pluronic F127 (EO_{100}PO_{70}EO_{100}) and pluronic P123 (EO_{20}PO_{70}EO_{20}). The 20-3500 base pair DNA fragments were separated by size first in agarose gels, and then in pluronic gels at room temperature. In agarose gels, the DNA mobility decreases monotonically with increasing DNA length. In pluronic gels, however, the mobility varies nonmonotonically according to fragment lengths that are strongly correlated with the diameter of the spherical micelles. Brownian dynamics (BD) simulations with short-ranged intra-DNA hydrodynamic interactions were performed to numerically calculate the length-dependent mobility in pluronic lattices. The rising and falling trends, as well as the oscillations of mobility, were captured by the coarse-grained BD simulations. Molecular dynamics simulations in pluronic F127, with explicitly modeled micelle coronas, justified that the hydrodynamic interactions mediated by the complex fluid of hydrated poly(ethylene oxide) are a possible reason for the initial rise of mobility with DNA length.

Effects of Polymer Length and Salt Concentration on the Transport of ssDNA in Nanofluidic Channels

Electrokinetic phenomena in micro/nanofluidic channels have attracted considerable attention because precise control of molecular transport in liquids is required to optically and electrically capture the behavior of single molecules. However, the detailed mechanisms of polymer transport influenced by electroosmotic flows and electric fields in micro/nanofluidic channels have not yet been elucidated. In this study, a Langevin dynamics simulation was used to investigate the electrokinetic transport of single-stranded DNA (ssDNA) in a cylindrical nanochannel, employing a coarse-grained bead-spring model that quantitatively reproduced the radius of gyration, diffusion coefficient, and electrophoretic mobility of the polymer. Using this practical scale model, transport regimes of ssDNA with respect to the ζ-potential of the channel wall, the ion concentration, and the polymer length were successfully characterized. It was found that the relationship between the radius of gyration of ssDNA and the channel radius is critical to the formation of deformation regimes in a narrow channel. We conclude that a combination of electroosmotic flow velocity gradients and electric fields due to electrically polarized channel surfaces affects the alignment of molecular conformations, such that the ssDNA is stretched/compressed at negative/positive ζ-potentials in comparatively low-concentration solutions. Furthermore, this work suggests the possibility of controlling the center-of-mass position by tuning the salt concentration. These results should be applicable to the design of molecular manipulation techniques based on liquid flows in micro/nanofluidic devices.

Structural Determination of a DNA Oligomer for a Molecular Spin Qubit Lloyd Model of Quantum Computers

The global molecular and local spin-site structures of a DNA duplex 22-oligomer with site-directed four spin-labeling were simulated by molecular mechanics (MM) calculations combined with Q-band pulsed electron-electron double resonance (PELDOR) spectroscopy. This molecular-spin bearing DNA oligomer is designed to give a complex testing ground for the structural determination of molecular spins incorporated in the DNA duplex, which serves as a platform for 1D periodic arrays of two or three non-equivalent electron spin qubit systems, (AB)n or (ABC)n, respectively, enabling to execute quantum computing or quantum information processing (Lloyd model of electron spin versions): A, B and C designate non-equivalent addressable spin qubits for quantum operations. The non-equivalence originates in difference in the electronic g-tensor. It is not feasible to determine the optimal structures for such DNA oligomers having molecular flexibility only by the MM calculations because there are many local minima in energy for their possible molecular structures. The spin-distance information derived from the PELDOR spectroscopy helps determine the optimal structures out of the possible ones acquired by the MM calculations. Based on the MM searched structures, we suggest the optimal structures for semi-macromolecules having site-directed multi-spin qubits. We emphasize that for our four molecular spins embedded in the DNA oligomer the Fajer’s error analysis in PELDOR-based distance measurements was of essential importance.

Translocation Time through a Nanopore with an Internal Cavity Is Minimal for Polymers of Intermediate Length

The translocation of polymers through nanopores with large internal cavities bounded by two narrow pores is studied via Langevin dynamics simulations. The total translocation time is found to be a nonmonotonic function of polymer length, reaching a minimum at intermediate length, with both shorter and longer polymers taking longer to translocate. The location of the minimum is shown to shift with the magnitude of the applied force, indicating that the pore can be dynamically tuned to favor different polymer lengths. A simple model balancing the effects of entropic trapping within the cavity against the driving force is shown to agree well with simulations. Beyond the nonmonotonicity, detailed analysis of translocation uncovers rich dynamics in which factors such as going to a high force regime and the emergence of a tail for long polymers dramatically change the behavior of the system. These results suggest that nanopores with internal cavities can be used for applications such as selective extraction of polymers by length and filtering of polymer solutions, extending the uses of nanopores within emerging nanofluidic technologies.

Waves of DNA: Propagating excitations in extended nanoconfined polymers

We use a nanofluidic system to investigate the emergence of thermally driven collective phenomena along a single polymer chain. In our approach, a single DNA molecule is confined in a nanofluidic slit etched with arrays of embedded nanocavities; the cavity lattice is designed so that a single chain occupies multiple cavities. Fluorescent video-microscopy data shows fluctuations in intensity between cavities, including waves of excess fluorescence that propagate across the cavity-straddling molecule, corresponding to propagating fluctuations of contour overdensity in the cavities. The transfer of DNA between neighboring pits is quantified by examining the correlation in intensity fluctuations between neighboring cavities. Correlations grow from an anticorrelated minimum to a correlated maximum before decaying, corresponding to a transfer of contour between neighboring cavities at a fixed transfer time scale. The observed dynamics can be modeled using Langevin dynamics simulations and a minimal lattice model of coupled diffusion. This study shows how confinement-based sculpting of the polymer equilibrium configuration, by renormalizing the physical system into a series of discrete cavity states, can lead to new types of dynamic collective phenomena.

Effects of nanopore size on the flow-induced star polymer translocation

We study the effects of the nanopore size on the flow-induced capture of the star polymer by a nanopore and the afterward translocation, using a hybrid simulation method that couples point particles into a fluctuating lattice-Boltzmann fluid. Our simulation demonstrates that the optimal forward arm number decreases slowly with the increase of the length of the nanopore. Compared to the minor effect of the length of the nanopore, the optimal forward arm number obviously increases with the increase of the width of the nanopore, which can clarify the current controversial issue for the optimal forward arm number between the theory and experiments. In addition, our results indicate that the critical velocity flux of the star polymer is independent of the nanopore size. Our work bridges the experimental results and the theoretical understanding, which can provide comprehensive insights for the characterization and the purification of the star polymers.

Physical confinement signals regulate the organization of stem cells in three dimensions

During embryogenesis, the spherical inner cell mass (ICM) proliferates in the confined environment of a blastocyst. Embryonic stem cells (ESCs) are derived from the ICM, and mimicking embryogenesis in vitro, mouse ESCs (mESCs) are often cultured in hanging droplets. This promotes the formation of a spheroid as the cells sediment and aggregate owing to increased physical confinement and cell-cell interactions. In contrast, mESCs form two-dimensional monolayers on flat substrates and it remains unclear if the difference in organization is owing to a lack of physical confinement or increased cell-substrate versus cell-cell interactions. Employing microfabricated substrates, we demonstrate that a single geometric degree of physical confinement on a surface can also initiate spherogenesis. Experiment and computation reveal that a balance between cell-cell and cell-substrate interactions finely controls the morphology and organization of mESC aggregates. Physical confinement is thus an important regulatory cue in the three-dimensional organization and morphogenesis of developing cells.

Coarse-grained simulations of polyelectrolyte complexes: MARTINI models for poly(styrene sulfonate) and poly(diallyldimethylammonium)

We present simulations of aqueous polyelectrolyte complexes with new MARTINI models for the charged polymers poly(styrene sulfonate) and poly(diallyldimethylammonium). Our coarse-grained polyelectrolyte models allow us to study large length and long time scales with regard to chemical details and thermodynamic properties. The results are compared to the outcomes of previous atomistic molecular dynamics simulations and verify that electrostatic properties are reproduced by our MARTINI coarse-grained approach with reasonable accuracy. Structural similarity between the atomistic and the coarse-grained results is indicated by a comparison between the pair radial distribution functions and the cumulative number of surrounding particles. Our coarse-grained models are able to quantitatively reproduce previous findings like the correct charge compensation mechanism and a reduced dielectric constant of water. These results can be interpreted as the underlying reason for the stability of polyelectrolyte multilayers and complexes and validate the robustness of the proposed models.

Flow-induced translocation of star polymers through a nanopore

We study the flow-induced translocation of the star polymers through a nanopore using a hybrid simulation method that incorporates a lattice-Boltzmann approach for the fluid into a molecular dynamics model for the polymer. Our simulation demonstrates the existence of an optimal forward arm number of the star polymers captured by the nanopore, and illustrates its significance in determining the critical velocity flux of the star polymer translocation through the nanopore. Importantly, we find that the critical velocity flux of the star polymers is independent of the arm polymerization degree, but exhibits a linear dependence on the arm number. Based on previous scaling arguments and our simulation results, we conclude a linear dependence of the critical velocity flux on the arm number of the star polymers, which can successfully describe the dynamics of the star polymer translocation. Our simulation results rationalize the experimental results for the dependence of the critical velocity flux on the arm polymerization degree and the arm number of the star polymers, which provide new insights for the characterization and the purification of the star polymers.

Computer simulations of single particles in external electric fields

Applying electric fields is an attractive way to control and manipulate single particles or molecules, e.g., in lab-on-a-chip devices. However, the response of nanosize objects in electrolyte solution to external fields is far from trivial. It is the result of a variety of dynamical processes taking place in the ion cloud surrounding charged particles and in the bulk electrolyte, and it is governed by an intricate interplay of electrostatic and hydrodynamic interactions. Already systems composed of one single particle in electrolyte solution exhibit a complex dynamical behaviour. In this review, we discuss recent coarse-grained simulations that have been performed to obtain a molecular-level understanding of the dynamic and dielectric response of single particles and single macromolecules to external electric fields. We address both the response of charged particles to constant fields (DC fields), which can be characterized by an electrophoretic mobility, and the dielectric response of both uncharged and charged particles to alternating fields (AC fields), which is described by a complex polarizability. Furthermore, we give a brief survey of simulation algorithms and highlight some recent developments.

Mesoscopic simulation of single DNA dynamics in rotational flows

In this numerical study, the transport and dynamics of an isolated DNA in rotational flow generated in a microchannel have been investigated using dissipative particle dynamics. Often, inertial flow through microchannels with a sudden change in surface structure facilitates a re-circulation or vortex region. The conformation and mobility of the bio-polymer under the influence of such rotating fluid inside a square cavity of the microchannel is analyzed. The flexible polymer chain is found to migrate towards the rotating region and follows the vortex streamline. The orientation, size and tumbling period of polymer strands are affected by the strength of the microvortex. At elevated flow rates, the macromolecule prefers to remain inside the vortex and a hydrodynamic trap is formed. Moreover, residence time of the single molecule in the microcavity is significantly influenced by the chain length and flow strength. Further, it has been demonstrated that, such entrapment duration can be strategically altered by modifying the hydrophobicity of the microchannel.