Continuous-time random walk models of DNA electrophoresis in a post array: part II. Mobility and sources of band broadening

Using the two-state, continuous-time random walk model, we develop expressions for the mobility and the plate height during DNA electrophoresis in an ordered post array that delineate the contributions due to (i) the random distance between collisions and (ii) the random duration of a collision. These contributions are expressed in terms of the means and variances of the underlying stochastic processes, which we evaluate from a large ensemble of Brownian dynamics simulations performed using different electric fields and molecular weights in a hexagonal array of 1 μm posts with a 3 μm center-to-center distance. If we fix the molecular weight, we find that the collision frequency governs the mobility. On the contrary, the average collision duration is the most important factor for predicting the mobility as a function of DNA size at constant Péclet number. The plate height is reasonably well described by a single post rope-over-pulley model, provided that the extension of the molecule is small. Our results only account for dispersion inside the post array and thus represent a theoretical lower bound on the plate height in an actual device.     

Brownian dynamics simulations of electrophoretic DNA separations in a sparse ordered post array

We use Brownian dynamics simulations to analyze the electrophoretic separation of λ-DNA (48.5 kbp) and T4-DNA (169 kbp) in a hexagonal array of 1 μm diameter posts with a 3 μm center-to-center distance. The simulation method takes advantage of an efficient interpolation algorithm for the non-uniform electric field to reach an ensemble size (100 molecules) and simulation length scale (1 mm) that produces meaningful results for the average electrophoretic mobility and effective diffusion (dispersion) coefficient of these macromolecules as they move through the array. While the simulated electrophoretic mobility for λ-DNA is close to the experimental data, the simulation underestimates the magnitude of the corresponding dispersion coefficient. The simulations predict baseline resolution in a 15 mm device after 7 min using an electric field around 30 V/cm, with the resolution increasing exponentially as the electric field further decreases. The mobility and dispersivity data point out two essential phenomena that have been overlooked in previous models of DNA electrophoresis in post arrays: the relaxation time between collisions and simultaneous collisions with multiple posts.     

Single molecule study of DNA collision with elliptical nanoposts conveyed by hydrodynamics

Periodic arrays of micro‐ or nanopillars constitute solid‐state matrices with excellent properties for DNA size separation. Nanofabrication technologies offer many solutions to tailor the geometry of obstacle arrays, yet most studies have been conducted with cylinders arranged in hexagonal lattices. In this report, we investigate the dynamics of single DNA collision with elliptical nanoposts using hydrodynamic actuation. Our data show that the asymmetry of the obstacles has minor effect on unhooking dynamics, and thus confirm recent predictions obtained by Brownian dynamics simulations. In addition, we show that the disengagement dynamics are correctly predicted by models of electrophoresis, and propose that this consistency is associated to the confinement in slit‐like channels. We finally conclude that elliptical posts are expected to marginally improve the performances of separation devices.     

Rotational dynamics in supercooled water from nuclear spin relaxation and molecular simulations

Structural dynamics in liquid water slow down dramatically in the supercooled regime. To shed further light on the origin of this super-Arrhenius temperature dependence, we report high-precision (17)O and (2)H NMR relaxation data for H(2)O and D(2)O, respectively, down to 37 K below the equilibrium freezing point. With the aid of molecular dynamics (MD) simulations, we provide a detailed analysis of the rotational motions probed by the NMR experiments. The NMR-derived rotational correlation time τ(R) is the integral of a time correlation function (TCF) that, after a subpicosecond librational decay, can be described as a sum of two exponentials. Using a coarse-graining algorithm to map the MD trajectory on a continuous-time random walk (CTRW) in angular space, we show that the slowest TCF component can be attributed to large-angle molecular jumps. The mean jump angle is ～48° at all temperatures and the waiting time distribution is non-exponential, implying dynamical heterogeneity. We have previously used an analogous CTRW model to analyze quasielastic neutron scattering data from supercooled water. Although the translational and rotational waiting times are of similar magnitude, most translational jumps are not synchronized with a rotational jump of the same molecule. The rotational waiting time has a stronger temperature dependence than the translation one, consistent with the strong increase of the experimentally derived product τ(R)?D(T) at low temperatures. The present CTRW jump model is related to, but differs in essential ways from the extended jump model proposed by Laage and co-workers. Our analysis traces the super-Arrhenius temperature dependence of τ(R) to the rotational waiting time. We present arguments against interpreting this temperature dependence in terms of mode-coupling theory or in terms of mixture models of water structure.     

Motion of single long DNA molecules through arrays of magnetic columns

We present a videomicroscopy study of T4 DNA (169 kbp) in microfluidic arrays of posts formed by the self-assembly of magnetic beads. We observe DNA moving through an area of 10 000 microm(2), typically containing 100-600 posts. We determine the distribution of the contact times with the posts and the distribution of passage times across the field of view for hundreds of DNA per experiment. The contact time is well approximated by a Poisson process, scaling like the inverse of the field strength, independent of the density of the array. The distribution of passage times allows us to estimate the mean velocity and dispersivity of the DNA during its motion over distances long compared to our field of view. We compare these values with those computed from a lattice Monte Carlo model and geometration theory. We find reasonable quantitative agreement between the lattice Monte Carlo model and experiment, with the error increasing with increasing post density. The deviation between theory and experiment is attributed to the high mobility of DNA after disengaging from the posts, which leads to a difference between the contact time and the total time lost by colliding. Classical geometration theory furnishes surprisingly good agreement for the dispersivity, while geometration theory with a mean free path significantly overestimates the dispersivity.     

Molecular dynamics simulation of DNA‐directed assembly of nanoparticle superlattices using patterned templates

DNA‐directed assembly is a well developed approach in constructing desired nano‐architectures. On the other hand, E‐beam lithography is widely utilized for high resolution nano‐scale patterning. Recently, a new technique combining these two methods was developed to epitaxially grow DNA‐mediated nanoparticle superlattices on patterned substrates. However, defects are observed in epitaxial layers which restricts this technique from building large‐scale superlattices for real applications. Here we use molecular dynamics simulations to study and predict defect formation on adsorbed superlattice monolayers. We demonstrate that this epitaxial growth is energetically driven by maximizing DNA hybridization between the epitaxial layer and the substrate and that the shape anisotropy of the DNA‐mediated template posts leads to structural defects. We also develop design rules to dramatically reduce defects on epitaxial layers. Ultimately, with the assist of the computational study, this technique will open the door to constructing well‐ordered, three‐dimensional novel nanomaterials. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1687–1692     

DNA methylation-based age prediction with bloodstains using pyrosequencing and random forest regression

The use of DNA methylation to predict chronological age has shown promising potential for obtaining additional information in forensic investigations. To date, several studies have reported age prediction models based on DNA methylation in body fluids with high DNA content. However, it is often difficult to apply these existing methods in practice due to the low amount of DNA present in stains of body fluids that are part of a trace material. In this study, we present a sensitive and rapid test for age prediction with bloodstains based on pyrosequencing and random forest regression. This assay requires only 0.1 ng of genomic DNA and the entire procedure can be completed within 10 h, making it practical for forensic investigations that require a short turnaround time. We examined the methylation levels of 46 CpG sites from six genes using bloodstain samples from 128 males and 113 females aged 10–79 years. A random forest regression model was then used to construct an age prediction model for males and females separately. The final age prediction models were developed with seven CpG sites (three for males and four for females) based on the performance of the random forest regression. The mean absolute deviation was less than 3 years for each model. Our results demonstrate that DNA methylation-based age prediction using pyrosequencing and random forest regression has potential applications in forensics to accurately predict the biological age of a bloodstain donor.     

Temporal correlation functions of concentration fluctuations: an anomalous case

We calculate, within the framework of the continuous time random walk (CTRW) model, multiparticle temporal correlation functions of concentration fluctuations (CCF) in systems that display anomalous subdiffusion. The subdiffusion stems from the nonstationary nature of the CTRW waiting times, which also lead to aging and ergodicity breaking. Due to aging, a system of diffusing particles tends to slow down as time progresses, and therefore, the temporal correlation functions strongly depend on the initial time of measurement. As a consequence, time averages of the CCF differ from ensemble averages, displaying therefore ergodicity breaking. We provide a simple example that demonstrates the difference between these two averages, a difference that might be amenable to experimental tests. We focus on the case of ensemble averaging and assume that the preparation time of the system coincides with the starting time of the measurement. Our analytical calculations are supported by computer simulations based on the CTRW model.     

Decoupling of exchange and persistence times in atomistic models of glass formers

With molecular dynamics simulations of a fluid mixture of classical particles interacting with pairwise additive Weeks-Chandler-Andersen potentials, we consider the time series of particle displacements and thereby determine the distributions for local persistence times and local exchange times. These basic characterizations of glassy dynamics are studied over a range of supercooled conditions and were shown to have behaviors, most notably decoupling, similar to those found in kinetically constrained lattice models of structural glasses. Implications are noted.     

Structural dynamics of supercooled water from quasielastic neutron scattering and molecular simulations

One of the outstanding challenges presented by liquid water is to understand how molecules can move on a picosecond time scale despite being incorporated in a three-dimensional network of relatively strong H-bonds. This challenge is exacerbated in the supercooled state, where the dramatic slowing down of structural dynamics is reminiscent of the, equally poorly understood, generic behavior of liquids near the glass transition temperature. By probing single-molecule dynamics on a wide range of time and length scales, quasielastic neutron scattering (QENS) can potentially reveal the mechanistic details of water's structural dynamics, but because of interpretational ambiguities this potential has not been fully realized. To resolve these issues, we present here an extensive set of high-quality QENS data from water in the range 253-293 K and a corresponding set of molecular dynamics (MD) simulations to facilitate and validate the interpretation. Using a model-free approach, we analyze the QENS data in terms of two motional components. Based on the dynamical clustering observed in MD trajectories, we identify these components with two distinct types of structural dynamics: picosecond local (L) structural fluctuations within dynamical basins and slower interbasin jumps (J). The Q-dependence of the dominant QENS component, associated with J dynamics, can be quantitatively rationalized with a continuous-time random walk (CTRW) model with an apparent jump length that depends on low-order moments of the jump length and waiting time distributions. Using a simple coarse-graining algorithm to quantitatively identify dynamical basins, we map the newtonian MD trajectory on a CTRW trajectory, from which the jump length and waiting time distributions are computed. The jump length distribution is gaussian and the rms jump length increases from 1.5 to 1.9 A? as the temperature increases from 253 to 293 K. The rms basin radius increases from 0.71 to 0.75 A? over the same range. The waiting time distribution is exponential at all investigated temperatures, ruling out significant dynamical heterogeneity. However, a simulation at 238 K reveals a small but significant dynamical heterogeneity. The macroscopic diffusion coefficient deduced from the QENS data agrees quantitatively with NMR and tracer results. We compare our QENS analysis with existing approaches, arguing that the apparent dynamical heterogeneity implied by stretched exponential fitting functions results from the failure to distinguish intrabasin (L) from interbasin (J) structural dynamics. We propose that the apparent dynamical singularity at ～220 K corresponds to freezing out of J dynamics, while the calorimetric glass transition corresponds to freezing out of L dynamics.     

Impact of an error in the column hold-up time for correct adsorption isotherm determination in chromatography I. Even a small error can lead to a misunderstanding of the retention mechanism

The impact of a realistic error in the column hold-up time on the determination of the adsorption isotherm model was systematically investigated. Frontal analysis and the inverse method were used for the accurate determination of the adsorption isotherm. The true retention times of the breakthrough curves were used with a known hold-up time as reference. The adsorption isotherms were calculated using the same procedure that is used for real experimental adsorption isotherms, where the true hold-up time is unknown. The raw data were analyzed with calculations of adsorption energy distributions (AEDs), Scatchard plots, fitting to different rival adsorption models and finally their ability to predict true profiles. The results show that for a true Langmuir and bi-Langmuir model with an underestimated hold-up time the error may lead to a more heterogeneous model and for overestimated cases false adsorption processes like multi-layer adsorption or solute-solute interaction are assumed. The Scatchard plots for data obtained using a Langmuir adsorption isotherm are nonlinear and the AEDs show clear deviations from Langmuir behavior already at small deviations from the true hold-up time at a moderate surface coverage. The inverse method confirms the result that was obtained from the frontal analysis procedure.     

Influence of molecular weight and degree of segregation on local segmental dynamics of ordered block copolymers

Experiments in the context of block copolymer electrolyte materials have observed intriguing dependence of the ionic conductivities upon the polymer molecular weight and the degree of segregation between the blocks. Such results have been partly rationalized by invoking the spatial extent of dynamical inhomogeneities that manifest in ordered phases of block copolymers comprised of a rubbery and a glassy block. Motivated by such observations, we use molecular dynamics simulations to study the extent of spatial inhomogeneities in segmental dynamics of lamellar diblock copolymer systems where the blocks possess different mobilities. We probed the local average relaxation times and the dynamical heterogeneities as a function of distance from the interface. Our results suggest that the relaxation times of rubbery segments are strongly influenced by both the spatial proximity to the interface and the relative mobility of the glassy segments. Scaling of our results indicate that the interfacial width of the ordered phases serves as the length scale underlying the spatial inhomogeneities in segmental dynamics of the fast monomers. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 859–864     

A simple,fast, and accurate thermodynamic‐based approach for transfer and prediction of gas chromatography retention times between columns and instruments Part III: Retention time prediction on target column

This is the third part of a three‐part series of papers. In Part I, we presented a method for determining the actual effective geometry of a reference column as well as the thermodynamic‐based parameters of a set of probe compounds in an in‐house mixture. Part II introduced an approach for estimating the actual effective geometry of a target column by collecting retention data of the same mixture of probe compounds on the target column and using their thermodynamic parameters, acquired on the reference column, as a bridge between both systems. Part III, presented here, demonstrates the retention time transfer and prediction from the reference column to the target column using experimental data for a separate mixture of compounds. To predict the retention time of a new compound, we first estimate its thermodynamic‐based parameters on the reference column (using geometric parameters determined previously). The compound's retention time on a second column (of previously determined geometry) is then predicted. The models and the associated optimization algorithms were tested using simulated and experimental data. The accuracy of predicted retention times shows that the proposed approach is simple, fast, and accurate for retention time transfer and prediction between gas chromatography columns.     

Collective motions in computer models of water. Large-scale and long-time correlations

Two-particle correlation functions describing the simultaneous motion of a pair of molecules initially separated by a given distance R0 are calculated to study collective effects in the diffusive motion of water molecules in molecular dynamics models. Various types of such functions and their dependences on the interaction potential, temperature, and the number of particles in the model are considered. At short times (of the order of ten picoseconds), these functions exhibit irregular behavior depending on R0. The most nontrivial and unexpected result was the detection of correlations in the displacements of pairs of particles that extend for tens of angstroms and last for hundreds of picoseconds. Such correlations are not observed in the random walk models of noninteracting particles. It is suggested that the observed large-scale correlations reveal the vortex-like motions of the molecules.     

Generation of submicrometer structures by photolithography using arrays of spherical microlenses

This paper describes the fabrication of arrays of spherical microlenses by self-assembly of microspheres and the use of these arrays for nearfield photolithography to generate repetitive microstructures in photoresist. We used these arrays of microspheres to fabricate two types of elastomeric membranes: (i) membranes that have microspheres embedded in their surface and (ii) membranes that have hemispherical wells in their surface. Both types of membranes act as amplitude masks that pattern the intensity of illumination in the near field incident on the photoresist. Microspheres in the first type of membrane act as convergent lenses that generate recessed microstructures in positive photoresist. Hemispherical wells in the second type of membrane act as divergent lenses that produce protrusive microstructures in positive photoresist. This method can generate dense, regular arrays of microstructures with a variety of profiles--circular or hexagonal holes, circular posts, hollow posts, and cones--depending on the sizes and refractive indices of the spherical lenses and the distance between the lenses and the photoresist. This technique provides a simple route to large areas (>4 cm2) of repetitive, simple microstructures.     

On the Determination of the Hold-Up Time in Reversed Phase Liquid Chromatography

Abstract

The determination of the hold-up time in reversed phase liquid chromatography has been studied extensively for the mobile phase system methanol-water. Hold-up times obtained by static methods, linearization of homologous series and so-called “unretained compounds” are discussed and mutually compared. Several n-alkyldimethylsilyl bonded phases have been used for this investigation.

A rough estimate of the hold-up time can be obtained by using components of the mobile phase or highly concentrated salt solutions, but only for mobile phase compositions around 60% (v/v) methanol. Hold-up times accurate to 1% can be obtained over the complete range of mobile phase compositions from the linearization of net retention times of homologous series.     

Advances in square arrays through self‐assembly and directed self‐assembly of block copolymers

This review covers recent advances in developing square arrays in thin films using block copolymers. Theoretical and experimental results from self‐assembly of block copolymers in bulk and thin films, directed self‐assembly of block copolymers confined in small wells, on substrates with arrays of posts, and on chemically nanopatterned substrates, as well as applications as nanolithography are reviewed. Some future work and hypothesis are discussed. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Time-dependent quantum dynamical simulations of C2 condensation under extreme conditions

We report theoretical studies of the initial phase of bulk C(2) condensation into carbon nano-structures by means of Born-Oppenheimer and time-dependent quantum mechanical Liouville-von Neumann molecular dynamics based on the density-functional tight-binding (DFTB) framework for electrons. We observe that the time-dependent quantum mechanical approach leads to faster formation of carbon nanostructures than analogous Born-Oppenheimer simulations. Our results suggest that the condensation of bulk carbon is nonadiabatic in nature, with the critical role of electronic stopping as in ion-irradiation of materials. Contrary to time-dependent quantum mechanical simulations, Born-Oppenheimer dynamics incorrectly predict that the short carbon chains obtained from initial reactive collisions between C(2) quickly evaporate, leading to much lower probability of secondary collisions and condensation. We also discuss some deficiencies in Born-Oppenheimer dynamics that lead to unphysical charge polarization and electron transfer.     

New approach by Kriging models to problems in QSAR

Most models in quantitative structure and activity relationship (QSAR) research, proposed by various techniques such as ordinary least squares regression, principal components regression, partial least squares regression, and multivariate adaptive regression splines, involve a linear parametric part and a random error part. The random errors in those models are assumed to be independently identical distributed. However, the independence assumption is not reasonable in many cases. Some dependence among errors should be considered just like Kriging. It has been successfully used in computer experiments for modeling. The aim of this paper is to apply Kriging models to QSAR. Our experiments show that the Kriging models can significantly improve the performances of the models obtained by many existing methods.     

Structural models of protein-DNA complexes based on interface prediction and docking

Protein-DNA interactions are the physical basis of gene expression and DNA modification. Structural models that reveal these interactions are essential for their understanding. As only a limited number of structures for protein-DNA complexes have been determined by experimental methods, computation methods provide a potential way to fill the need. We have developed the DISPLAR method to predict DNA binding sites on proteins. Predicted binding sites have been used to assist the building of structural models by docking, either by guiding the docking or by selecting near-native candidates from the docked poses. Here we applied the DISPLAR method to predict the DNA binding sites for 20 DNA-binding proteins, which have had their DNA binding sites characterized by NMR chemical shift perturbation. For two of these proteins, the structures of their complexes with DNA have also been determined. With the help of the DISPLAR predictions, we built structural models for these two complexes. Evaluations of both the DNA binding sites for 20 proteins and the structural models of the two protein-DNA complexes against experimental results demonstrate the significant promise of our model-building approach.