Parallel computing for mobilities in periodic geometries.

We examine methods for calculating the effective mobilities of molecules driven through periodic geometries in the context of particle-based simulation. The standard formulation of the mobility, based on the long-time limit of the mean drift velocity, is compared to a formulation based on the mean first-passage time of molecules crossing a single period of the system geometry. The equivalence of the two definitions is derived under weaker assumptions than similar conclusions obtained previously, requiring only that the state of the system at subsequent period crossings satisfy the Markov property. Approximate theoretical analyses of the computational costs of estimating these two mobility formulations via particle simulations suggest that the definition based on first-passage times may be substantially better suited to exploiting parallel computation hardware. This claim is investigated numerically on an example system modeling the passage of nanoparticles through the slit-well device. In this case, the traditional mobility formulation is found to perform best when the Péclet number is small, whereas the mean first-passage time formulation is found to converge much more quickly when the Péclet number is moderate or large. The results suggest that, given relatively modest access to modern GPU hardware, this alternative mobility formulation may be an order of magnitude faster than the standard technique for computing effective mobilities of biomolecules through periodic geometries.

Studying first passage problems using neural networks: A case study in the slit-well microfluidic device.

This study presents deep neural network solutions to a time-integrated Smoluchowski equation modeling the mean first passage time of nanoparticles traversing the slit-well microfluidic device. This physical scenario is representative of a broader class of parametrized first passage problems in which key output metrics are dictated by a complicated interplay of problem parameters and system geometry. Specifically, whereas these types of problems are commonly studied using particle simulations of stochastic differential equation models, here the corresponding partial differential equation model is solved using a method based on deep neural networks. The results illustrate that the neural network method is synergistic with the time-integrated Smoluchowski model: together, these are used to construct continuous mappings from key physical inputs (applied voltage and particle diameter) to key output metrics (mean first passage time and effective mobility). In particular, this capability is a unique advantage of the time-integrated Smoluchowski model over the corresponding stochastic differential equation models. Furthermore, the neural network method is demonstrated to easily and reliably handle geometry-modifying parameters, which is generally difficult to accomplish using other methods.

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.

A sequential nanopore-channel device for polymer separation.

In this work, we investigated whether a series of nanopores connected by channels can be used to separate polymer mixtures by molecular size. We conducted multiscale coarse-grained simulations of semiflexible polymers driven through such a device. Polymers were modelled as chains of beads near the nanopores and as single particles in the bulk of the channels. Since polymers rarely escape back into the bulk of the channels after coming sufficiently close to the nanopores, the more computationally expensive simulations near the pores were decoupled from those in the bulk. The distribution of polymer positions after many translocations was deduced mathematically from simulations across a single nanopore-channel pair, under the reasonable assumption of identical and independent dynamics in each channel and each nanopore. Our results reveal rich polymer dynamics in the nanopore-channel device and suggest that it can indeed produce polymer separation. As expected, the mean time to translocate across a single nanopore increases with the chain length. Conversely, the mean time to cross the channels from one nanopore to the next decreases with the chain length, as smaller chains explore more of the channel volume between translocations. As such, the time between translocations is a function of the length and width of the channels. Depending on the channel dimensions, polymers are sorted by increasing length, decreasing length, or non-monotonically by length such that polymers of an intermediate size emerge first.

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.

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.