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.

Collective Dynamics of Model Pili-Based Twitcher-Mode Bacilliforms.

Pseudomonas aeruginosa, like many bacilliforms, are not limited only to swimming motility but rather possess many motility strategies. In particular, twitching-mode motility employs hair-like pili to transverse moist surfaces with a jittery irregular crawl. Twitching motility plays a critical role in redistributing cells on surfaces prior to and during colony formation. We combine molecular dynamics and rule-based simulations to study twitching-mode motility of model bacilliforms and show that there is a critical surface coverage fraction at which collective effects arise. Our simulations demonstrate dynamic clustering of twitcher-type bacteria with polydomains of local alignment that exhibit spontaneous correlated motions, similar to rafts in many bacterial communities.