Proximal Capture Dynamics for a Single Biological Nanopore Sensor

Abstract

Single nanopore sensors enable capture and analysis of molecules that are driven to the pore entry from bulk solution. However, the distance between an analyte and the nanopore opening limits the detection efficiency. A theoretical basis for predicting particle capture rate is important for designing modified nanopore sensors, especially for those with covalently tethered reaction sites. Using the finite element method, we develop a soft-walled electrostatic block (SWEB) model for the alpha-hemolysin channel that produces a vector map of drift-producing forces on particles diffusing near the pore entrance. The maps are then coupled to a single-particle diffusion simulation to probe capture statistics and to track the trajectories of individual particles on the μs to ms time scales. The investigation enables evaluation of the interplay among the electrophoretic, electroosmotic, and thermal driving forces as a function of applied potential. The findings demonstrate how the complex drift-producing forces compete with diffusion over the nanoscale dimensions of the pore. The results also demonstrate the spatial and temporal limitations associated with nanopore detection and offer a basic theoretical framework to guide both the placement and kinetics of reaction sites located on, or near, the nanopore cap.

Analytic atomic gradients in the fermi‐löwdin orbital self‐interaction correction

“…[18] The idea behind FLO-SIC is to use localized Fermi orbitals in the PZ energy functional. [13][14][15] The Fermi orbitals are defined via a transformation…”

“…This can be done with a gradientbased algorithm using the energy derivative with respect to the FOD positions. [14] In this work, a conjugate gradient algorithm was used to minimize the resulting forces on the FODs. These forces were minimized until the maximum force components fell below the criterion F FOD < 10 −4 Ha/Bohr.…”

“…Many tests in the literature show that, while PZ-SIC can improve the success of DFT in situations where SIE is important, it degrades the performance in cases where DFT already works well. [7][8][9][10][11][12] Recently, Pederson and coworkers [13][14][15] reformulated the original PZ-SIC method [3] using localized Fermi-Löwdin orbitals. This Fermi-Löwdin orbital self-interaction correction (FLO-SIC) methodology maintains the original PZ total energy expression, but effectively constrains the search for the optimized unitary transformation of the orbitals by replacing the original approach with an optimization of 3M Fermi-orbital descriptor (FOD) positions.…”

Magnetic Signatures of Hydroxyl‐ and Water‐Terminated Neutral and Tetra‐Anionic Mn12‐Acetate

“…Such problems can be fixed by inclusion of self-interaction corrections. [65][66][67][68] Since the possibility of meta-stability of the tetra-anion is a key aspect of the results discussed here, we have used a new Fermi-Löwdin Orbital Self-Interaction-Correction (FLOSIC) [69][70][71][72][73][74][75][76] to determine whether the HOMO level in the highly charged negative anion is closer to zero. The procedure for self-consistently performing FLOSIC calculations is discussed by Yang et al [71] and is briefly reviewed here.…”

“…Pederson et al [69][70][71][72][73] proposed a method that incorporated the SIC into density functional calculations in terms of a set Fermi-Orbitals (FO) designated by (F iσ ). A FO is determined from the ratio of the spin density matrix evaluated at a specific point in space to the square root of the spin density at that point.…”