Analytical description of Ogston-regime biomolecule separation using nanofilters and nanopores

Abstract

We present a theoretical model describing Ogston ͑pore size comparable to or larger than the characteristic molecular dimension͒ sieving of rigid isotropic and anisotropic biomolecules in nanofluidic molecular filter arrays comprising of alternating deep and shallow regions. Starting from a quasi-one-dimensional driftdiffusion description, which captures the interplay between the driving electric force, entropic barrier and molecular diffusion, we derive explicit analytical results for the effective mobility and trapping time. Our results elucidate the effects of field strength, device geometry and entropic barrier height, providing a robust tool for the design and optimization of nanofilter/nanopore systems. Specifically, we show that Ogston sieving becomes negligible when the length of shallow region becomes sufficiently small, mainly due to efficient diffusional transport through the short shallow region. Our theoretical results are in line with experimental observations and provide important design insight for nanofluidic systems.

Modeling the Electrophoretic Separation of Short Biological Molecules in Nanofluidic Devices

“…Specifically, in contrast to the analytical solution presented in Ref. [16], the threedimensional BD model developed below does not make any simplifying assumptions regarding the system geometry, and is significantly more efficient than descriptions of equivalent fidelity, such as numerical solution of the Fokker-Planck equation. In fact, by comparing our simulation results with BD simulations of more complex models (rigid-rod, WLC) [14], as well as the experimental results of Fu et al [3], we show that, provided the molecules modeled are sufficiently short, the partition-coefficient-based BD model Fig.…”

“…In a subsequent publication [17], Li et al obtained a finite difference numerical solution of the Fokker-Planck description of the original (effectively two-dimensional) geometry, aiming to quantify the error associated with the dimensionality reduction introduced in Ref. [16]. Comparison of the two solutions shows that the onedimensional model overestimates the molecule mobility at most by 10À20%.…”

“…Concurrently, Li et al [16] developed a theoretical model describing the separation of short, essentially rigid biomolecules in the same type of device. In this model, valid under conditions typically satisfied by actual separation devices (e.g., sufficiently low electric field), biomolecules are modeled as point particles, with their rotational degrees of freedom captured using a partition coefficient.…”

“…When the rotational Péclet number is small (Pe r 1), the torque due to electric effects is too small to bias the thermally induced distribution of rotational states, or in other words, the rotational diffusion is fast enough for the rigid molecule to sample all possible rotational configurations equiprobably. If additionally the characteristic rotational relaxation time for the molecules is much shorter than the average residence time in one device period [16], one can model the short rigid DNA molecules as Brownian point particles by augmenting their description with a position-dependent partition coefficient (see below) which includes information on the entropic barrier associated with the interaction between geometry and the molecule finite size.…”

“…Using this model, an effective (approximate) one-dimensional Fokker-Planck model was formulated and solved in Ref. [16], yielding an analytical description of the separation process. In a subsequent publication [17], Li et al obtained a finite difference numerical solution of the Fokker-Planck description of the original (effectively two-dimensional) geometry, aiming to quantify the error associated with the dimensionality reduction introduced in Ref.…”