Dispersive transport of biomolecules in periodic energy landscapes with application to nanofilter sieving arrays

Abstract

We present a theoretical model for describing the electric field-driven migration and dispersion of short anisotropic molecules in nanofluidic filter arrays. The model uses macrotransport theory to derive exact integral-form expressions for the effective mobility and diffusivity of Brownian particles moving in an effective one-dimensional energy landscape. The latter is obtained by modeling the anisotropic molecules as point-sized Brownian particles with their orientational degrees of freedom accounted for by an entropy penalty term, and using a systematic projection procedure for reducing the system dimensionality to the device axial dimension. Our analytical results provide guidance for the design and optimization of nanofluidic separation systems without the need for complex numerical simulations. Comparison with numerical solution of the macrotransport equations in the actual, effectively two-dimensional, geometry shows that the one-dimensional model faithfully describes the field- and size-dependences of mobility and diffusivity, with maximum difference on the order of 10% under the experimentally relevant electric fields.

Continuous-flow macromolecular sieving in slanted nanofilter array: stochastic model and coupling effect of electrostatic and steric hindrance

“…τ trap can be obtained using the flux-over-population method from the solution of the Fokker–Planck equation under a periodic potential U ( x ) (Fig. 1d) as 22,24 where β = 1/ k B T ( k B is Boltzmann's constant, T is temperature), ε = d S / d D ( d S and d D are depths of shallow and deep regions, respectively), and α = e − β Δ F ) (Δ F is the free energy difference between the shallow and deep regions). By substituting τ trap in eqn (3) into eqn (2) and l D , l S into l ( l D = l S = l ), we obtained the stream deflection angle as follows:where Ψ = βlQE x = βlQE 0 cos θ E (Ψ: dimensionless potential energy drop).…”

“…τ trap can be obtained using the flux-over-population method from the solution of the Fokker-Planck equation under a periodic potential U(x) (Fig. 1d) as 22,24…”

“…16 These patterned nanofilter arrays have also been considered ideal experimental platforms to quantitatively understand the hindered molecular transport in porous systems. Many analytical and numerical studies have been performed on such systems for various sieving mechanisms, 10,[17][18][19][20][21][22][23][24][25] however, most theoretical studies have focused on molecular sieving in 1D nanofilter arrays and purely steric interactions. A theoretical attempt at molecular sieving in a 2D nanofilter array was briefly conducted using a steric interaction-based kinetic model derived from a 1D system, but the study did not provide a comprehensive understanding of the 2D nanofilter array.…”

Modeling the Electrophoretic Separation of Short Biological Molecules in Nanofluidic Devices

“…[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. [16].…”

Choosing the Optimal Gel Morphology in Electrophoresis Separation by a Differential Evolution Approach (Dea)

“…Their results showed the potential impact of axiallyvarying shapes within a microvoid and found qualitative differences in the dependence of effective mobility and diffusion coefficient on the driving force in capillary domains formed by cylindrical and spherical compartments. Li et al (2011) modeled dispersion of anisotropic particles moving in nanofilters operating in Ogston regime. They compared these transport parameters obtained from the 1-D analytical model (based on macrotransport theory) to the ones obtained from 2-D numerical model.…”