Blocker Effect on Diffusion Resistance of a Membrane Channel: Dependence on the Blocker Geometry

Abstract

Being motivated by recent progress in nanopore sensing, we develop a theory of the effect of large analytes, or blockers, trapped within the nanopore confines, on diffusion flow of small solutes. The focus is on the nanopore diffusion resistance which is the ratio of the solute concentration difference in the reservoirs connected by the nanopore to the solute flux driven by this difference. Analytical expressions for the diffusion resistance are derived for a cylindrically symmetric blocker whose axis coincides with the axis of a cylindrical nanopore in two limiting cases where the blocker radius changes either smoothly or abruptly. Comparison of our theoretical predictions with the results obtained from Brownian dynamics simulations shows good agreement between the two.

Figure 6.

Cylinder of radius $R$ and length $b$ with reflecting side wall. The left face of the cylinder is absorbing except its central part covered by a reflecting circular disk of radius $a$. The absorbing part of this face is colored in red.

Figure 7.

Interpolating function $g\left(\zeta \right)$, eq 3.5, $\zeta a/R$, (solid curve) and the values of this function obtained from our Brownian dynamics simulations (circles).

Figure 1.

(a, b) Schematic representation of a cylindrical channel with a blocker formed by two cones connected by their bases, an example of a smoothly varying blocker radius (panel (a)) and with a blocking cylinder, an example of an abruptly varying blocker radius (panel (b)).

Figure 2.

Constant flux $J$ injected into the channel near its left opening and two its components $J_{-}$ and $J_{+}$ escaping the channel through its left and right openings, respectively.

Figure 3.

Schematic representation of a cylindrical channel containing a blocking cylinder.

Figure 4.

Function $M\left(\zeta \right)$, eq 3.16, $\zeta =a/R$.

Figure 5.

(a, b) Constant fluxes injected near the reflecting end of the interval and flowing to its absorbing end: from left to right in panel (a) and in the opposite direction in panel (b).