Molecular Detection and Force Spectroscopy in Solid-State Nanopores with Integrated Optical Tweezers - Nanopores: Sensing and Fundamental Biological Interactions - page 43

Phenomenologically, one can interpret this force as the electrophoretic

pulling force F ¼ Q eff D V on the molecule, where Q eff is the effective molecular

line charge density and DV is the applied voltage [ 6 ]. Comparison of the slope of the

1D force curve to the known line charge density of dsDNA (2 e /bp) would in
this view yield a measure of the charge reduction caused by screening in the
ionic solution.
Further measurements, however, prove this model to be too simple. The dsDNA
force curves, while always linear, are found to vary in slope when performed under
different experimental conditions. Particularly, the slope is found to depend on
nanopore diameter [ 16 ]; smaller pores are found to yield higher levels of force per
unit voltage when all other conditions are kept constant (Fig. 2.7b ). Concurrently,
the ionic strength of the measurement solution is also found to affect the slope [ 13 ],
with lower molarity salt resulting in greater measured force per unit voltage
(Fig. 2.7c ). As pure counterion screening should not be changed by shifting in
these conditions, the purely electrophoretic model is shown to be incomplete; there
must be forces that are unaccounted for in the current description. A revised model
[ 16 - 19 ] that captures the results well reveals at least one of those additional forces:
electroosmotic drag.

2.5 Modeling: Electrophoresis and Electroosmotic Shear

Charged ions in an electric field experience an electrostatic force. When these ions
are in solution, their motion due to this force tends to drag along surrounding liquid
molecules. Near a charged surface, the density of counterions is much higher than
that of coions, creating a unidirectional net fluid flow in a process called electroos-
mosis. This effect is especially pertinent to nanopore measurements: because of the
small scale, the entire volume contained inside the pore is effectively near a charged
surface (the walls of the pore). The introduction of a charged molecule like dsDNA
into that confined space will further modify the fluid flow profile. Fluid motion
creates a drag force on the captured molecule, affecting the net force acting on it,
and it must therefore be accounted for in a model describing the system. The forces
used in the present model are detailed in Fig. 2.8a . The net force created by the
applied voltage is in fact the electrophoretic force reduced by the electroosmotic
drag on the molecule, and it is this combination that is opposed by the restoring
force of the optical tweezer.
Ghosal [ 17 ] and independently van Dorp et al. [ 16 ] showed that the Poisson-
Boltzmann relation can be combined with the Stokes equation such that it describes
the force on a captured molecule in a nanopore:

2 pe F ðaÞ F ðRÞ ð Þ

F meas ¼ D V; (2.1)

ln ðR=aÞ