2.2. Methods
The permeation coefficient of the denaturant through the dialysis
membrane was obtained as described in Section 2.2.1, and this
coefficient was used to design microchannels with a high specific
surface area, in order to enable dialysis with short residence times, as
described in Section 2.2.2. Using these microchannels, the reduction of
the denaturant concentration with a predetermined residence time was
measured, as described in Section 2.2.3. Finally, refolding of the model
protein was performed using the microchannels, and refolding with a
short residence time was investigated as described in Section 2.2.4.
2.2.1.Measurement of the
permeation coefficient of GdnHCl through dialysis membranes
The characteristics of mass transfer through a dialysis membrane in
both conventional dialysis and microchannel dialysis are the same when
the same dialysis membrane is used. Therefore, the permeation
coefficient of the denaturant through the dialysis membrane obtained by
normal dialysis can be used for microchannel design. The permeation
coefficient was determined using a custom permeation cell (Fig. 1). The
dialysis membrane was sandwiched between the feed chamber and the
permeation chamber, and 1 M GdnHCl aqueous solution was poured into the
feed chamber, while pure water was poured into the permeation chamber.
In each chamber 117 mL of the appropriate solution was introduced; the
effective area of the dialysis membrane was 9.62 cm2.
Each chamber was thoroughly stirred with a stirrer tip. The absorbance
of the solution in the permeation chamber, collected at a predetermined
time, was measured to determine the GdnHCl concentration using an
ultraviolet-visible (UV-vis) spectrophotometer (JASCO, V-650
spectrometer).
By considering the mass balance of GdnHCl in the feed and permeation
chambers, and through the dialysis membrane, the following formula can
be derived.
\begin{equation}
\ \ \frac{V_{p}+V_{f}}{V_{p}\cdot V_{f}}\cdot\frac{\text{PA}}{L}dt=d(\ln{\left(\Delta c\right))},\ (1)\nonumber \\
\end{equation}where the concentration difference between the two chambers Δc =c f–c p[mol/m3], c f andc p [mol/L] are the GdnHCl concentration in
the feed and permeation chambers, and V f andV p [m3] are the volume of
the feed and permeation chambers, P [m2/s]
represents the permeation coefficient of the dialysis membrane, L[m] represents its thickness, and A[m2] is its area.
In the early stages of the permeation experiment, the GdnHCl
concentration in the permeation chamber, c p, was
low enough to assume that the concentration difference, Δc , was
almost equal to the initial concentration of the feed chamber,c f0, and the mass balance equation can be
approximated as
\begin{equation}
\text{\ \ }\frac{\text{PA}}{L}c_{f0}\cdot t=c_{p}\cdot V_{p}\ \ (2)\nonumber \\
\end{equation}The permeation coefficient of GdnHCl through dialysis membrane was
calculated using eq. (2). Atomistic molecular dynamics simulations
predicted that the diffusivity of GdnHCl depends on the concentration of
GdnHCl; for example, diffusivity at 5 M GdnHCl is around one third of
that at 1 M GdnHCl (Gannon, Larsson, Greer, & Thompson, 2008). The
permeation coefficient, P , used for the microchannel design was
modified accordingly.