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 fc 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.