2.2.2. Design and fabrication of microchannels
From the permeation coefficient determined in Section 2.2.2 and the designated dialysis residence time, the specific surface area of the dialysis membrane—the channel area with respect to the channel volume—was determined. As shown in Fig. 2, a microchannel is assumed to have a dialysis membrane sandwiched between a feed-side channel and a permeation side channel, and GdnHCl permeates from the feed side to the permeation side through the dialysis membrane. When GdnHCl solution was supplied with the concentrations c f0 [mol/L] and c p0 [mol/L] and flow ratesv f [m3/s] andv p [m3/s] from the inlet of the feed-side channel and the permeation side channel, the following equation can be derived for the mass balance of GdnHCl, assuming thatv f and v p are constant throughout the flow channel:
\begin{equation} \text{\ \ }\frac{v_{p}+v_{f}}{v_{p}\cdot v_{f}}\cdot\frac{P\cdot WZ}{L}=\ln\frac{c_{f0}-c_{pZ}}{c_{fZ}-c_{p0}},\ (3)\nonumber \\ \end{equation}
where W [m] and Z [m] represent the width and length of the microchannel, and c fZ [mol/L] and c pZ [mol/L] are the concentrations of GdnHCl at the feed side and permeation side outlets, respectively. The following formula can be established for the mass balance of the inlet and outlet:
\begin{equation} \text{\ \ }\left(c_{fZ}-c_{f0}\right)\cdot v_{f}+\left(c_{pZ}-c_{p0}\right)\cdot v_{p}=0\ (4)\nonumber \\ \end{equation}
At the flow channel design stage, assuming that a sufficient permeate flow rate is applied (v p>> v f), eq. (3) can be simplified to eq. (5).
\begin{equation} \text{\ \ }\frac{1}{v_{f}}\cdot\frac{P\cdot WZ}{L}=\ln\frac{c_{f0}-c_{pZ}}{c_{fZ}-c_{p0}}\ \ (5)\nonumber \\ \end{equation}
When using the channel height on the feed side d [m] and the residence time τ [s], the channel volume is WZd =v f·τ , and eq. (5) becomes
\begin{equation} \text{\ \ }\frac{\tau}{d}\cdot\frac{P}{L}=\ln\frac{c_{f0}-c_{pZ}}{c_{fZ}-c_{p0}}\text{\ \ }\left(6\right).\nonumber \\ \end{equation}
In this study, the standard residence time, τ , of the microchannel was set to 20 minutes, much shorter than the residence time of conventional dialysis processes, which usually take several days, and longer than the time required for the folding of the model enzyme, CA, which is around 10 minutes (Ikai et al., 1978). Within this residence time, the channel height d (= WZd /WZ ) required to reduce the GdnHCl concentration from c f0 = 5 M for protein unfolding to c fZ = 0.5 M required for refolding (Cleland & Wang, 1992; Wetlaufer & Xie, 1995) was determined to be 500 μm, using eqs. (4) and (6).
The channel length was determined by setting a feed volume flow ratev f = 0.05 mL/min and a channel width of 5 mm, to be 40 cm. Using these values, serpentine type microchannels were fabricated (Figure 3). A GdnHCl solution with or without CA was fed into the feed-side inlet, and pure water or folding buffer was fed from the permeation side inlet. As the permeate side channel, poly (methyl methacrylate) (PMMA), which has strength, transparency, and chemical resistance, was used. As the feed-side channel for introducing proteins, poly (dimethylpolysiloxane) (PDMS), which has transparency, low damage, and low adsorptivity to protein, was used. The PDMS flow path was prepared by first fabricating a machined PMMA (convex) mold, into which PDMS prepolymer mixture (Sylgard 184) was poured, and an incubator LTI-601SD (EYELA, Tokyo, Japan) was used for curing the PDMS for one hour at 60 °C (Briones et al., 2006).