## 4 Discussion  
For water solutions containing protein and photoinitiator, we attributed the cross-linking to two-photon polymerization when using femtosecond lasers with wavelengths of 522 nm and 525 nm due to the very small absorption (see Supplementary Materials, Figure S2 and Table S3). Curve fitting using a simple logarithmic equation based on two-photon polymerization sufficiently fitted the experimental data for both in-channel and on-surface fabrication. It is noteworthy that this curve fitting equation was sufficient for both polymerization processes despite the differences in surface properties and light propagation. We showed that the total accumulated fluence was the physically relevant parameter to determine the feature size. Feature sizes become broader for in-channel fabrication. The broader feature sizes are most likely caused by a combination of the following three aspects. The first one is spherical aberration related to laser propagation in the three different refractive index media. Specifically, the laser beam must traverse through air, glass, and protein solution for in-channel fabrication, which significantly decreases the fabrication resolution. The second is scattering due to the roughness of glass surfaces induced by microchannel fabrication. The last is the refraction of the laser beam by the curved surface, probably produced by the second heat treatment for surface smoothing, as seen in Figure 2c. Another issue of employing a pure water solution was the formation of cavitation bubbles, which inhibited us from fabricating the protein structure at the bottom of a microchannel. These facts motivated us to change the solvent to glycerol-water solvents, as further discussed later. The multi-protein integration concept was demonstrated by the two-step integration of EGFP and BSA line patterns. In our experiments, we struggled with background signals originating from EGFP and R6G that non-specifically adhered to the roughened surfaces. Neutralizing the microchannel surfaces before fabrication by incubation with BSA or milk buffer for non-specific surface coating could eliminate the adsorption of those molecules to reduce the background noise. In particular, the roughened areas of the microchannel seemed to adsorb more protein molecules, creating strong background signals. One could also consider coating the channel with a thin layer of inert polymer such as parylene. We introduced glycerol-water solvents due to three motivations: (i) the reduction of water fraction to eliminate the generation of cavitation bubbles, (ii) the replacement of DMSO in fabrication for better fabrication resolution, and (iii) the improvement of the refractive index matching. From our results, it seems that we achieved improvements of the three points in combination. One should note that although glycerol itself is viscous, glycerol-water mixtures can increase fluidity due to the polarity of water molecules [28]. Higher viscosity would be advantageous for well-connected fabrication, while higher fluidity is advantageous for microfluidic flow. From the marginal difference in feature size for the fabrication on the surface and inside the microchannels when using the glycerol-water solvents, we can deduce that refractive index matching has abolished most of the factors increasing the feature size discussed before, i.e., aberration, scattering, and refraction. We expect the refractive index to vary with protein concentration as well as glycerol concentration. We envision that one could adjust the glycerol concentration to meet the refractive index matching for any protein concentration. Further, we assume that glycerol hardly contributes to the cross-linking process. It could be locally radicalized at the hydroxyl residues in a manner comparable to the local radicalization of water molecules when the photoinitiator or radicalized protein interacts with solvent molecules.