**4. Conclusions**

We determined LOD for detection of chymotrypsin by gravimetric (LOD = 1.40 ± 0.30 nM) spectrophotometric (LOD = 0.15 ± 0.01 nM) and DLS method (LOD = 0.67 ± 0.05 nM). Spectrophotometric method showed the best value of LOD, even when compared to commercial ELISA (LOD = 0.5 nM). We also determined a steady-state constant KM for the different methods with reverse Michaelis—Menten equation. The largest KM value was found for gravimetric method of chymotrypsin detection (KM = 8.6 ± 3.6 nM), followed by spectrophotometric method (KM = 3.89 ± 1.24 nM),) and then DLS method (KM = 1.03 ± 0.26 nM). We can explain observed differences in KM values by difference in α-chymotrypsin activity, which is highest and least impeded on gold nanoparticles modified with β-casein. Addition of MCH decelerates the reaction and immobilization of β-casein on the gold surface slows the α-chymotrypsin ability to cleave β-casein. The detection time for methods that we tested was comparable and takes around 30 min for chymotrypsin determination. All methods required preparation of the sensing layers or modification of AuNPs overnight. The AuNPs or gravimetric sensors could be stored for a long time (more than one month) at 4 ◦C. In terms of difficulty in operation, the optical methods offered the easier way to measure chymotrypsin. With prepared AuNPs modified by β-casein and MCH, the spectrophotometric method required only one step of protease detection based on measurement of absorbance changes after 30 min, which was simpler in comparison with ELISA. DLS method based on AuNPs requires also only one step of measurement of the Z-average. The spectrophotometric method required only 50 μL of sample, the DLS method used 100 μL, while the gravimetric method used around 2 mL. One of the advantages of the gravimetric method is that it is more robust to "impurities" in the sample. The gravimetric method can be used with natural, no-transparent samples containing fat, minerals, or other proteins, just like in milk. Optical assays require a transparent sample; however, DLS method is a little less sensitive to changes in chymotrypsin concentrations. In terms of cost of analysis, the production of gold nanoparticles is relatively inexpensive and can be scaled to industrial amounts. For optical detection of chymotrypsin, gold nanoparticles should be surface-modified using inexpensive chemicals (β-casein and MCH). While gravimetric methods also use inexpensive chemicals for modification, but the cost of quartz crystal would raise the overall cost of the sensor. This cost offset can be reduced by multiple use of the same crystal when the sensing layer is regenerated. All methods have a distinct advantage and disadvantage compared to the currently used ELISA. In contrast with ELISA, the optical and gravimetric assay are not specific to the protease. Non-specificity of response can be addressed by using chymotrypsin-specific peptide substrate [13] or by integration of advanced machine learning algorithms [14]. In conclusion, we demonstrated advantages and disadvantages of spectrophotometric, DSL and gravimetric methods in detecting chymotrypsin. These methods can be applied also for detection of other proteases and can be useful for further application in the food industry and in medicine for real-time monitoring of the protease activity. In future work we plan to explore application of the presented techniques for analysis of natural milk samples (paying particular attention to gravimetric methods). Many new analytical methods use fluorometric or colorimetric molecules for detection of protease activity [31]. Gold nanoparticles seem to be good alternative component for colorimetric detection or for amplification of existing signal (for example increase of Raman signal from a sample using gold nanoparticles). It is clear that efforts furthering the development of new low-cost methods, easily implementable in practice, which would be sensitive, and exhibiting long-term stability, still need to be developed [32].

**Author Contributions:** Conceptualization, T.H. and I.N.I.; methodology, I.P.; formal analysis, I.P.; investigation, I.P.; resources, T.H. and I.N.I.; writing—original draft preparation, I.P.; writing—review and editing, T.H. and I.N.I.; visualization, I.P.; supervision, T.H. and I.N.I.; project administration, T.H.; funding acquisition, T.H. and I.N.I. All authors have read and agreed to the published version of the manuscript.

**Funding:** A portion of this research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility, project No. CNMS2018-293. This work was funded

under the European Union's Horizon 2020 research and innovation program through the Marie Skłodowska-Curie gran<sup>t</sup> agreemen<sup>t</sup> No 690898 and by Science Agency VEGA, project No. 1/0419/20.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
