## 3 Results and Discussion  
The Order of Monolayers Defines the Effectiveness of Energy Transfer by Altering the Donor/Acceptor Ratio  
Sequential monolayers are a relatively old concept realized, for example, by electrodeposition, to obtain cadmium selenide films [33]. Organic monolayers are one of the options for surface functionalization [34; 35], with the option of islands of multidomains in the base material built in by sequential deposition [36]. Here, we obtained sequential monolayers of fluorescent proteins and QDs. The immobilization of proteins as monolayers is not broadly studied; however, it was already employed for the deposition of alcohol dehydrogenase, formaldehyde dehydrogenase, and formate dehydrogenase on gold electrodes [35]. These proteins are the enzymes of the enzymatic cascade, oxidizing methanol to CO\({}_{2}\). In our study, we focused on the fluorescent properties of monolayer-forming particles. The order of deposition should not influence the FRET direction, as the vector of energy transfer depends on the fluorescent properties of fluorophores forming the layers and the distance between them [25]. However, we found in several tests with fluorescent proteins that the order of deposition influences observed FRET-related changes. The simplest explanation for this is the different densities of both layers, resulting in varied donor/acceptor stoichiometry. Therefore, with such knowledge, one should be able to build a system with donor excess or a system with acceptor excess just by changing the protein that was deposited first. To test this hypothesis, we addressed the question of FRET efficiency between differently organized fluorescent protein monolayers, using Monte Carlo computational methods. We also examined the change in the process yield in the presence of a spacer, Jeffamine or BSA molecule. Figure 2A-C compares the results obtained for the system composed of a GFP (a donor) deposited as a first layer and an mBanana or an mCherry as a second layer, with different average densities. Similar tests were carried out for a first layer composed of an mBanana (a donor) and a second layer of an mCherry as an acceptor. In all three cases, the computational results confirm the intuitional assumption of FRET efficiency growing with an increase in the relative amount of acceptor. The final yield reaches 0.08 for a GFP-mBanana and about 0.3 for the two other tested systems. The yield is strictly defined by fluorescent protein properties (see Supplementary Files, Table S1, for detailed characteristics and parameters used in the calculation). The presence of spacers reduced FRET efficiency by about 10-40% for the shorter molecule (Jeffamine) and 30-90% for the longer spacer (BSA molecule). The actual reduction was stronger for the less efficient FRET pair, a GFP-mCherry; however, this did not significantly depend on the relative amount of acceptor. When simulations were carried out for a constant acceptor concentration and an increasing donor concentration, the FRET yield was always maximal. The yield might be reduced by the spacer introduction, without any relation to the relative concentration of a donor (Supplementary Figure S1). To verify theoretic calculations in a real experiment, we obtained several versions of the sequential protein layers deposited on a PVDF substrate (Figure 3A). The deposition was optimized for the maximum possible layer density. With a donor being the second layer, we might clearly calculate the FRET yield using fluorescent lifetime values. For this assumption, we obtained a yield of 0.055 for the GFP-mBanana pair, 0.103 for the GFP-mCherry pair, and 0.13 for the mBanana-mCherry pair.