## 2 Materials and Methods
### Atomic Force Microscopy Measurements  
AFM measurements were performed in air analogously to our previous papers [22; 25; 26]. The AFM images were obtained with a Titanium multimode atomic force microscope (which pertains to the equipment of the \"Human Proteome\" Core Facility of the Institute of Biomedical Chemistry, supported by the Ministry of Education and Science of the Russian Federation, agreement 14.621.21.0017, unique project IDRFMEFI62117X0017; NT-MDT, Zelenograd, Russia) equipped with NSG10 cantilevers (\"TipsNano\", Zelenograd, Russia; 47-150 kHz resonant frequency, 0.35-6.1 N/m force constant). The microscope was operated in intermittent contact mode. The microscope was preliminarily calibrated using a TGZ1 calibration grating (NT-MDT, Russia; step height 21.4 \(\pm\) 1.5 nm). The atomic force microscope was operated with the standard NOVA Px software (NT-MDT, Moscow, Zelenograd, Russia) supplied with the microscope. For each substrate incubated in the HRP solution, the number of frames was \(\geq\)10, and the number of objects imaged in each sample was \(\geq\)500. The AFM images were obtained, treated and exported in ASCII format with the standard NOVA Px software (NT-MDT, Moscow, Zelenograd, Russia). The relative density of the distribution of the imaged objects with height \(\rho(h)\) was calculated as reported by [PERSON] et al. [28] as follows:  
\[\rho(h)=(N_{h}/N)\times 100\% \tag{1}\]  
Figure 2: Schematic illustration of the direct surface adsorption of HRP from its aqueous solutions on mica substrates to study its adsorption using AFM. In Equation (1), \(N_{h}\) is the number of AFM-imaged objects with height \(h\), while \(N\) is the total number of AFM-imaged objects [28]. The so-calculated distributions are presented in the form of \(\rho(h)\) curves (density function plots [28]). The aggregation state of the HRP enzyme was characterized using parameter \(\alpha\), which was calculated as the ratio between the relative content of aggregates and that of monomers:  
\[\alpha=\rho_{2}(h)/\rho_{1}(h) \tag{2}\]  
where \(\rho_{1}\) and \(\rho_{2}\) are the values of the density of distributions, corresponding to monomeric and oligomeric (aggregated) HRP, respectively. For mica-adsorbed HRP, the density function plot \(\rho(h)\) typically has two characteristic peaks corresponding to aggregated and monomeric HRP, respectively [25]. Accordingly, the \(\alpha\) value was used to characterize the ratio between the content of aggregates and monomers. In order to determine the relative content of HRP monomers and aggregates after adsorption on mica substrates, we performed an approximation of the experimental \(\rho(h)\) curves using the root mean square method [7]:  
\[\rho(h)=\rho_{1}(h)+\rho_{2}(h)=K_{1}\frac{\left(h-m_{1}\right)^{2}}{b_{1}^{2 }}\exp\left(\frac{-\left(h-m_{1}\right)^{2}}{2b_{1}^{2}}\right)+K_{2}\frac{ \left(h-m_{2}\right)^{2}}{b_{2}^{2}}\exp\left(\frac{-\left(h-m_{2}\right)^{2} }{2b_{2}^{2}}\right) \tag{3}\]  
where \(K_{1}\), \(m_{1}\) and \(b_{1}\) are the parameters of the distribution corresponding to monomers, and \(K_{2}\), \(m_{2}\) and \(b_{2}\) are those corresponding to aggregates. The number of AFM-visualized objects, normalized per 400 \(\upmu\)m\({}^{2}\) area of the substrate surface (\(N_{norm}\)), was calculated according to [28] as follows:  
\[N_{norm}=\left(N\times 400\right)/\left(n\times a^{2}\right) \tag{4}\]  
where \(N\) is the number of objects visualized in one and the same experiment, \(n\) is the number of frames obtained in this experiment, and \(a\) is the linear frame size (\(\upmu\)m). In order to check whether the noise resulting from the unspecific adsorption from buffer solution is within its normal range (which typically makes up 500 objects per 400 \(\upmu\)m\({}^{2}\)[29]), blank experiments with the use of pure buffer instead of HRP enzyme solution were performed. No objects with height \(>\)0.5 nm was observed on the mica surface in the blank experiments.