## 2 Materials and Methods
### Methods  
ESR measurements were performed using an X-band Bruker EMX-10 spectrometer with a magnetic field modulation frequency of 100 kHz. The samples were transferred from cells suspension into Pasteur pipettes and measured at 295 K (modulation amplitude 0.01 mT) and 240 K (modulation amplitude 0.1 mT). The ones transferred into the tubes for the measurements at 240 K were frozen without cryoprotectant addition already in the  
Figure 1: The structures of the spin probes studied.  
spectrometer using a cryogenic system. The temperature of measurements was controlled using a Bruker temperature controller unit ER 4131 VT. The magnetic sweep field range of 8 mT was applied for the sample measurements at 295 K, while for those carried out at 240 K--the magnetic sweep range of 13 and 15 mT was used. The microwave power (MW) was 7.97 mW. Some saturation of the frozen samples, manifested by a small increase in spectrum width, was observed for the microwave power above 50 mW, while for all the samples studied with MW 7.97 mW there were no such effects. The number of averages for each spectrum was nine, while the average time to record each scan was 41.9 s, conversion time was 40.96 ms, and the time constant was 40.96 ms. The concentration of the spin probes studied was calculated from the integrated intensity of appropriate ESR signals with an accuracy of 10%.  
To improve ESR spectra resolution and obtain a more detailed analysis, selected ESR spectra were subjected to increasing their resolution by the computer resolution enhancement method (CREM). The method can also improve the signal-to-noise ratio and eliminate high-frequency noise [34]. CREM method was successfully applied in our previous papers [35; 36; 37; 38] and was confirmed by the Electron Nuclear Double Resonance ENDOR method [39]. It is a linear transformation method, and its mathematical fundamentals were described by [PERSON] and [PERSON] [40], [PERSON] and [PERSON] [41], and [PERSON] and [PERSON] [42]. The details of the CREM procedure were previously described [43]. Briefly, an ESR signal \(F(x)\) is treated as a convolution of two functions. One of them informs about the number of lines in the ESR spectrum and their positions and intensities \(\psi(x^{\prime})\), and the second one \(K(x-x^{\prime})\), the so-called core, describes the shape of an individual line (Equation (1)):  
\[F(x)=\int\limits_{-\infty}^{\infty}K\big{(}x-x^{\prime}\big{)}\psi\big{(}x^{ \prime}\big{)}dx^{\prime} \tag{1}\]  
The correctness and effectiveness of the CREM procedure were confirmed by independent researchers, e.g., in a study where the ENDOR spectroscopy method was used to verify hyperfine interactions [34; 39]. Currently, the procedure that is a modification of so-called linear transformations is commonly used in MRI and CT imaging and ESR imaging as deconvolution. The beneficial effect of spectra postprocessing by CREM procedure for the samples studied is presented in the supplementary material. The spectra of TEMPO and TEMPO detected at 295 K before and after the CREM method are shown in Figures SI-S4, respectively. The resolution of the spectra was increased significantly.  
In the case of spectra shown in Section 3.5, we subtracted the baseline recorded for clear cells without a spin probe.  
A confocal microscope Olympus FV1200 with an excitation laser (a wavelength of 488 nm) was used to confirm the endocytosis process. The pictures were taken after two hours of incubation of TEMPO-Fluorescein with yeast cells at 37 \({}^{\circ}\)C. The influence of the breathing cycle in a cell on free radical disappearance was studied by cell culture measurements performed in the air (aerobic atmosphere) and the nitrogen (anaerobic atmosphere).