Application of Fixed-Length Ultrasonic Interferometry to Determine the Kinetics of Light-/Heat-Induced Damage to Biological Membranes and Protein Complexes

: This manuscript describes the application of a ﬁxed-length ultrasonic spectrometer to determine the kinetics of heat- and photo-induced damage to biological membranes and protein complexes and provides examples of the test measurements. We implemented a measurement scheme using the digital analysis of harmonic signals. To conduct the research, the ﬁxed-length ultrasonic spectrometer was modernized: the speed was increased; lighting was supplied to the sample cells; the possibility of changing the gas atmosphere and mixing the sample was given. Using solutions containing natural concentrations of deuterium oxide, a high sensitivity of the spectrometer was shown. The spectrometer performed well in the measurement of phase state of dimyristoylphosphatidylcholine liposomes, both in the absence and in the presence of additions, which are capable of changing the lipid properties (sodium dodecyl sulfate, palmitic acid, and calcium ions). The heat- and photo-induced changes in the state of photosystem II core complexes were demonstrated using a ﬁxed-length ultrasonic spectrometer. Transitions at 35.5 ◦ C, 43.5 ◦ C, 56.5 ◦ C, and 66.7 ◦ C were revealed. It is proposed that the transitions reﬂect the disassembly of the complexes and protein denaturation. Thus, the present study demonstrates that a ﬁxed-length ultrasonic spectrometer can be applied to determine the kinetics of heat- and photo-induced damage to biological membranes and protein complexes.


Introduction
Biological membranes are unique heterogeneous three-dimensional structures, consisting of proteins embedded in a lipid matrix, the architecture and stability of which are strongly related to their functions. One of the most important characteristics of biological membranes is their phase state, including the state of protein molecules integrated into the membrane. It is known that lipids, the main structural components of biological membranes, may have three phase states: liquid (liquid crystal), ripple and solid (gel) [1]. The phase transition point depends on many factors: the structure and packing of lipid molecules, hydrostatic pressure, salt concentration, and so on. Phase transitions of lipid membranes are the basis of important biological processes: the fusion of cells, osmosis, the transport of substances, etc. [2][3][4][5][6][7]. Proteins can also exist in several thermodynamically stable states, for example the native state, denatured state, and compact state of the molten globule with a loss of unique side chain packaging. The transitions between these states in compressibility determines the phase velocity of sound in the medium, and its relaxation part determines the value of sound absorption. Therefore, simultaneous measurements of the velocity and absorption of ultrasound, as well as the density of the medium make it possible to determine the compressibility of the medium and its relaxation part with very high accuracy. In addition, the compressibility of an aqueous solution is highly dependent on the hydration of the solute. Almost all molecular processes (including phase transition) in solution are accompanied by a change in hydration, which can be recorded and characterized by the measurement of compressibility [42]. On the one hand, compressibility is a sensitive characteristic of the state of aggregation of a substance. On the other hand, a protein molecule and a lipid membrane are systems with a large number of internal degrees of freedom, being delimited from the medium. Therefore, they can be considered as a phase of small size, and their properties can be described in "macroscopic" terms [43].
One of the most accurate methods is the assessment of the state and phase transitions of biomolecules by changing the compressibility and absorption of ultrasound using a setup containing a fixed-length ultrasonic. To do this, we previously used a phase-locked loop (PLL) [41], which was later replaced by an alternative measurement scheme based on the methods of digital analysis of harmonic signals [44][45][46]. In the present work, the installation was further modernized, which made it possible to increase the speed, as well as to perform studies to determine the kinetics of heat-and photo-induced damage to biological membranes and protein complexes. The approach proposed in this work can be the basis for obtaining such important characteristics of a phase transition as the type of melting and denaturation of proteins, interfacial tension, and the rate constant of the elementary act of the growth and decomposition of a new phase, providing information about the physical properties of lipid membranes and protein molecules and on intermolecular interactions in aqueous solutions. This method combines high sensitivity, accuracy (10 -4 %), and a small volume (100 Ml-1000 µL) of the test sample [39].

Materials and Methods
The dependence of the relative velocity of ultrasound in water on temperature at various concentrations of deuterium oxide were analyzed using different ratios of light water ("Legkaja voda, Standart", Komponent-Reactiv, Moscow, Russia) (without deuterium oxide) and ordinary water. The ordinary water was obtained by distillation and subsequent deionization of tap water.
During the ultrasonic measurement, the samples in both the reference and experimental cells were mixed with a magnetic stirrer. All measurements were repeated at least three times. Figure 1 shows the structure of the measuring scheme of a fixed-length digital computer ultrasonic spectrometer. In comparison with the previous version [44], in order to overcome the limitations of the method associated with the speed of measuring the phasefrequency characteristic, the measurement channel of the experimental cell was upgraded. The directions of modernization were as follows:
Acceleration of the operation of the controller that tunes the DDS generator: an 8-bit ATMega family (Atmel, Microchip Technology Inc., Chandler, AZ, USA) with a clock frequency of 16 MHz was replaced with a 32-bit SAM3 controller (Atmel, Microchip Technology Inc., Chandler, AZ, USA), that is replacing the Arduino Uno controller with the Arduino DUE controller.

2.
Transition from a circuit with one oscillator and one oscilloscope serving two channels and a switch to a circuit with one 125 MHz master oscillator and two DDS generators.

3.
Replacement of the digital oscilloscope in the channel of the experimental cell with a high-speed recorder with 32 MB of RAM and a USB3.0 interface. The recorder is started by an external trigger. The trigger signal is generated by the Arduino DUE.

4.
The measurement procedure in the channel of the experimental cell was changed. The Arduino DUE controller independently forms a grid of 15 frequencies and the 16th interval with the generator turned off. The entire frequency grid is automatically fed to the input of the experimental cell without the participation of a personal computer. The measurement result (in the form of a continuous recording with a sampling frequency of 50 MHz and eight million samples long) is transferred to a computer and analyzed. Thus, the procedure for measuring the characteristics of one resonant peak takes 160 ms, rather than 4 s as in the previous version.
The program used to implement the algorithm for signal analysis (using digital signal processing) and control of the experimental conditions was developed with C++. The program performs the following tasks in real-time: (i) obtains raw digitized sinusoidal signals at the input and output of each cell, (ii) sets the frequency of the DDS generator, (iii) calculates the phase frequency dependence and amplitude transmission coefficient (AFC) and determines the position of the maximum of the resonant peak in the frequency range, (iv) visualizes the data, and (v) scans the temperature in the cells and controls the thermostat.  The program used to implement the algorithm for signal analysis (using digital signal processing) and control of the experimental conditions was developed with C++. The program performs the following tasks in real-time: (i) obtains raw digitized sinusoidal signals at the input and output of each cell, (ii) sets the frequency of the DDS generator, (iii) calculates the phase frequency dependence and amplitude transmission coefficient (AFC) and determines the position of the maximum of the resonant peak in the frequency range, (iv) visualizes the data, and (v) scans the temperature in the cells and controls the thermostat.
In comparison to the method described earlier [44], in the present work, the principle of determining the position of the resonance peak was changed ( Figure 3). If the algorithm did not change much for the sample cell, then a simplified procedure was used for the reference cell. The phase frequency dependence near the resonant frequency was measured to perform steady-state measurement of the frequency and width of a resonant  The program used to implement the algorithm for signal analysis (using digital signal processing) and control of the experimental conditions was developed with C++. The program performs the following tasks in real-time: (i) obtains raw digitized sinusoidal signals at the input and output of each cell, (ii) sets the frequency of the DDS generator, (iii) calculates the phase frequency dependence and amplitude transmission coefficient (AFC) and determines the position of the maximum of the resonant peak in the frequency range, (iv) visualizes the data, and (v) scans the temperature in the cells and controls the thermostat.
In comparison to the method described earlier [44], in the present work, the principle of determining the position of the resonance peak was changed ( Figure 3). If the algorithm did not change much for the sample cell, then a simplified procedure was used for the reference cell. The phase frequency dependence near the resonant frequency was measured to perform steady-state measurement of the frequency and width of a resonant In comparison to the method described earlier [44], in the present work, the principle of determining the position of the resonance peak was changed ( Figure 3). If the algorithm did not change much for the sample cell, then a simplified procedure was used for the reference cell. The phase frequency dependence near the resonant frequency was measured to perform steady-state measurement of the frequency and width of a resonant peak in a cell with a sample. The estimation of the position of the resonant peak was made by determining the position of the zero of the second derivative of the phase frequency dependence (Equation (1)). To obtain one point of the second derivative of the PFC, it is necessary to perform three dimensions of phase frequency dependence. This was repeated five times at small, regular frequency intervals. After that, the dependence of the second derivative of the phase frequency dependence was approximated by a straight line, which intersects the zero of the ordinate at the position of the resonant peak. In parallel, the first derivative was calculated (Equation (2)) for the calculation of the fork pitch at the Inventions 2022, 7, 87 6 of 16 next determination of the position of the resonance peak (Equation (3)). The width of the resonance peak was calculated using Equation (4).
where ∆f φ is the fork pitch and a φ is the trimming factor. We used ∆f to determine the Q-factor for the energy losses in our resonant system (Equation (5)): PFC, it is necessary to perform three dimensions of phase frequency dependence. This was repeated five times at small, regular frequency intervals. After that, the dependence of the second derivative of the phase frequency dependence was approximated by a straight line, which intersects the zero of the ordinate at the position of the resonant peak. In parallel, the first derivative was calculated (Equation (2)) for the calculation of the fork pitch at the next determination of the position of the resonance peak (Equation (3)). The width of the resonance peak was calculated using Equation (4).
where Δfϕ is the fork pitch and aϕ is the trimming factor. We used Δf to determine the Q-factor for the energy losses in our resonant system (Equation (5)): As the Q-factor rises with losses falling, we used the 1/Q parameter to characterize the losses in the system due to scattering and viscosity. As mentioned above, a simplified procedure was used for the reference cell, in which the phase was determined once for a frequency close to the frequency of the resonant peak. The current position of the resonant peak was determined by linear regression of the phase frequency dependence with a known slope. As a reference substance, it is better to use a known substance, for example pure water. As the Q-factor rises with losses falling, we used the 1/Q parameter to characterize the losses in the system due to scattering and viscosity.
As mentioned above, a simplified procedure was used for the reference cell, in which the phase was determined once for a frequency close to the frequency of the resonant peak. The current position of the resonant peak was determined by linear regression of the phase frequency dependence with a known slope. As a reference substance, it is better to use a known substance, for example pure water. Figure 4 presents the results of the measurement of the relative velocity of ultrasound in water. Line 1 indicates that the ultrasonic spectrometer had a good stability in all temperature ranges. Replacement of 50% (line 2) or 100% (line 3) light water in the experimental cell with ordinary water led to a decrease in the relative velocity of ultrasound. Moreover, this difference increased with increasing temperature. If we take into account the content of deuterium oxide in ordinary water (about 0.015%), the presented data confirm the high sensitivity of the ultrasound spectrometer. perature and decreased the cooperativity of the transition (two phase transitions were observed: at 26.10 °C and 28.90 °C). These data are consistent with the previous data [62][63][64][65][66], including those obtained using ultrasonic measurements [67]. The addition of 200 mM Ca 2+ eliminates the SDS-and palmitic acid-induced changes, probably due to the binding of Ca 2+ to palmitic acid [46]. It is known that photosystem II is the pigment-protein complex, which consists of 20 protein subunits and about 20 lipid molecules [68][69][70][71]. The study of the state and phase transitions in such large complexes is a very difficult task, since the contribution of each component of the complex will overlap with the others. Figure 6A shows the kinetics of the ultrasonic velocity in the suspension containing untreated photosystem II (PSII) core complexes (black curve). The relative ultrasonic velocity gradually decreased with increasing temperature. The decrease in velocity with the temperature increase was nearly linear. However, in some parts of the kinetics, a decrease in the slope angle was observed, which may indicate changes in the protein complexes. The calculation of the derivative of   [62][63][64][65][66], including those obtained using ultrasonic measurements [67]. The addition of 200 mM Ca 2+ eliminates the SDS-and palmitic acid-induced changes, probably due to the binding of Ca 2+ to palmitic acid [46].

Measurements
It is known that photosystem II is the pigment-protein complex, which consists of 20 protein subunits and about 20 lipid molecules [68][69][70][71]. The study of the state and phase transitions in such large complexes is a very difficult task, since the contribution of each component of the complex will overlap with the others. Figure 6A shows the kinetics of the ultrasonic velocity in the suspension containing untreated photosystem II (PSII) core complexes (black curve). The relative ultrasonic velocity gradually decreased with increasing temperature. The decrease in velocity with the temperature increase was nearly linear. However, in some parts of the kinetics, a decrease in the slope angle was observed, which may indicate changes in the protein complexes. The calculation of the derivative of the kinetics makes it possible to visualize the changes in the kinetics ( Figure 6B). There are several regions of sharp growth on the derivative curve, which may indicate the decomposition of protein complexes into small components or a change in the structure of the peptides themselves. Several regions of this kind can be distinguished on the curve. The first starts at 43.5 • C, the second at 56.5 • C, and the third at 66.7 • C. Preliminary photoinhibition of the samples somewhat changed the character of the curves ( Figure 6A,B, red curves). The relative ultrasonic velocity increased, which can indicate light-induced damage to the complexes ( Figure 6A). The first shoulder on the derivative (observed at 43.5 • C) decreased greatly, which may indicate that those PSII components that undergo changes at this temperature were damaged by light prior to the ultrasonic measurement ( Figure 6B). The curve shows a significant increase in the amplitude of the second shoulder (observed at 56.5 • C). Further, the character of both the changes in the The first starts at 43.5 °C, the second at 56.5 °C, and the third at 66.7 °C. Preliminary photoinhibition of the samples somewhat changed the character of the curves ( Figure 6A and Figure 6B, red curves). The relative ultrasonic velocity increased, which can indicate light-induced damage to the complexes ( Figure 6A). The first shoulder on the derivative (observed at 43.5 °C) decreased greatly, which may indicate that those PSII components that undergo changes at this temperature were damaged by light prior to the ultrasonic measurement ( Figure 6B). The curve shows a significant increase in the amplitude of the second shoulder (observed at 56.5 °C). Further, the character of both the changes in the ultrasound velocity and their derivatives was practically the same in both types of samples (native and photoinhibited).  Figure 6C describes the dependence of the Q-factor (which can describe the change in the shape or size of particles) on temperature. The figure shows that the initial value of the Q-factor for samples pre-treated with high-intensity light was higher than for untreated samples. This may indicate that PSII core complexes were damaged as a result of pre-illumination. When the temperature reached 33.5 °C, the Q-factor significantly increased in both types of samples and then did not change. At the same time, its value became the same for untreated and pre-illuminated preparations. It is important to note that the presented curves were the result of filtering the original curves (shown in the insert in Figure 6D). The original curves showed that the signal-to-noise ratio also changed with increasing temperature, which is reflected in Figure 6D. It is shown that the value of the Q-factor RMS began to increase with increasing temperature, which correlates well with the data presented in Figure 6A-C. The Q-factor RMS returned to the initial values when all the main processes, reflected in Figure 6B, ended.  Figure 6C describes the dependence of the Q-factor (which can describe the change in the shape or size of particles) on temperature. The figure shows that the initial value of the Q-factor for samples pre-treated with high-intensity light was higher than for untreated samples. This may indicate that PSII core complexes were damaged as a result of preillumination. When the temperature reached 33.5 • C, the Q-factor significantly increased in both types of samples and then did not change. At the same time, its value became the same for untreated and pre-illuminated preparations. It is important to note that the presented curves were the result of filtering the original curves (shown in the insert in Figure 6D). The original curves showed that the signal-to-noise ratio also changed with increasing temperature, which is reflected in Figure 6D. It is shown that the value of the Q-factor RMS began to increase with increasing temperature, which correlates well with the data presented in Figure 6A-C. The Q-factor RMS returned to the initial values when all the main processes, reflected in Figure 6B, ended.
It is known that photosystem II complexes depriving the water-oxidizing complex are very sensitive to photoinhibition [72][73][74][75][76]. Therefore, we decided to perform a study of the kinetics of photoinhibition using preparations with the WOC removed. In order to avoid additional thermal inactivation of the preparations, it was decided to conduct the experiments at a low temperature (≈6.4 • C). Figure 7 shows the photoinduced changes of the relative velocity of ultrasound in the suspension containing photosystem II core complexes with the removal of the WOC. Before illumination, the ultrasonic velocity remained stable.  [26] was used), and A2 (33.5 °C) (the nomenclature accepted in [28] was used).
It is known that photosystem II complexes depriving the water-oxidizing complex are very sensitive to photoinhibition [72][73][74][75][76]. Therefore, we decided to perform a study of the kinetics of photoinhibition using preparations with the WOC removed. In order to avoid additional thermal inactivation of the preparations, it was decided to conduct the experiments at a low temperature (≈6.4 °C). Figure 7 shows the photoinduced changes of the relative velocity of ultrasound in the suspension containing photosystem II core complexes with the removal of the WOC. Before illumination, the ultrasonic velocity remained stable.
The kinetics of the photoinduced changes of the relative velocity of ultrasound can be divided into two parts: a fast phase, associated with sample heating, and a slow phase, reflecting photoinduced changes occurring in PSII complexes. The fast phase is a completely reversible decrease in the relative speed of ultrasound immediately after turning on the light, which is completely dependent on the heating of the sample (∆t = 0.04 °C). The slow phase is a gradual irreversible increase in the speed of sound as a result of the photoinhibition of the samples, which was not detected upon repeated illumination. Note that the rate of the light-induced increase of the ultrasound velocity after the second illumination was three-times lower that after the first one. These data correlate well with those presented in Figure 6A (increase in the speed of sound in the photoinhibited sample).
Thus, it was shown that the fixed-length ultrasonic spectrometer can be used to determine the kinetics of the light-/heat-induced damage to biological membranes and protein complexes.  [26] was used), and A2 (33.5 • C) (the nomenclature accepted in [28] was used).

Discussion
The development of technologies for the study of the phase state of biological samples concentrates on the increase of the resolution and on the decrease of the noise in comparison to the signal. Ultrasonic technologies are also constantly being developed The kinetics of the photoinduced changes of the relative velocity of ultrasound can be divided into two parts: a fast phase, associated with sample heating, and a slow phase, reflecting photoinduced changes occurring in PSII complexes. The fast phase is a completely reversible decrease in the relative speed of ultrasound immediately after turning on the light, which is completely dependent on the heating of the sample (∆t = 0.04 • C). The slow phase is a gradual irreversible increase in the speed of sound as a result of the photoinhibition of the samples, which was not detected upon repeated illumination. Note that the rate of the light-induced increase of the ultrasound velocity after the second illumination was three-times lower that after the first one. These data correlate well with those presented in Figure 6A (increase in the speed of sound in the photoinhibited sample).
Thus, it was shown that the fixed-length ultrasonic spectrometer can be used to determine the kinetics of the light-/heat-induced damage to biological membranes and protein complexes.

Discussion
The development of technologies for the study of the phase state of biological samples concentrates on the increase of the resolution and on the decrease of the noise in comparison to the signal. Ultrasonic technologies are also constantly being developed [77][78][79][80][81][82][83][84][85][86][87]. However, the majority of the attention is paid either to fairly simple or model objects or to the assessment of the quality or readiness of food products, as well as research for medical purposes [34][35][36][37][38][39][40]45,46,84,85,[88][89][90][91][92][93]. In our work, we tested the potential possibility of studying the state and phase transitions of a large and complex multiprotein, the photosystem II of higher plants (containing peptides, lipids, photosynthetic pigments, and electron transport cofactors). Photosystem II (PSII) is the pigment-protein complex located in the thylakoid membrane of chloroplasts and cyanobacteria. PSII catalyzes the transformation of light energy into electrochemical energy with separate charges [94]. A by-product of PSII's operation is molecular oxygen. A minimal molecular structure capable of water oxidizing is PSII core complexes. X-ray analysis of PS2 core complexes isolated from cyanobacteria showed that each PSII monomer consists of 20 protein subunits, 20 lipid molecules, as well as 35 chlorophyll and 12 carotenoid molecules [68,69,95,96]. Modernization of a fixed-length ultrasonic spectrometer, the acceleration of the speed, changes in the algorithm of determining the position of the resonance peak, and mixing the sample allowed performing measurements of heat-induced damage to PSII. In addition, such measurements became possible in the direction from low to high temperature without degassing of the measuring medium. Before the modernization, such measurements were not possible. Figure 6 indicates that heating of PSII core complexes led to changes in the state of the preparations, which led to the destruction of the complex. The first one started at 33.5 • C ( Figure 6C), the second at 43.5 • C, the third at 56.5 • C, and the fourth at 66.7 • C ( Figure 6B). To simplify the discussion, we call these transitions A (43.5 • C), B1 (56.5 • C), C (66.7 • C) (the nomenclature accepted in [26] was used), and A2 (33.5 • C) (the nomenclature accepted in [28] was used). A sharp increase in the Q-factor value at 33.5 • C indicated changes in the size or shape of the particles in the suspension. Indeed, using differential scanning calorimetry and gel electrophoresis separation, the dissociation of the proteins of the PSII water-oxidizing complex (without protein denaturation) was previously demonstrated [28]. Transition A observed in Figure 6B may be due to the degradation of the WOC [26,28,97], PSII core monomerization [98], and damage to the PSII acceptor side with denaturation of 43 kDa, 28 kDa, and 22 kDa proteins [27,28]. Moreover, lipid phase transitions may occur at this temperature, but in PSII core complexes, its contribution should be minimal [99]. Practically the full disappearance of transition A in pre-illuminated particles may be due to photodamage to the corresponding components of PSII [100,101]. As has been shown earlier, transition B1 reflects denaturation of the proteins of the PSII core (47 kDa, D1 and D2) [26,28,102]. Surprisingly, the amplitude of transition B1 in pre-illuminated samples was several times higher than in untreated PSII core complexes. Now, it is difficult to explain what this is connected with. It is likely that 10 min of illumination of the samples in an environment containing oxygen caused significant damage to PSII's components. These damages can lead to a change in the properties of polypeptides due to their oxidation by reactive oxygen species [51,75,[103][104][105][106][107][108][109][110][111][112][113][114][115][116][117], as well as the formation of cross-links between them [118][119][120][121][122][123]. On the one hand, the damages can reduce the thermal stability of the peptides, and on the other hand, cross-links can increase it. It is likely that during photoinhibition, additional covalent cross-links of the protein complex appear, leading to an increase in thermal stability. As a result of photoinhibition, the process of the destruction of the complex observed in the control samples at 44-52 • C may be shifted to the region of 57-60 • C and occurs in a much narrower temperature range. Note that the properties of untreated and pre-illuminated particles became similar after ≈60 • C. It is believed that transition C (identical in both types of preparations) reflects the degradation of minor light-harvesting complexes [20]. However, the PSII core complexes used in the present work did not contain these components. We assumed that transition C may reflect the denaturation of the PsbO protein of the water-oxidizing complex. Phase transitions of PsbO were observed at temperatures from 68 • C to 76 • C, depending on the presence of calcium and manganese ions and the pH of the medium [124].
Our data show that a fixed-length ultrasonic interferometry can be used not only to analyze simple compounds, but also complex ones, such as photosynthetic complexes isolated from the thylakoid membranes of higher plants, as well as the kinetics of heat-and photo-induced processes in them.

Conclusions
The present study showed the high sensitivity of the ultrasonic spectrometer we developed. The spectrometer proved itself in studies of both relatively simple compounds (for example, solutions of deuterium oxide and liposomes) and extremely complex multicomponent enzymes (for example, the core complexes of photosystem II of higher plants). Thus, the present study demonstrates that a fixed-length ultrasonic spectrometer can be applied in further investigations to determine the kinetics of heat-and photo-induced damage to biological objects.