Analysis are of the hidden properties of the macromolecular system as an example of the reaction centers of bacteria Rhodobacter sphaeroides

Relevant: Is the study of the response of biological macromolecules to external stimuli. Often the reaction of macromolecules has an effect of structural self-regulation. In this case, their reaction is not only external infl uence, but also the spatial-temporal motions of the macromolecule. In this situation deserves the attention of electronic-conformational interactions of macromolecules. As objects are isolated Reaction Centers (RC) of bacteria Rhodobacter sphaeroides, the structure of which is well studied. During prolonged illumination, the RC occurs intramolecular electron transfer of RC, the kinetics of which has expressed as a sum of three different exponential functions with negative values decrements. In this case, can considered two models of electron transfer with variable or constant with time of the kinetic parameters. Problem: Arises of analyzing the kinetics of electron transfer, which infl uenced by the latent parameters of the RC protein structure, which are diffi cult to determine in the experiment. Aim: Of the work is to determine the features of intramolecular electron transfer between the conformational states of RC, which are associated with a change in the structure of the macromolecule. Result: It was determined that the position of the maxima of the wavelet transform spectrum of the logarithmic derivative of the electron transfer kinetics corresponded to the minimax values of the time dependence of the probability density of the presence of an electron in various redox-conformational states of the RC (population of redox states). Minimax values of the population of RC states corresponded to: 1–6s, 30–60s, 100–140s for various parameters of RC photoexcitation. Conclusion: That the existence of minimax values of the probability density is the electron in the conformational states of the RC can related to the effects of structural self-regulation of the electron transfer process. Research Article Analysis are of the hidden properties of the macromolecular system as an example of the reaction centers of bacteria Rhodobacter sphaeroides YM Barabash1*, TV Serdenko1, PP Knox2 and OYu Bondarenko3 1Institute of Physics NAS Ukraine, Prospect Nauky, 46, 03028 Kyiv, Ukraine 2MV Lomonosov, Moscow State University, 119991 Moscow, Russia 3Institute of Plant Physiology and Genetics, NAS Ukraine, Vasylkivska St. 31/17, Kyiv, 03022, Ukraine Received: 29 August, 2019 Accepted: 16 September, 2019 Published: 17 September, 2019 *Corresponding author: YM Barabash, Institute of Physics NAS Ukraine, Prospect Nauky, 46, 03028 Kyiv, Ukraine, Tel: +38(044) 525-98-51; E-mail:

They play an equally important role in the RC relaxation processes, when the electron returns to the bacteriochlorophyll dimer after switching off the light. Upon a prolonged photoexcitation of RC the process of electron transfer repeats and becomes cyclic. Once again the absorption of a quantum of light and the transfer of an electron from a donor to an acceptor Q B takes place. As a rule, the kinetics of cyclic electron transfer has a multi-exponential character with negative decrements both at the stage of oxidation of the donor and at the stage of its reduction. The kinetics of cyclic electron transfer was associated with the probability density (population of state) of the electron being in various electron-conformational states RC, that is, with the probability of fi nding the RC in different electron-conformational states. At the same time, the mathematical form of the exponential functions has no clear features. Their parameters are interrelated and depend on the parameters of the photo excitation RC [5][6][7][8]. This makes diffi cult to physically interpret the exponential components of the electron transfer kinetics. Therefore, further analysis of the kinetics of oxidation and reduction of the donor RC it carried out using two RC models that used the multi exponential nature of the electron transfer kinetics. In one model, a two-level scheme with time-varying parameters was considered. The kinetics of cyclic electron transfer was analyzed using wavelet analysis. Wavelet analysis consists in convolving a wavelet with the function under study and allows revealing its frequency-time characteristics. However, the features of the studied function are diffi cult to interpret, since they depend on the type and parameters of the used wavelets [9,10]. The second model represented by a four-level scheme with parameters constant in time. It used a system of four differential equations with constant coeffi cients and one equation of material balance. The identifi cation of the system of equations has carried out by comparing one of the solutions of differential equations with the experimental kinetics of electron transfer [11]. This made it possible to determine the time dependence of the probability density of fi nding RC in four electron-conformational states for different photo excitation conditions. However, determining the values of the constant coeffi cients of a system of differential equations is not a simple task.
The purpose of work is to analyze the features of the kinetics of electron transfer of RC in various models of electron transfer and to estimate the assumption that these features are due to the regulatory role of the RC protein.

Materials and Methods
Isolated wild type RC Rhodobacter sphaeroides were provided by the Department of Biophysics MSU Moscow State University M.V. Lomonosov. They has placed in a 0.01M Na-P buffer with pH of 7.2, which contained 0.05% LDAO. RCs were studied using two-channel PC-controlled spectrometer. In the absorption measurement channel, light was used with a frequency of 5kHz and intensity (0.2μW/cm 2 , =865±10nm), which provided absorption measurements in the range of values of 0÷1 with an accuracy of 0,0005. The RC excitation channel used light with a wavelength of =870±50nm and an intensity of 0÷10mW/ cm 2 with a step of 5μW/cm 2 . The time measurement step did >=0.01 seconds. The measuring cuvette had dimensions of 3×1×2.5cm with a wall thickness of 2mm. After dilution, the RC suspension with a concentration of 10 -6 M was kept in the dark at room temperature for 12 hours (the dark-adapted RC state). The light-adapted state was formed by illuminating the RC by light pulses of different durations (Texp=1, 5, 50, 120, 300, 600s) with an intensity of 0.5, 1.5, 3.5mW/cm 2 . After the end of illumination and the attainment of dark absorption value, the RC solution was additionally kept in the dark for 1500s to reach an equilibrium state [12]. Then the lighting of RC was repeated with the next light pulse. The relative number of absorption centers and the rate of RC transition from one state to another were determined from the kinetics of fading of the 865nm line of the RC absorption spectrum, and were associated with the kinetics of electron transfer from donor to acceptor [6]. The change in RC absorption determined the time dependence of the probability of the electron being on the donor (population of the RC donor). The probability has normalized to the maximum change in the absorption of the RC suspension at a wavelength of 870nm with an exciting light intensity of 7.2mW/cm 2 . For the analysis of electron-conformational processes in RC two models of electron transfer were used: a two-level model [6,7] and a model with four sub states [12]. According to the two-level model, the RCs are in the ground (1) state when the electron localized on the donor P. When the light quantum is absorbed, the electron moves to the Q B acceptor, and the RC goes to the excited state. The kinetics of electron transfer in this model is determined by the rate constant of direct (k 01 (t)) electron transfer at the RC illumination stage (fi rst stage of electron transfer) and the electron back transfer rate constant (k T 10 (t)) at RC relaxation stage after illumination (second stage of transfer electron). The kinetics of the fi rst stage of photoinduced electron transfer RC can be described by a differential equation and a material balance equation: dp(t)/dt=-k 01 (I)·p(t)+k 10

(I,t)·(1-p(t)), p(t)+q(t)=1
(1) where p(t), q(t) is the probability density of fi nding the RC in such a state when the electron is on the donor (acceptor), i.e. their populations, with the initial condition p(0)=1 q(0)=0. The kinetics of electron transfer from the acceptor to the donor (upon restoration of the donor) after switching off the light (I 0 =0) is: where k T 10 (t) is the rate constant of electron transfer from acceptor (Q) to donor (P) after switching off the light. presented as the sum of three exponential functions (Table 1).
In this case, the logarithmic derivative of the probability p(t) of fi nding an electron on the donor under RC illumination is expressed not only in terms of electron transfer rate constants.
However, if we do not consider the equilibrium absorption values, the absorption kinetics when illuminating the RC could also be well approximated by the sum of three exponential functions ( Figure 4b). This allowed us to study the kinetics of electron transfer using the logarithmic derivative p(t). CWT determines the characteristics of the signal, their frequency and temporal localization. The CWT spectrum represented by the formula: where s(t) is the function under analysis, (t) is the wavelet, a is the parameter that determines the width of the wavelet, and b is the wavelet time shift parameter.
A complex Morlet wavelet used, which is a harmonic function with a Gaussian envelope: This wavelet has good spectrogram convergence. This minimizes the time-frequency uncertainty and ambiguity of interpretation of the obtained wavelet spectra [14]. However, the parameters of the characteristics of the spectrum depend on the type of wavelet used [14,15]. It has known that the system of N-homogeneous differential equations with constant coeffi cients and with the material balance equation has a solution in the form of the sum N-1 of exponential functions [12]. The parameters of the electron transfer kinetics it presented as a sum of three different exponential functions that have a minimum mean-square approximation error (Tables 2-4). Therefore, a system of four differential equations with constant coeffi cients used to study the kinetics of electron transfer. The identifi cation of a system of equations is a multi-

Experimental Results and Discussion
The measurement protocol included the setting of the intensity, the duration of the RC excitation pulse, and the time step of the measurements. After the start of measurements, the value of the dark absorption of the suspension has recorded during the fi rst 20 steps. When the light pulse was turned on and Texp<5 seconds, the data were recorded in 0.01s increments, if Texp>5 seconds, the data were recorded in increments (0.1s).
After turning off the light, the data were recorded for the fi rst In Figure 3a,b shows the electron transfer kinetics of the RC for various parameters of photo excitation.
First, a measurement has made in Figure 3a, then Figure 3b and Figure3c, according to the measurement protocol described above.
In Figure 4 shows the approximation by three exponential the rate constants for two systems of differential equations.
One described the electron transfer kinetics when the reaction center was illuminated. Another system described the electron Table 4: Parameter of the exponential components of the absorption kinetics of RC after switching off the exciting light of different durations with intensity 3.50mW/cm 2 .   Texp  1s  5s  50s  120s  300s  600s   e  t  a  t  s  e  h  t  f  o  n  o  i  t  a  l  u  p  o      the probabilistic dependences of the presence of RC in various electron-conformational states are due to the infl uence of a change in the structure of the RC during cyclic electron transfer. This is especially true for a simpler RC relaxation process after the photo excitation stops Figure 8