CHARACTERIZATION OF ZIGZAG PATTERNS ON THE SURFACE OF BOVINE SERUM ALBUMIN FILMS

Analysis of the patterns formed during the drying of biological fluids is employed for research and diagnosis in medicine and agriculture. Saline solutions of native proteins and DNA are characterized by zigzag patterns, which could be quantitatively described using the specific length of zigzags L specific . The aim of this study was to analyze a wide number of characteristics in order to identify those most sensitive to the effects of various physical and chemical factors on the protein structure. We examined the films prepared from salt solutions of bovine serum albumin (BSA) under varying conditions, viz.: a proportional change in the concentration of the components, substitution of NaCl with NaF and NaBr, temperature treatment, gamma irradiation, and addition of trivalent iron and biologically active flavin mononucleotide. The results revealed that the distribution of zigzag segment lengths was approximately lognormal, and the distribution of angles between the segments was approximately logistic. Two parameters appeared to be the most informative, viz. the average length of the segments, mainly depending on Cl – concentration, and the number of segments, depending on: Cl – concentration, concentration of the non-aggregated (but not necessarily unfragmented) protein, and the excess concentration of ions and low molecular weight compounds.

Drying biofluids and saline solutions of biomolecules are known for their ability to form patterns on the substrate surface, the specific form of which depends, in particular, on the structural state of biomolecules [1][2][3][4]. This fact has found practical application in some research and diagnostic methods of medicine and agriculture: the study of the interaction of biomolecules [5], the diagnosis of the patient's blood condition [6][7][8][9][10], the analysis of the quality of wheat grains [11,12] and carrot roots [13,14].
An important factor determining the practical applicability of such methods is the ability to numerically characterize the patterns formed on the substrate. Such a numerical characteristic is useful for assessing the degree and nature of the changes in the test sample compared to the control.
Depending on the type of pattern or texture, various authors offered such evaluation criteria as: the number of optical density fluctuations [9] or the brightness distribution of the digital image [11] in circular sections of different diameters; the fractal dimension of Minkowski [5] and the local connected fractal dimension of the image [12]; parameters of gray-scale histograms at several scales [13][14][15]; the structural and spectral characteristics of an image region as a function of time [10].
In previous studies we found that zigzag (hexagonal) patterns [16][17][18][19], similar to those observed in [20,21], are formed on films obtained from saline solutions of native DNA or protein. For a quantitative description of this type of texture, we introduced the value L specific , which corresponds to the total length of zigzag patterns per unit area. L specific has random character due to the chaotic nature of the drying process and depends on the salt concentration, the biopolymer concentration, the conditions of solution preparation and drying (temperature, humidity, substrate material and roughness), as well as the properties of the biopolymer, salt and solvent.
As a result of significant physical or chemical influences that disrupt the structure of the biopolymer, zigzag patterns on the dried films are not formed (L specific = 0). However, it is often difficult to identify reliable differences between smaller levels of exposure due to a significant variance in the values of L specific within the same dose of exposure [17,18]. In this regard, the purpose of the current study was to analyze the extended series of characteristics of zigzag patterns on the surface of BSA films, including the parameters of their statistical distributions, and to find which ones are the most sensitive to the action of various physical and chemical factors.

MATERIALS AND METHODS
The analysis was carried out on the basis of data obtained during the previous experiments [18,19,22,23]. The films were obtained from saline BSA solutions via vacuum drying at 40 °C in 20x20x1 mm 3 glass cells. Each film was photographed (using a Meopta microscope and a Logicfox LF-PC011 webcam) in 100 positions uniformly distributed over the cell area, and segments of zigzag patterns were marked on each photograph (using custom software). The data was analyzed and plotted using numpy, scipy and matplotlib libraries.

RESULTS AND DISCUSSION
Zigzag patterns ( Fig. 1) are presumably the result of crystallization in alternating crystallographic directions [20,24]. They consist of connected linear segments of length L i , each pair of which is at an angle α i,j (i, j are neighboring segments) to each other. Another important characteristic is the density of patterns (i.e. how densely they cover the surface of the film). Fig. 1 shows photographs illustrating the variability of these parameters for films obtained from identical BSA solutions under identical conditions.
The films obtained in our experiments have an area of 20x20 mm 2 . The photographs of the patterns (100 photographs for each film) together cover about 10% of the film area, which gives a sufficient sample for estimating the statistical distributions of zigzag characteristics. Fig. 2 shows the characteristic histograms of the distributions of zigzag segment lengths and of angles between the segments. Via curve fitting, it was found that the typical distribution of segment lengths is closest to the lognormal distribution (which, presumably, corresponds to the model of multiplicative growth [25]), and the typical distribution of angles is closest to the logistic distribution. Preliminary analysis has shown that the most informative in one or more series of experiments are the values of L count (total number of zigzag segments), L sum (total length of segments), L mean (mean segment length), α mean (mean angle between segments), as well as shape parameters of fitted functions of Burr XII [26] and Inverse Weibull [27] where x is the independent variable (segment length in our case), and c, d are the shape parameters of the distributions.
In addition to these characteristics, the median, standard deviation, skewness and kurtosis of the distributions, as well as parameters of Log-Normal, Johnson S U , Generalized Logistic and Exponentially modified Gaussian fitted functions were also considered. However, they did not prove to be informative at describing zigzag patterns, and so will be omitted.
The value of L specific (the specific length of zigzags), which was used in our previous publications [17-19, 22, 23], is proportional to L sum : where N photos is the number of photographs (100), and S microscope is the area of the film visible under the microscope (0.414 mm 2 ). As such, we will not mention it further. L sum , L count and L mean relate to each other as count sum mean with L sum and L count in most cases having nearly identical dependence on the degree of exposure to a physical or chemical factor. Due to this, plots of L sum will be presented only in a number of cases. The behavior of the abovementioned characteristics in the corresponding series of experiments is analyzed below. The most illustrative dependencies are shown in the figures.

Proportional change in component concentration
In this experiment, the concentration of BSA (1 mg/ml) and NaCl (40 mM/l) was doubled compared to the normally used concentration (0.5 mg/ml BSA, 20 mM/l NaCl). L count (Fig. 3, a), L sum and α mean (Fig. 3, b) remained in the range of the values for the 100% concentration. L mean (Fig. 3, c) at a doubled concentration does not go beyond the limits of the values observed at the usual concentration, but on average is much higher. For the 200% concentration, the Burr XII C parameter (Fig. 3, d) is smaller than for the 100% concentration (the decrease of Burr XII C corresponds to the distribution "stretching" and shifting towards larger values). With an increase in the concentration of salt and protein, the average length of segments and the spread of segment lengths increase. Based on the model descibed in [20], it can be assumed that a higher concentration of components allows the crystal to grow for a longer time in one direction.
Substituting Clwith Brand F -In this experiment [18], it was investigated whether zigzags can form when chlorine ions are partially or completely replaced by other halides (bromine or fluorine). The concentration of salts varied from 20 to 0 mM/l for NaCl and from 0 to 20 mM/l for NaBr and NaF, respectively.
Replacing sodium chloride with sodium bromide resulted in the following (Fig. 4, a, c, e): up to 4 mM/l NaBr, L count and L sum stay in the range of control values; at 8 mM/l NaBr, they noticeably decrease; at 16 mM/l NaBr and more, zigzags are not formed. α mean , L mean and the parameters of fitted functions do not go beyond the range of values for control. Replacing sodium chloride with sodium fluoride resulted in the following (Fig. 4, b, d, f): up to 8 mM/l NaF, L count values are in the range of control values; up to 8 mM/l NaF L sum tends to decrease, but the ranges of its values are at least partly overlapping. At 16 mM/l NaF and more, zigzags are not formed. α mean tends to decrease, but does not go beyond the extreme values of control. L mean decreases with increasing NaF concentration, and the ranges of its values at 0, 4 and 8 mM/l NaF practically do not overlap.
At 4 mM/l Cl -(20% of the usual concentration) and below, zigzags do not form, which indicates a high specificity of the zigzag aggregation mode to the physical parameters of the anions (size, surface charge, etc.). Brand Falso influence the conformation of BSA and have a lower degree of hydration than Cl -(which affects electrostatic interactions) [18]. Brand Fthemselves do not create conditions for the formation of zigzag patterns, but their presence has different effects: at 8 mM/l Br -, the number of zigzag segments markedly decreases, while Fnoticeably reduces the average length of zigzag segments.

Heat treatment of BSA solutions
In this experiment [18], solutions of BSA with NaCl were heated to 45, 70 and 95 °C to find out what contribution the structural state of the protein makes to the formation of zigzag patterns. The values of L count (Fig. 5, a) and L sum for 20 and 45 °C are in the same range, at 70 °C they decrease considerably, and at 95 °C zigzags are not formed. The values of α mean for 20 and 45 °C are in the same range, and at 70 °C they increase (Fig. 5, b). L mean practically does not change at different temperatures (Fig. 5, c). At 70 °C, the Burr XII C parameter (Fig. 5, d) decreases compared to 20 and 45 °C.
At 60 °C, BSA begins to unfold and form primary aggregates, at 70 °C it forms primary and secondary aggregates, and at 80 °C it forms aggregates of large size [28]. Since at 70 °C the amount of zigzags is noticeably reduced, and at 95 °C they are completely absent, it can be unequivocally asserted that protein aggregation disrupts the conditions for the formation of zigzag patterns. Also, at 70 °C, compared to the control, the mean angle between the α mean segments slightly increases and scatter of segment lengths increases (which is reflected in the reduced Burr XII C), but the average length L mean remains almost the same. These observations suggest that the state of the biopolymer mainly affects the number of zigzag segments, and the concentration of chlorine mainly affects the length of the segments.

Gamma irradiation of BSA solutions by 60 Co
In this experiment [22], solutions of BSA with NaCl were subjected to gamma irradiation in 0.16 -12000 Gy dose range. L count (Fig. 6, a) and L sum for the intermediate doses have both values close to zero, and values that fall in the confidence interval of the control; from a statistical point of view, doses of 1 -2000 Gy are practically indistinguishable. Only at 12000 Gy zigzags completely cease to form. α mean and L mean (Fig. 6, b, c) vary in approximately the same range at all doses. Parameters of the fitted functions, for example, Burr XII C (Fig. 6, d), also have too large variations to distinguish intermediate doses.
Gamma irradiation leads to the formation of free radicals in solution, which cause protein fragmentation. According to the data of SDS-PAGE (dodecyl sulfate polyacrylamide gel electrophoresis), polypeptide chain breaks down at doses up to 1 kGy, and at 5 kGy or higher fragments of the destroyed protein begin to form large molecular weight aggregates [29]. Specifically, doses up to 0.2 kGy damage 10-20% of BSA [30]; at 1 kGy, 50-60% of BSA is damaged [30], and even at 2.5 kGy some amount of undamaged BSA still remains [31]. In our case, the ionizing radiation changes the number of zigzag segments, but the average length L mean , angles (α mean ) and other distribution parameters are practically independent of the dose. At 12 kGy (aggregation of protein fragments), zigzags never form, but in the dose range of 1 -2000 Gy (protein destruction), the amount of zigzags on a given film can turn out to be anything from near-zero to the amount typical for the control. This suggests that, unlike the formation of aggregates, biopolymer fragmentation does not have unambiguous effect on the formation of zigzag patterns. Fig. 6. Pattern characteristics after gamma irradiation of the biopolymer solution: (a) number of zigzag segments; (b) average angle between zigzag segments; (c) average length of zigzag segments; (d) shape parameter C of the Burr XII distribution. Box plot notation: boxes correspond to 25 and 75 percentiles, dotted lines correspond to 5 and 95 percentiles, crosses correspond to minimum and maximum values, horizontal lines correspond to medians, and squares correspond to mean values. Control: 18 films; 0.16 Gy: 3 films; 1 Gy: 12 films; 10 Gy: 4 films; 100 Gy: 8 films; 200 Gy: 6 films; 1 kGy: 4 films; 2 kGy: 10 films; 12 kGy: 4 films.

Addition of FeCl 3 to BSA solutions
In this experiment [19], FeCl 3 salt in the concentration range of 0.05 -0.4 mM/l was added to the solutions of BSA with NaCl. L sum and L count (Fig. 7, a, b) up to 0.15 mM/l of FeCl 3 stay in the range of control values, but starting from 0.2 mM/l they noticeably decrease. When FeCl 3 concentration reaches 0.3 mM/l, the probability of zigzag formation decreases even more, and starting from 0.4 mM/l of FeCl 3 zigzags stop forming completely. For α mean and L mean (Fig. 7, c, d), there is no evident dependence on the concentration of FeCl 3 . The parameters of the fitted functions also behave in a manner similar to either L count or L mean .
If FeCl 3 is added to the BSA solution, the number of zigzag segments (L count ) changes, but no dependence of distribution parameters on the iron concentration is observed. L count has several very distinct areas: up to 0.15 mM/l FeCl 3 , L count is in the range of control values and even has an upward tendency; between 0.2 and 0.25 mM/l FeCl 3 , the amount of zigzags is markedly reduced and varies in approximately the same range; at 0.3 mM/l, L count decreases again, and at 0.4 mM/l FeCl 3 zigzags cease to form. At the moment, we find it difficult to hypothesize what could be the cause of such a threshold effect. According to the data of [32], even at a 50:1 concentration ratio, only 0.79 mole of Fe 3+ binds to 1 mole of BSA, and this does not cause obvious changes in the secondary structure of BSA. It might be that, upon reaching a certain concentration of FeCl 3 , another morphology with a higher growth rate becomes possible, which, according to the hypothesis of [33], will lead to the suppression of other types of patterns.

Addition of flavin mononucleotide to BSA solutions
In this experiment [23], flavin mononucleotide (FMN) in the concentration range of 0.01 -0.3 mM/l was added to the solutions of BSA with NaCl. L count (Fig. 8, a) and L sum at 0.01 mM/l still fall within the range of control values, but 0.03 mM/l of FMN already significantly inhibits the formation of zigzag patterns. At 0.3 mM/l, zigzags completely cease to form. α mean and L mean (Fig. 8, d, c) remain approximately in the range of control values. The parameter Inverse Weibull C (Fig. 8, b) increases with the increase of FMN concentration (the growth of Inverse Weibull C corresponds to the distribution "shrinkage" and shifting towards larger values). Addition of 0.01 mM/l FMN does not shift the characteristics of zigzag patterns beyond the range of control values. However, starting from 0.03 mM/l, the number of segments and the spread of segment lengths are sharply reduced. Average segment lengths (L mean ) and angles between segments (α mean ) practically do not change. According to the studies [34][35][36], HSA and BSA form complexes with riboflavin (RF), flavin adenine dinucleotide (FAD) and FMN at a ratio of 1:1 and with high binding constants; in [36] it was also shown that, in the presence of RF, BSA conformation changes and its hydration increases. This agrees with the results obtained by spectroscopy and microwave dielectrometry for solutions of FMN with BSA [23]. In our case, at 0.01 mM/l FMN, the number of FMN moleculer is 1.3 times the number of BSA molecules, and at 0.03 mM/l it is 4 times the number of BSA molecules. It can be assumed that the conditions for the formation of zigzag patterns are violated by the presence of free FMN, but not by the binding of FMN to BSA. Table 1 summarizes the effect of the factors studied in this paper on the values of L count and L mean . The behavior of these characteristics is compared to the structural state of the protein according to the published data. Up to 0,15 mM/l FeCl 3 , L count stays in the range of control values, at 0,2 mM/l and 0,3 mM/l it decreases in discrete manner, and becomes 0 at 0,4 mM/l Fe 3+ does causes no obvious changes in the secondary structure of BSA [32] Addition of flavin mononucleotide L count is significantly reduced in the presence of an excess amount of FMN not bound to the protein Flavin derivatives lead to a change in the conformation and an increase in the hydration of BSA [36] An additional observation, which is valid for all experiments, is that all the considered characteristics have a significant spread. It can be caused both by insufficient accuracy of the control of experimental conditions (the degree of purity of the cuvettes, the homogeneity of the solution, the inclination of the cuvette during drying), and by the chaotic character of the process of texture formation. The authors of [14,15] consider the latter to be the case, as they also report low reproducibility and high variability of the results of the method of biocrystallization. According to their analysis, the crystallization stage is the primary source of the variability of results.

CONCLUSIONS
A number of characteristics of zigzag patterns, which form on films of dried BSA solutions, were analyzed in this paper. It was determined that the most informative among the characteristics considered are the number of zigzag segments L count and their average length L mean , and the least informative is the average angle between segments. Other parameters either correlate with L count or L mean , or do not exhibit any dependence on the strength of the investigated factors. The data suggest that L mean mainly depends on the chlorine concentration, whereas L count is sensitive to any violations in the conditions of zigzag formation. These violations occur, in particular, at low chlorine concentrations, at protein aggregation (but not necessarily at fragmentation), and also in the presence of an excess amount of low molecular weight compounds (ligands) and ions not associated with the protein in the solution. Clarification of the role of these factors in the process of zigzag formation, accounting for other types of patterns and finding more efficient and reproducible methods for obtaining films will be the directions of our further research.