## 3 Results
### Docking of L-Asparaginase with Sperm  
To explain the effect of the spermine conjugation on the enzyme equilibrium shifted from the dimer toward the tetrameric form of RrA, we modeled the interaction of the dimer and tetramer of RrA with spermine using the UCSF Chimera and Autodock vina programs. We also calculated the interatomic distances between the closest carboxyl groups, Asp and Glu (Table 5). The table illustrates the possible pairs of amino acids that can form electrostatic interactions with spermine [18; 19]. When the carboxyl groups on the amino acids are modified with Woodward's reagent, spermine, a bifunctional agent, can form covalent bonds between these amino acid pairs. Spermine has a molecular length of about 16.5 A. This means that it is most likely to form bonds between amino acid pairs whose distance between them does not exceed this value. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**RrA Preparation** & \
\begin{tabular}{c} **Degree of** \\ **Modification \({}^{*}\)** \\ \end{tabular} & **Zeta Potential, mV** &
\begin{tabular}{c} **Specific Activity,** \\ **IU/mg** \\ \end{tabular} \\ \hline
**RrA** & NA & \(-9.0\pm 1.3\) & \(47\pm 4\) \\
**RrA-PEI-PEG** & 2 & \(1.4\pm 0.3\) & \(61\pm 4\) \\
**RrA-PEI** & 6 & \(-4.0\pm 1.8\) & \(49\pm 2\) \\
**RrA-Spm** & 18 & \(-8.1\pm 0.9\) & \(58\pm 3\) \\ \hline \hline \end{tabular}  
* Degree of modification = n(polyamine)/n(enzyme).  
\end{table} 
Table 4: Zeta potential and specific activity values of native RrA and its conjugates. The hydrolysis activity of 20 mM L-Asn was measured in 10 mM PBS pH 7.5 at 37 \({}^{\circ}\)C. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Pair of Amino Acids** & **Distance, Å** & **Spermine (16.1 Å)** \\ \hline Asp123–Glu166 & 15.8 & + \\ Glu166–Glu166 & 10.3 & + \\ Glu166–Asp169 & 19.7 & +/ – \\ Asp123–Asp123 & 11.2 & + \\ Glu25-Asp79 & 21.1 & +/ – \\ Glu25-Glu24 & 17.5 & + \\ Glu24-Glu24 & 20.9 & +/ – \\ Asp152–Asp170 & 12.4 & + \\ Glu166–Asp170 & 12.0 & + \\ Asp152–Asp152 & 16.0 & + \\ Asp169–Asp88 & 18.4 & +/ – \\ Asp169–Asp123 & 20.3 & +/ – \\ Glu25–Asp20 & 24.4 & \\ Glu24–Asp20 & 16.5 & + \\ Glu24–Glu37 & 25.1 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Interatomic distances between Asp and Glu residues for the RrA subunits. Pairs of amino acids that can potentially form two-point cross-links are marked with “+”. The pairs that turn out to be closest to spermine as a result of docking are highlighted in bold. There are almost no bonds between the active center and spermine when different sites of the protein are selected, including the whole molecule, according to the results of docking with the dimer and tetramer (Figure 5). Spermine should not interfere with the hydrolysis of L-asparagine, which is consistent with the obtained activity results. When docking with the RrA dimer, spermine is located close to at least five Asp and Glu pairs from Table 5. However, only three are suitable for cross-linking formation: between Asp170 and Glu166, between Asp152 and Asp152, and between Asp169 and Asp88. In the case of the tetramer, the number of potential contacts increases. So, the simulation of the spermine interaction with the tetramer realizes six fifteen possible contacts. Indeed, additional contacts between Glu24 and Asp20, Glu166 and Glu166, and Glu166 and Asp169 emerged in the case of the tetramer. In the case of a dimer, one RrA subunit interacts with only one side of the other subunit. In the case of a tetramer, an additional interaction surface is formed between the subunits. In this case, additional amino acids of each monomer are involved in the interaction. The model does not show the real distance between the subunits, so other amino acid pairs cannot be excluded. We can assume that spermine, as a highly active cross-linking agent, will tend to form more bonds in the tetramer than in the dimer. The experimental results suggest that spermine stabilizes the tetrameric structure.