## 1 Introduction  
L-asparaginase preparations from _Eslerichia coli_ (EcA) and its PEGylated form, as well as _Erwinia chrysanthemi_ (ErA), are currently used in leukemia chemotherapy [1; 2]. The principal mechanism of action of the enzymes is associated with their ability to hydrolyze L-asparagine, which results in a decrease in its concentration in the bloodstream. Tumor cells are more sensitive to a lack of L-asparagine, which plays an important role in cell life by participating in the synthesis of proteins and nucleic acids. Contrary to normal cells, cancer cells are often unable to synthesize L-asparagine on their own. As a result, cancer cells undergo apoptosis when this amino acid is deficient. The main drawback of the use of these L-asparaginases in chemotherapy is the hypersensitivity that occurs in patients taking EcA or ErA. To prevent allergic reactions, new types of L-asparaginases derived from other microorganisms can be applied.  
One of the promising enzymes for use in the chemotherapy of leukemia is _Rhodospirillum rubrum_ L-asparaginase. It has a low homology with EcA and ErA, as well as a shorter amino acid sequence (172 a.a., 18 kDa), which makes the enzyme potentially less immunogenic. The RrA has pronounced antitumor activity on a number of leukemia cell lines in vitro as well as in vivo [3]. A shifted pH optimum and a high Michaelis constant are the disadvantages of RrA.  
One of the methods to improve the physicochemical properties of L-asparaginase is the covalent modification of the enzyme [4]. Modification of EcA with polyethylene glycol (PEG) made it possible to develop a drug with reduced immunogenicity and an increased lifetime in the bloodstream [5; 6]. In our earlier works, it was found that chitosan-based copolymers allow us to increase the activity, thermostability, trypsin resistance, and cytotoxicity of _Erwinia carotovora_ L-asparaginase (EwA) [7; 8]. The mentioned polycations also had a positive effect on RrA. In our previous article, we found that a non-covalent complex formation with polycations such as polyethyleneimine (PEI), PEGylated polyethyleneimine (PEI-PEG), and PEGylated chitosan (chit-PEG) have a positive effect on RrA activity [9]. In particular, 25 kDa of PEI, as part of a polyelectrolyte complex with RrA, increased the rate of L-asparagine hydrolysis for this enzyme by up to 30%. Covalent conjugates of RrA with chit-PEI and chit-PEG also increased the activity by 17 and 32%, respectively. On the other hand, PEI and its copolymers are actively used for the development of anti-cancer drug delivery systems, as well as in gene therapy [10]. Therefore, also focusing on the positive results obtained for RrA, PEI-based polycations are of particular interest for studying further effects on the properties of L-asparaginase. Shorter polyamines, such as spermine and spermidine, also have a cationic nature and have an effect on various biochemical functions of cells [11]. Polyamines are also bifunctional cross-linking agents. They can be used to form covalent cross-links between the subunits of L-asparaginases and influence the activity and stability of the enzyme. Thus, it is of interest in this work to investigate how the cross-linking of spermine affects the properties of RrA.  
The aim of the study was to find out how the properties of RrA are affected by conjugation with polyamines based on polyamines: branched PEI-PEG copolymers with an MW of 30 kDa, linear PEI with an MW of 2 kDa, and Spm. Since strong polyelectrolytes can have a negative effect on the enzyme, it is also intended to compare the effect of PEI on RrA compared to its PEGylated form.