## 1 Introduction  
Magnetotactic bacteria (MTB) are organisms that have been deeply studied in recent years, due to their interesting magnetic behavior and their potential applications in theranostics and hyperthermia, and as biosensor devices. MTB produce organelles arranged as intracellular chains of submicron-sized membrane-enclosed magnetic particles called magnetosomes, composed of magnetite (Fe\({}_{3}\)O\({}_{4}\)) or greigite (Fe\({}_{3}\)S\({}_{4}\)) single crystals [1; 2; 3; 4; 5]. They orient and move along the Earth's geomagnetic field lines searching the areas of aqueous reservoirs where the magnetic field helps MTB to locate at the oxic-anoxic transition zone within chemical gradients.  
The crystalline properties of magnetosomes make them very attractive for bioengineering applications, including use as contrast agents in nuclear magnetic resonance imaging or nano-heaters in hyperthermia therapy [6]. In the latter case, the heating efficiency demonstrated by magnetosomes was reported to be higher than the heating efficiency that characterized the nanoparticles prepared by the chemical synthesis protocols [7; 8]. Since the competitive chemical procedures yield wide-range nanoparticle distributions [9; 10] and smaller heating efficiencies, it became appealing to use MTB as bioreactors to produce high-quality magnetic nanoparticles for medical purposes. MTB of the genus _Magnetospirillum_ are the best studied MTB, due to their relatively easy cultivation. _Magnetospirillum_ spp. are basically spirilla-shaped bacteria, which produce magnetite-containing magnetosomes organized in a single chain [11]. Mature crystals have a truncated octahedral shape and an average diameter of 40-45 nm [12]. All _Magnetospirillum_ species are chemoorganoheterotrophs and require microaerophilic conditions for magnetosome biosynthesis. Minor differences between species relate to the use of different sets of substrates and the range of the amount of oxygen in which cells can grow [11; 13]. It was shown that model strains _Magnetospirillum__magneticum_ AMB-1 and _Magnetospirillum__gryphiswaldense_ MSR-1 have distinct strategies in the magnetosome chain organization. In AMB-1, the chain is fragmented, while in MSR-1, the magnetic crystals are arranged as a continuous chain [14; 15; 16]. The magnetosome size and the amount of magnetosomes in the chains depend on the stage of growth [17]. In addition, physical properties, including magnetic ones, are influenced by the growth conditions and the composition of the medium [18; 19; 20; 21; 22].  
Despite a large amount of information accumulated on the magnetic behavior of MTB [9; 23; 24], there is still lack of information concerning the magnetic parameters (primarily static as well as dynamic) of magnetosomes inside the cells of different _Magnetospirillum_ species. Therefore, the main purpose of this study was to investigate freshly grown magnetotactic spirilla strains of the genus _Magnetospirillum_ that were then fixed with 5% formalin in comparison with strains that were grown and fixed a year before, to estimate the magnetic parameters of the magnetosomes inside the cells and to trace their time evolution in the nutrient medium via adding 5% formalin.  
In magnetic measurements, we employed a nonlinear longitudinal response to a weak _ac_ field with the registration of the second harmonic of magnetization \(M_{2}\) (NLR-M2). The recorded dependences of the \(M_{2}\) phase components on the static magnetic field \(H\) were further processed using formalism based on the Gilbert-Landau-Lifshitz equation for the stochastic dynamics of superparamagnetic (SP) particles underlying the Fokker-Planck (FP) kinetic equation [25; 26]. This allowed us to estimate the magnetic parameters of the magnetosomes, to establish their two-mode distribution over magnetic moments, and, accordingly, to determine their sizes, and to compare the results for some strains with electron magnetic resonance (EMR), atomic force microscopy (AFM), and known transmission electron microscopy (TEM) data.