It can be seen in Fig. 1 that dimers and hexamers generally tend to stabilize as the box size increases. As expected, the absolute RMSF values for hexamers are higher (by 2 orders of magnitude) than for dimers.

RMSF values of dimers (1) and hexamers (2) averaged over all Cα atoms depending on the distance between the box face and protein atoms.

The deviations of the dimer atoms are practically independent of the box size, since the average RMSF values of its atoms vary within 0.1 Å. In contrast, the difference between the maximum and minimum RMSF values of the hexamer is approximately 8 Å.

Figure 2 demonstrates that the dimer tends to become more compact as the box size increases. However, in general, the distance between the protein and the box edge does not significantly affect the volume of the dimer, since the Rg values vary slightly (in the range of 0.5% of the absolute Rg value). Considering that the gyration radius of the hexamer isolated from the crystal structure of lysozyme is 2.7 nm, its compactness is closest to the original one at distances (between the protein and the box) of 2, 2.5, and 3 nm. For the smallest (1 and 1.5 nm) boxes, the deviations of the hexamer volume from the initial one are very significant.

Radius of gyration of dimers (1) and hexamers (2) averaged over the entire simulated time (1 μs) depending on the distance between the box face and protein atoms.

According to the SAXS data [10], protein dimers are formed in the crystallization solution of lysozyme, but its hexamers are absent. Thus, the results of modeling dimers and hexamers are consistent with experimental ones [10] regardless of the box size, since dimers are generally stable (although slightly more flexible in small boxes), and hexamers dissociate (as shown by visual inspection of the hexamer trajectories) within 1-μs dynamics in all considered boxes. However, MD showed that the most noticeable transformations of the hexamer structure occur when the distances between the protein and the box edge are 1 and 1.5 nm (Figs. 1–2). Therefore, the modeling of protein oligomers in relatively small boxes can lead to more obvious results and faster prediction of the oligomer instability.

This phenomenon can be explained by the fact that small simulation boxes can better reproduce the real crystallization conditions of protein solutions, since real oligomers are surrounded not only by one solution and precipitant ions, but also by other protein molecules. Despite the fact that the initial concentration of lysozyme in a drop with the crystallization solution is low (40 mg/mL [10]), it gradually increases due to the evaporation of water. In addition, the molecules in solution are in constant motion, which increases the likelihood of collisions and interactions of oligomers with other protein molecules. Since periodic boundary conditions were used in the work, in relatively small boxes the oligomers “feel” their virtual copies from neighboring boxes, which more accurately models the real environment of the oligomers in the crystallization solution. Moreover, the smaller the size of the simulation box, the less computational resources (including time) are required to perform MD calculations. For lysozyme, it was found that the minimum distance between protein atoms and the box edge should be 1 nm for adequate modeling of its oligomers in the crystallization solution.