The effect of excluded volume (EV) interactions on the manifestation of the local dynamics in the spin–lattice NMR relaxation in dendrimers has been studied by using Brownian dynamics simulations. The study was motivated by the theory developed by Markelov et al., [J. Chem. Phys., 2014, 140, 244904] for a Gaussian dendrimer model without EV interactions. The theory connects the experimentally observed dependence of the spin–lattice relaxation rate 1/T_¹H on the location of NMR active groups with the restricted flexibility (semiflexibility) of dendrimers. Semiflexibility was introduced through the correlations between the orientations of different segments. However, these correlations exist even in flexible dendrimer models with EV interactions. We have simulated coarse-grained flexible and semiflexible dendrimer models with and without EV interactions. Every dendrimer segment consisted of two rigid bonds. Semiflexibility was introduced through a potential which restricts the fluctuations of angles between neighboring bonds but does not change orientational correlations in the EV model as compared to the flexible case. The frequency dependence of the reduced 1/T_¹H(ω_H) for segments and bonds belonging to different dendrimer shells was calculated. It was shown that the main effect of EV interactions consists of a much stronger contribution of the overall dendrimer rotation to the dynamics of dendrimer segments as compared to phantom models. After the exclusion of this contribution the manifestation of internal dynamics in spin–lattice NMR relaxation appears to be practically insensitive to EV interactions. For the flexible models, the position ω_max of the peak of the modified 1/T_¹H(ω_H) does not depend on the shell number. For semiflexible models, the maximum of 1/T_¹H(ω_H) for internal segments or bonds shifts to lower frequencies as compared to outer ones. The dependence of ω_max on the number of dendrimer shells appears to be universal for segments and bonds in dendrimer models with and without EV interactions.

In this paper, we perform computer simulation of two lysine-based dendrimers with Lys-2Lys and Lys-2Gly repeating units. These dendrimers were recently studied experimentally by NMR (Sci. Reports, 2018, 8, 8916) and tested as carriers for gene delivery (Bioorg. Chem., 2020, 95, 103504). Simulation was performed by molecular dynamics method in a wide range of temperatures. We have shown that the Lys-2Lys dendrimer has a larger size but smaller fluctuations as well as lower internal density in comparison with the Lys-2Gly dendrimer. The Lys-2Lys dendrimer has larger charge but counterions form more ion pairs with its NH ${}_3^{+}$ groups and reduce the bare charge and zeta potential of the first dendrimer more strongly. It was demonstrated that these differences between dendrimers are due to the lower flexibility and the larger charge (+2) of each 2Lys spacers in comparison with 2Gly ones. The terminal CH₂ groups in both dendrimers move faster than the inner CH₂ groups. The calculated temperature dependencies of the spin-lattice relaxation times of these groups for both dendrimers are in a good agreement with the experimental results obtained by NMR.

The radius of gyration, Rg, and the hydrodynamic radius, Rh, are the main experimental parameters that characterize the size of linear and branched macromolecules. In the case of dendrimers in solution, the ratio Rg/Rh, depending on the global conformation, varies from 1 (for a Gaussian soft sphere) to 3/5 (for a hard sphere). However, for high-generation dendrimers, this ratio may be less than the limiting value for a hard sphere. To understand the reasons of the low Rg/Rh value (<0.77), we have studied the second-generation peptide dendrimer containing pH-sensitive histidine amino acid residues (Lys-2His dendrimer) using small-angle x-ray (SAXS) and dynamic light scattering (DLS) experiments, as well as molecular dynamics simulations. The Lys-2His dendrimer takes a swollen conformation at pH = 2 and a collapsed 1 at pH = 7. Our results show that the Rg/Rh ratio for the considered dendrimer decreases from ≈3/5 at pH = 2 to 0.5 at pH = 7. We have found that the very low Rg/Rh value is due to (1) the formation of a dense impenetrable core (i.e., the transformation of the dendrimer from a Gaussian soft sphere into a sphere with a dense core) and (2) the presence of a larger number of solvent molecules in the dendrimer corona than in a typical macromolecule. In addition, in this work, we have directly confirmed in the experiments for the first time, the collapse of the Lys-2His dendrimer with increasing pH.