Introduction

Dendrimers are highly branched monodisperse macromolecules with a well-defined structure. The main difference between dendrimers and other nanoscale molecules is the possibility to control their chemical composition, size, and architecture. It allows designing structures with unique properties for various applications.

In recent years poly-L-lysine (PLL) dendrimers have attracted attention from researchers due to their high biocompatibility and relatively low toxicity in comparison with most of other dendrimers1. They were used in many biomedical application, in particular as carriers for drug and gene delivery2,3,4,5,6.

The structural properties of lysine dendrimers were studied both experimentally7,8 and by computer simulation using molecular dynamics9,10,11,12 and Brownian dynamics methods13. In our papers10,11 we applied algorithms and computer programs elaborated by us for charged and branched polymers earlier14,15,16,17.

More general peptide dendrimers could contain not only lysine but also other amino acid residues. Such branched peptides were synthesized18,19,20 and used for several biomedical applications including drug and gene delivery, artificial enzymes, antimicrobial peptides etc21,22,23,24,25,26. In the last years the properties of the group of peptide dendrimers of the same topology but of different amino acid composition have been compared for possible use in DNA and siRNA delivery27,28. In the review29 the use of peptides for drug and gene delivery was also discussed. Beside experimental works on application of peptide dendrimers, there are several papers where computer simulation of peptide dendrimers was performed using molecular dynamics method30,31,32. In our opinion, peptide dendrimers have almost unlimited potential for use in biomedicine, since they allow the creation of a huge number of artificial branched peptides, the number of which is even greater than the number of natural (linear) peptides and proteins.

NMR relaxation methods are widely used to study the local mobility in macromolecules (see review33). Over the last 15 years, the description of NMR relaxation in dendrimers in dilute solution has been developed in theoretical34, computer simulations35,36,37,38, and experimental39,40,41,42,43 works. These results were summarized in the recent review by Markelov et, et al.44. It was established that the local orientational mobility of NMR active groups in a dendrimer depends on their topological distance from the periphery. This regularity is practically independent of the excluded volume (EV)38 and the hydrodynamic interactions45. Note that in ref.38 the EV effects for dendrimer segments were simulated by using the Lennard-Jones potential. Moreover, computer simulations demonstrated that EV effects only rotation of a dendrimer as a whole and this influence depends on the dendrimer size38. The rotation of a dendrimer as a whole was calculated from the finite slope of orientational autocorrelation functions for vectors from the dendrimer core to a terminal segment. Effect of EV is small for terminal groups and is big for groups in the dendrimer core37. However, the semiflexibility of dendrimers results in suppression of EV effects on the orientational mobility in the dendrimer38. We would also like to note recent studies of orientation mobility in dendrimer melts46,47,48,49.

The theory of orientational mobility has been developed for classical (“ideal”) dendrimers where there are no defects in the tree-like structure. The next logical step is the development of the theory of orientational mobility for non-regular hyperbranched polymers in which regular tree-like structure is not expected. Branching points in this kind of polymers could have different functionality and branches containing a random number of generations50,51,52,53.

In the first theoretical papers on branched macromolecules with side fragments, the viscoelastic models without EV were used54,55,56,57,58. It was obtained that for this model, the local mobility of the side fragments and mobility of the terminal segments are equal. This statement follows from the conclusion that the mobility of a dendrimer segment is determined by its topological distance from the periphery. In the terminology used, the side fragment is a terminal one. In real systems, such behavior would be observed if suppression of excluded volume interactions occurs, which the developed theory does not take into account.

Therefore, the aim of this work is to experimentally verify the following theoretical conclusions:

  1. (1)

    Excluded volume effects do not influence the orientational mobility of groups observed by NMR relaxation;

  2. (2)

    The mobility of groups in the side fragments coincides with the mobility of the terminal groups.

In this paper, we study two types of second generation peptide dendrimers (G = 2, 16 terminal groups) that are suitable for these purposes. The first dendrimer consists of repeating units containing one lysine residue and two linear glycine residues between each two neighboring branching points (Lys-2Gly-dendrimer) (Fig. 1a). The second dendrimer consists of repeating units containing three lysine amino acid residues one of which is branched while two other lysines are linear and connect neighboring branching points (Lys-2Lys-dendrimer) (Fig. 1b). Each segment of the Lys-2Lys-dendrimer comprises two side fragments containing the ε-part of lysine (Fig. 2c,d).

Figure 1
figure 1

Schematic structures of the second generation (a) Lys-2Gly and (b) Lys-2Lys dendrimers. The colors mark following dendrimer parts: cores (green), inner segments of main chains (black), side fragments (blue), terminal segments (red). Red solid circles are the branching points.

Full size image
Figure 2
figure 2

Chemical structures of inner and terminal segments in the Lys-2Gly and Lys-2Lys dendrimers. Lys-2Gly inner segments containing (a) ε-part and (b) α-part of lysine and two glycine residues; Lys-2Lys inner segments containing (c) ε-part and (d) α-part of lysine and two lysine residues; and (e) the terminal segment is the same for both dendrimers. Black color marks the main chain, blue one corresponds to the side fragments. Red open circles show the branching points. NMR active methylene groups of the main chain connected with NH groups are highlighted in orange color and CH2 groups connected with protonated NH3+ groups are highlighted in magenta color.

Full size image

Both dendrimers have an asymmetrical branching (see Fig. 2). The contour lengths of the segments between the branching points in both are equal.

According to Fig. 2, Lys-2Gly-dendrimer has the CH2-(NH) groups inside the main chain and we consider them as “inner” groups in this study. Also, the Lys-2Gly-dendrimer has the “terminal” CH2 groups of lysine residue connected with terminal protonated NH3+ groups, which are located in terminal segments. Lys-2Lys-dendrimer has the “inner” CH2 groups in the main chain, but only in those segments, which contain the ε-part of lysine. In Lys-2Lys-dendrimer both CH2 groups connected with protonated NH3+ groups in the side fragments and in the terminal segments are considered as “terminal” one.

Due to an absence of charged NH3+ groups in the inner segments, the interior of the Lys-2Gly-dendrimer is less hydrophilic compared to the interior of the Lys-2Lys-dendrimer. We assume that it should lead to a more compact structure of the Lys-2Gly-dendrimer and, consequently, to the intensification of EV effects. Comparison of NMR relaxations of groups in the main chain of inner segments of Lys-2Gly and Lys-2Lys allows us to estimate the effect of excluded volume interactions and to check the first statement.

For the second statement, the same structures distinguished by the presence of side fragments help to evaluate the mobility of the segments.

We also present data for usual G2 lysine dendrimer, containing only one branched repeating lysine residue (Lys-dendrimer) for comparison. This dendrimer was studied in our earlier work37,43.

Experimental

Lysine-based dendrimers of 2nd generation were synthesized by standard solid phase peptide synthesis (SPPS) (see Supplementary Information). Dendrimers were purified, analyzed and characterized as described previously20.

Some structural parameters of the dendrimers are presented in Table 1.

Table 1 Some parameters of dendrimers.
Full size table

We dissolved samples in 0.17 M NaCl D2O. Concentrations of dendrimers in the solvent were 2.69 g/dl, 1.49 g/dl, and 1.46 g/dl for Lys, Lys-2Lys, and Lys-2Gly, respectively. All systems correspond to the condition of the dilute solution.

1H NMR measurements were performed on a Bruker Avance III 500 MHz spectrometer using a Bruker Diff 30 diffusion probe with a Great 1/60 A amplifier. The 1H spin-lattice relaxation times, T1H, were acquired with an “inversion-recovery” sequence modified by the destructive gradient pulses at the beginning of the sequence (“spoiler recovery” sequence)59. Parameters for the pulses were 12–18 μs duration of π/2 pulse, 16 tau delays and a 3 s recycle time between scans. The diffusion coefficients were measured by a stimulated echo sequence with bipolar gradients60 to compensate for the effects of convection. The gradient pulse length and the diffusion time were set to 1 ms and 20 ms, respectively. We used 16 gradients and 16 scans for each gradient.

We explored the signals from the СН2 groups chemically connected with N-atoms to study the orientational mobility in the samples by NMR relaxation because the signals from these groups are in the well-separated region of peptide dendrimer spectrum (chemical shift ~3 ppm), and because we can observe separate peaks for inner СН2-(NH) and terminal CH2-(NH3+) groups (peak 1 and peak 2 in Fig. 3, respectively)37,43,58,61,62. In the case of the Lys-2Lys dendrimer (Fig. 3a), the terminal CH2-(NH3+) groups in the side fragments (Fig. 2c,d) move freely like those in terminal segments (Fig. 2e) and, consequently, have the same chemical shift.

Figure 3
figure 3

1Н NMR spectra of the Lys-2Lys (a), Lys-2Gly (b) and Lys (c) G2 dendrimers at T = 293 K. Peak 1 corresponds to inner СН2-(NH) and peak 2 to terminal CH2-(NH3+) groups.

Full size image

We also checked that a possible hydrated shell of charged NH3 groups does not influence on T1H for neighboring CH2 groups (see Sections 2 and 3 in Supplementary information).

Results and Discussion

To study local orientational mobility in the peptide dendrimers we consider temperature dependences of 1H spin-lattice NMR relaxation time, T1H. In the framework of the dipole-dipole relaxation mechanism of 1H nuclei (protons) 1/T1H function can be written as63,64,65,66,67:

$$1/{T}_{1H}={A}_{0}(J({\omega }_{H},{\tau }_{i})+4J(2{\omega }_{H},{\tau }_{i})),$$
(1)

where ω H is the cyclic resonance frequency (2πf0) for 1H nuclei; A0 is a constant that does not depend on temperature and frequency; and J is the spectral density which corresponds to Fourier transform from P2 orientational autocorrelation functions averaged over groups contributing to a corresponding peak. In the general case, the spectral density function for 1H nuclei has the form:

$$J(n{\omega }_{H},{\tau }_{i})=\sum _{i}\frac{{C}_{i}{\tau }_{i}}{1+{({\tau }_{i}n{\omega }_{H})}^{2}},$$
(2)

where τ i and C i are ith correlation times and their contribution to J, respectively, and n = 1, 2. The correlation time is determined by Arrhenius dependence

$$\tau ={\tau }_{0}\exp (\frac{{E}_{a}}{{k}_{b}{\rm{T}}}),$$
(3)

where E a is the activation energy for the chosen group, T and k b are temperature and Boltzmann constant, respectively.

Figure 4 illustrates the experimental results for the temperature dependence of spin-lattice relaxation rate, 1/T1H. There is a significant difference between the 1/T1H temperature dependences for peaks 1 (inner CH2-(NH) groups) and 2 (terminal CH2-(NH3+) groups) in the Lys-2Lys and Lys-2Gly, as well as for dendrimers with the simple repeating unit (Lys-dendrimer). The dispersion region (i.e., 1/T1H maximum) is observed for the inner groups (peak 1), whereas for the terminal groups the 1/T1H values increase exponentially with decreasing temperature. Thus, the terminal groups have higher mobility than inner segments37.

Figure 4
figure 4

Temperature dependence of the spin-lattice relaxation rate, 1/T1H, of inner СН2-(NH) groups and terminal CH2-(NH3+) groups.

Full size image

The temperature dependences of 1/T1H for inner groups in the Lys-2Lys and Lys-2Gly dendrimers practically coincide. Therefore, the local mobility of the inner groups in the Lys-2Lys and Lys-2Gly is practically the same. This fact confirms the computer simulations results38 that NMR relaxation in dendrimer is not sensitive to EV effects because the density in these dendrimers is significantly different. To demonstrate the density difference in Lys-2Lys and Lys-2Gly dendrimers we measured their diffusion coefficients and calculated their hydrodynamic radii, R h , using the Stokes-Einstein equation (3)

$$D=\frac{{k}_{B}{\rm{T}}}{6\pi \eta {R}_{h}}$$
(4)

where η is the viscosity. If almost all atoms of the dendrimer concentrate in the sphere with a radius R h , we can estimate the density within the dendrimers, ρ, by using equation (4)

$$\rho =\frac{{M}_{d}}{\frac{4}{3}\pi {R}_{h}^{3}}$$
(5)

where M d is the molecular weight of the dendrimer. The results of the calculation given in Table 1 shows that the density in Lys-2Gly is 1.5 times higher than in the Lys-2Lys.

We found it interesting that the maximum of 1/T1H for inner groups in Lys dendrimer shifts to higher temperatures than the maxima of Lys-2Lys and Lys-2Gly dendrimers. This points out that the local mobility of the Lys-dendrimer inner segments is lower. The density of Lys-dendrimer is effectively the same as for Lys-2Lys. It means that the EV effects for both dendrimers are practically the same too; however, their relaxation rates are different. This result confirms the fact that volume effects are not the main and important factor in the NMR relaxation of inner dendrimer segments. According to the computer simulations38 based on the theory34, the main factor which effects on NMR relaxation is semiflexibility. The contour length of the Lys inner segment is shorter than that of the Lys-2Lys approximately in 3 times, and the decrease in the segment length leads to an increase in the semiflexibility. At the same time, the increase in the semiflexibility coefficient leads to the suppression of small-scale motions and to the increase of the contribution of the rotation of the dendrimer as a whole37,38. Thus, the increase of rigidity will result in a shift of the maximum to the low frequencies area (or high temperatures), that we observe for Lys in Fig. 4.

As mentioned above, the temperature dependence of 1/T1H for peak 2 (terminal CH2-(NH3+) groups) in the dendrimers under study increases exponentially with temperature decrease and we can observe narrow region where ωτ << 1 for each correlation time. In this region, 1/T1H can be proportional to

$$\frac{1}{{T}_{1H}}\approx {\tau }_{\max }$$
(6)

where τ max is the maximal relaxation time of macromolecules. According to Eq. (6), a larger value of 1/T1H corresponds to a slower local orientation mobility of the NMR active group.

As seen in Fig. 4, the 1/T1H values for peak 2 for all three dendrimers differ only slightly. This can be the fact that the peak 2 is determined by the contribution of terminal groups, and the mobility of terminal groups is practically independent of size and macromolecule tree-like structure, except the Lys-2Lys dendrimer. In the case of the Lys-2Lys dendrimer, peak 2 is the sum of the contribution of terminal groups (33.3%) and side fragments (66.6%). The small difference of 1/T1H dependence for Lys-2Lys from analogous 1/T1H dependences for other dendrimers means that the orientational mobility of the groups in the side fragments coincides with the mobility of the terminal groups. Otherwise, a more complex temperature behavior (superposition of the peaks 1 and 2) of 1/T1H should be observed for the Lys-2Lys dendrimer. This conclusion agrees well with results of the analytic theory55.

As a summary, our experimental results show that NMR relaxation of groups in semiflexible dendrimers is not sensitive to changes in volume interactions and is determined by a topological distance from the periphery. We believe that this confirmation of theoretical conclusions is important for the development of the theory of the orientational mobility of hyperbranched systems. Additionally, our results will be useful for biomedical applications of peptide dendrimers.