NMR studies of excluded volume interactions in peptide dendrimers
Peptide dendrimers are good candidates for diverse biomedical applications due to their biocompatibility and low toxicity. The local orientational mobility of groups with different radial localization inside dendrimers is important characteristic for drug and gene delivery, synthesis of nanoparticles, and other specific purposes. In this paper we focus on the validation of two theoretical assumptions for dendrimers: (i) independence of NMR relaxations on excluded volume effects and (ii) similarity of mobilities of side and terminal segments of dendrimers. For this purpose we study 1 H NMR spin-lattice relaxation time, T 1H , of two similar peptide dendrimers of the second generation, with and without side fragments in their inner segments. Temperature dependences of 1/T 1H in the temperature range from 283 to 343 K were measured for inner and terminal groups of the dendrimers dissolved in deuterated water. We have shown that the 1/T 1H temperature dependences of inner groups for both dendrimers (with and without side fragments) practically coincide despite different densities of atoms inside these dendrimers. This result confirms the first theoretical assumption. The second assumption is confirmed by the 1/T 1H temperature dependences of terminal groups which are similar for both dendrimers.
<!>Experimental<!>Results and Discussion
<p>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.</p><p>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 dendrimers 1 . They were used in many biomedical application, in particular as carriers for drug and gene delivery [2][3][4][5][6] .</p><p>The structural properties of lysine dendrimers were studied both experimentally 7,8 and by computer simulation using molecular dynamics [9][10][11][12] and Brownian dynamics methods 13 . In our papers 10,11 we applied algorithms and computer programs elaborated by us for charged and branched polymers earlier [14][15][16][17] .</p><p>More general peptide dendrimers could contain not only lysine but also other amino acid residues. Such branched peptides were synthesized [18][19][20] and used for several biomedical applications including drug and gene delivery, artificial enzymes, antimicrobial peptides etc [21][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 delivery 27,28 . In the review 29 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 method [30][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.</p><p>NMR relaxation methods are widely used to study the local mobility in macromolecules (see review 33 ). Over the last 15 years, the description of NMR relaxation in dendrimers in dilute solution has been developed in theoretical 34 , computer simulations [35][36][37][38] , and experimental [39][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 interactions 45 . 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 size 38 . 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 core 37 . However, the semiflexibility of dendrimers results in suppression of EV effects on the orientational mobility in the dendrimer 38 . We would also like to note recent studies of orientation mobility in dendrimer melts [46][47][48][49] .</p><p>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 generations [50][51][52][53] .</p><p>In the first theoretical papers on branched macromolecules with side fragments, the viscoelastic models without EV were used [54][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.</p><p>Therefore, the aim of this work is to experimentally verify the following theoretical conclusions:</p><p>(1) Excluded volume effects do not influence the orientational mobility of groups observed by NMR relaxation;</p><p>(2) The mobility of groups in the side fragments coincides with the mobility of the terminal groups.</p><p>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).</p><p>Both dendrimers have an asymmetrical branching (see Fig. 2). The contour lengths of the segments between the branching points in both are equal.</p><p>According to Fig. 2, Lys-2Gly-dendrimer has the CH 2 -(NH) groups inside the main chain and we consider them as "inner" groups in this study. Also, the Lys-2Gly-dendrimer has the "terminal" CH 2 groups of lysine residue connected with terminal protonated NH 3 + groups, which are located in terminal segments. Lys-2Lys-dendrimer has the "inner" CH 2 groups in the main chain, but only in those segments, which contain the ε-part of lysine. In Lys-2Lys-dendrimer both CH 2 groups connected with protonated NH 3 + groups in the side fragments and in the terminal segments are considered as "terminal" one.</p><p>Due to an absence of charged NH 3 + 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.</p><p>For the second statement, the same structures distinguished by the presence of side fragments help to evaluate the mobility of the segments.</p><p>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 work 37,43 .</p><!><p>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 previously 20 .</p><p>Some structural parameters of the dendrimers are presented in Table 1.</p><p>We dissolved samples in 0.17 M NaCl D 2 O. 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.</p><p>1 H 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 1 H spin-lattice relaxation times, T 1H, 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 gradients 60 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.</p><p>We explored the signals from the СН 2 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 СН 2 -(NH) and terminal CH 2 -(NH 3 + ) 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 CH 2 -(NH 3 + ) groups in the side fragments (Fig. 2c,d) move freely like those in terminal segments (Fig. 2e) and, consequently, have the same chemical shift.   1. Some parameters of dendrimers. G is the number of generation; M d is the molecular weight of a dendrimer. N ter is the number of terminal lysine segments containing two protonated NH 3 + groups, N in is the number of inner segments, and N ch is the number of charged groups; D is the diffusion coefficient (measured at room temperature); R h is the hydrodynamic radius and ρ is the effective density. We also checked that a possible hydrated shell of charged NH 3 groups does not influence on T 1H for neighboring CH 2 groups (see Sections 2 and 3 in Supplementary information).</p><!><p>To study local orientational mobility in the peptide dendrimers we consider temperature dependences of 1 H spin-lattice NMR relaxation time, T 1H . In the framework of the dipole-dipole relaxation mechanism of 1 H nuclei (protons) 1/T 1H function can be written as [63][64][65][66][67] :</p><p>where ω H is the cyclic resonance frequency (2πf 0 ) for 1 H nuclei; A 0 is a constant that does not depend on temperature and frequency; and J is the spectral density which corresponds to Fourier transform from P 2 orientational autocorrelation functions averaged over groups contributing to a corresponding peak. In the general case, the spectral density function for 1 H nuclei has the form:</p><p>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</p><p>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/T 1H . There is a significant difference between the 1/T 1H temperature dependences for peaks 1 (inner CH 2 -(NH) groups) and 2 (terminal CH 2 -(NH 3 + ) 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/T 1H maximum) is observed for the inner groups (peak 1), whereas for the terminal groups the 1/T 1H values increase exponentially with decreasing temperature. Thus, the terminal groups have higher mobility than inner segments 37 .</p><p>The temperature dependences of 1/T 1H 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 results 38 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)</p><p>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)</p><p>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/T 1H 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 simulations 38 based on the theory 34 , 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 whole 37,38 . 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.</p><p>As mentioned above, the temperature dependence of 1/T 1H for peak 2 (terminal CH 2 -(NH 3 + ) 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/T 1H can be proportional to</p><p>where τ max is the maximal relaxation time of macromolecules. According to Eq. ( 6), a larger value of 1/T 1H corresponds to a slower local orientation mobility of the NMR active group.</p><p>As seen in Fig. 4, the 1/T 1H 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/T 1H dependence for Lys-2Lys from analogous 1/T 1H 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/T 1H should be observed for the Lys-2Lys dendrimer. This conclusion agrees well with results of the analytic theory 55 . 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.</p>