A Molecular Dynamics Simulation of Complexes of Fullerenes and Lysine-Based Peptide Dendrimers with and without Glycine Spacers.

The development of new nanocontainers for hydrophobic drugs is one of the most important tasks of drug delivery. Dendrimers with hydrophobic interiors and soluble terminal groups have already been used as drug carriers. However, the most convenient candidates for this purpose are peptide dendrimers since their interiors could be modified by hydrophobic amino acid residues with a greater affinity for the transported molecules. The goal of this work is to perform the first molecular dynamics study of the complex formation of fullerenes C60 and C70 with Lys-2Gly, Lys G2, and Lys G3 peptide dendrimers in water. We carried out such simulations for six different systems and demonstrated that both fullerenes penetrate all these dendrimers and form stable complexes with them. The density and hydrophobicity inside the complex are greater than in dendrimers without fullerene, especially for complexes with Lys-2Gly dendrimers. It makes the internal regions of complexes less accessible to water and counterions and increases electrostatic and zeta potential compared to single dendrimers. The results for complexes based on Lys G2 and Lys G3 dendrimers are similar but less pronounced. Thus, all considered peptide dendrimers and especially the Lys-2Gly dendrimer could be used as nanocontainers for the delivery of fullerenes.

Hydrodynamic radius of dendrimers in solvents.

The diffusion properties and hydrodynamic radius, Rh, of macromolecules are important for theoretical studies and practical application. Moreover, comparison of Rh values obtained from simulation and experimental data is used to check the correctness of simulation results. Here, we study the translation mobility of poly(butylcarbosilane) dendrimers in chloroform solution using molecular dynamics simulations and consider simulation details that may influence the accuracy of the result. Different methods to estimate Rh for a dendrimer are discussed with comparison to our experimental data. It was shown that the traditional MD simulation method for extraction of the diffusion coefficient (and calculation of Rh) of dendrimers as a rule faces difficulties and requires simulation resources several times greater than, for example, the same for a linear analogue. In the majority of MD simulation papers, the diffusion coefficient and/or Rh are calculated incorrectly. Also, we establish that correction of Rh according to the simulation box or estimation of Rh by using the gyration radius does not give values close to experimental data. To avoid the mentioned problems, we found an alternative way: to consider rotational diffusion, which gives an Rh similar to that from experiment and is practically independent of the size of the simulation box and other simulation parameters.

Influence of the Chemical Structure on the Mechanical Relaxation of Dendrimers.

The rheological properties of macromolecules represent one of the fundamental features of polymer systems which expand the possibilities of using and developing new materials based on them. In this work, we studied the shear-stress relaxation of the second generation PAMAM and PPI dendrimer melts by atomistic molecular dynamics simulation. The time dependences of relaxation modulus G(t) and the frequency dependences of the storage G'(ω) and loss G″(ω) moduli were obtained. The results were compared with the similar dependences for the polycarbosilane (PCS) dendrimer of the same generation. The chemical structure of the dendrimer segments has been found to strongly influence their mechanical relaxation. In particular, it has been shown that hydrogen bonding in PAMAM dendrimers leads to an entanglement of macromolecules and the region is observed where G'(ω) > G″(ω). This slows down the mechanical relaxation and rotational diffusion of macromolecules. We believe that our comprehensive research contributes to the systematization of knowledge about the rheological properties of dendrimers.

NMR Studies of Two Lysine Based Dendrimers with Insertion of Similar Histidine-Arginine and Arginine-Histidine Spacers Having Different Properties for Application in Drug Delivery.

In this paper we study two lysine-based peptide dendrimers with Lys-His-Arg and Lys-Arg-His repeating units and terminal lysine groups. Combination of His and Arg properties in a dendrimer could be important for biomedical applications, especially for prevention of dendrimer aggregation and for penetration of dendrimers through various cell membranes. We describe the synthesis of these dendrimers and the confirmation of their structure using 1D and 2D Nuclear Magnetic Resonance (NMR) spectroscopy. NMR spectroscopy and relaxation are used to study the structural and dynamic properties of these macromolecules and to compare them with properties of previously studied dendrimers with Lys-2Arg and Lys-2His repeating units. Our results demonstrate that both Lys-His-Arg and Lys-Arg-His dendrimers have pH sensitive conformation and dynamics. However, properties of Lys-His-Arg at normal pH are more similar to those of the more hydrophobic Lys-2His dendrimer, which has tendency towards aggregation, while the Lys-Arg-His dendrimer is more hydrophilic. Thus, the conformation with the same amino acid composition of Lys-His-Arg is more pH sensitive than Lys-Arg-His, while the presence of Arg groups undoubtedly increases its hydrophilicity compared to Lys-2His. Hence, the Lys-His-Arg dendrimer could be a more suitable (in comparison with Lys-2His and Lys-Arg-His) candidate as a pH sensitive nanocontainer for drug delivery.

Mechanical relaxation of functionalized carbosilane dendrimer melts.

Functionalizing the internal structure of classical dendrimers is a new way of tailoring their properties. Using atomistic molecular dynamics simulations, we investigate the rheological behavior of functionalized dendrimer (FD) melts obtained by modifying the branching of carbosilane dendrimers (CSD). The time (relaxation modulus G(t)) and frequency (storage G' and loss G'' moduli) dependencies of the dynamic modulus are obtained. Fourth generation FD melts present a region where G' > G''. In contrast, their non-functionalized counterparts (i.e., classical dendrimers with regular branching) do not show such a region. The comparative analysis of FD and CSD suggests that the internal densification due to functionalization prevents the penetration of branches and causes FD to behave like colloidal particles in a crowded environment. Since CSD have no special interactions, we expect that this effect will be common for other dendrimer macromolecules.

Size and Structure of Empty and Filled Nanocontainer Based on Peptide Dendrimer with Histidine Spacers at Different pH.

Novel peptide dendrimer with Lys-2His repeating units was recently synthesized, studied by NMR (Molecules, 2019, 24, 2481) and tested as a nanocontainer for siRNA delivery (Int. J. Mol. Sci., 2020, 21, 3138). Histidine amino acid residues were inserted in the spacers of this dendrimer. Increase of their charge with a pH decrease turns a surface-charged dendrimer into a volume-charged one and should change all properties. In this paper, the molecular dynamics simulation method was applied to compare the properties of the dendrimer in water with explicit counterions at two different pHs (at normal pH with neutral histidines and at low pH with fully protonated histidines) in a wide interval of temperatures. We obtained that the dendrimer at low pH has essentially larger size and size fluctuations. The electrostatic properties of the dendrimers are different but they are in good agreement with the theoretical soft sphere model and practically do not depend on temperature. We have shown that the effect of pairing of side imidazole groups is much stronger in the dendrimer with neutral histidines than in the dendrimer with protonated histidines. We also demonstrated that the capacity of a nanocontainer based on this dendrimer with protonated histidines is significantly larger than that of a nanocontainer with neutral histidines.

Why the Orientational Mobility in Arginine and Lysine Spacers of Peptide Dendrimers Designed for Gene Delivery Is Different?

New peptide dendrimer with Lys-2Arg repeating units was recently studied experimentally by NMR (RSC Advances, 2019, 9, 18018) and tested as gene carrier successfully (Int. J. Mol. Sci., 2020, 21, 3138). The unusual slowing down of the orientational mobility of 2Arg spacers in this dendrimer was revealed. It has been suggested that this unexpected behavior is caused by the Arg-Arg pairing effect in water, which leads to entanglements between dendrimer branches. In this paper, we determine the reason for this slowing down using atomistic molecular dynamics simulation of this dendrimer. We present that the structural properties of Lys-2Arg dendrimer are close to those of the Lys-2Lys dendrimer at all temperatures (Polymers, 2020, 12, 1657). However, the orientational mobility of the H-H vector in CH2-N groups of 2Arg spacers in Lys-2Arg dendrimer is significantly slower than the mobility of the same vector in the Lys-2Lys dendrimer. This result is in agreement with the recent NMR experiments for the same systems. We revealed that this difference is not due to the arginine-arginine pairing, but is due to the semiflexibility effect associated with the different contour length from CH2-N group to the end of the side arginine or lysine segment in spacers.

Comparison of Structure and Local Dynamics of Two Peptide Dendrimers with the Same Backbone but with Different Side Groups in Their Spacers.

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 CH 2 groups in both dendrimers move faster than the inner CH 2 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.

Stable Deuterium Labeling of Histidine-Rich Lysine-Based Dendrimers.

Peptide dendrimers, due to their biocompatibility and low toxicity, are highly promising candidates as nanocarriers for drugs and genes. The development of this kind of delivery system requires reliable monitoring of their metabolic and biological pathways. In this respect, hydrogen isotope labeling has tremendous importance, being a safe tool for detection of the labeled nanocarriers. In this work, we have synthesized new histidine-rich lysine-based dendrimers (Lys-2His dendrimer) with two linear histidine (His) residues in every inner segment. The presence of His residues has enabled us to perform controlled deuteration of Lys-2His dendrimers. The high deuteration degree (around 70%) does not practically change after redissolving the samples in H2O and heating them at 40 °C, which indicates the isotopic label stability.

Lysine-based dendrimer with double arginine residues.

Due to their well-defined structure, multivalency, biocompatibility, and low toxicity, lysine dendrimers can be used as safe and efficient nanocarriers for drug and gene delivery. One useful strategy for improving the gene delivery properties of dendrimers is modification with arginine amino acid (Arg) residues. Incorporation of Arg residues could be favorable for the enhancement in transfection efficiency of lysine based dendrimers. In this work, we have synthesized a new second-generation poly-l-lysine dendrimer with repeating units containing two linear Arg residues between neighboring lysine branching points (Lys-2Arg dendrimer) and studied its physicochemical properties. We confirmed the structure of Lys-2Arg dendrimer using various one- and two-dimensional 1H and 13C NMR spectroscopy methods. Comparison of T 1H relaxation data for Lys-2Arg and Lys-2Lys dendrimers showed that the replacement of double Lys residues with double Arg residues resulted in a sharp decrease in the mobility of methylene groups in side segments and in the main chain of ε-Lys inner segments. We suggest that this unexpected effect is caused by a guanidine-guanidine pairing effect in water, which leads to entanglements between dendrimer branches.

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 1H NMR spin-lattice relaxation time, T1H, of two similar peptide dendrimers of the second generation, with and without side fragments in their inner segments. Temperature dependences of 1/T1H 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/T1H 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/T1H temperature dependences of terminal groups which are similar for both dendrimers.

Molecular mobility in several imidazolium-based ionic liquids according to data of 1 H and 13 C NMR relaxation.

Temperature dependences are compared for 1 H and 13 C NMR 1/T1 curves relaxation rates in three imidazolium-based ionic liquids (ILs), namely, in [bmim]PF6 , [bmim]BF4 , and [emim]CH3 COO. 13 C curves show alike behavior for all three ILs and follow a well-known Bloembergen-Pound-Purcell (BPP) equation. On the contrary, an essential part of 1 H curves differ strongly from corresponding 13 C ones and also have different shapes for different ILs. For the first time, we have detected the specific, two-maximum shape of 1 H relaxation curve for hydrogen atom of C(2)H group of the [emim]CH3 COO. Assuming that this maximum reflects the correlated rotation of several adjoining ion pairs, we have tried to destroy this rotation by addition of glycerol to the [emim]CH3 COO. The second, high-temperature maximum has disappeared in the [emim]CH3 COO-glycerol mixture, and this fact confirms our assumption. Copyright © 2017 John Wiley & Sons, Ltd.

Investigation of Melts of Polybutylcarbosilane Dendrimers by 1H NMR Spectroscopy.

Melts of polybutylcarbosilane (PBC) dendrimers from third (G3) up to sixth (G6) generations are investigated by 1H NMR spectroscopy in a wide temperature range up to 493 K. At room temperature, NMR spectra of G3-G5 dendrimers exhibit resolved, solution-like spectra ("liquid" phase). In contrast, the spectrum of the G6 dendrimer is characterized by a single unresolved broad line at whole temperature range, which supports the presence of an anomalous phase state of G6 at temperatures higher than glass transition temperature. For the first time, an unexpected transition of G5 dendrimer from a molecular liquid state to an anomalous state/phase upon temperature increase has been detected using NMR data. Specifically, an additional wide background line appears in the G5 spectrum above 473 K, and this line corresponds to a G5 state characterized by restricted molecular mobility, i.e., a state similar to the "anomalous" phase of G6 melt. The fraction of the G5 dendrimers in "anomalous" phase at 493 K is approximately 40%. Analysis of the spectral shapes suggests that changes in the G5 dendrimers are reversible with temperature.

Local orientational mobility in regular hyperbranched polymers.

We study the dynamics of local bond orientation in regular hyperbranched polymers modeled by Vicsek fractals. The local dynamics is investigated through the temporal autocorrelation functions of single bonds and the corresponding relaxation forms of the complex dielectric susceptibility. We show that the dynamic behavior of single segments depends on their remoteness from the periphery rather than on the size of the whole macromolecule. Remarkably, the dynamics of the core segments (which are most remote from the periphery) shows a scaling behavior that differs from the dynamics obtained after structural average. We analyze the most relevant processes of single segment motion and provide an analytic approximation for the corresponding relaxation times. Furthermore, we describe an iterative method to calculate the orientational dynamics in the case of very large macromolecular sizes.

Unexpected Temperature Behavior of Polyethylene Glycol Spacers in Copolymer Dendrimers in Chloroform.

We have studied copolymer dendrimer structure: carbosilane dendrimers with terminal phenylbenzoate mesogenic groups attached by poly(ethylene) glycol (PEG) spacers. In this system PEG spacers are additional tuning to usual copolymer structure: dendrimer with terminal mesogenic groups. The dendrimer macromolecules were investigated in a dilute chloroform solution by (1)H NMR methods (spectra and relaxations). It was found that the PEG layer in G = 5 generations dendrimer is "frozen" at high temperatures (above 260 K), but it unexpectedly becomes "unfrozen" at temperatures below 250 K (i.e., melting when cooling). The transition between these two states occurs within a small temperature range (~10 K). Such a behavior is not observed for smaller dendrimer generations (G = 1 and 3). This effect is likely related to the low critical solution temperature (LCST) of PEG and is caused by dendrimer conformations, in which the PEG group concentration in the layer increases with growing G. We suppose that the unusual behavior of PEG fragments in dendrimers will be interesting for practical applications such as nanocontainers or nanoreactors.

Molecular dynamics simulation of spin-lattice NMR relaxation in poly-L-lysine dendrimers: manifestation of the semiflexibility effect.

NMR relaxation experiments are widely used to investigate the local orientation mobility in dendrimers. In particular, the NMR method allows one to measure the spin-lattice relaxation rate, 1/T1, which is connected with the orientational autocorrelation function (ACF) of NMR active groups. We calculate the temperature (Θ) and frequency (ω) dependences of the spin-lattice NMR relaxation rates for segments and NMR active CH2 groups in poly-L-lysine (PLL) dendrimers in water, on the basis of full-atomic molecular dynamics simulations. It is shown that the position of the maximum of 1/T1(ω) depends on the location of the segments inside the dendrimer. This dependence of the maximum is explained by the restricted flexibility of the dendrimer. Such behavior has been predicted recently by the analytical theory based on the semiflexible viscoelastic model. The simulated temperature dependences of 1/T1 for terminal and inner groups in PLL dendrimers of n = 2 and n = 4 generations dissolved in water are in good agreement with the NMR experimental data, which have been obtained for these systems previously by us. It is shown that in the case of PLL dendrimers, the traditional procedure of the interpretation of NMR experimental data - when smaller values of 1/T1 correspond to higher orientation mobility - is applicable to the whole accessible frequency interval only for the terminal groups. For the inner groups, this procedure is valid only at low frequencies.

Formation of a "Hollow" Interior in the Fourth-Generation Dendrimer with Attached Oligomeric Terminal Segments.

By using the Scheutjens-Fleer self-consistent field approach, the structure of the fourth-generation dendrimer with attached terminal chemically different oligomeric segments is studied theoretically. It is demonstrated that an incompatibility of terminal segments with inner dendrimer units leads to formation of a "hollow" core with reduced polymer density in the dendrimer center. This effect is enhanced with a deterioration in the solvent quality for terminal segments. This observation is in accordance with experimental results and molecular dynamics simulation data for an analogous system. It is established that the main factor determining the hollow core formation is the segregation between inner and terminal units because the main driving force for the effect is the localization of the terminal segments at the dendrimer periphery. The influence of structural parameters of dendrimer such as the number of generations and length of the terminal chain on this effect is also studied.

NMR relaxation of the orientation of single segments in semiflexible dendrimers.

We study the orientational properties of labeled segments in semiflexible dendrimers making use of the viscoelastic approach of Dolgushev and Blumen [J. Chem. Phys. 131, 044905 (2009)]. We focus on the segmental orientational autocorrelation functions (ACFs), which are fundamental for the frequency-dependent spin-lattice relaxation times T1(ω). We show that semiflexibility leads to an increase of the contribution of large-scale motions to the ACF. This fact influences the position of the maxima of the [1/T1]-functions. Thus, going from outer to inner segments, the maxima shift to lower frequencies. Remarkably, this feature is not obtained in the classical bead-spring model of flexible dendrimers, although many experiments on dendrimers manifest such a behavior.

13C NMR relaxation and reorientation dynamics in imidazolium-based ionic liquids: revising interpretation.

The temperature dependencies of (13)C NMR relaxation rates in [bmim]PF6 ionic liquid have been measured and the characteristic times (τc) for the cation reorientation have been recalculated. We found the origin of the incorrect τc temperature dependencies that were earlier reported for ring carbons in a number of imidazolium-based ILs. After a correction of the approach (13)C T1, the relaxation data allowed us to obtain the characteristic times for an orientation mobility of each carbon, and a complicated experiment, such as NOE, was not required. Thus the applicability of (13)C NMR relaxation rate measurements to the calculation of the characteristic times for reorientation of all the carbons of the [bmim](+) cation was confirmed and our findings have shown that a (13)C NMR relaxation technique allowed its application to ionic liquids to be equally successful as for other liquid systems.

Adsorption of a single polymer chain on a surface: effects of the potential range.

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth U and width W is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value U(c) corresponding to the adsorption transition scales as W(-1/ν), where the exponent ν=1/2 for ideal chains and ν≈3/5 for self-avoiding walks. Lattice corrections for finite W are incorporated in the analytical prediction of the ideal chain theory U(c)≈(π(2)/24)(W+1/2)(-2) and in the best-fit equation for the MC simulation data U(c)=0.585(W+1/2)(-5/3). Tail, loop, and train distributions at the critical point are evaluated by MC simulations for 1≤W≤10 and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction θ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: θ(N,U,W)=θ(NU(c),U/U(c)). By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value /=0.320±0.003 only at N~5000. Finite-N corrections for this ratio turn out to be of the opposite sign for W=1 and for W≥2. We also study the N dependence of the apparent crossover exponent φ(eff)(N). Strong corrections to scaling of order N(-0.5) are observed, and the extrapolated value φ=0.483±0.003 is found for all values of W. The strong correction to scaling effects found here explain why for smaller values of N, as used in most previous work, misleadingly large values of φ(eff)(N) were identified as the asymptotic value for the crossover exponent.