Orientational mobility and relaxation spectra of dendrimers: Theory and computer simulation

Analytical Model to Deduce the Conformational and Dynamical Behavior in Dendrimers: A Review

This review utilizes an optimized Rouse-Zimm discrete hydrodynamic model and the preaveraged Oseen tensor, which accurately consider hydrodynamic interactions to study model dendrimers. We report the analytical theories that have been previously developed for the creation of generalized analytical models for dendrimers. These generalized theories were used to assess the conformational and dynamical behavior of the dendrimers. By including stiffness in the bonds, the neglect of excluded volume interactions may be somewhat offset. This is true at least in the case of short spacers. While the topological limitations on the directions and orientations of the individual bond vectors in dendrimers implement semiflexibility, the intensity of these contacts was determined by the potential geometric orientations of the bonds, and later on the excluded volume interactions in dendrimers, which were described in terms of the effective co-volume between nearest non-bonded monomers and modeled using the delta function pseudopotential. With the aid of the models developed, the authors condensed various conformational and dynamic properties of dendrimers that depend on their degree of semiflexibility and the strength of the excluded volume. These analyses came to the conclusion that the flexible dendrimer in one limit and the earlier described freely rotating model of dendrimers in the other constitute a highly generalized way of capturing a wide range of conformations in the developed mathematical model in dendrimers.

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.

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.

Orientational Relaxation of Poly(propylene imine) Dendrimers at Different pH

The dilute solution dynamics of poly(propylene imine) (PPI) dendrimers is investigated at three different solution pH through molecular dynamics (MD) simulations. The dynamics of PPI dendrimers is characterized by both global and local relaxations that occur at different time and length scales. While the global dynamics may be described in terms of rotational diffusion, the local motion may be characterized through orientational relaxation dynamics measured in terms of the time autocorrelation function (ACF), second-order orientational ACF, and the spin-lattice relaxation rate. The global motion of dendrimers decreases with an increase in the size from high pH to low pH with increasing generations of growth. The results reveal that the segments at low pH relax faster than those at high pH, and the local mobility of the segments near the periphery is higher than the core segments. This observation is also evident from the spectral density and spin-lattice relaxation rate. High values of the spectral density at higher frequencies imply higher segmental mobility of the dendrimer at low pH relative to that at high pH. A shift in the maximum of the spin-lattice relaxation rate toward lower frequencies with decreasing generations indicates the dependence of local mobility on the topological distance of the segment from the periphery at all pH conditions.

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.

A new poly-l-lysine dendrimer with arginine residues was synthesized and its structure and physical–chemical properties were analyzed by NMR spectroscopy.

A Comparative Study of Intramolecular Mobility of Single Siloxane and Carbosilane Dendrimers via Molecular Dynamics Simulations

A comparative analysis of intramolecular dynamics of four types of isolated dendrimers from the fourth to the seventh generations belonging to the siloxane and carbosilane families, differing in spacer length, core functionality, and the type of chemical bonds, has been performed via atomic molecular dynamics simulations. The average radial and angular positions of all Si branching atoms of various topological layers within the dendrimer interior, as well as their variations, have been calculated, and the distributions of the relaxation times of their radial and angular motions have been found. It has been shown that the dendrons of all the dendrimers elongate from the center and decrease in a solid angle with an increasing generation number. The characteristic relaxation times of both angular and radial motions of Si atoms are of the order of a few nanoseconds, and they increase with an increasing generation number and decrease with temperature, with the angular relaxation times being larger than the radial ones. The relaxation times in the carbosilanes are larger than those in the siloxanes. The rotational angle dynamics of the carbosilane dendrimers show that the chain bending is mainly realized via trans-gauche transitions in the Si branching bonds.

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.

Is the manifestation of the local dynamics in the spin-lattice NMR relaxation in dendrimers sensitive to excluded volume interactions?

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(1)H 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(1)H(ωH) 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 ωmax of the peak of the modified 1/T(1)H(ωH) does not depend on the shell number. For semiflexible models, the maximum of 1/T(1)H(ωH) for internal segments or bonds shifts to lower frequencies as compared to outer ones. The dependence of ωmax on the number of dendrimer shells appears to be universal for segments and bonds in dendrimer models with and without EV interactions.

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.

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

Spin–lattice NMR relaxation rate vs. reversed temperature for terminal and inner CH₂ groups of n = 2 and 4 generation poly-l-lysine dendrimers.

Investigation of glycofullerene dynamics by NMR spectroscopy

Mannose residues linked to flexible spacers on slowly diffusing glycofullerenes may facilitate efficient rebinding to receptors.

Hyperbranched polymer stars with Gaussian chain statistics revisited

Conformational properties of regular dendrimers and more general hyperbranched polymer stars with Gaussian statistics for the spacer chains between branching points are revisited numerically. We investigate the scaling for asymptotically long chains especially for fractal dimensions df = 3 (marginally compact) and df = 2.5 (diffusion limited aggregation). Power-law stars obtained by imposing the number of additional arms per generation are compared to truly self-similar stars. We discuss effects of weak excluded-volume interactions and sketch the regime where the Gaussian approximation should hold in dense solutions and melts for sufficiently large spacer chains.

Orientational relaxation in semiflexible dendrimers

The orientational relaxation dynamics of semiflexible dendrimers are theoretically calculated within the framework of optimized Rouse-Zimm formalism. Semiflexibility is modeled through appropriate restrictions in the direction and orientation of the respective bond vectors, while the hydrodynamic interactions are included via the preaveraged Oseen tensor. The time autocorrelation function M(i)(1)(t) and the second order orientational autocorrelation function P(i)(2)(t) are analyzed as a function of the branch-point functionality and the degree of semiflexibility. Our approach of calculating M(i)(1)(t) is completely different from that of the earlier studies (A. Perico and M. Guenza J. Chem. Phys., 1985, 83, 3103; J. Chem. Phys., 1986, 84, 510), where the expression of M(i)(1)(t) obtained from earlier studies does not demarcate the flexible dendrimers from the semiflexible ones. The component of global motion of the time autocorrelation function exhibits a strong dependence on both degree of semiflexibility and branch-point functionality, while the component of pulsation motion depends only on the degree of semiflexibility. But it is difficult to distinguish the difference in the extent of pulsation motion among the compressed (0 < φ < π/2) and expanded (π/2 < φ < π) conformations of semiflexible dendrimers. The qualitative behavior of P(i)(2)(t) obtained from our calculations closely matches with the expression for P(exact)(2)(t) in the earlier studies. Theoretically calculated spectral density, J(ω), is found to depend on the degree of semiflexibility and the branch-point functionality for the compressed and expanded conformations of semiflexible dendrimers as a function of frequency, especially in the high frequency regime, where J(ω) decays with frequency for both compressed and expanded conformations of semiflexible dendrimers. This decay of the spectral density occurs after displaying a cross-over behavior with the variation in the degree of semiflexibility in the intermediate frequency regime. The characteristic area increases with the increase in the semiflexibility parameter, where the expanded conformations of semiflexible dendrimers record the maximum characteristic area. For the compressed conformations the relative increment of this area is considerably lower than that of the expanded conformations of semiflexible dendrimers.

Average relaxation time of internal spectrum for carbosilane dendrimers: nuclear magnetic resonance studies

A new theoretical description of the interior mobility of carbosilane dendrimers has been tested. Experiments were conducted using measurements of the (1)H NMR spin-lattice relaxation time, T(1H), of two-, three- and four-generation carbosilane dendrimers with three different types of terminal groups in dilute chloroform solutions. Temperature dependences of the NMR relaxation rate, 1/T(1H), were obtained for the internal CH(2)-groups of the dendrimers in the range of 1/T(1H) maximum, allowing us to directly evaluate the average time of the internal spectrum for each dendrimer. It was found that the temperature of 1/T(1H) maximum is practically independent of the number of generations, G; therefore, the theoretical prediction was confirmed experimentally. In addition, the average time of the internal spectrum of carbosilane dendrimers was found to be near 0.2 ns at room temperature, and this value correlates well with the values previously obtained for other dendrimer structures using other experimental techniques.

The dynamics of GATG glycodendrimers by NMR diffusion and quantitative (13)C relaxation

The dynamics of GATG glycodendrimers have been investigated by NMR translational diffusion and quantitative (13)C relaxation studies (Lipari-Szabo model-free), allowing the determination of the correlation times describing the dendrimer segmental orientational mobility.