Molecular Dynamics of Lysine Dendrigrafts in Methanol-Water Mixtures

The molecular dynamics method was used to study the structure and properties of dendrigrafts of the first and second generations in methanol-water mixtures with various volume fractions of methanol. At a small volume fraction of methanol, the size and other properties of both dendrigrafts are very similar to those in pure water. A decrease in the dielectric constant of the mixed solvent with an increase in the methanol fraction leads to the penetration of counterions into the dendrigrafts and a reduction of the effective charge. This leads to a gradual collapse of dendrigrafts: a decrease in their size, and an increase in the internal density and the number of intramolecular hydrogen bonds inside them. At the same time, the number of solvent molecules inside the dendrigraft and the number of hydrogen bonds between the dendrigraft and the solvent decrease. At small fractions of methanol in the mixture, the dominant secondary structure in both dendrigrafts is an elongated polyproline II (PPII) helix. At intermediate volume fractions of methanol, the proportion of the PPII helix decreases, while the proportion of another elongated β-sheet secondary structure gradually increases. However, at a high fraction of methanol, the proportion of compact α-helix conformations begins to increase, while the proportion of both elongated conformations decreases.

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.

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.

Application of new lysine-based peptide dendrimers D3K2 and D3G2 for gene delivery: Specific cytotoxicity to cancer cells and transfection in vitro

In order to enhance intracellular uptake and accumulation of therapeutic nucleic acids for improved gene therapy methods, numerous delivery vectors have been elaborated. Based on their origin, gene carriers are generally classified as viral or non-viral vectors. Due to their significantly reduced immunogenicity and highly optimized methods of synthesis, nanoparticles (especially those imitating natural biomolecules) constitute a promising alternative for virus-based delivery devices. Thus, we set out to develop innovative peptide dendrimers for clinical application as transfection agents and gene carriers. In the present work we describe the synthesis of two novel lysine-based dendritic macromolecules (D3K2 and D3G2) and their initial characterization for cytotoxicity/genotoxicity and transfection potential in two human cell line models: cervix adenocarcinoma (HeLa) and microvascular endothelial (HMEC-1). This approach allowed us to identify more cationic D3K2 as potent delivery agent, being able to increase intracellular accumulation of large nucleic acid molecules such as plasmids. Moreover, the dendrimers exhibited specific cytotoxicity towards cancer cell line without showing significant toxic effects on normal cells. These observations are promising prognosis for future clinical application of this type of nanoparticles.

Orientational relaxation of ring polymers in dilute solutions

The segmental relaxation dynamics of ring polymers in dilute solutions is investigated via optimized Rouse-Zimm theory. To the best of our knowledge, this is the first study that characterizes the orientational relaxation dynamics of ring polymers in dilute solutions. The orientational time autocorrelation functions are governed by two major processes that span a broad range of timescales: (i) local segmental motion at short times, independent of the ring size, and (ii) overall motion of the ring at long times that depends on the limiting ring size. Smaller rings relax faster than larger rings and their respective linear analogues. The hydrodynamic interactions decrease the higher relaxation rates corresponding to the local relaxation modes and increase the smaller relaxation rates which correspond to the collective relaxation modes. The spectral density is independent of frequency in the low frequency regime while it decreases with increasing frequency. Regardless of the ring size, the spin-lattice relaxation rate exhibits a single characteristic maximum as a function of frequency that shifts to a lower value with increasing strength of hydrodynamic interactions.

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.

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

Lysine Dendrigraft Nanocontainers. Influence of Topology on Their Size and Internal Structure

Poly-l-ysine dendrigrafts are promising systems for biomedical applications due to their biodegradability, biocompatibility, and similarity to dendrimers. There are many papers about the use of dendrigrafts as nanocontainers for drug delivery. At the same time, the number of studies about their physical properties is limited, and computer simulations of dendrigrafts are almost absent. This paper presents the results of a systematic molecular dynamics simulation study of third-generation lysine dendrigrafts with different topologies. The size and internal structures of the dendrigrafts were calculated. We discovered that the size of dendrigrafts of the same molecular weight depends on their topology. The shape of all studied dendrigrafts is close to spherical. Density profile of dendrigrafts depends on their topology.

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.

Self-Assembly of Lysine-Based Dendritic Surfactants Modeled by the Self-Consistent Field Approach

Implementing a united atom model, we apply self-consistent field theory to study structure and thermodynamic properties of spherical micelles composed of surfactants that combine an alkyl tail with a charged lysine-based dendritic headgroup. Following experiments, the focus was on dendron surfactants with varying tail length and dendron generations G0, G1, G2. The heads are subject to acetylation modification which reduces the charge and hydrophilicity. We establish a reasonable parameter set which results in semiquantitative agreement with the available experiments. The critical micellization concentration, aggregation number, and micelle size are discussed. The strongly charged dendronic surfactants micelles are stable for generation numbers G0 and G1, for progressively higher ionic strengths. Associates of G2 surfactants are very small and can only be found at extreme surfactant concentration and salt strengths. Micelles of corresponding weaker charged acetylated variants exist up to G2, tolerate significantly lower salt concentrations, but lose the spherical micelle topology for G0 at high ionic strengths.

Marginally compact fractal trees with semiflexibility

We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the trees' behavior and to consider larger structures. Due to the local stiffness, the self-contact density gets drastically reduced.

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.

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.

Relaxation Dynamics of Semiflexible Fractal Macromolecules

We study the dynamics of semiflexible hyperbranched macromolecules having only dendritic units and no linear spacers, while the structure of these macromolecules is modeled through T-fractals. We construct a full set of eigenmodes of the dynamical matrix, which couples the set of Langevin equations. Based on the ensuing relaxation spectra, we analyze the mechanical relaxation moduli. The fractal character of the macromolecules reveals itself in the storage and loss moduli in the intermediate region of frequencies through scaling, whereas at higher frequencies, we observe the locally-dendritic structure that is more pronounced for higher stiffness.

Dynamics of internally functionalized dendrimers

The internally functionalized dendrimers are novel polymers that differ from conventional dendrimers by having additional functional units which do not branch out further. We investigate the dynamics of these structures with the inclusion of local semiflexibility and analyze their eigenmodes. The functionalized units clearly manifest themselves leading to a group of eigenvalues which are not present for homogeneous dendrimers. This part of the spectrum reveals itself in the local relaxation, leading to a corresponding process in the imaginary part of the complex dielectric susceptibility.

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 ¹H 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 coarse-grained poly(L-lysine) dendrimers

Poly(L-lysine) (PLL) dendrimer are amino acid based macromolecules and can be used as drug delivery agents. Their branched structure allows them to be functionalized by various groups to encapsulate drug agents into their structure. In this work, at first, an attempt was made on all-atom simulation of PLL dendrimer of different generations. Based on all-atom results, a course-grained model of this dendrimer was designed and its parameters were determined, to be used for simulation of three generations of PLL dendrimer, at two pHs. Similar to the all-atom, the coarse-grained results indicated that by increasing the generation, the dendrimer becomes more spherical. At pH 7, the dendrimer had larger size, whereas at pH 12, due to back folding of branching chains, they had the tendency to penetrate into the inner layers. The calculated radial probability and radial distribution functions confirm that at pH 7, the PLL dendrimer has more cavities and as a result it can encapsulate more water molecules into its inner structure. By calculating the moment of inertia and the aspect ratio, the formation of spherical structure for PLL dendrimer was confirmed.