Supercharged Polyplexes: Full-Atom Molecular Dynamics Simulations

Publication Date (Web): July 13, 2018. Copyright © 2018 American Chemical Society. *(P.I.S.) E-mail [email protected]. Cite this:Macromolec...
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Supercharged Polyplexes: Full-Atom Molecular Dynamics Simulations and Experimental Study Pavel I. Semenyuk,*,† Marina V. Zhiryakova,‡ and Vladimir A. Izumrudov‡ †

Belozersky Institute of Physico-Chemical Biology and ‡Faculty of Chemistry, Lomonosov Moscow State University, Moscow, Russia

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ABSTRACT: Quite recently, we reported the synthesis of supercharged polycations bearing pH-insensitive doublecharged repeat units with either three or five methylene groups in the space between charges. The developed approach is based on the quaternization of the parent poly(4-vinylpyridine) with different alkylating agents, providing the possibility to perform the modification as a one-step reaction, which occurs in mild conditions with a controllable degree of conversion. In the present work, we used the above approach for preparing and investigating supercharged polyplexes (polyelectrolyte complexes of nucleic acids), in particular to elucidate the reason for the key feature, i.e., the clearly defined stability of the polyplexes formed by supercharged polyamines. The main findings of the experimental study were confirmed by the results of full atomic modeling, and the principal regularities responsible for the structure, stability, and properties of the supercharged polyplexes have been elucidated for the first time.

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INTRODUCTION Polyelectrolytes of high linear charge density but carrying no more than one charged group in the repeat unit, specifically conventional vinylic polyions, are well characterized and widely used in biotechnology and medicine, e.g., for the separation of multicomponent protein systems,1,2 protein stabilization,3,4 immobilization,5−7 or the delivery of cargo nucleic acids into the cell.8,9 The information on polyelectrolytes with a higher charge density, specifically bearing two ionic or ionogenic groups in the repeat unit, is rather scant. Meanwhile, there are grounds for believing that such “supercharged” polyelectrolytes are prone to binding efficiently with oppositely charged polymers, in particular enzymes10 and nucleic acids,11−14 yielding (bio)polylectrolyte complexes. Quite recently,15 we reported the synthesis and study of supercharged polycations bearing pH-insensitive doublecharged repeat units with either three or five methylene groups in the space between charges (compare the sketches of the sPP-3 and sPP-5 structure formulas, depicted in Figure 1). The advantage of the developed approach based on the quaternization of parent poly(4-vinylpyridine) (Figure 1, PVP) with different alkylating agents is the possibility to perform the modification as a one-step reaction, which occurs under mild conditions with a controllable degree of conversion, especially the exhaustive one. Also, the approach provided correct comparison studies of polyelectrolyte complexes formed by the supercharged and conventional pyridinium polycations with synthetic poly(methacrylic acid) (Figure 1, PMAA), since the DP and molar mass distribution of the polyamines were the same and identical to those of the parent polymer PVP. © XXXX American Chemical Society

Motivated by this success, we prepared and investigated supercharged polyplexes, i.e., polyelectrolyte complexes of nucleic acids with supercharged polycations. It was of special interest to verify whether the clearly defined stability revealed in water−salt media is a key feature of polyplexes formed by different supercharged polyamines. The findings of the experimental study based substantially on the ethidium bromide assay were confirmed by the results of full atomic modeling, which is a powerful approach used to look inside the mechanism of polyelectrolyte interaction with DNA16−18 and proteins19,20 as well as the behavior of free polyelectrolytes.21 By combining experimental and modeling results, the main regularities responsible for the structure, stability, and properties of the supercharged polyplexes have been elucidated for the first time at an atomic level.

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RESULTS AND DISCUSSION EtBr Fluorescence Study. An important question to be answered first when studying the polyplexes is whether all of the quaternized amino groups of the supercharged polycations are accessible for ion pairing with DNA. To check this assumption, the fluorescence quenching technique was used. The fluorescence approach, which was developed by our group and published in the pioneering paper almost 20 years ago,22 is based on the well-documented ability of the cationic dyes, specifically ethidium bromide (EtBr), to penetrate into the Received: April 25, 2018 Revised: June 27, 2018

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Figure 1. Structure of the polycations and PMAA. NR and N denote pyridinium and tail nitrogen atoms of the supercharged polycations, respectively.

Figure 2. Fluorescence quenching of EtBr intercalated in DNA double helix upon the titration with sPP-3 (curve 1), sPP-5 (2), and PEVP (dashed line) as a function of repeat units molar ratio (A) and positive/negative charge ratio (B).

Figure 3. Fluorescence intensity of DNA−EtBr solution upon titration with different sPP-3β containing the specified percentage of alkylated repeat units (β): 100% (sPP-3), 60%, 30%, 20%, and 15%, as a function of repeat units molar ratio (A) and positive/negative charge ratio (B).

cations sPP-3 and sPP-5 typify the fluorescence quenching that is inherent in mixtures of a nucleic acid and cationic polymer, in particular conventional polyamine. The only difference is that the inflection points correspond to significantly lower values of repeat unit molar ratio polycation/DNA compared to other systems such as PEVP/DNA complexes. The reason for this apparent discrepancy arises from the routine calculation of concentration ratio, used as a molar ratio of the repeat units. Contrary to DNA monomers, the units of the supercharged polyamines are double charged. Accordingly, in order to express the above parameter in terms of charge− charge ratio, [+]/[−], the concentration should be reduced by half (Figure 2B). The run of the rearranged curves for sPP-3 and sPP-5 came to closely resemble the curve for the conventional polycation PEVP, which is depicted in Figure

DNA helix and intercalate between nucleobase pairs. The intercalation and formation of a DNA−EtBr complex are accompanied by an increase in fluorescence intensity, whereas further electrostatic binding of the complex with added cationic polymer, in particular poly(N-ethyl-4-vinylpyridinium bromide) or its derivatives,22,23 is shown by the fluorescence quenching caused by the competitive displacement of EtBr. In other words, the stoichiometry and efficacy of DNA binding with polycations can be evaluated by the fluorescent intensity of the intercalated dye in experiments on the titration of DNA with a polycation. Nowadays, the above fluorescence approach is widely employed under the name “ethidium bromide assay”.24−27 The curves in Figure 2A corresponding to the titration of the DNA−EtBr complex solution with the supercharged polyB

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Macromolecules 2B by a dashed line. This finding conclusively proves the accessibility of the majority of the units for ion pairing with DNA, as it occurs on PEVP binding. However, since the inflection point corresponds to a value larger than 1.0, one can conclude that part of the charged groups of sPP is not accessible for the interaction with DNA. According to the results, this can be estimated as 30% and 22% for sPP-3 and sPP-5, respectively. In all likelihood, the close proximity of the two charged groups in the same repeat unit imposes spatial limitations, which are less pronounced in the case of sPP-5 because of the longer length of the flexible linker between the charged groups, i.e., aromatic and aliphatic nitrogen groups (Figure 1). The same procedure could be followed in cases of partially alkylated supercharged polycations which differ in the degree of β-modification (the structure of the sPP-3 derivative sPP-3β is depicted in Figure 1). At pH 7.0, nonalkylated units of sPP3β are not protonated and play the role of noncharged defects;23 this feature has been taken into account in calculations of the average mass of the repeat unit. As it follows from the family of sPP-3β titrations (Figure 3A), the curves are arranged in a clearly defined row: the lower the β, the higher the amount of polycation required to reach the stoichiometric ratio. However, after the rearrangement in order to express data in terms of the charge−charge ratio, [+]/[−], all curves fall on the master curve with relatively low but noticeable deviations (Figure 3B). According to Figure 3B, all quaternized charged groups in sPP-3β with a β of 15% (black line) are accessible for ion pairing with DNA, since the stoichiometry of the binding is equal to 1. When the β value increases, the inflection point shifts to higher values for the [+]/[−] ratio, i.e., stoichiometry becomes higher than 1. Therefore, some quaternized nitrogen atoms are not accessible for DNA (otherwise the charge−charge stoichiometry should be equal to 1), and their amount increases with the growth in alkylation degree up to 30% in the case of the exhaustively alkylated sample, i.e., sPP-3 (Figure 3B, blue line). In addition, the ethidium bromide assay allows the stability of polyplexes to be evaluated in water−salt media.23 The approach is based on the titration of preformed polyplexes with salt, generally sodium chloride, and measurements of the increase in EtBr fluorescence intensity caused by the reintercalation of dye molecules between DNA bases, which become available because of disruption of the polyplex ion pairs by the added salt. The polyplex dissociation, which is exemplified by a welldocumented destruction profile of DNA−PEVP, is depicted by a dashed line in Figure 4. Contrary to this conventional polycation, exhaustively alkylated supercharged sPP-3 forms an excessively stable polyplex (Figure 4, blue line) that remained highly tolerant to the low-molecular-weight electrolyte, even at a much higher ionic strength, at least 1 order of magnitude in the case of sodium chloride. Likewise, polyplexes of sPP-5 polycation also demonstrate very high stability (Figure 4, red line). It is particularly remarkable that polyplexes of the partially alkylated sPP-3β polycations, which contain the majority of non-alkylated units (defects) in the chains, likewise demonstrate high stability (Figure 4) but could be eventually destroyed in individual cases. Thus, a noticeable but not complete destruction of the polyplexes occurs at β = 30 (green line), while the polyplex formed by sPP-3β at β = 15, the

Figure 4. Destruction profiles of DNA complexes with PEVP (dashed line), sPP-3β, β = 15, 30, and 100 (sPP-3) (violet, green, and blue lines, respectively), and sPP-5 (red line) presented as dependences of fluorescence intensity of intercalated EtBr on the ionic strength.

majority of repeat units of which are non-alkylated, dissociated completely (violet line). Note that the pronounced stability of sPP-3 and sPP-5 polyplexes revealed is inherent in double charged polycations of different families.11−14 However, this phenomenon does not exhibit the above property when studying the complexing of sPP with synthetic polyanions, specifically poly(methacrylic) acid (PMAA). Thus, according to fluorescence quenching data taken from our previous paper and presented in Figure 5 by

Figure 5. Salt-induced dissociation of PMAA (Mw of 300 kDa) complexes with PEVP (dashed line) and supercharged polycations sPP-3 and sPP-5 (see the details in ref 15).

the dissociation profile, both sPP-3 and sPP-5 curves are noticeably but not dramatically shifted to the higher ionic strength compared with the PMAA−PEVP complex. Nevertheless, being relatively stable, all of the studied PMAA complexes can be destroyed completely (at I/I0 = 1.0) in contrast to DNA complexes with supercharged polycations, i.e., sPP-3 and sPP-5. In other words, the reason for the pronounced stability of polyplexes could be associated with some of the unique features of the DNA double helix. C

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Figure 6. Center of mass of the polycations movement along the simulations. Red, green, blue, orange, and violet lines correspond to different independent simulations with different start position; DNA backbone is shown in gray; view along the principal axis of DNA helix. Average RMSD of the COM in nm is labeled.

Figure 7. Averaged RDF of aromatic nitrogen (NR, left column) and quaternary nitrogen in tail (N, right column) around DNA electronegative atom groups as a function of distance from the corresponding group in nm. See Materials and Methods for the details and description of the groups. D

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Figure 8. (A) Time dependences of a number of ion pairs between DNA and the polycations. See the Materials and Methods for the details and description of the groups. (B) Total count of bonds averaged on 10−200 ns. From bottom to top: major groove/NR (blue), major groove/N (cyan), minor groove/NR (green), minor groove/N (olive), backbone oxygens/NR (red), and backbone oxygens/N (orange). (C) Total number of ion pairs between the polycations and PMAA averaged on 10−200 ns: carboxylic groups/NR (red) and carboxylic groups/N (orange).

than the mobility of the supercharged polycations (Figure 6). Thus, once bound to DNA, sPP-3 was almost completely immobile, in contrast to PEVP, which was prone to move around the DNA helix. Calculations of the average root-meansquare deviation of the center of mass (see the values in Figure 6) corroborated this statement: the corresponding value for PEVP was much higher compared to supercharged polycations. Noteworthy, the value observed for sPP-3 was lower than that for sPP-5, suggesting the lower mobility of sPP-3. In other words, the binding of both supercharged polycations, especially sPP-3, is characterized with reduced fluctuations compared to that of PEVP. This finding seems to indicate a higher stability of the polyplex formed by supercharged polycations, especially sPP-3, which demonstrated the highest affinity of binding. To elucidate the role of the DNA double helix in the formation of polyplexes, the above result was compared with data on the interaction of polycations with a model polyanion,

To further investigate the mechanism of interaction and elucidate the reason for the extreme stability of the polyplexes formed by supercharged pyridinium polycations, we performed atomistic molecular dynamics simulations. MD Simulations: Mobility of the Polycation. Five independent simulations with different initial positions of the polycation were conducted for each polycation, i.e., conventional PEVP and the supercharged polycations sPP-3 and sPP5. In all 15 simulations, the polycation chain quickly approached the DNA double helix and bound it. Although some ion pairs appeared and disappeared during the simulations, once bound, the polycation chain remained bound throughout the entire simulation in all cases. First, the mobility of the polycation molecule bound to DNA was estimated. Visual inspection of the center of mass (COM) trajectories of the polycation molecule suggested that the mobility of the model PEVP chains is significantly higher E

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Figure 9. Typical examples of the binding of PEVP (A, D), sPP-3 (B, E), and sPP-5 (C, F) with DNA (A−C) and PMAA (D−F). The DNA molecule is shown in cartoon representation with detailed bases; polycations are shown in sticks representation and colored by elements: green for carbon and blue for nitrogen; PMAA molecules are shown in sticks and colored by elements: white for carbon and red for oxygen. Hydrocarbon backbone of the polycations and PMAA is shown in thick sticks. Ion pairs are presented with dashed lines. Red and green arrows point out nitrogen atoms bound and nonbound with DNA phosphate backbone, respectively. See the text for the details for the asterisks.

poly(methacrylic acid) (PMAA). Since PMAA has no rigidrod-like conformation, as in the case of DNA, we fitted the frames to the polymer structure and analyzed the center of mass of the PMAA chains. Similarly to simulations with DNA, the mobility of PMAA proved to be much lower in the case of supercharged polycations compared to PEVP (Figure S1). The values of the average root-mean-square deviation were 0.59 ± 0.15, 0.24 ± 0.04, and 0.29 ± 0.06 nm for PMAA bound to PEVP, sPP-3, and sPP-5, respectively. This finding indicates a higher stability of the PMAA complexes with supercharged polycations. Note that these data do not allow a comparison of the binding of polycations to DNA and PMAA because the movement of the same molecules could not be accurately compared. Contribution of Different Groups. The large size and the complexity of the polycations charged groups hinder the investigation of ion pair formation between the polycations and DNA. For a proper analysis, radial distribution functions (RDF) for nitrogen atoms around the DNA helix were calculated separately for pyridinium ring nitrogen (NR) and tail nitrogen (N). To study the nature of the interaction, negatively charged DNA groups were also subdivided into phosphate groups, the major groove, and the minor groove (see Materials and Methods and Figure S4 for details). The comparison of RDF graphs for polycations revealed a difference in the binding of PEVP and supercharged polycations to DNA. Thus, a sharp low-radius peak was observed for charged groups of both supercharged polycations around phosphate groups and the major groove of DNA

(Figure 7). This sharp peak indicates that many nitrogen atoms are located the same small distance from the DNA for a long time and, in other words, are bound to the DNA. The same peak for PEVP is much less pronounced; the difference is especially high for sPP-3. Furthermore, a peak in Figure 7, right column, clearly indicates that the tail nitrogen significantly contributes to the binding. Besides, the interaction of sPP-5 with the DNA minor groove proved to be negligible since the corresponding low-radius peak is small. Visual inspection of the RDF graphs grouped on polycations (Figure S2) suggests that PEVP mainly interacts with the DNA backbone phosphate groups, sPP-3 interacts with the phosphate groups and the major groove, and sPP-5 interacts with the phosphate groups and both the major and minor grooves. Noteworthy, the lowradius peak on RDF graphs for DNA phosphate groups is much sharper in the case of sPP-3 than in the case of PEVP or sPP-5. On the basis of this finding, one can expect the enhanced binding of sPP-3 with DNA via interactions with phosphate groups. Based on the RDF graphs, a threshold distance between nitrogen and oxygen atoms in ion pairs was selected to be 0.55 nm, aiming to cover the most pronounced peak on the RDF curve. The value is higher than the usual one (0.3−0.35 nm) because the positive charge is distributed on a bulky trimethylammonium group and pyridinium ring. The number of ion pairs between the nitrogen groups of the polycation (NR and N) and different electronegative groups of DNA was calculated separately, i.e., six combinations overall. The corresponding time dependences averaged among five F

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limitations. Therefore, only a few cases of the simultaneous binding of both nitrogens in one sPP-5 repeat unit with DNA were observed. Thus, sPP-5 formed fewer ion pairs with DNA phosphate groups, and consequently the binding of sPP-3 should be the most pronounced. We compared the binding of the polycations with DNA and PMAA. For PMAA, two sets of simulations with different numbers of counterions were conducted. When an equivalent number of sodium ions was added, artificial complexation of the PMAA molecule with counterions up to the formation of completely uncharged complexes, and subsequent aggregation of two PMAA molecules was observed (Figure S3, left). The number of ion pairs formed between PMAA and PEVP was twice lower than that in the case of DNA. These results completely disagree with the experimental data since PMAA is highly soluble, and the stability of the PEVP complex with DNA and PMAA is similar. We checked two different models of low-molecular-weight ions: “usual” from AMBER99parmbsc0 force field28 and improved ones29 with the same artificial result. Therefore, we removed the counterions from the box to avoid the artificial aggregation of the polyanion and performed simulations with two sodium cations to achieve electroneutrality. In this case, PMAA chains were stable in solution, and the number of ion pairs between PMAA and PEVP coincided with that for DNA. Since such behavior agrees with the experimental data, these parameters were used for further investigations. According to the results of simulations, both supercharged pyridinium polycations formed more ion pairs with PMAA than PEVP (Figure 8C). The average number of ion pairs was greater in the case of sPP-3 than in the case of sPP-5, suggesting the more efficient binding of sPP-3 with PMAA. This agrees well with recent experimental results15 presented in Figure 5. However, both of the above values are significantly lower than in the case of DNA. Thus, the results of simulations corroborate the experimental results with regard to the extremely high affinity of supercharged pyridinium polycations for DNA (Figures 4 and 5). The typical complexes of the polycations and PMAA shown in Figure 9D−F did not reveal any noticeable regularity in the binding poses. However, an additional charged group of sPP-3 and sPP-5 contributed in a pronounced way to the binding, forming 3−4 additional ion pairs with PMAA (see Figure 8C). Besides, a labile tail provided an opportunity for spatial tuning of the binding and surrounding of the PMAA chain with positively charged groups. It may be of special importance for interactions with PMAA because its negatively charged groups are located close to each other and therefore could not face to one side because of repulsion. According to the simulation results, this effect is more pronounced in the case of sPP-3 (Figure 9E). Thus, contrary to sPP-5, sPP-3 often binds PMAA via both nitrogens in the same repeat unit. This phenomenon seems to explain the enhanced binding of sPP-3 with PMAA in comparison to sPP-5. However, the binding of supercharged pyridinium polycations with DNA differs from their binding with PMAA. First, the number of ion pairs is 1.5 times greater in the case of DNA (Figure 8). Of particular note, the binding of supercharged polycations with phosphate groups of DNA is strengthened by the binding of tail nitrogen groups with polar groups in the major or minor groove of DNA (Figures 8B and 9B,C). Furthermore, almost all repeat units of sPP-3 are bound to DNA phosphate groups via both nitrogens. A proper distance

simulations for each polycation are shown in Figure 8A. The number of ion pairs quickly increased for the first 10 ns of simulations and was then generally constant. This indicates that a stable complex was formed while the center of mass movement mentioned above represents the fluctuation of polycations within the complex. According to the number of ion pairs formed, in all cases, the binding is mainly determined by the interaction of polycations with the backbone phosphate groups of DNA. The binding of supercharged polycations, especially sPP-3, is also supported by the interaction of a tail charged group with the major groove of DNA. For the sake of simplicity, we averaged a number of ion pairs throughout the simulation, except for the initial 10 ns (Figure 8B). The total number of ion pairs formed between DNA and supercharged polycations was much higher (by 2.5−3 times) than that of PEVP. This agrees well with our experimental data which suggest that sPP-3 and sPP-5 bind DNA extremely tightly. The number of ion pairs formed by sPP-3 was slightly higher than that of sPP-5. Noteworthy, a contribution of each negatively charged group of DNA and two charged groups of the polycations greatly differed. On the one hand, a significant number of pairs are formed between positively charged tails of supercharged polycations and DNA grooves, whereas the binding of PEVP, which does not have additional charged groups located on the flexible tail, is almost completely determined by interactions with the phosphate groups of DNA. In addition, sPP-3 practically did not interact with the DNA minor groove, while some charged tails of sPP-5 penetrated into the minor groove. On the other hand, sPP-3 interacted with the major groove by the positively charged tails more efficiently than sPP-5 (compare the corresponding cyan bars in Figure 8B). The interaction of the supercharged polymers with the DNA backbone also differed. Thus, the number of ion pairs between DNA phosphate groups and both nitrogens in sPP-3 was onethird higher than that of sPP-5 (Figure 8B, red and orange bars). Visual analysis of the trajectories allowed the reason for this difference to be determined. Typical examples of the binding of different polycations with DNA are presented in Figure 9A−C. There were simulations with different final poses of the PEVP chain-aligned along DNA helix, penetrated into the major groove, and combined. In other words, PEVP can interact with both grooves of DNA. However, in both cases, the binding was generally determined by interactions with the phosphate groups of DNA instead of with nitrogenous bases (Figure 9A), which agrees well with data on a number of corresponding ion pairs. Supercharged polycation sPP-3 mainly interacted with the DNA major groove via both backbone phosphate groups and nucleotides. It is noteworthy that almost all repeat units of sPP-3 bound to the DNA backbone interacted with phosphate groups via both aromatic and tail nitrogens (Figure 9B, red arrows). Positively charged groups in sPP-3 tails and the two neighboring phosphate groups in the DNA backbone form a kind of tetrahedron. On the contrary, sPP-5, the poses of which are varied in different simulations, interacted with DNA phosphate groups via no more than one nitrogen in each repeat unit (see red and green arrows in Figure 9C for the bound and nonbound nitrogens, respectively). The only possibility to bind DNA phosphate groups via both nitrogens in one repeat unit is to align the tail along the DNA backbone (red asterisks in Figure 9C), but the binding of other repeat units in this case seems to be retarded due to spatial G

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23 for the detailed description of this approach). The excitation wavelength was 535 nm, and the registration wavelength was 595 nm. The interpolyelectrolyte complexes of DNA with polycations were prepared through titration of the DNA−EtBr complex solution with solutions of the polycation. Titrant portions were added at 2 min intervals. The preformed polyplexes were disrupted by titration with sodium chloride; EtBr fluorescence was measured in the same manner. Fluorescence intensity values were normalized for initial fluorescence of the pure DNA−EtBr complex and denoted as I/I0; i.e., a value of 1.0 indicates complete dissociation of the polyplex. Molecular Dynamics Simulations. Drew−Dickerson dodecamer with a sequence of d(CGCGAATTCGCG)2 was used as a model double-stranded DNA (PDB ID 1bna). The poly(methacrylic acid) (PMAA) and the polycation molecules were parametrized by using the RED III tools.31 Geometry optimization of the monomers was performed in the Firefly QC package,32 which is partially based on the GAMESS (US)33 source code. The interaction of the polycations with DNA was modeled using GROMACS 5.1 software.34 The AMBER99-parmbsc0 force field was used28 with improved parameters for monovalent counterions.29 Separate presimulation of the polymer molecules was performed for the structure relaxation in water with ions: 100 ns for DNA and 50 ns for the polycations. The resulted structures were used for the main simulations. The simulation box contained a double-stranded DNA molecule, a decameric strand of the polycation, water, 22 sodium ions, and 10 or 20 chloride ions for PEVP or sPP-3/sPP-5, respectively. The start distance between DNA and the polymers was at least 1.4 nm. For each polycation, five independent simulations differed in relative position of DNA, and the polycation were performed; four of them were constructed from the first one by rotation of DNA around the axis of the helix (see the start points in Figure 6). The principal axis of the polycation chain was aligned to the axis of the DNA helix. The control simulations were performed to investigate interaction of the polycations with PMAA. The simulation box contained two hendecameric chains of PMAA, a decameric strand of the polycation, water, and counterions. We tried two regimeswith the same amount of counterions as in the case of DNA (22 sodium and 10/20 chloride ions) and with only two sodium ions for electro neutrality. The second regime was chosen because of artificial aggregation of PMAA in high concentration of sodium ions. Two independent simulations with different initial positions of PMAA molecules were performed for each the polycation. The start distance between PMAA and the polymers was at least 1.4 nm. Principal axes of the polycation and PMAA chains were aligned to each other. All main simulations lasted 200 ns with the step of 2 fs. Periodic boundary conditions and the particle mesh Ewald method for handling long-range electrostatic interaction were used. The simulations were conducted using a NPT ensemble. Temperature in the simulation box was stabilized at 300 K using a Berendsen thermostat. Pressure coupling was performed with the Berendsen algorithm.35 To estimate a mobility of the polycation molecules bound to DNA, the position of center of mass (COM) of the polycation molecule was plotted for every 1 ns and connected with a line. The root-meansquare deviation of the COM was calculated for each simulation and averaged among five simulations. The initial interval before the start of interaction was ignored. A number of ion pairs between the polycation and the DNA/ PMAA was evaluated. DNA backbone oxygens and electronegative atoms in minor (TO2, CO2, AN3, and GN3) and major (TO4, AN7, GN7, and GO6) grooves were considered separately (see Figure S4 for atom names). Oxygen atoms in the same phosphate group in DNA as well as oxygen atoms in the same carboxyl group in PMAA were grouped for a fair comparison with other atoms. Two positively charged groups of the polycations were also considered separately. For the sake of convenience, ring nitrogen atom located in pyridinium cycle and nitrogen atom located in tail of the supercharged polycations were denoted as NR and N, respectively (Figure 1). The distance of the ion pair (0.55 nm) was selected on the basis of the radial distribution

between charged groups in the sPP-3 molecule favored the formation of a tetrahedron-like structure with two neighboring DNA phosphate groups. Most likely, this feature is responsible for the extremely high affinity of binding. In turn, the distance between phosphate groups in DNA together with a rigid structure of the double-stranded DNA results in the extremely high stability of polyplexes of the supercharged polycations compared with their complexes with PMAA.

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CONCLUSIONS Summarizing the above results, we declare the extreme stability of DNA interpolyelectrolyte complexes with supercharged pyridinium polycations. In contrast to polyplexes formed by conventional polycation, poly(N-ethyl-4-vinylpyridinium) bromide, the polyplexes formed by supercharged polycations are stable, at least in 0.8 M low-molecular-weight salt. Furthermore, such a phenomenon seems to be unique for DNA, since a similar enforcement of the binding, which was previously found for poly(methacrylate), is much less pronounced. According to the results of full-atomic modeling, supercharged polycations formed a significantly higher number of ion pairs with DNA compared to PMAA. The number of ion pairs with DNA increased by considerably more than 2 times compared to the conventional polycation, poly(N-ethyl-4vinylpyridinium) bromide, which only has one charge per repeat unit. This seems to be because of a “proper” distance between phosphate groups in a rigid double-stranded DNA: cationic groups of the supercharged polycations can fit with phosphate groups to form an ion pair, and the distance between them is large enough for a lack of repulsion between them. Furthermore, the “ideal” distance between cationic groups in sPP-3 (with three methylene groups between quaternized nitrogens) results in the formation of a kind of tetrahedron by two positively charged and two negatively charged (phosphate) groups, with the simultaneous binding of both nitrogen atoms in the same repeat unit. In turn, it should additionally increase the stability of polyplexes formed by sPP3.

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MATERIALS AND METHODS

All polycations were obtained by alkylation of parent poly(4vinylpyridine) (PVP, Mw 60 000, Aldrich) with different alkylation agents. Thus, model highly charged vinylic polycation PEVP with Mw of 124 kDa was synthesized by exhaustive alkylation of the PVP sample with ethyl bromide as described in ref 30. Supercharged pyridinium polycations sPP-3 and sPP-5 with three and five CH2 groups in spacer between nitrogen atoms, respectively, were synthesized by alkylation of the PVP sample with corresponding alkylation agents as described elsewhere.15 Structures of the polycations are depicted in Figure 1. Concentration of the polymers in mixtures was expressed in terms of molar concentration of repeat units, unless otherwise specified. The sodium salt of calf thymus DNA (∼10 000 base pairs) was purchased from Sigma and used without additional purification. The concentration of the phosphate groups of DNA in solution was measured spectrophotometrically using the molecular extinction coefficient at 260 nm of 6500 L/(mol cm). EtBr Fluorescense Assay. Fluorometric experiments were carried out on a Jobin Yvon-3CS spectrofluorometer in a temperaturecontrolled quartz cell (25 °C) under constant stirring in water at pH 7. DNA and EtBr solutions were mixed directly in the cuvette. The final concentration of the phosphate groups of DNA was 40 μM, and the concentration of ethidium bromide was 10 μM. At this ratio (4:1), the maximal fluorescence intensity was observed since one EtBr molecule is intercalated between two nucleobase pairs (see refs22 and H

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Macromolecules function (RDF) graphs to cover a low-radius peak (see the Results section for the details). The distributions were calculated for the last 50 ns and averaged among five simulations. The distance value is higher than usual one because the net charge is distributed on the methyl groups, and the entire trimethylamine group interacts with DNA. The time dependences were averaged among all five simulations for each polycation (and among two simulations in the case of PMAA). Besides, we averaged the values along 10−200 ns for a convenient comparison of the contribution of each group in the binding.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00885. Figure S1: trajectory of center of mass for PMAA; Figure S2: rearranged RDF graphs the polycations’ charged groups around DNA; Figure S3: artificial results for PMAA in the presence of counterions; Figure S4: names of atoms in nucleobases (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(P.I.S.) E-mail [email protected]. ORCID

Pavel I. Semenyuk: 0000-0001-7759-6445 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by Russian Foundation for Basic Research, Project No. 16-34-60089, and Russian Federation President Fellowship for young scientists for Pavel Semenyuk (Project No. 3410.2016.4). The molecular dynamics simulations were performed in the Supercomputing Center of Lomonosov Moscow State University.36

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ABBREVIATIONS COM, center of mass; DNA, DNA; PEVP, poly(N-ethyl-4vinylpyridinium bromide); PMAA, poly(methacrylic acid); PVP, poly(4-vinylpyridine); RDF, radial distribution function; RMSD, root-mean-square deviation of atomic positions; sPP-3 and sPP-5, supercharged pyridinium polycations with 3 and 5 methylene groups in spacer between charges, respectively.

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DOI: 10.1021/acs.macromol.8b00885 Macromolecules XXXX, XXX, XXX−XXX