DNA Compaction by a Dendrimer - The Journal of Physical Chemistry

J. Phys. Chem. B 2011, 115, 217–230

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DNA Compaction by a Dendrimer Bidisha Nandy and Prabal K. Maiti* Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, 560012, India ReceiVed: July 21, 2010; ReVised Manuscript ReceiVed: NoVember 13, 2010

At physiological pH, a PAMAM dendrimer is positively charged and can effectively bind negatively charged DNA. Currently, there has been great interest in understanding this complexation reaction both for fundamental (as a model for complex biological reactions) as well as for practical (as a gene delivery material and probe for sensing DNA sequence) reasons. Here, we have studied the complexation between double-stranded DNA (dsDNA) and various generations of PAMAM dendrimers (G3-G5) through atomistic molecular dynamics simulations in the presence of water and ions. We report the compaction of DNA on a nanosecond time scale. This is remarkable, given the fact that such a short DNA duplex with a length close to 13 nm is otherwise thought to be a rigid rod. Using several nanoseconds long MD simulations, we have observed various binding modes of dsDNA and dendrimers for various generations of PAMAM dendrimers at varying charge ratios, and it confirms some of the binding modes proposed earlier. The binding is driven by the electrostatic interaction, and the larger the dendrimer charge, the stronger the binding affinity. As DNA wraps/ binds to the dendrimer, counterions originally condensed onto DNA (Na+) and the dendrimer (Cl-) get released. We calculate the entropy of counterions and show that there is gain in entropy due to counterion release during the complexation. MD simulations demonstrate that, when the charge ratio is greater than 1 (as in the case of the G5 dendrimer), the optimal wrapping of DNA is observed. Calculated binding energies of the complexation follow the trend G5 > G4 > G3, in accordance with the experimental data. For a lowergeneration dendrimer, such as G3, and, to some extent, for G4 also, we see considerable deformation in the dendrimer structure due to their flexible nature. We have also calculated the various helicoidal parameters of DNA to study the effect of dendrimer binding on the structure of DNA. The B form of the DNA is well preserved in the complex, as is evident from various helical parameters, justifying the use of the PAMAM dendrimer as a suitable delivery vehicle. 1. Introduction In a living organism, DNA compaction is vital for its functions and information storage.1 The practical application of DNA compaction is also seen in gene therapy and antisense therapy where either a dsDNA or an oligonucleotide needs to be compacted and delivered in the interior of the cell nuclei. DNA compaction can be achieved by various means: by low molecular cationic species, such as spermine, spermidine, etc. Interaction of protein with DNA can also lead to a highly compact form of the DNA structure. In a cell nucleus, DNA is wrapped around positively charged protein known as histone and forms the nucleosome structure. These nucleosomes form higher-order structures like beads on a string and produce the chromatin structure.2 In the recent past, there has been numerous experimental and theoretical studies on DNA compaction on various nanoscale objects, such as dendrimers, nanoparticles, and nanotubes.3,4 All these studies stem from the need to understand the phenomenon of DNA compaction mediated by proteins, which can be considered as nano-objects. DNA molecules exhibit a conformational change from elongated coil structures to compact globules, in the presence of proteins, and is usually interpreted as a first-order transition. Being a long anionic polymer, DNA is soluble in aqueous solutions, and in the absence of any compacting agent, DNA chains usually exhibit an elongated coil state. Chemical agents help in * To whom correspondence should be addressed. E-mail: maiti@ physics.iisc.ernet.in.

compaction by modifying electrostatic interactions between DNA segments, by modifying DNA and solvent interactions, by excluding the volume to the wormlike coil (and/or counterions), by producing localized bending or distortion of the helical structure, or by some combination of these effects. DNA compaction by nanoscale objects can help us to understand some of the fundamental questions on the nature of phase transition in semiflexible polyelectrolyte chain as well as help us in the design of suitable nanoscale objects for controlled DNA compaction for gene delivery purposes. The semiflexible nature and high density of negative charges on the DNA chain determines its interaction with nanoscale objects. Depending on the size of the nanoscale object and the rigidity of the DNA chain, two mechanisms of DNA compaction are usually found: DNA either is freely adsorbed on the nanoscale objects or forms beads on a stringlike object. One such nano-object that has found immense importance in mimicking DNA interaction with proteins is the dendrimer.5-7 Dendrimers are perfectly branched monodisperse molecules, which have a well-defined structure and molecular weight. As a function of generation, the PAMAM dendrimer has an exponentially growing number of primary and tertiary amines that can be protonated or deprotonated depending on the pH of the solvent molecules. The pH-controlled charging of the PAMAM dendrimer helps its usage as a perfect binder for negatively charged oligonucleotides or double-stranded DNA, which has application in antisense therapy as well as gene

10.1021/jp106776v  2011 American Chemical Society Published on Web 12/20/2010

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therapy.8,9 There are also indications that the PAMAM dendrimer has very lower level of toxicity.3 Low toxicity and high positive surface charge of protonated PAMAM dendrimers make them a suitable candidate for DNA/ RNA and oligonucleotide complexation, which can be used in gene transfection. Another important aspect for gene therapy is that the bound DNA should be protected from in vivo degradation by the delivery vector. Using the AFM technique, Roberts and co-workers10 demonstrated that DNA delivered using the PAMAM dendrimer is protected from such degradation. Another advantage of using PAMAM is better transfection efficiency compared with other delivery materials. It is believed that, under physiological conditions, hydrolysis of the ester functionality in PAMAM can cause a gradual reduction in the positive charge density and, subsequently, a change in the electrostatic interaction between DNA and the dendrimer,11 which, in turn, accelerate the release of DNA from the dendrimer. Apart from their obvious application in gene therapy, the exceptional demand of studying DNA interaction with dendrimers lies in the fact that dendrimers can also be used as templates for the design of novel drug carriers,12,13 imaging or contrast agents,14-21 cell-labeling agents,22 biosensors,23-27 artificial catalytic sites,28-32 DNA/protein microarrays,33-35 bacterial toxin inhibitors,36 and various anticancer drugs,12,37-44 including 5-fluorouracil.45 There exist several computational studies where complexation of a PAMAM dendrimer with an oppositely charge model polyelectrolyte has been studied using all-atom MD and coarsegrained MD as well Borwnian dynamics simulations.46-48 Welch and Muthukumar49 first reported the complexation between a model dendrimer (chemically closer to poly(propyl-imine) (PPI) dendrimer) with charged terminal groups and charged linear chains under varying pH conditions using Monte Carlo (MC) simulations. They also predicted theoretically adsorption/desorption criteria depending on the salt concentration, size of the dendrimer, charge density of the dendrimer and polyelectrolyte chain, and length of the linear polymer and found good agreement with the simulation results. The complexation between a macroion and an oppositely charged polyelectrolyte has also been studied using linearized Possion-Boltzmann theory by Netz and co-workers.50-52 They reported various configurations of the complex depending on the ionic strength and valency of the macroion. Very recently, Smith et. al53 have also studied the complexation of DNA and several types of dendrons/dendrimer using all-atom MD simulations. However, in their simulation, due to a short time scale, no compaction of DNA was observed. Mills et al.54 have used MD simulation to characterize the DNA force-extension when DNA is complexed with the G3 PAMAM dendrimer and have also reported the free energy of DNA-dendrimer binding using umbrella sampling. Complexation of siRNA with a dendrimer using all-atom MD simulations has also been reported recently.48,55 Earlier, we reported a comprehensive study on the complexation of singlestranded DNA (ssDNA) and PAMAM dendrimers of generations G2-G4.56 It was shown that ssDNA coils around the G4 PAMAM dendrimer where the positive overcharges on the dendrimer surface overcome the bending rigidity of the DNA, leading to a wrapping of the single-stranded DNA on the surface of the dendrimer. For generation two and three (G2 and G3), only partial adsorption of the ssDNA on the dendrimer was observed. We also elucidated the role of counterions, water, and sequence effect in the complexation of single-stranded DNA with the PAMAM dendrimer (G2-G4). Here, we extend our effort to study the complexation of dsDNA with various

Nandy and Maiti generations of PAMAM dendrimers. Specifically, we report the various binding modes observed for the complexation between the PAMAM dendrimer of generations G3-G5 and a 38 bp dsDNA at neutral pH where the primary amines of the dendrimer are protonated. dsDNA is a semiflexible negatively charged polyelectrolyte having a Kuhn segment length of 106 nm and a linear charge density equal to electronic charge per 1.7 Å. The semiflexible nature of DNA, however, depends on the length and experimental conditions. DNA having a length shorter than its persistence length can be viewed as a rigid rod.57 Because here we have taken a DNA length of 38 base pairs (38 bp), it is supposed to behave as a rigid rod. Therefore, a complete DNA wrapping on the dendrimer is supposed to be observed. However, our present study shows remarkable bending of the DNA backbone, which allows DNA with a length much shorter than the persistent length to wrap around the dendrimer. It is worth mentioning that, when the charge ratio (number of positive amines/number of negative phosphates) is smaller than 1, the dendrimer is not completely wrapped and could dissociate to a certain extent. With an increasing amount of cationic charges, the complex becomes more stable and dissociation becomes restricted. This is very important, as just prior to nuclear entry, DNA must be released from the complex, and the inefficiency of disassembly is considered as a limiting factor of the efficient cationic gene delivery carriers. We have also studied the nature of the complex at various salt concentrations to elucidate the role of electrostatics58 in the complexation process. The rest of the paper is organized as follows: in the next section (section 2), we give the details of system preparation as well as simulation conditions. In section 3, we discuss various results from our all-atom MD simulations and compare them with existing simulation/theoretical and experimental results where available. Finally, in section 4, we give a summary of the results and conclusions. 2. Simulation Methodology The sequence of the DNA used is (GCCGCGAGGTGTCAGGGATTGCAGCCAGCATCTCGTCG), which has been studied earlier.59,60 MD simulations reported in this article used the PMEMD software package61 with the all-atom AMBER03 force field (FF).62 AMBER03 FF has been validated for molecular dynamics (MD) simulations of B-DNA in explicit water with salt, starting from the crystal structure. These validation studies found that the CRMS (coordinate root-meansquare) deviation from the crystal structure for a dodecamer structure is typically less than 4 Å. The electrostatic interactions were calculated with the particle mesh Ewald (PME) method63,64 using a cubic B-spline interpolation of order 4 and a 10-4 tolerance set for the direct space sum cutoff. A real space cut off of 9 Å was used for both the electrostatics and the van der Waals interactions with a nonbond list update frequency of 10. First, we create a regular B-DNA molecule using the nucleic acid builder program Namot2 (version 2.2.). Using the LEAP module in AMBER, dendrimers of various generations at various protonation levels were put in the major groove of dsDNA. We have used the same molecular model of dendrimers developed and used in our earlier studies.65-70 The resulting structure was immersed in a water box using the TIP3P model for water.71 In addition, some water molecules were replaced by Na+ counterions to neutralize the negative charges on the phosphate groups of the backbone of the DNA structures. The appropriate numbers of Cl- ions were then added to neutralize the positive charges on the dendrimer amine sites. For example, for G4 at

DNA Compaction by a Dendrimer

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TABLE 1: Details of the Simulation Conditions Reported in This Paper complex

dendrimer charges

DNA charges

charge ratio

number of Cland Na+ atoms

total atom number in the system

number of water molecules

G3 + DNA G4 + DNA G5 + DNA G5 + DNA (50 mM) G5 + DNA (100 mM)

+32 +64 +128 +128 +128

-74 -74 -74 -74 -74

0.43 0.86 1.72 1.72 1.72

32 + 74 64 + 74 128 + 74 173 + 118 218 + 164

179 234 231 117 279 023 150 481 156 848

58 533 75 422 90 580 47 703 49 795

neutral pH, we put 74 Na+ and 64 Cl- in the systems to bring charge neutrality. This procedure resulted in solvated structures, containing approximately 230 000 atoms (for G4), which include the 2405 DNA atoms, 138 counterions, and 75 422 water molecules in a simulation box with lengths of 121, 141, and

137 Å along the three axes. The details of the simulation conditions are given Table 1. The solvated structures were then subjected to 1000 steps of steepest descent minimization of the potential energy, followed by 2000 steps of conjugate gradient minimization. During this minimization, the DNA molecule was

Figure 1. (a) Structure of the DNA-G5 dendrimer complex during various stages of complex formation at the interval of a few nanoseconds. (b) Time evolution of the radius of gyration (RG) of DNA, the dendrimer, and the complex for the complexation with G3, G4, and G5 dendrimers at neutral pH.

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Figure 2. Distance between the COM (center of mass) of DNA and the dendrimer as a function of time. As the dendrimer size increases (positive charge also increases), the COM distance between the two molecules decreases. This indicates that the penetration of DNA inside the dendrimer depends on the dendrimer generation.

kept fixed in its starting conformation using harmonic constraint with a force constant of 500 kcal/mol/Å2. This allowed the water molecules to reorganize to eliminate bad contacts with the DNA molecule. The minimized structure was initially subjected to 40 ps of MD, using a 2 fs time step for integration. During the MD, the system was gradually heated from 0 to 300 K using weak 20 kcal/mol/Å2 harmonic constraints on the solute to its starting structure. This allows for slow relaxation of the built DNA structure. In addition, SHAKE constraints72 using a geometrical tolerance of 5 × 10-4 Å were imposed on all covalent bonds involving hydrogen atoms. This is needed to prevent dynamical changes in the NH and OH bonds from disrupting associated hydrogen bonds. Subsequently, MD was performed under constant pressure-constant temperature conditions (NPT), with temperature regulation achieved using the Berendsen weak coupling method73(0.5 ps time constant for heat bath coupling and 0.2 ps pressure relaxation time). This was followed by another 5000 steps of conjugate gradient minimization while decreasing the force constant of the harmonic restraints from 20 kcal/mol/Å2 to zero in steps of 5 kcal/mol/ Å2. We then carried out 100 ps of unconstrained NPT MD to equilibrate the system at 300 K. We have found that, for other systems, the above equilibration protocol produces very stable MD trajectories for simulating large DNA nanostructures.59,60 Finally, 20-30 ns long NVT runs were carried out using a heat bath coupling time constant of 1 ps. 3. Results Structural Aspects. At neutral pH, G3, G4, and G5 PAMAM dendrimers have 32, 64, and 128 protonated amines, respec-

tively, whereas dsDNA has 74 negative charges. When the dendrimer binds to the DNA, dsDNA charges become neutralized by dendrimer charges and they can form a compact complex. MD simulations reveal that, as the size of the dendrimers and, consequently, dendrimer charges increase, the degree of compaction increases, as can be seen from the snapshots of the complex for various generations, as shown in Figures 1a and 3. For a higher-generation dendrimer, such as G5 (charge ratio, 1.64 > 1), DNA takes around 5 ns to start wrapping around the dendrimer. After that, DNA faces several energetic and entropic bottlenecks to overcome, and finally, DNA finds an optimal wrapping pattern on dendrimer surface. Figure 1a gives the snapshots of the DNA-G5 dendrimer complex in the interval of a few nanoseconds over a 25 ns long MD simulation and reveals several different wrapping conformations of DNA within the complex. This result is remarkable in nature: a 38 bp dsDNA with a length of 12 nm (much shorter than the persistence length of the DNA), which can otherwise be considered as a rigid rod, bends completely to make a complex with the dendrimer. This is the first demonstration where such a short DNA is shown to bend so much as a result of the neutralization of the phosphate charge in one of the faces of the DNA that is facing the dendrimer (asymmetric charge neutralization). The distance between the center of mass (COM) of the two molecules, as shown in Figure 2, serves as a reliable marker to study the interesting binding dynamics during this complexation. As time increases, both DNA and the dendrimer approach close to each other and also DNA wraps around the dendrimer. For example, in the case of the DNA-G5 complex, the COM



Figure 3. (a) Structure of the DNA-G4 dendrimer complex during various stages of complex formation at the interval of a few nanoseconds and (b) the same for the DNA-G3 complex.

distance decreases from 29 to 12 Å with increasing time, as shown in Figure 2c. From the snapshots, swelling of the dendrimer is clearly noticeable (see Figure 1a). A significant penetration of DNA inside the dendrimer can also be clearly observed from the snapshots shown in Figure 1a. Another very important observation is that, for all the cases, the dendrimer noticeably expands in the early stage to make enough contact with the DNA, as can be seen from the RG of the dendrimer shown in Figure 1b. After that, for several nanoseconds, the dendrimer tried to optimize its binding affinity with DNA by finding a suitable DNA-binding site. To optimize the electrostatic interaction between the amine groups of the dendrimer and phosphate groups of DNA, the dendrimer tries to cover up the whole DNA. For a lower-generation, such as G3, due to the smaller surface area of the dendrimer, this results in the strong deformation of the dendrimer. This is clearly visible from the snapshot shown in Figure 3b. To have a quantitative measure of dendrimer deformation, we have calculated the asphericity, δ, of dendrimers.65 For G3, asphericity (δ) ) 0.112 ( 0.039; for G4, δ ) 0.051 ( 0.004; and for G5, δ ) 0.015 (

0.0007. The asphericity values along with the snapshots shown in Figures 1a and 3a,b point toward a transformation from a compact spherical structure to a asymmetric structure for the G5-G3 dendrimers, respectively. G5 has more protonated amines (128) than negative phosphates (74) in DNA. Therefore, the larger number of positive amines as well as bigger size of the dendrimer help to cover up the whole DNA without distorting its spherical shape. On the other hand, G3 has fewer numbers of positive amines (32) than negative phosphates of DNA. The positive amines are equally distributed surrounding the core and form a spherical structure. To form a stable complex with DNA, all protonated amine branches of G3 come on the side of negatively charged DNA and form a distorted spherical structure. A similar asymmetric conformation for the dendrimer bound to DNA was observed by Ritort et. al in their experiment.74 For a lower-generation dendrimer, such as G4, when the dendrimer size decreases (charge ratio, 0.82 < 1), the complexation behavior changes compared with the case for G5. From the snapshots (Figure 3), we can see that, at the beginning, for

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Figure 4. Density distribution for DNA, the dendrimer, and water in the complex corresponding to different dendrimer generations. The distribution has been calculated with respect to the center of mass of the dendrimer.

several nanoseconds, the dendrimer continues to search for a suitable binding position on DNA and the dendrimer slides along the DNA backbone (for both G3 and G4). As the dendrimer moves along the DNA length, at some time instant, DNA finds a suitable binding position and DNA starts wrapping around dendrimer. In the case of G5, from the snapshots (Figure 1a), we notice that, at around 25 ns, DNA wrapping is maximum. This is also clearly visible from Figure 7, where local bending is plotted against the time, and we see that maximum DNA bending occurs at around 20 ns and remains at a similar conformation for the next several nanoseconds. In Figure 2b, we plot the COM distance between the DNA and the dendrimer in the case of G4 and we see that the COM distance is decreasing with time. The sudden drop in the COM distance at around 10 ns implies that the DNA has started wrapping around the dendrimer. Another interesting feature to observe is that the dendrimer approaches much closer to DNA in the case of G4 as compared with G5, as revealed by the low COM distance. This can happen when there is significant penetration of DNA in the interior of the dendrimer. In the next section, we study the density distribution, which will give a quantitative estimation of the degree of penetration of DNA inside the dendrimer. For an even lower charge ratio, such as in the case of G3, we do not observe any wrapping. The dendrimer just binds to the DNA backbone. Density Distribution. Prior to the nuclear entry, DNA should be released from the complex easily to make the transfection faster. The DNA release gets complicated if too much DNA penetration occurs in the interior of the dendrimer. To measure the DNA penetration inside the dendrimer, one objective marker is to calculate the radial

monomer density distribution F(r) of DNA in the complex and compare that with those of the dendrimer and water density at various generations. The average radial monomer density F(r) can be calculated by counting the number N(r) of atoms whose center of mass is located within the spherical shell of radius r and thickness ∆r. Integration of this radial density over r yields the total number of monomers as ∞

N(r) ) 4π

∫ r2F(r) dr 0

Figure 4 shows the radial monomer density profile for DNA, the dendrimer, and water for various generations. The density distribution shows many similarities between the ssDNA-dendrimer complex and the dsDNA-dendrimer complex. The positively charged surface amino groups of the dendrimer bind with the negatively charged phosphate terminals of the DNA. From the density distribution curves, we see that, irrespective of dendrimer generation, the DNA monomer density is maximum near the dendrimer terminal groups. Going from G3 to G5, we see more and more DNA penetration in the interior of the dendrimer. DNA penetration inside the G5 dendrimer is the most. Therefore, the DNA penetration inside the dendrimer can be controlled by the charge ratio of the DNA/dendrimer. We also see significant swelling of the dendrimer. As the dendrimer swells, a large amount of water penetrates inside it. Near the core region (almost 10 Å away from the core), we


Figure 5. (A) The number of contacts between DNA and the dendrimer (number of DNA atoms within 3 Å of any dendrimer atom) as a function of time for different generations of dendrimers. Note that the number of contacts increases with the increase in dendrimer generation. (B) The number of water molecules in a spine of hydration (within 3 Å of the DNA backbone) as a function of time for complexation with dendrimers of generations 3, 4, and 5.

can see a strong hydration layer that corresponds to a dip in the dendrimer density in that region. The first hydration layer of the dendrimer from G3 to G5 is at a distance ∼7 Å from the center of mass of the dendrimer. The dendrimer density decreases and size increases from G3 to G5 as more and more water molecules penetrate inside it. Contacts between DNA-Dendrimer. Electrostatic interaction is the major binding force for the DNA-dendrimer in the complex.75 MD simulations reveal that it takes first few nanoseconds (around 7 ns for G4 and G5) for the dsDNA to form a stable complex with the dendrimer. Afterward, DNA engages to overcome different energetic hindrances and finds its optimal binding pattern on the dendrimer surface. A recent experiment on DNA-dendrimer complexation75 suggests that DNA binding with dendrimers can be divided into a “tightly bound DNA” region and a “linker DNA” region. Figure 5a gives the number of contacts between DNA and the dendrimer as a function of simulation time and shows interesting binding dynamics of the complex. We define two atoms belonging to DNA and the dendrimer, respectively, to be in contact if their distance of separation is within 3 Å. The number of contacts is maximum for the G5 dendrimer. This is expected as the charge ratio between the dendrimer and DNA is maximum and the wrapping is maximum. On the other hand, with decreasing charge ratio, the number of contacts decreases (for G4 and G3). Figure 5b demonstrates the role of water in the wrapping process. Here, we show the time evolution of the number of water molecules that are within 3 Å around the DNA backbone.

J. Phys. Chem. B, Vol. 115, No. 2, 2011 223 We find a clear correlation between the number of contacts and the amount of water in the vicinity of the DNA-dendrimer interface. As the number of contacts between DNA and dendrimer increases, water molecules move away from the DNA backbone. The precise role of water in the binding process is beyond the scope of this paper and will be studied in a separate work. DNA Bending. When a DNA chain concentrates near the oppositely charged surface of a nanoscale object, such as a dendrimer, the geometry and size of the dendrimer play a significant role in the mechanism of DNA compaction. The degree of bending of DNA depends on the dendrimer generation as well as on the DNA-dendrimer charge ratio. Global bending of dsDNA is an important parameter to understanding the DNA-dendrimer complex formation mechanism, and it measures DNA wrapping. We have calculated global helical bending for each of the two helices using the algorithm developed by Strahs and Schlick.76 This method computes the DNA curvature by summing the projected components of the local base pair step tilt and roll angles after adjusting the helical twist. Our analysis for the global angle was based on the values of the local tilt and roll angles for each base pair steps computed by the Curves program.77 Bends in the helical axis are defined by a negative roll angle, indicating bending toward the minor groove, whereas bends defined by a positive roll angle correspond to bending toward the major groove.76 In Figure 6a, we plot the global bending of DNA as a function of simulation time for the case of G3, G4, and G5 dendrimers. For comparison, we also calculate the time-dependent change of the DNA end-to-end length shortening. Strand shortening was calculated using Curve. The Curve algorithm outputs the vectorial direction of each local helical axis segment U and its reference point P. The path length between successive helical axis reference points can be calculated as

path )

∑ |Pbi - bPi-1| i

and the end-to-end distance of the DNA fragment can be calculated as

b1 - b Re ) |P PN | PN are the reference points for the two end where b P1 and b helical axes corresponding to two terminal nucleotides. Strand shortening is calculated as the difference between the sum of all the path lengths and the end-to-end distance. The strand shortening also indicates the overall flexibility of the DNA. In Figure 6b, we show the DNA strand shortening when it is complexed with dendrimers of generations G3, G4, and G5. Note that a clear correlation exists between DNA strand shortening and DNA bending: the shortening of DNA becomes large as the bending increases. DNA shortening correlates also very well with the radius of gyration of the DNA chain, shown in Figure 1b. DNA shortening is least in the case of G3 and most for G5. Significant DNA length shortening is the indication of a very compact DNA structure, leading to small values of RG. It is worth noting that, for a smaller-generation dendrimer, such as G3, the sliding of the dendrimer along the DNA backbone complicates the calculation of the global bending. As the dendrimer slides along the DNA backbone, the position of

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Figure 6. (a) Global bending of DNA around the dendrimer as a function of time for G3, G4, and G5 dendrimers. (b) DNA strand shortening as a function of time for G3, G4, and G5 dendrimers.

the bend region changes. Considering this fact, the global bending should not be considered the only measure of DNA

bending. Bending can also be characterized by local bending of the DNA as well. The bending angle is defined as θ ) s/RLB,



Figure 7. Time evolution of DNA local bending: for the case of the (a) G3 dendrimer, (b) G4 dendrimer, and (c) G5 dendrimer.

where s is the contour length of the DNA during the dynamics and

∑ NP

RLB )

ri2

i)1

where ri is the distance of the ith phosphate site on the dsDNA from the center of the dendrimer and NP is the number of phosphates in the DNA backbone. The value of RLB decreases with increasing bending of DNA around the surface of the dendrimer. In the case of the G3 dendrimer, the degree of bending is less due to the smaller charge ratio as well as the dendrimer movement along DNA backbone. From Figure 7, we can see that, at some time instant, the local bending increases for G3 due to variation of the local bending region along the DNA length, and for the whole time interval, there is no net change in the local bending. But in the case of G4 and G5, we see a steady increment of local bending as a function of time. Therefore, local bending for this case is a reliable marker of the binding of the dendrimer. Helicoidal Parameters. The helicoidal parameters, such as rise, roll, twist, shift, tilt, and slide, describe the overall backbone structure of the dsDNA in the complex. These are important DNA properties that can demonstrate how well the B-form of DNA is preserved in the complex. In the present study, we have calculated these parameters by averaging over the last 3 ns of the total 24-25 ns long MD runs (depending on the dendrimer generation). The calculation was carried out using the Curve 5.1 software package.77,78 The observed helical twist in the B-DNA crystal structure is in the range of 35-36°.79 The

simulation results of B-DNA in solution give the helical twist in the range of 30-36°.80 The calculated helical parameters are shown in Figure 8, and we see that DNA maintains its B-form nicely in all the cases. At some base pair step level, the helical twist of the dsDNA bound to the G5 dendrimer deviates significantly compared with the values corresponding to B-DNA. This might indicate that the G5 dendrimer bound to dsDNA is not a stable structure like B-DNA. This is likely to be an important structural feature for choosing/designing a synthetic polymer for DNA delivery. Because of the conformational distortion of DNA, dsDNA-G5 may not be a good candidate for a DNA microarray. In general, DNA conformational distortion is measured with kink formation. A kink is referred to as the distortion of the DNA helix when a base pair step has a local roll value greater than 20°.81 DNA double helices bend significantly in the presence of one or more numbers of kinks. From Figure 8, we see that, for DNA bound to G5, there are some roll angles whose values exceed 20°. Thermodynamics of the Complexation. When DNA is mixed with PAMAM dendrimers, it undergoes a transition from a semiflexible coil to a more compact conformation due to the electrostatic interaction present between the cationic dendrimer and the anionic polyelectrolyte.82 It is known that, when a cationic polymer almost or completely neutralizes an anionic DNA, the intermolecular interaction is expected to be purely electrostatic. Some studies report that, for total neutralization, the number of primary amines is not necessarily equal to the number of positively charged groups in a polyamine at neutral pH. The primary amines of linear polymers have lower pKa’s than expected because of suppression of protonation by closely spaced charged groups.83,84

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Figure 8. Average rise, roll, shift, twist, slide, and tilt for all generation (G3, G4, G5) dendrimers and DNA complexes. The horizontal solid line represents the corresponding values of a B-DNA structure.

The bending nature of DNA depends on its length, and when the length of the DNA is of the order of a hundred base pairs, it behaves as a rigid rod. In the present study, the DNA has been taken as a length of 38 base pairs, and despite that, DNA wrapping around the dendrimer is remarkable. This is achieved by the partial neutralization of the DNA charge by the dendrimer. As DNA wraps around the dendrimer, it gains electrostatic energy. In the case of G3, the total positive charges on the dendrimer is not enough to neutralize the negative charges on the DNA and so the binding is very weak and the dendrimer moves along the DNA backbone. In the case of G5, electrostatic interaction is much stronger than in the other generations. In Figure 9, we plot the total electrostatic energy of the DNA-dendrimer complex for G3, G4, and G5 as a function of time and see that, as the dendrimer generation increases, the gain in the electrostatic energy is more. At equilibrium in the complexed state, DNA interacting with G5 has more energy (≈-37600 kcal/mol) compared with the DNA-G4 (≈-27450 kcal/mol) and the DNA-G3 complexes (≈-22400 kcal/mol), as is evident from Figure 9. During the complexation, both DNA

Figure 9. Total electrostatic energy of the DNA-dendrimer complex for G3, G4, and G5 as a function of time. Note that this includes the contribution from water and ions also. The solid red represents the running average to highlight the variation as a function of time.

DNA Compaction by a Dendrimer and the dendrimer gain in electrostatic energy compared with the case of free DNA and dendrimer in solution. Several experimental85,86 and theoretical87,88 studies have demonstrated that the complexation of an oppositely charged polyelectrolyte is governed by an unusual electrostatics mechanism, namely, counterion release. We have calculated the entropy of the counterions released using the recently developed 2PT methods.89,90 Na+ ions, which were initially condensed to the spine of the DNA, get released when DNA complexed with the dendrimer and, in the process, gain in entropy. The gain in entropy per Na+ ion is 104 J/mol for G3, which increases to 390 J/mol for G5. Similarly, we see the entropy gain for Clions, which were initially condensed with the amines of the dendrimer. The entropy gain per Cl- ion is 32, 85, and 152 J/mol for G3, G4, and G5, respectively. The free energy of complexation is then dominated by the entropy increase of the released counterions that had been condensed before complexation. This electrostatic contribution to the free energy has to compete with the energy cost of deforming one or both macromolecules to bring them in close contact.91 Free Energy of Binding. Recently stopped-flow circular dichroism and fluorescence spectroscopy were used to study the kinetics of the DNA-dendrimer complexation.92 It was found that activation energies for the DNA-dendrimer complexation follow the trend G4 > G7 > G9, and G2 shows an opposite trend. So far, none of the experiments have reported binding energies of this complexation. The equilibrium rate constant (K) of the binding can be computed from the binding energy using the well-known relation

∆G ) RT ln K To compute the equilibrium rate constant, we have calculated the binding enthalpy of the DNA-dendrimer complexation using the following definition.

∆E ) EDNA-DEN - EDNA - EDEN - ∆Edeform where EDNA-DEN, EDNA, and EDEN represent the potential energy of the DNA-dendrimer complex and potential energies of the DNA and the dendrimer in the bound state. ∆Edeform accounts for the fact that there is significant deformation (conformational change) of the DNA and the dendrimer in the bound state compared with their native conformation and is defined as 0 0 ∆Edeform ) (EDNA - EDNA ) + (EDEN - EDEN ) 0 0 and EDEN are the potential energies of the DNA where EDNA and dendrimer in the native state. A similar definition was used earlier93 to compute the binding enthalpies of the DNA and bucky ball complex. We calculated the binding energy for each of these cases, and the results are given in the following. The binding energies of the complexation follow the trend G5 (-398.89 kcal/mol) > G4 (-145.15 kcal/mol) > G3 (-134.94 kcal/mol). This indicates that the larger the dendrimer generation and charge ratio between the DNA-dendrimer, the better is the binding affinity. We have also calculated the binding free energies for the DNA-dendrimer complex using the MM-PB/GB-SA (MM, Molecular Mechanics; PB, Poison Boltzmann; GB, Generalized Born; SA, Surface Area) approach using the MM-PBSA tool in the AMBER9 software suite.94 The general objective of the

J. Phys. Chem. B, Vol. 115, No. 2, 2011 227 MM-PBSA method is to calculate the free energy difference between the bound and the unbound state of two solvated molecules. In general, the binding free energy for the noncovalent association of two molecules may be written as

∆G(A + B f AB) ) GAB - GA - GB For any species on the right-hand side, G(X) ) H(X) - TS(X); in view of this expression, the above binding energy can be written as

∆Gbind ) ∆Hbind - T∆Sbind where

∆Hbind ) ∆Egas + ∆Gsol ∆Hbind is the change in enthalpy and is calculated by summing the gas-phase energy (∆Egas) and the solvation free energy (∆Gsol). Where Egas ) Eele + Evdw + Eint, here, Eele is the electrostatic energy calculated from the Coulomb potential, Evdw is the nonbond van der Walls energy, and Eint is the internal energy contribution from bonds, angles, and torsions. Gsol ) Ges + Gnes, where Ges is the electrostatic energy calculated from a Poisson-Boltzmann (PB) method and Gnes is the nonelectrostatic energy calculated as γ/SASA + β, where γ is the surface tension parameter (γ ) 0.00542 kcal/Å2), SASA is the solvent-accessible surface area of the molecule, and the free energy of the nonpolar salvation for a point solute β ) 0.92 kcal/mol. The gas-phase energy (∆Egas) or molecular mechanical energy is obtained using the sander module of AMBER9 with no cutoff for nonbonded interaction. The SASA is computed using the molsurf module in AMBER9. The grid spacing is set to 0.5 Å with dielectric constants 1 and 80 for the interior and exterior of the molecules, respectively. The dielectric boundary is defined by a 1.4 Å probe water on the atomic surface. For the PBSA calculation, the Poison Boltzmann solver is used, as is implemented in AMBER9 with the abovementioned parameter values. Despite being a promising method, MMPBSA has several inherent limitations, the major one being the calculation of solvation free energy by a continuum model, such as PBSA or GBSA, particularly, in cases where hydrogen-bonded interactions are important. Another area of great concern is the use of thesametrajectorybothforthecomplexstate(e.g.,DNA-dendrimer) as well as for the unbound state for the individual solute (e.g., DNA and dendrimer separately), which can lead to significant conformational issues for the individual solute. Finally, it is not clear if the simple SASA term can adequately describe the hydrophobic effect. Despite all these drawbacks, this method, nevertheless, is remarkably successful in predicting and calculating the free energy of binding in a wide variety of systems in good agreement with available experimental results. For the entropy calculation, we have used the recently developed twophase (2PT) thermodynamic model. We have estimated the binding free energies by averaging gas-phase energies (MM) and solvation free energies as determined by Generalized Born model (GB/SA) analysis using snapshots obtained from the last 2 ns of the total 24-25 ns long simulation time (depending on the dendrimer generation).

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TABLE 2: MMPB/GB SA Binding Energy complex

electrostatic energy (PB) (kcal/mol)

G3 + DNA G4 + DNA G5 + DNA G5 + DNA (50 mM)

–1639.76 ( 703.61 –6019.65 ( 559.28 –7429.57 ( 618.87 –4220.18 ( 327.73

PB energy (kcal/mol)

GB energy (kcal/mol)

–1702.17 ( 704.08 –253.78 ( 5.75 –6411.78 ( 545.05 –789.71 ( 10.78 –7742.02 ( 622.64 –1283.42 ( 16.07 –4484.88 ( 380.25 –1175.48 ( 14.57

The calculated binding free energies are given in Table 2 and follow the same trend as earlier, G5 > G4 > G3. Note that the electrostatic contribution dominates the binding free energies for all the cases. Another interesting feature is that the entropy loss due to binding increases with the increase in dendrimer generation. This entropy loss is compensated by the gain in the electrostatic energy upon binding, which increases with the increase in dendrimer generation. As DNA binds strongly to the dendrimer, binding becomes entropically unfavorable due to loss of degrees of freedom for both the dendrimer and DNA. Entropy loss is minimal for G3, which is very flexible. This also causes maximum deformation of the dendrimer structure when it binds to the DNA. G4 and G5 have the largest entropy loss and hence less deformation compared with G3. Another interesting feature emerges while computing the binding free energy per dendrimer amine charge: we find that G4 has the maximum binding efficiency on the basis of per dendrimer amine charge, followed by G5 and G3, respectively. This confirms our hypothesis that G4 is a better candidate to delivery compared with G5, which causes maximum distortion to the DNA geometry, as is evident from the calculated helicoidal parameters. Effect of Salt Concentration. From the binding free energy as well as from the energetic of the complexation, it is evident that the DNA-dendrimer complexation is driven by the electrostatic interaction and hence will be significantly influenced by the physiological salt concentration. To study the effect of salt concentration on the structure and energetic of the complexation, we have done the simulation of DNA with the G5 dendrimer at 50 and 100 mM NaCl solutions. With the increase in the salt concentration, electrostatic interaction is screened and, hence, the binding affinity decreases. We see a significant lowering of the number of contacts compared with the charge neutral case, as shown in Figure 10. This is also reflected in the lesser degree of bending of the DNA at a 50 mM salt concentration shown in Figure 11. The calculated binding energy using the MM-PBSA method also shows that the binding free energy decreases (from -60.48 kcal/mol charge

Figure 10. Number of contacts between the amine groups of the dendrimer and phosphate of DNA for the case of G5 at a 50 mM salt concentration and physiological pH.

-T∆S (kcal/mol) ∆G (PB) (kcal/mol) ∆G (GB) (kcal/mol) 7.506 53.191 52.862 10.782

–1694.66 –6358.58 –7689.16 –4474.09

–346.27 –736.52 –1230.56 –1164.69

neutral case to -35 kcal/mol at 50 mM per primary amine) dramatically with an increase in salt concentration. However, even at a 50 mM salt concentration, we have a very stable complex over a several nanoseconds long simulation. At this salt concentration, we still have a very compact complex, but release may be better at this salt concentration due to the decrease in the strength of binding. 4. Conclusion The simulation study presented here is the first theoretical demonstration of the complexation between dsDNA and a dendrimer with a fully atomistic description. Using several hundred nanoseconds long MD simulations, we have observed the various binding modes of dsDNA and the dendrimer for various generations of PAMAM dendrimers at varying charge ratios. MD simulations demonstrate that, when the charge ratio is greater than 1 (as in the case of the G5 dendrimer), the binding is optimal. The binding is driven by the electrostatic interaction, and the larger the dendrimer charge, the stronger the binding interaction. At the beginning of the complex formation, the dendrimer expands in order to increase the DNA-dendrimer surface contacts. Afterward, the complex formation leads to a significant amount of water repulsion from the DNA backbone, and DNA overcomes several energetic bottlenecks to find its optimal wrapping pattern on the dendrimer surface. The binding free energy calculation reveals that the higher the charge ratio between DNA and the dendrimer, the better the binding affinity. We have not yet detected any base specificity for the dsDNA and dendrimer interaction, although our earlier results demonstrated strong sequence dependence binding for oligonucleotide-dendrimer binding. From the consideration of molecular dimension, a DNA of this length cannot wrap around any of the dendrimer generations studied in this paper. Instead, what is remarkable is the degree of bending that the DNA undergoes when the dendrimer binds to it. The partial charge neutralization of DNA by the oppositely charged dendrimer makes the DNA backbone flexible enough so that it bends toward the neutralized surface. The degree of bending increases with dendrimer

Figure 11. Global bending of DNA as a function of time for the case of G5 at a 50 mM salt concentration.

DNA Compaction by a Dendrimer generation, as more and more DNA charges get neutralized with the increased positive charges on the dendrimer. Therefore, G5 causes maximum bending of the DNA. MD simulations reveal that DNA can penetrate in the interior of the dendrimer for larger charge ratios (like in the case of G5), which can make the subsequent release difficult. For a lower-generation dendrimer, such as G3, there is significant deformation of the dendrimer due to their flexible nature. Therefore, for G3, DNA deformation or bending is very low compared with G4 and G5. Dendrimer deformation for the lower generation was also observed in an earlier single-molecule experiment on the DNA-dendrimer pulling experiment.74 Acknowledgment. We thank DST, India, for financial support. We acknowledge the computational resource supported by the DST Centre for Mathematical Biology at IISc. References and Notes (1) Zinchenko, A. A.; Chen, N. J. Phys.: Condens. Matter 2006, 18, R453. (2) Schiessel, H. J. Phys.: Condens. Matter 2003, 15, R699. (3) Kukowska-Latallo, J. F.; Bielinska, A. U.; Johnson, J.; Spindler, R.; Tomalia, D. A.; Baker, J. R. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 4897. (4) Tang, M. X.; Redemann, C. T.; Szoka, F. C. Bioconjugate Chem. 1996, 7, 703. (5) Zimmerman, S. C.; Zeng, F. W.; Reichert, D. E. C.; Kolotuchin, S. V. Science 1996, 271, 1095. (6) Bosman, A. W.; Janssen, H. M.; Meijer, E. W. Chem. ReV. 1999, 99, 1665. (7) Grayson, S. M.; Frechet, J. M. J. Chem. ReV. 2001, 101, 3819. (8) Haensler, J.; Szoka, F. C. Bioconjugate Chem. 1993, 4, 372. (9) Dufes, C.; Uchegbu, I. F.; Schatzlein, A. G. AdV. Drug DeliVery ReV. 2005, 57, 2177. (10) Abdelhady, H. G.; Allen, S.; Davies, M. C.; Roberts, C. J.; Tendler, S. J. B.; Williams, P. M. Nucleic Acids Res. 2003, 31, 4001. (11) Shen, X. C.; Zhou, J.; Liu, X.; Wu, J.; Qu, F.; Zhang, Z. L.; Pang, D. W.; Quelever, G.; Zhang, C. C.; Peng, L. Org. Biomol. Chem. 2007, 5, 3674. (12) Wang, D.; Kopeckova, P.; Minko, T.; Nanayakkara, V.; Kopecek, J. Biomacromolecules 2000, 1, 313. (13) Pillai, O.; Panchagnula, R. Curr. Opin. Chem. Biol. 2001, 5, 447. (14) Roberts, J. C.; Adams, Y. E.; Tomalia, D.; Mercer-Smith, J. A.; Lavallee, D. K. Bioconjugate Chem. 1990, 1, 305. (15) Wiener, E. C.; Brechbiel, M. W.; Brothers, H.; Magin, R. L.; Gansow, O. A.; Tomalia, D. A.; Lauterbur, P. C. Magn. Reson. Med. 1994, 31, 1. (16) Wiener, E. C.; Konda, S.; Shadron, A.; Brechbiel, M.; Gansow, O. InVest. Radiol. 1997, 32, 748. (17) Kim, S.; Kim, J. H.; Moon, W. K.; Min, B. G. J. Digit. Imaging 2000, 13, 193. (18) Kobayashi, H.; Kawamoto, S.; Saga, T.; Sato, N.; Hiraga, A.; Ishimori, T.; Konishi, J.; Togashi, K.; Brechbiel, M. W. Magn. Reson. Med. 2001, 46, 781. (19) Kobayashi, H.; Kawamoto, S.; Saga, T.; Sato, N.; Hiraga, A.; Ishimori, T.; Akita, Y.; Mamede, M. H.; Konishi, J.; Togashi, K.; Brechbiel, M. W. Magn. Reson. Med. 2001, 45, 795. (20) Nicolle, G. M.; Toth, E.; Schmitt-Willich, H.; Raduchel, B.; Merbach, A. E. Chem.sEur. J. 2002, 8, 1040. (21) Konda, S. D.; Wang, S.; Brechbiel, M.; Wiener, E. C. InVest. Radiol. 2002, 37, 199. (22) Roy, R.; Baek, M. G.; Rittenhouse-Olson, K. J. Am. Chem. Soc. 2001, 123, 1809. (23) Singh, P.; Moll, F.; Lin, S. H.; Ferzli, C.; Yu, K. S.; Koski, R. K.; Saul, R. G.; Cronin, P. Clin. Chem. 1994, 40, 1845. (24) Orentas, R. J.; Rospkopf, S. J.; Casper, J. T.; Getts, R. C.; Nilsen, T. W. J. Virol. Methods 1999, 77, 153. (25) Snowden, T. S.; Anslyn, E. V. Curr. Opin. Chem. Biol. 1999, 3, 740. (26) Yoon, H. C.; Hong, M. Y.; Kim, H. S. Anal. Biochem. 2000, 282, 121. (27) Chang, A. C.; Gillespie, J. B.; Tabacco, M. B. Anal. Chem. 2001, 73, 467. (28) Cordova, A.; Janda, K. D. J. Am. Chem. Soc. 2001, 123, 8248. (29) de Groot, D.; de Waal, B. F. M.; Reek, J. N. H.; Schenning, A.; Kramer, P. C. J.; Meijer, E. W.; van Leeuwen, P. J. Am. Chem. Soc. 2001, 123, 8453. (30) Astruc, D.; Chardac, F. Chem. ReV. 2001, 101, 2991.

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DNA Compaction by a Dendrimer - The Journal of Physical Chemistry

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