Tuning the Stability of DNA Nanotubes with Salt - The Journal of

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C: Physical Processes in Nanomaterials and Nanostructures

Tuning the Stability of DNA Nanotubes with Salt Supriyo Naskar, Mounika Gosika, Himanshu Joshi, and Prabal K. Maiti J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10156 • Publication Date (Web): 19 Mar 2019 Downloaded from http://pubs.acs.org on March 21, 2019

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The Journal of Physical Chemistry

Tuning the Stability of DNA Nanotubes with Salt Supriyo Naskar§, Mounika Gosika§, Himanshu Joshi§, †and Prabal K Maiti§, *

§ Center

for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India

†

Current Address: Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States * Corresponding author. E-mail: [email protected] , Tel: (091)80-2293-2865

ACS Paragon Plus Environment

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Abstract We report the enhancement of the structural stability of DNA nanotube (DNT) by changing the salt concentrations for three different salt species namely: NaCl, KCl, MgCl2. Using fully atomistic molecular dynamics simulations, we find that, with the gradual increment in the NaCl salt concentration, the DNT becomes compact and rigid. The significant reduction in the average RMSD, RMSF and effective radius of the DNT with an increase in the NaCl concentration, quantifies our observation. We explain how the DNTion interactions play a vital role in the conformational fluctuation of the DNT. To understand the salt dependence of the mechanical properties of the DNTs, we have calculated the stretch modulus () and persistence length (lp) as a function of salt concentration. The calculated stretch moduli of the DNTs change from 8.3 nN to 13 nN and the persistence length of the DNT varies from 6 to 10 µm when the NaCl salt concentration is varied from 0 molar (M) to 1 M. Both the stretch modulus and the persistence length calculations reaffirm the structural stability of the DNT at higher salt concentrations. We find similar trends for another monovalent salt (KCl). However, for divalent salt (MgCl2) we find minimal variation in the structural properties with an increase in the salt concentration.


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Introduction DNA is one of the potential materials for building engineered and synthetic nanostructures1-3. The unique base pairing between adenine-thymine and guanine-cytosine makes it a promising bio-polymer for containing and expressing genetic information. Its linear helix axis and canonical Watson-Crick base pairing, aid in constructing easily programmable complex self-assembled DNA structures4-5. The proposition of nucleic acid junctions by Ned Seeman in 1982’s initiated the field of DNA nanotechnology which is expanding rapidly1-3, 6-7. Owing to the specific interactions of the nucleobases of the nucleic acids, DNA can form a basis for building various desired nanoscale structures; the idea that is vastly implemented in DNA nanotechnology8-9. Several novel nanostructures having fascinating physical and chemical properties have been synthesized since then10-17. DNA nanotubes (DNTs) are the recent addition to the growing repository of the DNA based nanostructures and receiving attention because of their application in designing membrane spanning nanopores12,

18-28.

DNTs are synthetic nanopores with a

programmable interface where DNAs are arranged in a tubular structure24, 29-31. The assembled DNAs in the DNTs are connected by Holliday like junctions with double crossover (DX) or triple crossovers (TX)1820, 29, 32-35.

Several groups have already synthesized DNA nanotubes possessing different shapes and well-

defined structures. Experimental techniques like cryo-electron microscopy, atomic force microscopy, Xray diffraction have been developed to study the complex atomic structures of the DNTs19-20, 36-37. Also, several aspects of their structures at the nanoscale level have been investigated using computer simulations16, 24, 29-31, 36, 38. It has been well established that depending on the external environment, the DNT pore can have different topology31, 36. Hence, by tuning the physiological conditions like salt concentration, it is possible to control the DNT’s pore radius and gating behavior, the properties that have a crucial role in drug delivery31, 36, 39-40 applications. Owing to their high stretch moduli DNTs29-30 can be used for different biotechnological applications, for instance, as replacement materials for actin filaments and other cytoskeletal purposes. Recently, the 6-helix DNA bundle is reported to behave as a robotic arm in transporting nanoparticles41. Therefore, it is important to study the mechanical properties of the DNT structures at various external conditions. Also, to build the structures of micrometer length scale it is important to have these DNT tiles very rigid and stable at the nanometer length scale. Stretch modulus and persistence length are the key measurements for estimating of rigidity and flexibility for the DNTs. The flexibility of the constituent DNA helices is very much dependent on the physiological conditions like salt concentration level, temperature42-



44.

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Though the flexibility of nucleic acids such as DNA, RNA has been studied significantly, not many

studies have explored the salt concentration effects on the structural rigidity and flexibility of DNTs. Previously for these type of systems, molecular dynamics (MD) has proven to be very much effective in understanding the atomic structures24, 29-30, 32, 35, 38, 45. Hence, we have also employed the fully atomistic MD simulations for this study. In this article, we have attempted to understand and explain the effects of increasing the salt concentration on the structural stability of the DNA nanotubes, using MD simulation. We have used two different monovalent salts (NaCl, KCl) and a salt with divalent cation (MgCl2) and built systems at 0 M, 0.5 M and 1 M salt levels for each of these salts. In the main text of this article, we have mainly discussed the results for NaCl salt. The other two types of salts have almost same kind of behavior, the details of which have been provided in the supplementary information (SI) [Chapter 6 and 7]. We performed three statistically independent MD simulations of 200 ns long for each of the cases to collect the MD trajectories. The details of system building protocols and MD methodology are given in the method section. In the results section, we demonstrate how the ion-mediated interactions between the DNT atoms, shape the DNT’s structure and stability. We observe that the dominant mode of motion of the DNTs comes from the end region which effectively increases the radius of the DNTs at terminals. The core region of the DNTs for all the systems is found to be stable. We find that the ion distribution has a vital role on the structural stability of the DNT. The other physical properties of the DNTs such as flexibility, rigidity also very much rely on the salt conditions. Our simulation study has also captured these dependencies of the physical properties on the salt concentration. Three additional systems with NaCl molarity of 0.25M, 0.75M, and 1.25M were also studied to see the consistency of the calculated physical quantities. The results from these simulations have been provided in SI chapter 5. All these studies of ion-DNT interaction and quantified parameters of the DNTs will be very much helpful to build more stable DNA nanostructures with a greater level of control and functionality.

Methods System Details and Simulation Protocol Custom made program written using NAB module46 of AmberTools1647 is used extensively to build all the DNT structures. The sequence chosen for the DNT is the same as the experimental design by Wang et al.20


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( SI figure S1 ). All the 6 dsDNA are placed in a hexagonal arrangement and the distance between two hexagonal arms is chosen to be around 20 Å. The different dsDNA strands are connected by four-way Holliday like junctions48. In particular, these DNTs are the DX49 or TX50 crossover structures assembled in a hexagonal geometry. The Crossovers and the nicks are also designed in the manner akin to the experimental design. The interstrand crossover distances among the helices are chosen after 7 base pairs (bp) or an integer multiple of that to ensure the nucleobases involved in crossovers are nearest to each other. Using xLEAP module of AmberTools1647, the built structure is then solvated using TIP3P water model51. The negative charges of the phosphate backbone are charge neutralized by adding an appropriate number of Na+ counterions. To achieve systems with a desired salt concentration, we added additional number of NaCl molecules to the system. In particular, we have built three systems for NaCl salt at 0 M, 0.5 M, and 1 M concentrations respectively. The representative snapshots of one such system is shown in figure 1 (a) and (b). The details of the simulated systems are given in SI table S1. Periodic boundary conditions are used in all the 3 dimensions, to mimic the bulk properties of the systems. The interaction of the DNA fragments is defined by DNA.OL15 forcefield52 which includes parmbasc053 and OL1552 correction to the ff10 forcefield54. The interaction of the monovalent ions (Na+, K+, Cl-) with the external water and DNT is defined by Joung-Chetham ion parameter set55. For divalent ion (Mg2+) the Li-Merz ion parameters are chosen56. The system built this way is then subjected to an initial energy minimization to eliminate unwanted bad contacts between the solute and solvent atoms. The system is first subjected to 1000 steps of steepest descent minimization and 2000 steps of conjugate gradient minimization. During this process, the DNT is held fixed with a force constant of 500 kcal/(mol-Å2). Then the systems are subjected to several thousands of conjugate-gradient minimization steps, where the solute restraint is gradually reduced from 20 kcal/(molÅ2) to 0 kcal/(mol-Å2). After the energy minimization, the systems are gradually heated from 0K to 300 K over 50 picoseconds(ps). During this process, the DNTs are kept fixed to their energy minimized configurations with a harmonic restraint of force constant 20 kcal/(mol-Å2). Langevin thermostat57 with a coupling constant of 3 ps-1 is used to attain the temperature regulation. Finally, 0.2 µs of production runs were done in NPT ensemble with an integration timestep of 2 femtoseconds at 300K temperature and 1 atm pressure. The pressure regulation is attained using anisotropic pressure scaling58 with a pressure relaxation time of 1 ps and temperature regulation using Langevin thermostat57 with the same coupling constant. Similar protocols have been successfully implemented and validated in our previous studies on DNTs24, 2930, 38

and DNA systems32-35, 45. During the course of the simulation, SHAKE59 constraints were applied on

all bonds involving hydrogen with a tolerance of 1×10-7. The long-range interaction is calculated using the



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particle mesh Ewald (PME) method60 with a cutoff distance of 10 Å. To average the whole phase space effectively we simulated 3 statistically independent systems for all 3-different salt concentrations. The CUDA version of PMEMD.MPI61-63 module of Amber1464 is used mainly for all the simulations. For the data analysis purpose, we have used CPPTRAJ65 of AmberTools1647 and Visual Molecular Dynamics (VMD) package66 extensively. The visualization of the systems and trajectories are done using the VMD package66.

Results and Discussions Salt Concentration Dependent Structural Properties of the DNT (a) Microscopic picture of the DNT at various molarities of NaCl Figure 1 shows the instantaneous snapshots of the various DNT systems after 200 ns long MD simulation. From the snapshots, it is apparent that the DNT maintains its tubular geometry throughout the simulation and at all the salt concentrations studied in this work. Due to the highly negatively charged DNA backbones, the adjacent DNA helices repel each other strongly. This is clear in the 0 M concentration case, where we have found both the mouth regions of the DNTs open and fluctuate heavily [see figure 1(c) and (d)]. At higher salt concentrations, in the presence of excessive Na+ and Cl-, the inter helix electrostatic repulsions become partially weakened due to screening. To quantify the effect of this screening, we have calculated the effective electrostatic energy for the interaction between DNT and the other components of the simulation system [see table 1]. This calculation is performed with the aid of “rerun” and “group/group” commands of LAMMPS package67 where the electrostatic energies between various charged groups68 are calculated with appropriate k-space corrections. From this calculation, it is evident that the effective electrostatic energy of the DNT becomes more negative with an increment in the salt concentration, making the DNT most stable energetically, at 1M. Also, it is interesting to look at the trends of various contributions to the total DNT electrostatic energy i.e., DNT-self interaction, DNT-water and DNT-ion interactions as shown in table 1. For instance, the self-electrostatic energy of the DNT, increases with salt concentration, as the DNT atoms come closer to each other at higher salt concentrations (see figure 1 (c), (d), (e), (f), (g), (h)). The water – DNT electrostatic interaction significantly reduces at 1M, as the waters can access a spread out 0 M structure better than a compact 1M structure. For the DNT-ion interaction, as the number of counterions


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increase with salt concentration, we observe an enhanced interaction at 1M than at 0 M. All these combined effects make the 1 M structure energetically stable over 0.5 M and 0 M cases. In other words, the electrostatic repulsions between the DNT helices reduce when we increase the salt concentration. Hence, at 0.5 M, we find reduced deformation in the mouth regions when compared with 0 M case, and at 1 M the deformation mitigates even further making the DNT acquire a structure akin to its native state. The video provided in the supplementary information [ SI video V1, V2, V3] also substantiates the above observation. (b) Root mean square deviation (RMSD) Ion-mediated interactions among the constituent DNA helices of the DNT play a key role in its stability and structural deformation. To quantify the structural deformation observed in the DNT, we have also calculated the time evolution of its RMSD with respect to the initial energy minimized structure. The decrease in the structural deformation with an increase in salt concentration can be seen in the RMSD plot [figure 2(a)]. In case of 0 M salt concentration, the RMSD value settled at around 14 Å whereas for 0.5 M and 1 M salt concentration the RMSD value got significantly lowered (around 11 Å and 8 Å respectively). This decrease in RMSD value indicates a less conformational change of the DNT from its native state, at higher salt concentrations. (c) Root mean square fluctuation (RMSF) The RMSD data suggests that the increase in salt concentration reduces the structural deformation of the DNT. However, it is not clear how the local areas of the DNT fluctuate in the presence of the excess salt. To capture these local changes in the conformation of the DNT, we have calculated the RMSF of the DNTs as a function of DNT slice. The RMSF for atom j is defined as, 𝑅𝑀𝑆𝐹𝑗 =

1 𝑇 ∑ 𝑇 𝑡𝑖 = 1||𝑟𝑗(𝑡𝑖)

― 〈𝑟𝑗〉||2; where 𝑟𝑗

(𝑡𝑖) is the position of the j-th atom at time 𝑡𝑖, < 𝑟𝑗 > is the time averaged position and 𝑇 is the total time over which averaging is done. The DNT is composed of 57 bp per helical domain. Accordingly, the DNT has been divided into 57 slices such that each slice contains 1 bp from each of the 6 double helices forming the DNT ( The definition of the slice is same as defined by Joshi et al.

30

). To get the RMSF value for a

particular slice we averaged 𝑅𝑀𝑆𝐹𝑗 over all the atoms in that particular slice, 𝑅𝑀𝑆𝐹 = 1/𝑁∑𝑗𝑅𝑀𝑆𝐹𝑗 ; where 𝑁 is total number of atoms in that slice. The RMSF for each of the slices is calculated from the snapshots corresponding to the last 100 ns of the 200 ns long simulation. Shown in figure 2(b) are the RMSF values of the DNT as a function of the slice index for three different salt concentrations. The central region has minimal RMSF at all the three molarities and hence the cylindrical structure is maintained well in this



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region. In contrast, the terminal portions of the DNT fluctuate heavily as the RMSF is higher for these portions. The overall RMSF of the DNT is decreasing as we increase the salt concentrations, which is consistent with the lower RMSD discussed in previous section. The large fluctuations between individual runs in RMSF for 0.5 M and 1M cases are purely statistical [See SI figure S4], but the overall RMSF averaged over different ensembles is effectively reduced with increasing salt concentration.

Conformational Dynamics and Time Evolution of the Pore Radius (a) Principal Component Analysis Data obtained from MD simulation with large number of degrees of freedom (dof) is not often interpretable. To get something meaningful out of such huge dataset we perform the principal component analysis (PCA) of the system. PCA can be very helpful to have an additional insight into the collective dynamics of the DNA fragments. PCA is a dimension reduction tool used widely to reduce a large set of dof into a small set of interpretable dof. It extracts the main dominant mode of motion out of the MD trajectory. The PCA analysis is done on the 684 phosphorus (P) atoms of the DNA backbone using CPPTRAJ of AmberTools16. First, we construct the covariance matrix from the time series of cartesian coordinates of the P atoms. Using the RMS fit of CPPTRAJ we then remove all rotational and translational modes of motion. Then the covariance matrix is diagonalized to obtain the 2052 eigenvalues (684 P atoms x 3) and the corresponding eigenvectors. Figure 3 contains the first principle component (PC1) and the corresponding eigen direction of the P atoms for different salt concentrations. With increasing salt concentration, the dominant PC1 motion in both end region suppresses which is visible in the supplementary video [SI video V4, V5, V6]. Also, from the cumulative fraction of eigenvalues, we observe that the main PC1 motion is made up of 23%, 31% and 33% for DNT system composed of 0 M, 0.5 M and 1 M NaCl respectively. In figure 3 the cartesian coordinates are projected along the first 5 PCs to see how much the trajectories and PCs match with each other. All these analyses are very useful to understand the conformal dynamics which is dominant in the terminal region of DNT. But none of above analysis can quantify how much the terminal region opens, or whether the opening is dependent on the salt concentration? To address these questions, we also calculate the pore radius of the DNT along the long axis. (b) Radius profiles The inner pore of the nanotube play a crucial role as ions’, water, and cargo transport channels to perform all the essential function. So, the radius of the nanopore is an important measure as depending on radius


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the pore can undergo a transition between ‘Open’ and ‘Closed’ states31. We calculate the pore radius of the nanotube along the pore axis or the long axis of the DNT. The time evolution of the radius profile is shown in figure 4 (a)-(c). We found that with increasing salt concentration the radius of the DNT is reducing effectively. Both the end regions of the DNTs are mainly influenced by the salt concentration where the fluctuation of DNA fragments and inter-helix repulsion is reduced due to the screening of the electrostatic interaction by the excessive salts resulting low radius. The central region is also compressed by the excess salts. At 0 M NaCl, there are no Cl- ions and only 664 Na+ counterions to neutralize the net charge of the system. In the presence of these Na+ ions, screening of electrostatic interaction is not adequate, and both the ends open up due to high repulsion between adjacent DNA backbones. This makes the radius profile very symmetric at 0 M. Also, in case of 1 M electrostatic screening is better due to the presence of higher numbers of Na+ and Cl- (1564 NaCl molecule and 664 Na+ counterions) and the DNT structure is more compact. So, radius profile for 1 M case is very symmetric. But, in case of 0.5 M system, moderate number of ions (782 NaCl molecule and 664 counterions) are present to screen the electrostatic repulsions as compared to 1M system. We observed that in these kind of moderate ionic conditions, the local distributions of ions play crucial role in determining the pore radius of both mouth regions. So, the pore radius of the mouth region of DNT may show open or close state depending on the local ion distribution of NaCl. Figure 4 (d) shows the average radius profile of the DNTs for different salt concentration as a function of pore axis. The data is averaged over last 100 ns of the 200 ns MD simulation trajectories. From the radius analysis, it is also clear that the fluctuation in radius is decreasing with increasing salt concentration and in the mouth region pore radius of one end is independent of another end. Also, the transition between ‘Open’ state and ‘Close’ state can happen stochastically during the whole simulation31. So, the analysis of RMSD, RMSF and pore radius yielded the following major observations, 1. Stability of whole DNT structure in terms of RMSD and RMSF increases with salt concentration. 2. The overall pore radius reduces with increasing salt concentration. 3. The pore radius of both ends of the DNT is not symmetric with each other which introduces the gating like behavior of the DNT pore. 4. Effective reduction of the backbone-backbone repulsion with increasing salt concentration which has a direct consequence on the pore radius.



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Though it is not clear from the above analyses how the ion distribution influences the DNT structure. We address this in the next section.

Understanding the Effect of the Ion Distribution on DNTs To relate the structural changes in the DNT with the salt molarity variation, we have calculated the radial distribution functions between the phosphate groups and the ions as shown in figure 5. The radial distribution function is defined same way as in reference 69 and is given by 𝑔(𝑟) =

𝑛(𝑟, 𝑟 + 𝑑𝑟) , 𝑁𝑝𝑎𝑖𝑟𝑠 2 4𝜋𝑟 𝑑𝑟 𝑉

(1)

( )

where 𝑛(𝑟, 𝑟 + 𝑑𝑟) are the number of atoms in the range [𝑟, 𝑟 + 𝑑𝑟], 𝑁𝑝𝑎𝑖𝑟𝑠 is the number of atom pairs for which 𝑔(𝑟) is calculated and V is the volume of the simulation box. From the P-P distributions, we find a very slight increment in the probabilities as we go for higher molarities. The conformational changes in the DNT structures with salt concentration variation are not reflected from these P-P distributions. Although, the available number of counter-ions for the DNT increases with molarity, we observe that the probability of finding Na+ ions near to P groups is more for 0 M case compared to the 0.5 M and 1M cases (see the red curves in figure 5 (a), (b) and (c)). This is because the number of Na+ ions surrounding the P groups (𝑛(𝑟, 𝑟 + 𝑑𝑟), the numerator of equation 1) will not be very different at the three salt levels considered, whereas the denominator in the equation (1) i.e., 𝑁𝑝𝑎𝑖𝑟𝑠 increases with salt concentration, making the g(r) reduce at higher molarities. This observation is in agreement with the previously reported salt concentration-dependent study of DNTs36. We found that for the P-P distribution, the first peak is at around 7 Å for all the three salt concentrations, whereas the phosphate-sodium RDF has its first peak at around 3 Å. Since phosphate groups are negatively charged and sodium ion is positively charged, the attractive electrostatic interaction between them causes the RDF peak to occur at a smaller distance. In contrast, the repulsive interaction between phosphate groups produces the RDF peak at higher distances. The Cl- ions in 0.5 M and 1M cases, are mostly located in the bulk of the system, much beyond the P groups, owing to the electrostatic repulsions from the DNT backbone groups (green curves in figure 5(b) and (c)). Although, various radial distribution functions g(r) give a significant insight into the ion-DNT interactions, they alone cannot explain the increasing stability of the DNT with increasing salt concentration.


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In order to understand the relative positions of Na+, Cl- surrounding the phosphate groups better, we have also calculated their distributions in concentric cylinders growing radially outward from the DNT axis [See SI chapter 3]. From the plots, we observe that the distribution of the phosphate groups becoming narrower with the increasing salt concentration. With increasing molarity, the fluctuation of phosphates groups in radial direction reduces which essentially becomes more apparent in these plots. Also, the distribution of the Cl- ion plays a crucial role in the stability of the structures. Since both Cl- ions, and phosphate groups are negatively charged they strongly repel each other. That is the reason for the abundant regions of Cl- ions and phosphate groups being in different positions. The Cl- ion acts as a circular shield to the phosphate ions in the sense that it is preventing the DNT backbone to spread radially out [see figure S2 (b), (c)]. With increasing molarity, the distribution of Cl- becomes sharper which increases the electrostatic repulsions between phosphate groups and the Cl- ions. Therefore, the motion of the phosphate groups along the radial direction is diminished. Also, with the increase in the number of counterions, the accumulation of Na+ and Cl- around the DNA backbone increased which effectively reduced the inter strand repulsions among the DNA helices. A significant number of Na+ ions are likely to be found in the vicinity of DNT walls which can be seen from SI figure S2 (d), (e), (f). Also, at the atomistic level from the careful visualization of the trajectories, we found that the water and ions breaches into the DNT walls which shows the porous or sponge-like nature of the DNT walls [See figure S2 (d), (e), (f)].



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Dependency of DNT’s Mechanical Properties on Salt Concentration (a) Stretch Modulus Mechanical properties of the DNA such as stretch modulus, persistence length, bending rigidity strongly depend on the salt concentration of the surrounding medium. Since DNT is made of dsDNAs, we expect the dominant effect of salt concentration on its mechanical properties will arise from the salt dependence mechanics of individual dsDNA as well as the intra strand interaction. Inter strand repulsions of the DNA fragments are reduced in the presence of excess salt, and beyond a certain salt concentration, the nature of the interactions between the DNA fragments becomes attractive fragment increases with salt concentration

42, 72.

70-71.

Stretch modulus of a dsDNA

In contrast, persistence length varies inversely with the

salt concentration 42, 45, 72-73. Also, contour length of a DNA decreases almost linearly with increasing salt concentration74-75. In the light of the above findings, we will now try to figure out, how DNT responds to the excess salt in the external environment. First, we will try to understand how stretch modulus of the DNT changes with salt concentration. The stretch modulus can be calculated from the contour length distributions as discussed below. If the contour length (𝐿) of an elastic rod fluctuates about the equilibrium length (𝐿0), then the probability distribution of the contour length (𝑃(𝐿)) can be written as,

[

)]

𝛾𝛽𝐿0 𝐿 𝛾𝛽 𝑃(𝐿) = 𝑒𝑥𝑝 ― ―1 2𝜋𝐿0 2 𝐿0 ⟹ln 𝑃(𝐿) = ―

(

𝛾𝛽𝐿0 𝐿 ―1 2 𝐿0

(

2

)

2

(2)*

1 𝛾𝛽 + ln , 2 2𝜋𝐿0

(3)

*

We have simulated the systems using NPT ensemble. For NPT ensemble an additional pressure coupling is maintaining the system’s pressure. Because of this, the effective Hamiltonian associated with the length fluctuation of the system will become, 𝐻𝑒𝑓𝑓(𝐿) = 𝐻(𝐿) + 𝑃𝑉. Therefore, the probability distribution can be expressed as, 𝑃(𝐿) ∝ 𝑒𝑥𝑝[ ― 𝛽(𝐻(𝐿) +𝑃𝑉)]. Taking logarithm in both sides, 𝑙𝑜𝑔(𝑃(𝐿)) = ―𝛽𝐻(𝐿) + 𝑜𝑡ℎ𝑒𝑟 𝑡𝑒𝑟𝑚𝑠. 𝑙𝑜𝑔(𝑃(𝐿)) = ―

𝛾𝛽𝐿0 𝐿 ―1 2 𝐿0

(

2

)

+ 𝑜𝑡ℎ𝑒𝑟 𝑡𝑒𝑟𝑚𝑠.

Since, we are extracting the stretch modulus from the slope of the graph of 𝑙𝑜𝑔(𝑃(𝐿)) 𝑣𝑠

(

𝐿 𝐿0

2

)

― 1 , the pressure coupling

only comes in the constant part. And stretch modulus remains same for both NVT and NPT ensemble. Same argument holds for the equation (7) also.


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1

where 𝛾 is the stretch modulus and 𝛽 = 𝐾𝐵𝑇 . Similar methodology was used in our previous works 30, 45 and has proven to produce physically relevant results. The contour length of the DNT is calculated by adding all the rise between two consecutive base pairs. First, we calculate the contour length (Li) of all the six DNA of the constituent DNT and then by 6

averaging we get the contour length (𝐿 = ∑𝑖 = 1𝐿𝑖) of the DNT (See figure 6(a) for the definition of contour length of a DNT). The equilibrium contour length, L0 is the time averaged value for L. The last 100 ns of the MD trajectory was used to calculate the contour length and values were averaged over 3 independent runs. In figure 6(b) we plot the contour length distribution. The simulation data is then fitted with the gaussian using the equation (2). In figure 6(c) we plot the ln 𝑃(𝐿) vs

(

𝐿 𝐿0

2

)

― 1 and using the least

square fitting we draw the straight lines. The stretch modulus calculated from the slopes and the average contour length is listed in table 242,

72.

The fluctuation in length is mainly due to the electrostatic

interaction between the conjugate base pairs. Increasing the salt concentration partially screens this interaction which effectively increases the structural stability of the DNT. The increased stability reflects in the average contour length. With the increasing stability, the fluctuation in the longitudinal direction reduces and stretch modulus increases.

(b) Persistence Length The flexibility of DNT can also be quantified by measuring its persistence length. Here we try to measure how the salt concentration influences the flexibility and calculate the persistence length (𝐿𝑃) of the DNT as a function of the salt concentration. The 𝐿𝑃 is calculated with two different methods – one is from the bending angle distribution and another is using the microscopic elasticity theory (MET). First, we describe how 𝐿𝑃 was calculated using MET. Assuming DNT as an elastic rod, the 𝐿𝑃 of the DNT can be written as, 𝐿𝑃 =

𝑌𝐼 , 𝑘𝐵𝑇

(4)

where Y is the Young’s modulus and I is the area moment of inertia (AMI). Y is related to the stretch modulus by the following relation, 𝑌=

𝛾 , 𝐴2


(5)


Page 14 of 32

where 𝐴2 = 𝜋𝑅22 is the cross-sectional area of the DNT assuming it a cylinder of radius 𝑅2. The I can be written as

[

1 𝐼= 2

𝑅22

∑𝐼0 + (4𝑅21 + 2𝑅22)𝐴1 + 𝐼0(16

― 10) 2

𝑅1

6

]

(6)

where, 𝐴1 = 𝜋𝑅21 is the cross-sectional area of the DNA assuming it a cylinder of radius 𝑅1 and 𝐼0 =

1 4

𝜋𝑅41

, is the AMI of the dsDNA. The detailed description of the calculation of I is given in our previous study 30.

Since the radius of the DNT is decreasing with the ionic strength we took the average radius of the

whole DNT as 𝑅2. The calculated 𝑅2 is given in the SI table S3. The radius of a DNA is taken to be 10.0 Å. Then the persistence length calculated using equation (4) is given in table 2. We see a similar trend for the 𝐿𝑃 like 𝛾 i.e. 𝐿𝑃 is increasing with increasing salt concentration. This observation is sharp contrast to that of dsDNA’s properties where 𝐿𝑝 decreases with increasing salt concentration. In case of dsDNA, the electrostatic repulsion of the phosphate backbone has the major contribution in rigidity. With increasing salt concentration, the phosphate-phosphate repulsion is screened, which makes it easier to bend. However, in case of DNT along with the intra-helix phosphate-phosphate repulsion, inter-helix repulsions are also present. As shown previously, these inter-helix repulsions are also screened by increasing salt concentration70. These inter-helix repulsions are dominant in case of 0 M DNT, which tries to keep individual DNA helices apart from each other. With increasing salt molarity inter-helix repulsion decreases and, we observe more compact structure of DNTs. Although, each DNA becomes flexible, but as a bundle, they become stable and try to retain the DNT’s tubular structure. To see whether 𝐿𝑃 calculated using bending angle distribution follows a similar trend or not we divide the whole DNT into 9 segments. The definition of these segments is given in the work by Joshi et al30. A vector is drawn by joining the center of mass between two consecutive segments. The bending angle is calculated between two consecutive vectors [see figure 7(a)]. Then the probability of the bending angle (𝜃) is fitted with a gaussian using the following relation, 𝛽𝜅 𝛽𝜅 2 𝑒𝑥𝑝 ― 𝜃 , 2𝜋𝐿0 2𝐿0

(7)

𝐿𝑃

(8)

[

𝑃(𝜃) = ⟹ln 𝑃(𝜃) = ―

]

1 𝛽𝜅 . (1 ― cos 𝜃) + ln 𝐿0 2 2𝜋𝐿0


Page 15 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


From the slope of the logarithm of probability distribution vs (1 ― cos 𝜃) plot, we calculate the 𝐿𝑃[See figure 7(b) and (d)]. Although the 𝐿𝑃 calculated from above relation [See table 2] does not show any clear trend, the 𝐿𝑃 for 1 M is higher than 0 M and 0.5 M and 0.5 M has lower 𝐿𝑃 than 0 M. The main reason for this nonmonotonic behavior comes from the gating like behavior of the DNT. For 0.5 M and 1 M we can see that one of the ends is more opened than the other (see figure 1(e), (f), (g), (h), SI video V2, V3), which effectively increases the bending angle. Also, this gating behavior is stochastic in nature which essentially gives rise to different bending angle distributions for different simulation sets. We do not have a microscopic explanation for the origin of the stochasticity of this kind of gating behavior. Though, at the individual base pair level, we find that the inclination and twist spread better for 0.5 M case as compared to the spreads for 0 M and 1 M [see figure 7(c)] which essentially gives more bending for 0.5 M. Of course, our consideration of DNT as a cylindrical rod is an important assumption worth questioning. In fact, all the atoms and hence the charges, masses of the DNT are not uniformly distributed. A better description of the DNT as a non-uniform cylindrical rod might give better trends in the persistence lengths and explain the flexibility of the DNT better. Effect of Different Species of Salt on DNT stability In order to understand the effect of ionic charge on the DNT we have simulated with different species of salt (NaCl, KCl, MgCl2). It is well known from numerous simulations and experiment that divalent ions like Mg2+ binds more strongly to the DNA/RNA backbones than monovalent ions like Na+, K+ .Also Mg2+ is more efficient in neutralizing nucleic acid backbones than any monovalent salt 42, 76. Similar observation has been found also for our DNT system. In the divalent salt such as MgCl2, DNT structures are equally stable in all molarity and does not show molarity dependence as in case of NaCl. In contrast, KCl has similar effect as NaCl. In the figure 8 we have plotted the RMSD profiles of DNT in different salts. From the plot we conclude that with increasing KCl molarity the DNT structures becomes more stable and rigid whereas in MgCl2 no such trend has been found [See SI section 4 and 5 for more details of the calculation]. Similar behavior of DNT in MgCl2 is also reported in recent experimental findings36-37.



Page 16 of 32

Conclusions In this article, using fully atomistic MD simulation we have studied the effect of salt concentration on the stability and the flexibility of the DNTs. Our MD simulations demonstrate that the DNT structures adopt more compact conformation as we increased the salt concentration. The RMSD and RMSF profiles are also consistent with the above observation. We have explicitly shown that the reduction in the effective electrostatic energy of the DNT in the presence of excess salt drives this compaction. From the PCA analysis, we observe the dominant mode of motion which is mainly coming from the mouth region of the DNTs. The pore radius analysis shows the gating like motion of DNT for all salt concentrations considered. We also observe that the average pore radius is gradually decreasing with increasing molarity. The average base step and base pair parameters show that the individual dsDNA maintains canonical BDNA structure during the whole simulation [SI section 2]. The mechanical properties of DNT which are very important in several biotechnological applications are very much sensitive to the physiological conditions. Our simulation results demonstrate increase in stretch modulus and persistence length as calculated from the microscopic elasticity theory with increasing salt concentration. Distribution of ions around the phosphate backbone at different ionic concentration qualitatively explained the bending in the radial direction of the DNT. The present work enhanced the understanding of the dependence of stability and mechanical properties of the DNT on the external salt concentration. With a different monovalent salt (KCl) also we observed the similar trends in all the physical properties of the DNT as a function of salt concentration [SI section 5]. For MgCl2, we observed stronger effect on the structural stability of the DNT, even at molarities as low as 0 M [SI section 6]. Another way to prevent the low-salt denaturation of the DNA nanostructures is to covalently functionalize the DNA backbones77-78. We aim to explore these functionalization effects and understand the impact of multivalent ions, other solvents like ionic liquids, on the structural stability of the DNT in near future.

Supplementary Information Supplementary Information Contains the following sections, Section 1: Sequence and Crossover design of the DNTs. Section 2: Helicoidal Parameters of the DNTs. Section 3: Ion Distribution around DNTs.


Page 17 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Section 4: Analysis of each Trajectory. Section 5: Analysis with Three Other NaCl Salt Concentration (0.25M, 0.75M, 1.25M). Section 6: Analysis with KCl Salt. Section 7: Analysis with MgCl2 Salt. Movie V1: Visualization of 200 ns trajectory of DNT in 0 M of NaCl. Movie V2: Visualization of 200 ns trajectory of DNT in 0.5 M of NaCl. Movie V3: Visualization of 200 ns trajectory of DNT in 1 M of NaCl. Movie V4: The pseudo-trajectories of DNT along the first PC in 0 M of NaCl. Movie V5: The pseudo-trajectories of DNT along the first PC in 0.5 M of NaCl. Movie V6: The pseudo-trajectories of DNT along the first PC in 1 M of NaCl.

Conflict of Interest The authors declare no competing financial interests.

Acknowledgements We thank DST, India for the financial support and computational support through TUE-CMS, IISc. We also thank Supercomputer Education and Research Center (SERC), IISc, for providing supercomputer time @SAHASRAT machine. S.N. acknowledges JRF fellowship and M.G. acknowledges SPM fellowship from CSIR, India.

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Tables Table 1:

Effective electrostatic energy for the interaction between the DNT and other sub groups, per DNT base pair, of the system with NaCl salt. All energies are in kcal/mol/base-pair units. Salt Conc.

DNT self

DNT-ions

DNT- water

DNT-total

0M

-58 (±2)

-529(±5)

-367 (±4)

-954 (±6)

0.5 M

128 (±5)

-1011(±10)

-259 (±5)

-1142(±13)

1M

183 (±3)

-1157 (±17)

-225 (±7)

-1199 (±19)

Table 2:

Stretch Modulus and Persistence length calculations Molarity

0M

0.5 M

1M

Contour Length (Å)

203.34 (±1.03)

202.47

201.64

(± 1.21)

(± 0.88)

8294.87

10540.9

13066.8

(±148.19)

(±148.13)

(±155.91)

LP using MET (µm)

6.35(±0.11)

8.28 (± 0.12)

10.42(±0.12)

LP from Bending

2.45(±0.04)

1.86 (±0.02)

3.01 (±0.04)

Stretch Modulus (pN)

Angle Distribution (µm)



Page 24 of 32

Figures

Figure 1. (a) Initially built DNT immersed in a rectangular water box with Na+ ions and excess salt (NaCl). Molarity of NaCl in the solution is 0.5 M. The green and red dots represent the Na+ and Cl- ions respectively. (b) Side view of the same system. VMD has been used to generate all the structures. (c)-(h) Snapshots of the systems after 200 ns simulation. (c) Top view of the system with zero molarity of NaCl. (d) Same system with a side view. Both the terminal regions of the DNT stretch radially outwards, whereas the central portion remains intact. (e) Top view and (f) Side view of the system containing 0.5 M NaCl. The fluctuation in the terminal region reduces significantly in the system. (g) Top view and (h) Side view of the system at 1 M NaCl. The DNT structure at this molarity is closer to the native structure, as the fluctuations in the terminal region along with the central portion are quite minimal for this case.


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Figure 2. (a) The time evolution of the RMSD profiles of the DNT for the three different molarities chosen. RMSD is calculated with respect to the initial energy minimized structure of the DNTs. The data is averaged over three sets of statistically independent simulations. 1 M case has the least deviation as compared to 0.5 M and 0 M. (b) Average RMSF of the DNT as function of the Slice index averaged over last 100 ns of the 200 ns long MD trajectory. At any given NaCl molarity, the terminal regions of the DNT have more fluctuations over the central region. The fluctuations throughout the DNT reduce as we increase the molarity.



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Figure 3. (a), (b), and (c) First principal component and the corresponding eigendirection for different salt concentration. These motions are composed of 23%, 31% and 33% of the total motion for 0 M, 0.5 M and 1 M respectively. (d) Cumulative Fraction of the eigen values extracted from the principal component analysis. Almost for all the systems 90% of the total motion is made up of the first 50 eigen values. The projection of the cartesian trajectories along the first 5 PCs for the system with molarity (e) 0 M (f) 0.5 M, and (g) 1 M respectively.


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Figure 4. Time Evolution of the average radius profile along the pore axis of the DNTs for the system with molarity (a) 0 M (b) 0.5 M, and (c) 1 M respectively. The colour bar represents value of the radius in units of Å. (d) Final radius profile of the DNTs averaged over the last 100 ns and 3 sets of independent simulation.



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Figure 5. Radial distribution functions of various ions in the system from the phosphate groups at a) 0 M b) 0.5 M and c) 1 M NaCl concentrations. The black curves in all the plots represent the distributions for phosphate atoms. Similarly, the red and green curves correspond to Na+ and Cl- ions respectively.


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Figure 6. (a) Definition of the contour length of the DNTs. First the com to com distance has been joined to get the contour length of an individual DNA helix (Li). Then all the six Li ‘s are averaged to get the contour length of the DNT. (b) Probability distribution of the normalized contour length of the DNTs. The data is averaged over the last 100 ns and 3 sets of independent simulation. (c) Logarithm of the probability as a function of slope of the graphs, stretch modulus has been extracted.


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𝐿0 ― 1 . From the


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Figure 7. (a) Definition of the bending angle used in this work. (b) Probability distribution of the bending angle for the last 100 ns trajectory. (c) Scatter plot of the inclination and twist angle of the individual base pairs of the DNTs. (d) Logarithm of 𝑃(𝜃) versus 1 ― 𝑐𝑜𝑠(𝜃). Persistence length has been calculated from the slope of this graph.


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Figure 8. The time evolution of the RMSD profiles of the DNT in three different kind of salts (NaCl, KCl, MgCl2). RMSD is calculated with respect to the initial energy minimized structure of the DNTs.



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Tuning the Stability of DNA Nanotubes with Salt - The Journal of

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