A Simple and Fast Semiautomatic Procedure for the Atomistic

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A SIMPLE AND FAST SEMIAUTOMATIC PROCEDURE FOR THE ATOMISTIC MODELLING OF COMPLEX DNA POLYHEDRA Cássio Alves, Federico Iacovelli, Mattia Falconi, Francesca Cardamone, Blasco Morozzo della Rocca, Cristiano Luis Pinto de Oliveira, and Alessandro Desideri J. Chem. Inf. Model., Just Accepted Manuscript • DOI: 10.1021/acs.jcim.5b00586 • Publication Date (Web): 06 Apr 2016 Downloaded from http://pubs.acs.org on April 9, 2016

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Journal of Chemical Information and Modeling

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A SIMPLE AND FAST SEMIAUTOMATIC PROCEDURE FOR THE ATOMISTIC MODELLING OF COMPLEX DNA POLYHEDRA

Cassio Alves1#, Federico Iacovelli2#, Mattia Falconi2, Francesca Cardamone2, Blasco Morozzo della Rocca2, Cristiano L.P. de Oliveira*3 and Alessandro Desideri*2

1

Instituto de Fisica, Grupo de Fluidos Complexos, Universidade de São Paulo, Caixa Postal 66318,

05314-970 Sao Paulo, Brasil and Department of Engineering and Sciences, Federal University of Paraná, 85950-000, Palotina, Paraná, Brazil. 2

Department of Biology, University of Rome “Tor Vergata”, Via della Ricerca Scientifica, 00133,

Rome, Italy. 3

Instituto de Fisica, Grupo de Fluidos Complexos, Universidade de São Paulo, Caixa Postal 66318,

05314-970 Sao Paulo, Brasil.

Author contributions: #These authors contributed equally to this work.

Corresponding authors: Prof. Alessandro Desideri Department of Biology, University of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Rome, Italy. *E-mail: [email protected], Tel. +39.06.72594376; Fax. +39.06.2022798. Prof Cristiano Luis Pinto Oliveira, Instituto de Fisica, Grupo de Fluidos Complexos, Universidade de São Paulo, Caixa Postal 66318, 05314-970 Sao Paulo, Brasil. *E-mail: [email protected]

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Abstract A semiautomatic procedure to build complex atomistic covalently linked DNA nano-cages has been implemented in a user-friendly, free and fast program. As a test set seven different truncated DNA polyhedra, composed by B-DNA double helices connected through short single stranded linkers have been generated. The atomistic structures, including a tetrahedron, a cube, an octahedron, a dodecahedron, a triangular prism, a pentagonal prism and a hexagonal prism, have been probed through classical molecular dynamics and analysed to evaluate their structural/dynamical properties and to highlight possible building faults. The analysis of the simulated trajectories also allows to investigate the role of the different geometries in defining nano-cages stability and flexibility. The data indicate that the cages are stable and that their structural/dynamical parameters measured along the trajectories are slightly affected by the different geometries. These results demonstrate that the constraints imposed by the covalent links induce an almost identical conformational variability independently of the three-dimensional geometry and that the program presented here is a reliable and valid tool to engineer DNA nanostructures.


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Introduction In structural nanotechnology applications DNA loses the role of hereditary material being employed as building block to design and assemble complex nanostructures. Its high thermodynamic stability together with the reliable auto-assembly characteristics due to its unique self-recognition properties have made this biopolymer an essential material for bionanotechnology. Consequently a large variety of precisely programmed two- or three-dimensional (3D) DNA nanostructures have been presented during the last years.1–5 Despite the successful fast growth of this research area, several problems must still be solved since an user-defined assembly of the DNA polymer requires a reliable design of the DNA strands that must specifically interact to produce a unique final 3D nanostructure. Over the last 20 years, several methodologies for the design of DNA nanostructures have been implemented. A first covalently closed molecular complex, whose DNA double-helical edges have the connectivity of a truncated octahedron, has been assembled starting from squares of DNA basic units that, after being covalently linked one with the other, create the hexagonal faces of the structure.6 The Joyce group reported the design and synthesis of a 1669-nucleotide, singlestranded DNA molecule that may be amplified by polymerases and that, in the presence of five 40mer synthetic oligodeoxynucleotides, folds into an octahedral structure through a simple denaturation-renaturation procedure.7 In this case the structural units used to build the cage are the double and paranemic crossovers motifs, originally developed by Seeman group,8,9 that are able to assemble into supramolecular structures taking advantages of designed sticky ends. A year later Tuberfield and collaborators reported the building of a DNA tetrahedral family made by mixing four oligonucleotides that can self-assemble in seconds and that can be connected by programmable DNA linkers.10 The procedure has been extended to the creation of a complex DNA trigonal bipyramidal structure.11 In 2007, the Sleiman group presented an elegant method to quantitatively build a large number of 3D DNA assemblies using a small number of building blocks ACS Paragon Plus Environment


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(triangles, squares, pentagons and hexagons). In this approach, the target 3D object is modularly assembled in a minimum number of steps using a set of single-stranded and cyclic DNA building blocks, containing rigid organic molecules as vertices.12 In 2008 Knudsen and colleagues presented the design, construction and structural analysis of a covalently closed 3D DNA structure with the connectivity of a truncated octahedron, defined by twelve double-stranded DNA helices that assembles from eight properly designed oligonucleotides.13 In this approach, the designed oligonucleotides assemble one with the other, positioning their ends in close proximity to permit their covalent linking upon addition of a ligase. In the same year, the Mao group proposed the use of identical DNA building units that may assemble into 3D structures and that allow the fabrication of a wide range of relatively complex 3D assemblies.14 According to the assumption that platonic solids polyhedra maximize the encapsulation volumes, and hence are able to trap large biomolecules such as proteins, the Krishnan group constructed an icosahedron through a modular assembly strategy involving a stepwise merge of discrete modules, using three distinct five-wayjunction components with programmable overhangs.15 In 2013 the Mao group proposed a DNA tetrahedron that self-assembles in an acidic environment, the key element being the formation/dissociation of a short, cytosine-containing, DNA triplex.16 Recently, complementary tetrahedral small molecule-DNA hybrid have been used as building blocks to form polymeric nanoparticles, whose size can be tailored adjusting the assembly conditions such as the SMDH concentration, the assembly time and the NaCl concentration. The paper shows a systematic, efficient strategy for the construction as well as for the surface functionalization of the sizetunable nucleic acids building blocks.17 Experimental production of complex DNA nanostructures requiring the assembly of a large number of strands is quite expensive. Computational screening based on the building of an atomistic model to be probed by classical molecular dynamics simulations (MD), represents a valid help to probe the stability and reliability of the designed architecture and DNA sequences. A ACS Paragon Plus Environment

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recent work addressed the subject of computer-assisted polyhedral DNA nanostructures construction using a complex procedure implemented through a plug-in that can be executed only within a costly program18 and the final generated product is not an atomistic model. Up to now the CanDO program19 combined with the free external program cadnano (cadnano.org),20 represents the only tool providing DNA origami atomistic models. In this paper we present an advanced feature of the Polygen program, originally developed for the modelling of polyhedra with different shapes using spherical subunits,21 consisting in an automatic generator of oligonucleotide sequences coupled with a simple and fast semiautomatic DNA nanocage builder able to model 3D atomistic truncated DNA nanocages with different geometries. To evaluate the quality of the models generated through the Polygen program we performed a set of classical MD simulations selecting seven different polyhedra. The simulative results indicate that their structures are stable, can be characterized by common dynamical features, and that the atomistic modelling tool described in this manuscript represents a free and user-friendly instrument for the design of covalently closed cages with different geometry to be used before their experimental production.



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Simulative methods Design strategy of cages in Polygen The here presented polyhedra have been generated by Polygen that can build convex polyhedra having multiple geometries.20 The selected models are truncated polyhedra made by large and small faces. The large faces are delimited by edges composed by long double stranded (ds) helices interconnected by short single stranded (ss) linkers. The small truncated faces are delimited by single strands linkers and can be of different shape, depending of the chosen geometry or by a user defined interconnectivity. Every built polyhedron is defined “truncated” accounting to the fact that double helices do not form sharp points at vertices but are connected by short single strands forming blunt corners. The number of oligonucleotides required to assemble the polyhedron is identical to the number of the large faces. For instance, eight properly designed oligonucleotides can be used to form a truncated octahedron, composed by eight large and six small square faces, whilst four oligonucleotides are required to assemble a truncated tetrahedron having four large and four small triangular faces. A large set of possible geometries may be chosen but we selected some representative examples consisting of polyhedra with an increasing number of faces, separated in two groups: “Platonic solids” made by faces with identical area and prisms where the faces have different areas. The geometries have been chosen according with the number of faces, from the tetrahedron (4 large and 4 small faces), triangular prism (5 large and 6 small faces), cube (6 large and 8 small faces), pentagonal prism (7 large and 10 small faces), octahedron (8 large and 6 small faces), hexagonal prism (8 large and 12 small faces) up to the dodecahedron (12 large and 20 small faces) (Fig. 1). The diameter of the polyhedra ranges from 8 nm of the tetrahedron up to 21 nm of the dodecahedron. These represent the most usual geometries that are experimentally assembled7,13,22–26 and have been taken as a test case. Polygen can be used to build these models, as well as many others, and the user only needs to define the specific set of sequences, according with number of faces of the desired polyhedron ACS Paragon Plus Environment

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(Fig. 1 and 2).

The atomistic Polygen tool To build the atomistic cage models, two procedures are applied: geometrical modelling, based on a previous work,21 and atomistic modelling. A scheme of the creation of the DNA cage atomistic structure is shown in Fig. 2. The program can generate polyhedral structures taking them from a polyhedron database included in the program (based on the Andrew Hume’s Polyhedron Database http://www.netlib.org/polyhedra/), with the possibility to build convex polyhedral structures that are not available in the database. In this case it is necessary to provide the coordinates of the polyhedral vertices. The program reads the coordinates and uses the gift-wrapping algorithm27–29 to build the structure. This algorithm uses each three-dimensional coordinate as a vertex of the polyhedral structure, considering the coordinates that are distributed on the surface of a topological equivalent sphere. If there are coordinates which do not fulfil this requirement, they are discarded. The user can also specify a definite interconnection between each vertex (edges) to define a non-regular polyhedron. The program builds the polyhedron by creating small faces and edges that connects the vertices. The choice of a polyhedron from the database makes the modelling procedure a semiautomatic and simple process, since it is possible to build any geometry by choosing only a small set of parameters, namely 1) the desired polyhedron geometry; 2) the DNA sequences associated to the structure: 3) an overall scale factor to define the cage dimension.21 Regular polyhedra have sharp corners that cannot be reproduced by DNA double helices due to the polymer constraints. Therefore the here described procedure refers to truncated polyhedra, obtained connecting the double helices through single stranded DNA linkers. Once the polyhedron is built, the program generates the DNA ds and ss sequences required to build the cage and finally the atomistic model. The sequences can be automatically generated by the Polygen program (which generates random ACS Paragon Plus Environment


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sequences that fulfil the base-pairing complementarity) or can be provided by the user editing the configuration file, introducing sequences obtained with a sequence generator, as the one described later. The linker conformations can be either automatically generated by the Polygen program or provided by the user in an external PDB format file.30

Atomistic modelling procedure The first step in building a DNA cage in a given geometry involves the correct alignment of position and orientation of the DNA ds that will be then connected through the ss DNA linkers. The simulated annealing procedure is used to achieve the minimization of the distances between the DNA double helices (i.e. the distance between the oxygen atom O3', in one helix strand and the phosphate atom P in the strand of the helix to connect). For regular geometries, as the ones here presented, every distance between the DNA ds is imposed to be identical. Each DNA ds position and orientation is modelled considering its reference frame located at the center of mass of the double strand with the Z axis corresponding to the helical axis (Fig. 3). Each DNA ds can rotate around its three main axes and can be translated varying the distance between its center of mass and that of the entire cage. Since the DNA cage has N double strands, it is necessary to optimize 4N coordinates. This has been obtained by using a simulated annealing algorithm to simultaneously achieve identical distances between all the DNA double helices. This condition permits the insertions of the single strand linkers that form the blunt corners. To speed up the calculation the program stores and uses only the positions of the tips of each DNA double helix and repeats the same procedure for all the tips. Quaternions and rotation matrices are used to store the coordinates and to carry out the rotations. When the helices are minimized the program generates the all atoms final structure for the DNA double helices and this scaffold is used to insert the DNA ss linkers. If steric clashes are detected during the linker insertion process, they are removed using local ACS Paragon Plus Environment

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optimizations. Each linker is rotated either as a solid structure or by rotating each nucleotide, until all clashes are removed. In both procedures the rotation step is set to 0.01 rad.

Sequence generator Besides the Polygen integrated sequence generator that, while fulfilling the base pairing rules, generates random sequences, we have also developed an independent, external sequence generator made by a set of Ruby scripts, that can be applied to rule out sequences combinations that can form unwanted structures. The tool takes as input the polyhedron geometry, the length of the double helix elements, the length of the single-stranded linkers and the desired similarity between the sequences. Once a first sequence is generated, the subsequent ones are defined by the following rules: the generated strand must not contain more than 4 sequential identical nucleotides, it must have the lowest degree of complementarity with the previously generated strands and the sequence identity, resulting from global sequence alignment between the different strands, must be lower than that defined by a threshold value. If the sequence does not meet these requirements a mutation function is applied to the sequence that is randomly mutated until the desired rules are fulfilled. Once the sequences are correctly generated, the program assembles them in the format requested by Polygen and calculates the thermodynamic properties of the oligonucleotides to verify their propensity to form unwanted secondary structures. The sequence generator has been written in Ruby (https://www.ruby-lang.org/en/), handling the DNA sequence objects through the BioRuby open source library.31 The global alignment of the sequences is executed through an external call to the needle program32, that creates an optimal global alignment of two sequences using the Needleman-Wunsch algorithm33 and the thermodynamics calculations are performed through the mfold package a versatile program for nucleic acid folding and hybridization prediction.34 This sequence generator makes use of open source external programs, anyway the user can make use of any other method to generate its own ACS Paragon Plus Environment


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sequences.

Nanocage models preparation for MD simulation The system topologies and the coordinates, used as input for the NAMD 2.10 MD package35 have been obtained through the AmberTools14 tLeap36 module, parameterizing the structures through the AMBERFF14SB force-field with the parmbsc1 correction.37 The structures have been immersed in a suitable box (Table 1) filled with TIP3P water molecules,38 imposing a minimum distance between the solute and the box of 14 Å, whereas the charges have been neutralized adding Mg++ counter-ions to the solvated systems39 in favourable positions (Table 1), as implemented in the AMBER 14 program.32

Equilibration and molecular dynamics protocol For each structure, a minimization run has been performed for 5000 steps using the steepest descent algorithm, imposing harmonic constraint of 50 kcal·mol-1·Å−2, to remove any unfavourable interaction and to prevent irreversible Mg++ binding to DNA. The systems have been gradually heated in the NVT ensemble from 0 K to 300 K over a period of 500 ps using Langevin thermostat40 with coupling coefficient of 1.0 ps and a weak constraint of 15 kcal·mol-1·Å−2 on nucleotides. In the last equilibration step, the systems were subjected to an equilibrium simulation for 500 ps removing all constraints. The optimized systems have been then simulated using the isobaricisothermal ensemble (NPT) for 50 ns, using periodic boundary conditions, a 2.0 fs time-step, a cutoff of 9 Å for the evaluation of short-range non-bonded interactions and the PME method41 for the long-range electrostatic interactions. The SHAKE algorithm has been used to constrain covalent bonds involving hydrogen atoms.42 Temperature has been fixed at 300K using the Langevin dynamics,40 while pressure has been held constant at 1 atm through the Langevin piston method.43 The atomic positions have been saved every 500 steps (1.0 ps) for the analyses. The ACS Paragon Plus Environment

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simulations have been entirely performed using 256 nodes for a total of 4096 cores of the FERMI HPC Cluster hosted by CINECA, Bologna, Italy.

Structural analyses Root mean square fluctuations (RMSFs) and radii of gyration have been calculated over the entire 50 ns trajectories by using the GROMACS44 4.6.7 analysis tools. The RMSFs values have been calculated, on the phosphorous atoms, using two different approaches. The first one, called local RMSF, has been evaluated for each of the double helices extracted from the total cages, singly fitted without taking into account the total cages motions. The second one, called global RMSF, has been calculated fitting the total cages conformations, taking into account the total cages motions. The hydrogen bonds number has been evaluated, through the GROMACS g_hbond program44 using an angle cut-off of 30° (angles varying from 150° to 180°) and a donor-acceptor distance of 3.5 Å. The stacking between the bases has been evaluated through a previously described homemade program45. The average bending angles of the DNA double helices have been investigated through the program CURVES+46.



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Results and discussion

Modelling of the DNA nano-cages Seven DNA nanocages with different geometries have been modelled, namely 4 regular truncated polyhedra (tetrahedron, cube, octahedron and dodecahedron) and 3 truncated prisms (triangular, pentagonal and hexagonal) (Fig. 1). These geometries have been chosen from the many available for their varying degrees of complexity (i.e. the number of faces) and for their diameter ranging from 8 to 21 nm. The largest polyhedron, i.e. the dodecahedron, has been chosen to evaluate the reliability of the program when a large nanocage is selected. In all the polyhedra the DNA ds helices are composed by 18 nucleotides, able to ensure a good double strand stability and sufficient sequence variability to avoid unwanted pairings. The DNA ss linkers, connecting the double helices, are composed by 5 nucleotides that provide the appropriate flexibility in the assembling phase.45 The smallest nanocage is the tetrahedron composed by 4 large faces and 276 nucleotides, while the biggest one is the dodecahedron composed by 12 large faces and 1380 nucleotides. The octahedron and the hexagonal prism have the same number of faces, but the total nucleotides number is 552 and 828, respectively (Fig. 1). All the geometries are truncated near each vertex, due to the presence of DNA single strand linkers that forms small squared or triangular faces (Fig. 1).

Building a DNA polyhedron atomistic model Once the initial geometry is defined the DNA ds are individually created according to the sequences, selected as described in the previous paragraph, using the atomistic structure of known DNA double helices as a template (Fig. 2 B). The DNA ds are rotated and translated in order to overlap the polyhedron edges (Fig. 2 C). At this stage, the cage has the polyhedron overall shape, but the DNA ds are not yet interconnected by the DNA ss representing the bridging linkers.


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After the initial positioning of all DNA ds on the polyhedron edges, the atomic coordinates of O3’ and P atoms, belonging to the nucleotides at the tips of ds, are stored. These four atoms coordinates are used to perform translation and rotation of each DNA ds, allowing the optimization of their distances, according to the number of nucleotides composing the DNA ss linker (Fig. 2 C). The last step involves the building of the linkers and their positioning to connect the DNA ds pairs. The ss modelling starts building a fully elongated linker (Fig. 2 D) and if its length is larger than the distance necessary to connect two helices ends, systematic changes are applied on the torsion angles of each nucleotide until the desired distance is achieved. In this phase the positions of the other atoms is taken into account as previously described in the Simulative methods section. If, after an exhaustive search on all possible torsions and rotations of the DNA ss backbone, it is not possible to find a reasonable match, a warning message is shown, the procedure is stopped and the optimization algorithm is restarted until a local minimum is reached. The final outcome represents a DNA cage with the desired geometry made by nucleotides at atomistic level (Fig. 2 E). The PDB files of the generated nanocage structures presented here are available as supplementary material.

Structural/dynamical analysis of the nanocages through classical MD simulation

Gyration radius The radius of gyration (RG), a measure of the structure compactness and overall size, has been used to verify the stability of the models, as large fluctuations of these values are a marker of instable and/or unreliable structures. The analysis of RG values of the seven cages over the entire 50 ns trajectories indicates a general trend toward the contraction with the exception of the tetrahedron that, being the smallest tested polyhedron, easily reaches the equilibrium and oscillates around 4.05 nm (Fig. S1). The other trajectories are in line with what already observed in ACS Paragon Plus Environment


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our previous simulations of several DNA octahedral cages1,45,47,48 and are enough long to monitor any structural changes due to a not properly built initial structure. The RG contraction is relatively small for all the cages indicating the stability and the reliability of the modelled starting structures. This parameter must be taken into consideration to predict dimensions of payloads to be trapped inside the cages, when these structures are planned to be used as a carrier for biomedical purposes.

Helices behaviour The double helices are pretty stable over the entire trajectories independently of the cage complexity. The average number of hydrogen bonds evaluated during the simulations is 47 for all the double helices (Fig. S2), almost the same of that defined by the Watson Crick base pairing rules in the starting helices models, indicating that the models generated by Polygen are very stable and that the helices maintain their original arrangement. The local RMSF values of the dodecahedral cage, calculated over the phosphorous atoms singly fitting each helix without taking into consideration the cage global motions, are reported in Fig. 4 as a test case. The local RMSF values show a similar behaviour for each strand composing the double helices, with the lowest values located in the central part of the helix and the highest ones at the strands tails. A similar result is observed for the other cages independently of the geometry (Fig S3, A-F). Despite their high internal stability the helices undergo a quite large fluctuation, exhibiting the previously observed rotational motion.45,47,48 The global RMSF values, calculated fitting the helices on the total cage conformation, display a complex behaviour showing a sinusoidal trend triggered by the contribution of the double helices rotational motion common to all the simulated polyhedra. As an example the global RMSF values obtained for the dodecahedron is represented in Fig. 5 and in Fig. S4 A-F for the other cages. A similar behaviour has been reported for the simulation of different octahedral geometries,45 indicating that the motion of the cages is dominated by the helices ACS Paragon Plus Environment

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rotation, leading to the observed shrinking behaviour, independently of the chosen geometry. As a further check of the helices quality, the standard geometrical parameters characterizing a B-DNA helix have been monitored and analyzed along the trajectory. The averaged calculated parameters are very close to those of the typical B-DNA for all the cages (data not shown). However, double helices are characterized by an evident change in the helix axis curvature. The average bending angles, shown in Fig. S5 and evaluated using the program CURVES+46, indicate a comparable curvature for all the simulated cages, higher than that observed for a classical B-DNA helix. This similar curvature is probably imposed by the presence of the ss linkers independently of the cages geometry and dimensions.

Linkers behaviour In Fig. S6 the average number of the stacking interactions, occurring among the bases belonging to the linkers, has been reported for the seven simulated cages. The number is similar for all the different geometries, indicating that the linkers conformations, randomly generated by Polygen, undergo a similar space sampling independently of their starting positions and of the polygonal geometry. For each cage, the degree of conformational variability present in each linker region has been evaluated by separately clustering each linker in the seven trajectories. The percentages of the three most populated clusters, reported in Fig. S7 A-G for all the nanocages, are similar, suggesting that the degree of conformational variability is independent of the geometry of the analyzed nanocages and it is likely determined by the linker length that is identical for all the analysed polyhedra. The unique exception is represented by the dodecahedron that, being the most complex among the tested polyhedra (30 double helices and 60 linkers), is yet relatively far from the equilibrium and shows a large number of clusters. In line investigation of a series of truncated DNA octahedral cages having linkers of different ACS Paragon Plus Environment


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length or chemical composition indicated that the conformational variability is directly correlated to the linker length and is independent of the linker sequence composition39,42. These results represent a further evidence of the linkers role in defining structural/dynamical features of covalently closed DNA nanostructures.

Conclusions In this manuscript we have described a new feature of the Polygen program that simplifies the construction of complex atomistic DNA nanocages with different polyhedral geometries (more than 100). The tool also permits to generate optimal oligonucleotide sequences to be used to experimentally self-assemble the selected nanocage. The program has been tested building seven different polyhedra, whose structural/dynamical properties have been probed by classical MD simulations. This procedure allows us to validate the DNA nano-structures obtained through the semiautomatic Polygen procedure and demonstrates that the modelled DNA cages are reliable, accurate and stable. The use of Polygen is not the only option for modelling complex DNA polyhedra. For instance in our group the atomistic model of several truncated octahedral cages has been previously generated1,45,47,48 using the SYBYL program (www.tripos.com), however the procedure is very time consuming and SYBYL is a relatively expensive tool. The vHelix program18 (www.vhelix.net), a plugin of the Maya autodesk program (www.autodesk.com), permits the building of DNA polyhedra but Maya is a costly program and the final product is not an atomistic model. The CanDO program19 is able to provide atomistic models (see http://cando-dna-origami.org for a list of tutorials), using a free external program named cadnano20 (cadnano.org), and represents a valid tool for the building of origami-type DNA structures. Polygen is a user-friendly, stand-alone and free of charge program that automatically builds, at atomistic level, complex non-origami 3D polyhedra and requires the user only three parameters (i.e. geometry, size and sequence). This ACS Paragon Plus Environment

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tool has been implemented to make as easy as possible the design of atomistic DNA nanostructures with specific geometry and can be used to test structural-dynamical properties of the cages before their experimental production.

Polygen is available upon request to CLPO corresponding author.

Acknowledgements We acknowledge PRACE for awarding us access to resource FERMI based in Italy at CINECA, Bologna. The MD calculations have been carried out under the 10th PRACE project PRA10_2630. CLPO was supported by FAPESP, CAPES, CNPQ and INCT-Fcx. CA was supported by CAPES, CNPQ and INCT-Fcx. AD acknowledge the CNPQ support with a “Science without border” grant.

Associated Content Supporting Information Available: Minimization procedure description. Gyration radii, local and global RMSF, hydrogen bonds, stackings and cluster analyses carried out on the seven trajectories. PDB files of the seven simulated cages. This material is available free of charge via the internet at http://pubs.acs.org.



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Tables Table 1 Nanocages simulation systems Nanocage

Tetrahedron

Cube

Octahedron

Triangular

Pentagonal

Hexagonal

prism

prism

prism

Dodecahedron

Box size in Å 129,129,129

169,169,169

145,145,145

261,261,261

149,149,149

197,201,163

153,222,227

147498

342098

207762

1277906

233612

576174

696984

8772

17543

17544

43832

13157

21900

26295

276

552

552

1380

414

690

828

46196

108093

63314

411128

73416

184643

223563

138

276

276

690

207

345

414

(X,Y,Z) Total number of atoms DNA atoms Number of nucleotides Water molecules (TIP3P) Number of ions (Mg++)



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Figures

Figure 1. Seven truncated polyhedral geometries have been chosen for the DNA nanocages modelling: 4 regular truncated polyhedra (tetrahedron, cube, octahedron and dodecahedron) and 3 truncated prisms with different bases types (triangular, pentagonal and hexagonal). In the left side of the picture the standard polyhedra are represented, while in the right the corresponding DNA truncated polyhedra are shown. The truncated geometry has DNA ds and ss in edges of large face and has only DNA ss in the each edge of small (truncated) faces. The nanocages are ordered according with number of faces, or number of oligonucleotides sequences, necessary to experimentally build them.


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Figure 2. Procedure to model the nanocages. A) Initial geometry. B) Creation of the DNA ds using known atomic resolution structures. C) DNA ds are placed and aligned to the polyhedron edges forming a large face. In this step an optimization (simulated annealing) of the distances between the DNA ds tips it is performed to obtain similar distances for the connection. D) Creation of the DNAs single strands. E) All the linkers are inserted in the model to connect the DNA ds and form a small face. To build a truncated octahedron 8 oligonucleotides sequences are necessary, of which some parts corresponds to doublehelices (the large faces) and others to single strands (the small faces).



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Figure 3. Three degrees of freedom, used to rotate DNA ds


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Figure 4. Local RMSF values calculated for the double helices of the truncated dodecahedral cage. Black and red filled circles specify the two strands.



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Figure 5. Global RMSF values calculated for the double helices of the truncated dodecahedral cage. Black and red filled circles specify the two strands.


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For Table of Contents Use Only

A simple and fast semiautomatic procedure for the atomistic modelling of complex DNA polyhedra. Cassio Alves, Federico Iacovelli, Mattia Falconi, Francesca Cardamone, Blasco Morozzo della Rocca, Cristiano L.P. de Oliveira and Alessandro Desideri.



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Figure 1. Seven truncated polyhedral geometries have been chosen for the DNA nanocages modelling: 4 regular truncated polyhedra (tetrahedron, cube, octahedron and dodecahedron) and 3 truncated prisms with different bases types (triangular, pentagonal and hexagonal). In the left side of the picture the standard polyhedra are represented, while in the right the corresponding DNA truncated polyhedra are shown. The truncated geometry has DNA ds and ss in edges of large face and has only DNA ss in the each edge of small (truncated) faces. The nanocages are ordered according with number of faces, or number of oligonucleotides sequences, necessary to experimentally build them. 793x1057mm (72 x 72 DPI)


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Figure 2. Procedure to model the nanocages. A) Initial geometry. B) Creation of the DNA ds using known atomic resolution structures. C) DNA ds are placed and aligned to the polyhedron edges forming a large face. In this step an optimization (simulated annealing) of the distances between the DNA ds tips it is performed to obtain similar distances for the connection. D) Creation of the DNAs single strands. E) All the linkers are inserted in the model to connect the DNA ds and form a small face. To build a truncated octahedron 8 oligonucleotides sequences are necessary, of which some parts corresponds to double-helices (the large faces) and others to single strands (the small faces). 190x254mm (300 x 300 DPI)



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Figure 3. Three degrees of freedom, used to rotate DNA ds 190x254mm (300 x 300 DPI)


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Figure 4. Local RMSF values calculated for the double helices of the truncated dodecahedral cage. Black and red filled circles specify the two strands. 190x254mm (300 x 300 DPI)



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Figure 5. Global RMSF values calculated for the double helices of the truncated dodecahedral cage. Black and red filled circles specify the two strands. 190x254mm (300 x 300 DPI)


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A Simple and Fast Semiautomatic Procedure for the Atomistic

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