Model

Engineering Precision: Unfolding the Potential of DNA Origami Structures

As SublimeStone we embarked on the journey to harness the precision and programmability of DNA origami, aiming to create intricate DNA templated nanoparticles (DNA-NPs). For this project we are leveraging state-of-the-art software, including TALOS, CanDo and ChimeraX (Talos, n.d.; Cando_admin, 2018; Meng et al., 2023).^[1][2][3][4] These tools are instrumental for designing sequences of scaffold and staples that will fold the DNA into distinct octahedron structures. Each precisely crafted octahedron is not only a site for biomineralization; it is also a building block capable of binding with its peers, weaving a lattice structure that spans about two micrometers.

The challenge at hand is two-fold. First, we strive to define the optimal sequences for our envisioned shape. Each octahedron is designed with “sticky-ends", engineered extensions of the DNA sequence that require a custom script. In the second step, we assess how well these structures can maintain their form and stability under laboratory conditions using oxDNA ^[5] simulations. Our primary objective is to develop DNA origami with precision, ensuring their ability to self-assemble into larger stable lattice structures.

DNA Origami

With the discovery of DNA origami, DNA is transcending its biological role to become a medium of artistic expression and craftmanship. Dr. Paul Rothemund’s (2006)^[6] pioneering work demonstrated the feasiblity of folding DNA strands into virtually any desired shape, marking the inception of a new era in which biological organisms can become factories for nanomaterials.

For generating the staples of the experiments, we utilize TALOS. The tool selects sequences that bind specifically to intended scaffold regions, reduces cross-reactivity and unwanted interactions.

The sequence for the scaffold was chosen to be the sequence present in our phagemid. This phagemid was designed by Nafisi et al. (2018)^[7] and contains the 3024 base pair scaffold sequence.

The output of the algorithm is the 3D polyhedral wireframe of our desired octahedron shape (Figure 1) as a PDB file that can be loaded into UCSF’s ChimeraX.^[4:1] The black ribbon illustrates the 3024bp long scaffold sequence binding to the staples — depicted in pastel colors — creating twelve bundles of 6 DNA double helices that line the edges of the octahedron.

This results in a list of scaffold and staple sequences that are needed for our initial folding experiment. The full list can be downloaded on our team’s GitLab as a CSV file. The staples were ordered as primers from IDT.

Including the “sticky-ends" into the octahedron

One essential step that needs to be addressed is the formation of larger Higher-Order structures. The goal is to build a lattice where each octahedron lives on each of the lattice points.

A superlattice is composed of vertices and edges connecting them. The mineralisation process is enhanced by the presence of nucleation sites. These sites are regions of space where the desired chemical reaction has a higher chance of occurring. In the case of an ionic reaction, this is usually described as a region that attracts ions to a singular place.

We can control the design of vertex and edge staples to add so called “sticky-ends", single stranded pieces of DNA that bind the octahedrons to each other through complementary base pairing to form a lattice macro-structure.

However, Min et al. (2020)^[8] offer a different approach where they designed a programmable dynamic superlattice with the use of so-called “sticky ends". Indeed, at each vertex of the octahedron, 4 staples are chosen to be extended with 20 additional base pairs. 10 base pair are a repeat of T bases and 10 base pair are designed such that they are complementary to a neighbouring octahedron.

Designing the Sticky Ends

To our knowledge, there is no existing algorithm nor software that can be used to design sticky-end staples. To address this, we decided to investigate how we could design an algorithm to enhance our origami model and include sticky ends.

Sticky ends are extension of existing staples. As such, from a existing DNA origami model, the challenge is to find and select which staples need to be altered with the sticky ends. For a small construct of a few dozen staples, one can imagine the amount of time it would take to manually sift through the existing staples and extending them.

The algorithm

The algorithm takes as input a PDB file containing the atomic positions that are generated, either by TALOS directly or with a supplementary file.

It is worth noting that TALOS generates files that describe the topology of the desired shape, however, we decided to restrict the possible input to a PDB file to allow custom origami shape to be extended in an identical manner.

The algorithm can be broken down as follows:

1. Identifying the staples to extend

2. Generating random complementary sequences

3. Extending the staples

Identifying the staples to extend

The first step is the most complicated one and thus requires the most amount of work.

The theory behind staple identification is the following:

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TALOS provides BILD files, which define the geometry of the shape but a decision was made to rely solely on the PDB file and Sequence files in order to simplify the process.

This was achieved by noting the central characteristic of vertex staples, the repeat of T’s that form the angle. Since no such repeat exist in the staple, this allows for consistent identification of the vertex. Combining that information with the PDB model, atomic positions can be extracted. An average of these positions is first calculated for each individual vertex staple.

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These average positions are then group by distance using the similar k-nearest neighbour grouping based on a distance map. The average position of these groups can then be calculated, yielding the final spatial position of each of the vertices.

Establish the geometry of the given DNA origami model.

Locating the vertices.

ChimeraX render of the octahedron model

Average positions of the T repeat in each vertex staples calculated via the algorithm.

Here they are falsely connected to show that the shape is recovered through the algorithm.

By taking the average of the points at each vertex, we obtain one position for each vertex.

Other shapes

To investigate if the algorithm could perform on other shapes, we generated via TALOS a tetrahedron and a cube. Using the same scaffold sequence, we wanted to verify that the script was not too specific to the octahedron.

Cube

ChimeraX render of the cube model (42bp)

Average positions of the T repeat in each vertex staples calculated via the algorithm.

Recovered shape.

Recovered average location of vertices.

Tetrahedron

ChimeraX render of the tetrahedron model

Average positions of the T repeat in each vertex staples calculated via the algorithm.

Recovered shape.

Recovered average location of vertices.

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This allowed us to find 2 design flaws in the original script. The first one was the grouping of vertices which was chosen to specifically 4 since that is the situation in the octahedron. Hence, a new variable was introduced to allow for further flexibility. Furthermore, in the generation of the DNA sequences, this depends on 2 parameters:

• The number of vertices

• The number of staples per vertex

Find which edges staples are the closest to each vertex

These positions are essential as they provide a comparative point to identify which staples are closest to the vertices.

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In our case, the octahedron edges was 42 base pairs long, thus there was only 2 staples in the length of one edge. As such, every edge staples has an end at a vertices. However, when generating larger structures, some edge staples are positioned in the middle of the edge, which then need to be ignored.

The location of the vertices allows for a further step in the algorithm. Indeed, an essential aspect of the lattice generation is that the sticky ends need to be complementary on opposite side of the octahedron. As such, another distance map is calculated to establish which staples are the furthest from one another. This allows for a mapping of which vertices, and hence which sticky ends need to be complementary between them.

Generating random complementary sequences

The last remaining step in the algorithm is to randomly generate the sticky ends. To achieve this, a loop is done to generate $N/2$ DNA sequences, where N is the number of vertices.

The results are then written to a CSV table, similar to the input table with the sequences updated with the sticky end extension.

Implementing the sticky ends into the model

After generating the new sequence for the staples, we were interested in extending our PDB model of the octahedron. This was achieved in ChimeraX, which allows for manipulation of DNA structures. Via the build option, the extension for each staples was first generated. However, at this time, there is no option for generating new single-stranded DNA, only double-stranded DNA. Thus, 1 chain was removed of every staple that was generated.

Tips

When creating the extensions, the staple has to be first be selected as the target model in the build section.

From that point, the process involves merging the staple with the extension. This is achieved via manipulation of the atomic positions. Once the strand is located in close proximity of the staple, the 2 strands can be connected. In ChimeraX, there exist a “Adjust Bond" method, which allows for control and manipulation of interatomic bonds. As such, the 5’ end can be connected to the 3’ end in this fachion. This process is repeated for each sticky end.

Julia Packages

The script was developed in Julia using the following packages:

• BioStructures.jl
  • Greener JG, Selvaraj J and Ward BJ. BioStructures.jl: read, write and manipulate macromolecular structures in Julia, Bioinformatics 36(14):4206-4207 (2020)
• BioAlignements.jl
  • Thomas A. Christensen II, Ciarán O'Mara, Alexey Stukalov, Kenta Sato, Jakob Nybo Nissen, Sabrina Jaye Ward, Kevin Bonham, Daniel C. Jones, Tim Holy, Kapara newbie, Morten Piibeleht, & tanhevg. (2023). BioJulia/BioAlignments.jl: v3.1.0 (v3.1.0). Zenodo. https://doi.org/10.5281/zenodo.7502559
• BioSequences.jl
  • Jakob Nybo Nissen, Sabrina Jaye Ward, Kenta Sato, Ciarán O'Mara, cjprybol, Kevin Bonham, Tony Kelman, Dave T. Johnson, Harry Scholes, Isaac Virshup, cossio, Morten Piibeleht, Peter Haverty, Thomas Poulsen, Tim Holy, Karl Dyrhage, lhnguyen-vn, & tanhevg. (2023). BioJulia/BioSequences.jl: v3.1.5 (v3.1.5). Zenodo. https://doi.org/10.5281/zenodo.8070757
• CSV.jl
  • Jacob Quinn, Milan Bouchet-Valat, Nick Robinson, Bogumił Kamiński, Gem Newman, Alexey Stukalov, Curtis Vogt, cjprybol, Tim Holy, Andreas Noack, Tony Kelman, Eric Davies, ExpandingMan, Ian, Lilith Orion Hafner, Morten Piibeleht, Rory Finnegan, evalparse, Aaron Michael Silberstein, … kragol. (2023). JuliaData/CSV.jl: v0.10.11 (v0.10.11). Zenodo. https://doi.org/10.5281/zenodo.8004128
• Plots.jl
  • Tom Breloff. (2023). Plots.jl (v1.39.0). Zenodo. https://doi.org/10.5281/zenodo.8300728
• Combinatorics.jl
  • https://juliamath.github.io/Combinatorics.jl/dev/
• NearestNeighbors.jl
  • Kristoffer Carlsson, Daniel Karrasch, Nicholas Bauer, Okon Samuel, Tony Kelman, Ed Schmerling, Júlio Hoffimann, Martijn Visser, Pablo San-Jose, Josh Christie, Andy Ferris, Anthony Blaom, PhD, Benoit Pasquier, Carlo Lucibello, c42f, Elias Carvalho, Elliot Saba, Gustavo Goretkin, Ilya Orson, … Tamas Nagy. (2022). KristofferC/NearestNeighbors.jl: v0.4.13 (v0.4.13). Zenodo. https://doi.org/10.5281/zenodo.7468949
• Distances.jl
  • https://github.com/JuliaStats/Distances.jl
• DataFrames.jl
  • Bogumił Kamiński, John Myles White, Milan Bouchet-Valat, powerdistribution, Sean Garborg, Jacob Quinn, Simon Kornblith, cjprybol, Alexey Stukalov, Douglas Bates, Tom Short, Chris DuBois, Harlan Harris, Kevin Squire, Alex Arslan, pdeffebach, David Anthoff, Dave Kleinschmidt, Andreas Noack, … Florian Oswald. (2023). JuliaData/DataFrames.jl: v1.6.1 (v1.6.1). Zenodo. https://doi.org/10.5281/zenodo.8174885

Molecular Dynamics Simulation

To understand the dynamics of our envisioned nanomaterial scaffold, we perform molecular dynamic simulations using oxDNA^[5:1], a corse-grained DNA origami simulator. It allows us to simulate the interactions and mechanical properties of the DNA octahedron structure under varied conditions. In the input parameter file we define a simulated temperature, a salt concentration equivalent to 0.1M of NaCl, and set external forces to zero. The interaction type is set to DNA2 in order to use the newest version of oxDNA that was published in 2015 (Snodin et al., 2015).^[9]

##############################
####    SIM PARAMETERS    ####
##############################
interaction_type = DNA2
steps = 1e7
dt = 0.003
ensemble = nvt

T = 20C # simulated temp
salt_concentration = 1.0
thermostat = brownian
newtonian_steps = 103
external_forces = 0

The core of oxDNA lies in the formulation of interaction potentials that represent various forces acting between nucleotides, including hydrogen bonding and base stacking. Then, the dynamic behavior and movement of the nucleotides over time are modeled using a set of differential equations with several atoms grouped together into single beads and their behavior described by brownian motion. To effectively perform the simulations under varying conditions we build oxDNA with CUDA, such that we can run the molecular dynamics (MD) simulations in parallel and with mixed precision.

##############################
####  PROGRAM PARAMETERS  ####
##############################
sim_type = MD
backend = CUDA
backend_precision = mixed

use_edge = 1
edge_n_forces = 1
CUDA_list = verlet
CUDA_sort_every = 0
verlet_skin = 0.5

If the distance between some of the bonded neighbors exceeds unit length, it may be necessary to relax the structure by running 1e3 steps of the Monte Carlo (MC) simulation on the CPU backend. An input file that can achieve this is added to our iGEM GitLab. After running oxDNA for around 15 minutes with the input parameters shown here, the trajectory file can be viewed on the modeled topology using the oxView visualization tool (Bohlin et al., 2022)^[10]:

This video shows the trajectory of the DNA origami molecule over 1 million steps. From the trajectory, we can assess whether our DNA octahedrons will exhibit the required robustness for being used as a mineralization template. The designed shape remains stable under laboratory conditions and only disassembles at temperatures above 50 degrees. Therefore, we can ensure that the assembled DNA origami will maintain its desired shape.

Biomineralization of Nanoparticles

In our project DNA nanoparticles (DNA-NPs) are crafted from biomineralization of the DNA origami structure by controlling the local ion concentrations and geometry. The negatively charged DNA, acting as nucleation sites, guides the precipitation of bicarbonate (HCO₃⁻) and calcium (Ca²⁺) ions as calcium carbonate.

MODEL PARAMETERS

Turnover [1/s]	Substrate	Organism	Conditions	References
kcat+=4400000	CO2	Sulfurihydrogenibium azorense	pH 7.5, 25°C, without activator	729371
kcat+=15000000		3.4x increase	pH 7.5, 25°C, 10 µM L-Phe	729371
kcat+=33000000		7.5x increase	pH 7.5, 25°C, 10 µM D-Phe	729371
kcat-=4400000	H2CO3	Sulfurihydrogenibium azorense	pH 7.5, 20°C	747974

The SazCA carbonic anhydrase used in our system is a particularly efficient variant of this enzyme, and it can be used to accelerate the interconversion between carbon dioxide $CO_2$ and water $H_2O$ to bicarbonate $HCO₃⁻$ and protons $H⁺$. We can use reversible Michaelis-Menten kinetics to model the catalytic mechanism of the enzyme.

$$v = \frac{kcat_+ \frac{[CO2]}{Ks}-kcat_{-}\frac{[H2CO3]}{Kp} }{1+\frac{[CO2]}{Ks}+\frac{[H2CO3]}{Kp}}[SazCA]_T$$

The rate of the reaction depends on the amount of solved $CO_2$ in the medium as well as the total concentration of the SazCA enzyme. We can solve this equation as a system or ordinary differential equations using an ODE solver. By running it for 279mM of $CO_2$, we reach an equilibrium of 140M for $H_2CO_3$. With L-Phe [$H_2CO_3$] increases to 216mM and with D-Phe to 247mM. Together with a value of 100mM for [$Ca^{2+}$] we can calculate the solubility product constant at which we formed calcite.

$$Ksp,calcite = [Ca^{2+}][HCO_3^-] = 1.40 \times 10^{-2}$$

Our goal is to decrease Ksp by introducing DNA nucleation sites when precipitating calcite along the scaffold.

Conclusion

Our goal in this project is to provide a proof of concept for the biotechnological production of nanoparticles. Our modeling workflow contributed the scaffold and staple strands that are necessary to fold a DNA origami octahedron, we showed that this configuration will be stable under the assembly conditions by running oxDNA molecular dynamics simulations and we calculated a metric to quantify the increased calcite precipitation by introducing DNA nucleation sites.

References

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1. TALOS – three-dimensional, algorithmically-generated library of DNA origami shapes. (n.d.). http://talos-dna-origami.org/ ↩︎

2. Cando_admin. (2018). Home. CanDo. https://cando-dna-origami.org/ ↩︎

3. Castro, C. et al. (2011). A primer to scaffolded DNA origami. Nat Methods 8, 221–229. https://doi.org/10.1038/nmeth.1570 ↩︎

4. Meng E. C., et al. (2023). UCSF ChimeraX: Tools for structure building and analysis.  Protein Sci. :e4792. Online ahead of print. ↩︎ ↩︎

5. Poppleton, E., et al. (2021). OxDNA.org: a public webserver for coarse-grained simulations of DNA and RNA nanostructures, Nucleic Acids Research, gkab324, https://doi.org/10.1093/nar/gkab324 ↩︎ ↩︎

6. Rothemund P. W. (2006). Folding DNA to create nanoscale shapes and patterns. Nature, 440(7082), 297–302. https://doi.org/10.1038/nature04586 ↩︎

7. Nafisi, P. M. et al., (2018) Construction of a novel phagemid to produce custom DNA origami scaffolds, Synthetic Biology, Volume 3, Issue 1, https://doi.org/10.1093/synbio/ysy015 ↩︎

8. Min, J. et al. (2020). Programmable Cocrystallization of DNA Origami Shapes. Journal of the American Chemical Society, (), jacs.0c08525–. doi:10.1021/jacs.0c08525 ↩︎

9. Snodin, B. E. K., et al. (2015). Introducing improved structural properties and salt dependence into a coarse-grained model of DNA. Journal of Chemical Physics, 142(23), 234901. https://doi.org/10.1063/1.4921957 ↩︎

10. Bohlin, J. et al. (2022) Design and simulation of DNA, RNA and hybrid protein–nucleic acid nanostructures with oxView. Nat Protoc 17, 1762–1788. https://doi.org/10.1038/s41596-022-00688-5 ↩︎