# Calculations

1. Conversion from Mass to Moles of ssM13mp18 DNA

ssM13mp18 DNA = 7249 nucleotides (nt) Concentration of M13mp18 from NEB = 250 $\mu$/mL

From NEB website:​​

Per 1 mL of M13mp18, the moles of ssDNA is calculated to be:

The concentration of ssM13mp18 is:

2. Concentration of IDT Oligionucleotides (Staple Strands)

IDT oligionucleotides were received in 364 well plates with varying masses.

The average number of moles in each well was calculated to be around ~10 nM. All wells were resuspended with $100\; \mu$L of 1x TE buffer to make up a final concentration of 100 $\mu$M

The calculation is shown as follows:

3. Concentration of Pre-Stock Solution and Working Stock Solution

To make the pre-stock solution, 10 $\mu$L of each staple strand for each section of the DNA-origami structure were combined.

The pre-stock solutions for each section were combined at certain ratios to form the whole DNA-origami structure.

A sample calculation for Cholesterol Anchor pre-stock solution for final 60 nm DNA-origami structure:

Number of Cholesterol Anchor Staple Strands = 9 Concentration of Staple Strands = 100$\mu$M Volume of Staple Strands Added = 10$\mu$L

Surface Area of the DNA-origami structure:

Dimensions:

• 60 x 60 nm​

• 20 x 20 nm hole

• 4 nm thickness

Cross Sectional Area of Au NP

Diameter of AuNP = 5 nm

Area of AuNP = $\small{\pi(\frac{d}{2})^2 = \pi(\frac{5 nm}{2})^2 = 19.6\; nm^2}$

Ratio of AuNP to DNA origami structure is calculated to be:

If we want to use 2 $\mu$L DNA in each batch: 2 $\mu$L DNA ${\small \times \; 2.5 \times 10^{-15}\; mol/\mu L = 5 \times 10^{-15}}$ moles of DNA

$\therefore$ we want ${\small 5 \times 10^{-15}\; \mbox{moles DNA} \times 391\; \frac{AuNP}{DNA} = 1.955 \times 10^{12}}$ moles of DNA

5. Number of Liposomes in a Given Volume

POPC Molecular Weight = 760.076 g/mole Cholesterol Molecular Weight = 386.65 g/mole

Lipid Concentration = 30 mg/mL Composition = 55% POPC + 45% Cholesterol Surface Area of a POPC Lipid: SA = 0.7 nm$^2$ Diameter: d = 100 nm Bilayer Thickness: h = 34.6 ${\small \buildrel {\circ} \over {\mathrm{A}}} \rightarrow$ 3.46 nm

Number of Lipids per Liposome

Assuming that 45% cholesterol does not change POPC Surface Area, the total number of lipids (N${total}$) per liposome can be calculated as:

Composition of Liposome: 55% POPC + 45 % Cholesterol = 100% (mole ratio)

Liposomes in 1 mL

​Liposome Concentration: 9.05 $\times \mbox{10}^7$g/mol Mass Concentration of Liposomes: 30 mg/mL $% $

6. DNA Anchor Solution Volume

Number of Liposomes ​ Actual Liposome Concentration: ${\small 2.46 \times 10^{14}\; liposomes/1 mL \rightarrow 2.46 \times 10^{11}\; liposomes/1\mu L}$

We want a ratio of 1:1 (DNA:liposome) in a final volume of $\tilde{} 20 \mu$L total volume​. If we use 10 $\mu L\; \mbox{of}\; 2.46 \times 10^{12}$M final solution, we need to determine the amount of DNA anchor solution.

• Aim for 1:1 DNA to lipsome

• Each DNA has 9 anchors

• Use 1.6 x excess

​Number of DNA-Origami Structures

10 $\mu$L Liposomes + 10$\mu$L DNA

So 10 $\mu$L of DNA will have: $2.45 \times 10^{23}$ DNA structures.

Number of DNA Anchors

Cholesterol Anchor Concentration: 100.000 nM

DNA-Liposome Anchoring Recipe:

• 10 $\mu$L of Liposomes

• 10 $\mu$L of DNA-Origami Structures

• 0.59 $\mu$L of DNA Anchors