User:Andy Maloney/Notebook/Lab Notebook of Andy Maloney/2009/06/25/Liposomes and kinesin

Calculating the amount of liposomes needed

The first thing I want to do is to calculate the amount of liposomes we will be using to coat each chamber. To do this I will start with the surface area for a lipid from a paper that I will need to find the reference for.

[math]\displaystyle{ 0.4 \mathrm{\ } \frac{\mathrm{nm}^2}{\mathrm{Lipid}} }[/math]

I have 100 nm filters that will make (nominally) 100 nm diameter liposomes. The number of lipid molecules per liposomes is

[math]\displaystyle{ \begin{align} \mathrm{Surface\ area\ of\ a\ liposome} = 4\pi r^2&\approx 31416\mathrm{\ nm}^2\\ \mathrm{Surface\ area\ of\ the\ bilayer\ of\ a\ liposome} = 2\times 4\pi r^2 &= 62832\mathrm{\ nm}^2\\ \frac{\mathrm{Lipid}}{\mathrm{Liposome}} = \frac{62832}{0.4} &= 157080\mathrm{\ }\frac{\mathrm{Lipids}} {\mathrm{Liposome}} \end{align} }[/math]

Using the average molecular weight of L-α-phosphatidylcholine of 770 g/mole, I can find the number of liposomes I can make with the 25 mg of lipid molecules I have.

[math]\displaystyle{ \begin{align} \left(770\mathrm{\ }\frac{\mathrm{g}}{\mathrm{mole}}\right)^{-1}\mathrm{\ }6.022\times10^{23}\mathrm{\ }\frac{\mathrm{Lipids}}{\mathrm{mole}} &= 7.8\times 10^{20}\mathrm{\ }\frac{\mathrm{Lipids}}{\mathrm{g}}\\ 7.8\times 10^{20}\mathrm{\ }\frac{\mathrm{Lipids}}{\mathrm{g}}\mathrm{\ }25\times 10^{-3}\mathrm{g} &= 2\times10^{19}\mathrm{\ Lipids}\\ \mathrm{\#\ of\ Liposomes} &= 1.2\times10^{14}\mathrm{\ Liposomes} \end{align} }[/math]

The next thing I want to find is the amount of liposome solution required to fully coat the surface area of our chamber. We are using cover slips and cover glass slides that are 24 mm and 25 mm in width respectfully.

[math]\displaystyle{ \begin{align} \mathrm{Surface\ area\ of\ chamber} &= 600\times10^{12}\mathrm{\ nm}^2\\ 1.2\times 10^{14}\mathrm{\ Liposomes} / 2.5 \mathrm{\ mL} &= 48\times10^{12}\mathrm{\ }\frac{\mathrm{Liposomes}}{\mathrm{mL}}\\ 600\times 10^{12}\mathrm{\ }\frac{\mathrm{nm}^2}{\mathrm{Sample\ chamber}}\mathrm{\ }\frac{\mathrm{Liposome}}{31416\mathrm{nm}^2} &= 1.9\times 10^{10}\mathrm{\ }\frac{\mathrm{Liposomes}}{\mathrm{Chamber}}\\ \frac{1.9\times 10^9\mathrm{\ }\frac{\mathrm{Liposomes}}{\mathrm{Chamber}}}{48\times 10^{12}\mathrm{\ }\frac{\mathrm{Liposomes}}{\mathrm{mL}}} &= 0.4\mathrm{\ }\frac{\mathrm{mL}}{\mathrm{Chamber}} \end{align} }[/math]

Thus the amount of liposome sauce needed to coat our sample chambers is

[math]\displaystyle{ \begin{align} 400\mu\mathrm{L} \end{align} }[/math]