Calculating the number of lipids in a liposome
Where N total is the total number of DSPC lipids, SA is the surface area of the DSPC head, d is the diameter of the liposome, and h is the thickness of the lipid bilayer.
Assume that the majority of the lipid composition is from DSPC and that cholesterol doesn’t change the surface area. DSPEPEGmaleimide lipid is in such small molar ratio that it is assume to not effect liposome size.
The liposome size based on Dynamic Light Scattering (DLS) is 157.3 nm.
Thickness of lipid bilayer = 4.78 nm ^{1}
Surface are of DSPC head = 0.516 nm^{2} ^{2}
The liposomes composition is 2:1:0.04 molar ratio of DSPC:cholesterol:DSPEPEGmaleimide, respectively. One mole percent of the cholesterol was replaced with a fluorescent tracker, Top Fluor Cholesterol.
In mole percent, the liposome composition is as follows:
DSPC: 65.8 mol%
Cholesterol: 31.9 mol%
Top Fluor Cholesterol: 1.0 mol%
DSPEPEGmaleimide: 1.3 mol%
With approximately 283537 DSPC lipids, using the above mole percents, the number of lipids and molecules of cholesterol can be determined.
DSPC: 283537 lipids
Cholesterol: 137459 molecules
Top Fluor Cholesterol: 4310 molecules
DSPEPEGmaleimide: 5671 lipids
Total Number of Lipids: 289208 lipids
Total Number of Molecules: 430977 molecules
Calculating the molecular weight of a liposome
Knowing the composition of the liposome and the total number of molecules a weighted average can be performed using the molecular weight or each component.
MW DSPC: 790.145 g/mol
MW cholesterol: 386.654 g/mol
MW Top Fluor cholesterol:
MW DSPEPEGmaleimide: 2941.605 g/mol
In one liposome:
Determining the number of liposomes per milliliter of solution
In 30 mg/mL of liposome solution, the number of liposomes in a mL of solution can be determined by using the molecular weight of the liposome as well as using Avogradro’s number.
Liposome Concentration (mg/mL): 30 mg/mL
Avogadro’s Number: 6.022 x 1023 molecules/mole
In 30 mg/mL:
Calculating amount of EGF to conjugate onto DSPEPEGmaleimide
Based on literature^{3}, we want to have a minimum of 1015 molecules of EGF conjugated onto DSPEPEGmaleimide to achieve a satisfactory cellular uptake of antibodytargeted liposomes and in our case, allow for appropriate binding with EGF receptors on the U251 cells. From the liposome composition, we know that there is approximately 5671 ligands of DSPEPEGmaleimide available to bind thiolated EGF. In the initial design process, around 200 EGF ligands were targeted to be conjugated onto the liposome, which equates to around 3.5% of the DSPEPEGmaleimide ligands binding to EGF. Using this information, we can determine the amount of EGF to add to 1 mL of liposome solution.
In 1 mL of liposomes, the number of DSPEPEGmaleimide ligands available is:
To achieve ~200 EGF ligands into each liposome, the amount of EGF required is:
Due to inprocess sampling and taking into account losses, the EGF stock solution was prepared at 23.87 nM This was performed by dissolving 500 ug of powered EGF in a final volume of 3378 uL:
Note: the size of EGF is 6.2 kDa which is equivalent to a molecular weight of 6200 g/mol.
Calculating amount of APOE to conjugate onto DSPEPEGmaleimide
To confirm the versatility of this process and that another protein can be thiolated with 2iminothiolane and reacted with DSPEPEGmaleimide, similar loading was performed with APOE to produce a APOE ligand. Given the amount of APOE available for use, 1 vial of 50 ug APOE was used. Since APOE is a larger molecule at 34 kDa, 50 ug of APOE has a lower number count than 50 ug of EGF.
To determine the amount of liposomes required to react with 50 ug of APOE, the calculations were performed as follows:

“Structural Parameters of Aqueous Phospholipid Mixtures”, Brocku.ca, 2016. [Online]. Available: https://brocku.ca/researchers/peter_rand/lipid/#eggPC. [Accessed: 21 Oct 2016]. ↩

P. Yeagle, The structure of biological membranes. Boca Raton: CRC Press, 2012. ↩

E. Bohl Kullberg, N. Bergstrand, J. Carlsson, K. Edwards, M. Johnsson, S. Sjöberg and L. Gedda, “Development of EGFConjugated Liposomes for Targeted Delivery of Boronated DNABinding Agents”, Bioconjugate Chem., vol. 13, no. 4, pp. 737743, 2002. ↩