Team:Hong Kong HKU/Model
Model
-Doxorubicin loading and release from NDC
X Indicates the concentration of NDC. And the X-Axis Log [X] describes the concentration on a logarithmic scale.
Y indicates the concentration of bound doxorubicin when incubated with NDC of a different ratio. Since the ratio of unbound doxorubicin is unknown, it is represented by the formula
which the samples fluorescence was divided by reference doxorubicin fluorescence, which represents the fraction of fluorescence emitted. The fraction of fluorescence represents the fraction of free doxorubicin to total doxorubicin, with the assumption that fluorescence quenching is consistent for every doxorubicin molecule bound to DNA double helix.
Y1-Yrepresents the ratio of bound doxorubicin Y, to unbound doxorubicin (1-Y).
A general Hill’s equation[1] indicates that:
n is the cooperativity of the binding. For any n < 1, the system exhibits negative cooperativity, which means the binding of a ligand onto a molecule decreases the affinity of the second ligand. For any n > 1, the system exhibits positive cooperativity[1].
The Hills equation is invalid for any (1-Y) approaches 0, which means for unbound doxorubicin (1-Y) approaches 0 μM, we cannot accurately estimate the number of available binding sites left, as maximum quenching occurs for all the doxorubicin available for quenching. The maximum quenching is denoted by a zero slope.
A Hill Plot and Klotz Plot with sigmoidal curve fitting was plotted eliminating the part with zero slope. A linear regression was performed on the best fit range of Hill Slope and denoted by the formula. X Indicates the concentration of NDC. Log [X] describes the concentration on a logarithmic scale.
y = 2.0132x + 14.8121 (R-square = 0.9956)
Hill Slope n>1 indicates positive cooperative binding. It shows that the NDC with loading ratio higher than 1:20 have positive cooperative binding, and favors the loading of more doxorubicin with higher affinity. Doxorubicin exhibits primary and secondary binding [2]. Primary binding utilize the property in which doxorubicin intercalates into the DNA double helix, which exhibits a higher binding affinity. Secondary binding is a doxorubicin binding onto another molecule of doxorubicin by hydrogen bonding, which exhibits a lower affinity.
From the Hills Plot, the slope (n value) decreases with the increase of NDC to Doxorubicin ratio, indicating the decline of cooperativity due to more doxorubicin molecule bound onto the NDC. Maximum quenching starts from 1:1 until 1:20 NDC to doxorubicin ratio, indicating primary binding, which has the highest affinity and produces the most stable drug loaded NDC, which is optimal for drug carrying due to high stability and low dissociability. Cooperativity of the range could not be determined due to the inability to determine the available binding site on NDC.
Positive cooperativity remains stable from 1:20 to 1:30 ratio, shown by the linearity in Hill Plot. Cooperativity decreases after the 1:30 ratio. It was not able to determine the maximum ratio for secondary binding due to the lack of data from large loading ratios. However, due to the low affinity, it would not be a useful loading ratio for therapeutic purposes.
Model for Drug Release from NDC at pH 5
The data analysis above shows that the release of doxorubicin from the NDC is likely to be a second order kinetics. The binding mechanics as shown from Hill Plot shows that the equilibrium position is dependent on the concentration of both the drug and NDC. The increase in R-square with a higher order indicates the involvement of multiple components on the release process. Lower pH with a higher hydrogen ion concentration are shown to destabilize the NDC, which causes fast release of drug. It has an implication for a fast release of drug in acidic environments like tumour microenvironment and also in endosome, which the drug carrier stays relatively stable in blood.
References:
- Lee, C.M. & Tannock, I.F. (2006, March 27). Inhibition of endosomal sequestration of basic anticancer drugs: Influence on cytotoxicity and tissue penetration. British Journal of Cancer, 94(6), 863-869.
- Pérez-Arnaiz, C., Busto, N., Leal, J., & García, B. (2014). New insights into the mechanism of the DNA/doxorubicin interaction. The Journal of Physical Chemistry. B, 118(5), 1288-95.
- Sabouri, Ali Akbar, and Ali Akbar Moosavimovahedi. "Evaluation of the Hill Coefficient from Scatchard and Klotz Plots." Biochemical Education 22, no. 1 (1994): 48-49. doi:10.1016/0307-4412(94)90175-9.