Team:Hong Kong HKU/Model
Modelling: Drug Loading Ratio of Doxorubicin to NDC
A Hill Plot for Doxorubicin Loading to NDC was constructed using the data from doxorubicin fluorescence binding to different concentrations of NDC (with 95% Confidence Interval). Because the the curve level off at about range 1 to 10, this range is considered the most stable and effective range for the Dox to bind on the NDC. In the range 1 to 10, more Dox will bind onto the NDC and there will hence be less Dox in the environment. When it reaches this range and reach equilibrium, the dissociation constant could be calculated as below:
X-intercept = Log [Kd] = -0.6317
Kd = 10^-0.6317 = 0.2335
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<,p>
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.
Y/1-Y represents 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. For any n = 1, the system exhibits independent binding[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.
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 ratio between Hill slope and Hill Coefficient, which is close to 1, indicates the binding of the doxorubicin is independent of the concentration of NDC. However, there is not ample literature about the independent binding in this range. 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.
Reference
- 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.