Kinetic Limitations of Cooperativity-Based Drug Delivery Systems

We study theoretically a novel drug delivery system that utilizes the overexpression of certain proteins in cancerous cells for cell-specific chemotherapy. The system consists of dendrimers conjugated with “keys” (ex: folic acid) which “key-lock” bind to particular cell-membrane proteins (ex: folate receptor). The increased concentration of “locks” on the surface leads to a longer residence time for the dendrimer and greater incorporation into the cell. Cooperative binding of the nanocomplexes leads to an enhancement of cell specificity. However, both our theory and detailed analysis of in vitro experiments indicate that the degree of cooperativity is kinetically limited. We demonstrate that cooperativity and hence the specificity to particular cell type can be increased by making the strength of individual bonds weaker, and suggest a particular implementation of this idea.

Figure 1

A picture of the dendrimer “key-lock” binding to the cell-membrane surface.

Figure 2

Top: Plot of the association rate constant [Eq. (2)] $k_a[{\mathrm{M}}^{-1}{\mathrm{s}}^{-1}]$ versus $\overline{m}$. Bottom: Plot of the effective dissociation rate constant [Eq. (4)] $k_d[{\mathrm{s}}^{-1}]$ versus $\overline{m}$. In the fit, $k_d^{(o)}={10}^{-5}[{\mathrm{s}}^{-1}]$ and $\alpha =0.15$. The experimental data points are taken from Figure 5 in 11.

Figure 3

The ratio of surface concentrations of dendrimers on cancerous to normal cells $\frac{n(10{\sigma }_o)}{n({\sigma }_o)}$ as a function of $\Delta$ with $r=10$. The dotted line corresponds to an endocytosis time $1/\gamma =1[\mathrm{hr}]$, and the solid line is $1/\gamma =10[\mathrm{hr}]$. Here, $\overline{m}=15$, $m_{\max }=4$, $\xi =3[\mathrm{nm}]$, and ${\sigma }_o=2\times {10}^{-3}[{\mathrm{nm}}^{-2}]$. ${\epsilon }_{el}^{(m)}=3k_{B}T$ for $m\ge 3$ bridges.

Figure 4

Single-stranded DNA (ssDNA) on the dendrimer hybridize to the ssDNA attached to the folic acid (FA) key.