of the cells. This concentration is commensurate with the smallest background concentrations in which cells can perform gradient sensing (Table \[sense\_table\]). Assuming a cell length of $20$ $\mu$m, which is typical of carcinoma cells [@leber2009molecular], this concentration corresponds to only a few thousand drug molecules in the volume of a cell (Table \[drug\_table\]). Evidently lung cancer cells are affected by drug concentrations that are near the fundamental limits of what can be sensed.

                                                             Drug Concentration   Molecules per Cell
  --------------------------------------------------------- -------------------- --------------------
  Physical change [@torres1998mechanisms]                          $1$ nM             $5$,$000$
  Cell death [@grantab2006penetration]                           $10^4$ nM          $5\times 10^7$
  Cell death, nanoparticle delivery [@malam2009liposomes]         $100$ nM           $500$,$000$
  Communication blockage [@ellison2016cell]                       $50$ nM             $30$,$000$

Although cancer cells may be very sensitive to small drug concentrations, that does not translate to successful treatment. In order to achieve cell death, much larger drug concentrations are required. In the same study on lung carcinoma cells, cell death was observed for drug concentrations on the order of $10$ nM and greater. More typical drug concentrations required for cell death are on the order of micromolars. For instance, it has been shown *in vitro* that anticancer drug concentrations on the order of $10$ $\mu$M are required to kill at least $90\%$ 