both amoeba [@van2007biased] and tumor cells [@shields2007autologous] are sensitive to a roughly $1\%$ change in concentration across the cell body. However, this method of reporting sensitivity may be misleading. Experiments imply very different sensory thresholds for these cells in terms of absolute molecule numbers, as we will now see.

The key is that it takes two numbers to specify the conditions for gradient sensing: the mean gradient $\bar{g}$ and the mean background concentration $\bar{c}$. For the amoeba *Dictyostelium*, these numbers are $\bar{g} = 10$ nM/mm and $\bar{c} = 7$ nM at the sensory threshold [@van2007biased]. Given a typical cell size of $a = 10$ $\mu$m, these values imply a mean percent concentration change of $\bar{p} = a\bar{g}/\bar{c} = 1.4\%$ (Table \[sense\_table\]). However, we may also compute from these values the mean molecule number difference $\Delta\bar{n} = a\bar{g}s^3$ from one side of the cell to the other, within the effective compartments of size $s$. Taking $s\sim a$ gives the maximal molecule number difference of $\Delta\bar{n} = a^4\bar{g} = 60$ for *Dictyostelium* (Table \[sense\_table\]). Together $\bar{p}$ and $\Delta\bar{n}$ specify the sensing conditions as completely as $\bar{g}$ and $\bar{c}$ do.

Experiments [@shields2007autologous] have shown that breast cancer tumor cells exhibit a chemotactic response 