cell collectives. We discuss metastatic cells explicitly, and emphasize that physical insights gained from other cellular systems can inform our understanding of metastatic invasion. We focus on simple physical models and order-of-magnitude numerical estimates in order to quantitatively probe the extent of, and the limits to, cell sensory and migratory behavior. Our hope is that a more quantitative understanding of metastatic invasion will inform treatment protocols, and to that end we conclude by discussing drug sensitivity and potential treatment strategies (Fig. \[overview\]C).

![Metastatic invasion is guided by chemical attractants and can occur via (A) single cells or (B) multicellular groups. (C) Drugs are delivered to the tumor environment in order to prevent tumor growth and metastasis. Drugs may cause cell death (orange), block cell-to-cell communication (purple), or prevent cell migration (blue).[]{data-label="overview"}](fig1.png){width="0.9\columnwidth"}

Physical limits to sensory precision
====================================

Tumor cells sense very small concentration gradients[@shields2007autologous] and act in a collective manner[@cheung2013collective; @friedl2012classifying; @aceto2014circulating; @puliafito2015three]. Here we review the basic theory of concentration and gradient sensing by cells and cell collectives. This theory places physical bounds on sensory precision and allows us to quantitatively compare the capabilities of tumor cells to other cell types.

Single-cell concentration sensing
---------------------------------

Theoretical limits to the 