Zipper-mediated uptake can be described by a power-law.

<p>(<b>A</b>) Schematic of a 3-stage zipper model. Free bacteria (B) reversibly bind to β₁-integrins in three stages: Unstable, singly bound (B₁); stable attachment via a minimal number of interactions (B_m); and a maximal number of interactions (B_n). Uptake is defined as the sum of B_m and B_n. (<b>B</b>) Simulated bacterial uptake per cell as a function of total β₁-integrins ranging from 10⁵ to 10⁶ per cell for various MOI. Lines indicate the linear dependence of bacterial uptake on receptor concentration and circles indicate mean bacterial uptake in the infected host cells for each bacterial MOI. Inset shows linear fit to means. (<b>C</b>) The dependence of the uptake probability by a single bacterium on the host receptor concentration is independent of the bacterial concentration. Note that the uptake curves for larger MOI span a larger region of the same trajectory. The uptake probability is defined as the overall bacterial uptake normalized with respect to the total bacterial MOI. Inset shows power-law fit to means. (<b>D</b>) Power-law dependence arises in a limiting case of a more general Hill-type dose response. The zipper mechanism is a cooperative, multistep, and reversible process well-described by a Hill function. A power-law is a limiting case when the receptor concentration is less than the scaled effective dissociation constant i.e. R<<<i>K</i>_<i>Deff</i>^1/β (blue shaded region). This condition is met when a highly cooperative, multistep, reversible process reduces the likelihood of finding bacteria in intermediate states. This regime corresponds to the linear region in a log-log plot (shaded region in inset).