Ordered, Random, Monotonic and Non-Monotonic Digital Nanodot Gradients

Cell navigation is directed by inhomogeneous distributions of extracellular cues. It is well known that noise plays a key role in biology and is present in naturally occurring gradients at the micro- and nanoscale, yet it has not been studied with gradients in vitro. Here, we introduce novel algorithms to produce ordered and random gradients of discrete nanodots – called digital nanodot gradients (DNGs) – according to monotonic and non-monotonic density functions. The algorithms generate continuous DNGs, with dot spacing changing in two dimensions along the gradient direction according to arbitrary mathematical functions, with densities ranging from 0.02% to 44.44%. The random gradient algorithm compensates for random nanodot overlap, and the randomness and spatial homogeneity of the DNGs were confirmed with Ripley's K function. An array of 100 DNGs, each 400×400 µm2, comprising a total of 57 million 200×200 nm2 dots was designed and patterned into silicon using electron-beam lithography, then patterned as fluorescently labeled IgGs on glass using lift-off nanocontact printing. DNGs will facilitate the study of the effects of noise and randomness at the micro- and nanoscales on cell migration and growth.