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.

细胞定向迁移由胞外信号分子的非均匀分布所调控。众所周知，噪声在生物学过程中发挥关键作用，且天然存在的微纳尺度梯度中均伴随噪声，但目前尚未有基于体外梯度开展相关研究的报道。本研究提出了可根据单调与非单调密度函数生成离散纳米点有序与随机梯度的新型算法，该梯度被称为数字纳米点梯度（digital nanodot gradients, DNGs）。该算法可生成连续型DNGs，其点间距可沿梯度方向在二维平面内依据任意数学函数变化，点密度覆盖范围为0.02%至44.44%。随机梯度算法可补偿纳米点的随机重叠问题，且通过里普利K函数（Ripley's K function）验证了DNGs的随机性与空间均匀性。本研究设计了包含100个DNGs的阵列，每个DNG尺寸为400×400平方微米，总计包含5700万个200×200平方纳米的纳米点；通过电子束光刻将该阵列制备于硅片之上，再通过剥离式纳米接触印刷技术将其制备为玻璃基底上的荧光标记免疫球蛋白G（IgG）图案。DNGs将为研究微纳尺度下噪声与随机性对细胞迁移与生长的影响提供有力的研究工具。