The study of cellular responses to chemical gradients in vitro would greatly benefit from experimental systems that can generate precise and stable gradients comparable to chemical nonhomogeneities occurring in vivo. Recently, microfluidic devices have been demonstrated for linear gradient generation for biological applications with unmatched accuracy and stability. However, no systematic approach exists at this time for generating other gradients of target spatial configuration. Here we demonstrate experimentally and provide mathematical proof for a systematic approach to generating stable gradients of any profile by the controlled mixing of two starting solutions.Replication of complex chemical gradients is essential for many in vitro experimental studies in prokaryotic and eukaryotic cells. Investigation of fundamental processes such as the migration of prokaryotic cell toward sources of nutrients, 1 immune cells against intruders, 2,3 the growth or regeneration of axons toward their connection target, 4 and the differentiation of embryonic cells in response to morphogens 5 require precise duplication of the in vivo spatial distribution of various signaling molecules. Such distributions usually occur in nonhomogeneous mediums, under various production, transport, and degradation conditions, and gradients of nonlinear, more or less complex shapes are usually formed. 6,7 Although linear gradients represent a good first-order approximation for in vivo gradients, and are useful in gaining insights into the biology of cellular responses, growing evidence suggests that a lot of complexity arises and many cellular responses are specific to spatial gradients that are not linear. For example, in bacteria migrating in chemoattractant gradients, the interplay between sensory adaptation and concentration changes due to displacement can lead to variations in chemotactic responses. 8 Similarly, cancerous cells that typically do not respond to linear chemotactic gradients have been recently shown to migrate in response to nonlinear gradients. 9 As a result, it is critical for better understanding of cellular polarization, migration, growth, or division responses of cells to biochemical heterogeneities in their microenvironment to be able to consistently replicate chemical concentration profiles comparable to those experienced by cells in vivo. Still, most of the current experimental systems for generating chemical gradients, e.g., Boyden chambers, 10 Dunn chambers, 11 or microfluidic gradient generators, 12 only produce linear gradients of soluble biochemical factors, and few alternatives exist for producing gradients of other spatial profiles at scales comparable to cell size. While some gradients that are not linear have been generated using asymmetric flow in symmetric networks, 13 or serial dilutions schemes, 14,15
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