Building RNA Concentration Fields

In living systems, biomolecular concentration fields create maps that pattern a fly’s compound eyes, weave growing nerves into brain circuitry, and organize microbial communities. A simple, generalizable way to construct such concentration maps in vitro, with precise control over the position and shape of each feature and applicability to diverse length-scales, timescales, and downstream processes, would open opportunities to direct the synthesis and dynamics of systems ranging from optics and electronics to living tissues. Here we introduce a strategy for creating intricately patterned, stable RNA concentration fields by designing the arrangement and overlap of local concentration fields that act as geometric primitives for pattern design. Each primitive field is produced by a “generator” hydrogel, allowing field positions and overlaps to be arbitrarily chosen by prescribing the generator locations. This design flexibility derives from a straightforward approach: combining primitive fields through the direct addition of their concentrations at each point. As a result, combining fields by modulating inter-generator distance can introduce new pattern features such as hills or valleys. Using an empirical model that enables rapid and accurate prediction of the composite fields produced by arbitrary numbers and arrangements of generators, we show how a desired field can be generated from first principles by optimizing the set of generator locations that accurately reproduces it. The construction of patterns from primitive fields, using RNA synthesis and degradation reactions easily generalized to any sequence, enables the patterning of a range of RNA species, independent scaling of local and composite fields, and multi-hour pattern stability using only NTPs as fuel. This approach provides a foundation for applying the operations of constructive geometry to patterning materials in solution that could be extended to three-dimensional and multi-species concentration fields to drive the self-assembly of particles and materials, orchestrate the growth and self-organization of cell architectures, or precisely direct reconfiguration or healing.