Spatially Encoded Protocell Network for Non-Cascaded Parallel Biocomputation.

Biological systems inspire computing paradigms by autonomously regulating material and information flows through molecular interactions. While biomolecules such as enzymes and DNA have been harnessed for biocomputation, implementing complex logic operations remains challenging due to signal attenuation, crosstalk, and instability inherent in molecular cascades. To overcome these limitations, we present a non-cascaded biocomputing architecture based on spatially encoded, gradient-responsive protocell communities embedded in a three-dimensional hydrogel matrix. By leveraging differential reaction-diffusion dynamics of input signals, distinct output regions are established across the spatial domain, enabling parallel, multi-threshold computation without signal routing. This architecture achieves continuous spatial encoding and allows simultaneous readout of all output regions, supporting nonlinear logic operations with high fault tolerance. Using this framework, we demonstrate the successful implementation of both half-adder and full-adder logic operations via two-input/two-output and three-input/two-output configurations, respectively. Our approach provides a scalable, programmable platform for parallel biocomputation, offering a promising route toward low-complexity, robust, and non-cascaded molecular computing systems that bridge synthetic biology and computational science.