Bacterial gene regulatory neural network as a biocomputing library of mathematical solvers.

Current biocomputing approaches predominantly rely on engineered circuits with fixed logic, offering limited stability and reliability under diverse environmental conditions. Here, we use the gene regulatory neural network (GRNN) framework introduced in our previous work to transform bacterial gene expression dynamics into a biocomputing library of mathematical solvers. We introduce a sub-GRNN search algorithm as a general computational framework for identifying functional subnetworks within native transcriptional networks by evaluating gene expression patterns across chemically encoded input conditions. Mathematical calculation and classification tasks, including identifying Fibonacci numbers, prime numbers, multiplication, and Collatz step counts, are used as case studies to validate the proposed framework. The identified problem-specific sub-GRNNs are then assessed using gene-wise and collective perturbation, as well as Lyapunov-based stability analysis, to evaluate robustness and reliability. Our results demonstrate that native transcriptional machinery can be harnessed to perform diverse mathematical calculation and classification tasks, while maintaining computing stability and reliability.