Spatial Computation of Quorum Sensing Bacterial Hopfield Networks

Bacteria use diffusive molecular exchange to coordinate collective behaviors, a process known as quorum sensing (QS). Prior work has shown that some cells exchange distinct signals which elicit a weighted response to the various signal types. We show that the dynamics of interacting QS communities can be captured by a class of nonreciprocal Hopfield networks, where asymmetric couplings encode the directionality of signal propagation. In this framework, the QS activation state of each community functions as a binary variable, enabling the construction of spatial logic circuits among microbial populations. We demonstrate that such networks can implement logic gates and directional information flow purely through the spatial arrangement and nonreciprocal coupling of QS communities. A half-adder circuit composed of QS logic gates is designed and simulated to illustrate how distributed computation can emerge from biochemical signaling. These results establish a theoretical foundation for a method of tunable information processing in living systems which further highlights the intersection of collective behavior, neural computation, and physical systems.