Robust multicellular computing using genetically encoded NOR gates and chemical 'wires'

Abstract

Computation underlies the organization of cells into higher-order structures, for example during development or the spatial association of bacteria in a biofilm. Each cell performs a simple computational operation, but when combined with cell-cell communication, intricate patterns emerge. Here we study this process by combining a simple genetic circuit with quorum sensing to produce more complex computations in space. We construct a simple NOR logic gate in Escherichia coli by arranging two tandem promoters that function as inputs to drive the transcription of a repressor. The repressor inactivates a promoter that serves as the output. Individual colonies of E. coli carry the same NOR gate, but the inputs and outputs are wired to different orthogonal quorum-sensing 'sender' and 'receiver' devices. The quorum molecules form the wires between gates. By arranging the colonies in different spatial configurations, all possible two-input gates are produced, including the difficult XOR and EQUALS functions. The response is strong and robust, with 5- to >300-fold changes between the 'on' and 'off' states. This work helps elucidate the design rules by which simple logic can be harnessed to produce diverse and complex calculations by rewiring communication between cells.

Figure 1. The genetic NOR gate

a, b, Symbol, truth table (a) and genetic diagram (b) of the NOR gate. c, The transfer function is defined as the output as a function of input at steady state. The transfer functions of P_BAD and P_Tet (top), the P_BAD–P_Tet tandem promoter (middle), and the NOR gate (bottom) are shown. The inducer concentrations for the tandem promoter and NOR gate characterizations are 0, 0.0005, 0.005, 0.05, 0.5 and 5 mM Ara (squares from left to right) and 0, 0.025, 0.25, 2.5, 25 and 250 ng ml⁻¹ aTc (squares from bottom to top). Fluorescence values and their error bars are calculated as mean ± s.d. from three experiments. a.u., arbitrary units.

Figure 2. Input modularity of the gates

a, Transfer functions for three OR gates (left) are compared with the predicted transfer function (right). The predicted transfer function is the simple sum of the transfer functions measured for the individual promoters (Supplementary Information). The Ara and aTc concentrations used are the same as in Fig. 1 and those for 3OC12-HSL are 0, 0.001, 0.01, 0.1, 1 and 10 μM (squares from bottom to top). b, Transfer functions for three NOR gates (left) are compared with the predicted transfer functions (right). The data represent means calculated from three experiments.

Figure 3. Construction of an XOR gate by programming communication between colonies on a plate

a, Four colonies—each composed of a strain containing a single gate—are arranged such that the computation progresses from left to right, with the result of each layer communicated by means of quorum signals. The inputs (Ara and aTc) are added uniformly to the plate. b, Spatial arrangement of the colonies. c, Each colony responds appropriately to the combinations of input signals. Fluorescence values and their error bars are calculated as mean ± s.d. from three experiments. d, Cytometry data for the XOR gate (cell 4).

Figure 4. Construction of all 16 two-input Boolean logic gates

a, Library of simple logic gates carried by different strains (corresponding to plasmids in Supplementary Table 5). b, Colonies containing different gates were spotted to mimic the spatial arrangement of each logic circuit (Fig. 3b). For each circuit, the final colony was assayed by flow cytometry for all combinations of inducers added to the plate. The data correspond to the cytometry distributions in Supplementary Figure 6. Fluorescence values and their error bars are calculated as mean ± s.d. from three experiments. NIMPLY, NOT IMPLY.