A synthetic genetic edge detection program

Abstract

Edge detection is a signal processing algorithm common in artificial intelligence and image recognition programs. We have constructed a genetically encoded edge detection algorithm that programs an isogenic community of E. coli to sense an image of light, communicate to identify the light-dark edges, and visually present the result of the computation. The algorithm is implemented using multiple genetic circuits. An engineered light sensor enables cells to distinguish between light and dark regions. In the dark, cells produce a diffusible chemical signal that diffuses into light regions. Genetic logic gates are used so that only cells that sense light and the diffusible signal produce a positive output. A mathematical model constructed from first principles and parameterized with experimental measurements of the component circuits predicts the performance of the complete program. Quantitatively accurate models will facilitate the engineering of more complex biological behaviors and inform bottom-up studies of natural genetic regulatory networks.

Figure 1

Bacterial edge detection. (A) Light is projected through a mask onto a large community (lawn) of bacteria grown on a Petri dish. The lawn computes the edges, or boundaries between light and dark regions, and visually presents the output. (B) To find the edges, bacteria in the dark produce a communication signal (green circles) that diffuses across the dark/light boundary. Bacteria in the dark cannot respond to the communication signal. Only bacteria that are exposed to light and receive the signal become positive for the expression of a visible reporter gene. The sum of this activity over the entire two-dimensional population is equivalent to the edges of the input image. (C) (Top) A NOT light gate (lightning box + adjacent triangle) drives a cell-cell communication circuit (green X) and an inverter (red Y + adjacent triangle). These two signals combine as inputs for a downstream AND gate (semi-circle) which drives the final output (Z). Because signal is inverted at Y, the gate driving Z can also be described as an X AND (NOT Y) gate, and it is referred to as such throughout this work. (Bottom) Z is produced in only one of four possible combinations of X and Y (presence of X, absence of Y). (D) Conversion of the edge detection algorithm into a molecular genetic system. (Left) The light-sensitive protein Cph8 is a chimeric sensor kinase bearing the photoreceptor domain of the Synechocystis phytochrome Cph1 and the kinase domain of E.coli EnvZ (Levskaya et al., 2005). Cph8 requires the covalently associated chromophore phycocyanobilin (PCB, blue pentagons) which is produced from heme by the products of the two constitutively expressed genes ho1 and pcyA (Gambetta and Lagarias, 2001). In the presence of red light, the kinase activity of Cph8 is inhibited, precluding the transfer of a phosphoryl group (light green circle) to the response regulator OmpR (orange dumbbell) and subsequent transcription from the ompC promoter (P_ompC). The dark sensor therefore functions as a NOT light transcriptional logic gate. (Center) luxI and cI are expressed polycistronically from the NOT light gate. LuxI is a biosynthetic enzyme from V.fischeri that produces the cell-cell communication signal 3-oxohexanoyl-homoserine lactone (AHL). CI is the transcriptional repressor protein from phage λ. AHL binds to the constitutively expressed transcription factor LuxR to activate expression from the P_lux-λ promoter while CI dominantly represses it. P_lux-λ therefore functions as an X AND (NOT Y) transcriptional logic gate. (Right) The output of P_lux-λ is lacZ, the product of which (β-galactosidase) cleaves a substrate in the media to produce black pigment (Experimental Procedures). The edge detection algorithm is encoded as 10,020 basepairs of DNA, carried on three plasmid backbones (Experimental Procedures).

Figure 2

Transfer functions of the dark sensor and X AND (NOT Y) logic gate. (A) The transfer function of the dark sensor is determined in batch culture (Experimental Procedures and Figure S4) and fit to a sigmoidal function (Equation 1). The error bars indicate ±1 standard deviation. (B) (Left) The transfer function of the X AND (NOT Y) logic gate as determined in batch culture experiments. AHL (X) was added exogenously to the growth media while CI (Y) levels were controlled by varying the intensity of light (Experimental Procedures and Figure S5). The data shown are single replicates of 5 assays taken over 5 separate days where the concentration of CI was altered in each assay. (Right) Mathematical Model. The output of f_logic (Equation 2) as a function of AHL and CI. β-galactosidase output levels (Z) for the experiment and the model are normalized by dividing by the output value in the absence of CI with maximum exogenous AHL (Experimental Procedures).

Figure 3

Construction of the edge detector from individual genetic circuits. Various combinations of the circuits are constructed and the effect on image processing is assayed (left) and compared to the mathematical model (right). The details of the genetic circuits and simulations are presented in the Experimental Procedures and Figure S2. (A) The bacterial photography circuit, where the β-galactosidase output is expressed directly under the control of the light-sensitive P_ompC1157 promoter. This produces a positive print of the projected image. (B) Cell-cell communication components are added by placing luxI under the control of the dark sensor and expressing luxR constitutively. This produces a positive image with an additional blurring component due to AHL diffusion. (C) A genetic inverter is inserted between the dark sensor input and the β-galactosidase output. This produces an inverted (negative) print of the image, where the light regions are printed as dark and vice-versa. (D) A population of cells programmed with the complete edge detector system produces black pigment only at the boundary between light and dark regions. The model solutions are reported in Miller units (color bars, right).

Figure 4

Edge detection of complex patterns. Circle (top), square (middle) and silhouette (bottom) images are projected onto lawns of bacteria programmed with the edge detector. Signal intensities and distances are shown under each bacterial lawn. For the asymmetrical silhouette pattern, the signal intensity profile is computed for a small horizontal rectangle centered at the two red arrows. The model solutions are reported in Miller units (color bars, right).

Figure 5

Quantitative comparison of model and experimental edges in one and two dimensions. (A) Comparison of the in vivo (black) and in silico (red) radial intensity profiles for the circle pattern. The average of three circle images (Figure S3) is shown along with the standard deviation (gray region) (Experimental Procedures). (B) The relationship between the intersection angle (θ = degrees of light) of edges and the signal intensity is shown. Six points with five different θ values are sampled from the silhouette plate in Figure 4 (circles). The background intensity is subtracted from each point and the data is divided by the maximum intensity value. For each intersection angle, the maximum edge intensity is computed from the solution of the model with a unit circle mask with θ degrees of light (solid line) (Experimental Procedures).