Figure 2

Decipherment of two input chemicals from output responses of E. coli cells. (a) Typical responses to l-Glu (left column) and l-Asn (right column). Output traces of CW bias show a common profile consisting of a strong attractant response immediately after chemical stimulation (CW bias ≅ 0.0) and a recovery phase returning to near initial CW bias after sufficient time. Each graph is coloured according to chemical species (purple, l-Glu; green, l-Asn). The concentrations of chemicals increase from top to bottom. (b) Construction of characteristic vectors. Individual vectors representing each CW bias trace were calculated by matching a geometric template consisting of 6 lines (L1–L6). The template shape (both amplitudes and durations of lines) was modified to fit CW bias traces and 15 arbitrary parameters were obtained (see SI for details). As examples, parameters of y₁, y₂ and y₄ are shown, where y1 is the duration of L2 and y₂ and y₄ are the amplitude and duration of L3, respectively. (c) Concentration dependencies of 2 indexes, \(y_{1} , y_{4}\), of characteristic vectors (all in Fig. S5). The values of \(y_{1} ,\; y_{4}\) (positions are indicated in b) of characteristic vectors obtained as response activities to l-Glu (purple) and l-Asn (green) are plotted. Each graph is coloured according to chemical species as in (a). Plot makers of ‘o’ indicate data used to successfully identify the blind samples, whereas ‘x’ indicates failure. Solid lines show model functions representing concentration dependencies. Based on these model functions, Bayesian estimation is performed using observation values of blind samples, and we decipher type of blind sample (see text for details). Dashed red lines, green and purple arrows are added as examples of observations for explanation. The accuracy rates of decipherment and model functions were evaluated with leave-one-out cross validation. (d) Accuracy rate of decipherment for attractants groups consisting of l-Glu (n = 32) and l-Asn (n = 32). The left bar shows the theoretical accuracy rate of RS (≅ 1/2). The black line on left bar represents the standard deviation calculated numerically (± 0.09 =  ± 5.7/64, see Table S1 and SI for details). The right bar shows the accuracy rate by DeSIRAM (decipherment accuracy = 0.91). The probability of an accurate identification rate of 0.91 by RS was 4.1 × 10⁻¹². This small probability confirms the validity of the procedure.