FIGURE 2 

Illustration of principal component analysis (PCA) applied to dose–response curves of receptor activity to obtain principal modes of data variation. Receptor activity at various concentrations of attractant (MeAsp) was measured through in vivo FRET for E. coli cells expressing only Tar receptors. (A) Measured dose–response curves show large variability, as exemplified by M=7 individual curves for the receptor modification state QEQE in a cheRcheB mutant. (B) Illustration of a scatter plot of data from (A) in a space of dimension D equal to the number of different attractant concentrations (projected onto two dimensions for clarity). Each data point (square) corresponds to one dose–response curve. The average dose–response curve is shown as an open circle. PCA involves diagonalizing the covariance matrix C, where the principal components—eigenvectors _i and eigenvalues _i of C with i=1,..., D—indicate the direction and magnitude of variation of the data. The sum of the eigenvalues equals the total variance of the data. The open square illustrates our practice of leaving out one data point when determining the optimal number of principal components to be included for fitting (see Supplementary Figure 6B).