Accurate information transmission through dynamic biochemical signaling networks

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Science  12 Dec 2014:
Vol. 346, Issue 6215, pp. 1370-1373
DOI: 10.1126/science.1254933

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  1. Fig. 1 Single-cell measurement of the dynamic response of ERK, Ca2+, and NF-κB.

    (A) Overview of single-cell data analyzed in this work. (B) Examples of single-cell response dynamic trajectories. (C to E) Temporal histograms of several representative dosages for ERK (C), Ca2+ (D), and NF-κB (E). Color intensity reflects the probability density of a cellular response magnitude at each time point. Y axis in (B) to (E) is the same for each pathway and is in arbitrary units (AU), representing the Förster resonance energy transfer (FRET) to cyan fluorescent protein (CFP) ratio reported by the EKARev ERK biosensor (C), intensity of Ca2+ indicator dye Fluo-4 (D), and ratio of nuclear to cytoplasmic localization of an enhanced yellow fluorescent protein (EYFP)–p65 reporter (E). (F) Violin plot of the maximally separable static response in the three signaling pathways. Shape width shows response distribution (areas are equal), and point is the median response in each condition. EGF, epidermal growth factor; ATP, adenosine triphosphate; LPS, lipopolysaccharide.

  2. Fig. 2 Information transmission capacity of static and dynamic ERK, Ca2+, and NF-κB responses.

    (A) Information transmission capacity calculated from static scalar response distribution based on single–time point measurements. (B) Information transmission capacity calculated from multivariate dynamic responses as a function of the dimension of the multivariate vector. The multivariate vector was subsampled using a uniform grid centered on the middle time point (fig. S19). (C) Comparison of the multivariate vector (V) measurement to the following scalar responses: maximum response amplitude (A), maximum response time (T), maximal rate of response (D), ratio of maximum response amplitude to initial response amplitude (R). Error bars are SEMs from six biological replicates for ERK and four for Ca2+, and SDs from five jackknife iterations for NF-κB (tables S1 to S3). The multivariate vector information transfer was significantly greater than all scalar measures (P < 0.05, Student’s t test, table S6).

  3. Fig. 3 Theoretical decomposition of information loss caused by intrinsic and extrinsic noise.

    (A) Graphical representation of the analytical expression for the gain in mutual information from overcoming intrinsic (cyan) and extrinsic (magenta) noise sources obtained from random linear Gaussian inputs and outputs with three parameters (19). (B) Information transmission capacity of dynamic (orange) and static (maximal response, purple) responses calculated using simulated trajectories from the computational model of ERK (22) with only the extrinsic noise contributing to cell response variability. (C) Example of ERK trajectory variability for two different inputs levels (red and blue). Variability was generated using a uniform distribution of a single parameter, MEK values, that was varied by ±20%. (D). Two-dimensional histogram (center) and marginal distributions (left and bottom) for the two input levels (shown in red and blue) at two time points (t = 9 and 24 min) from the trajectories in (C). Because only a single parameter was varried, the responses vary on a 1D curve. As a result, although the univariate marginal distributions show substantial response overlap, the 2D distribution shows completely separated response levels (inset).

  4. Fig. 4 Measured information gain is a result of ERK dynamics’ ability to mitigate extrinsic noise.

    Experimental measurement of the mutual information between ERK response and EGF measured as a function of the response signal-to-noise ratio (SNR). Each marker represents calculations of SNR and mutual information from the dynamic (dot) and maximal scalar (cross) responses of cells from an eight-well dose-response experiment. Data shown are calculated based on 535,107 single-cell responses from 29 experiments with six doses of MEK inhibitor U0126 (tables S4 and S5). Lines represent theoretical predictions of the mutual information as a function of SNR for three types of responses: static scalar (red line), redundant measurements where the multivariate response has no dynamics (dark and light blue lines) calculated based on two independent estimates of IER (19) (fig. S21), and dynamic response (orange) that can mitigate both intrinsic and extrinsic noise.