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. 2017 Feb 7;6:e24040. doi: 10.7554/eLife.24040

Figure 1. Redundancy and synergy in a gene expression code.

(A) Information content depends on the overlap between gene expression distributions under different environmental conditions, which in turn depends on both the response magnitude (signal) and the variability across the population (noise). (B) Diagrams illustrating redundancy versus synergy, calculated as the difference between the whole (combinatorial information in NSM/ASI/ADF; darkest bar) and the sum of parts (information in NSM + ASI + ADF; stacked bars). (C–E) Analysis of redundancy and synergy based on tph-1 expression in ADF and NSM, and daf-7 expression in ASI. Genotype color key: Wild-type (black), tph-1(-) (blue), daf-7(-) (red), and tph-1(-); daf-7(-) (purple). (C) Effect of tph-1(-) and daf-7(-) mutations on food encoding in the whole circuit (darkest bars) and the sum of parts (lighter stacked bars). (D) Effect of tph-1(-) and daf-7(-) on redundancy and synergy among ADF, NSM, and ASI, as defined in Equation 2 and (B). As described in Equation 2 and in the main text, redundancy and synergy are indicated by positive and negative R values, respectively. (E) Fraction of redundant or synergistic information in ADF, NSM, and ASI, which is the amount of redundancy or synergy in (D) normalized to the information encoded. (F–H) Analysis of redundancy and synergy only in the tph-1 expressing neurons, ADF, and NSM. (F) Effect of daf-7(-) in the information encoded by tph-1 expression in ADF and NSM (darkest bars) and the sum of their parts (lighter stacked bars). (G) Effect of daf-7(-) on redundancy/synergy of ADF and NSM. (H) Fraction of redundant or synergistic information in tph-1 expression in ADF and NSM, which is the amount of redundancy or synergy in (G) normalized to the total information encoded from (F). (I) Loss of tph-1 and daf-7 degrades information about food abundance at the level of lifespan responses.

DOI: http://dx.doi.org/10.7554/eLife.24040.002

Figure 1—source data 1. Information and redundancy across genotypes.
(Tab 1) Combinatorial mutual information in the NSM/ASI/ADF neural circuit (‘Whole’ column) and the individual mutual information in ADF, ASI and NSM neurons across different genotypes. (Tab 2) Combinatorial information in the NSM and ADF neurons (‘Whole’ column) and the individual information in ADF and NSM neurons in wild-type and daf-7(-) strains. (Tab 3) Mutual information in the lifespan response of different genotypes. All values are presented as bits ± error.
DOI: http://dx.doi.org/10.7554/eLife.24040.003
elife-24040-fig1-data1.xlsx (11KB, xlsx)
DOI: 10.7554/eLife.24040.003
Figure 1—source data 2. Fluorescence values for animals carrying both Pdaf-7::mCherry and Pdaf-7::Venus across four food levels for Figure 1—figure supplement 2.
DOI: http://dx.doi.org/10.7554/eLife.24040.004
elife-24040-fig1-data2.xlsx (17.3KB, xlsx)
DOI: 10.7554/eLife.24040.004
Figure 1—source data 3. Optimal input distributions for ADF, ASI and NSM neurons across genotypes (data for Figure 1—figure supplement 3).
Optimal input distributions obtained by maximizing the information encoded individually by ADF, ASI, and NSM neurons. Values are presented as probabilities ± uncertainty.
DOI: http://dx.doi.org/10.7554/eLife.24040.005
elife-24040-fig1-data3.xlsx (11.3KB, xlsx)
DOI: 10.7554/eLife.24040.005
Figure 1—source data 4. Validation of information and redundancy estimates for Figure 1—figure supplement 4.
(Tab 1) Information (MI/channel capacity) and redundancy encoded by food-responsive gene expression in wild-type animals computed using different methodologies for density estimation. From left to right: plug-in method, least squares cross-validation, and smoothing cross-validation (kernel density estimation with fixed bandwidth selection), balloon estimator (kNN), Jack-knife correction of sample size bias. (Tab 2) Jack-knife analysis for information and redundancy across all genotypes. Values are calculated using a fraction of the total dataset indicated in first column.
DOI: http://dx.doi.org/10.7554/eLife.24040.006
elife-24040-fig1-data4.xlsx (11.8KB, xlsx)
DOI: 10.7554/eLife.24040.006
Figure 1—source data 5. Information, redundancy, and optimal input distribution by food level across genotypes.
Data for Figure 1—figure supplement 5. Mutual information of ADF, ASI, and NSM neurons, redundancy and optimal input distribution of the whole circuit by food level across genotypes.
DOI: http://dx.doi.org/10.7554/eLife.24040.007
elife-24040-fig1-data5.xlsx (11.1KB, xlsx)
DOI: 10.7554/eLife.24040.007

Figure 1.

Figure 1—figure supplement 1. Schematic of experimental and analytical workflow.

Figure 1—figure supplement 1.

(A) Experimental procedure for imaging gene expression responses to different food levels in adult C. elegans. Animals carrying fluorescent reporters were cultured and exposed to six food levels. A custom microfluidics-based platform was used for quantitative high-throughput imaging of the reporters. (B) Image analysis pipeline to identify individual neurons and quantify their fluorescence. (C) Information theoretic analysis for dissecting coding strategy in multicellular gene expression circuits. We first used a kernel density estimator to obtain gene expression response probabilities from our data. Next, we obtained theoptimal food distributions and the maximal mutual information between food stimuli and gene expression response. This analysis highlights the relationships between several parameters that describe the multi-neuron gene expression responses (light green boxes) and their contributions to the overall encoding strategy (dark green box).
DOI: http://dx.doi.org/10.7554/eLife.24040.008

Figure 1—figure supplement 2. Experimental variability.

Figure 1—figure supplement 2.

(A) Animals carrying Pdaf-7::mCherry and Pdaf-7::Venus at different genomic locations were used to estimate experimental variability. (B) The strain described in (A) was shifted to four different food levels (legend) and then imaged simultaneously for mCherry and Venus fluorescence. The graph shows a good correlation between mCherry and Venus reporter expression (R=0.8319). A total of 400 animals were imaged in this experiment.
DOI: http://dx.doi.org/10.7554/eLife.24040.009

Figure 1—figure supplement 3. Neurons differ in their optimal input distributions.

Figure 1—figure supplement 3.

Optimal input distributions obtained by maximizing the information encoded individually by ADF, ASI and NSM neurons qualitatively differ. This feature may allow different neurons to detect different food input levels to broaden the sensory range of the whole circuit. The optimal input distribution for each neuron also differ by genotype: (A) wild-type, (B) tph-1(-) mutants, (C) daf-7(-) mutants, and (D) tph-1(-); daf-7(-) double mutants. Uncertainties are obtained from sampling the 80% of the data and taking the standard deviation.
DOI: http://dx.doi.org/10.7554/eLife.24040.010

Figure 1—figure supplement 4. Robustness of information theoretic analyses.

Figure 1—figure supplement 4.

(A) Information (MI/channel capacity) encoded by food-responsive gene expression in wild-type animals computed using different methodologies for density estimation. From left to right: plug-in method, least squares cross-validation, and smoothing cross-validation (kernel density estimation with fixed bandwidth selection), balloon estimator (kNN), Jack-knife correction of sample size bias. All this methods result in similar information values. (B) Information encoded by food-responsive gene expression in wild-type, tph-1(-), daf-7(-), and tph-1(-); daf-7(-) animals. The relative changes in information between different approaches do not display significant differences. (C) and (D) illustrate the same analysis for redundancy. The switch from redundancy in wild-type to synergy in daf-7(-) is consistently present for all the methodologies used. (E) Details of jack-knife analysis for information and redundancy across all genotypes. Information and redundancy values are calculated using a fraction of the total data indicated in the x-axis. Dashed line (bottom) indicates a redundancy value of zero, separating redundancy and synergy. Both information and redundancy are stable to the sample size, as indicated by the flat lines of best fit. Error bars are standard deviation derived from sampling 80% of the data.
DOI: http://dx.doi.org/10.7554/eLife.24040.011

Figure 1—figure supplement 5. Information and redundancy by food level.

Figure 1—figure supplement 5.

(A) The sum of information encoded by ADF, ASI, and NSM for each food level across different genotypes is indicated by stacked bars. Information in each neuron is indicated by the legend (bottom right). Dashed lines indicate the information encoded by the combinatorial gene expression in the whole circuit, which is constant across food levels (see Supplemental Materials and methods for mathematical details). (B) Redundancy values across food levels for each genotype. (C) The optimal distribution of food input that maximizes information encoded by the whole circuit.
DOI: http://dx.doi.org/10.7554/eLife.24040.012