Genetic control of encoding strategy in a food-sensing neural circuit.

Neuroendocrine circuits encode environmental information via changes in gene expression and other biochemical activities to regulate physiological responses. Previously, we showed that daf-7 TGFβ and tph-1 tryptophan hydroxylase expression in specific neurons encode food abundance to modulate lifespan in Caenorhabditis elegans, and uncovered cross- and self-regulation among these genes (Entchev et al., 2015). Here, we now extend these findings by showing that these interactions between daf-7 and tph-1 regulate redundancy and synergy among neurons in food encoding through coordinated control of circuit-level signal and noise properties. Our analysis further shows that daf-7 and tph-1 contribute to most of the food-responsiveness in the modulation of lifespan. We applied a computational model to capture the general coding features of this system. This model agrees with our previous genetic analysis and highlights the consequences of redundancy and synergy during information transmission, suggesting a rationale for the regulation of these information processing features.

Introduction

Signaling pathways convey information about the environment, enabling organisms to generate appropriate physiological response to changing conditions (Gendron et al., 2015). We recently established that tph-1 tryptophan hydroxylase expressed in ADF and NSM neurons and daf-7 TGF expressed in ASI neurons in Caenorhabditis elegans transmit environmental information to physiology by modulating the response of lifespan to food (Entchev et al., 2015). Our previous analytical framework estimated the accuracy of tph-1 and daf-7 expression in decoding food input; however, it could not reveal the type of encoding strategy used by tph-1 and daf-7 within these neurons, nor could it quantify the contribution of these genes to lifespan modulation. Here, we applied information theory (Shannon, 1948) to address these issues. Information theory has been proposed as a general framework to characterize how biological signals are encoded and transmitted (Bowsher and Swain, 2014; Levchenko and Nemenman, 2014) and has been used to study information processing in the nervous system (Borst and Theunissen, 1999) as well as biochemical and genetic pathways (Cheong et al., 2011; Tkačik et al., 2015).

Groups of neurons can encode information redundantly or synergistically (Brenner et al., 2000; Puchalla et al., 2005). This form of informational redundancy is conceptually distinct from genetic redundancy. Redundant encoding systems replicate the same information in more than one neuron, analogous to a computer backup, which provides robustness to perturbations in single neurons at the expense of coding efficiency. In contrast, synergistic circuits encode more information than the sum of their component neurons, but this efficiency is vulnerable to disruptions in the constituent neurons. Redundancy and synergy have been defined using information-theoretic measures (Averbeck et al., 2006; Schneidman et al., 2003), and both of these strategies for encoding information have been characterized in many neural and genetic circuits (Averbeck et al., 2006; Puchalla et al., 2005; Schneidman et al., 2011; Tkačik et al., 2015; Tkačik and Walczak, 2011).

Previously, we identified regulatory interactions among tph-1 and daf-7 that influence their coding accuracy (Entchev et al., 2015). Here, we show that cross-talk between daf-7 and tph-1 further affects the adoption of redundancy or synergy during discrimination between food levels. We found that the regulation of signal-to-noise in gene expression underlies shifts between redundancy and synergy across genotypes. Finally, we use a computational model to explore the consequences of redundant and synergistic coding at the level of downstream targets.

Results and discussion

Information theory allows us to quantify the information encoded by daf-7 and tph-1 based on the overlap of their expression distributions (Figure 1A). By associating environmental stimuli (food level) and neuronal responses (gene expression) with the input and the output of a communication system, the encoding capacity of ASI, ADF, and NSM is given by the mutual information (MI) between gene expression responses (G) and food stimuli (F),

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

(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

DOI: http://dx.doi.org/10.7554/eLife.24040.004

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

(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

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

(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

(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 (). A total of 400 animals were imaged in this experiment.

DOI: http://dx.doi.org/10.7554/eLife.24040.009

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

(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 -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

(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

where denotes the chances of encountering the food condition , is the response under each specific food level, and is the average response across all the food stimuli (see Appendix and Figure 1—figure supplement 5). The MI measures the ability of the gene expression response to discriminate between food conditions.

Figure 1—figure supplement 5.

Information and redundancy by food level.

(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

Information and redundancy across genotypes.

Fluorescence values for animals carrying both Pdaf-7::mCherry and Pdaf-7::Venus across four food levels for Figure 1—figure supplement 2.

Optimal input distributions for ADF, ASI and NSM neurons across genotypes (data for Figure 1—figure supplement 3).

Validation of information and redundancy estimates for Figure 1—figure supplement 4.

Information, redundancy, and optimal input distribution by food level across genotypes.

Schematic of experimental and analytical workflow.

Robustness of information theoretic analyses.

To define the redundancy of the system (Schneidman et al., 2003), we considered the difference between the sum of the information independently encoded by gene expression in the ADF, ASI, and NSM neurons, and the MI obtained from their combinatorial expression (Figure 1B):

Conceptually, redundancy occurs when the whole is less than the sum of parts (), whereas synergy occurs when the whole is greater than the sum of parts () (Figure 1B).

This analysis revealed that ASI, ADF, and NSM neurons encode bits of information about food abundance in wild-type animals (Figure 1C), which is in the same range of information encoded by other biochemical pathways (Cheong et al., 2011), and it is consistent with the requirement for sensing the two states (boom or bust) experienced by C. elegans in the wild (Félix and Braendle, 2010). Approximately 40% of this information is encoded redundantly in wild-type animals (Figure 1D–E), consistent with the genetic evidence that tph-1 and daf-7 act in parallel pathways to modulate lifespan (Entchev et al., 2015). tph-1(-) and daf-7(-) mutants show respective increases and decreases in food information (Figure 1C), consistent with our prior decoding analysis. tph-1(-) mutants also show a modest decrease in the fraction of redundant information (Figure 1E), suggesting that the added information is more efficiently but less robustly encoded.

Remarkably, changes in the expression distributions of the daf-7 and tph-1 reporters in daf-7(-) mutants shift the encoding strategy of ASI, ADF, and NSM from redundancy to synergy (Figure 1C–D), such that of the total information in the circuit is now encoded synergistically (Figure 1E). This effect is not due to the loss of ASI function in daf-7(-) mutants, as we observed the same shift to synergy when only tph-1(-) expressing neurons are analyzed (Figure 1F–H), indicating that crosstalk between daf-7 and tph-1 as well as daf-7 autoregulation control the coding strategy adopted by the circuit. Importantly, the coding strategy shift is daf-7-specific, as disruption of tph-1 does not result in a similar phenotype (Figure 1C). In the tph-1(-); daf-7(-) double mutant, cross- and self-regulation are abolished, and ASI, ADF, and NSM neurons approach the independence regime () (Figure 1C–E), confirming the idea that redundancy and synergy arise from the communication between neurons via daf-7 and tph-1.

The same information-theoretic analysis can be applied to quantify more directly the contribution of daf-7 and tph-1 to the food-responsiveness of the physiological output. The lifespan response to food abundance consists of bits of information in wild-type animals, and approximately 80% of this food information is lost in the tph-1(-); daf-7(-) double mutant (Figure 1I), strengthening our previous assertion that the majority of the food information encoded in the lifespan response is mediated by tph-1 and daf-7. While other genetic pathways may also play important roles, this central role of tph-1 and daf-7 suggests that their coding features weigh heavily on the physiological outcome.

Multicellular coding strategies rely on response correlations between cells (Schneidman et al., 2003). Specifically, redundancy can be dissected into two components: the signal correlation, which reflects correlated average responses (Figure 2A) and increases redundancy; and the noise correlation, which captures co-fluctuations among different cells under fixed food levels (Figure 2B–C) and promotes synergy (Schneidman et al., 2003) (Appendix). As opposed to the wild-type animals, where the negligible value of noise correlation leads to redundancy (Figure 2D–E), all mutants display a general increase of noise correlations. tph-1(-) animals retain redundancy by compensating this effect with an increase of signal correlation; however, this balance shifts in the daf-7(-) mutant due to the dramatic reduction of signal correlation (Figure 2F), bringing the system to the synergistic regime (Figure 1D). The tph-1(-); daf-7(-) double mutant has nearly equal signal and noise correlations which generate independent encoding.

Figure 2.

Signal and noise correlations influence redundancy and synergy.

(A–B) Hypothetical expression distributions of two neurons at three food levels, illustrating signal and noise correlations and their effects on redundancy (Schneidman et al., 2003). Centre: their 2D distributions. Top and side: the distributions of each neuron. Signal correlation between two neurons across three food levels, and noise correlation at one selected food level are denoted by dotted lines marked ‘S’ and ‘N’ in (A) and (B), respectively. (C) shows how signal and noise correlations are related to redundancy and synergy as previously established (Schneidman et al., 2003). When signal correlations are higher (A), each neuron provides similar information (top and side distributions), reflecting redundancy. When noise correlations are higher (B), the combinatorial expression shows reduced overlaps and contains more information than individual neurons, providing synergy. (D–E) The effects of daf-7 and tph-1 on redundancy and synergy are explained by their effects on the signal correlation (D) and noise correlation (E). (F) Signal and noise correlation in each genotype and their relation to redundancy and synergy as indicated in (C).

DOI: http://dx.doi.org/10.7554/eLife.24040.013

DOI: http://dx.doi.org/10.7554/eLife.24040.014

Signal and noise correlations across genotypes.

Redundancy and synergy is strongly affected by noise and correlation among neurons. To characterize their effects, we rescaled noise and correlations in the original response distributions of daf-7 and tph-1 over a biologically relevant range (Figure 3, Appendix). In wild-type animals, redundancy is highly sensitive to noise, and weakly sensitive to correlation, providing a rationale for daf-7 in noise reduction (Entchev et al., 2015). tph-1(-) mutants displayed increased sensitivity to both noise and correlations. Redundancy in daf-7(-) mutants was more sensitive to correlation than noise, a reversal of the wild-type situation. tph-1(-); daf-7(-) double mutants were less sensitive to noise and correlations than either single mutant. These results suggest that the sensitivity of redundancy to noise is controlled by daf-7, while robustness to correlation is maintained by both daf-7 and tph-1.

Figure 3.

Interplay between noise and correlation affects redundancy.

(A) Heat maps showing redundancy when correlation and noise are scaled from their baseline values in wild-type and mutants. Redundancy values are indicated by legend. Contour lines denote equal redundancy. The number of contour lines crossed along each axis indicates the sensitivity to that parameter. (B) The steps leading from genes to coding strategy.

DOI: http://dx.doi.org/10.7554/eLife.24040.015

Heat maps showing how channel capacity (A), signal correlation (B) and noise correlation (C) vary under a rescaling of the baseline covariance matrix. For this analysis, response distributions were modeled using multivariate normal distributions (see Appendix).

DOI: http://dx.doi.org/10.7554/eLife.24040.016

Sensitivity analysis of channel capacity, signal, and noise correlation.

Redundancy or synergy in daf-7 and tph-1 expressing neurons serves as one constraint but does not necessarily lead to the same coding strategy in their targets. The coding strategy used by these targets will depend on their connectivity to ASI, ADF, and NSM, as well as their noise, correlation, and dynamic range. Since little is known about the immediate targets of TGF and serotonin signaling in relation to the food response in C. elegans, we considered a minimal model of three ideal sensors detecting an input and transmitting to a target that integrates linearly their signals (Figure 4A, Appendix). This simple model shows that decreasing signal-to-noise ratio favors synergy (Figure 4B, Appendix), in agreement with the observation that daf-7(-) mutants show reduced signal-to-noise, and adopt synergistic encoding (Figure 1D–F). This model also explains the decrease in synergy in tph-1(-); daf-7(-) double mutants compared to daf-7(-) single mutants (Figure 1D–F): loss of tph-1 increases signal separation (Entchev et al., 2015), which increases signal-to-noise, thus reducing synergy. Thus, that signal-to-noise ratios can contribute significantly to the coding strategy.

Figure 4.

Computational model reveals advantages of redundancy.

(A) Model for information encoding and transmission, where three sensors activate one target that integrates their signals linearly (see Appendix). (B) Effect of signal-to-noise ratio on coding strategy. (C) Effect of coding strategy on transmitted information. (D) Sensors that transmit more information tend to use redundancy.

DOI: http://dx.doi.org/10.7554/eLife.24040.017

(A) Illustration of the model. represent single sensors receiving information from the binary input. The sensor response is then combined linearly by the output. (B) The joint sensor response distribution is modeled as a three-dimensional Gaussian centered at input-dependent average values. (C, D, E, F) display the result of the numerical analysis of the model. Each point represents a specific choice of the parameters used in the model. For all sampled parameter sets (), we obtained the relevant information-theoretic measures shown. Red and blue colors are used to distinguish redundant and synergistic regimes, respectively. (G) The sampled conditions sliced according to dynamic range () and noise () (left). Redundant configurations populating the low signal-to-noise ratio () provide typically low information. becomes a discriminant between redundancy and synergy when applying a non-zero cutoff to the information encoded by the sensors (right). (H) Fraction of redundant/synergistic configurations obtained by in the numerical exploration of the model (left). When sensors are required to encode a minimum level of information, parametric configurations with low are forced to be synergistic, providing a rational for the coding strategy switch observed in daf-7(-).

DOI: http://dx.doi.org/10.7554/eLife.24040.018

Gaussian model of sensory neurons and information transmission.

Our model also illustrates the advantages of redundancy in the case of linear integration. Redundant strategies increase the minimum information transmitted to a downstream target when compared to a synergistic encoding (Figure 4C). Additionally, redundant encoding not only allows higher information transmission, but can also be accommodated by a broader set of signaling parameters (Figure 4D), avoiding the need to fine tune biological properties. When considering lifespan as the downstream target, our model suggests that lifespan responsiveness to food should decrease in daf-7(-) mutants, because wild-type animals employ redundancy, whereas daf-7(-) mutants employ a synergistic encoding. Indeed, we find that the ability to accurately discriminate between different food inputs based on lifespan is degraded in daf-7(-) mutants (Figure 1I) (Entchev et al., 2015).

By extending the analysis of our previous work, we have found that the ADF, NSM and ASI neurons employ a redundant strategy to encode food information. Critically, this redundant encoding strategy is controlled by daf-7 TGF and modified by tph-1 tryptophan hydroxylase; this is a novel effect of neuromodulators on circuit function. In particular, we revealed two roles for daf-7: as an encoder of food information, and as a regulator of redundancy via regulation of tph-1. In principle, redundancy and synergy could be specified by many different biological mechanisms, with obvious candidates being developmental changes in sensor types or numbers in a neural circuit. These mechanisms are ruled out in daf-7(-) and tph-1(-) animals, as the mutations do not affect the development of the ASI, ADF, and NSM neurons, which remain food-responsive. Instead, we show that daf-7 and tph-1 influence information processing via effects on the signal and noise properties of these sensory neurons, and on their correlations, representing additional roles for these genes in controlling information encoding. The discovery of other genes that regulate the signal-to-noise ratio will likely provide further insights into genetic regulatory mechanisms that modulate neural coding.

Computational methods

Minimization and quantification of experimental noise

Information theory relies on accurate estimates of response distributions, requiring the minimisation of experimental variability. We took several steps to achieve this. First, we only considered animals oriented in a dorso-ventral position. The microfluidic chip was constructed to bias animals towards this correct orientation, the orientation was checked during automated cell identification and verified manually, ensuring that only image stacks with animals in dorso-ventral orientations were used in the analysis. Second, we used direct imaging of transcriptional fusions to fluorescent protein reporters integrated in single copy. This approach ensures that biological variance in promoter activity is not artificially washed out by averaging in conventional high-copy reporters that are more traditionally used to generate C. elegans transgenics. Using fluorescent reporters also eliminates experimental noise associated with antibody staining due to variability in fixation, in permeabilizing the C. elegans cuticle, and in signal amplification from secondary antibodies. Third, we minimized bleaching by using a combination of low excitation from an LED light source, and rapid image acquisition using a Piezo Z stage (Prior Scientific) that precisely moves the sample in the Z axis at high speed.

In addition, we used simultaneous quantification of mCherry and Venus/YFP driven by the same promoter to estimate our experimental noise (Figure 1—figure supplement 2). We generated animals with Pdaf-7::mCherry and Pdaf-7::Venus reporters integrated at single copy in precise genomic locations on LG I and LG II, respectively (Figure 1—figure supplement 2A). These animals were shifted to four different food levels and imaged 1 day after the food shift. This experimental measurement incorporates experimental noise associated with different fluorescent proteins (mCherry and Venus) and different chromosomal locations for reporters, as well as other methodological noise. We found that the two measurements were in good agreement (, Figure 1—figure supplement 2B). Dissecting the variance in these measurements showed that 30% () of the observed variability in these measurements was due to variability between the mCherry and Venus readouts. We note that this variability includes intrinsic noise as the reporters are on different chromosomes; the actual experimental variability would therefore be lower, since intrinsic noise is non-zero.

Figure 1—figure supplement 2.

Experimental variability.

(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 (). A total of 400 animals were imaged in this experiment.

DOI: http://dx.doi.org/10.7554/eLife.24040.009

Computational analysis

The computational analysis of all the data was performed using custom-made C++ programs and built-in implementations of standard multivariate analysis algorithms in R (R Core Team, 2016). C++ programs are available through GitHub repositories (https://github.com/giovannidiana/Information, https://github.com/giovannidiana/KDE and https://github.com/giovannidiana/ModelRS). Mathematical details of these procedures and the results are discussed in the Appendix.

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

[Editors’ note: minor issues and corrections have not been included, so there is not an accompanying Author response.]

Thank you for submitting your article "Genetic Control of Encoding Strategy in a Food-sensing Neural Circuit" for consideration as a Research Advance by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor (Oliver Hobert) and a Senior Editor. The reviewers have opted to remain anonymous.

The reviewers have discussed the reviews with one another and are in agreement that this work qualifies as an interesting Research Advance to your original eLife paper.

The only comment we would like you address is extremely minor in nature: Figure 1—figure supplement 3: panels A-D are shown, but the legend refers to A-E.

Figure 1—figure supplement 3.

Neurons differ in their optimal input distributions.

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