The ability to sense the environment is heterogeneously distributed in cell populations

Reviewer #1 (Public Review):

The manuscript by Goetz et al. takes a new perspective on sensory information processing in cells. In contrast to previous studies, which have used population data to build a response distribution and which estimate sensory information at about 1 bit, this work defines sensory information at the single cell level. To do so, the authors take two approaches. First, they estimate single cells' response distributions to various input levels from time-series data directly. Second, they infer these single-cell response distributions from the population data by assuming a biochemical model and extracting the cells' parameters with a maximum-entropy approach. In either case, they find, for two experimental examples, that single-cell sensory information is much higher than 1 bit, and that the reduction to 1 bit at the population level is due to the fact that cells' response functions are so different from each other. Finally, the authors identify examples of measurable cell properties that do or do not correlate with single-cell sensory information.

The work brings an important and distinct new insight to a research direction that generated strong interest about a decade ago: measuring sensory information in cells and understanding why it is so low. The manuscript is clear, the results are compelling, and the conclusions are well supported by the findings. Several contributions should be of interest to the quantitative biology community (e.g., the demonstration that single cells' sensory information is considerably larger than previously implied, and the approach of inferring single-cell data from population data with the help of a model and a maximum-entropy assumption).

Reviewer #2 (Public Review):

In this paper the authors present an existing information theoretic framework to assess the ability of single cells to encode external signals sensed through membrane receptors.

The main point is to distinguish actual noise in the signaling pathway from cell-cell variability, which could be due to differences in their phenotypic state, and to formalize this difference using information theory.

After correcting for this cellular variability, the authors find that cells may encode more information than one would estimate from ignoring it, which is expected. The authors show this using simple models of different complexities, and also by analyzing an imaging dataset of the IGF/FoxO pathway.

The implications of the work are limited because the analysed data is not rich enough to draw clear conclusions. Specifically,
- the authors do not distinguish what could be methodological noise inherent to microscopy techniques (segmentation etc), and actual intrinsic cell state. It's not clear that cell-cell variability in the analyzed dataset is not just a constant offset or normalization factor. Other authors (e.g. Gregor et al Cell 130, 153-164) have re-centered and re-normalized their data before further analysis, which is more or less equivalent to the idea of the conditional information in the sense that it aims to correct for this experimental noise.
- in the experiment, each condition is shown only once and sequentially. This means that the reproducibility of the response upon repeated exposures in a single cell was not tested, casting doubt on the estimate of the response fidelity (estimated as the variance over time in a single response).
- another dataset on the EGF/EGFR pathway is analyzed, but no conclusion can be drawn from it because single-cell information cannot be directly estimated from it. The authors instead use a maximum-entropy Ansatz, which cannot be validated for lack of data.

Reviewer #3 (Public Review):

Goetz, Akl and Dixit investigated the heterogeneity in the fidelity of sensing the environment by individual cells in a population using computational modeling and analysis of experimental data for two important and well-studied mammalian signaling pathways: (insulin-like growth factor) IGF/FoxO and (epidermal growth factor) EFG/EFGR mammalian pathways. They quantified this heterogeneity using the conditional mutual information between the input (eg. level of IGF) and output (eg. level of FoxO in the nucleus), conditioned on the "state" variables which characterize the signaling pathway (such as abundances of key proteins, reaction rates, etc.) First, using a toy stochastic model of a receptor-ligand system - which constitutes the first step of both signaling pathways - they constructed the population average of the mutual information conditioned on the number of receptors and maximized over the input distribution and showed that it is always greater than or equal to the usual or "cell state agnostic" channel capacity. They constructed the probability distribution of cell state dependent mutual information for the two pathways, demonstrating agreement with experimental data in the case of the IGF/FoxO pathway using previously published data. Finally, for the IGF/FoxO pathway, they found the joint distribution of the cell state dependent mutual information and two experimentally accessible state variables: the response range of FoxO and total nuclear FoxO level prior to IGF stimulation. In both cases, the data approximately follow the contour lines of the joint distribution. Interestingly, high nuclear FoxO levels, and therefore lower associated noise in the number of output readout molecules, is not correlated with higher cell state dependent mutual information, as one might expect. This paper contributes to the vibrant body of work on information theoretic characterization of biochemical signaling pathways, using the distribution of cell state dependent mutual information as a metric to highlight the importance of heterogeneity in cell populations. The authors suggest that this metric can be used to infer "bottlenecks" in information transfer in signaling networks, where certain cell state variables have a lower joint distribution with the cell state dependent mutual information.

The utility of a metric based on the conditional mutual information to quantify fidelity of sensing and its heterogeneity (distribution) in a cell population is supported in the comparison with data. Some aspects of the analysis and claims in the main body of the paper and SI need to be clarified and extended.

1. The authors use their previously published (Ref. 32) maximum-entropy based method to extract the probability distribution of cell state variables, which is needed to construct their main result, namely p_CeeMI (I). The salient features of their method, and how it compares with other similar methods of parameter inference should be summarized in the section with this title. In SI 3.3, the Lagrangian, L, and Rm should be defined.
2. Throughout the text, the authors refer to "low" and "high" values of the channel capacity. For example, a value of 1-1.5 bits is claimed to be "low". The authors need to clarify the context in which this value is low: In some physically realistic cases, the signaling network may need to simply distinguish between the present or absence of a ligand, in which case this value would not be low.
3. Related to (2), the authors should comment on why in Fig. 3A, I_Cee=3. Importantly, where does the fact that the network is able to distinguish between 23 ligand levels come from? Is this related to the choice (and binning) of the input ligand distribution (described in the SI)?
4. The authors should justify the choice of the gamma distribution in a number of cases (eg. distribution of ligand, distribution cell state parameters, such as number of receptors, receptor degradation rate, etc.).
5. Referring to SI Section 2, it is stated that the probability of the response (receptor binding occupancy) conditioned on the input ligand concentration and number of receptors is a Poisson distribution. Indeed this is nicely demonstrated in Fig. S2. Therefore it is the coefficient of variation (std/mean) that decreases with increasing R0, not the noise (which is strictly the standard deviation) as stated in the paper.
6. In addition to explicitly stating what the input (IGF level) and the output (nuclear GFP-tagged FoxO level) are, it would be helpful if it is also stated what is the vector of state variables, theta, corresponding to the schematic diagram in Fig. 2C.
7. Related to Fig. 2C, the statement in the caption: "Phosphorylated Akt leads to phosphorylation of FoxO which effectively shuttles it out of the nucleus." needs clarification: From the figure, it appears that pFoxO does not cross the nuclear membrane, in which case it would be less confusing to say that phosphorylation prevents reentry of FoxO into the nucleus.
8. The explanations for Fig. 2D, E and insets are sparse and therefore not clear. The authors should expand on what is meant by model and experimental I(theta). What is CC input dose? Also in Fig. 2E, the overlap between the blue and pink histograms means that the value of the blue histogram for the final bin - and therefore agreement or lack thereof with the experimental result - is not visible. Also, the significance of the values 3.25 bits and 3 bits in these plots should be discussed in connection with the input distributions.
9. While the joint distribution of the cell state dependent mutual information and various biochemical parameters is given in Fig. S7, there is no explanation of what these results mean, either in the SI or main text. Related to this, while a central claim of the work is that establishing this joint distribution will allow determination of cell state variables that differentiate between high and low fidelity sensing, this claim would be stronger with more discussion of Figs. 3 and S7.
10. The related central claim that cell state dependent mutual information leads to higher fidelity sensing at the population level would be made stronger if it can be demonstrated that in the limit of rapidly varying cell state variables, the I_CSA is retrieved.