1. Cell Biology
  2. Computational and Systems Biology
Download icon

Limits on information transduction through amplitude and frequency regulation of transcription factor activity

  1. Anders S Hansen
  2. Erin K O'Shea  Is a corresponding author
  1. Howard Hughes Medical Institute, Harvard University, United States
  2. Harvard University, United States
Research Article
  • Cited 47
  • Views 3,739
  • Annotations
Cite this article as: eLife 2015;4:e06559 doi: 10.7554/eLife.06559

Abstract

Signaling pathways often transmit multiple signals through a single shared transcription factor (TF) and encode signal information by differentially regulating TF dynamics. However, signal information will be lost unless it can be reliably decoded by downstream genes. To understand the limits on dynamic information transduction, we apply information theory to quantify how much gene expression information the yeast TF Msn2 can transduce to target genes in the amplitude or frequency of its activation dynamics. We find that although the amount of information transmitted by Msn2 to single target genes is limited, information transduction can be increased by modulating promoter cis-elements or by integrating information from multiple genes. By correcting for extrinsic noise, we estimate an upper bound on information transduction. Overall, we find that information transduction through amplitude and frequency regulation of Msn2 is limited to error-free transduction of signal identity, but not signal intensity information.

https://doi.org/10.7554/eLife.06559.001

eLife digest

The way that a cell responds to an external stimulus is governed by a sequence of events called a signalling pathway. While cells are exposed to a wide range of external stimuli—such as different types of chemicals and different forms of radiation—the last stage of the signalling pathway usually involves a gene being expressed as a protein or some other gene product. The amount of protein that is produced depends on the intensity of the signal that reaches the end of the pathway.

Proteins called transcription factors have an important role in this gene expression stage, and it is quite common for several signalling pathways to pass through the same transcription factor. How does the cell ensure that the information travelling along a particular pathway reaches the relevant gene and that the correct level of gene expression takes place?

Biologists have been using information theory—a set of ideas developed by computer scientists and engineers—to understand signalling pathways at a fundamental level. It turns out that just as radio stations can broadcast on FM (which is short for frequency modulation) or AM (amplitude modulation), cells can do something similar. Msn2 is a transcription factor that is found in yeast: when the supply of glucose to the yeast cells is limited, Msn2 becomes active in short bursts, with the frequency of the bursts depending on the severity of the glucose shortage (which is similar to FM radio). However, when the yeast cells are exposed to chemicals that cause oxidative stress, Msn2 becomes active for prolonged periods, with the amplitude of this activity depending on level of oxidative stress (similar to AM radio).

In the language of information theory, the behaviour of Msn2 encodes two types of information: information about identity (short bursts of activity, or FM, mean that there is a shortage of glucose; sustained bursts, or AM, mean that the cell is experiencing oxidative stress), and information about intensity (that is, information about the severity of the glucose shortage or the level of oxidative stress). But how much of this information is transmitted to the relevant genes?

Hansen and O'Shea have used a combination of experiment and information theory to explore this question. For both the AM and FM cases, it is found that the cell can transmit the identity information but not the intensity information. However, the amount of information transmitted can be increased by having multiple copies of the same gene, by combining information from more than one gene, or by modifying a region of DNA called a promoter that is involved in the regulation of genes.

Finally, unlike radio broadcasting, where FM is generally favoured over AM, Hansen and O'Shea find that AM signalling is more reliable than FM signalling in cells. In the future, it will be a priority to investigate whether these results apply more generally beyond the Msn2 system in yeast.

https://doi.org/10.7554/eLife.06559.002

Introduction

Cellular signaling pathways often exhibit a bowtie topology (Csete and Doyle, 2004): multiple distinct signal inputs converge on a single master regulator, typically a transcription factor (TF), which then controls the expression of partially overlapping sets of downstream target genes. This raises two general questions: first, how can the cell encode information about different signals in the activity of a single master TF? Second, can this information be decoded by target genes to elicit a specific output for each input?

One way the cell can encode signal information is by regulating the activation dynamics of a single master TF (Figure 1A). For example, p53, a tumor suppressor TF, exhibits an intensity-dependent number of nuclear pulses in response to γ-radiation, but a sustained pulse of nuclear localization with intensity-dependent amplitude during UV-radiation (Lahav et al., 2004; Batchelor et al., 2011). Akin to p53, the yeast multi-stress response TF Msn2 exhibits short pulses of nuclear localization with intensity-dependent frequency under glucose limitation, but sustained nuclear localization with intensity-dependent amplitude under oxidative stress (Hao et al., 2013; Hao and O'Shea, 2012; Jacquet et al., 2003; Petrenko et al., 2013). Thus, p53 and Msn2 dynamics encode both signal identity and signal intensity. Beyond p53 and Msn2, amplitude- or frequency encoding of signal identity and intensity information is conserved throughout eukaryotic signaling pathways (see also Berridge et al., 2000; Werner et al., 2005; Cai et al., 2008; Warmflash et al., 2012; Albeck et al., 2013; Aoki et al., 2013; Imayoshi et al., 2013; Dalal et al., 2014; Harima et al., 2014). Such encoding of signal identity and intensity information in TF activation dynamics has led to the hypothesis that TF target genes can reliably decode this dynamical information to elicit distinct gene expression programs with fine-tuned expression levels (Figure 1A) (Behar et al., 2007; Behar and Hoffmann, 2010; de Ronde and ten Wolde, 2014; Hansen and O'Shea, 2013; Levine et al., 2013; Purvis and Lahav, 2013; Yosef and Regev, 2011).

Encoding and transmitting signal identity and intensity information in the dynamics of a single transcription factor (TF).

(A) Different signals (e.g., stress or ligand exposure) can be encoded in the dynamics of a single TF. Signal identity is encoded in the type of TF dynamics: a sustained pulse (signal A) or nuclear pulsing (signal B). Signal intensity (e.g., ligand concentration) is encoded in the amplitude for signal A, but in the frequency for signal B. Different dynamical patterns of TF activation can activate distinct, but specific, downstream gene expression programs. (B) Applying an information theoretic framework to cell signaling, a gene promoter can be considered a channel. A graded population-level dose–response belies the complexity of the single-cell response: it shows the mean expression at points a, b, c, and d, but not the width or variance of their distributions. (C) Two extreme models. In the ‘rheostat model’, signal intensity information encoded in the frequency or amplitude of a TF leads to non-overlapping gene expression distributions (a, b, c, and d). Thus, by reading the gene expression output the cell can accurately determine the input signal intensity and high information transmission is achieved. Conversely, in the ‘noisy switch model’, as a consequence of overlapping gene expression distributions (a, b, c, and d) information about signal intensity is permanently lost: the cell can distinguish ON/OFF (signal identity), but the expression of a target gene cannot be fine-tuned to the stress intensity.

https://doi.org/10.7554/eLife.06559.003

However, non-genetic cell-to-cell variability (noise) in gene expression limits the fidelity with which information can be decoded by TF target genes (Coulon et al., 2013; Sanchez and Golding, 2013). This is important because the capacity of any signaling pathway for information transduction is limited by the capacity of its weakest node or bottleneck (Cover and Thomas, 2006). Thus, even though information can reliably be encoded in TF activation dynamics (Selimkhanov et al., 2014), this information will be lost unless genes can reliably decode it. We therefore focus on the response of single genes and ask: can cells reliably transmit both signal identity and intensity information in the amplitude and frequency of TFs to target genes in the presence of biochemical noise? In other words, what are the limits on amplitude- and frequency-mediated information transduction? We investigate this by applying tools from information theory to quantify how much of the information (in bits) encoded in the amplitude and frequency of a TF can be transmitted through gene promoters to fine-tune the gene expression level.

Originally developed by Claude Shannon for communication systems (Shannon, 1948), information theory has recently been applied to cell signaling (reviewed in Tkacik and Walczak, 2011; Waltermann and Klipp, 2011; Nemenman, 2012; Rhee et al., 2012; Bowsher and Swain, 2014; Levchenko and Nemenman, 2014; Mc Mahon et al., 2014). Mutual information quantifies how much information an output can carry about an input across a noisy channel (Figure 1B). Mathematically, information is quantified in bits: to resolve two different signal intensities without error requires at least 1 bit of information, to resolve four different signal intensities without error requires at least 2 bits of information and so forth. However, 1 bit of information does not guarantee that two intensities can be distinguished without error. Similarly, 1 bit may allow multiple intensities to be distinguished, albeit with some associated error (Bowsher and Swain, 2014). As an example of how information theory can be applied, consider a dose–response relationship (Figure 1B). A graded population-level dose–response can belie the complexity of the single-cell response (Ferrell and Machleder, 1998). For example, if different TF amplitudes or frequencies lead to distinguishable gene expression outputs (points a, b, c and d), signal intensity information is accurately transmitted and the cell can fine-tune the expression of stress genes to the stress intensity like a ‘rheostat’ (Figure 1C, rheostat model). However, biochemical noise can degrade signal information: if gene expression outputs are no longer resolvable, the cell can no longer fine-tune the expression level of stress genes to stress intensity (Figure 1C, noisy switch model). In the noisy switch model, the cell can distinguish no stimulus (point a, OFF) from maximal stimulus (point d, ON)—but intermediate stimuli (points b and c) cannot reliably be distinguished based on the gene expression output and signal intensity information has been lost (Figure 1C). Information theory provides a framework for capturing and quantifying these differences. Thus, we can distinguish these two models by measuring information transduction by promoters: the noisy switch model requires ∼1 bit, whereas the rheostat model requires substantially higher mutual information.

Previous applications of information theory have been theoretical (Ziv et al., 2007; Tostevin and ten Wolde, 2009; Lestas et al., 2010; de Ronde et al., 2011; Bowsher and Swain, 2012; Rieckh and Tkacik, 2014) or have focused on upstream signaling and development (Gregor et al., 2007; Tostevin et al., 2007; Skerker et al., 2008; Tkacik et al., 2008, 2009; Mehta et al., 2009; Cheong et al., 2011; Dubuis et al., 2013; Uda et al., 2013; Selimkhanov et al., 2014; Voliotis et al., 2014). However, despite gene expression being the final bottleneck in cell signaling, gene expression has received little attention (Uda et al., 2013). Estimating an upper limit on the information transduction capacity of a gene has not previously been possible due to extrinsic noise: even when studying genetically identical single cells, the cells can exhibit non-genetic differences, that is, in cell cycle phase or variability in TF concentration, which means the measured mutual information will be an underestimate (Elowitz et al., 2002; Toettcher et al., 2013). Here, we overcome this limitation through a combined experimental and theoretical approach that corrects for extrinsic noise and allows us to estimate an upper limit on the information transduction capacity of individual Msn2 target genes.

We combine high-throughput microfluidics to control the amplitude and frequency of Msn2 nuclear translocation with information theory to determine the information transduction capacity of Msn2 target genes. We find that Msn2 target genes can transduce just over 1 bit of information, consistent with the ‘noisy switch model’. Although individual Msn2 target genes can only transduce little information, we illustrate how the cell can improve information transduction capacity by modulating promoter cis-elements, by integrating the response of more than one gene, or by having multiple copies of the same gene. We show that more information can be transduced through amplitude than through frequency modulation (FM) of Msn2 activation dynamics. Nevertheless, while previous studies have shown that significant amounts of information can be encoded in TF activation dynamics (Selimkhanov et al., 2014), we find that noise in the decoding step severely limits information transduction. Specifically, our results indicate that information about signal identity, but not signal intensity, can be transmitted nearly without error in the amplitude and frequency of Msn2 and decoded by Msn2-responsive promoters.

Results

Quantifying information transduction using information theory

Information theory quantifies information transduction across a channel between a signal and a response (Shannon, 1948; Cover and Thomas, 2006). If a channel is noisy, a given signal input will give rise to a distribution of response outputs. This represents a loss of information since the signal input can no longer reliably be learned from observing the response output (Figure 1B–C). A ‘black-box’-framework, information theory was originally developed for telecommunication channels, but it can also be applied to other ‘channels’ such as gene promoters or cell signaling pathways provided that the signal input (here amplitude or frequency of Msn2 activation) can be precisely controlled and the response output distribution precisely measured (here single-cell gene expression). Mutual information, MI(R;S), measured in bits, quantifies the amount of information about the signal input (S) that can be obtained by observing the response output (R) and, given discretized data, is defined as:

(1) MI(R;S)=i,jp(Ri,Sj)log2(p(Ri,Sj)p(Ri)p(Sj)).

The response distribution, p(R), is the experimentally measured distribution of gene expression output. The signal distribution, p(S), is the relative probability of each Msn2 amplitude or frequency. Since MI(R;S) depends on p(S) and since p(S), that is, how often a cell might be exposed to a particular intensity of oxidative stress, is unknowable, hereafter we consider the maximal mutual information, I (I(R;S)=maxp(S)[MI(R;S)]) which is the maximal amount of information that can be transduced through a ‘promoter channel’. I can be thought of as a channel capacity, though a gene promoter is effectively a ‘single-use’ channel and I therefore has units of bits, whereas messages are sent repeatedly through a Shannon channel and, accordingly, the channel capacity has units of bits/s ([Bowsher and Swain, 2014]; a detailed discussion is given in Supplementary file 2).

Natural Msn2 target genes have low information transduction capacities

To measure how much information Msn2 target genes can transduce, we took advantage of a pharmacological method for controlling Msn2 nuclear localization using a small molecule, 1-NM-PP1, (Bishop et al., 2000; Hao and O'Shea, 2012; Zaman et al., 2009) and high-throughput microfluidics coupled to quantitative time-lapse microscopy (Hansen et al., 2015; Hansen and O'Shea, 2013). With this setup (Figure 2—figure supplement 1A; Video 1), we can control and measure the amplitude and frequency of activation of an Msn2-mCherry fusion protein over time and generate single-cell traces that mimic the natural Msn2 dynamics under oxidative stress (a sustained nuclear pulse with signal intensity–dependent amplitude; Figure 2A) and glucose limitation (short pulses with signal intensity–dependent frequency; Figure 2B) (Hao and O'Shea, 2012; Petrenko et al., 2013). To measure stress-relevant gene expression, we use dual cyan and yellow fluorescent protein (CFP/YFP) reporters and focus on two specific Msn2 target genes: HXK1, which is induced under glucose limitation (Herrero et al., 1995) and SIP18, which is induced in response to oxidative stress (Rodriguez-Porrata et al., 2012). Using this setup, we have previously shown that, at the population level, individual genes differentially decode Msn2 dynamics (Hansen and O'Shea, 2013; Hao and O'Shea, 2012): oscillatory Msn2 activation induces gene class B (e.g., HXK1) without inducing gene class A (e.g., SIP18), whereas sustained Msn2 activation preferentially induces gene class A (Figure 1A). Thus, this represents an ideal setup for studying promoter decoding of Msn2 dynamics in single cells, which enables us to quantify information transduction.

Video 1
A typical experiment.

Mut B cells were grown in a microfluidic device and exposed to six 5-min Msn2 pulses separated by 10 min and phase contrast (top left), Msn2-mCherry (top right), CFP (bottom left), and YFP (bottom right) reporter expression monitored. Video 1 consists of 64 frames at 2.5 min resolution and images have been compressed, cropped, and contrast adjusted, but not corrected for photobleaching.

https://doi.org/10.7554/eLife.06559.004
Figure 2 with 2 supplements see all
Information transduction by promoters with respect to amplitude and frequency modulation.

(A) Cells containing either the hxk1::YFP or sip18::YFP reporter were exposed to either no activation or a 70-min pulse of seven increasing amplitudes from ca. 25% (100 nM 1-NM-PP1) to 100% (3 μM 1-NM-PP1) of maximal Msn2-mCherry nuclear localization and single-cell gene expression monitored. For each single-cell time-trace, YFP concentration is converted to a scalar by taking the maximal YFP value after smoothing. For each Msn2-mCherry input (a fit to the raw data is shown on the left (AM: Msn2 input)), the gene expression distribution is plotted as a histogram of the same color on the right for HXK1 and SIP18. The population-averaged dose–response (top) is obtained by calculating the YFP histogram mean for each Msn2 input condition. (B) Cells containing either the hxk1::YFP or sip18::YFP reporter were exposed to either no activation or from one to nine 5-min pulses of Msn2-mCherry nuclear localization (ca. 75% of maximal nuclear Msn2-mCherry, 690 nM 1-NM-PP1) at increasing frequency. All calculations were performed as in (A). (C) Cells containing either the pSIP18 mut A::YFP reporter or the pSIP18 mut B::YFP reporter were exposed to amplitude modulation (AM) as in (A). (D) Cells containing either the pSIP18 mut A::YFP reporter or the pSIP18 mut B::YFP reporter were exposed to frequency modulation (FM) as in (B). Maximal mutual information, I, and its error are calculated as described in Supplementary file 2. Full details on data processing are given in ‘Materials and Methods’. Each plot of an Msn2 input pulse and YFP expression is based on data from ca. 1000 cells from at least three replicates. All raw single-cell time-lapse microscopy source data for HXK1 (15,259 cells), SIP18 (21,242 cells), pSIP18 mut A (18,203 cells), and pSIP18 mut B (17,655 cells) for this Figure are available online as Supplementary file 1 and in (Hansen and O'Shea, 2015).

https://doi.org/10.7554/eLife.06559.005

To measure information transduction through the HXK1 and SIP18 promoters with respect to amplitude modulation (IAM), we exposed thousands of cells to increasing amplitudes of a 70 min Msn2 pulse to mimic oxidative stress, measured the single-cell distribution of responses for each amplitude with minimal measurement noise (Figure 2—figure supplement 2), and determined the population-averaged dose–response (Figure 2A; all raw single-cell data are available online as Supplementary file 1 and in (Hansen and O'Shea, 2015); see also Figure 2—figure supplement 1B). We quantify gene expression as the maximal YFP concentration after the YFP time-trace has reached a plateau (‘Materials and Methods’). Surprisingly, for both HXK1 and SIP18, IAM was 1.2–1.3 bits—enough to distinguish ON from OFF without error (the ‘no Msn2 input’ and the ‘brown’ distributions are clearly distinguishable; Figure 2A), but with limited ability to distinguish signal intensities. One way to think about this result is to ask, given the HXK1 YFP expression output, how much information does that provide about the input amplitude? For example, considering the HXK1 AM histograms in Figure 2A, for most YFP outputs the cell can exclude the ‘no Msn2 input’ condition, but appears to be unable to discern which of the other amplitudes it was exposed to without a high error rate. Consequently, HXK1 and SIP18 can distinguish no stress from high oxidative stress (high Msn2 amplitude) without error, but cannot accurately transmit information about stress intensity.

Next, we measured information transduction of HXK1 and SIP18 with respect to frequency modulation (IFM) using 5-min Msn2 pulses at frequencies similar to those observed under glucose limitation (Figure 2B). Even though HXK1 is physiologically induced during Msn2 pulsing, IFM was only 1.11 bits—again enough for distinguishing ON from OFF essentially without error like a ‘noisy switch’, but insufficient to accurately fine-tune the HXK1 expression level to each Msn2 frequency like a ‘rheostat’. SIP18, required only under oxidative stress, largely filters out Msn2 pulsing and therefore has a negligible IFM.

The promoter information transduction capacity is tunable and can be increased for natural Msn2 target genes

It is generally assumed that gene expression levels are fine-tuned (de Nadal et al., 2011), but the very low IAM and IFM of HXK1 and SIP18 are incompatible with this idea. One possibility is that mutual information for promoters is biophysically constrained to ∼1.0–1.3 bit, but another possibility is that HXK1 and SIP18 are not optimized for AM- and FM-mediated information transduction. To investigate this and explore the relationship between promoter cis-elements and information transduction, we focused on SIP18, which has the lowest I and suffers from high gene expression noise (Figure 2—figure supplement 1D), and asked if altering promoter architecture could improve information transduction. We removed the two functional Msn2 binding sites in the SIP18 promoter and added three and four new binding sites in the nucleosome-free region closer to the transcription start site (promoter architecture maps are shown in Figure 2—figure supplement 1C) to generate pSIP18 mut A and pSIP18 mut B, which differ from the wild-type SIP18 promoter by 14 and 18 nucleotides, respectively. We then repeated the experiments for mut A and mut B to measure their IAM and IFM.

With respect to AM, both mutants had significantly higher IAM of 1.42 bits (mut A) and 1.55 bits (mut B) (Figure 2C). We attribute this increase to a combination of three factors: a more linear dose–response, a higher dynamic range, and significantly lower gene expression noise (Figure 2—figure supplement 1D).

The wild-type SIP18 promoter filters out oscillatory input and therefore has a negligible IFM. In contrast, with respect to FM mut A shows a slightly higher IFM of 0.88 bits and mut B a significantly higher IFM of 1.39 bits (Figure 2D). Notably, although HXK1 presumably evolved to decode Msn2 pulsing, as is observed under glucose limitation, mut B now shows a higher IFM than even HXK1. Although I could be different for natural Msn2 dynamics (Hao and O'Shea, 2012), these results show that for the AM and FM signals studied here, natural Msn2 target genes are not optimized for information transduction and do not have their maximal I even though promoters with higher IAM/FM are only a few mutations away. Furthermore, IAM exceeds IFM for all four promoters, which shows that, at least in these four cases, transmitting gene expression information in the amplitude of TF activation dynamics is more reliable than transmitting it in the frequency. Thus, the promoter information transduction capacity is tunable in cis: by modulating Msn2 binding sites, we can control both how a promoter decodes Msn2 dynamics and how much information it can transmit.

Estimating the intrinsic information transduction capacity of promoters

Natural Msn2 target promoters appear to have I ≤ 1.3 bits. Thus, we observe high information loss during gene expression. Information loss comes from two sources: gene-intrinsic and gene-extrinsic noise (Elowitz et al., 2002). Intrinsic noise originates from the inherently stochastic nature of biochemical reactions, such as stochastic binding of Msn2 at individual promoters. Information loss due to intrinsic noise is therefore unavoidable for the cell. Extrinsic noise comes from the intracellular environment, which may differ between cells in a population. Even though we consider genetically identical cells grown in a microfluidic chemostat, the cell population could exhibit non-genetic differences in cell-cycle phase and Msn2 abundance or dynamics, etc. This could cause the dose–response to be different between single cells (Figure 3A), as was observed in a recent study on Ras/ERK signaling (Toettcher et al., 2013). For example, a cell with a higher-than-average Msn2 abundance might show higher gene expression. When we carefully quantify Msn2-mCherry dynamics, we observe loss of information between the microfluidic 1-NM-PP1 input and nuclear Msn2 due to variability in Msn2 abundance between cells (Figure 3—figure supplement 1). Likewise, the cell cycle is a major source of extrinsic gene expression noise (Zopf et al., 2013). Therefore, measuring mutual information in a cell population subject to extrinsic noise, as we did in Figure 2, underestimates the intrinsic information transduction capacity of a promoter.

Figure 3 with 1 supplement see all
An algorithm for estimating intrinsic mutual information.

(A) Genetically identical cells can have shifted single-cell dose-responses due to gene-extrinsic effects, such as variation in Msn2 abundance and cell cycle phase. Measuring the response of a single reporter (YFP) therefore underestimates mutual information. By introducing an additional reporter (CFP), we can distinguish extrinsic noise such as a shifted dose–response since this affects both CFP and YFP equally, from true intrinsic stochasticity. (B) Overview of algorithm. By fitting a gamma distribution to the raw YFP data, calculating the CFP/YFP covariance and filtering this component out of the total variance, an intrinsic YFP distribution can be estimated (left). By repeating this for each dose–response distribution, intrinsic mutual information can be estimated (right). Full details on the algorithm are given in Supplementary file 2. (C) By applying the algorithm to the data from Figure 2 (solid bars), we can estimate intrinsic mutual information (hatched bars).

https://doi.org/10.7554/eLife.06559.008

Although it is in principle possible to correct for cell cycle phase, Msn2 abundance and other gene-extrinsic factors individually, it is impossible to correct for all factors. To overcome this limitation and estimate the intrinsic I (Iint), we developed a method based on the dual-reporter approach (Elowitz et al., 2002; Swain et al., 2002; Hilfinger and Paulsson, 2011). By having two gene expression reporters in diploid cells on homologous chromosomes that differ only by their color (CFP and YFP) but share the same intracellular environment, the extent to which they co-vary in the same cell allows us to infer how much gene-extrinsic factors, such as cell-cycle phase and Msn2 variability, and so on. contribute altogether (extrinsic noise), without having to specify each factor. Or phrased differently, if the dose–response is shifted in a cell, both the CFP and YFP reporter will be affected in a correlated manner and their covariance allows us to quantify this (Figure 3A). Therefore, we developed an algorithm that uses the CFP/YFP covariance to estimate what the intrinsic I (Iint) would have been in the absence of extrinsic noise. Briefly, our algorithm takes the following steps (Figure 3B): First, the raw YFP histogram is fitted to a gamma distribution (YFPΓ(a,b)). Second, the extrinsic component (covariance) of the total variance is determined (σext2=CFP·YFPCFPYFP). Third, keeping the mean constant, a new gamma distribution without the extrinsic component is inferred (YFPintΓ(aint,bint)). Fourth, this is repeated for each Msn2 input (e.g., amplitude or frequency). Finally, this inferred data set is discretized and then used to estimate Iint (Figure 3B; see Supplementary file 2 for a detailed discussion of the algorithm). We verified our algorithm in silico by systematically simulating five linear and five non-linear gene expression models with and without extrinsic noise and compared the true Iint to the algorithm-inferred Iint. The algorithm tended to slightly underestimate the true Iint, but the mean error was less than 2% and the error was always less than 5% (Supplementary file 2).

Therefore, by using dual-reporter strains we can determine how much of the information loss is extrinsic, apply the algorithm and estimate Iint in each case (IAM,int and IFM,int). We find that filtering out extrinsic noise significantly increases I (hatched bars, Figure 3C). Since the cell most likely incorporates some gene-extrinsic factors into a decision, but most likely does not incorporate all gene-extrinsic factors, we interpret Iraw and Iint as a lower and upper bound, respectively, on the true I. Thus, our approach allows us to estimate an upper bound, Iint, on a promoter's information transduction capacity.

Even after correcting for extrinsic noise, IAM,int for HXK1 and SIP18 only reach ∼1.5–1.6 bits (Figure 3C). And IFM,int for HXK1 is just 1.36 bits—that is, three ranges of inputs can only be distinguished with some associated error. Thus, even when considering Iint, which is the upper limit on the maximal mutual information, neither natural Msn2 target gene can transmit information about stress intensity without some error. That is, consistent with the ‘noisy switch model’, expression of HXK1 and SIP18 is not reliably fine-tuned to stress intensity. In contrast, for mut B, IFM,int is 1.55 bits and IAM,int is ∼2 bits (Figure 3C). Thus, mut B almost approaches a range where information about both signal identity and intensity could conceivably be transduced nearly without error like a ‘rheostat’, though the natural Msn2 target genes, HXK1 and SIP18, do not.

Multiple gene copies reduce information loss due to intrinsic noise

Filtering out extrinsic noise substantially increases I (Figure 3C). Next, we considered how reducing intrinsic noise might increase I. In principle, as the number of gene copies increases, information loss due to intrinsic noise decreases due to simple ensemble averaging and mutual information increases—in the limit of infinite copies, intrinsic noise is zero and all information loss is due to extrinsic noise (Cheong et al., 2011). To test this we generated diploid strains with either one (1×) or two (2×) copies of the hxk1::CFP and sip18::YFP reporters in the same cell.

We repeated the AM and FM experiments for the 1× and 2× diploids (Figure 4—figure supplement 1 and Figure 4—figure supplement 2). Comparing the 1× and 2× diploids (Figure 4A), we see that having two copies of a gene generally improves I by ∼0.05–0.20 bits. For example, on going from haploid (1×) to diploid (2×), HXK1 IAM increases from 1.30 to 1.47 bits. Therefore, in terms of information transduction, being diploid confers a small but robust advantage.

Figure 4 with 2 supplements see all
Integrating the response of more than one gene improves information transmission.

(A) The AM and FM experiments (Figure 2) were repeated for diploid strains containing either one copy (1×) of the hxk1::CFP and sip18::YFP reporters or two copies (2×) of the hxk1::CFP and sip18::YFP reporters and individual and joint mutual information determined (full details on calculations are given in Supplementary file 2). (B) 2× sip18::YFP vs 2× hxk1::CFP scatterplot showing expression for three experiments: no input (light purple), five 5-min pulses of 690 nM 1-NM-PP1 separated by 13-min intervals (orange) or one 70-min pulse of 3 μM 1-NM-PP1 (green). For each condition, 600 cells are shown. The YFP/CFP expression is the maximal value after each time-trace has reached a plateau. The inset shows a zoom-in highlighting the ‘no input’ condition. All raw single-cell time-lapse microscopy source data for the 1× reporter diploid (21,236 cells) and 2× reporter diploid (19,222 cells) for this Figure are available online as Supplementary file 1 and in (Hansen and O'Shea, 2015).

https://doi.org/10.7554/eLife.06559.010

Circuits integrating the response of two genes can transduce more information than single gene circuits

So far we have considered information transduction from Msn2 to a single gene. Yet, Msn2 controls the expression of hundreds of genes in response to different stresses (Elfving et al., 2014; Hao and O'Shea, 2012; Huebert et al., 2012), we therefore extend our approach to information transduction from Msn2 to multiple genes. We next asked whether one way the cell might overcome the low I of individual genes would be to integrate the response of two or more different genes. To simulate and test this, we used diploid strains with both hxk1::CFP and sip18::YFP in the same cell, which allows us to measure the joint mutual information, I(R1,R2;S).

We find that the AM joint mutual information (IAM,joint) is significantly higher in both the 1× and 2× cases than the individual IAM of HXK1 and SIP18 (Figure 4A). For example, the total joint mutual information (IAM+FM,joint; combining both the AM and FM responses) is 1.67 bits and 1.83 bits for the 1× and 2× diploids, respectively (Figure 4A). Therefore, although HXK1 and SIP18 individually can only distinguish ON from OFF without error (Figure 2A), their joint response can distinguish three inputs (no input, FM, or AM) nearly without error (Figure 4B).

Thus, these results show that although the information transduction capacities of individual genes may be low, by integrating the response of two different genes the cell can improve information transduction. Therefore, by integrating the response of even more than two genes, the cell could potentially substantially improve the information transduction capacity of a pathway.

Discussion

Here, we use information theory to investigate the hypothesis that cells can transduce both signal identity and signal intensity information in the amplitude and frequency of TF activation dynamics to control gene expression. As a conceptual framework, we introduce two extreme models of information transmission (Figure 1C): in the ‘noisy switch model’, the cell only transmits information sufficient to turn ON or OFF particular genes or pathways in response to external signals or stresses, whereas in the ‘rheostat model’ the cell is accurately fine-tuning the expression levels of relevant genes to the intensity of a signal or stress. For a TF responding to multiple stresses, we can extend this framework beyond a single gene. Extending the noisy switch model to two genes, the stress-relevant gene HXK1 is reliably induced during FM pulsing of Msn2 (as seen under glucose limitation), whereas both HXK1 and the stress-relevant SIP18 gene are reliably induced during AM activation of Msn2 (as seen under oxidative stress) (Figure 4B). Therefore, three inputs (no input, FM, or AM) can be distinguished essentially without error (Figure 4B). However, given the modest joint information transduction capacities with respect to AM and FM combined (IAM+FM,joint; Figure 4A), the cell cannot fine-tune HXK1 and SIP18 expression levels without significant error to the stress intensity. Thus, signal identity information for two distinct stresses can be transduced in the amplitude and frequency of Msn2 essentially without error, but intensity information can only be transduced with high error.

A central result in information theory is that the information transduction capacity of a signaling pathway is limited by and equal to the capacity of its weakest node or bottleneck (see also Supplementary file 2 for a discussion). In other words, once information has been lost, no amount of post-processing can recover it, as is seen in the game of ‘broken telephone’. Therefore, by measuring information transduction of individual Msn2 target genes to be ∼1.0–1.3 bits, we can establish that the expression of Msn2 target genes cannot transduce stress signal intensity information without significant error at least for the AM and FM signals studied here—we can draw this conclusion without knowing all the relevant upstream components of the signaling pathway, how they mechanistically interact and how much information they can transmit. Thus, this approach can provide insight into the purpose of a pathway (e.g., noisy switch vs rheostat) and can readily be applied to other signaling pathways.

Why does information transduction by Msn2 resemble a ‘noisy switch’ rather than a ‘rheostat’? Or phrased differently, why should the cell not fine-tune the expression level of stress genes to the stress intensity? One possibility is that the stochasticity inherent in the biophysical process of transcription fundamentally constrains information transduction by a promoter to ∼1.0–1.3 bit. However, since the information transduction capacity of SIP18 can be substantially increased by modulating promoter cis-elements (Figures 2 and 3), the low I of natural Msn2 target genes is not solely due to inherent biophysical constraints. Another speculative possibility is that variability is selected for: since evolutionary selection works at the population-level, variability in gene expression can create phenotypic diversity within an isogenic population (Balaban et al., 2004; Blake et al., 2006). It is also important to note that under natural stress a network of factors could be activated, whereas here we study the limits on amplitude- and frequency-mediated transduction of gene expression information in the dynamics of a single master TF.

Many biological signaling pathways transmit information through the amplitude or frequency of a shared signaling molecule (Figure 1A) and this has raised the long-standing question: can more information be transmitted through the amplitude or the frequency of a signaling molecule (Rapp et al., 1981; Li and Goldbeter, 1989)? This question has not previously been experimentally addressed for TFs responding to multiple signals in an amplitude- or frequency-dependent manner. We show that more gene expression information can be transduced through the amplitude than through the frequency of Msn2 activation dynamics for all genes studied here (Figures 2 and 3). Although the FM dose-responses tend to be more linear, the AM dose-responses have higher dynamic range and lower noise (Figure 2 and Figure 2—figure supplement 1D). While we show that gene promoters have higher information transduction capacities for amplitude- than frequency-encoded information (Figures 2 and 3), maximal information transduction can be achieved for TFs that exhibit both amplitude- and frequency-encoding (Figure 4).

The amount of information promoters measured in this study can transmit is limited (Figures 2–4); yet we stress that for many ‘house-keeping’ genes or genes expressed at steady-state information transduction is likely significantly higher, in part due to time-averaging. Indeed, the gene expression response to a transient signal is noisier than a response at steady-state (Hansen and O'Shea, 2013) and inducible genes tend to show higher expression noise (Bar-Even et al., 2006; Newman et al., 2006). One way the cell can improve information transduction is by integrating the response of more than one gene or by having multiple copies of a gene (Figure 4). An example of this is ribosome biogenesis where, by having multiple copies of each gene encoding a subunit and employing elaborate feedback control, the cell can fine-tune its translational capability to its growth and energy status (Lempiainen and Shore, 2009). Another example is morphogen or cytokine secretion: although the amount produced by each single cell might be noisy, the average amount produced by a large number of cells can be highly precise (Gregor et al., 2007; Cheong et al., 2011). Hence, a number of strategies for increasing information transmission exist.

In conclusion, we have investigated the reliability of transmitting gene expression information in the amplitude and frequency of a TF. We show that the information transduction capacity of a gene can be tuned in cis and the amount of information transmitted increased by integrating the response of multiple genes. Nonetheless, for individual genes our results are consistent with the Msn2 pathway transmitting essentially error-free signal identity information, but unreliable signal intensity information, and therefore functioning more like a ‘noisy switch’ than a ‘rheostat’. Since many similar master regulators, such as p53, NF-κB, ERK, and Hes1, also transduce information through the regulation of signaling dynamics, it will be interesting to investigate whether dynamic cell signaling is generally limited to error-free transduction of only signal identity information.

Materials and methods

Microfluidics and time-lapse microscopy

Request a detailed protocol

Microscopy experiments were performed essentially as described previously (Hansen et al., 2015; Hansen and O'Shea, 2013). Briefly, yeast cells were grown overnight at 30°C with shaking at 180 rpm to an OD600 nm of ca. 0.1 in low fluorescence medium, quickly collected by suction filtration, loaded into the five channels of a microfluidic device pretreated with concanavalin A and the setup mounted on a Zeiss Axio Observer Z1 inverted fluorescence microscope (Carl Zeiss, Jena, Germany) equipped with an Evolve EM-CCD camera (Photometrics, Tuscon, AZ), 63× oil-immersion objective (NA 1.4, Plan-Apochromat), Zeiss Colibri LEDs for excitation and an incubation chamber kept at 30°C. Solenoid valves programmed using custom-written software (MATLAB) control whether medium with or without 1-NM-PP1 is delivered to each microfluidic channel and the flow (ca. 1 μL/s) is driven by gravity. Control of 1-NM-PP1 delivery enables the control of Msn2 pulsing (Figure 2) and a unique pulse sequence can be delivered to each of the five microfluidic channels. The microscope maintains focus and moves between each channel to acquire phase-contrast, YFP, CFP, RFP (mCherry), and iRFP images for 64 frames with a 2.5 min time resolution. For the AM experiments, 1-NM-PP1 was added to each microfluidic channel for 70 min at the following concentrations: 100 nM, 175 nM, 275 nM, 413 nM, 690 nM, 1117 nM, 3 μM. For the FM experiments, a concentration of 690 nM 1-NM-PP1 was used together with the following pulse sequences: one 5-min pulse; two 5-min pulses separated by a 40-min interval; three 5-min pulses separated by 25-min intervals; four 5-min pulses separated by 17.5-min intervals; five 5-min pulses separated by 13-min intervals; six 5-min pulses separated by 10-min intervals; seven 5-min pulses separated by 7.86-min intervals; eight 5-min pulses separated by 6.25-min intervals; nine 5-min pulses separated by 5-min intervals. Control software for the microfluidic device and a full protocol are provided elsewhere (Hansen et al., 2015). Image analysis was performed using custom-written software (MATLAB) that segments, tracks and quantifies single-cell time-traces and has been described previously (Hansen et al., 2015; Hansen and O'Shea, 2013). All raw single-cell data are available online as Supplementary file 1 and in (Hansen and O'Shea, 2015).

Computation of mutual information

Request a detailed protocol

The mutual information for a single reporter is defined in Equation 1 and the maximal mutual information given by:

I(R;S)=maxp(S)[MI(R;S)]   for   ip(Si)=1;   p(Si)0.

The p(S) that maximizes the mutual information is determined using the iterative Blahut-Arimoto algorithm. An unbiased I was estimated using jackknife sampling to correct for undersampling as it has previously been described (Strong et al., 1998; Slonim et al., 2005; Cheong et al., 2011). The data were discretized by binning as shown in Figure 2. Maximal mutual information, I, and its error are reported as the mean and standard deviation, respectively, from calculating the unbiased I using 15 to 35 bins, inclusive.

To determine the maximal joint mutual information, I (Figure 4A), first consider the joint mutual information between the signal S and two responses R1 (e.g., YFP) and R2 (e.g., CFP):

MI(R1,R2;S)=MI(R1;S)+MI(R2;S|R1),

Where MI(R1;S) is known from Equation 1 and MI(R2;S|R1) is given by:

MI(R2;S|R1)=i,j,kp(R1(i),R2(j),S(k))log2(p(R1(i))p(R1(i),R2(j),S(k))p(R1(i),R2(j))p(R1(i),S(k))).

The maximal joint mutual information is then given by:

I(R1,R2;S)=maxp(S)[MI(R1,R2;S)]   for   ip(Si)=1;   p(Si)0.

As before, p(S) is obtained using the Blahut-Arimoto algorithm, and the mean and error of I are obtained as for a single reporter, except using 8 to 20 bins, inclusive. Full details are given in Supplementary file 2.

Algorithm to estimate the intrinsic mutual information

Request a detailed protocol

Briefly, the total, intrinsic and extrinsic noise for each condition is calculated using dual-reporters (CFP/YFP) (Elowitz et al., 2002; Swain et al., 2002). The expression distributions in the absence of extrinsic noise are required to determine Iint. This is an intractable problem (Hilfinger and Paulsson, 2011). To estimate it, the raw, empirical YFP distribution is fitted to a gamma distribution (YFPΓ(a,b)). Keeping the mean fixed, a new gamma distribution representing the YFP response in the absence of extrinsic noise is then inferred by filtering out the extrinsic contribution to the variance. This is repeated for each condition, each distribution is then discretized and the maximal mutual information, I, determined as above.

The accuracy of the algorithm was tested by simulating five linear and five non-linear stochastic gene expression models for both a fast and a slow promoter using the Gillespie algorithm under AM (10 conditions). Extrinsic noise is added by picking the translation rate and TF concentration for each iteration from a gamma distribution. The algorithm was then applied to each data set with extrinsic noise and compared to simulation results with only intrinsic noise and the error calculated. In all 80 cases (10 models, 2 promoters, 4 levels of extrinsic noise), the error was less than 5% (in bits) and the mean error was less than 2%. Full details are given in Supplementary file 2.

Measurement noise, data processing, and YFP quantification

Request a detailed protocol

Measurement noise is a major concern for information theoretical calculations and can lead to underestimates of mutual information. To control and minimize effects of noise, the following data processing pipeline was employed. For each single-cell, a time-trace of 64 YFP measurements is made (2.5 min interval). The fluorescence (in AU) is the mean pixel-intensity per cell corresponding to the YFP concentration. As can be seen in Figure 2—figure supplement 1B and Figure 2—figure supplement 2 from the single-cell YFP traces, YFP concentration generally reaches a plateau around or after the 100 min time-point (element 43 in the YFP vector). So the maximal YFP level in the cell is measured approximately 20 times before the experiment ends (element 64 in the YFP vector). Although there is slight noise in each measurement of the YFP concentration as shown in Figure 2—figure supplement 2A (black circles), because YFP is independently measured ∼20 times after it has reached a plateau, the actual YFP level can accurately be determined by smoothing (Figure 2—figure supplement 2A, red line). The YFP trace is smoothed using an 11-point moving average filter and the vector is subsequently converted to a scalar by taking the maximal YFP value in the (33;64) range of elements. The scalar YFP concentration (Figure 2—figure supplement 1B) is used for all information theoretical calculations. We believe that the protein concentration is the most biologically relevant measure of gene expression. For example, the activity of a stress response enzyme is generally determined by its concentration. But we note that had a different measure been used, that is, had the dynamics of the YFP time-trace been included, different estimates of I would be obtained (see also Supplementary file 2 for a further discussion).

The following factors, among others, contribute to measurement noise: slight variations in microscope focusing; fluctuations in cellular autofluorescence; instrumentation variability (e.g., camera noise); day-to-day experimental variability; slight errors from automated image analysis. Nonetheless, as is also evident from Figure 2—figure supplement 2 measurement noise is small. For HXK1 and SIP18 IAM and IFM were independently measured twice in different strains: the SIP18 dual-reporter strain (EY2813/ASH94), the HXK1 dual-reporter strain (EY2810/ASH91), and the 1× reporter diploid (EY2972/ASH194). The results are shown in the table below:

IGene::YFP / gene::CFP strain1x sip18::YFP / hxk1::CFP strain
IAM(sip18::YFP)1.21 ± 0.03 bits1.17 ± 0.02 bits
IFM(sip18::YFP)0.52 ± 0.06 bits0.50 ± 0.05 bits
IAM(hxk1::CFP/YFP)1.30 ± 0.01 bits1.30 ± 0.01 bits
IFM(hxk1::CFP/YFP)1.11 ± 0.01 bits1.14 ± 0.01 bits

As is clear from the table above, the measurements of IAM and IFM between different strains (with slightly different genetic backgrounds) are highly similar and within error. This provides high confidence in the measurements and shows that the measurements are robust between different clones. Nonetheless, a constant noise source would cause all measurements to be underestimates by similar amounts. Therefore, the consistency of the measurements does not exclude the presence of a constant noise source. However, it is also important to note that most noise sources are ‘extrinsic’ to the gene and will therefore partially be filtered out by the algorithm during the correction for extrinsic noise.

Strain construction

All strains used in this study are listed in Table 1. The diploid strains containing fluorescent reporters for the SIP18 (ASH94/EY2813) and HXK1 (ASH91/EY2810) promoters have been described previously (Hansen and O'Shea, 2013). These and all other Saccharomyces cerevisiae strains used in this study are from an ADE+ strain in the W303 background (MATa [EY0690] and MATα (EY0691) trp1 leu2 ura3 his3 can1 GAL+ psi+). Standard methods for growing and genetically manipulating yeast were used throughout this study and all manipulations were performed in the same manner in both haploid mating types unless otherwise stated. Mating was performed by mixing haploids and selecting for diploids on SD–TRP–LEU plates. All genetic manipulations were verified by polymerase chain reaction (PCR).

Table 1

List of strains.

https://doi.org/10.7554/eLife.06559.013
StrainTypeStrain details
EY0690MATaW303 (trp1 leu2 ura3 his3 can1 GAL+ psi+) (not generated in this study)
EY0691MATαW303 (trp1 leu2 ura3 his3 can1 GAL+ psi+) (not generated in this study)
EY2808/
ASH89
MATaTPK1M164G TPK2M147G TPK3M165G msn4Δ::TRP1 MSN2-mCherry NHP6a-iRFP::kanMX hxk1::mCitrine_V163A-spHIS5 (not generated in this study)
EY2809/
ASH90
MATαTPK1M164G TPK2M147G TPK3M165G msn4Δ::LEU2 MSN2-mCherry NHP6a-iRFP::kanMX hxk1::SCFP3A-spHIS5 (not generated in this study)
EY2810/
ASH91
DiploidTPK1M164G TPK2M147G TPK3M165G msn4Δ::TRP1/LEU2 MSN2-mCherry NHP6a-iRFP::kanMX hxk1::mCitrineV163A/SCFP3A-spHIS5 (not generated in this study)
EY2811/
ASH92
MATaTPK1M164G TPK2M147G TPK3M165G msn4Δ::TRP1 MSN2-mCherry NHP6a-iRFP::kanMX sip18::mCitrine_V163A-spHIS5 (not generated in this study)
EY2812/
ASH93
MATαTPK1M164G TPK2M147G TPK3M165G msn4Δ::LEU2 MSN2-mCherry NHP6a-iRFP::kanMX sip18::SCFP3A-spHIS5 (not generated in this study)
EY2813/
ASH94
DiploidTPK1M164G TPK2M147G TPK3M165G msn4Δ::TRP1/LEU2 MSN2-mCherry NHP6a-iRFP::kanMX sip18::mCitrineV163A/SCFP3A-spHIS5 (not generated in this study)
EY2964/
ASH139
MATaTPK1M164G TPK2M147G TPK3M165G msn4Δ::TRP1 MSN2-mCherry NHP6a-iRFP::kanMX sip18::mCitrine_V163A-HIS3 pSIP18 Mut A 3 STREs
EY2965/
ASH140
MATaTPK1M164G TPK2M147G TPK3M165G msn4Δ::TRP1 MSN2-mCherry NHP6a-iRFP::kanMX sip18::mCitrine_V163A-HIS3 pSIP18 Mut B 4 STREs
EY2966/
ASH188
MATαTPK1M164G TPK2M147G TPK3M165G msn4Δ::LEU2 MSN2-mCherry NHP6a-iRFP::kanMX sip18::SCFP3A-HIS3 pSIP18 Mut B 4 STREs
EY2967/
ASH189
DiploidTPK1M164G TPK2M147G TPK3M165G msn4Δ::TRP1/LEU2 MSN2-mCherry NHP6a-iRFP::kanMX sip18::mCitrine_V163A/SCFP3A-HIS3 pSIP18 Mut B 4 STREs
EY2968/
ASH190
MATαTPK1M164G TPK2M147G TPK3M165G msn4Δ::LEU2 MSN2-mCherry NHP6a-iRFP::kanMX sip18::SCFP3A-HIS3 pSIP18 Mut A 3 STREs
EY2969/
ASH191
DiploidTPK1M164G TPK2M147G TPK3M165G msn4Δ::TRP1/LEU2 MSN2-mCherry NHP6a-iRFP::kanMX sip18::mCitrine_V163A/SCFP3A-HIS3 pSIP18 Mut A 3 STREs
EY2970/
ASH192
MATaTPK1M164G TPK2M147G TPK3M165G msn4Δ::TRP1 MSN2-mCherry NHP6a-iRFP::kanMX sip18::mCitrine_V163A-HIS3 hxk1::URA3
EY2971/
ASH193
MATαTPK1M164G TPK2M147G TPK3M165G msn4Δ::LEU2 MSN2-mCherry NHP6a-iRFP::kanMX hxk1::SCFP3A-HIS3 sip18::URA3
EY2972/
ASH194
DiploidTPK1M164G TPK2M147G TPK3M165G msn4Δ::TRP1/LEU2 MSN2-mCherry NHP6a-iRFP::kanMX sip18::mCitrine_V163A-HIS3 hxk1::URA3 / hxk1::SCFP3A-HIS3 sip18::URA3 (1x reporter diploid)
EY2973/
ASH195
MATaTPK1M164G TPK2M147G TPK3M165G msn4Δ::TRP1 MSN2-mCherry NHP6a-iRFP::kanMX sip18::mCitrine_V163A-HIS3 hxk1::SCFP3A-HIS3
EY2974/
ASH196
MATαTPK1M164G TPK2M147G TPK3M165G msn4Δ::LEU2 MSN2-mCherry NHP6a-iRFP::kanMX hxk1::SCFP3A-HIS3 sip18::mCitrine_V163A-HIS3
EY2975/
ASH197
DiploidTPK1M164G TPK2M147G TPK3M165G msn4Δ::LEU2 MSN2-mCherry NHP6a-iRFP::kanMX 2x hxk1::SCFP3A_JCat-HIS3 2x sip18::mCitrine_V163A-HIS3 (2x reporter diploid)

To generate the pSIP18 promoter mutants, the relevant segment of the promoter was replaced by URA3 and followed by replacing the URA3 fragment with a PCR generated fragment containing the relevant mutations and counterselection against URA3. The full sequence of the wild-type SIP18 promoter and the mutant promoters is listed below.

> WT SIP18 promoter

Request a detailed protocol

GCTCACTTTTTGTTGGTCTGTATTCATTCTGGATGTCTTGGTTGTAGAAATTTCTTTTATTGGTTCATTAAAGTCAAGGTAAATGGCGAGAACTAGAATAGAGTTTTATTCTTTTTACCGTTATATAGATAATTCTAGCCGGGGGCGGTCGCCCCTGAGATTCCCGACATCAGTAAGACATAGTACTGTACGATTACTGTACGATTAATCTATCCACTTCAGATGTTCAACAATTCCTTTTGGCATTACGTATTAATACTTCATAGGATCGGCACCCTCCCTTAAGCCTCCCCTAAATGCTTTCGGTACCCCTTTAAGACAACTATCTCTTAACCTTCTGTATTTACTTGCATGTTACGTTGAGTCTCATTGGAGGTTTGCATCATATGTTTAGGTTTTTTTGGAAACGTGGACGGCTCATAGTGATTGGTAAATGGGAGTTACGAATAAACGTATCTTAAAGGGAGCGGTATGTAAAATGGATAGATGATCATGAATACAGTACGAGGTGTAAAGAATGATGGGACTGAGAGGGCAATTATCATCCCTCAGAATCAACATCACAAACATATATAAAGCTCCCAATTCTGCCCCAAAGTTTTGTCCCTAGGCATTTTTAATCTTTGTATCTGTGCTCTTTACTTTAGTAGAAAGGTATATAAAAAAGTATAGTCAAG

> pSIP18 mut A promoter

Request a detailed protocol

GCTCACTTTTTGTTGGTCTGTATTCATTCTGGATGTCTTGGTTGTAGAAATTTCTTTTATTGGTTCATTAAAGTCAAGGTAAATGGCGAGAACTAGAATAGAGTTTTATTCTTTTTACCGTTATATAGATAATTCTAGCCGGGGGCGGTCGCCCCTGAGATTCCCGACATCAGTAAGACATAGTACTGTACGATTACTGTACGATTAATCTATCCACTTCAGATGTTCAACAATTCCTTTTGGCATTACGTATTAATACTTCATAGGATCGGCACCCTCCCTTAAGCCTCAACTAAATGCTTTCGGTACAACTTTAAGACAACTATCTCTTAACCTTCTGTATTTACTTGCATGTTACGTTGAGTCTCATTGGAGGTTTGCATCATATGTTTAGGTTTTTTTGGAAACGTGGACGGCTCATAGTGATTGGTAAATGGGAGTTACCCCTAAACGTATCTTAAAGGGACCCCTATGTAAAATGGATAGCCCCTCATGAATACAGTACGAGGTGTAAAGAATGATGGGACTGAGAGGGCAATTATCATCCCTCAGAATCAACATCACAAACATATATAAAGCTCCCAATTCTGCCCCAAAGTTTTGTCCCTAGGCATTTTTAATCTTTGTATCTGTGCTCTTTACTTTAGTAGAAAGGTATATAAAAAAGTATAGTCAAG

> pSIP18 mut B promoter

Request a detailed protocol

GCTCACTTTTTGTTGGTCTGTATTCATTCTGGATGTCTTGGTTGTAGAAATTTCTTTTATTGGTTCATTAAAGTCAAGGTAAATGGCGAGAACTAGAATAGAGTTTTATTCTTTTTACCGTTATATAGATAATTCTAGCCGGGGGCGGTCGCCCCTGAGATTCCCGACATCAGTAAGACATAGTACTGTACGATTACTGTACGATTAATCTATCCACTTCAGATGTTCAACAATTCCTTTTGGCATTACGTATTAATACTTCATAGGATCGGCACCCTCCCTTAAGCCTCAACTAAATGCTTTCGGTACAACTTTAAGACAACTATCTCTTAACCTTCTGTATTTACTTGCATGTTACGTTGAGTCTCATTGGAGGTTTGCATCATATGTTTAGGTTTTTTTGGAAACGTGGACGGCTCATAGTGACCCCTAAATGGGAGTTACCCCTAAACGTATCTTAAAGGGACCCCTATGTAAAATGGATAGCCCCTCATGAATACAGTACGAGGTGTAAAGAATGATGGGACTGAGAGGGCAATTATCATCCCTCAGAATCAACATCACAAACATATATAAAGCTCCCAATTCTGCCCCAAAGTTTTGTCCCTAGGCATTTTTAATCTTTGTATCTGTGCTCTTTACTTTAGTAGAAAGGTATATAAAAAAGTATAGTCAAG

To remove the Msn2 binding site (STRE 5′-CCCCT′-3′), the two central Cs were replaced by As (5′-CCCCT′-3′ → 5′-CAACT′-3′), as shown in bold in the above sequences. The most upstream site in the SIP18 promoter appears to be non-functional—deleting it has no effect on gene induction. Conversely, the two sites between −350 and −400 bp appear to be solely responsible for gene induction—deletion of both sites completely abolishes gene induction to below our detection limit. Mut A and Mut B have 3 and 4 new STRE sites, respectively, instead of the 2 STREs in the WT promoter. The position was chosen to be closer to the transcription start site, but in the largely nucleosome free region between two nucleosomes (Figure 2—figure supplement 1C). The same manipulations were performed in both mating types and all microscopy experiments were conducted in diploid strains (Mut A: EY2969/ASH191; Mut B: EY2967/ASH189).

To generate the 1× and 2× reporter diploid strains (1×: EY2972/ASH194; 2×: EY2975/ASH197), strain EY2811/ASH92 (MATa sip18::mCitrineV163A-HIS) and strain EY2809/ASH90 (MATα hxk1::SCFP3A-HIS) were used as base strains. In EY2811, the HXK1 ORF was replaced by URA3 to generate EY2970/ASH192, which was used for the 1× reporter diploid, and URA3 further replaced by a PCR fragment containing SCFP3A followed by the ADH1 terminator and the spHIS5 selection marker (AddGene plasmid #64686) using counterselection against URA3. This gave strain EY2973/ASH195, which was used for the 2× reporter diploid. Likewise, in EY2811 the SIP18 ORF was replaced by URA3 to generate EY2971/ASH193, which was used for the 1× reporter diploid, and URA3 further replaced by a PCR fragment containing mCitrineV163A followed by the ADH1 terminator and the spHIS5 selection marker (AddGene plasmid #64685) using counterselection against URA3. This gave strain EY2974/ASH196, which was used for the 2× reporter diploid. Furthermore, the 1x reporter diploid (EY2972/ASH194) was generated by mating EY2970/ASH192 and EY2971/ASH193 and the 2x reporter diploid (EY2975/ASH197) generated by mating EY2973/ASH195 and EY2974/ASH196. In the 1× reporter diploid, no WT copies of the SIP18 and HXK1 genes are present to ensure that, in the case the encoded protein product could have an autoregulatory effect, this complication would be avoided.

Finally, we note that 1-NM-PP1 mediated gene induction of HXK1 and SIP18 is specific to Msn2. In an msn2Δ-deletion strain, neither HXK1 nor SIP18 is induced by 1-NM-PP1 (Hansen and O'Shea, 2013) and both promoters have been shown to directly bind Msn2 in ChIP experiments (Huebert et al., 2012; Elfving et al., 2014).

All strains are available upon request and all strains are derived from EY0690 and EY0691.

References

  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6
  7. 7
  8. 8
  9. 9
  10. 10
  11. 11
  12. 12
  13. 13
  14. 14
  15. 15
  16. 16
    Elements of information theory (2nd edition)
    1. TM Cover
    2. JA Thomas
    (2006)
    Hoboken, NJ: Wiley-Interscience.
  17. 17
  18. 18
  19. 19
  20. 20
  21. 21
  22. 22
    Positional information, in bits
    1. JO Dubuis
    2. G Tkacik
    3. EF Wieschaus
    4. T Gregor
    5. W Bialek
    (2013)
    Proceedings of the National Academy of Sciences of USA 110:16301–16308.
    https://doi.org/10.1073/pnas.1315642110
  23. 23
  24. 24
  25. 25
  26. 26
  27. 27
  28. 28
  29. 29
  30. 30
  31. 31
    Data from: Limits on information transduction through amplitude and frequency regulation of transcription factor activity
    1. AS Hansen
    2. EK O'Shea
    (2015)
    Dryad Digital Repository, 10.5061/dryad.97vt8.
  32. 32
  33. 33
  34. 34
  35. 35
  36. 36
  37. 37
  38. 38
  39. 39
  40. 40
  41. 41
  42. 42
  43. 43
  44. 44
  45. 45
  46. 46
  47. 47
  48. 48
  49. 49
    Quantitative biology: from molecular to cellular systems
    1. I Nemenman
    (2012)
    Quantitative biology: from molecular to cellular systems, CRC Press.
  50. 50
  51. 51
  52. 52
  53. 53
  54. 54
  55. 55
  56. 56
  57. 57
  58. 58
  59. 59
    A mathematical theory of communication
    1. CE Shannon
    (1948)
    At&T Technical Journal 27:623–656.
  60. 60
  61. 61
    Information-based clustering
    1. N Slonim
    2. GS Atwal
    3. G Tkacik
    4. W Bialek
    (2005)
    Proceedings of the National Academy of Sciences of USA 102:18297–18302.
    https://doi.org/10.1073/pnas.0507432102
  62. 62
  63. 63
  64. 64
  65. 65
  66. 66
    Optimizing information flow in small genetic networks
    1. G Tkacik
    2. AM Walczak
    3. W Bialek
    (2009)
    Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 80:031920.
    https://doi.org/10.1103/PhysRevE.80.031920
  67. 67
  68. 68
  69. 69
  70. 70
  71. 71
  72. 72
  73. 73
  74. 74
  75. 75
  76. 76
  77. 77
  78. 78

Decision letter

  1. Naama Barkai
    Reviewing Editor; Weizmann Institute of Science, Israel

eLife posts the editorial decision letter and author response on a selection of the published articles (subject to the approval of the authors). An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent (see review process). Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.

[Editors' note: this article was originally rejected after discussions between the reviewers, but the authors were invited to resubmit after an appeal against the decision.]

Thank you for choosing to send your work entitled “Limits on information transduction through regulation of signaling dynamics” for consideration at eLife. Your full submission has been evaluated by Detlef Weigel (Senior editor), a Reviewing editor and two peer reviewers. We are potentially very interested in the work—provided that your premises hold up—,but because it is eLife policy to only invite revision when it is clear that required experiments can be done in a short time frame, we are declining the work for now.

The reviewers were overall positive in the sense that it was agreed on all that the approach is interesting and that the results are potentially important, but the reviewers were concerned that you did not address the (likely) possibility of loss of information between input and MSN dynamics. If a large fraction of information is lost already at this point, this could, unfortunately, invalidate your claims.

Reviewer 2 suggests how this can be measured experimentally, and further specify a criterion to when this loss can be ignored (and when it cannot). We will be very interested in considering again a manuscript that includes such experiments. Since we are uncertain whether the results would indeed verify your model, we are declining the work for now, but we are leaving the door open for a re-submission, provided the new experimental data will be supportive of your model.

Reviewer #1:

The paper from Hansen et al. addresses a key open question in signal transduction on limits the ability of gene promoters to accurately to decode signaling dynamics. Overall the paper presents interesting results that I would like to see published in eLife. I do have a major concern about input noise that I am worried could invalidate many of the major results and therefore must be addressed. Furthermore, I found the writing of the paper to have many unnecessary overstatements and over simplistic interpretation that need to be corrected through a major revision of the text. I discuss two key concerns related to overstatements and over simplistic interpretation below. I made two suggestions that are constructive, but not essential. The first is for an additional analysis that I think could improve the paper and is easy to do and therefore I strongly recommend it will be performed. The second require additional experiment and while I think it would improve the paper substantially but might be outside the scope of this work and I do not see them as essential as long as the statements made by the authors are appropriately toned down.

Quantifying noise in inputs:

The system the authors analyze has three components: microfluidics manipulation => MSN2 translocation => gene expression. They analyze the mutual information between microfluidics input class and gene expression. Therefore they make an implicit assumption that the information transmission between microfluidics class and the patterns of MSN-2 is “noise free” and that all the information loss is in the decoding MSN2=>YFP. However, in their 2013 MSB paper, the authors showed non-negligible variability in MSN-2-mCherry localization within their microfluidics setup. Furthermore, other factors could contribute to this such as the variation in MSN2-mCherry between cells. There are two ways to address this issue. The best way will be to repeat the experiments when measuring both MSN-2-mCherry localization and gene expression in the same cells and to calculate the MI between all steps in the pathway similar to Uda et al. 2013. However, this might require substantial new experiments that are potentially beyond the scope of this work. The second best way is to just show the mutual information between the inputs and MSN-2 dynamics (in absolute units to address MSN2-mCherry concentration variability issues). If this value is close to 3 (log2(8)) than the assumption that the input noise is negligible is justified is reasonable, otherwise the information loss could be in the “signaling” or the response . They should have at least some of the required for this in their MSB 2013 paper. If there is substantial information loss between microfluidics and MSN2 response then I must recommend that the paper be rejected and more experiment done to carefully analyze loss at different steps along the artificial “pathway”.

Statements that need to be revised:

Real upper bound limits on dynamics?

The claim that this paper shows a limit on decoding of dynamics is overstated. The real physiological dynamics of MSN-2 are much more complex than simple amplitude and frequency as shown by Nan and O'Shea, Nat Struct Mol Biol, 2012. It is very likely that the SIP18 and HXK1 are tuned to the real physiological dynamics and not to artificial AM and FM signals. In fact the authors actually show in Figure 2CD that these promoters are not optimized for these simple modes! The authors should restrict their claims to the information transduction through AM and FM signaling. This needs to be revised throughout the paper, Title, Abstract, main text etc.

Number of distinguishable states interpretation.

In this paper the authors constantly interpret their results as the number of distinguishable states. While this simplistic interpretation is tempting, I find it to be misleading for reasons explained nicely in Bowsher et al. 2014 which the authors cite. Mutual information should be interpreted as the increase in actionable information the cells has. Even a value of 0.77 bit could allow distinguishing between three states with some small associated inference error (see Bowsher 2014 Figure 1 and discussion in Box 2). I found section 2.4 in Supplementary file 2 that was supposed to address this issue to be very lacking. The paper should be revised completely to address this point including removal of Figure 5 and the many statements that argue that cells are limited to decoding identity and not intensity.

The use of information theory analysis is a great tool to analyze noise in signal transduction networks. This is a complicated tool and needs to be interpreted with care. However, as a community there was substantial disservice to this approach by using the over-simplistic interpretation of bits as number of distinguishable states. This was done in previous works by others and resulted in unnecessary resentment to information theory approaches. While I understand that it is a bit more challenging to write a paper that uses the more complex and accurate interpretation of the bit value, it is essential that we do so.

Constructive suggestions:

1) Compare analysis from Figure 3 to Figure 4.

It would be interesting to see in Figure 4 additional bars that show the mutual information done on the CFP/YFP cells from Figure 3. I believe that an analysis of the joint response of I(CFP, YFP; input) where CFP and YFP should show higher mutual information than a simple diploid YFP cell and basically similar level to the intrinsic mutual information calculated by the authors. This will provide validation to the analysis shown in Figure 3 and will allow better comparison of the results of the diploid.

2) Analyze the mutant promoters from Figure 2 in respect to physiological inputs.

Experiments that could be very helpful in general in addressing some of the issues mentioned above are the calculation of mutual information on physiological responses and not just manipulation of the dynamics. Specifically, it would be great to see if the mutants from Figure 2 also increase the mutual information from physiological response? I suspect that they will not and this will provide a relatively easy way to show that information is really encoded and decoded in the complex pattern of MSN-2 dynamics that goes beyond AM and FM.

Reviewer #2:

In this manuscript, Hansen and O'Shea reported the information theory-based analysis of the Msn2 signal transduction system. By controlling Msn2-mCherry nuclear localization dynamics and measuring its downstream target promoters, the authors revealed that the extent of information transduction for a single target promoter depends on the dynamics of Msn2 (AM or FM) as well as the number of STRE sites on the promoter. Additionally, the authors showed that integration of multiple target promoters enhances information transduction. Overall, I really like the information-theoretical analysis of signal transduction. While the conclusions presented are not overly exciting, i.e. there are limits on information processing through Msn2 dynamics, the experiments and analysis presented in this work opens up a new and interesting way of understanding single-cell signaling dynamics in general.

Major comments:

1) Cellular signal transduction is composed two steps: encoding step where (chemical) inputs are encoded into intracellular representation such as Msn2 dynamics, and decoding step where Msn2 dynamics are then decoded into target expression. In this manuscript, the authors focused on the decoding step, i.e., from Msn2 dynamics to promoter output. In all the analysis, the authors have assumed that Msn2 dynamics always follows the input chemical signal in every cell and thus the input TF signal equates the external chemical waveforms. However, I feel this assumption could present a fundamental problem in the analysis since it is hard to imagine that every cell in the population has the same Msn2 dynamics under a defined chemical waveform. More specifically, the distribution of responses (YFP level) could likely arise from the heterogeneous Msn2 dynamics among a population. Therefore, I feel that uncoupling the heterogeneity of Msn2 dynamics seems necessary for understanding how Msn2 dynamics contribute to the extent of information transduction.

2) Following the point above, the observed difference in signal transmission capacity between AM and FM Msn2 input may likely due to the difference in the degree of heterogeneity of Msn2 dynamics. For example, Msn2 may not follow the FM chemical signal as faithfully as the AM chemical signal. Thus, Msn2 dynamics could be more heterogeneous among cells in FM condition than in AM condition, leading to a more faithful signal transmission for AM. One might need to compare the variability in Msn2 response between AM and FM in order to study the role of Msn2 dynamics in the extent of information transmission in these conditions.

3) It occurred to me that the extent of information transduction positively correlates with the dynamic range of promoter response (Figure 2). In other words, by simply looking at the top rows (i.e., dose response curves) of each figure panel in Figure 2, I can immediately tell which condition transmits the most information (i.e., mut B AM). Is there any underlying principle that results in such a correlation? This correlation suggests that the dynamic range of the measurement may somehow affect the calculation of mutual information. A potential way to test if this is the case is to characterize the mutual information of the same condition under different lamp power or camera gain settings.

4) Regarding the calculation of the mutual information, maximum YFP level was used. The authors made the argument that final protein level is a biologically relevant quantity, which I agreed. In section 2.5 of Supplementary file 2, the authors made arguments about why other quantities are less desirable. I think the authors may want to make the argument more quantitatively. It could be that maximum YFP is the least noisy quantity and thus most suited for calculating mutual information. Such argument can be supported by comparing the CV of possible quantities, such as rate of YFP production, max YFP level, YFP level at a chosen time, etc..

5) I am not sure if the authors performed control experiments (in this or previous papers) to show that all the YFP expression (from promoters studied) comes from Msn2 alone (i.e., no other regulators involved). In other words, deletion of Msn2 abolishes the promoter expression under 1-NM-PP1.

[Editors' note: what now follows is the decision letter after the authors submitted for further consideration.]

Thank you for choosing to send your work entitled “Limits on information transduction through regulation of signaling dynamics” for consideration at eLife. Your article and your letter of appeal have been considered by the original reviewers of the manuscript, and there are still some issues that need to be resolved before we can accept a revised paper.

Specifically, the appeal letter now includes the new experiment suggested by the reviewers, in which the information loss between the input and MSN2 dynamics is measured. As the reviewers originally worried, this information loss is quite substantial. This is a bit worrisome, especially as this value is inconsistent with lower loss inferred from the instrinsic/extrinsic analysis (Figure 3). Another issue is that this loss was measured only for the AM signal, and not from the FM signal. This may call for a major rethinking of how to interpret the results in the paper, and in this context, the reviewers suggested the following:

1) Change some of the interpretation of their data and present the paper with a careful analysis of the information loss due to intrinsic and extrinsic noise sources. This way, the fact that there is substantial loss between chemical input and MSN-dynamics is not a problem anymore, rather an interesting result. Between that and the comparison of AM/FM and the different mutants with increased dynamic range, there should be enough there for an interesting paper. The inconsistencies of the two methods would need to be addressed of course.

2) Quantify more directly the information transmission capacity between MSN2 dynamics and MSN2 promoter by measuring in the same cell MSN2 the dynamics of localization in the nucleus and the resulting promoter reporter. Since mutual information is a symmetric quantity, one could bin the promoter response into 8 or 16 bins. Than calculate the mutual information between the scalar MSN2 promoter response and the distribution of multivariate dynamics responses in each bin. This could be done by pooling all the chemical input data together and use an approach such as described e.g. in Selimkhanov et al. 2014 to calculate mutual information between scalar input and dynamic response. Perhaps the data in Figure 2-figure supplement 2 is sufficient, or if not, additional experiments are required.

https://doi.org/10.7554/eLife.06559.016

Author response

[Editors' note: the author responses to the first round of peer review follow.]

Thank you for reviewing our submission “Limits on information transduction through regulation of signaling dynamics”. In your decision you state that you are interested in a revised manuscript provided that our premises hold up, but you decline our manuscript for now because it is not clear whether the suggested experiments can be performed in a short timeframe. You state that: “We will be very interested in considering again a manuscript that includes such experiments”.

The major concern is whether variability in Msn2 dynamics for a given microfluidic 1-NM-PP1 input invalidates our claims. The reviewers are very clear: they suggest a specific experiment to measure mutual information between Msn2 nuclear localization and 1-NM-PP1 input. We performed this experiment (please see below).

However, we would like to stress that we can also address the major concern of the reviewers with the algorithm in Figure 3 of the manuscript. Even if there is high cell-to-cell variability in Msn2 dynamics in response to a specific 1-NM-PP1 input (extrinsic noise), this will affect the dual CFP and YFP expression reporters in the same cell to the same extent. When we apply our algorithm, we filter out extrinsic noise irrespective of its magnitude. Thus, when we calculate Iint, we estimate what I would have been, had there been no variability in Msn2 dynamics.

We apologize if the algorithm and its use were not clear in our original submission. But to understand why, consider for example a cell with a very high concentration of Msn2. In this cell, both the CFP and YFP gene expression reporter will tend to show high expression. By measuring the co-variance between CFP and YFP in the same cell across the cell population, we can infer the extent to which their shared environment contributes to the observed gene expression variability (extrinsic noise). This shared environment includes variability in Msn2 level, Msn2 dynamics in response to 1-NM-PP1 input, cell cycle phase or any other variable that affect CFP and YFP levels in a correlated manner. Using the measured CFP/YFP co-variance and our algorithm, we can determine the intrinsic mutual information (Iint in Figure 3). Iint is the information transduction capacity of a promoter in the absence of extrinsic noise, that is, Iint is what I would have been had there been no Msn2 variability or input noise. Thus, Iint is the quantity the reviewers are asking for.

The reviewers made insightful suggestions regarding improvement of the text and further analysis of existing data. Since we can address the major concern of the reviewers—Msn2 input noise—with our algorithm (Figure 3), we would like to submit a revision of our manuscript that incorporates these suggestions.

In this letter, we first discuss the experiment the reviewers requested in detail. Next, we elaborate on our algorithm (Figure 3) and illustrate how this algorithm actually addresses the issue of Msn2 input noise independently of the result of the experiment requested by the reviewers.

Quantifying input noise between 1-NM-PP1 and Msn2:

We thank the reviewers and the editor for carefully reviewing our manuscript and emphasizing the crucial point regarding Msn2 input noise, and also for being very clear about which experiment they would like to see performed. Specifically, they want us to “… show the mutual information between the inputs and MSN-2 dynamics (in absolute units to address MSN2-mCherry concentration variability issues). If this value is close to 3 (log2(8)) than the assumption that the input noise is negligible is justified is reasonable… ”.

We performed this experiment. We exposed cells to a 70-min pulse of either no 1-NM-PP1 or one of the seven 1-NM-PP1 concentrations used in Figures 2A and 2C of the manuscript. We measured cell-to-cell variability in nuclear Msn2-mCherry using time-lapse microscopy. There are three major possible sources of Msn2 variability:

a) Measurement noise when quantifying how much Msn2-mCherry is nuclear.

b) Input noise when microfluidic 1-NM-PP1 input is converted into Msn2 dynamics.

c) Biological variability in Msn2 expression between cells.

Regarding measurement noise (a), we measured Msn2-mCherry nuclear localization every 10 min to minimize photobleaching. A major technical challenge is that the nucleus moves in and out of focus in diploid yeast cells during time-lapse experiments. We therefore collected a z-stack series of images for each time point. We quantified Msn2 nuclear localization in absolute units as the average nuclear level during the 70-min pulse. This also corresponds to the Msn2 AUC. The result is shown in Figure 3–figure supplement 1B. However, Msn2 is a low abundance protein present at only a few hundred molecules per cell. Therefore, to measure the difference between 25% and 37.5% of maximal nuclear localization (100 nM vs. 175 nM 1-NM-PP1), our measurement precision has to be on the order of tens of molecules. This is challenging even with state-of-the-art equipment. Therefore, our measurements likely slightly overestimate variability in nuclear Msn2-mCherry.

We cannot readily distinguish (b), input noise, from measurement noise. However, when we expose cells to 1-NM-PP1 in the microfluidic chemostat all cells in a field of view respond deterministically by activating Msn2 with essentially identical kinetics (see Figure 3–figure supplement 1C). Therefore, input noise when 1-NM-PP1 is converted into Msn2 dynamics is likely relatively minor. More importantly, however, our algorithm allows us to correct for variability in Msn2 dynamics regardless of the origin and magnitude of the variability.

Based on our measurements (Figure 3–figure supplement 1B), the mutual information between the 1-NM-PP1 input and Msn2 nuclear concentration is ∼2.06 bits. This is lower than the maximal value of 3 bits. However, a value of 3 bits would mean that there was no cell-to-cell variability in the Msn2 concentration. We estimate that the variability in nuclear Msn2-mCherry between cells is less than CV∼15% (σ/μ or std/mean; see Figure 3–figure supplement 1C). This is an upper bound because any measurement noise would cause us to overestimate the Msn2 abundance CV. To put this into context, a proteomic study measured cell-to-cell variability among ∼2,500 yeast proteins (Newman et al., 2006). According to this study, essentially no yeast proteins have a CV below 10% (Figure 2G in Newman et al., 2006).

How low would the cell-to-cell variability of Msn2 have to be in order to obtain 3 bits? In other words, is it biologically possible to obtain a value of 3 bits? To investigate this, we simulated Msn2 variability and calculated mutual information for different CV's assuming that Msn2 abundance is gamma distributed. We simulated cells within a range of CV=20% to CV=10%, which is the lowest level of variability observed for any yeast protein (Newman et al., 2006). We find that if Msn2 was one of the least variable proteins in yeast with a CV∼10%, we would still expect mutual information less than 2.4 bits even if there was no loss of information between input and Msn2 dynamics (Author response image 1). Furthermore, we emphasize that biological variability in Msn2 abundance between cells is not an artifact of our experimental system, but an inherent property of any biological pathway: a population of yeast cells responding to natural stress will have similar levels of variability in Msn2 abundance between cells.

Author response image 1

Msn2 nuclear localization was simulated with different CVs of Msn2 abundance. Briefly, we assume that Msn2 abundance is gamma distributed and that a given percentage of Msn2 is nuclear for a given inhibitor concentration (e.g. 50% for 275 nM or 75% for 690 nM in accordance with our measurements). The mean Msn2 abundance in the cell was chosen to be 1000 AU. A gamma distribution was then simulated with a and b parameters chosen such that the indicated CV was obtained. Note that the simulation with CV=15% (2.04 bits) closely matches our experimental result (2.06 bits).

https://doi.org/10.7554/eLife.06559.018

We would also like to address Reviewer 2's specific concern regarding FM input. Reviewer 2 wrote: “for example, Msn2 may not follow the FM chemical signal as faithfully as the AM chemical signal”. During all experiments for this manuscript we simultaneously measured Msn2-mCherry and CFP and YFP gene expression in the same cell. We did not do a finely spaced z-stack series, which is necessary to accurately quantify the concentration of Msn2 in the nucleus—this causes too much photobleaching to be compatible with imaging at high temporal resolution. However, as shown in Figure 3–figure supplement 1C and in our previous paper (Hansen and O'Shea, 2013), Msn2-mCherry deterministically and faithfully follows the 1-NM-PP1 input during FM as well as AM. Finally, even if there had been higher input noise during FM, this would affect the CFP and YFP gene expression reporters in a correlated manner. Therefore, we correct for this when we apply our algorithm and calculate Iint.

An algorithm to filter out extrinsic noise:

The reviewers have pointed out the issue of noise in Msn2 dynamics—either coming from variability in Msn2 abundance between cells or from variability in how 1-NM-PP1 input is converted into Msn2 dynamics—which would cause us to underestimate I. There are several other extrinsic variables that will have the same effect. For example, previous studies have shown that the rate of transcription varies approximately 2-fold across the cell cycle in yeast (Zopf et al., 2013). Thus, since we do not synchronize cells, some of the gene expression variability we observe is really because we do not control for cell cycle phase. However, the advantage of our approach is that we can correct for variability in Msn2 abundance, cell cycle phase and all other extrinsic variables, without specifying them or knowing which are the most important.

Since this is a crucial point, we briefly discuss the algorithm here (a full discussion is given in Section 4 of Supplementary File 2). We take advantage of a key insight from the gene expression noise field, where noise is divided into intrinsic and extrinsic noise (Elowitz et al., 2002). Intrinsic noise is due to the inherent stochasticity of biochemical reactions. Extrinsic noise, the extent to which the shared intracellular environment contributes to cell-to-cell variability, can be measured using two equivalent gene expression reporters (e.g. CFP and YFP). This is because the intracellular environment affects the CFP/YFP reporters to the same extent. The relative contributions of intrinsic and extrinsic noise are shown in Figure 2–figure supplement 1C.

Suppose for example that gene expression variability was mainly caused by differences in Msn2 abundance between cells. In a cell with high Msn2 concentration, both CFP and YFP expression would be high. Conversely, in a cell with low Msn2 concentration, both CFP and YFP expression would be low. In this example, the CFP-YFP co-variance would be very high. Our algorithm allows us to use the CFP-YFP co-variance to estimate how much of the information loss is due to extrinsic noise (e.g. variability in Msn2 abundance) and, crucially, to calculate what I would have been in cell without extrinsic noise. As mentioned, there are many extrinsic variables such as Msn2 levels, cell cycle, cell size etc. Although it is in principle possible to correct for each extrinsic variable individually, our algorithm allows us to correct for all extrinsic variables at once and therefore to estimate an upper bound on information transduction of a promoter, Iint.

Reviewer #1:

The paper from Hansen et al. addresses a key open question in signal transduction on limits the ability of gene promoters to accurately to decode signaling dynamics. Overall the paper presents interesting results that I would like to see published in eLife. I do have a major concern about input noise that I am worried could invalidate many of the major results and therefore must be addressed. Furthermore, I found the writing of the paper to have many unnecessary overstatements and over simplistic interpretation that need to be corrected through a major revision of the text. I discuss two key concerns related to overstatements and over simplistic interpretation below. I made two suggestions that are constructive, but not essential. The first is for an additional analysis that I think could improve the paper and is easy to do and therefore I strongly recommend it will be performed. The second require additional experiment and while I think it would improve the paper substantially but might be outside the scope of this work and I do not see them as essential as long as the statements made by the authors are appropriately toned down.

We thank the reviewer for their fair and constructive comments and suggestions. Regarding the first suggestion made by Reviewer 1, we have performed the additional analysis suggested by Reviewer 1. To address the second major point of Reviewer 1, as described below, we have toned down and re-written the relevant sections and claims.

Quantifying noise in inputs:

The system the authors analyze has three components: microfluidics manipulation => MSN2 translocation => gene expression. They analyze the mutual information between microfluidics input class and gene expression. Therefore they make an implicit assumption that the information transmission between microfluidics class and the patterns of MSN-2 is “noise free” and that all the information loss is in the decoding MSN2=>YFP. However, in their 2013 MSB paper, the authors showed non-negligible variability in MSN-2-mCherry localization within their microfluidics setup. Furthermore, other factors could contribute to this such as the variation in MSN2-mCherry between cells. There are two ways to address this issue. The best way will be to repeat the experiments when measuring both MSN-2-mCherry localization and gene expression in the same cells and to calculate the MI between all steps in the pathway similar to Uda et al. 2013. However, this might require substantial new experiments that are potentially beyond the scope of this work. The second best way is to just show the mutual information between the inputs and MSN-2 dynamics (in absolute units to address MSN2-mCherry concentration variability issues). If this value is close to 3 (log2(8)) than the assumption that the input noise is negligible is justified is reasonable, otherwise the information loss could be in the “signaling” or the response . They should have at least some of the required for this in their MSB 2013 paper. If there is substantial information loss between microfluidics and MSN2 response then I must recommend that the paper be rejected and more experiment done to carefully analyze loss at different steps along the artificial “pathway”.

We performed the experiment that Reviewer 1 recommended and measured the mutual information between 1-NM-PP1 input and nuclear Msn2-mCherry for both AM and FM and quantified information loss. We estimate that IAM(Msn2; 1-NM-PP1)≥2.06 bits and IFM(Msn2; 1-NM-PP1)≥2.23 bits, but note that these are challenging measurements subject to measurement noise. The values given are therefore likely underestimates. We show the results in the new Figure 3–Figure supplement 1.

Most importantly, we correct for input noise (1-NM-PP1→Msn2) and variability in Msn2 abundance with our algorithm in Figure 3. As Reviewer 1 also states, the key goal is estimating I(YFP; Msn2). As illustrated in Author response image 2, we can estimate an upper limit on I(YFP; Msn2). As both reviewers pointed out, I(YFP; 1-NM-PP1) from Figure 2 is a lower bound on I(YFP; Msn2) since there is some information loss from 1-NM-PP1→Msn2 due to cell-to-cell variability in Msn2 abundance. Our algorithm allows us to estimate Iint(YFP; 1-NM-PP1), which is an upper limit on I(YFP; Msn2), because any information loss from 1-NM-PP1→Msn2 will affect the dual CFP/YFP reporters in a correlated manner and we can correct for this information loss when we filter out extrinsic noise (Figure 3). Therefore, we can estimate both the lower (Figure 2) and upper (Figure 3) limit on I(YFP; Msn2) and thus achieve bounds on I(YFP; Msn2). Since I(YFP; Msn2) is the quantity both we and the reviewers are interested in, we believe our algorithm addresses this concern. We have re-written the manuscript text pertaining to Figure 3 to make clear how the algorithm corrects for Msn2 input noise.

Statements that need to be revised:

Real upper bound limits on dynamics?

The claim that this paper shows a limit on decoding of dynamics is overstated. The real physiological dynamics of MSN-2 are much more complex than simple amplitude and frequency as shown by Nan and O'Shea, Nat Struct Mol Biol, 2012. It is very likely that the SIP18 and HXK1 are tuned to the real physiological dynamics and not to artificial AM and FM signals. In fact the authors actually show in Figure 2C,D that these promoters are not optimized for these simple modes! The authors should restrict their claims to the information transduction through AM and FM signaling. This needs to be revised throughout the paper, Title, Abstract, main text etc.

Studying the response to natural stress is an interesting future direction. Previously, we used “dynamics” as shorthand for AM/FM signaling. Following the recommendation of Reviewer 1, we now explicitly say AM/FM signaling instead of “dynamics” throughout the text, Title and Abstract.

Number of distinguishable states interpretation.

In this paper the authors constantly interpret their results as the number of distinguishable states. While this simplistic interpretation is tempting, I find it to be misleading for reasons explained nicely in Bowsher et al. 2014 which the authors cite. Mutual information should be interpreted as the increase in actionable information the cells has. Even a value of 0.77 bit could allow distinguishing between three states with some small associated inference error (see Bowsher 2014 Figure 1 and discussion in Box 2). I found section 2.4 in Supplementary file 2 that was supposed to address this issue to be very lacking. The paper should be revised completely to address this point including removal of Figure 5 and the many statements that argue that cells are limited to decoding identity and not intensity.

The use of information theory analysis is a great tool to analyze noise in signal transduction networks. This is a complicated tool and needs to be interpreted with care. However, as a community there was substantial disservice to this approach by using the over-simplistic interpretation of bits as number of distinguishable states. This was done in previous works by others and resulted in unnecessary resentment to information theory approaches. While I understand that it is a bit more challenging to write a paper that uses the more complex and accurate interpretation of the bit value, it is essential that we do so.

This is a crucial point and we thank Reviewer 1 for their comments. Following Reviewer 1's comments, we have completely revised all discussions of “bits” and we have systematically removed interpretations such as “binary/ternary decision”. We have removed all “number of distinguishable states” annotation from the figures. And we have completely re-written and greatly expanded the discussion in section 2.4 Supplementary file 2 using the Bowsher and Swain example Reviewer 1 refers to (Bowsher and Swain, 2014).

As Reviewer 1 points out, I = 1 bit may allow error free distinction between two states but it also may not. Likewise, I < 1 bit may allow distinguishing between multiple states with some error. Therefore, it is important to also inspect the probability distributions when interpreting I. Considering the distributions in Figure 2A, we see that both HXK1 and SIP18 can distinguish ON (‘brown distribution’) from OFF without error. Based on Figure 2A, we believe that this is clear. This is what we meant in our statements about “reliable transduction about signal identity, but not signal intensity information”. But as Reviewer 1 points out, it is correct that some information about signal intensity is also transmitted, albeit with a seemingly high error rate based on Figure 2A. Therefore, we believe that our results are consistent with essentially error-free transduction of signal identity information, but that transduction of signal intensity information is only possible with some associated error. As Reviewer 1 points out, in some instances this associated error could be small. We thank Reviewer 1 for pointing this out and we have attempted to make this distinction much more clearly in the text and by including the new Figure 4B.

Constructive suggestions:

1) Compare analysis from Figure 3 to Figure 4.

It would be interesting to see in Figure 4 additional bars that show the mutual information done on the CFP/YFP cells from Figure 3. I believe that an analysis of the joint response of I(CFP, YFP; input) where CFP and YFP should show higher mutual information than a simple diploid YFP cell and basically similar level to the intrinsic mutual information calculated by the authors. This will provide validation to the analysis shown in Figure 3 and will allow better comparison of the results of the diploid.

We thank the reviewer for the suggestion and have performed this analysis. When we refer to “intrinsic” and “extrinsic” noise in this paper, we follow the “gene-centric” definition by Elowitz et al. (Elowitz et al., 2002). In principle, in the limit of infinite promoter copies, there should be no intrinsic noise due to ensemble averaging and all information loss comes from extrinsic noise. Conversely, when we filter out extrinsic noise, we can determine what I is when there is no information loss from gene-extrinsic sources, but all information loss comes from gene-intrinsic noise. Therefore, the joint I(CFP,YFP) corresponds to reducing intrinsic noise by adding one extra promoter copy, which is the same as what we did in Figure 4 when we compare the 1x and 2x reporter diploids. Thus, the joint I(CFP,YFP) can provide an independent confirmation of the 1x vs. 2x reporter comparison in Figure 4.

Using our dual YFP/CFP reporter data for SIP18, HXK1, mut A and mut B, we calculated IAM,joint(CFP,YFP) and IFM,joint(CFP,YFP) and now show this result in Supplementary file 2 section 3.3..

In general, since the effect of adding an additional promoter leads to only a small increase in I the effect is difficult to measure precisely given the error in our mutual information estimates. Nonetheless, within error, we see agreement between the 1x/2x comparisons.

2) Analyze the mutant promoters from Figure 2 in respect to physiological inputs.

Experiments that could be very helpful in general in addressing some of the issues mentioned above are the calculation of mutual information on physiological responses and not just manipulation of the dynamics. Specifically, it would be great to see if the mutants from Figure 2 also increase the mutual information from physiological response? I suspect that they will not and this will provide a relatively easy way to show that information is really encoded and decoded in the complex pattern of MSN-2 dynamics that goes beyond AM and FM.

We agree that studying information transduction between stress and Msn2 and also between Msn2 and gene expression (Stress → Msn2 → Gene expression, e.g. using the approach of Uda et al. (Uda et al., 2013)) is a very interesting future direction, but this is beyond the scope of this work. We would like to emphasize that the natural dynamics of Msn2 under stress are noisy (Hao and O'Shea, 2012). One advantage of our synthetic 1-NM-PP1 approach is that we can more precisely control Msn2 translocation dynamics such as pulse number or frequency and therefore more accurately measure I for promoters. However, we agree with Reviewer 1 that the promoter response to natural dynamics could be different, but is beyond the scope of this study.

Reviewer #2:

1) Cellular signal transduction is composed two steps: encoding step where (chemical) inputs are encoded into intracellular representation such as Msn2 dynamics, and decoding step where Msn2 dynamics are then decoded into target expression. In this manuscript, the authors focused on the decoding step, i.e., from Msn2 dynamics to promoter output. In all the analysis, the authors have assumed that Msn2 dynamics always follows the input chemical signal in every cell and thus the input TF signal equates the external chemical waveforms. However, I feel this assumption could present a fundamental problem in the analysis since it is hard to imagine that every cell in the population has the same Msn2 dynamics under a defined chemical waveform. More specifically, the distribution of responses (YFP level) could likely arise from the heterogeneous Msn2 dynamics among a population. Therefore, I feel that uncoupling the heterogeneity of Msn2 dynamics seems necessary for understanding how Msn2 dynamics contribute to the extent of information transduction.

We thank Reviewer 2 for bringing this important point to our attention. Since Reviewer 1 raised the same concern, we have addressed this concern in the response to Reviewer 1 above. Furthermore, we have now quantified information loss from 1-NM-PP1→Msn2 for both AM and FM and show this in the new Figure 3–figure supplement 1. We estimate that IAM(Msn2; 1-NM-PP1)≥2.06 bits and IFM(Msn2; 1-NM-PP1)≥2.23 bits, but note that these are challenging measurements subject to measurement noise. The values given are therefore likely underestimates. Most importantly, however, our algorithm allows us to correct for information loss from 1-NM-PP1→Msn2 and determine what I would have been, had there been no information loss from 1-NM-PP1→Msn2.

2) Following the point above, the observed difference in signal transmission capacity between AM and FM Msn2 input may likely due to the difference in the degree of heterogeneity of Msn2 dynamics. For example, Msn2 may not follow the FM chemical signal as faithfully as the AM chemical signal. Thus, Msn2 dynamics could be more heterogeneous among cells in FM condition than in AM condition, leading to a more faithful signal transmission for AM. One might need to compare the variability in Msn2 response between AM and FM in order to study the role of Msn2 dynamics in the extent of information transmission in these conditions.

This is an important point and we thank Reviewer 2 for bringing this issue to our attention. To assess the loss, we have now measured information loss from 1-NM-PP1→Msn2 (I(Msn2; 1-NM-PP1)) for both AM and FM. We get IAM(Msn2; 1-NM-PP1)≥2.06 bits and IFM(Msn2; 1-NM-PP1)≥2.23 bits. Thus, information loss from 1-NM-PP1→Msn2 is higher for AM than for FM, but IFM(YFP; 1-NM-PP1) is smaller than IAM(YFP; 1-NM-PP1) when it comes to gene expression for the four promoters. Together, this shows that the higher promoter information capacity for AM than for FM is not an artifact of higher information loss from 1-NM-PP1→Msn2 under FM than AM, but a real result.

Finally, we would also like to emphasize that even if there had been higher information loss from 1-NM-PP1→Msn2 under FM than AM, this would affect the CFP and YFP gene expression reporters in a correlated manner. Therefore, we correct for this when we apply our algorithm and calculate Iint(YFP; 1-NM-PP1). Since IAM,int also always exceeds IFM,int, we believe that our conclusion, that I(YFP; 1-NM-PP1) is higher for AM than for FM for the four promoters studied here, holds.

However, we thank Reviewer 2 for pointing this out and we now show example traces of Msn2 dynamics under FM signals in a new figure (Figure 3–figure supplement 1C). We also provide full details on the I(Msn2; 1-NM-PP1) calculations and experiments for both AM and FM in the new Figure 3–figure supplement 1.

3) It occurred to me that the extent of information transduction positively correlates with the dynamic range of promoter response (Figure 2). In other words, by simply looking at the top rows (i.e., dose response curves) of each figure panel in Figure 2, I can immediately tell which condition transmits the most information (i.e., mut B AM). Is there any underlying principle that results in such a correlation? This correlation suggests that the dynamic range of the measurement may somehow affect the calculation of mutual information. A potential way to test if this is the case is to characterize the mutual information of the same condition under different lamp power or camera gain settings.

We agree with Reviewer 2 that there is a strong dependence on dynamic range as also mentioned in the original submission and Figure 2–figure supplement 1D. Considering a dose-response, there are three factors that determine I: the dynamic range, the noise level and the dose-response shape. The dynamic range and noise level are related – what really matters is the signal-to-noise ratio. It is well-established that noise decreases with increasing expression level (Bar-Even et al., 2006; Newman et al., 2006) and we also observe this (Figure 2–figure supplement 1D). Therefore, since the signal-to-noise ratio increases with dynamic range, we generally see a positive relationship between I and dynamic range.

The other important factor is the shape of the dose-response. For example, after saturation no further inputs can be distinguished. Therefore, the more linear the dose-response, the higher I will be.

As the reviewer suggests, measurement noise is more of a concern at low expression. However, as we show in Figure 2–figure supplement 2, we can accurately measure YFP expression even at quite low expression levels. Furthermore, in our previous paper we showed that DCS2 exhibits 2-fold lower noise than SIP18 (supplemental figure S6B in that paper) even when SIP18 expression is almost 2-fold higher than DCS2 (Figure 3B) (Hansen and O'Shea, 2013). Since these experiments were performed on the same microscope with the same LED excitation settings, this shows that the higher noise observed for lower expressed genes with lower dynamic range in this study is not an artifact of our measurement system (such as lamp power or LED intensity).

4) Regarding the calculation of the mutual information, maximum YFP level was used. The authors made the argument that final protein level is a biologically relevant quantity, which I agreed. In section 2.5 of Supplementary file 2, the authors made arguments about why other quantities are less desirable. I think the authors may want to make the argument more quantitatively. It could be that maximum YFP is the least noisy quantity and thus most suited for calculating mutual information. Such argument can be supported by comparing the CV of possible quantities, such as rate of YFP production, max YFP level, YFP level at a chosen time, etc..

We thank Reviewer 2 for their suggestion and we have performed this analysis. We have extended the discussion in section 2.5 and 2.6 of Supplementary file 2, where we now also add a Figure showing what IAM would have been, had an alternative YFP quantification method been used. Briefly, we find that using the YFP value at a specific timepoint instead of the max YFP value has almost no effect on the IAM calculation. Conversely, we find that using the YFP production rate for the calculations leads to a serious underestimation of IAM. We have now also mentioned this issue in the Materials and methods section.

5) I am not sure if the authors performed control experiments (in this or previous papers) to show that all the YFP expression (from promoters studied) comes from Msn2 alone (i.e., no other regulators involved). In other words, deletion of Msn2 abolishes the promoter expression under 1-NM-PP1.

This is a crucial point and we thank Reviewer 2 for pointing this out. We have previously performed precisely the control experiment that Reviewer 2 requests (Hansen and O'Shea, 2013). We have the following evidence for specificity in gene expression:

A) In response to 3 μM 1-NM-PP1, both SIP18 and HXK1 are strongly transcriptionally upregulated (> 10-fold) in a strain with Msn2 as measured by microarrays. But in an msn2Δ strain without Msn2, neither SIP18 nor HXK1 changes in expression (Supplementary Figure S1C in (Hansen and O'Shea, 2013)). Thus, Msn2 is required for induction of SIP18 and HXK1 under 1-NM-PP1 exposure.

B) According to genome-wide Msn2 ChIP experiments, Msn2 binds the promoters of both SIP18 and HXK1 (Huebert et al., 2012).

C) In the case of SIP18, if we mutate the two Msn2 binding sites (STREs 5′-CCCCT-3′) at positions -386 bp and -367 bp in the promoter, YFP expression decreases at least 20-fold. This shows that the Msn2 binding sites are required for gene activation during 1-NM-PP1 exposure.

We now write that both HXK1 and SIP18 are specific target genes of Msn2 in the main text.

[Editors' note: the author responses to the re-review follow.]

Specifically, the appeal letter now includes the new experiment suggested by the reviewers, in which the information loss between the input and MSN2 dynamics is measured. As the reviewers originally worried, this information loss is quite substantial. This is a bit worrisome, especially as this value is inconsistent with lower loss inferred from the instrinsic/extrinsic analysis (Figure 3). Another issue is that this loss was measured only for the AM signal, and not from the FM signal.

As requested, we have performed additional experiments to quantify information loss for the FM signal. We estimate that IFM(1-NM-PP1; Msn2) = 2.23 ± 0.03 bits for FM. We provide full details in the new Figure 3–figure supplement 1C-E which is also shown below; the experiments and analyses were carried out in a manner analagous to the AM calculation described in our previous letter to you. Therefore, information loss due to variability in Msn2-dynamics is not higher for FM than for AM. Most importantly, however, although the input information loss is significant for both AM and FM, we can calculate what I would be in the absence of 1-NM-PP1→Msn2 information loss using our algorithm in Figure 3 (Iint).

Regarding the inconsistency referred to by the reviewers, we emphasize that the IFM/AM(1-NM-PP1; Msn2) analysis quantifies information loss from 1-NM-PP1→Msn2. Our intrinsic/extrinsic algorithm estimates information transfer from Msn2→YFP in the idealized scenario where there is no information loss from extrinsic variables (which include variability from 1-NM-PP1→Msn2, cell cycle phase, ribosome abundances etc.). Therefore, we do not believe that there should be a direct correspondence between the IFM/AM(1-NM-PP1; Msn2) analysis and the Figure 3 analysis.

This may call for a major rethinking of how to interpret the results in the paper, and in this context, the reviewers suggested the following:

1) Change some of the interpretation of their data and present the paper with a careful analysis of the information loss due to intrinsic and extrinsic noise sources. This way, the fact that there is substantial loss between chemical input and MSN-dynamics is not a problem anymore, rather an interesting result. Between that and the comparison of AM/FM and the different mutants with increased dynamic range, there should be enough there for an interesting paper. The inconsistencies of the two methods would need to be addressed of course.

Recent studies have used alternative definitions of “intrinsic” and “extrinsic” noise in characterizing multivariate signaling dynamics (Selimkhanov et al., 2014). We have used the “gene-centric” definitions introduced by Elowitz (Elowitz et al., 2002) and we have re-written large sections of the manuscript to emphasize the analysis of information loss due to “gene-intrinsic” and “gene-extrinsic” sources. In the Elowitz definition, “extrinsic noise” is any noise that affects the equivalent CFP and YFP reporters in a correlated manner, such as variability in Msn2 abundance or ribosome abundance. In other words, extrinsic noise comes from cell-to-cell variability in the shared intracellular environment. With our algorithm we can correct for extrinsic noise (including 1-NM-PP1→Msn2 information loss), and with the analysis of I for multiple promoter copies (Figure 4) we can estimate how reducing intrinsic noise increases I. It is not necessarily the case that I without gene-intrinsic noise would equal I without gene-extrinsic noise. We have followed suggestion 1 and rewritten the manuscript accordingly.

Furthermore, based on the previous comments, we have also made the following changes to the manuscript:

A) We no longer use the “number of distinguishable states” interpretation and we have removed all instances of “binary”, “ternary”, etc. We have completely revised how we discuss the interpretion of “bits”.

B) We have removed Figure 5, Figure 4A and introduced a new Figure 4B as requested by the reviewers.

C) We no longer say “dynamics” but restrict our claims to AM and FM input as suggested by Reviewer 1. We have also changed the Title, Abstract etc. accordingly.

D) We have revised the discussion of “signal identity vs. intensity” transduction as requested by the reviewers.

E) We have performed the suggested additional analysis including: 1) calculating the joint I(CFP, YFP; input) as suggested by Reviewer 1; and 2) calculating I using different YFP measures (max value, production rate, value at specific timepoint etc.) as suggested by Reviewer 2.

F) We have included evidence that the transcriptional response of SIP18 and HXK1 are specific to Msn2 as suggested by Reviewer 2.

2) Quantify more directly the information transmission capacity between MSN2 dynamics and MSN2 promoter by measuring in the same cell MSN2 the dynamics of localization in the nucleus and the resulting promoter reporter. Since mutual information is a symmetric quantity, one could bin the promoter response into 8 or 16 bins. Than calculate the mutual information between the scalar MSN2 promoter response and the distribution of multivariate dynamics responses in each bin. This could be done by pooling all the chemical input data together and use an approach such as described e.g. in Selimkhanov et al. 2014 to calculate mutual information between scalar input and dynamic response. Perhaps the data in Figure 2-figure supplement 2 is sufficient, or if not, additional experiments are required.

We performed the suggested analysis. We find that Msn2-mCherry measurement noise during the full time-lapse experiments is too high for us to gain insight from this analysis. We therefore cannot include this analysis in the manuscript. For reference, we describe below how we performed the analysis.

For all experiments, we measured Msn2-mCherry dynamics and YFP+CFP reporter expression in single cells at 2.5 min time-resolution without collecting a finely-spaced z-stack series. As mentioned in our previous letter, suggestion 2 is technically challenging for two reasons. First, the nucleus moves in-and-out of focus during time-lapse acquisition which makes accurate quantification challenging. Second, to partially overcome this problem, z-stack images through the nucleus must be acquired, which causes high photobleaching and makes time-lapse imaging challenging. For example, to accurately quantify Msn2-dynamics during FM, it is necessary to image with 1-min time resolution and perform a finely-spaced z-stack series with long exposure times (as performed in new Figure 3–figure supplement 1D). However, such intense imaging causes too severe photobleaching within 20-25 frames to enable accurate quantification Therefore, measurement noise in nuclear Msn2-mCherry quantification makes the suggested approach challenging.

Nevertheless, we have performed this analysis using two approaches:

Approach 1: We pooled all data for a given promoter (e.g. HXK1 for AM input). We bin data based on the measured Msn2-mCherry amplitude in each cell. Then we calculate IAM(YFP; Msn2-mCherry).

Approach 2: For each condition (e.g. 100 nM 1-NM-PP1 for AM input), we removed cells where the measured Msn2-mCherry amplitude was outside the mean±10% range. That is, for each 1-NM-PP1 input, we removed outlier cells with too high or too low measured Msn2-mCherry amplitude relative to the mean. Then we calculate IAM(YFP; 1-NM-PP1) using the trimmed data set.

With both approaches, we find an IAM that is nearly identical, within error, to the IAM we calculate in Figure 2 (e.g IAM for HXK1 is 1.30 (Figure 2A), but 1.29 bits using approach 2). Since variability in Msn2-mCherry almost certainly contributes to YFP expression variability, this indicates that the time-lapse Msn2-mCherry measurements suffer from too high measurement noise to meaningfully interpret these observations.

Finally and most importantly, we would like to emphasize that our algorithm allows us to estimate the maximal information transduction capacity of a promoter—and this is the focus of our manuscript—in an idealized cell without variability in Msn2 dynamics and abundance. In conclusion, suggestion 2 asks us to condition the YFP response on measured Msn2 variability. Our algorithm achieves this goal by estimating the YFP response in an idealized cell without Msn2 variability.

https://doi.org/10.7554/eLife.06559.017

Article and author information

Author details

  1. Anders S Hansen

    1. Department of Chemistry and Chemical Biology, Howard Hughes Medical Institute, Harvard University, Cambridge, United States
    2. Faculty of Arts and Sciences Center for Systems Biology, Harvard University, Cambridge, United States
    Contribution
    ASH, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents
    Competing interests
    No competing interests declared.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-7540-7858
  2. Erin K O'Shea

    1. Department of Chemistry and Chemical Biology, Howard Hughes Medical Institute, Harvard University, Cambridge, United States
    2. Faculty of Arts and Sciences Center for Systems Biology, Harvard University, Cambridge, United States
    3. Department of Molecular and Cellular Biology, Harvard University, Cambridge, United States
    Contribution
    EKO'S, Conception and design, Drafting or revising the article
    For correspondence
    Erin_Oshea@harvard.edu
    Competing interests
    EKO'S, Chief Scientific Officer and a Vice President at the Howard Hughes Medical Institute, one of the three founding funders of eLife.

Funding

Howard Hughes Medical Institute (HHMI)

  • Erin K O'Shea

National Science Foundation (NSF) (ECS-0335765)

  • Anders S Hansen
  • Erin K O'Shea

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank Raymond Cheong, Gašper Tkačik, and Mikhail Tikhonov for insightful discussions. We thank Nan Hao, Dann Huh, Arvind Subramaniam, Matthew Brennan, Roshni Wadhwani, Andrian Gutu, Shankar Mukherji, Kapil Amarnath, Bodo Stern, Sharad Ramanathan and members of the O’Shea lab for discussions and critically reading the manuscript. This work was performed in part at the Center for Nanoscale Systems at Harvard University, a member of the National Nanotechnology Infrastructure Network (NNIN), which is supported by the National Science Foundation under NSF award no. ECS-0335765. Image analysis and model simulations were run on the Odyssey cluster supported by the FAS Division of Science, Research Computing Group at Harvard University. The Howard Hughes Medical Institute supported this work.

Reviewing Editor

  1. Naama Barkai, Weizmann Institute of Science, Israel

Publication history

  1. Received: January 19, 2015
  2. Accepted: May 17, 2015
  3. Accepted Manuscript published: May 18, 2015 (version 1)
  4. Version of Record published: June 16, 2015 (version 2)

Copyright

© 2015, Hansen and O'Shea

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

Metrics

  • 3,739
    Page views
  • 996
    Downloads
  • 47
    Citations

Article citation count generated by polling the highest count across the following sources: Scopus, Crossref, PubMed Central.

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Download citations (links to download the citations from this article in formats compatible with various reference manager tools)

Open citations (links to open the citations from this article in various online reference manager services)

Further reading

    1. Cell Biology
    2. Genetics and Genomics
    Karina Perlaza et al.
    Research Article
    1. Cell Biology
    2. Genetics and Genomics
    Felix Kessler, Paolo Longoni
    Insight