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Robustness and Compensation of Information Transmission of Signaling Pathways

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Science  02 Aug 2013:
Vol. 341, Issue 6145, pp. 558-561
DOI: 10.1126/science.1234511

Simple Signals?

Cells process information about themselves and their surroundings through biochemical signaling pathways. Uda et al. (p. 5588) used a recently developed cytometric method to quantitate signaling through biochemical pathways in individual rat pheochromocytoma cells responding to growth factors. The signaling pathways studied provided about 1 bit of information, or only enough for a binary (on or off) decision. In spite of the simplicity, the results showed interactions between pathways with shared components. In some cases, information carried between inputs and intermediate outputs was less than that between the input and more “downstream” outputs, indicating that information was carried through multiple paths. Similarly, in the presence of pharmacological inhibitors of one pathway, others were able to compensate to allow robust transfer of information. Thus, in spite of noise and variation in signal intensities in individual cells, robust transfer of information from the growth factors was achieved.

Abstract

Robust transmission of information despite the presence of variation is a fundamental problem in cellular functions. However, the capability and characteristics of information transmission in signaling pathways remain poorly understood. We describe robustness and compensation of information transmission of signaling pathways at the cell population level. We calculated the mutual information transmitted through signaling pathways for the growth factor–mediated gene expression. Growth factors appeared to carry only information sufficient for a binary decision. Information transmission was generally more robust than average signal intensity despite pharmacological perturbations, and compensation of information transmission occurred. Information transmission to the biological output of neurite extension appeared robust. Cells may use information entropy as information so that messages can be robustly transmitted despite variation in molecular activities among individual cells.

Signaling pathways transmit signals from growth factors to downstream gene expression, influencing various cell fate decisions such as cell differentiation (1). To control cellular responses by stimulation intensity, signaling pathways must reliably transmit stimulation intensity through their signaling activities. The reliability of signal transmission depends on the balance between signal intensity and variation. The smaller the signal variation, the more information can be transmitted through a pathway with the same dynamic range of signal intensity. Even high-intensity signals cannot be reliably transmitted if the variation in signal intensity is large. In contrast, even signals with low intensity can be reliably transmitted if the variation in signal intensity is small (Fig. 1A). Thus, the reliability of signal transmission depends on both average (mean) intensity and variation. As a consequence, the number of controllable states of cellular responses is determined by the number of reliably transmitted signals. Intuitively, the larger the number of reliably transmitted signals, the more information the signal pathway can transmit. If cellular signaling pathways are treated as communication channels in the framework of Shannon’s information theory (212), the amount of information that can be reliably transmitted through a cellular signaling pathway can be measured by mutual information, which corresponds to the logarithm of the average number of controllable states of a cellular response that can be defined by varied upstream signals (1315).

Fig. 1 Information transmission of signaling pathways.

(A) Reliability of information transmission depends on both signal intensity and variation. More information can be transmitted with the same dynamic range of signal intensity if signal variation is smaller. Dots denote intensities of pERKs in individual cells, and lines denote the average intensity of pERKs. p(pERKs|NGF) denotes the distribution (a normalized histogram) of pERKs for a given dose of NGF. (B) Signaling pathways from growth factors, such as NGF, PACAP, and PMA to the IEGs, such as c-FOS and EGR1. Solid lines indicate the reported pathways for each growth factor, and gray dashed lines indicate other possible pathways. The colored boxes are the measured molecules, and white ovals are unmeasured molecules in this study.

We evaluated the information transmission from growth factors to the immediate early genes (IEGs) through various signaling pathways in PC12 cells. Nerve growth factor (NGF), pituitary adenylate cyclase-activating peptide (PACAP), and phorbol 12-myristate 13-acetate (PMA) induce phosphorylation of extracellular signal-regulated kinase (ERK) and 3′-5′-cyclic adenosine monophosphate (cAMP) response element-binding protein (CREB) and expression of the IEGs such as c-FOS and early growth response protein 1 (EGR1), mainly through Ras-dependent, cAMP-dependent protein kinase A (PKA)–dependent, and conventional and novel protein kinase C (PKC)–dependent signaling pathways, respectively (1618) (Fig. 1B, solid lines). We measured the amount of phosphorylated ERK1 and ERK2 (pERKs) and CREB (pCREB) and protein abundance of c-FOS and EGR1 in the cell population (fig. S1). We used quantitative image cytometry (QIC) (19) and obtained simultaneous measurements for two signaling molecules at single-cell resolution. We calculated mutual information byEmbedded Imagewhere p(x) and p(y) are input and output distributions, respectively, and p(y|x) is a conditional distribution. For example, x and y correspond to the intensity of pCREB and c-FOS in an individual cell, and p(x) and p(y) correspond to the normalized histograms of pCREB and c-FOS. The conditional distribution p(y|x) represents the histogram of c-FOS for a given intensity of pCREB. An information set of 1 bit means that the downstream molecules receive two distinguishable states from upstream signals. The measurement by QIC appeared reliable for calculating the joint and conditional distribution of two signaling molecules (fig. S2), as needed for the calculation of mutual information.

To explore information transmission by growth factors, we measured the mutual information between the growth factors and pCREB under conditions for which the distribution of growth factors gives the maximum mutual information between the growth factors and the IEGs (i.e., channel capacity) (Fig. 2A and fig. S3). Hereafter, we used the optimal input distribution so that mutual information between growth factors and the IEGs becomes maximum. In response to NGF and PACAP, the mutual information between growth factors and pCREB was ~1 bit (Fig. 2A, gray, fig. S3), indicating that pCREB receives the information of NGF and PACAP for a binary decision. In response to PMA, the mutual information was ~0.5 bits.

Fig. 2 Information transmission of growth factors to pCREB and the IEGs.

(A) Mutual information (MI) between the indicated growth factors (GF) and pCREB. MI through PATHWAY:G-C (green) and through PATHWAY:E-C (blue), and their sum, the total MI between GF and pCREB (gray). Hereafter, unless otherwise specified, MI is calculated at the time when the total MI reached a maximum. On average, ~1000 cells in response to 11 doses of NGF (0.05 to 12.15 ng/ml with exponential increase to the power of Embedded Image), 11 doses of PACAP (0.05 to 3000 nM with exponential increase to the power of 3), 11 doses of PMA (1 to 1024 ng/ml with exponential increase to the power of 2), and no stimulation were used for calculation of MI (see supplementary materials). The distribution of growth factors that gives the maximum MI (i.e., channel capacity) for c-FOS was used (see supplementary materials). A similar result was obtained when the distribution of growth factors that gives the channel capacity for EGR1 was used (fig. S3). Multivariate MI can either be positive or negative (see supplementary materials). Hereafter, the error bars indicate standard deviations estimated from 20 bootstrap sample sets in each figure. (B) MI between the growth factors and the IEGs (gray) through PATHWAY:E-I (blue), PATHWAY:C-I (green), and PATHWAY:G-I (red). c-FOS (left), EGR1 (right). The maximum of MI in the time course is shown in (A) (also see fig. S3, left column) and (B) (also see fig. S5).

Many kinases, including ERKs and PKA, phosphorylate CREB (20). Therefore, growth factors can transmit information to pCREB through pERKs or through other pathways. We decomposed the mutual information and analyzed the contribution of pERKs for information transmission to pCREB (Fig. 2A). We defined the contribution of information transmission of a specific pathway by decomposing the mutual information, which is represented by multivariate mutual information (fig. S4), e.g., from A to B as PATHWAY:A-B. The information transmission from the growth factors (G) to pCREB (C) through pERK (E) is represented as PATHWAY:E-C (Fig. 2A, blue). The information transmission from the growth factors (G) to pCREB (C) not through pERK (E) is represented as PATHWAY:G-C (Fig. 2A, green). PATHWAY:E-C corresponds to multivariate mutual information of growth factors, pERKs, and pCREB. PATHWAY:G-C corresponds to conditional mutual information between growth factors and pCREB given pERK. The total information transmission from growth factor to pCREB is the mutual information between growth factors and pCREB, which is equal to the sum of PATHWAY:E-C and PATHWAY:G-C. Although pCREB receives similar information from NGF and PACAP, NGF mainly used PATHWAY:E-C, whereas PACAP used PATHWAY:G-C for information transmission to pCREB (Fig. 2A). These results indicate that, for information transmission to pCREB, NGF mainly uses pERKs-dependent pathways and PACAP mainly uses pERKs-independent pathways, probably the PKA pathway.

We also measured the mutual information between growth factors and the IEGs (Fig. 2B and fig. S5). In response to NGF, the mutual information between NGF and the IEGs was ~1 bit, indicating that the IEGs receive enough information from NGF for a binary decision (Fig. 2B). The mutual information between PACAP and the transcriptional factor c-FOS was also ~1 bit, whereas that between PACAP and EGR1 was ~0.5 bits, indicating that only c-FOS receives enough information from PACAP for a binary decision.

We decomposed information (fig. S4) transmitted from growth factor through pERK to the IEG (PATHWAY:E-I) (Fig. 2B, blue), from growth factor through pCREB not through pERK to the IEG (PATHWAY:C-I) (Fig. 2B, green), and from growth factor not through pERK and pCREB to the IEG (PATHWAY:G-I) (Fig. 2B, red). In general, mutual information is non-negative, but multivariate mutual information of more than three variables can be negative (fig. S4). NGF used PATHWAY:E-C as the main pathway for information transmission to pCREB (Fig. 2A, blue) and PATHWAY:E-I as the main pathway to the IEGs (Fig. 2B, blue). PACAP used PATHWAY:G-C as the main pathway for information transmission to pCREB (Fig. 2A, green) and PATHWAY:C-I as the main pathway to the IEGs (Fig. 2B, green). PMA used PATHWAY:G-I as the main pathway to EGR1 (Fig. 2B, red). We identified the main pathway for information transmission to the IEGs solely by measuring cell populations, without conventional pharmacological perturbation. We also calculated the contribution of unmeasured molecules, which can not be calculated by conventional methods using only averaged intensity. For example, the contribution of pERK3 (21, 22), which was not recognized by the antibody used in this study, to information transmission to pCREB was implicitly included in PATHWAY:G-C (Fig. 2A, green). Similarly, the contributions of NFκB (nuclear factor κB) (23)—which is activated in response to the p75 neurotrophin receptor (p75NTR, a low-affinity receptor for NGF)—to information transmission to the IEGs was implicitly included in PATHWAY:G-I (Fig. 2B, red). PMA also activates multiple isoforms of PKCs (16). Contributions of PKCs were also included in PATHWAY:G-I (Fig. 2B, red). Given that the mutual information between PMA and the IEGs was larger than that between PMA and pCREB, PMA appears to use pathways other than pCREB, probably PKCs, for information transmission to the IEGs. Consequently, we conclude that NGF, PACAP, and PMA use different pathways to transmit information to the IEGs for a binary decision.

We pharmacologically perturbed specific pathways by the addition of inhibitors and examined the effects on information transmission (Fig. 3 and fig. S6). PD0325901, MAPK/ERK kinase (MEK) inhibitor that inhibits activation of pERKs, decreased information transmission from growth factors to pCREB through PATHWAY:E-C (Fig. 3A). However, in response to PACAP and PMA, information transmission through PATHWAY:G-C increased in cells treated with PD0325901 and compensated for the decreased information transmission through PATHWAY:E-C, allowing robust information transmission from growth factors to pCREB. H89, a PKA inhibitor, did not affect information transmission to pCREB, although the average intensity of pCREB was decreased by the inhibitor (Fig. 3A and fig. S6). Thus, mutual information appears to be more robust than average intensity, despite some specific perturbations. Addition of bisindolylmaleimide (BIS/GF109203X), a PKC inhibitor, did not affect information transmission from NGF or PACAP to pCREB through PATHWAY:E-C but decreased information transmission from PMA through PATHWAY:E-C. Thus, there appears to be cross-talk between the PKCs and ERK pathways (24). Information transmission from NGF to the IEGs and from PACAP to c-FOS remained at ~1 bit despite the pharmacological perturbations (Fig. 3B), indicating robust information transmission in these pathways. In the presence of PD0325901, information transmission to the IEGs through PATHWAY:E-I decreased, whereas that through other pathways compensatorily increased. In contrast, H89 and BIS did not strongly affect information transmission through any pathway. Pharmacological perturbation allowed us to analyze the robustness and compensation of information transmission to perturbation. Although inhibitors can inhibit other kinases besides their main targets (25, 26), such additional side effects of the inhibitors were implicitly included in one of the pathways, such as PATHWAY:E-C and PATHWAY:G-C (Fig. 3 and supplementary text).

Fig. 3 Information transmission despite pharmacological perturbations.

(A) MI between the indicated growth factors and pCREB (gray) through PATHWAY:G-C (blue) and PATHWAY:E-C (green) in the absence (–) or the presence of PD (5 nM PD0325901, a MEK inhibitor), H89 (5 μM PKA inhibitor), or BIS/GF109203X (0.5 nM PKC inhibitor). Low doses of the inhibitors were used to avoid complete loss of signals and side effects (fig. S6). Here, the distribution of the indicated growth factors optimized for c-FOS in the absence of the inhibitor was used. Similar results were obtained for EGR1 (fig. S7). (B) MI between the indicated growth factors and the IEGs (gray) in the presence of the indicated inhibitor through PATHWAY:E-I (blue), PATHWAY:C-I (green), and PATHWAY:G-I (red). The MI at 50 min after stimulation is shown in (A) and (B).

Fig. 4 Robustness and compensation of information transmission.

(A) ∆Ave (open bar) and ∆MI (closed bar) were defined by subtracting normalized average intensity and MI in the absence of the inhibitor from those in the presence of the inhibitor. (B) Examples of ++ (negative ∆Ave and positive ∆MI; MI is robust), + (negative ∆MI is 40% bigger than negative ∆Ave; MI is weakly robust), and ~ (positive ∆Ave and negative ∆MI; MI is not robust) in (A) and (F) are shown. (C) Main and Other were the subtracted MI of the main and other pathways in the absence of the inhibitor from those in the presence of the inhibitor, respectively. The combinations of decrease of information transmission through the main pathway and increase of information transmission through other pathways are indicated by #. (D) ∆Ave (open bar) and ∆MI (closed bar) in the presence of the inhibitor subtracted from those in the absence of the inhibitor are shown. (E) Compensation of information transmission through the indicated pathways in the presence of the inhibitors. Subtracted normalized information transmission through PATHWAYs:E-C or E-I (blue), PATHWAYs:G-C or C-I (green), and PATHWAY:G-I (red) in the presence of the inhibitor from those in the absence of the inhibitor are shown. # indicates that compensation occurred. (F) Information transmission to NGF-dependent neurite lengths at 24 hours after stimulation in the presence or absence of the indicated inhibitors (left panel) (fig. S15). The optimal distribution of NGF in the absence of the inhibitor was used for calculation of MI. Robustness of information transmission to neurite extension in the presence of the indicated inhibitors (right panel). ++ indicates the negative ∆Ave (open bar) and positive ∆MI (closed bar); MI is robust.

We further examined the robustness of information transmission by comparing the effect of the inhibitors on the average intensity of the signal and mutual information (Fig. 4A, B, and D and fig. S6). Pharmacological perturbations that decreased the average intensity without changes in the shape of distribution also decrease the mutual information. However, despite decreased average intensity, in some cases, mutual information such as that to pCREB in response to NGF in the presence of H89 actually increased (Fig. 4D, ++). In some cases, mutual information such as that to pCREB in response to NGF in cells treated with PD0325901 (or that to c-FOS in response to NGF in cells exposed to PD0325901 or H89) decreased less than the average intensity of the signal (Fig. 4D, +). Only a few pathways showed a greater decrease of mutual information than that of average intensity (Fig. 4D, ~). These results indicate that mutual information is generally more robust than average intensity in the presence of the tested perturbations.

We examined compensation in information transmission (Fig. 4, C and E). Treatment of cells with PD0325901 decreased information transmission from NGF to pCREB and the IEGs through PATHWAY:E-C and PATHWAY:E-I but increased information transmission through PATHWAY:G-C and PATHWAYs:C-I or G-I. This indicates compensation through other pathways in the signaling pathway. Such compensation was also seen in information transmission from NGF to pCREB and the IEGs, from PACAP to pCREB and c-FOS, and from PMA to pCREB and the IEGs (Fig. 4E, #). Both robustness and compensation occurred concomitantly in some cases, such as information transmission from NGF to pCREB, c-FOS, and EGR1 in the presence of PD0325901 (Fig. 4D and E), suggesting that compensation may increase robustness in these pathways. However, only compensation, but not robustness, was seen in some cases, such as information transmission from PACAP to pCREB in the presence of PD0325901 and from PMA to c-FOS in the presence of PD0325901 or BIS. Increased information transmission through the other pathway apparently does not always compensate for the decrease in information carried by the main pathway. Only robustness, but not compensation, was seen in some cases, such as information transmission from PACAP to EGR1 in the presence of BIS. Therefore, the compensation does not always make robustness, and the robustness is not always caused by compensation. For the pathways that were robust despite perturbations (Fig. 4D), the mutual information with respect to the average intensity was hyperbolic and saturated at a high average intensity (fig. S8), indicating that mutual information was less sensitive to the changes in concentration of the growth factors than was average intensity. This may be one of the reasons for the robustness of information transmission to perturbation, and the mechanism of robustness was analyzed by a toy model (figs. S9 to S14).

We investigated whether information transmission to a final biological output—neurite extension—was similarly robust to perturbation (Fig. 4F and fig. S15). Mutual information between NGF and neurite lengths were 0.5 bits in the presence or absence of the inhibitors. Mutual information between growth factors and neurite lengths, the final biological output, was also more robust than the average intensity of neurite lengths under perturbation, as was the case for the mutual information between growth factors and signaling molecules. Thus, although neurite lengths were reduced by the inhibitors, precision of neurite length control was retained. The effects of each inhibitor on the mutual information and average intensity of neurite lengths were similar to those on signaling from NGF to pCREB and to EGR1 rather than signaling to c-FOS. Thus, information on precise control of neurite length appears to be transmitted by pCREB and EGR1 rather than c-FOS, although both EGR1 and c-FOS regulate NGF-dependent neurite extension in PC12 cells (27, 28). Robustness of the mutual information between growth factors and neurite length to perturbation can be interpreted to imply that the average number of controllable states of the population of neurite lengths controlled by growth factors can be maintained despite changes in average neurite lengths caused by perturbation. The property of independence of absolute chemical concentration for information transmission to a biological phenotype may be advantageous as a design principle of body planning independent of body size. Otherwise, as the body size increased, higher concentration of growth factors would be required to maintain the same precision.

Mutual information was calculated from the distribution at each time point in this study. Ideally, mutual information of the transient response should be calculated from the distribution of the temporal trajectories of the input and output molecule activities (4, 8, 10, 29). Mutual information between input and output is always decreased compared with that between input and intermediate, that is, data-processing inequality holds. The inequality seems to be useful to understand the information transmission of the signaling network (supplementary text).

We found the robustness and compensation of signaling pathways at the cell population level (fig. S16). Our results indicate that robust signaling pathways that use information entropy as information are more robust to noise than is signal intensity. Despite the variation of signal intensity and abundance of molecules between individual cells, cells can reliably receive growth factor information through robust signaling pathways.

Supplementary Materials

www.sciencemag.org/cgi/content/full/341/6145/558/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S16

Tables S1 and S2

References (3037)

References and Notes

  1. Acknowledgments: We thank our laboratory members for critical reading of the manuscript and for technical assistance with the experiments and Y. Kabashima (Tokyo Institute of Technology) and K. Horimoto (Computational Biology Research Center, AIST) for helpful discussion and critical reading of manuscript. This work was supported by the Dynamic Mechanisms of and Fundamental Technology for Biological Systems and the Creation of Fundamental Technologies for Understanding and Control of Biosystem Dynamics, CREST, from Japan Science and Technology (JST); by a KAKENHI Scientific Research grant (A) (no. 21240025) and a Young Scientists grant (B) (no. 25830142) from the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT); by the Strategic International Cooperative Program (Research Exchange Type), JST; and by a Human Frontier Science Project (HFSP) grant (RGP0061/2011).
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