Information transfer by leaky, heterogeneous, protein kinase signaling systems Margaritis Voliotisa, Rebecca M. Perrettb, Chris McWilliamsa, Craig A. McArdleb, and Clive G. Bowshera,1 a

School of Mathematics and bLaboratories for Integrative Neuroscience and Endocrinology, School of Clinical Sciences, University of Bristol, Bristol BS8 1TW, United Kingdom Edited* by Ken A. Dill, Stony Brook University, Stony Brook, NY, and approved November 20, 2013 (received for review July 31, 2013)

Cells must sense extracellular signals and transfer the information contained about their environment reliably to make appropriate decisions. To perform these tasks, cells use signal transduction networks that are subject to various sources of noise. Here, we study the effects on information transfer of two particular types of noise: basal (leaky) network activity and cell-to-cell variability in the componentry of the network. Basal activity is the propensity for activation of the network output in the absence of the signal of interest. We show, using theoretical models of protein kinase signaling, that the combined effect of the two types of noise makes information transfer by such networks highly vulnerable to the loss of negative feedback. In an experimental study of ERK signaling by single cells with heterogeneous ERK expression levels, we verify our theoretical prediction: In the presence of basal network activity, negative feedback substantially increases information transfer to the nucleus by both preventing a near-flat average response curve and reducing sensitivity to variation in substrate expression levels. The interplay between basal network activity, heterogeneity in network componentry, and feedback is thus critical for the effectiveness of protein kinase signaling. Basal activity is widespread in signaling systems under physiological conditions, has phenotypic consequences, and is often raised in disease. Our results reveal an important role for negative feedback mechanisms in protecting the information transfer function of saturable, heterogeneous cell signaling systems from basal activity.

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heterogeneity of proteins over time (10), and the promiscuity of signaling intermediaries (11). Many extracellular stimuli control cell fate decisions using PK signaling, often through MAPK cascades such as the well-known ERK pathway (12, 13). Basal MAPK activity is known to be functionally relevant. Basal ERK activity enhances cell substrate interactions (14) and is essential for survival of quiescent, unstimulated cells (15). In yeast, basal activity in one branch of the Hog1 MAPK pathway, combined with negative feedback from Hog1, results in faster response to osmotic stress and higher sensitivity to external signals (16). Most mammalian cells express receptor tyrosine kinases (RTKs) and G protein-coupled receptors (GPCRs) that act to stimulate the Raf-MEK-ERK cascade (12, 13, 17). Basal activity is often observed in signaling from RTKs (18) and is evident in the measured levels of activated ERK in unstimulated cells (14, 19, 20). Most antagonists of GPCRs behave as inverse agonists, suppressing the response caused by the basal (or constitutive) activity of the receptor, and most drugs acting on GPCRs that are in clinical use are now recognized as inverse agonists (21). Raised basal activity is also known to be important in various diseases (21), including the roles of the NGF receptor in breast cancer (22) and the V600EB-Raf protein in melanoma. In fact, the ERK pathway is dysregulated in about one-third of all human cancers, frequently through gain-of-activity mutations in the RAS and RAF genes (23). Here, we use mutual information to quantify the effects on information transfer of basal activity and heterogeneity in network componentry, comparing our systems with and without

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ells must sense extracellular concentrations and transfer the information contained about their environment reliably to make appropriate decisions. Understanding the process of information transfer from the biological environment to the nucleus (1) and studying quantitatively how information about the signal is lost along the way are essential in understanding cellular decision-making (2, 3). The signal transduction networks used by cells are subject to various sources of noise, and we are only beginning to explore how these affect the process of information transfer (4, 5). Here we focus, in the context of protein kinase (PK) signaling, on the little-studied effects of two important types of biological noise: cell-to-cell variability in the componentry of the network and basal network activity. The effect on information transfer of cell-to-cell variation (heterogeneity) in the protein componentry of signaling networks remains largely unexplored. Such variation is expected under physiological conditions (6) and underlies the variable responses observed for genetically identical cells exposed to the same stimulus or drug treatment (7–9). By basal activity, we mean the propensity for activation of the signaling system in the absence of the stimulus or signal of interest. Basal activity is widespread in signaling systems under physiological conditions (with observable phenotypic consequences) and is often raised in disease. Although its source is not always well-characterized, such activity arises in numerous ways—for example, the constitutive activity of receptors, basal enzymatic activity caused by the conformational E326–E333 | PNAS | Published online January 6, 2014

Significance Extracellular concentrations convey information to cells about their environment. To sense these signals, cells use biomolecular networks that exhibit inevitable cell-to-cell variability and basal activity. Basal activity is widespread under physiological conditions (with phenotypic consequences), is often raised in disease, and can eradicate the transfer of information. In an experimental study of ERK signaling by single cells exhibiting heterogeneous ERK expression and basal activity, we verify our central theoretical prediction: Negative feedback substantially increases information transfer to the nucleus by preventing a near-flat average response curve and reducing sensitivity to variation in the ERK expression level. Our results reveal an important role for negative feedback mechanisms in protecting information transfer by saturable cell signaling systems from basal activity. Author contributions: C.A.M. and C.G.B. designed research; M.V., R.M.P., and C.M. performed research; M.V., R.M.P., and C.G.B. contributed new reagents/analytic tools; M.V., C.M., and C.G.B. analyzed data; and C.A.M. and C.G.B. wrote the paper. The authors declare no conflict of interest. *This Direct Submission article had a prearranged editor. 1

To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1314446111/-/DCSupplemental.

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Results Loss of Negative Feedback Can Eradicate Information Transfer by Leaky Heterogeneous PK Signaling Systems. Negative feedback is

a common feature of PK signaling systems. For example, activated ERK inhibits Raf by phosphorylation (30), and ligandinduced phosphatases (e.g., MAPK phosphatases and Sprouty proteins) negatively regulate MAPK activation (31, 32). In this paper, we argue that negative feedback protects information transfer by these systems from the combined effects of basal activity and cell-to-cell variation in network componentry. We begin with the simple building block in which a PK phosphorylates

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negative feedback and of different sources of noise that harm signaling. In our experimental study of ERK signaling, we examine the effect of cell-to-cell variation in expression levels of the ERK protein itself and show that the interplay between such variation, basal activity, and negative feedback is critical for the effectiveness of PK signaling.

Fig. 1. Output–signal relationships for phosphorylation–dephosphorylation cycles: the effects of basal activity and negative feedback. We consider enzymatic cycles (A) without and (B) with basal kinase activity [i.e., catalytic activity of the kinase in the absence of ligand (L)] and in each case, without and with negative feedback (no FB and FB, respectively; indicated by dotted lines). p-ase, phosphatase; Sub, substrate. Basal activity eradicates the switch-like response, but the output dynamic range is mostly restored by negative feedback. (C–F) For each value of the signal (total level of L) and five different fixed levels of total substrate (color-coded), we show the average level of the output (solid lines) together with the 0.1 and 0.9 percentiles of the output distribution (output is the log of the level of pSub). Rate parameters in C and E, and in D and F, are identical except for the presence of basal kinase activity. (G–J) The same as in C–F but with stochasticity in the level of total substrate (the log10 of total substrate is approximately normally distributed as shown, with a mean of 3.9 and constant over time); output distributions are depicted by the probabilities attaching to each bin. Results are based on stochastic simulation of the reaction networks (SI Appendix, Table S1 shows networks and parameters).

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negative feedback. Mutual information and information capacity are becoming increasingly important for quantifying information transfer by biochemical systems (4, 24–26). Mutual information allows the comparison of systems in terms of how well a given signal can be inferred using the Bayesian posterior distribution (27) based on each system’s intracellular output. We use statistical decision theory to explain in what sense higher mutual information (SI Appendix, Eq. S6) implies better inferences of the biological environment in question (SI Appendix). This approach motivates our experimental measurement of the mutual information between stimulus concentration and nuclear activated ERK levels for single cells. We propose to quantify the effect of heterogeneity in network componentry by computing the increase in mutual information under the assumption that the levels of the variable components in each cell are monitored in addition to the outputs of the signaling network. Recent methods for decomposing variation in the output of biochemical systems (28, 29) are used to provide additional insight into the effects of

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its substrate and a phosphatase dephosphorylates it. This phosphorylation–dephosphorylation cycle is a widespread motif in biochemical signaling networks, including MAPK cascades. Because cellular signaling networks are complex and partially characterized, this cycle also provides us with a parsimonious theoretical model for generating hypotheses, which we then investigate experimentally. Loss of Negative Feedback Can Eradicate Output Dynamic Range in the Phosphorylation–Dephosphorylation Cycle with Basal Activity.

The standard model of the phosphorylation–dephosphorylation cycle has no basal activity or negative feedback. It is well-known that this model generates a sharp, switch-like (or ultrasensitive) response when the modifying enzymes are well-saturated with substrate (33). We performed simulations of the stochastic, steady state dynamics of the cycle in this regime, explicitly allowing for the binding of an activating ligand to the PK. The signal value, S, is the total number of ligand molecules in the system. Initially, only the liganded kinase can bind the substrate (Fig. 1A). Fig. 1C depicts the signal dependence of the mean and variability of the phosphorylated substrate (pSub) level for different total numbers of substrate proteins in the system. The response is sharp, as expected, with high response uncertainty near to the threshold (34). The effect of negative feedback on the properties of the standard cycle does not seem to have been studied. To introduce negative feedback, we assume that binding of pSub to either form of the kinase causes its reversible inactivation. We observe a more graded response as a function of the signal in the presence of negative feedback, as has been reported for some other biochemical networks (35–37), while the threshold value is unchanged (Fig. 1D). Next, we introduce basal activity into the system (Fig. 1B, red arrow). To do so, we hold other rate parameters constant and allow substrate phosphorylation by the unliganded kinase to proceed at a reduced rate compared with phosphorylation by the liganded kinase. With basal activity, the response becomes a shallow, linear function of the signal (Fig. 1E). Due to its switch-like response, the signaling system is particularly vulnerable to basal activity because the switch can be activated in the absence of the appropriate signal—if the basal activity is sufficiently high compared with the phosphatase activity (SI Appendix), there is no signal value for which low output is a steady state of the switch mechanism. As expected, the effect emerges in a sudden transition as the basal catalytic activity is increased (SI Appendix, Fig. S1) and, depending on the phosphatase activity, can occur despite the basal catalytic activity being small relative to that of the liganded kinase (10% in Fig. 1). The range of the cycle’s output collapses to near zero, and with some variation (uncertainty) present in the total amount of substrate in the system, different signal values become essentially impossible to tell apart (Fig. 1I). Variability in the output is now mostly because of the sensitivity of the average response to the value of total substrate. This is a surprising effect: Loss of negative feedback results in loss of all information transfer. The zero information transfer arises because the output distributions are essentially the same for different values of the signal in the no feedback cycle (Fig. 1I). Importantly, negative feedback provides a solution to the signaling problem posed here by basal activity, restoring the (dynamic) range of the output of the leaky system (Fig. 1 F and J). In the presence of variation in the total substrate level, negative feedback substantially increases the mutual information between the phosphorylated substrate level and the signal, I(pSub; S), from 0.00 in Fig. 1I to 0.84 bits (for the lognormal signal distribution yielding the highest mutual information) in Fig. 1J. To understand further how different sources of noise in the output affect information transfer, we make use of recently introduced methods for decomposing variation in the output of E328 | www.pnas.org/cgi/doi/10.1073/pnas.1314446111

biochemical systems (28). The fidelity of signaling (29) is based on the output-signal relationships that play a prominent role in most cell signaling research, is computed by decomposing the output variance, and can be seen as a generalized signal-to-noise ratio. The components of the output variance used correspond to widespread measures for understanding biochemical systems (dynamic range, intrinsic variation, etc.). The fidelity is related to mutual information, because it sets a lower bound on mutual information equal to log(1 + fidelity)1/2 when evaluated under the appropriate signal distribution (28). Because we are interested in the effects of heterogeneity in the componentry of signaling networks, we focus here on the kinase– phosphatase systems where the total substrate level has a distribution (Fig. 1 G–J), modeling cell-to-cell variability in the timeinvariant total substrate level. We can explain almost all of the large increase in mutual information caused by negative feedback using the fidelity measure. It is given here by the dimensionless expression (28, 29), VarfE½ZjSg o fidelity ¼ n ; [1] E ðE½ZjS; tSub − E½ZjSÞ2 þ EfVar½ZjS; tSubg with Z as the output (log of the level of pSub), S as the signal, tSub as the total level of substrate, and E denoting the expectation or average. The numerator is a precisely defined measure of the output dynamic range, while the denominator gives the noise arising from two sources: first, the global sensitivity of the average response to total substrate levels and second, the stochasticity of the biochemical reactions comprising the transduction mechanism. Because there is no upper limit mathematically on how large fidelity can be, it is sometimes convenient to use the measure 1 − ( fidelity + 1)−1, the fraction of the variance in Z explained by variation in the signal. This measure is an increasing function of fidelity that takes values between zero and one. Negative feedback causes the fidelity of the leaky phosphorylation–dephosphorylation cycle to increase from 0.01 to 2.0 as a result of the large increase in the output dynamic range in the numerator of Eq. 1 (Fig. 1 I and J). This corresponds to an increase in the implied lower bound on the mutual information, I (pSub; S) = I(pSub; logS), from 0.00 to 0.80 bits (using that logS is normally distributed and E[ZjS] is approximately linear here). The sensitivity to total substrate decreases slightly, whereas the contribution of biochemical stochasticity increases (but is an order of magnitude smaller than the other terms for the system with feedback). We conclude that it is the effect of negative feedback on the output dynamic range which explains the substantial increase in mutual information (SI Appendix, Table S4). It is worth noting that the response function for the leaky cycle with negative feedback (Fig. 1J) is not obtained simply by translating to the left the one for the same cycle without basal activity (Fig. 1H). What is unusual about the effect of negative feedback in this leaky signaling system? Previous work has found that negative feedback tends to decrease both the output dynamic range and the variance caused by biochemical stochasticity, because it suppresses means as well as variances (29, 38). Information transfer can increase or decrease, depending on which of the two effects dominates (4). Here, as a result of the basal activity, the output dynamic range dramatically increases with negative feedback (and variance caused by biochemical stochasticity also increases) (Fig. 1E cf. Fig. 1F), the opposite effects to those reported previously. Negative Feedback Protects Information Transfer from the Combined Effects of Basal Activity and Heterogeneity in Substrate Levels. Fig. 2

explores the effects in the leaky cycle of varying both the signal Voliotis et al.

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distribution and the extent of variation in the total substrate level. We use a lognormal distribution for total substrate to capture the nonnegativity and skewness of the distribution of numbers of proteins and consider, for the lognormal signals, a broad range of locations and scale (or range) parameters. For the vast majority of cases considered, negative feedback increases the mutual information between the signal and the phosphorylated substrate level (Fig. 2 A–D, Upper). An exception is the case with no variation in total substrate level, where the mutual information, I( pSub; S), for the feedback and no feedback cycles is broadly comparable in magnitude. The results highlight the benefit of careful quantification of information transfer using mutual information—it is the combined effects of basal activity and heterogeneity that make information transfer vulnerable to loss of negative feedback. In the complete absence of variability in total substrate, the cycle without feedback can give surprisingly good information transfer if the level of substrate is not too high (Figs. 1E and 2A). Although its output dynamic range is small, variation around the mean response is also small. Nevertheless, in the absence of feedback, the information in the phosphorylated substrate level is nonrobust and falls rapidly to low levels when variation in total substrate is introduced. Variability in the output caused by the sensitivity of the average response to the total substrate level then overwhelms the small output dynamic range. Negative feedback, however, is able to substantially increase the information transfer, I(pSub; S), in these circumstances, for the majority of the signal distributions considered (Fig. 2 B–D). The information loss caused by variation in total substrate can be evaluated (SI Appendix) as the difference between I(pSub, tSub; S)—the joint information when the level of total substrate is also monitored in interpreting the output—and I( pSub; S). This difference is equal to the amount that the information in Voliotis et al.

phosphorylated substrate would increase, on average, if total substrate were fixed (SI Appendix, Eq. S5). As the variation in total substrate increases, the joint information I( pSub, tSub; S) remains fairly constant for the cycle with feedback (Fig. 2 B–D, Lower). However, the information loss due to total substrate variation tends to increase, as expected, and the information in the phosphorylated substrate level, I( pSub; S), is gradually eroded (Fig. 2 A–D, Upper compared with Fig. 2 B–D, Lower). Analogous results for the cycle without basal activity are given in SI Appendix. The entropies of the signal distributions used in Fig. 2 vary between 2.3 and 10.4 bits approximately (as a result of discretizing the distribution of S so that its value is an integer number of molecules). We thus observe substantial loss of information relative to the maximum possible information transfer for these distributions (the signal entropy), despite the kinase, phosphatase, and substrate not being present in low numbers of molecules. Finally, in the context of Fig. 1, we explored the relationship between the strength of the negative feedback, the magnitude of the basal kinase activity, and information transfer, I(pSub; S), by the leaky cycle. We parameterize negative feedback strength by the binding rate of pSub to the kinase. Information transfer is hump-shaped as a function of feedback strength, peaking at an optimal strength that is quite insensitive to the magnitude of the basal activity (SI Appendix, Fig. S3). Intuitively, information transfer can decrease for higher feedback strengths because of the detrimental effects of biochemical stochasticity encountered with lower numbers of molecules. The optimal mutual information decreases as the basal activity is increased, as expected. We then varied the negative feedback mechanism, instead having the phosphorylated substrate activate gene expression of phosphatase (or an allosteric activator of the phosphatase). Negative feedback can again restore information transfer to 1 bit or PNAS | Published online January 6, 2014 | E329

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Fig. 2. Information transfer by leaky, heterogeneous phosphorylation–dephosphorylation cycles: the effect of negative feedback. We consider enzymatic cycles with basal kinase activity and heterogeneity in total substrate level, with and without negative feedback (FB and no FB, respectively). Negative feedback protects the information transmitted in the level of pSub. The variance of total substrate increases from A to D as shown; the distribution of total substrate is lognormal, and mean[log10tSub] is 3.9. A–D plot mutual information for the network with negative FB against mutual information for the network without feedback (no FB), with lines having a gradient of one shown in black: Upper shows I(pSub; S), and Lower shows the joint information I(pSub, tSub; S) (SI Appendix, Eq. S5). The changing scales of the axes are highlighted by red boxes. Each dot corresponds to a particular discretized lognormal signal distribution (with color indicating the entropy of the signal, S). The means of the distributions of log10(S) vary uniformly between 1.0 and 2.8, and the SDs vary between 0.025 and 0.25. Results are based on stochastic simulation of the reaction networks (SI Appendix, Table S1 shows networks and parameters).

more. Interestingly, the response functions with negative feedback are switch-like, and the feedback, therefore, causes the opposite effect to response linearization (because it converts a linear response to a sigmoidal one) (SI Appendix, Fig. S5). Expressing additional phosphatase molecules when signal detection is needed (in the presence of ligand) is an attractively simple, although energetically costly, solution to the basal activity problem. A main conclusion, then, of our theoretical modeling (extended below) is the prediction that information transfer by leaky heterogenous PK signaling systems is highly vulnerable to mutations causing loss of negative feedback. We now turn to experimental testing of this prediction in the context of Raf/MEK/ERK signaling in HeLa cells, where there is cell-to-cell variation in the expression level of ERK, the final substrate in the cascade. Information Transfer by ERK Signaling Systems: The Interplay of Basal Activity, Heterogeneity, and Negative Feedback. Raf kinases phos-

phorylate and activate MEK which, in turn, phosphorylates ERK1

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and ERK2 on Thr and Tyr residues of a TEY activation loop (12, 13). ERK (used here to denote ERK1 and ERK2) is mostly cytoplasmic in resting cells, but activation causes nuclear accumulation of dual phosphorylated ERK (ppERK) (39), enabling phosphorylation of nuclear substrates, including transcription factors that control cell fate. ERK-mediated negative feedback is known to influence response kinetics rapidly by inhibitory phosphorylation of Raf or SOS (30), and also more slowly by increasing expression of MAPK phosphatases (31). Furthermore, recent work emphasizes that the ERK cascade exhibits the properties of a negative feedback amplifier, with ERK-mediated negative feedback limiting the responsiveness of tumor cells to MEK inhibitors (37). Here, we use automated cell imaging to monitor both the level of ppERK in the nucleus and the total level of ERK expression in HeLa cells (SI Appendix). We stimulate the cells (after 24 h in low-serum conditions) with either EGF (to activate ErbB1 receptors) or phorbol 12,13 dibutyrate (PDBu; to activate PKC),

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Fig. 3. ERK-mediated negative feedback substantially increases information transfer to the nucleus. (A) The Raf-MEK-ERK signaling network is shown activated by both RTK and PKC, with negative feedback from activated ERK. (B and C) Time courses of mutual information for stimulation by a constant level of (B) PDBu or (C) EGF. Comparison of the signaling systems with feedback (FB; solid lines) and without feedback (no FB; dashed lines) from ppERK. Mutual information between nuclear levels of ppERK and the signal, I(nppERKt; S) are shown in green, and joint mutual information (assuming that the total ERK level is also taken into account), I(nppERKt, TotERKt; S), is shown in black. Results based on uniform signal distributions with signal concentrations as in D and E (yielding signal entropies of 2.8 and 3.0 bits, respectively). Time is time from stimulus. (D) For the responses to PDBu at an early and a late time, the distributions of the output (nppERKt) corresponding to each signal concentration, with the probability in each output bin color-coded. Means (dark blue lines) and SDs (light blue lines; right axes) of output are also shown. AFU; arbitrary fluorescence units. Data are the same as data used in B. (E) The same as in D but for the EGF stimulus and using the data from C.

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ERK-Mediated Negative Feedback Substantially Increases Information Transfer to the Nucleus. We measure information transfer to the

nucleus using I(nppERKt; S), the mutual information between nuclear levels of ppERK at time t and the concentration of signal molecules (either PDBu or EGF). Comparing time courses of this mutual information for cells expressing WT and catalytically inactive ERK2-GFP (Fig. 3 B and C, solid and dashed green lines), we observe that negative feedback is needed to maintain effective signaling to the nucleus. We assume uniform distributions of the signal throughout Fig. 3 across the concentrations shown, giving a signal entropy of 2.8 bits for PDBu and 3.0 bits for EGF (we generalize our conclusions to a broad range of signal distributions below). The results from a duplicate experiment are shown in SI Appendix, Fig. S6. For the system with feedback from ERK, measured values of I(nppERKt; S) range for PDBu stimulation from 0.7 to 1.1 bits (Fig. 3B) and for EGF stimulation from 0.4 to 0.7 bits (Fig. 3C). Information transfer peaks more slowly for PDBu than EGF. The majority of the information transferred to the nucleus by this system is lost by the no feedback system (>60% for all times in Fig. 3 B and C, except 120 min for EGF). Recall that the joint mutual information, I(nppERKt, TotERKt; S), measures the information transfer when the cell-wide level of ERK expression (TotERKt) in each cell is taken into account. Much of this joint information transferred by the feedback system is again lost by the no feedback system under stimulation with PDBu (except at 5 min). The difference between the black and green lines in Fig. 3 B and C quantifies the information loss when the cell monitors nuclear ppERK levels alone. The minimum, average, and maximum such losses measured for the system with feedback were 0.14, 0.27, and 0.41 bits for PDBu and 0.10, 0.17, and 0.35 bits for EGF. Notice that the maximum mutual information that would be obtained on average if total ERK expression was fixed (SI Appendix, Eq. S5) is no higher than 1.3 bits for PDBu and 1.1 bits for EGF. To understand the effect of the ERK-mediated feedback, we examine the dependence on signal concentration of the distribution of nuclear ppERK levels across cells, focusing on an early and a late time point (Fig. 3 D and E). Here, the feedback converts an approximately linear mean response function, with small slope, to a sigmoidal one with substantially reduced basal level (reduced nuclear ppERK at zero ligand concentration). The no feedback system has diffuse and similar output distributions at all signal levels, including the zero one. By contrast, the output distributions for the system with feedback overlap to a lesser extent. Evaluating the contributions of the three terms in Eq. 1 to our fidelity measure provides additional insight. For PDBu at 30 min, ERK-mediated feedback increases fidelity from 0.16 to 2.7 [I(nppERKt; S) increases from 0.11 to 1.0 bits], and for EGF at 5 min, the increase is from 0.10 to 1.3 [I(nppERKt; S) increases from 0.08 to 0.70 bits]. The feedback increases the output dynamic range and decreases the sensitivity of the mean response to the total ERK level (Fig. 4), and usually also results in a small decrease in other sources of output variation (using the data in Fig. 3 D and E and a uniform signal distribution) (SI Appendix, Table S4). Overall, the fidelity therefore increases, driven by the first two effects. The increased sensitivity of the Voliotis et al.

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Fig. 4. Variation in network componentry: the effects of the expression level of the ERK protein in the systems without (no FB) and with feedback (FB). (A and B) For each concentration of PDBu, we plot the average output, E[nppERK t], at t = 30 min for six values of total ERK corresponding   tjS, TotERK to the 17,27, . . . ,67 quantiles of the observed distribution of total ERK [measured in log arbitrary fluorescence units (AFU)]. For the same values of total ERK, we show the band given by ±1 SD, V[nppERKtjS, TotERKt]1/2. Also plotted is the population average output, E[nppERKtjS], which is shown as a black line. (C and D) The same as in A and B but for EGF stimulus and the responses at 5 min. Results are computed using the same data as in Fig. 3 D and E and smoothing spline regression.

mean response to the total ERK level results in the diffuse output distributions seen for the no feedback system in Fig. 3 D and E. Under chronic rather than acute stimulation as here, ref. 30 also finds that negative feedback from ERK (by phosphorylation of Raf-1) confers increased robustness of the mean response to total ERK level. We propose that, in our cell system, negative feedback mediated by ERK is needed to preserve information transfer to the nucleus as a result of the combined effect of heterogeneity in ERK expression and the level of basal activity in the ERK pathway. The importance of negative feedback from ERK is well-established, and has already been discussed. Although positive feedback in other MAPK pathways and other cell types, such as oocytes, is known (41), there seem to be no previous reports of positive feedback from ERK in HeLa cells. Basal activity of ppERK has been shown previously (19, 20), and is clearly manifested on breaking feedback from ERK here (outputs for zero stimulus are shown in Fig. 3 D and E) and as shown in ref. 9. Our interpretation of the experimental results is strongly supported by the effects of breaking negative feedback that are predicted by our theoretical work. In the phosphorylation–dephosphorylation cycle with basal activity and heterogeneous substrate levels, we find near-zero information transfer and nearzero output dynamic range in the absence of negative feedback (Fig. 1 I and J, and Fig. 2 B–D, Upper). Both information transfer and output dynamic range can be restored by negative feedback. We also performed stochastic simulation of a MAPK cascade model in which Raf is activated by PKC, and the latter directly PNAS | Published online January 6, 2014 | E331

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studying populations of cells at a range of times after initial stimulation. We use siRNA to knockdown endogenous ERK and recombinant adenovirus to add back previously characterized imaging reporters (20, 40) consisting of either a WT ERK2-GFP fusion or a catalytically inactive mutant (K52R ERK2-GFP). Expression of the inactive mutant allows us to examine the network in the absence of ERK-mediated feedback. Our aim is to study the transfer of information by the signaling system to the nucleus, which is reflected in the nuclear levels of ppERK that occur in response to the different stimulus concentrations.

binds the signaling ligand (thus mimicking our system with PDBu stimulation). Basal activity is introduced through a constant level of a second, weakly activating ligand. Otherwise, the model is taken from ref. 37. Again, for the leaky heterogeneous system, negative feedback (from ERK to Raf) converts an approximately linear mean response function with small slope to a sigmoidal one with reduced basal level, substantially increasing the output dynamic range (SI Appendix, Fig. S7). These mean response functions are also less sensitive to variation in the total level of ERK than the response functions of the feedback intact system (SI Appendix, Table S4). The information transfer from the stimulus to activated ERK is, therefore, substantially increased by the negative feedback from 0.08 to 0.91 bits (under a uniform signal distribution). The inclusion of additional negative feedback by expression of phosphatase molecules (acting on phosphorylated ERK) increases the output dynamic range still further (SI Appendix, Fig. S8). For the experiments described above, we knocked down endogenous ERK and infected cells with adenovirus-expressing ERK2-GFP at 10 pfu/nL. This titer was used to obtain a broad range of ERK expression levels, but we also performed experiments with a lower adenoviral titer equal to 1 pfu/nL. With the lower titer, ERK-mediated feedback again improves information transfer to the nucleus by ppERK (PDBu stimulus) (SI Appendix, Fig. S9) and, for the uniform signal distribution, >44% of the information transferred is lost by preventing feedback. Breaking the feedback again reduces the output dynamic range, increases the sensitivity to total ERK variation, and reduces the fidelity (SI Appendix, Table S4). We also performed experiments with cells expressing endogenous ERK (i.e., without ERK knockdown or adenovirus treatment), and information transfer was mostly intermediate between the higher and lower titer systems. Information losses caused by variation in total ERK by all three systems with feedback intact were broadly similar. To assess the impact of the signal distribution (SI Appendix, Fig. S10), we evaluated the information transfer, I(nppERKt; S), for all signal distributions having the same support as the uniform one already used and with probabilities either zero or a multiple of 1/7 for PDBu (1/8 for EGF). We find, using either adenoviral titer, that our conclusion holds for this wide range of signal distributions: ERKmediated feedback enhances information transfer to the nucleus in the presence of basal activity and heterogeneity in ERK expression. Discussion Cells must sense concentrations in their environment and transfer the information contained reliably to make appropriate decisions (29, 42). The effects of different kinds of noise on the signal transduction networks that perform this task are still poorly understood. A recent study of TNF signaling by single cells (4) concluded that noise can substantially restrict information transfer about stimulus intensity, particularly when just one or two biochemical outputs are examined, but the principle sources of this noise are not known. In general, different types of noise are likely to play a role in reducing information transfer: basal network activity, cell-to-cell variation (or heterogeneity) in network componentry, promiscuity of signaling intermediaries (5), and fluctuations from the stochastic nature of the transduction mechanism. Here we focus, in the context of protein kinase (PK) signaling, on the effects of the first two of these types of noise. We quantify the effect of variation in network componentry by computing the increase in mutual information under the assumption that the levels of the variable components (e.g., levels of total substrate) are monitored in addition to the outputs of the signaling network. Our estimation algorithm for mutual information avoids the need to discretize or bin the output. Along with refs. 4 and 26, we provide measurements of mutual information for cell signaling experiments. We find, in common with refs. 4 and 26, values of ∼1 bit or less for the single cell E332 | www.pnas.org/cgi/doi/10.1073/pnas.1314446111

under conditions of constant stimulation using a single stimulus and output (the different studies, however, use different stimulus entropies). When the mutual information measured is 1 bit, an often-stated conclusion is that the cell can therefore distinguish (implicitly, without error) two states of the biological environment or signal but not more than two states, suggesting the prevalence of binary decisions by cells. We believe that this conclusion can be misleading. It seems to stem from the Shannon theory of communications engineering (43), particularly the asymptotic equipartition property, which considers infinitely (asymptotically) long sequences of inputs and outputs arising from the repeated use of the signaling mechanism. We prefer a different interpretation of the mutual information between the biological environment and the biochemical network output (perhaps at steady state or some fixed time, t): Mutual information quantifies the extent to which the Bayesian posterior prediction of the environment based on the network output improves on the (prior) prediction using the distribution of the signal in the environment alone. This interpretation recognizes that cellular inference about the environment is usually imperfect and makes clear that an output with mutual information of 1 bit can provide information about the state of nonbinary environments. We provide additional discussion and mathematical derivations in SI Appendix. Basal network activity describes the propensity for activation of the network output in the absence of the signal of interest. Basal activity is widespread in signaling systems under physiological conditions (with observable phenotypic consequences) and is often raised in disease. Its presence has been widely reported in cell signaling, including the fields of MAPK and GPCR signaling. Basal activity comes as no surprise given the modern understanding of the conformational heterogeneity of proteins (10, 44): Receptors and enzymes constantly transition among an ensemble of states, some of which are catalytically active (even in the absence of activating ligands and allosteric modulators). Due to their switch-like, nearly off–on responses, PK signaling systems without negative feedback are particularly vulnerable to basal activity, because the switch can be activated in the absence of the appropriate signal. With even small amounts of variation in protein substrate levels, different signal values are difficult to tell apart, and information transfer falls dramatically to near zero. Using theoretical models of leaky heterogeneous PK signaling systems, we predict that negative feedback substantially increases information transfer by both preventing the near-flat average response curve and reducing sensitivity to variation in expression levels of the substrate protein. This prediction is verified in an experimental study of ERK signaling by single cells with heterogeneous ERK expression. A conventional view of negative feedback is that it reduces both output dynamic range and variation from other sources, so that information transfer can increase or decrease depending on which effect dominates (4, 29). By contrast, negative feedback in our leaky systems substantially increases output dynamic range, reduces variation from other sources, and therefore substantially increases information transfer. Negative feedback by expression of additional phosphatase molecules, such as MAPK phosphatases, when signal detection is needed (in the presence of ligand) is an attractively simple negative feedback solution to the basal activity problem. However, the mechanism and speed of negative feedback turn out to not be crucial for the protection of information transfer at steady state. The Ras/Raf/MEK/ERK pathway is often dysregulated in human cancer, frequently through gain-of-function mutations in the RAS and RAF genes (45). The B-RAF mutation occurs in the majority of melanomas and results in increased activation of ERK, with the V600EB-RAF single substitution mutation occurring commonly (46). The V600EB-Raf protein has raised kinase activity, activating the pathway independently of Ras, and is Voliotis et al.

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feedback mechanisms in protecting the information transfer function of saturable, heterogeneous cell signaling systems from basal activity. They are an important step toward deciphering the design of biochemical signaling networks, their role in cellular decision-making, and their malfunction in disease. Methods To estimate mutual information for a continuous, possibly multivariate output, Z, we write I(Z; S) = −Es[h(ZjS = s)] + h(Z) and use nearest neighbor methods to estimate each term (SI Appendix). For the first term, we estimate the conditional entropy, h(ZjS = s), for each signal value s and then take the average according to the signal distribution. For the second term, we use an iterative scheme to sample from the joint distribution corresponding to that signal distribution. Cell culture, transfection, and imaging are described in Results and SI Appendix. ACKNOWLEDGMENTS. The authors thank Ramon Grima, Peter Swain, and Philipp Thomas for insightful feedback. M.V. acknowledges a Medical Research Council Fellowship in Biomedical Informatics, and C.A.M. acknowledges Biotechnology and Biological Sciences Research Council Grant JO14699/1 and Medical Research Council Grant G0901763.

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BIOPHYSICS AND COMPUTATIONAL BIOLOGY

insensitive to negative feedback from ERK (47). Mutated B-Raf proteins are transforming in NIH 3T3 cells and disrupt the balance between signal-independent (basal) kinase activity and negative feedback. Our work shows in a quantitative, experimental framework how sufficient basal activity combines with loss of negative feedback to cause elevated levels of activated ERK that are largely insensitive to the levels of proliferative stimuli (as observed in transformed cells). Basal activity makes the effectiveness of PK signaling particularly vulnerable to mutations causing the loss of negative feedback. Such mutations can result in almost complete abrogation of information transfer. Our findings should prove useful in comparing transformed with untransformed cells and designing drug interventions. Negative feedback protects information transfer in leaky heterogeneous PK signaling networks: In the presence of basal activity, it can convert a near-flat average response curve to a sigmoidal one, with output that has a much higher dynamic range. This effect combines with improved robustness to cell–cell variation in substrate expression levels to maintain the effectiveness of signaling. Our results reveal an important role for negative