Information transfer by leaky, heterogeneous, protein kinase signaling systems

Abstract

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.

Keywords: MAPK signaling; biomolecular networks; cell sensing; mutual information; ultrasensitivity.

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).

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).

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(nppERK_t; S) are shown in green, and joint mutual information (assuming that the total ERK level is also taken into account), I(nppERK_t, TotERK_t; 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 (nppERK_t) 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.

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|S, TotERK_t], at t = 30 min for six values of total ERK corresponding to the 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[nppERK_t|S, TotERK_t]^1/2. Also plotted is the population average output, E[nppERK_t|S], 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.