Noise decomposition of intracellular biochemical signaling networks using nonequivalent reporters

Abstract

Experimental measurements of biochemical noise have primarily focused on sources of noise at the gene expression level due to limitations of existing noise decomposition techniques. Here, we introduce a mathematical framework that extends classical extrinsic-intrinsic noise analysis and enables mapping of noise within upstream signaling networks free of such restrictions. The framework applies to systems for which the responses of interest are linearly correlated on average, although the framework can be easily generalized to the nonlinear case. Interestingly, despite the high degree of complexity and nonlinearity of most mammalian signaling networks, three distinct tumor necrosis factor (TNF) signaling network branches displayed linearly correlated responses, in both wild-type and perturbed versions of the network, across multiple orders of magnitude of ligand concentration. Using the noise mapping analysis, we find that the c-Jun N-terminal kinase (JNK) pathway generates higher noise than the NF-κB pathway, whereas the activation of c-Jun adds a greater amount of noise than the activation of ATF-2. In addition, we find that the A20 protein can suppress noise in the activation of ATF-2 by separately inhibiting the TNF receptor complex and JNK pathway through a negative feedback mechanism. These results, easily scalable to larger and more complex networks, pave the way toward assessing how noise propagates through cellular signaling pathways and create a foundation on which we can further investigate the relationship between signaling system architecture and biological noise.

Keywords: analysis of variance; extrinsic noise; intrinsic noise; noise decomposition; signal transduction.

Fig. 1.

(A) Schematic of the equivalent dual-reporter method. Two genes that encode for two distinguishable and statistically equivalent fluorescent reporters ($X$ and $Y$) can conceptually be reformulated as a four-node branch motif. $S$ can represent the cellular genetic background, $L$ can represent the overall activity of the gene expression machinery in a given cell, and $X$ and $Y$ can represent the expression levels of the reporters. Thus, extrinsic noise is introduced in the segment $S\to L$, and intrinsic noise is introduced in the segments downstream of $L$. (B) Simulated results for the reporters given in A. Each point corresponds to the expression level of both reporters in a single cell. Extrinsic noise causes points to spread out along the diagonal $Y=X$ whereas intrinsic noise causes the points to additionally spread out in the direction orthogonal to this line. For an isotropic interpretation see Fig. S1. (C) A region of interest (ROI, dashed rectangle) for decomposition is selected from a larger complex intracellular signaling system. The components within the ROI can then be further simplified to a four-node motif comprising a ligand $S$ that binds to its native receptor, which sends a signal to a signaling intermediary, the receptor complex $L$. The signal from $S$ then propagates down two parallel branches to the readouts $X$ and $Y$. We denote the factor that causes coordinated fluctuations in the reporters $X$ and $Y$ as the trunk noise, whereas the noise uniquely contributed by each branch is termed the branch noise. (D) Simulated results for individual cells expressing the readouts ($X$ and $Y$) given in C under five input levels as denoted by the distinct colors. The means of the readout for each input level are indicated by the circles and fitted by regression to form a basis for decomposition. The trunk noise adds noise along the basis, and each branch noise will add noise parallel to its corresponding axis and orthogonal to the axis associated with the other branch.

Fig. 2.

(A) Schematic of the TNF–NF-κB–JNK signaling pathway. Briefly, TNF activates the TNF receptor which then activates both the NF-κB pathway and the JNK mediated pathway causing the nuclear translocation of the transcription factors NF-κB, p-c-Jun, and p-ATF-2. The single-cell nuclear concentrations of the transcription factors can then be quantified via immunofluorescence. (B) Distributions of NF-κB and p-c-Jun nuclear concentrations in response to TNF. The coordinated single-cell nuclear localizations of NF-κB and p-c-Jun were measured for their response to a 30-min exposure of TNF and used in calculations to decompose pathway noise. (C) Scatter plot of the data given in B. Individual points represent single cells and each color represents a unique TNF concentration as listed in B. Means at each TNF concentration are denoted by the circles and fit with linear regression to form a basis for noise decomposition. (D) The noise decomposition of the TNF–NF-κB–JNK pathway of the data given in B (Top) and the corresponding mean nuclear concentration of both transcription factors (Bottom). This figure is shown again as Fig. 3C.

Fig. 3.

(A) Schematic illustrating the reduction of the TNF–NF-κB–JNK signaling pathway (Fig. 2A) into a six-node network which is then partitioned into three experimentally tractable four-node motifs (B–D) covering all possible transcription factor pairings. Each four-node motif consists of a TNF input, a signaling intermediary (either the TNF receptor complex or JNK), and two readouts of transcription factor activity. (B–D) The noise decomposition of the four-node motifs derived from A (Top) and the corresponding mean nuclear concentration of both transcription factors (Bottom). The JNK branch-specific noise is higher than both the NF-κB branch-specific noise and the TNF–TNFR trunk noise. Within the JNK pathway the c-Jun branch noise is greater than the ATF-2 branch noise at higher TNF concentrations. Fig. 3C is also presented as Fig. 2D.

Fig. 4.

(A) TNF signaling network noise normalized to the noise that is contributed by the common TNF–TNFR segment, based upon the data in Fig. 3 B–D. The map demonstrates asymmetry in the amount of noise contributed by the NF-κB and JNK pathways and shows that the majority of noise in the JNK pathway is contributed downstream of the TNF receptor complex. (B) Illustration of a noise decomposition of a larger network. Given a hypothetical signaling network of six nodes and two readouts (C and E), only three noise values can be ascertained. With the addition of two new readouts (F and G), a more comprehensive noise decomposition map can be constructed that can guide further investigations.

Fig. 5.

(A) Schematic of the A20 feedback loop. At 4 h, after up-regulation, A20 interferes with the functionality of the TNF receptor complex (solid line) and inhibits the activation of ATF-2 (dotted line). (B) Noise decomposition of the TNF–NF-κB–ATF-2 signaling pathway in WT and A20^−/− cells at 30 min and 4 h. Absence of the A20 protein does not affect the noise in the NF-κB branch but causes an increase in the amount of noise in the trunk and ATF-2 branch at both 30 min and 4 h. This observation corroborates known information about the mechanisms of A20 regulation.