Information transduction capacity of noisy biochemical signaling networks

Abstract

Molecular noise restricts the ability of an individual cell to resolve input signals of different strengths and gather information about the external environment. Transmitting information through complex signaling networks with redundancies can overcome this limitation. We developed an integrative theoretical and experimental framework, based on the formalism of information theory, to quantitatively predict and measure the amount of information transduced by molecular and cellular networks. Analyzing tumor necrosis factor (TNF) signaling revealed that individual TNF signaling pathways transduce information sufficient for accurate binary decisions, and an upstream bottleneck limits the information gained via multiple integrated pathways. Negative feedback to this bottleneck could both alleviate and enhance its limiting effect, despite decreasing noise. Bottlenecks likewise constrain information attained by networks signaling through multiple genes or cells.

Fig. 1

Information theoretic analysis of cell signaling fidelity. (A) Schematic showing information loss due to overlapping noisy response distributions. (B) Diagram of the TNF-NF-κB signaling pathway represented in biochemical form (left) and as a noisy communication channel (right). (C) Experimental flowchart for sampling the conditional response distribution at single cell resolution using immunocytochemistry, and resulting 4-dimensional compendium of multiple responses in cells of multiple genetic backgrounds to multiple TNF concentrations, at multiple time points. The data was collected in a single experiment, allowing controlled, quantitative comparisons along each dimension. (D) Distributions of noisy NF-κB nuclear translocation responses to 30 min. TNF (examples shown at top) used to compute the channel capacity of the TNF-NF-κB pathway. (Scale bars, 20 µm)

Fig. 2

Information gained by signaling through a network comprising multiple communication channels. (A) Schematic of a bush network with independent channels lacking an information bottleneck. (B) Schematic of a tree network with channels sharing a common trunk that forms an information bottleneck. (C) Comparison of bush and tree model predictions for the capacity of the TNF network to experimental values. At 30 min., the NF-κB and ATF-2 pathways together capture more information about TNF concentration than either pathway alone (bars 1–3), and the tree rather than bush model accurately predicts this increase (bars 3–5). The tree model further predicts a receptor level bottleneck of 1.26 ± 0.13 bits (bar 6). In all panels, circles represent noise introduced in the indicated portions of the signaling network; see text for definition of symbols. (D) Joint distribution of NF-κB and ATF-2 responses to 30 min. stimulation of TNF. Each datapoint represents a single cell, and each concentration of TNF examined is shown using a distinct color.

Fig. 3

Impact of negative feedback to the bottleneck on information transfer. (A) TNF signaling network diagram showing A20-mediated negative feedback to the information bottleneck. (B) Comparison of information about TNF concentration captured with and without A20 negative feedback. The information is larger at 30 min. but smaller at 4 hrs. in wildtype cells compared to A20^−/− cells. (C, D) Schematic of NF-κB dynamics in wildtype and A20^−/− mouse fibroblasts exposed to saturating concentrations of TNF. Average dynamics (black) and the expected magnitudes of the dynamic range (double arrow) and noise (single arrow) are shown. See Fig. S9 for experimental support. (E) Comparison of NF-κB responses to zero (basal) or saturating concentrations of TNF. Differences in the means with and without TNF indicate the dynamic range, and error bars indicate the noise.

Fig. 4

Information gained by signaling through networks of multiple genes. (A) Plot shows the unique curve (solid black) determined by the tree model (inset), passing through the experimentally determined values (circles), for information as a function of the number of copies of a NF-κB reporter gene. The upper limit, corresponding to the maximum information captured by integrating NF-κB activity over time, is 1.64 ± 0.36 bits (blue dashed line). (B) Expression level distributions of clonal cell lines containing different numbers of copies of an NF-κB reporter gene in response to ~10 hrs of TNF. (C) Time courses corresponding to individual cells showing cell-to-cell differences in the onset and rate of NF-κB reporter gene expression (left). In each cell, expression is nearly linear and deterministic in time, as quantified by the correlation coefficient (right) of the time course following onset of expression (shown schematically in inset on left).

Fig. 5

Information gained by signaling through networks of multiple cells. (A) Comparison of experimentally measured information obtained by collective cell responses (circles) versus logarithmic trend (solid black line) predicted the bush model (inset). (B) Schematic of methodology used to measure collective cell responses.