Systems biology. Accurate information transmission through dynamic biochemical signaling networks

Abstract

Stochasticity inherent to biochemical reactions (intrinsic noise) and variability in cellular states (extrinsic noise) degrade information transmitted through signaling networks. We analyzed the ability of temporal signal modulation--that is, dynamics--to reduce noise-induced information loss. In the extracellular signal-regulated kinase (ERK), calcium (Ca(2+)), and nuclear factor kappa-B (NF-κB) pathways, response dynamics resulted in significantly greater information transmission capacities compared to nondynamic responses. Theoretical analysis demonstrated that signaling dynamics has a key role in overcoming extrinsic noise. Experimental measurements of information transmission in the ERK network under varying signal-to-noise levels confirmed our predictions and showed that signaling dynamics mitigate, and can potentially eliminate, extrinsic noise-induced information loss. By curbing the information-degrading effects of cell-to-cell variability, dynamic responses substantially increase the accuracy of biochemical signaling networks.

Figure 1. Single cell measurement of the dynamic response of ERK, Ca²⁺ and NFκB

A. Overview of single cell data analyzed in this work. B. Examples of single cell response dynamic trajectories. CDE. Temporal histograms of several representative dosages for ERK (C) Ca²⁺ (D) and NFκB (E). Color intensity reflects the probability density of a cellular response magnitude at each time point. Y-axis in BCDE is the same for each pathway and is of Arbitrary Units representing the FRET/CFP ratio reported by the EKARev ERK biosensor (C), intensity of Ca²⁺ indicator dye Fluo-4 (D), and ratio of nuclear to cytoplasmic localization of an EYFP-p65 reporter (E). F. Violin plot of the maximally separable static response in the three signaling pathways. Shape width shows response distribution (areas are equal), and point is the median response in each condition.

Figure 2. Information transmission capacity of static and dynamic ERK, Ca²⁺ and NFκB responses

A. Information transmission capacity calculated from static scalar response distribution based on single time point measurements. B. Information transmission capacity calculated from multivariate dynamic responses as a function of the dimension of the multivariate vector. The multivariate vector was subsampled using a uniform grid centered on the middle time point (Fig. S20) C. Comparison of the multivariate vector (V) measurement to the following scalar responses: maximum response amplitude (A), maximum response time (T), maximal rate of response (D), ratio of maximum response amplitude to initial response amplitude (R). Error-bars are s.e.m from 6 biological replicates for ERK, 4 for Ca²⁺, and s.d. from 5 jackknife iterations for NFκB (Table S1–3). The multivariate vector information transfer was significantly greater than all scalar measures (p-values <0.05, Student’s t-test, Table S6).

Figure 3. Theoretical decomposition of information loss caused by intrinsic and extrinsic noise

A. graphical representation of the analytical expression for the gain in mutual information from overcoming intrinsic (cyan) and extrinsic (magenta) noise sources obtained from random linear gaussian inputs and outputs with three parameters (19). B. information transmission capacity of dynamic (orange) and static (maximal response, purple) responses calculated using simulated trajectories from the computational model of ERK (22) with only the extrinsic noise contributing to cell response variability. C. Example of ERK trajectory variability for two different inputs levels (red and blue). Variability was generated using a uniform distribution of a single parameter, MEK values that was varied by +/- 20%. D. Two dimensional histogram (center) and marginal distributions (left and bottom) for the two input levels (shown in red and blue) at two time points (T=9 & 24min) from the trajectories in C. Because only a single parameter was varried, the responses vary on a one-dimensional curve. As a result, although the univariate marginal distributions show substantial response overlap, the two dimensional distribution shows completely seperated response levels (inset).

Figure 4. Measured information gain is a result of ERK dynamics ability to mitigate extrinsic noise

Experimental measurement of the mutual information between ERK response and EGF measured as a function of the response signal-to-noise (SNR). Each marker represents calculations of SNR and mutual information from the dynamic (dot) and maximal scalar (cross) responses of cells from an 8-well dose-response experiment. Shown data are calculated based on 535,107 single cell responses from 29 experiments with six doses of MEK inhibitor U0126 (Table S4–5). Lines represent theoretical predictions of the mutual information as a function of SNR for three types of responses: static scalar (red line), redundant measurements where the multivariate response has no dynamics (dark and light blue lines) calculated based on two independent estimates of IER (19)(Fig S22), and dynamic response (orange) that can mitigate both intrinsic and extrinsic noise (Fig S19).