It’s All Relative

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Science Signaling  15 Dec 2009:
Vol. 2, Issue 101, pp. ec397
DOI: 10.1126/scisignal.2101ec397

We are all familiar with the fact that we can detect a whisper in a quiet room but not when it is noisy; similarly, we can see a tiny pinpoint of light in the dark, but not in a bright room. This ability to perceive the relative intensity of a stimulus taking into account the background state is called Weber’s law. Three papers (Cohen-Saidon et al., Goentoro and Kirschner, and Goentoro et al.) and associated commentary (Ferrell) describe how cells may also follow Weber’s law, perceiving the relative change (fold change) in a signal, not the absolute amount of the signal.

Cells are not uniform; even clones, genetically identical cells, exhibit stochastic variation that is detected only when individual cells are analyzed. Cohen-Saidon et al. developed a clonal cell line in which yellow fluorescent protein was integrated into one allele of the gene encoding extracellular signal–regulated kinase 2, forming a fusion protein, ERK2-YFP, that was regulated by the same processes as those regulating endogenous ERK2. Single-cell analysis of ERK2-YFP kinetics with automated imaging of protein dynamics showed that the cells exhibited different basal abundance of nuclear ERK2-YFP (about a four-fold variation), which did not correlate with differences in global cell morphological properties and thus appeared stochastic. In response to growth factor stimulation of the cells, the absolute nuclear intensity of ERK2-YFP was variable, with cells with higher basal nuclear ERK2-YFP showing higher stimulated nuclear ERK2-YFP intensity than did cells that started at a lower basal point. The nuclear amount of ERK2-YFP returned to the same original basal state (higher in cells that started higher, and lower in cells that started lower). However, the relative change was essentially the same, suggesting that cells may integrate the background state into the response, not just detect the absolute amount of the signal.

In another study, Goentoro and Kirschner started with a mathematical model of Wnt signaling and showed that changing the values of the parameters in the model changed the output (absolute increase in the amount of β-catenin), suggesting that the system was not robust to variation. In contrast, if the fold change in β-catenin abundance was monitored as the output, then the system was more robust, exhibiting a similar fold change under many different conditions. Finally, conditions that altered the abundance of β-catenin and the fold change were predicted to cause an altered phenotype. Analysis of the parameter space suggested that the fold change in β-catenin would be least affected by perturbations in the degradation arm of the pathway and that perturbations that altered β-catenin synthesis would alter the fold change. This suggests that the Wnt system may be set to respond to relative changes, not to monitor absolute amounts of β-catenin. The authors tested and confirmed their predictions in two experimental systems: the RKO colorectal cell line and Xenopus embryos. In the RKO cells, perturbing the degradation components, overexpression of Axin1 or moderate (but not strong) inhibition of glycogen synthase kinase-3β (GSK-3β), produced the same fold change in β-catenin in response to Wnt. When axin1 was increased or GSK-3β was moderately inhibited in Xenopus embryos, the embryos developed normally and did not show the dorsalization phenotype associated with excess Wnt signaling. In contrast, overexpression of β-catenin (to produce an amount similar to that resulting from inhibition of the degradation machinery) in the RKO cells increased the fold change in β-catenin in response to Wnt, and, in the Xenopus embryos, this caused dorsalization. Thus, Wnt signaling exhibits robustness (no alteration in phenotype) to perturbations that do not change the fold change in β-catenin abundance, but perturbations that exceed this buffering capacity result in hyperresponsiveness (more β-catenin and an increase in the fold change).

In the final paper, Goentoro et al. analyzed network motifs for the ability to allow fold-change detection in a gene regulatory response. They provide evidence that incoherent feedforward loops, in which one downstream element stimulates the output and one inhibits the output, can function as a fold-change detector. In their model, when a transcriptional activator (X) produces both the output signal (gene product Z) and a repressor (Y) of Z, then the abundance of Z depends on the fold change in X. The repressor provides a “memory” of the input. Fold-change detection required that the repressor be “strong” (the ratio of the concentration of Y to its effective binding constant on the Z promoter is large), which can be achieved by having a low concentration of Y with a very high affinity interaction or a low-affinity interaction with a high concentration of Y. Ferrell puts this work into the context of Weber’s law and ponders whether fold-change detection will wind up as a unifying theme in cellular networks, as well as macroscopic sensation.

C. Cohen-Saidon, A. A. Cohen, A. Sigal, Y. Liron, U. Alon, Dynamics and variability of ERK2 response to EGF in individual living cells. Mol. Cell 36, 885–893 (2009). [Online Journal]

L. Goentoro, M. W. Kirschner, Evidence that fold-change, and not absolute level, of β-catenin dictates Wnt signaling. Mol. Cell 36, 872–884 (2009). [Online Journal]

L. Goentoro, O. Shoval, M. W. Kirschner, U. Alon, The incoherent feedforward loop can provide fold-change detection in gene regulation. Mol. Cell 36, 894–899 (2009). [Online Journal]

J. E. Ferrell Jr., Signaling motifs and Weber’s law. Mol. Cell 36, 724–727 (2009). [Online Journal]

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