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. 2005 Oct;1(5):e54.
doi: 10.1371/journal.pcbi.0010054. Epub 2005 Oct 28.

Ultrasensitization: Switch-Like Regulation of Cellular Signaling by Transcriptional Induction

Free PMC article

Ultrasensitization: Switch-Like Regulation of Cellular Signaling by Transcriptional Induction

Stefan Legewie et al. PLoS Comput Biol. .
Free PMC article


Cellular signaling networks are subject to transcriptional and proteolytic regulation under both physiological and pathological conditions. For example, the expression of proteins subject to covalent modification by phosphorylation is known to be altered upon cellular differentiation or during carcinogenesis. However, it is unclear how moderate alterations in protein expression can bring about large changes in signal transmission as, for example, observed in the case of haploinsufficiency, where halving the expression of signaling proteins abrogates cellular function. By modeling a fundamental motif of signal transduction, the phosphorylation-dephosphorylation cycle, we show that minor alterations in the concentration of the protein subject to phosphorylation (or the phosphatase) can affect signal transmission in a highly ultrasensitive fashion. This "ultrasensitization" is strongly favored by substrate sequestration on the catalyzing enzymes, and can be observed with experimentally measured enzymatic rate constants. Furthermore, we show that coordinated transcription of multiple proteins (i.e., synexpression) within a protein kinase cascade results in even more pronounced all-or-none behavior with respect to signal transmission. Finally, we demonstrate that ultrasensitization can account for specificity and modularity in the regulation of cellular signal transduction. Ultrasensitization can result in all-or-none cell-fate decisions and in highly specific cellular regulation. Additionally, switch-like phenomena such as ultrasensitization are known to contribute to bistability, oscillations, noise reduction, and cellular heterogeneity.

Conflict of interest statement

Competing interests. The authors have declared that no competing interests exist.


Figure 1
Figure 1. Slow and Fast Regulation of Cellular Signal Transduction
(A) Schematic representation of cellular signal transduction. Upstream stimuli (e.g., hormones) result in altered gene expression by eliciting rapid intracellular responses such as transcription factors (fast regulation). The resulting changes in protein expression often in turn affect cellular signal processing of upstream inputs via transcriptional feedback or crosstalk (slow regulation). (B) Schematic representation of a phosphorylation–dephosphorylation cycle, where the kinase K and the phosphatase P catalyze the (de)phosphorylation of the substrate, S. Hormonal stimulation (i.e., fast regulation) was modeled by altering the total kinase concentration, Ktot = K + S0K, and the steady-state concentration of free phosphorylated substrate, S1, was taken as the response. The impact of slow regulation was modeled by varying the concentration of the substrate (Stot = S0 + S0K + S1 + S1P) or that of the phosphatase (Ptot = P + S1P).
Figure 2
Figure 2. Ultrasensitization in a Phosphorylation–Dephosphorylation Cycle
Stimulus-response of the phosphorylation–dephosphorylation cycle depicted in Figure 1B for varying substrate expression levels, Stot = S0 + S0K + S1 + S1P, on a double-logarithmic scale. The relative alterations in the response, S1, for a given stimulus, Ktot = K + S0K, elicited by a 5-fold change in substrate expression are indicated next to the vertical arrows. Parameters chosen: kon,K = koff,P = kcat,P = 0.01; koff,K = kcat,K = 1; kon,P = 1.6; Ptot = 1.25.
Figure 3
Figure 3. Ultrasensitization Due to Substrate Sequestration
The normalized maximal response of the phosphorylation–dephosphorylation cycle depicted in Figure 1B is plotted as a function of substrate expression on a semilogarithmic scale for the limit of strong stimulation (according to Equation 1), where Ktot >> Ptot. The threshold, Stot,T, (see Equation 2) was varied as indicated, while the Michaelis-Menten constant of the phosphatase, KM,P, was kept constant and assumed to be unity. The scheme on the top indicates the mechanism of ultrasensitization: for weak substrate-expression, most of the substrate is sequestered on the enzyme–substrate complexes, S0K and S1P, while signal transmission via S1 occurs as soon as substrate expression, Stot, exceeds the threshold, Stot,T.
Figure 4
Figure 4. Ultrasensitization Due to Activity Switching
The normalized response of the phosphorylation–dephosphorylation cycle depicted in Figure 1B is plotted as a function of substrate expression on a semilogarithmic scale for varying stimulus levels. To relate the plot to analytical results given in the main text (Equation 4), the stimulus, Ktot, is expressed as Vmax,K and given in times of Vmax,P. For the parameters chosen (kon,K = 0.02; koff,K = kcat,K = koff,P = 1; kon,P = 2; kcat,P = Ptot = 0.1), substrate sequestration is insignificant (i.e., Equation 3 does not hold) and the kinase is significantly less saturated than the phosphatase (Equation 5). The scheme on the top indicates the mechanism of ultrasensitization: increasing substrate expression induces a switch from high overall phosphatase activity (S1 → S0) to high overall kinase activity (S0 → S1).
Figure 5
Figure 5. Ultrasensitization Due to Synexpression within a Signaling Cascade
(A) Schematic representation of a signaling cascade subject to synexpression. An increase in the regulator, r, was assumed to result in a proportional increase in the expression of intermediates S and T, both of which are subject to covalent modification by (de)phosphorylation. (B) Ultrasensitization due to synexpression within a signaling cascade measured numerically by plotting the normalized response as a function of the regulator concentration, r, where Stot = Ttot = r (solid line). To show that synexpression enhances ultrasensitization, the case where the regulator, r, affects transcription of T only is also shown for Stot = 10 (dashed line). Similar results were obtained for other values of Stot or other stimulus strengths (data not shown). Parameters chosen: koff,1 = koff,5 = kcat,2 = kcat,6 = koff,3 = koff,7 = kcat,8 = PS,tot = PT,tot = 1; kon,1 = 0.02; kon,5 = 0.2; kon,3 = 2.1; kon,7 = 2; kcat,4 = 1.1; Ktot = 10.
Figure 6
Figure 6. Ultra(de)sensitization Can Bring About Specificity and Modularity
The response of a phosphorylation–dephosphorylation cycle (see Figure 1B) upon strong stimulation is shown as a function of the phosphatase expression level (Ptot = P + S1P) for varying the ratio of the turnover numbers, kcat,P/kcat,K. Equation 1 was used for plotting, because this expression also applies independently of the relative kinase and phosphatase expression levels provided that Ktot >> Stot and Ktot >> KM,K (see Protocol S1). The plots shown correspond to the scheme depicted in the upper-right corner, where the free unphosphorylated substrate, S, is phosphorylated by the three kinases, which differ in their turnover numbers, kcat,K: K1 (red line; kcat,P/kcat,K = 100), K2 (green line; kcat,P/kcat,K = 20), and K3 (blue line; kcat,P/kcat,K = 3). As indicated by the vertical dotted lines, ultradesensitization may result in four binary regulatory states depending on the phosphatase expression level, particularly if the phosphatase is strongly saturated with its substrate (Equation 6), which is what we assumed here (KM,P = 0.01; Stot = 1).

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