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

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.


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(1) Here, k K,i , k P,i and X tot,i are the kinase rate constant, the phosphatase rate constant and the total intermediate expression at the i-th cascade stage. The concentration of each phosphorylated intermediate X i is given in normalized form, i.e., As shown by Heinrich et al. (2002), the steady state of any phosphorylated intermediate can be written in Michaelis-Menten form: Here, ψ = X 0 is the stimulus, which mediates the phosphorylation of the first intermediate, X 1 (see Eq. 1). In the following we will derive analytical expressions for x max,i and K M,i in order to analyze signal transmission for varying levels of the regulator, r. The steady state solution of Eq. 1 reads: In the limit of infinitely strong stimulation (ψ → ∞), Eq. 4 can be rewritten as: By using Eq. 6 and the relationship 1 max, one derives for the half-maximal stimulus level To analyze how the regulator, r, affects signal transmission, we shall assume that the regulator r leads to a proportional increase in the expression of all substrates, i.e., all X tot,i . Thus, the local sensitivities, L i (see Eq. 4), modify to: Here, K i equals the first-oder rate constant for protein synthesis divided by that for protein degradation. Plotting the maximal activation level, x max,i , and the half-maximal stimulus, K M,i , (Eqs. 6 and 8) as a function of the regulator, r, reveals that both respond in an ultrasensitive fashion (not shown). In other words, simultaneous expression of multiple cascade intermediates results in ultrasensitization of signal transduction. To gain further insight into this 'ultrasensitization due to synexpression', we restrict the following analysis to weak (ψ → 0) and strong (ψ → ∞) stimulation.
Weak stimulation: Using Eqs. 6 and 8 signal transmission (Eq. 3) upon weak stimulation (i.e., ψ << K M,i ) can be approximated by: It should be noted that signal transmission via X i is given in normalized form (see Eq. 2), so that the impact of the regulator, r, on the expression of the cascade stage under consideration (i.e., X tot,i ) cancels out. Thus, Eq. 40 gives an estimate how signal transmission upon weak stimulation (ψ → 0) is regulated by, r, in addition to the obvious linear increase. Obviously, signal transmission upon weak stimulation is always subject to ultrasensitization as soon as two or more cascade stages are synexpressed, since any change in the regulator, r, results in an r i-1 -fold alteration in signal transmission in addition to the obvious linear increase.
Strong stimulation: By definition, signal transmission upon strong stimulation is determined by the maximal activation level, X max,i (Eq. 6). For simplicity, we shall restrict the following analysis to the limiting cases L i-1 << L i and L i-1 >> L i , which are analogous to negative and positive cooperativity in protein association. If one assumes that all rate constants within the cascade are equal, i.e., k P,i = k P and k K,i = k K , the limiting cases mean that the expression levels, X tot,i , strongly decrease (L i-1 << L i ) or increase (L i-1 >> L i ) along the cascade. In the limiting cases Eq. 6 (with i > 1) can be approximated by (see Eq. 9): Again, both expressions are given in normalized form to measure nonlinearity (see above). Since the approximation on the right (L i-1 >> L i ; 'positive cooperativity') has the form of the Hill equation, the regulator, r, alters signal transmission in a highly switch-like fashion, especially if many cascade stages are subject to synexpression (i.e., if the exponent i-1 is large). By contrast, weaker ultrasensitization is observed in the limit L i-1 << L i ('negative cooperativity'), since the corresponding approximation (see Eq. 11) has the form of the Michaelis-Menten equation. In addition, the degree of nonlinearity then no longer depends on the number of cascade stages simultaneously altered by the regulator, r.
Conclusions: Comparison of Eqs. 11 and 10 reveals that ultrasensitization upon weak stimulation is either equal to or stronger than that observed upon strong stimulation. Further analysis of Eq. 3 reveals that the degree of ultrasensitivity upon intermediate stimulation lies between that observed for the limits of weak and strong stimulation (not shown).
Hence we can conclude that synexpression always results in ultrasensitization (Eqs. 10 and 11). In addition, ultrasensitization usually increases the more cascade stages are coordinately affected by the regulator, r. If one assumes that all rate constants within the cascade are equal, i.e., k P,i = k P and k K,i = k K , ultrasensitization is strongly favoured if the absolute concentrations increase along the cascade, i.e., if X tot,i >> X tot,i-1 . Finally, it is worth noting that similar conclusions regarding ultra(de)sensitization also hold if multiple phosphatases/deactivators are synexpressed or if multiple kinase rate constants are simultaneously altered (see Eq. 9). Thus, ATP depletion due to hypoxia is predicted to switch off cellular signalling pathways in an all-or-none fashion as soon as the ATP level falls below a critical threshold (see also main text).