A design principle underlying the paradoxical roles of E3 ubiquitin ligases

Abstract

E3 ubiquitin ligases are important cellular components that determine the specificity of proteolysis in the ubiquitin-proteasome system. However, an increasing number of studies have indicated that E3 ubiquitin ligases also participate in transcription. Intrigued by the apparently paradoxical functions of E3 ubiquitin ligases in both proteolysis and transcriptional activation, we investigated the underlying design principles using mathematical modeling. We found that the antagonistic functions integrated in E3 ubiquitin ligases can prevent any undesirable sustained activation of downstream genes when E3 ubiquitin ligases are destabilized by unexpected perturbations. Interestingly, this design principle of the system is similar to the operational principle of a safety interlock device in engineering systems, which prevents a system from abnormal operation unless stability is guaranteed.

Figure 1. E3 ubiquitin ligases in the ubiquitin-proteasome system (UPS) play paradoxical roles in proteolysis and transcription.

(a) Protein degradation mediated by the UPS. E3 ubiquitin ligases determine the substrate specificity of UPS-dependent proteolysis. The specific biochemical reactions depend on the type of proteins in the UPS. (b) An E3 ubiquitin ligase can participate in the transcriptional activation of transcription factors, which also undergo proteolysis facilitated by the same E3 ligase.

Figure 2. Biological examples and the generic mathematical model.

(a) Examples of E3 ubiquitin ligases (blue) that play paradoxical roles in proteolysis and transcriptional activation of a transcription factor (orange). (b) The mathematical model of ITUD. For comparative analysis, SNFL and DTUD are introduced as alternatives. Basal production and degradation of each component are not denoted in this diagram. (c) A detailed illustration of ITUD in a cell. This schematic diagram depicts a RING-type E3 ubiquitin ligase and its role as a cofactor in transcriptional activation. Other types of E3 proteins can be described differently. (b–c) S is an upstream signal; T is a transcription factor; E3 is an E3 ubiquitin ligase; P is the final product (system output); and I is an intermediate node.

Figure 3. Graphical representation of the major parameters commonly used in SNFL, DTUD, and ITUD.

The numbers in brackets are parameter IDs and the dotted arrows represent the basal production or degradation rates. The red arrows represent the regulations which involve the identified five parameters, of which β_TE3 (ID: 13) and K_TE3 (ID: 14) are defined as the critical determinants.

Figure 4. The effects of the critical determinants on the three systems at steady state.

We examined the effects of the critical determinants (i.e., β_TE3 and K_TE3) on the steady-state outputs of the three systems under the activating signal (S = 1.0). E3 was perturbed by continuously varying (a) β_TE3 and (b) K_TE3 such that E3 was initially upregulated and subsequently downregulated. The decrease of β_TE3 leads to the downregulation of E3, and thereby the horizontal axis of (a) is set in a descending order (from 2.0 to 0). (c) The regulation of E3 by T was removed to observe the system response with respect to the steady-state level of E3 (E3_ss). The K_{m_E3T} and K_E3P represent the binding affinities (or the reaction intensities) of E3 for proteolysis and transcription, respectively. (d) The curves of the steady-state level of P (P_ss) generated by varying K_{m_E3T} under the activating signal (S = 1.0). (e) Identical curves generated by varying K_XP. K_TP2 and K_IP are the kinetic parameters that correspond to K_E3P of ITUD in SNFL and DTUD, respectively.

Figure 5. Temporal dynamics under the perturbation of the critical determinants.

(a) Temporal dynamics of the perturbation-free condition (control). The signal S changes from a low to a high level (specific values: 0.1 to 1.0). The temporal dynamics of the common negative feedback loop involving T, ubT, and E3 are identical in the three systems. The activation threshold (P_Threshold = 0.5, gray line) is defined as the threshold that the system output, P, must exceed to activate the system. (b) Temporal dynamics under the perturbation of β_TE3, which was decreased by 80% (0.2-fold). (c) Identical to (b), except the perturbation was applied on K_TE3, which was increased by 150% (2.5-fold). (d–e) Temporal dynamics under identical perturbations in (b–c) with noise in signal S. The initial states are all zero.

Figure 6. In silico cell population dynamics for cell proliferation and migration.

(a) The cell model includes SNFL, DTUD or ITUD as a subcellular pathway. The level of P in the subcellular pathway determines the activation of a cell. (b) The types of cells that comprise the cell population. (c) Cell proliferation dynamics under the perturbation of the critical determinants (i.e., β_TE3 and K_TE3). The shade of each curve represents standard errors at the respective time point (n = 3). For ‘DTUD-BE', refer to the main text. (d) Snapshots of the cell population at 8,000 h in the cell proliferation dynamics. (e) The simulation space of 200 μm × 80 μm for cell migration dynamics. The diffusion field of the signal molecule is shown in the right panel. (f) Mean displacement of the migrating 25 cells (n = 5). P1, P2, and P3 represent perturbation probabilities of 0.001, 0.01, and 0.1, respectively, in the unit simulation step. (g) Trajectory of a single cell migration in the harshest environment (P3). A red circle represents the position of the cell that is tracked at each time point (a blue number). Arrows indicate the displacement of the cell migration. ** P < 0.01 and ***P < 0.001.

Figure 7. In vitro experiments for cell proliferation and migration.

(a) Proliferation rates of HEK293T cells under the knockdown of Wwp2, β-TrCP1, or CRD-BP relative to the control. (b) Wwp2 was knocked down, and the migrated HEK293T cells were counted after TGF-β stimulation. * P < 0.05 and ** P < 0.01.

Figure 8. The design principles of the ITUD system.

(a) Biphasic response of ITUD with respect to the perturbation on E3. (b) Possible mechanisms underlying the biphasicity of ITUD mediated by E3 ubiquitin ligases. (c) Possible regulatory mechanisms that affect the shapes of the biphasic response in the ITUD system (d) A representative example of a safety interlock device can be found in a clothes washing machine (left). The E3 ubiquitin ligase in the ITUD system can serve as a safety interlock device based on its integrated roles in proteolysis and transcription (right). (e) ITUD may support tissue homeostasis in multicellular organisms. (f) Combinatorial therapy based on ITUD. The relative output is the ratio of P_ss between the inhibition of only T (single perturbation) and the inhibition of both T and E3 (dual perturbation) in the ITUD system. Perturbation strength is the percentage change of a kinetic parameter value to the perturbation of a system component, and the relative perturbation strength is the ratio between the single and dual perturbation strengths (see Methods for details).