Conceived and designed the experiments: TJL LY. Performed the experiments: TJL. Analyzed the data: TJL GY JRN LY. Wrote the paper: TJL. Critical reading of the manuscript: GY JRN.
The authors have declared that no competing interests exist.
The transcription factor Myc plays a central role in regulating cell-fate decisions, including proliferation, growth, and apoptosis. To maintain a normal cell physiology, it is critical that the control of Myc dynamics is precisely orchestrated. Recent studies suggest that such control of Myc can be achieved at the post-translational level via protein stability modulation. Myc is regulated by two Ras effector pathways: the extracellular signal-regulated kinase (Erk) and phosphatidylinositol 3-kinase (PI3K) pathways. To gain quantitative insight into Myc dynamics, we have developed a mathematical model to analyze post-translational regulation of Myc via sequential phosphorylation by Erk and PI3K. Our results suggest that Myc integrates Erk and PI3K signals to result in various cellular responses by differential stability control of Myc protein isoforms. Such signal integration confers a flexible dynamic range for the system output, governed by stability change. In addition, signal integration may require saturation of the input signals, leading to sensitive signal integration to the temporal features of the input signals, insensitive response to their amplitudes, and resistance to input fluctuations. We further propose that these characteristics of the protein stability control module in Myc may be commonly utilized in various cell types and classes of proteins.
The transcription factor Myc plays a critical role in regulating diverse cell-fate decisions, including growth, proliferation, and programmed cell death. Underscoring its importance, Myc expression is often found to be deregulated in cancers. However, the dynamic mechanism by which Myc is controlled by its upstream signaling proteins remains unclear. To address this issue, we analyze a well-defined signaling module for Myc regulation using a kinetic model constrained by experimental data and observations. In this module, Myc acts as an integrator of its upstream signals that differentially regulate its stability. We show that this module can enable highly sensitive Myc response to the temporal features of the input signals, but not to their maximum amplitudes. We further suggest that this module represents a generic post-translational mechanism for signal sensing and integration in diverse signaling networks. Our work offers insight into the “design” of natural biological networks and makes predictions that can guide further experimental studies on Myc regulation. Moreover, it defines a simple signal processing unit that may be useful for engineering synthetic gene circuits to carry out cell-based computation.
The proto-oncogene protein Myc is a transcription factor that regulates numerous signaling pathways involved in cell-fate decisions
Given its importance, Myc activity must be properly controlled in response to different environmental cues. Past studies have suggested that Myc is regulated at multiple levels, including auto-regulation of Myc transcription
(A) Stimulation with growth factors (GF) leads to activation of Ras and Myc synthesis. Active Ras induces activation of its downstream effector pathways: the MAPK and PI3K pathways. While the synthesized Myc is unstable with short half-life, its stability can be significantly increased via the Ras effector pathways. Active Ras induces Erk that stabilizes Myc by phosphorylation at Ser62. PI3K activation blocks Myc degradation by inhibiting phosphorylation at Thr58 by Gsk3β. As Ras activity declines, Gsk3β initiates phosphorylation of Myc at Thr58 and triggers degradation. Phosphorylation at Thr58 requires prior phosphorylation at Ser62, and phosphorylation at Thr58 induces dephosphorylation at Ser62. (B) Activation patterns of Erk and PI3K determine Myc stability pattern. The three forms of Myc are plotted independently. The unmodified Myc (blue line) and MycThr58 (green line) accumulate only to a limited level, but stabilized MycSer62 level increases via phosphorylation (red line). The total Myc level is the sum of the three forms of Myc (black line) and its dynamics are highly correlated with input signals, Erk, and PI3K. We define the shaded area under the Myc curve as “potency”, a measure of Myc accumulation.
The unique control of Myc dynamics by sequential phosphorylation allows Myc to integrate upstream signals from Erk and PI3K, which play critical roles in controlling diverse cell fates
The PI3K activation pattern depends on cell lines and stimulants, as detailed in
The temporal pattern of Myc activation closely correlates with those of Erk and PI3K (
To gain insight into this control mechanism, we have constructed a mathematical model to analyze dynamics of Myc accumulation controlled by sequential phosphorylation. Using this model, we aimed to investigate how signaling patterns of Erk and PI3K regulate Myc dynamics at the post-translational level. Also, how robust is Myc dynamics with respect to network parameters, such as phosphorylation and dephosphorylation rate constants? What is unique about this strategy of controlling Myc accumulation by sequentially modulating protein stability? Is this a common strategy by which cells achieve reliable temporal control of key regulatory proteins? By exploring these questions, our work may provide insights into design features of cell signaling networks and guidance for experimental intervention. Conceptually, our model defines a unique module that connects with other models that deal with upstream signaling dynamics leading to the activation of Erk
The Myc temporal dynamics, simulated with reaction kinetics and base parameter values in
As Myc accumulation was determined by conversion between its unstable forms and stable form, we expected Myc accumulation to depend on the degradation rate constant of each form. As a quantitative estimate for Myc accumulation, we used Myc potency, the shaded area in
Erk and PI3K activation patterns, which determine the temporal dynamics of Myc, may vary significantly under different growth conditions and in different cell lines (
For all analyses, black lines represent the base case. (A) The Erk signal was represented with the following parameters: duration (DurE), maximal Erk amplitude (ErkMax), and residual Erk level (ErkR). (B) The PI3K signal was represented with the following parameters: duration (DurP), maximal PI3K amplitude (PI3KMax), residual PI3K level (PI3KR), and the time interval between the two peaks of PI3K (IPP). The first peak of the PI3K was not considered, since its variations did not have a big impact. (C) Myc accumulation was insensitive to ErkMax. Fivefold increase in ErkMax resulted in little change in Myc (red line) in comparison to the base case (black line), whereas fivefold decrease in ErkMax resulted in light reduction in the main peak of Myc (blue line). (D) Doubling (red line) or halving (blue line) DurE leads to significant change in the initial peak of Myc accumulation. (E) Myc was sensitive to ErkR. The base value of ErkR was 10 percent of ErkMax (black line). A small increase in ErkR (20% of ErkMax) resulted in excessive Myc accumulation (red line). When Erk was completely removed (ErkR = 0), Myc responded only to the initial, transient Erk pulse and became unresponsive to the PI3K signal (blue line). (F) Myc accumulation was insensitive to PI3KMax. Fivefold increase (red line) or decrease (blue line) in PI3KMax resulted in little change in Myc accumulation. (G) The 2nd PI3K peak determined generation and maintenance of Myc hump. Doubling (red line) or halving (blue line) the duration of the second PI3K peak led to approximately twofold change in the Myc hump duration. Increasing IPP from 3 hours to 8 hours delayed the timing of the second rise in Myc accumulation (red dotted line). (H) A slight increase (20% of PI3KMax) in PI3KR from the base value (10% of PI3KMax) resulted in excessive Myc accumulation (red line). However, complete removal of PI3KR did not change Myc accumulation significantly (blue line overlapping with black line).
Our analysis predicted Myc accumulation to be insensitive to further increase in Erk amplitude. A fivefold increase in ErkMax caused little change in Myc accumulation (
Myc potency was sensitive to the residual Erk level (ErkR). Without it (ErkR = 0), the total Myc level quickly reduced to a low level following the Erk pulse (blue line in
Similarly, Myc accumulation was insensitive to the maximum amplitude of PI3K (PI3KMax), but much more sensitive to its residual level (PI3KR) and temporal features, including duration of the 2nd peak (DurP) and time interval between the two peaks (IPP). Five-fold increase or decrease in PI3KMax resulted in little change in Myc accumulation (
Another sensitive parameter of PI3K was its residual level. A mere two-fold increase in the residual level from the base case (10% of PI3KMax), resulted in excessive increase in Myc level (red line in
The results in
The Erk and PI3K pathways that control Myc protein turnover are conserved in yeast
(A) The dual-kinase mechanism.
Enzymes | Module function | References | |
Myc | Erk, PI3K | Protein stabilization | |
Fos | Erk | Protein stabilization | |
Jun | JNK, Erk | Protein stabilization | |
Β-catenin | CKIα, Gsk3β | Protein stabilization | |
LPR6 | Gsk3 β, CK1 | Axin binding | |
CDC25A | B-Cdk1, ATM-Chk2 | Stabilization |
The wide presence of this motif suggests its potential advantages for cellular signal processing. To gain insights into this issue, we developed a simplified model to analyze dynamics of the dual-kinase motif (see
To characterize the dual-kinase motif, we first examined dose response of the system with respect to the two inputs S1 and S2. Our results indicated that system activation (through phosphorylation by S1) was sensitive to input variations at an intermediate
(A) At a given synthesis rate constant (
Another salient feature of the dual kinase motif was the stabilization of X, which could be captured by the stabilization efficiency (
(A) The dynamic range for activation was
These results highlight two appealing features of the dual kinase motif. First, differential stability control on effector protein isoforms enables flexible modulation of the output dynamic range. This dynamic range can be fully exploited if the signal strengths are sufficiently large. Second, sufficiently strong signals will also result in desensitization of the system output to minor fluctuations in the levels of these signals.
While advantageous, however, increase in noise-resistance and dynamic range comes with increasing metabolic cost. On one hand, increasing destabilization of X or Xpp is associated with increasing metabolic cost. On the other, this will also require stronger input signals to fully exploit the increased dynamic range and to achieve noise-resistance, creating another metabolic burden as characterized by
Here we demonstrate that modulation of Myc stability by sequential phosphorylation enables Myc to precisely sense and integrate upstream Erk and PI3K signals. Such regulation is likely critical to cell fate decisions. Our analysis indicates that, when operating with appropriate parameters, this mechanism enables the temporal features, instead of maximum amplitudes, of the upstream signals to precisely modulate Myc accumulation. Supporting this notion, dynamics of a minimal dual-kinase motif provide direct, intuitive explanation for the key sensitivity properties of Myc output in the full model. In this work, we have limited our study to the well-defined post-translational control of Myc. It is possible that robust control of Myc accumulation is facilitated by additional mechanisms, including Myc stabilization by a signal in the carboxy-terminus of Myc
As Myc is often deregulated in cancers, quantitative understanding of the mechanisms for Myc regulation may be helpful for developing novel strategies for cancer treatment. Myc stabilization processes consist of two temporally coordinated events: Myc stabilization by Erk and prevention of Myc degradation by PI3K. While the significance of Myc degradation by the second PI3K activity has been suggested in cell proliferation
The priming ability of Erk for Myc modulation may play a critical role in distinct responses to different stimulations. Studies have shown that PC12 cells can be induced to undergo differentiation or proliferation in response to NGF or EGF
The assumed saturation of the input signals in the base model can also be experimentally tested. Our simulations indicate that the assumed saturation is a necessary condition for the overall robustness of Myc to parameters. This serves as an interesting question to explore experimentally. Also, as detailed in
The analysis of the Myc stabilization mechanism reveals a regulatory network motif that may be ubiquitously used in nature. Network motifs are small, recurring cellular regulatory networks, identified and characterized by their shared architectures and functions among diverse organisms. Well-known examples include feedback regulations, feed-forward loops, and their derivatives (see
The dual-kinase motif is similar to a well-studied phosphorylation-dephosphorylation enzymatic motif of protein modification. In both motifs, protein modification events occur sequentially, and the current state of the protein hinges upon its previous state. Given appropriate input signals and parameters, the sensitivity and amplitude of the output response can be precisely controlled
Based on the reaction network outlined in
To establish a framework that facilitates investigation of Myc modulation by its upstream signals, Erk and PI3K, we built the model with Erk and PI3K as the inputs and Myc as the output. Despite the extensive interactions between the MAPK and PI3K pathways, we decoupled Erk and PI3K signals and simplified them as a single or double rectangular pulses, respectively (
Based on experimental observations, we approximated input signals as rectangular pulses with three parameters: duration, the maximum level, and the residual level. To describe two-peak PI3K activation, we introduced another parameter, inter-peak delay. More sophisticated representations (for example, sinusoidal pulses) give similar results (data not shown). Although we focused on the two-peak activation of PI3K in the base model, the modeling framework can be extended to study other patterns of PI3K signals (such as a single peak pattern) by varying duration, steady-state values, or inter-peak delay (for example, see
As detailed in
Based on the connectivity in
Similar to Myc regulation, we used the total effector concentration X ( =
Detailed reaction diagram for Myc protein stabilization.
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Modeling a phosphorylation-dephosphorylation cycle. An enzymatic modification cycle of Gsk3β between phosphorylated and dephosphorylated states (A) is mathematically modeled (B).
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Impact of varying PI3K inputs on Myc accumulation. (A) A single peak of Myc is predicted if the second round of PI3K activity is removed. This results in reduced Myc accumulation compared to the wild-type. (B) Increased inter-peak time delay of PI3K (from 3 to 8 hours) results in wider separation between the two peaks of Myc, and the resulting Myc accumulation is less than the wild-type.
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Erk ‘primes’ Myc activity, and PI3K ‘fine-tunes’ Myc accumulation level. With the PI3K signal fixed, different residual Erk level leads to differential Myc accumulation by the second PI3K activity. The base value of the residual Erk level (ErkR) was 10 percent of maximal Erk level (black line). For increased level of ErkR (20%), the second PI3K activity increased Myc accumulation level significantly (red line). When ErkR was completely removed, Myc became unresponsive to the PI3K signal (blue line).
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The overall ultrasensitivity arises from the input/output response in each level and across different levels down the cascade. (A) The Akt Ph-dePh cycle (in response to PI3K) can be either graded (red line) or ultrasensitive (blue line) depending on the Michaelis-Menten constants. (B) Both types of PI3K-Akt responses can lead to ultrasensitive PI3K-Gsk3β responses (both red and blue), if the Akt-Gsk3β response remains ultrasensitive. (C) If Akt-Gsk3β response is not ultrasensitive, the overall PI3K-Gsk3β remains ultrasensitive if PI3K-Akt response is ultrasensitive, but may lose ultrasensitivity if PI3K-Akt response is not ultrasensitive. Note that here we have assumed that the output from the first step (AktP) has an appropriate dynamic range that “matches” the input of the second step. The dependence of the overall sensitivity of the PI3K-Gsk3β response will likely be much more complex if this matching condition is not satisfied.
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Erk signal pattern
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PI3K signal pattern
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Myc signal pattern
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Reaction kinetics
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Base model parameters and notes
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Parametric Sensitivity
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Parametric Sensitivity without ultrasensitivity
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We are grateful to the members of the You lab for helpful discussions.