Qualitative network modeling of the Myc-p53 control system of cell proliferation and differentiation

Abstract

A kinetic model of a molecular control system for the cellular decision to proliferate or differentiate is formulated and analyzed for the purpose of understanding how the system can break down in cancer cells. The proposed core of this control system is composed of the transcription factors Myc and p53. The network of interactions between these factors involves negative and positive feedback loops that are linked to pathways involved in differentiation, cell cycle, and apoptosis. Understanding the dynamics of the Myc-p53 control system is aided by the postulate that there exists a cancer zone defined as a range of oncogenic Myc activities where the probability of initiating cancer is high. We propose that an essential role of p53 is to prevent the system from entering or staying too long in the cancer zone by downregulating Myc or, when Myc activity somehow becomes too high, by inducing apoptosis, cell cycle arrest, or differentiation. Kinetic modeling illustrates how deletions or aberrations in PTEN, MDM2, and ARF (genes implicated in various cancers, including glioma) affect the Myc-p53 control system. In addition, computer simulations demonstrate how this control system generates different cellular phenotypes characterized by rates of cellular differentiation and proliferation.

Figure 1

(a) A qualitative network involving Myc and p53 in the control of cell proliferation and differentiation. (Arrows) Activation or upregulation. (Hammerheads) Inhibition or downregulation. Table S1 in the Supporting Material lists references supporting interactions 1–11. Abbreviations: sTF, stemness transcription factors; dTF, transcription factors inducing differentiation; P_C, cell cycle factors; P_A, apoptosis factors. (b) As Myc activity increases, a cell transitions from quiescence to the cell cycle, and eventually to apoptosis. The cancer zone is postulated to exist between normal cell cycle and apoptosis.

Figure 2

(a) The Myc-p53 core control system, and its (b) generalized phenomenological dynamical equations. See text for details.

Figure 3

Myc and p53 activities as functions of time according to Eqs. 3 and 4. (a) Activities of Myc (m^∗) and p53 (p^∗) versus time. For illustrative purposes only, a cancer zone (CZ) is arbitrarily indicated by the gray band between m^∗ = 3 and 4.5. (b) Myc versus time, for varying k₂′. (c) Myc versus time, for varying s₂′. (d) Myc versus time, for varying s₁^′. Parameter values: k₁′ = 0.01, k₂′ = 0.1 (varies in b), k₃′ = 0.01, s₁′ = 1 (varies in d), s₂′ =1 (varies in c), d′ = 0.5. Initial conditions: m^∗(0) = 0.1, p^∗(0) = 0.05.

Figure 4

Steady state of Myc (m_s^∗, dimensionless) versus s₁′ determined from Eqs. 3 and 4. The parameter s₁′ is associated with edge 3 in Fig. 1a. Negative steady states (lower curve, both solid and dashed portions) are in the shaded region, and are unphysical. (Solid curves) Stable steady states; (dashed curve) unstable steady states. Parameter values: k₁′ = 0.01, k₂′ = 1, k₃′ = 0.01, s₂′ = 1, and s₁′ varies through the range of the abscissa in this figure.

Figure 5

(a) Mutual antagonism between {p53, PTEN} and {AKT, MDM2}. (Arrows) Activation or upregulation. (Hammerheads) Inhibition or downregulation. (b) The Myc-p53 control system (edges 1–3) and its interactions with Pten, Mdm2, and Arf. Signaling pathways and degradation reactions are not shown.

Figure 6

Increases in the steady state of Myc by deletion of Pten, overexpression of Mdm2, and deletion of Arf. Dimensionless Eqs. A1–A5 and parameter Eqs. A6–A10 in the Appendix are used in these simulations. (a) Deleting Pten (by setting k₁₄′ = s₃′ = 0) increases the steady state of Myc. Initial q^∗(0) = 0. Parameters: s₃′ = 0 and 1, s₄′ = 0.5, s₅′ = 0.5, and k₁₄′ = 0. Other parameter values and initial conditions are listed at the bottom of this caption. (b) Overexpressing Mdm2 (by increasing s₄^′ from 0 to 1) increases the steady state of Myc. Initial q^∗(0) = 0.05. Parameters: s₄′ = 0 and 1, s₃′ = 1, s₅′ = 0.5, and k₁₄′ = 0.01. Other parameter values and initial conditions are listed at the bottom of this caption. (c) Deleting Arf (by setting s₅′ = 0) increases the steady state of Myc. Initial q^∗(0) = 0.05. Parameters: s₅′ = 0 and 1, s₄′ = 0.5, s₃′ = 1, and k₁₄′ = 0.01. Other parameter values and initial conditions are listed below. Other parameter values: k₁′ = 0.01, k₂′ = 0.1, k₃′ = 0.01, k₁₃′ = 0.01, k₁₅′ = 0.02, k₁₆′ = 0.02, k₁₇′ = 0.01, k₁₉′ = 0.01, s₁′ = 1, s₂′ = 1, e₃′ = 0.1, e₅′ = 0.1, d′ = 0.5, d″= 1, d″′ = 30, and d″″ = 12. Other initial conditions: m^∗(0) = 2.5, p^∗(0) = 0.1, w^∗(0) = 0.03, and v^∗(0) = 0.05.

Figure 7

Steady states D_d^∗s, P_c^∗s, and m^∗s versus signaling parameters s₁′ and s_d′ (a) for varying s_d′ with s₁′ = 1, (b) for varying s₁′ with s_d′ = 1, and (c) for varying s_d′ with s₁′ = 8. (d) Phase diagram showing the location of the phenotypes, with D⁺ assigned for D_d^∗s ≥ 10 and D⁻ otherwise, and C⁺ assigned for P_c^∗s ≥ 10 and C⁻ otherwise. For the initial conditions given below, the rightmost boundary between D⁺C⁻ and D⁺C⁺ is given by the line segment cd; this boundary shifts to the line segment ab when the initial conditions D_d^∗(0) and P_c^∗(0) are increased to 1 and 0.1, respectively (other initial conditions fixed as given below). This change in initial conditions also shifts the boundary between D⁻C⁻ and D⁻C⁺ from line segments ce to bf. Equations 3 and 4 and Eqs. A11–A14 in the Appendix are used in the simulations. Parameter values: k₁′ = 0.01, k₂′ = 1, k₃′ = 0.01, k₄′ = 100, k_4b′ = 0.1, k₅′ = 0.1, k_5b′ = 1, k₆′ = 2.1, k_6b′ = 1.6, k₇′ = 3, k_7b′ = 5, k₈′ = 10, k_8b′ = 20, k₉′ = 1, k₁₀′ = 1, k_10b′ = 1, k₁₁′ = 0.1, s₂′ = 1, s_s′ = 0.01, s_c′ = 0.01, s_a′ = 0.01, d′ = 0.5, d_ms′ = 2.5, d_md′ = 2.5, d_mc′ = 2.5, and d_ma′ = 2.5. Initial conditions: m^∗(0) = 0.1, p^∗(0) = 0.05, D_s^∗(0) = 1.1, D_d^∗(0) = 0.0001, P_c^∗(0) = 0.001, and P_a^∗(0) = 0.0001.