Figure - PMC

Skip to main content

An official website of the United States government

Here's how you know

Here's how you know

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

View full-text article in PMC

. 2004 Jun;86(6):3432–3443. doi: 10.1529/biophysj.103.036558

Search in PMC
Search in PubMed
View in NLM Catalog
Add to search

Copyright © 2004, Biophysical Society

PMC Copyright notice

Dynamical behaviors from the signaling transduction network shown in Fig. 1. (A–D) Active cyclin-CDK (x) versus time at different dynamical regimes. (A) Stable low kinase activity. (B) Stable high kinase activity. (C) Bistability. Starting from different initial conditions, the system approached to different steady state. (D) Bifurcation diagram of bistability. Dashed segment is the unstable steady state. Shaded arrows indicate the hysteresis loop. (E) Limit cycle oscillation. (F) Bifurcation diagram of limit cycle. Solid circles are stable steady states and open circles are the maxima and minima of the limit cycle oscillation. (G) Complex (period-2) dynamical behavior. (H) Complex (chaotic) dynamical behavior. (I) Active cyclin-CDK versus free CDK for the period-2 dynamics in G. (J) Active cyclin-CDK versus free CDK for the chaotic oscillations in H. The parameters for A–D are: = 0.5, = 8.64, = 0.094, = 0.72, = 0.75, = 0.57, = 15.8, = 1/3, = 3.92, = 1/3, = 26.31, = 1/3, = 0.215, = 0.8, = 0.085, = 0.8, = 0.06, = 0.37, = 6.3, = 7.6, = 5.6, = 5.2, = 2.5, = 7.4, α₀ = 0.015, α₁ = 0.015, α₂ = 1, β₀ = 1, β₁ = 0.72, β₂ = 0.19, γ₀ = 0.02, γ₁ = 0.91, and γ₂ = 1. The parameters for E and F are: = 0.5, = 0.4, = 0.33, = 0.83, = .013, = 1, = 24.8, = 1/3, = 5.6, = 1/3, = 24.5, = 1/3, = 0.12, = 0.65, = 0.82, = 0.74, = 0.74, = 0.17, = 7.9, = 0.31, = 9.5, = 3.5, = 5.2, = 9.0, α₀ = 0.011, α₁ = 0.61, α₂ = 1, β₀ = 1, β₁ = 0.70, β₂ = 0.19, γ₀ = 0.0058, γ₁ = 0.26, and γ₂ = 1. The cyclin synthesis rate in each panel is: (A) = 8.0; (B) = 30; (C) = 13.9; and (E) = 1.92. The parameters for G and I are: = 12.4, = 0.83, = 0.27, = 6.65, = 0.99, = 0.9, = 0.14, = 28.9, = 1/3, = 93, = 71.8, = 7.74, = 1/3, = 77.4, = 14, = 32.7, = 1/3, = 70.9, = 17.7, = 5.0, = 2.0, = 0.23, = 0.18, = 0.625, = 0.78, = 0.9, = 0.19, = 9.5, = 4.8, = 7.1, = 10, = 1.15, = 4.23, α₀ = 0.07, α₁ = 0.155, α₂ = 1, β₀ = 1, β₁ = 0.81, β₂ = 0.1, γ₀ = 0.02, γ₁ = 0.76, γ₂ = 1, and τ = 20. The parameters for H and J are: = 32.98, = 0.1, = 0.365, = 9.94, = 0.33, = 0.965, = 0.164, =19.1, = 1/3, = 99.9, = 97.5, = 8.68, = 1/3, = 86.8, = 88.9, = 29.96, = 1/3, = 79.3, = 39.45, = 5.0, = 1.0, = 0.07, = 0.07, = 0.71, = 0.054, = 0.066, = 0.0065, = 6.29, = 6.58, = 6.14, = 2.4, = 0.94, = 1.27, α₀ = 0.134, α₁ = 0.118, α₁ = 1, β₀ = 1, β₁ = 0.298, β₂ = 0.07, γ₀ = 0.013, γ₁ = 0.34, γ₂ = 1.0, and τ = 20.

Inline graphic — Dynamical behaviors from the signaling transduction network shown in Fig. 1. (A–D) Active cyclin-CDK (x) versus time at different dynamical regimes. (A) Stable low kinase activity. (B) Stable high kinase activity. (C) Bistability. Starting from different initial conditions, the system approached to different steady state. (D) Bifurcation diagram of bistability. Dashed segment is the unstable steady state. Shaded arrows indicate the hysteresis loop. (E) Limit cycle oscillation. (F) Bifurcation diagram of limit cycle. Solid circles are stable steady states and open circles are the maxima and minima of the limit cycle oscillation. (G) Complex (period-2) dynamical behavior. (H) Complex (chaotic) dynamical behavior. (I) Active cyclin-CDK versus free CDK for the period-2 dynamics in G. (J) Active cyclin-CDK versus free CDK for the chaotic oscillations in H. The parameters for A–D are: = 0.5, = 8.64, = 0.094, = 0.72, = 0.75, = 0.57, = 15.8, = 1/3, = 3.92, = 1/3, = 26.31, = 1/3, = 0.215, = 0.8, = 0.085, = 0.8, = 0.06, = 0.37, = 6.3, = 7.6, = 5.6, = 5.2, = 2.5, = 7.4, α₀ = 0.015, α₁ = 0.015, α₂ = 1, β₀ = 1, β₁ = 0.72, β₂ = 0.19, γ₀ = 0.02, γ₁ = 0.91, and γ₂ = 1. The parameters for E and F are: = 0.5, = 0.4, = 0.33, = 0.83, = .013, = 1, = 24.8, = 1/3, = 5.6, = 1/3, = 24.5, = 1/3, = 0.12, = 0.65, = 0.82, = 0.74, = 0.74, = 0.17, = 7.9, = 0.31, = 9.5, = 3.5, = 5.2, = 9.0, α₀ = 0.011, α₁ = 0.61, α₂ = 1, β₀ = 1, β₁ = 0.70, β₂ = 0.19, γ₀ = 0.0058, γ₁ = 0.26, and γ₂ = 1. The cyclin synthesis rate in each panel is: (A) = 8.0; (B) = 30; (C) = 13.9; and (E) = 1.92. The parameters for G and I are: = 12.4, = 0.83, = 0.27, = 6.65, = 0.99, = 0.9, = 0.14, = 28.9, = 1/3, = 93, = 71.8, = 7.74, = 1/3, = 77.4, = 14, = 32.7, = 1/3, = 70.9, = 17.7, = 5.0, = 2.0, = 0.23, = 0.18, = 0.625, = 0.78, = 0.9, = 0.19, = 9.5, = 4.8, = 7.1, = 10, = 1.15, = 4.23, α₀ = 0.07, α₁ = 0.155, α₂ = 1, β₀ = 1, β₁ = 0.81, β₂ = 0.1, γ₀ = 0.02, γ₁ = 0.76, γ₂ = 1, and τ = 20. The parameters for H and J are: = 32.98, = 0.1, = 0.365, = 9.94, = 0.33, = 0.965, = 0.164, =19.1, = 1/3, = 99.9, = 97.5, = 8.68, = 1/3, = 86.8, = 88.9, = 29.96, = 1/3, = 79.3, = 39.45, = 5.0, = 1.0, = 0.07, = 0.07, = 0.71, = 0.054, = 0.066, = 0.0065, = 6.29, = 6.58, = 6.14, = 2.4, = 0.94, = 1.27, α₀ = 0.134, α₁ = 0.118, α₁ = 1, β₀ = 1, β₁ = 0.298, β₂ = 0.07, γ₀ = 0.013, γ₁ = 0.34, γ₂ = 1.0, and τ = 20.