You are here: Home / Exposures / Romond, Rustici, Gonze, Goldbeter, 1999 / Alternating Oscillations and Chaos in a Model of Two Coupled Biochemical Oscillators Driving Successive Phases of the Cell Cycle

Model Mathematics

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Component: environment

Component: parameters

Component: C_1

\frac{d}{d time} (C_1) = \frac{v_i1 K_im1}{K_im1 + M_2} - (\frac{v_d1 X_1 C_1}{K_d1 + C_1}) - (k_d1 C_1)

Component: M_1

\frac{d}{d time} (M_1) = \frac{V_1 (1 - M_1)}{K_1 + (1 - M_1)} - (\frac{V_2 M_1}{K_2 + M_1})

Component: X_1

\frac{d}{d time} (X_1) = \frac{V_3 (1 - X_1)}{K_3 + (1 - X_1)} - (\frac{V_4 X_1}{K_4 + X_1})

Component: C_2

\frac{d}{d time} (C_2) = \frac{v_i2 K_im2}{K_im2 + M_1} - (\frac{v_d2 X_2 C_2}{K_d2 + C_2}) - (k_d2 C_2)

Component: M_2

\frac{d}{d time} (M_2) = \frac{U_1 (1 - M_2)}{H_1 + (1 - M_2)} - (\frac{U_2 M_2}{H_2 + M_2})

Component: X_2

\frac{d}{d time} (X_2) = \frac{U_3 (1 - X_2)}{H_3 + (1 - X_2)} - (\frac{U_4 X_2}{H_4 + X_2})

Component: V_1

V_1 = \frac{C_1}{K_c1 + C_1} V_M1

Component: V_3

V_3 = M_1 V_M3

Component: U_1

U_1 = \frac{C_2}{K_c2 + C_2} U_M1

Component: U_3

U_3 = M_2 U_M3

Source: Derived from workspace Romond, Rustici, Gonze, Goldbeter, 1999 at changeset 3ea71eee36e6.

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Alternating Oscillations and Chaos in a Model of Two Coupled Biochemical Oscillators Driving Successive Phases of the Cell Cycle