MY SIMULATOR

t 0 minmass 1.00Cdk1 0.00stage interphaseFPS 0

Cyclin / Cdk1 / APC clock

● cyclin C● Cdk1 M● APC X

Drag to orbit · wheel / pinch to zoom · the glowing cell is the live one · red dot = unattached kinetochore, green = attached

Cell Cycle Clock Lab: Cyclin–CDK Oscillator, Size Checkpoint and Spindle Checkpoint

A cell grows until its cyclin switch fires, Cdk1 rises, the cell goes through prophase, metaphase, anaphase and cytokinesis, and splits in two. Change growth, cyclin synthesis and the spindle checkpoint to see what keeps division on time and error-free.

Educational model. The cycle is much faster (about an hour) than in most human cells, like an early embryo. Only 8 of the 46 chromosomes are drawn. Not medical advice.

Scenario

Cell and checkpoints

The checkpoint holds the APC switch until almost every chromosome is attached to the spindle. A poison (like nocodazole) stops microtubules attaching.

Live readout

Cell mass and divisions

Experiment: growth rate vs size at first mitosis

Grows fresh cells with six doubling times and records the mass at which Cdk1 first rises above 0.5, then compares with an independent adaptive solver (Dormand–Prince 5(4)). Faster growth overshoots the cyclin threshold.

Independent numerical checks

Also run in Node: node src/check.js (adds the growing-cell comparison, a 1000 min stable-cycle run and both spindle-poison cases).

Controls

Drag / one finger: orbit; wheel / pinch: zoom; Five stages shows the textbook row, Live cell follows the simulated cell.
Doubling time sets how fast mass grows; cyclin synthesis capacity sets how steeply the size switch turns on; attachment time is how fast kinetochores catch microtubules.
Toggle the spindle checkpoint and the poison to compare arrest with error-prone division.

The science

The clock. Goldbeter's minimal model (1991) has cyclin C, active Cdk1 M and active anaphase-promoting complex X: dC/dt = v_i − v_d X C/(K_d + C) − k_d C, dM/dt = V₁(1−M)/(K₁+1−M) − V₂M/(K₂+M) with V₁ = V_M1C/(K_c+C), and dX/dt = V₃(1−X)/(K₃+1−X) − V₄X/(K₄+X) with V₃ = V_M3M. Parameters follow the paper (K_1..4 = 0.005, K_c = 0.5, V_M1 = 3, V₂ = 1.5, V_M3 = 1, V₄ = 0.5, v_d = 0.25, K_d = 0.02, k_d = 0.01 in min−1 units); at v_i = 0.025 the period is about 25 min.

Size checkpoint [model]. Mass grows as m = m₀2^t/T_d. The cyclin synthesis rate rises steeply with size, v_i = v_max m⁶/(m⁶ + 1.6⁶): a small cell cannot accumulate enough cyclin to trip the Cdk1 switch, and after division the daughters (half the mass) fall back below it. The Hill form is an illustrative device, not a measured law.

Stages. Prophase when M > 0.2, metaphase when M > 0.45, anaphase when APC X > 0.5, then sister chromatids move apart for about 3 min (real anaphase A: roughly 1–3 µm/min); the furrow closes during about 6 min of low Cdk1 (M < 0.3) [model durations].

Spindle assembly checkpoint [model]. At prophase all kinetochores are unattached (u = 1); attachment is first-order, du/dt = −u/τ. With the checkpoint on, APC activation is scaled by max(0, 1 − u/0.05), so anaphase waits until fewer than about 5 % are unattached. The chromosomes at risk at anaphase are illustrated as N·½·u with N = 46. A spindle poison keeps u = 1: with the checkpoint on the cell arrests in metaphase; with it off the cell divides anyway with about 23 chromosomes at risk.

Simplifications. No DNA replication or damage checkpoints, no cell-size feedback on the oscillator other than through v_i, deterministic attachment, all 46 chromosomes treated identically, the 3D cell is a stylised shape.