Phase —t -3.0 minUnattached kinetochores 10Checkpoint —Securin 100 %Pole to pole 0 µmFPS 0

Drag to orbit, wheel or pinch to zoom. Yellow threads are spindle microtubules, pink bodies are sister chromatids (blue = centromere), orange dots are centrosomes. Educational model, not a diagnostic or medical tool.

Mitotic Spindle Lab: Kinetochore Attachment, Checkpoint and Anaphase

Ten kinetochores must each grab a spindle microtubule before the checkpoint lets the cell divide. What happens when they do not?

Educational model of normal cell division with simplified, illustrative numbers. It is not a diagnostic tool and gives no medical advice.

Running…

Attachment and error handling

Forces and speeds

Checkpoint clock

Time

Live readouts

Securin and unattached kinetochores

Chromosome axial position |y|

Experiments

Each button runs many cells headless (same model, seeded) and tabulates the result.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom; three camera presets.
Sliders change the live model at once. "New cell" re-rolls the random attachment events (seeded, so a run is repeatable).
Checkpoint ON: anaphase waits for every kinetochore to be correctly attached. OFF: the securin clock runs regardless, like a cell with a broken checkpoint.
Time scale = simulated minutes per real second.

The science

Attachment. Each of the 2N = 10 kinetochores captures a microtubule at rate k_on; the waiting time is exponential, so the time until the last one is attached is the maximum of 10 exponentials with mean H₁₀/k_on, H_N = Σ 1/j (harmonic number). A second kinetochore attaches to the wrong (same) pole with probability p_err (a syntelic error); an Aurora-B-like process detaches it at rate k_corr.

Congression. A bi-oriented chromosome feels pulling and polar-ejection forces that act like a restoring force towards the plate, overdamped: γ dy/dt = −k y, so y(t) = y₀ e^−t/τ with τ = γ/k; a small noise term mimics kinetochore oscillations. Mono-oriented chromosomes glide to their pole at speed v_c. These are model values, not measurements [перевірити за джерелом].

Checkpoint clock. Securin S is degraded by APC/C: dS/dt = −ε k_apc S, with ε = 1 when the checkpoint is satisfied and a small leak ε = 0.03 while any kinetochore is unattached or wrongly attached. Anaphase starts when S < S_th (separase cleaves cohesin): the time from nuclear-envelope breakdown is ln(S₀/S_th)/k_apc when the checkpoint is off.

Anaphase and cytokinesis. Anaphase A: kinetochore-to-pole distance shrinks at constant v_A. Anaphase B: poles separate at v_B. The cell is kept at constant volume, (4/3) π R² L = const, while it elongates, and the furrow constricts linearly in time. Chromatids of a chromosome with a syntelic or unattached kinetochore at onset may go to the same daughter: counts such as 6 / 4 illustrate aneuploidy. Simplifications: one spindle axis, five chromosomes, no kinetochore stretch, no cyclin-CDK network, no real geometry of the metaphase plate. Not a medical model. Assets built with Blender; scene by Three.js.