Axonal Transport 3D: Kinesin vs Dynein Tug-of-War on a Microtubule, Cargo Vesicles, Stall Force and Switching Lab

Setting up the lab bench...

Presets

Live readouts

Graphs

Position of every cargo against time

Velocity and bound motors of the highlighted cargo

Force-velocity of the two motor teams: the cargo moves where they cross

Net displacement per second, all cargos (two peaks = switching)

What is happening now

Starting.

Numerical checks

running...

How to use

Pick a preset or set the number of kinesin and dynein motors on the cargo. The picture has two parts: the strip at the top is the whole 40 um axon with every cargo (yellow = the highlighted one), and the large view is a molecular close-up of the highlighted cargo: motors that are bound to the microtubule are drawn with their feet on the tubulin lattice, free motors dangle. Arrows show the pulls of the two teams. Graph 1 is position against time; graph 2 the velocity and the bound motor counts; graph 3 the force-velocity curves (the cargo moves where they cross); graph 4 collects the displacement of all cargos each second - two peaks mean back-and-forth switching. Things to try: (1) one kinesin, and read the mean run length in the checks; (2) the Balanced preset (2 kinesin vs 11 dynein) and watch the cargo reverse; (2b) 4 vs 4, to see that equal numbers are not equal strength; (3) lower the ATP to 30 uM; (4) coat the track with tau and see dynein win; (5) find the number of dynein that balances 2 kinesin (12 pN / 1.1 pN = 11). Drag to orbit, wheel to zoom. Space pauses, R restarts, the mouse wheel zooms the close-up.

The axon, microtubule bundle, neurofilaments, mitochondria, endoplasmic reticulum, cell-body end, synaptic bouton, transport vesicle, kinesin and dynein heads were modelled in Blender 5.2 with baked PBR textures and exported as one Draco GLB. Three.js r160 animates the cargos, the stalks, the stepping feet and the forces from exactly the same stochastic model as the 2D page.

The science

Neurons make their proteins in the cell body, but the synapse can be a metre away. Vesicles, mitochondria and lysosomes are hauled along microtubules by two motor families: kinesin-1 walks toward the plus end (the synaptic terminal) and cytoplasmic dynein toward the minus end (the cell body). Most cargos carry both, so the cargo is a rope in a tug-of-war. This lab is the standard Muller-Klumpp-Lipowsky model (PNAS 105, 4609, 2008) solved with an exact stochastic simulation.

Force-velocity of one motor. A bound motor pulling against a load F steps more slowly. Below stall the relation is close to linear; kinesin resists backward sliding strongly, dynein is dragged backward faster:

kinesin: F_K(v) = F_s(1 − v/v_f) for v ≥ 0, F_s(1 − v/v_b) for v < 0 (F_s = 6 pN, v_f = 1000 nm/s, v_b = 6 nm/s) dynein: F_D(v) = F_s(1 − |v|/v_f) for v ≤ 0, F_s(1 + v/v_b) for v > 0 (F_s = 1.1 pN, v_f = 650 nm/s, v_b = 72 nm/s)

Force balance. All motors that are bound move together at one cargo speed v. With n_k kinesin and n_d dynein bound, the net force is zero (drag is about 10⁻³ pN, negligible):

n_k F_K(v) = n_d F_D(v), load per motor = n_kF_K/n_k or n_dF_D/n_d

The root is found by bisection (graph 3 shows the crossing). For one kinesin against one dynein it has a closed form, v = (F_sK − F_sD)/(F_sK/v_fK + F_sD/v_bD) = 230 nm/s, and for equal team stall forces (n_kF_sK = n_dF_sD) the cargo stalls.

Load-dependent detachment. A motor under load lets go faster, e(F) = e₀ exp(F/F_d) (e₀ = 1.0 /s and F_d = 3 pN for kinesin; 0.27 /s and 0.75 pN for dynein). Free motors on the cargo re-attach at constant rates π₀ (5 /s kinesin, 1.6 /s dynein). When a team is stretched in a tug-of-war, the weaker side detaches under the stronger side's pull, which is why the cargo moves in bursts.

Stochastic simulation (Gillespie). The state is (n_k, n_d). Four event types have the rates (N_k − n_k)π_K, (N_d − n_d)π_D, n_ke_K, n_de_D. The next event time is −ln(1−u)/R_total; the cargo moves at the force-balance speed between events, so the position is integrated exactly, with no time-step error. Waiting times are memoryless, so the playback can be cut into frames without changing the statistics.

ATP and the track. Free speeds follow Michaelis-Menten, v_f([ATP]) = v_max[ATP]/(K_M + [ATP]) with K_M = 70 µM for kinesin and 250 µM for dynein (typical in-vitro values; the table speeds are those at 1 mM). Stall forces are left unchanged. The tau slider multiplies kinesin binding by (1 − 0.7 tau) and detachment by (1 + 1.5 tau); the dynein-inhibition slider reduces dynein speed and binding. Both are illustrative scalings of real, qualitative effects, not measured curves.

Numerical checks run in the page. (1) The mean run length of a lone kinesin, from 4000 simulated runs, against v₀/e₀ = 1000 nm; (2) the force-balance solver for 1 kinesin versus 1 dynein against its closed form; (3) 11 kinesin against 60 dynein (equal stall force 66 pN) has zero speed; (4) the time-averaged bound fraction of an unopposed 6-kinesin team against the binomial value π/(π + e₀) = 5/6; (5) the Michaelis-Menten speed at [ATP] = K_M equals half of v_max.

Simplifications. The model is one-dimensional: no sideways steps, no switching between protofilaments or microtubules, and no cargo rotation. Forces are shared equally among the bound motors of a species; coupling stiffness (the elasticity of the stalks) and the dynein catch-bond or super-stall behaviour are not included. Parameters are the published in-vitro means of Muller et al.; in cells, adaptors, other motors (kinesin-3, myosin V), MAP crowding and organelle drag change them. The 40 um axon is a stylised straight segment; the cargo that reaches an end is re-launched from the middle. The motors in the pictures are drawn schematically at the correct size (kinesin 80 nm, vesicle as set).