Kinessa: 8 nm per Step
Physics of Life & Earth arc, page 190 of 193. Back to The Pixelated Physics Universe
Who they are
Kinessa walks a microtubule tightrope with a cargo sphere on her back, one ATP per stride, hand over hand.
Kinessa is a character of the Physics of Life & Earth arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Kinesin-1 is a two-headed motor protein that carries cargo along microtubules. Using an optical trap, Svoboda, Schmidt, Schnapp and Block saw discrete 8 nm steps of the molecule's centre of mass. Yildiz and colleagues labelled one head and saw it move in alternating steps of about 17 nm and 0 nm: the heads swap places, hand over hand. With a force clamp, Visscher, Schnitzer and Block (1999) found one ATP hydrolysed per 8 nm step and a stall force that depends on ATP concentration. Summarising those measurements, Schnitzer, Visscher and Block (2000) put the motor's maximum load at about 5.5–7.5 pN.
$$ \begin{gathered} W = F \times d = 6\ \mathrm{pN} \times 8\ \mathrm{nm} = 48\ \mathrm{pN\,nm} \\ k_B T = 4.1\ \mathrm{pN\,nm}\ (298\ \mathrm{K}) \ \Rightarrow\ W \approx 12\,k_B T \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $W$ | work per step against the load (1 pN·nm = 10⁻²¹ J) | J |
| $F$ | load force near stall (1 pN = 10⁻¹² N) | N |
| $d$ | step size (1 nm = 10⁻⁹ m) | m |
| $k_B$ | Boltzmann constant, 1.380 649 × 10⁻²³ J/K (exact) | J/K |
| $T$ | temperature | K |
Honest caveat: The stall force is not always 6 pN; it depends on conditions. 48/4.1 is 11.7, so “about 12 k_BT”.
Sources
- Svoboda, Schmidt, Schnapp & Block (1993) Direct observation of kinesin stepping by optical trapping interferometry, Nature 365, 721
- Visscher, Schnitzer & Block (1999) Single kinesin molecules studied with a molecular force clamp, Nature 400, 184
- Yildiz, Tomishige, Vale & Selvin (2004) Kinesin walks hand-over-hand, Science 303, 676
Crossovers
Kinessa meets Axona (Hodgkin–Huxley Spike). Axona's spike runs on ion channels moving charge across a membrane. Kinessa's motor runs on ATP, stepping 8 nm at a time along a microtubule. Both are biology driven by physics at the nanoscale.
Kinessa meets Barrierwyn (Kramers Escape Rate). Kinessa's steps are biased by ATP, but thermal kicks are always around. Barrierwyn's escape over a barrier is part of how molecular motors move between states.
Wear the lore
Concept keywords: 8 nm per Step, Kinessa, Physics of Life & Earth, physics lore, Pixelated Physics