A single kinesin motor links a bead held in an optical trap

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Molecular machines, transport and bioenergetics · Molecular machines, transport and bioenergetics

Forces, Machines and Signals, Ch Measuring one molecule: traps, tweezers and single-molecule fluorescence

Problem

A single kinesin motor links a bead held in an optical trap, in water (

\eta = 1.0\times10^{-3}\,\mathrm{Pa\,s}

T = 298\,\mathrm{K}

), to a microtubule fixed to the coverslip. ATP is withheld, so the motor stays bound without stepping. The bead has radius

a = 0.5\,\mathrm{\mu m}

, and the trap's corner frequency is measured to be

f_c = 1500\,\mathrm{Hz}

. Once the trapping force builds up enough, the motor detaches from the microtubule; its force-dependent detachment rate (an activated process of the kind met for motors and enzymes) follows Bell's form

k(f) = k_0\exp(fx^\ddagger/k_BT)

, with zero-force detachment rate

k_0 = 1.0\,\mathrm{s^{-1}}

and distance

x^\ddagger = 1.5\,\mathrm{nm}

. The trap is moved away from the motor at a steady speed

v = 500\,\mathrm{nm\,s^{-1}}

, so the bead is pulled off the trap centre at that speed and the load on the bond rises at a steady rate

r = \kappa v

. ((a)) Calibrate the trap stiffness

\kappa

from the corner frequency. ((b)) Find the loading rate

r

and the most probable force

f^*

at which the motor detaches.

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