A newly isolated kinesin-family motor

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

Forces, Machines and Signals, Ch Enzymes and molecular motors

Problem

A newly isolated kinesin-family motor, call it motor X, is characterised by three separate single-molecule measurements. Translate each into the quantity it determines. ((a)) The stepping rate

v

(steps per second) is measured at two ATP concentrations:

v=100\,\mathrm{s^{-1}}

[\mathrm{ATP}]=100\,\mathrm{\mu M}

, and

v=160\,\mathrm{s^{-1}}

[\mathrm{ATP}]=400\,\mathrm{\mu M}

. Assuming Michaelis-Menten kinetics in ATP, find

k_{\rm cat}

and

K_M

. ((b)) At saturating ATP the randomness parameter is measured to be

r=0.33

. Treating the mechanochemical cycle as

n

equal, sequential, rate-limiting sub-steps with

r=1/n

, how many rate-limiting transitions occur per step? ((c)) Optical-trap records show that one of its heads stays bound to the microtubule for

8\,\mathrm{ms}

out of a total stepping cycle of

24\,\mathrm{ms}

(bound plus unbound time). Compute the duty ratio and state whether this value allows motor X to walk processively as a lone motor.

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