ATP-actin monomers add to the barbed end of an actin filament with on-rate constant…

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture · Macromolecules, membranes and cell architecture

Forces, Machines and Signals, Ch Filaments, networks and the mechanics of whole cells

Problem

ATP-actin monomers add to the barbed end of an actin filament with on-rate constant

k_{\rm on} = 11.6\,\mu\mathrm{M^{-1}\,s^{-1}}

and off-rate constant

k_{\rm off} = 1.4\,\mathrm{s^{-1}}

; each subunit added lengthens the filament by

\delta = 2.7\,\mathrm{nm}

. Work at

298\,\mathrm{K}

, where

k_BT = 4.11\,\mathrm{pN\,nm}

. Idealise the end as adding and losing subunits independently, one at a time, with no other filament or motor acting on it. ((a)) Starting from the rate equation for the filament's length,

dL/dt = \delta(k_{\rm on}c - k_{\rm off})

, derive the critical concentration

c_c

and evaluate it. ((b)) The filament grows unloaded in a solution held at

c = 5c_c

. Find its growth speed. ((c)) Now let the barbed end push against a rigid obstacle that exerts an opposing load

f

. In the Brownian ratchet picture, the load multiplies the forward rate by a Boltzmann factor,

k_{\rm on}(f) = k_{\rm on}c\,e^{-f\delta/k_BT}

, while

k_{\rm off}

is unaffected by the load. Derive the stall force

f_s

at which growth just ceases, in terms of

c

and

c_c

, and evaluate it at

c = 5c_c

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