A catalytic step inside a molecular motor's active site has an intrinsic…

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 catalytic step inside a molecular motor's active site has an intrinsic (uncatalysed) activation barrier of

33\,k_BT

and an attempt frequency

\nu = 1.0\times10^{13}\,\mathrm{s^{-1}}

, at

T = 298\,\mathrm{K}

(

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

). Catalytic residues in the active site lower this barrier by

15\,k_BT

, leaving the equilibrium constant unchanged. ((a)) Find the catalysed rate constant with no mechanical load. ((b)) This catalytic step lies along the motor's mechanical reaction coordinate with

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

. If a load of

3.0\,\mathrm{pN}

acts so as to assist (lower) this same barrier further, find the rate constant under load.

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