A newly characterised hydrolase has and

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 characterised hydrolase has kcat=1.2×103 s−1k_{\rm cat} = 1.2\times10^3\,\mathrm{s^{-1}} and KM=60 μMK_M = 60\,\mathrm{\mu M}. Its substrate has a diffusion coefficient D=4×10−10 m2 s−1D = 4\times10^{-10}\,\mathrm{m^2\,s^{-1}}, and the active site captures the substrate within a radius a=0.4 nma = 0.4\,\mathrm{nm} (the enzyme is taken as effectively immobile). ((a)) Estimate the Smoluchowski diffusion-limited association rate constant kdiff=4πDa×NA×103k_{\rm diff} = 4\pi Da \times N_A\times10^3 in M−1 s−1\mathrm{M^{-1}\,s^{-1}}. ((b)) Compute kcat/KMk_{\rm cat}/K_M and state whether the enzyme is diffusion limited.

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