A second regulatory protein is present at only copies in a bacterium of volume (a…
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Thermodynamic potentials and the formal structure of thermodynamics
Forces, Machines and Signals, Ch Free energy at work: states, weights and entropic forces
Problem
A second regulatory protein is present at only N=3 copies in a bacterium of volume V=0.70×10−15L (a typical bacterial volume). It binds a single site with dissociation constant Kd=0.50nM.
((a)) Treating the N copies as freely diffusing at the concentration c=N/(NAV), use states and weights for the two states of the site (empty and bound) to calculate the mean fractional occupancy.
((b)) Elsewhere it is reported that the Asakura-Oosawa depletion contact free energy between two large protein complexes (each of radius about 25nm) in the same cytoplasm is Fdep=−1.9kBT, a magnitude comparable with the thermal energy kBT itself. It is suggested that this depletion attraction explains why GFP, a small roughly monomeric protein of radius about 2.4nm, diffuses about elevenfold more slowly inside the bacterial cytoplasm than in dilute buffer (a measured slowing). Decide, with reasons, whether the depletion force can account for this.