A bacterial 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 bacterial regulatory protein is present at only N=8 copies in a bacterium of volume V=1.0×10−15L (a typical volume for a bacterial cell). It binds a single operator site on the chromosome with dissociation constant Kd=2.0nM.
((a)) Treating the N copies as freely diffusing at the concentration c=N/(NAV), use states and weights for the two states of the operator (empty and bound) to calculate the mean fractional occupancy of the site.
((b)) Elsewhere it is reported that the Asakura-Oosawa depletion contact free energy between two large protein complexes in the same cytoplasm is Fdep=−1.9kBT, a magnitude comparable with the thermal energy kBT itself. It is suggested that this depletion attraction could be what makes GFP, a small roughly monomeric protein of radius about 2.4nm, diffuse 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.