||Bacteria Escherichia coli
||"Physical Biology of the Cell", Rob Phillips, Jane Kondev and Julie Theriot (2009). Page 110
||Taking X, distance to be traveled, as 1µm (BNID 100 002) and D, diffusion coefficient in cytoplasm, as 10µm^2/sec (D in cytoplasm is in the range of 5-15µm^2/sec, GFP-BNID 100 193, 40kda dextran, similar weight to protein, BNID 100198). According to equation of diffusion (in 3 dimensions): t diffusion=X^2/(6×D). 1µm^2/60µm^2/sec=0.017sec≈0.01sec.
||For time it takes a protein to diffuse across a HeLa cell see BNID 105 339. In cytoplasm there are solutes and D is smaller than in water (100µm^2/sec). D in water can be calculated from the Einstein-Stokes eq. D=KBT/(6×π×Ƞ×R) where R=2.5nm, typical protein radius. KB=Boltzmann's constant, Ƞ=viscosity, 0.001 Pa×sec for water. (1.38×10^-23Kg×m^2×sec^-2×K^-1×300K)/ (6×3.14×0.001Kg×m^-1×sec^-1×2.5×10^-9m)=8.8×10^-11m^2/sec=
88µm^2/sec≈100µm^2/sec Please see "Physical biology of the cell" 2nd edition 2013 p.128 3rd paragraph: "Estimate: moving proteins from here to there-For molecules and assemblies that move passively within the cells, the time scale can be estimated using equation 3.18 (t(diffusion)≈X^2/D, where D is the diffusion constant). For a protein with a 5nm diameter, the diffusion constant in water is roughly 100µm^2/s - this estimate can be obtained from the Stokes-Einstein equation (to be discussed in more detail in Chapter 13 in equation 13.62 on p.531), which gives the diffusion constant of a sphere of radius R moving through a fluid of viscosity Ƞ at temperature T as D=KB/(6πȠR), The timescale for such a typical protein to diffuse a distance of [investigators’] standard ruler (that is, across an E. coli) is: t(E. coli)≈[L(E. coli)]^2/D≈1µm^2/100µm^2/sec≈0.01sec. (eq.3.19)."