Question

Estimate the diffusion coeeficient of a 70S ribosome in buffer in . The actual number in cytoplasm is Dribo=0.03.

Use the geometric results iin fig 17.11 to stimate the diffusion coefficient of a piece of double-standed DNA of length1000 base pairs. Treat it as an ellipsoid.

Answer 1

FCS volume of detection estimation fluorescent spherical polystyrene beads with a diameter of 44nm (G40, Duke scientifics, Palo Alto, Calif.) (fig. S1). We fit the autocorrelation functions with G(t) = 1/{N[(1+ (4Dt/ω 2 )]}, which describes a twodimension translational diffusion of fluorescent molecules. N is the number of fluorescent beads in the detection volume, D is the two-dimensional diffusion constant of the fluorescent beads, and t is the time variable. Using the Stokes-Einstein relationship D = kBT/6ПηR, where kB is the Boltzman constant, T is temperature in Kelvin (300K), η is the viscosity of water (0.01 cm 2 /s), and R is the radius of the beads (0.22nm), we determined that the diffusion constant (D) of the beads is 3.6 µm2 /s. We inferred ω (0.19 µm) using the equation D= ω 2 /(4ζ), where ω is the radius of the detection volume and ζ is the diffusion time of the polystyrene beads (0.9 ms, fig. S1). The FCS volume of detection is calculated with the equation Vprobe = Пω 2 h, where h is the height of this volume. Under our conditions and for in-vitro FCS measurements, h was estimated to be 8.8µm (1). The probe volume in-vitro was therefore found to be ~ 1 fl. For FCS measurements in a living E. coli cell, the thickness of an E. coli cell was estimated to be 0.4 µm. The probe volume in a living cell was calculated to be ~ 0.045 fl. One fluorescent molecule in the probe volume for in vitro measurements represents a concentration of 7nM. One MS2-GFP molecule in the detection volume within a living bacterium represents a concentration of 37nM. Finally, one ms2-RNA molecule, which binds to two MS2-GFP molecules, represents a concentration of 18nM. ms2-RNA and MS2-GFP protein purification The ms2-RNA binding sites from plasmid pZE31ms2 were amplified by PCR with primers carrying a T7 promoter and purified on 1.2% agarose gel. ms2-RNA was 2 transcribed using the AmpliScribe T7 transcription kit from Epicentre (Madison, WI). The concentration of ms2-RNA was determined with absorbance at 260nm. DNA sequence coding for MS2-GFP mutant was cloned into pRSETA vector (Invitrogen, Carlsbad, CA) and transformed into BL21 (DE3PlysS) competent cells. Cells were grown to 0.5 O.D. and induced with 1 mM IPTG overnight at 30o C. The Nterminus 6X Histidine tagged MS2-GFP was purified on Nickel column (Qiagen, Valencia, CA) and dialyzed in 1mM PBS buffer overnight. The 6X Histidine tag was removed with enterokinase at 0.25 mg/ml (Roche, Palo Alto, CA) for 4 hours at 30o C. The flow-through fraction of MS2GFP was collected from the Nickel column, dialyzed in 1mM PBS buffer overnight, and stored at 4o C. The concentration of MS2-GFP was determined by absorbance at 280nm.