Sedimentation etc Topic 4 Part 1 Biophysics

Academic Geneolgy Going from before 1453 to me. Ostwald – 1909 Nobel Cech – 1989 Nobel

National Academy of Science: Vinograd’s initial major contribution was the development of density gradient ultracentrifugation

General Principles f v F (like mg) Sphere: f 0 = 6  R Other particle: get r = f/ f 0 and f = r f 0 Example – prolate with  = 3 and  = 2

Problem 5.4 from Text

Sedimentation 1-  is the buoyancy factor ~ 1-  o /  (if  o >  then it floats). s = sedimentation coefficient, [s] = Svedberg, 1 x sec = 1 Svedberg. Density of medium,  = m o /  V, V = volume. is specific volume, volume/mass of substance in solution (V/m)

Determining s Analytical Centrifuge This instrument scans absorption along the centrifuge cell as a function of time – giving concentration.

Determining s v b = dr b /dt =  2 sr b, where the subscript b signifies the boundary (so r b is the boundary between solvent and solution). So plot ln(r b ) vs t and get slope which is equal to  2 s.

Determining s Diffusion blurs boundary D = RT/N A f,

Standard s Depends on temperature and viscosity so define for standard conditions, –Equation 5.19 s depends on M and f (shape and size) so if know M can get f (shape information/stokes radius). If know shape and size, can get M.

Sedimentation coefficient for sphere s proportional to M 2/3 Can plot log s vs M and get line with slope 2/3. Eq 5.26

M from s and D (HW hint) For a sphere Eq 5.34

Density Gradient used for separation

Real data on hemoglobin free and bound to haptoglobin

Electrophoresis Now have F = ZeE, fv = ZeE. Mobility, U = v/E = Ze/f Sphere: U = Ze/(6  R)

Gel Electrophoresis Could do free electrophoresis with moving boundary like sedimentation – but nobody does Actually –Do zonal technique –Use gel – Sieve effect Define, U ri is relative mobility, U d is dye mobility, d i is distance, K is constant proportional to size, C is gel concentraton, U ri 0 is the mobility with C = 0.

Movement with a constant Force This is a gaussian centered around x = x o +  Ft With rms of, velocity =  F,  = 1/(6  r) with r = radius and  = viscosity D =  k B T = diffusion constant

Running DNA on a Gel Closed small plasmids give discrete bands Long DNA tunnels and separation goes as 1/mass Can get screening from lots of cations 2-D electrophoresis good for large pieces of DNA Genome project used Saenger method

Genome Project – 1$/basepair SCIENCE VOL FEBRUARY 2014

Saenger method 2-D Electrophoresis  Pulsed Field electrophoresis, DNA snakes its way through Migrates as 1/mass, i.e. 1/length Mix DNA polymerase I, nucleotides and labeled didexoy base analogs (dATP, dTTP, dCTP, dGTP, each labeled with different fluorescent dye). Used to mix with one didexoy at a time. C T A G

Running Plectonemic helices L = T + W For DNA at several Kbp, helices run by writhe and hence (for constant twist), L Topoisomers for DNA of defined length give gaussian band due to different energies Wang Paper supercoil.jpg

Determination of Helical Repeat of DNA (Wang, 1979) Definitions –# base pairs = n + x –l 0 = distance between bands –h = helical repeat = #bp/turn If x is an integral number multiple of h then no change in pattern –L = T + W  L+z = T + z + W, z = integer (x = zh), W can stay same, l 0 doesn’t change If x is not an integral multiple of h then pattern shifted by(x/h) l 0

Example Wang found that h = 10.4 ± 0.1 Slightly different than W-C (crystal)

Some Sedimentation Exercises 1.A protein has a frictional coefficient of 2 × g/s and charge of 100e and another has a frictional coefficient of 4 × g/s and 600e in a particular buffer. You are trying to separate these by electrophoresis using a field of strength 10 statvolts (the cgs unit for electric field) at 300 K. Can you resolve these after 10 minutes? 2.A particular piece of DNA can essentially only have 0 or 1 supercoil. The energy state for 1 supercoil is 2 kT more than zero supercoils. Calculate the fraction of DNA with 1 supercoil. 3.Say you have DNA with 0, ±1, ±2, ±3, ±4 supercoils. Would a gel be able to separate positive and negative supercoils? What if you used chloroquine which (say) decreases T by 3?