Equilibrium Sedimentation & Sedimentation Velocity:

New Posts at the Course Website:Origin Assignment 3 on Analytical Ultracentrifugation (due 3/2/12)Problem SetData (xls file)Resource Booklet (R7) on Analytical UltracentrifugationEquilibrium Sedimentation &Sedimentation Velocity: RandomWalks in the presence of forces.

A Beckman Analytical Ultracentrifuge– circa 1950

The Beckman XL1 AUC– circa 2000

Sedimentation Velocity - HistoryTheodore Svedberg was awarded the 1926 Nobel Prize in Chemistry for“for his work on disperse systems”The (Theodor) SvedbergThe Nobel Prize in Chemistry 1926.Nobelprize.org. 26 Feb 2012 http://www.nobelprize.org/nobel prizes/chemistry/laureates/1926/UltraScan WebsiteBorris edburg(byIsaacGrunewald)UppsalaUniversityArtCollec gSciences(IVA)

Sedimentation VelocityInterference fringes vs. time & radial position‘Fringe number’ (the number of fringes that cross ahorizontal axis) is proportional to the solute(macromolecule or particle) concentration.When the fringes are horizontal, the concentration issteady ( constant). When the fringes turn vertical,the macromolecule concentration is changingrapidly. These are boundaries between regions thatcontain particles and are depleted of particles.In the series of interference patterns shown at right,the sample chamber has a uniform distribution(concentration) of particles at the beginning of theexperiment (t 0.0). As a function of time, threeboundaries move away from the top of the samplecolumn (at left, r 6.7 cm) at different rates. Thefastest moving boundary corresponds to acomponent in the sample with the largestsedimentation coefficient, s, the slowest movingboundary is characterized by the smallest value of s.Note that rate of movement of the boundariesincreases as the radial position of the boundarybecomes larger.

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comparing values of sSincethesedimenta tandardcondi onsarenecessarytocomparethesedimenta rentinves gators(underdifferentcondi ons),ortomakecomparisonsamongdifferentpar erentcondi nt.S20,w sedimentation coefficient in water at 20oCST,b sedimentation coefficient in buffer at ToCη20,w viscosity of water at 20oCηT,b viscosity of buffer at ToCρ20,w density of water at 20oCρT,b density of buffer at ToCv partial specific volume of particle (cm3/g)!!"# % %%!&#'!!"# % %%!&#'!!"# % %%!&#'((! !" ) (! )((! !" ) (! )!"# &#'&#'!"# ((! !" ) (! )((! !" ) (! )!"# &#'&#'!"# ((! !" ) (! ) (! )((! !" ) (! ) (! )!"# &#'&# &#'&# !"# Thepar alspecificvolumeofthepar hesedependencesusuallyaren’tknown.Theusualcorrec ables)asafunc onoftemperatureandsolventcomposi on.

Sedimentation Equilibrium - HistoryJean Baptiste Perrin was awarded the 1926 Nobel Prize in Physics for“for his work on the discontinuous structure of matter, and especially forhis discovery of sedimentation equilibrium”Jean Baptiste article123.html"Jean Baptiste Perrin - Biography".Nobelprize.org. 26 Feb 2012 http://www.nobelprize.org/nobel prizes/physics/laureates/1926/perrin.html

ConcentrationSedimentation EquilibriumTopBottomRadial PositionThe system is at equilibriumat every point in the centrifugecell. The decrease in potential energy of theUltraScan WebsiteBorris cle in a centrifugal field, by movement tothe right (rightward filled arrows), is matched adecrease in chemical potential energy thatresults from the concentration gradient(leftward pointing open arrows), which acts inopposition to sedimentaton.

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Total Chemical Potential Energy in the SedimentationEquilibrium Experiment!µ! "!#!! !!!µ "!#! ! ## '" (&'& " ! ! ) )!" ## " &&&&& &&# &'&#%))!"" !" #% %("!!! "! # !! !!#!" %# ! !" ' !" #& !!!( " #& !! !! # %&!! "#!#" ! ! ! # #!#(!!)!"#"#"# &!!! !!! ("# %&( % '&!### ##%&! '#) "# #!!! # ! ! %&') ! "#"# !!! !! ! %!%'# (!"!% # ! ! ) ()&'! )()" ( )#!# ! ! *""!" !#"## ##!" ! "%&' # * #!## * *!"#()(Theequilibriumdistribu onofthepar cleconcentra oninthecentrifugecellvariesexponen allyontheradius.Themolecularweightofthepar cleisdeterminedinashape- ‐independentmanner.%''&)

Equilibrium Sedimentation & Sedimentation Velocity: Random Walks in the presence of forces.