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Bios 532 Analytical Ultracentrifugation Sedimentation of Particles in a Gravitational Field The sedimentation coefficient, s: The s-value is the sedimentation velocity of a molecule. This may be measured by sucrose gradient sedimentation or by analytical ultracentrifugation. The s-value of a molecule is determined both by its shape and by its mass. Sedimentation of Particles in a Gravitational Field The sedimentation coefficient, s: s = u/2r where u = velocity of the particle = angular velocity of the rotor r = distance from axis of rotation s is related to the molar weight (MW) of the solute: s = MW(1-)/Nf = partial specific volume of the solute = density of the solvent N = Avogadro's number f = frictional coefficient WARNING: VALUES ARE TEMPERATURE DEPENDENT The sedimentation coefficient, s: s = u/2r 10-13 seconds is called a Svedberg, and given the symbol S S has implied units of s/radian2, but the radian2 is generally ignored = partial specific volume of the solute (units: cm3/g) The partial specific volume of a protein is the ratio between it's volume and molecular weight. The partial specific volume of a molecule is a measure of the change in volume (in mL) of the solution per gram of the molecule in that solution. Partial specific volume is equal to the inverse of the density of the particle; can be measured directly or estimated. If the exact sequence of the protein is known, then the partial specific volume may be calculated from the partial specific volumes of the constituent amino acids, using the following equation: =(∑ (n(i) M(i) (i) ) )/ (∑ n(i) M(i) ) n (i) = # of residues of type i M(i) = mass of residue type i (i) = psv for residue type i WARNING: estimate breaks down if you have detergent bound, modifications, etc. and M(i) = M(aa) -18 for all but the last amino acid because water is released forming the peptide bond! = partial specific volume of the solute (units: cm3/g) One rough estimation of the partial specific volume of a protein, which may be used if the sequence of the protein is not known, is: average partial specific volume of proteins = 0.725 cm^3/g Because the average of experimentally determined partial specific volumes for soluble, globular proteins is approximately 0.73 cm3/g (average of experimental values from 13 soluble proteins). This value varies from protein to protein, but the range is rather narrow, between 0.70 and 0.75 cm3/g. = density of the solvent units: g/cm^3 The density of many buffers may be approximately equal to the density of water. density of water = 0.998 g/cm^3 (at 20 deg. C) our software (Ultrascan) has a feature for calculating the density of common buffers with common additives f = frictional coefficient f = a (6 π 0) where a = Stokes radius approximately, the length of the "long axis" of a molecule. Stokes radius can be determined by gel filtration. and 0 = viscosity of the solvent Analytical Ultracentrifugation (AU) is a spectroscopic technique. AU spins a rotor at a controlled speed and constant temperature and records the concentration distribution of the sample at known times. The concentration is determined for solutes obeying the Beer-Lambert law (A=*c*l) by measuring the absorbance of the sample at a given wavelength at fixed positions in the cell. AU Methods: Sedimentation Equilibrium Sedimentation Velocity Sedimentation Velocity Figure 1. Cells have a double-sector centerpiece. SAMPLE REFERENCE Figure 2. SV absorbance spectrum Sedimentation Velocity Movement of the boundary in SV experiments Sedimentation Equilibrium The cell contains 6 columns. One row of 3 columns are for sample, the other is the reference row. SAMPLE REFERENCE FIGURE 2. SE absorbance profile Fundamental Applications of Analytical Ultracentrifugation 1. Examination of Sample Purity Quantitation of size distributions in polydisperse samples. 2. Molecular Weight Determination Applicable to MW ranges from 100 to 1,000,000. 3. Analysis of Associating Systems Determines components of a complex and stoichiometry. 4. Sedimentation and Diffusion Coefficients Measures macromolecular complex sizes and interactions. 5. Ligand Binding Distinguish ligands from acceptors of differing absorbance. Selection of the data for analysis in an SE experiment - select the area where the concentration distribution is exponential with the square of the radial position. Data Analysis 1. First, fit one individual scan in the single ideal species model. 2. Next, fit the data from our SE experiment to a model for more than one species in equilibrium. 3. Goodness of fit - the residual plot.