Summer Internship Article Summary Week 5.docx

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Ryan Cao Mrs. Dickerson Summer Internship Article Summary Week 5 July 8, 2015 Summary of: Sedimentation velocity analysis of highly heterogeneous systems The van Holde-Weischet analysis (vHW) method provides an abstract yet brilliant way to estimate sedimentation coefficient ranges for a single or multi-species solution (depends on if you’re using Dr. Demeler’s enhanced vHW or not), and can be used to find a suitable range of sedimentation values to perform a 2DSA on. Here’s how the method works-given a standard set of concentration profiles for various radii (positions relative to the cell itself), baseline and plateau regions are determined (by the user; basically flat areas on either side of the main curve), and the region between them is partitioned into j “boundary fractions”. Since the graph is always plotted as concentration as a function of the radius (again, distance within the cell relative to the cell itself), these boundary fractions are spaced equally apart in terms of concentration (i.e. the difference in concentration between each r, c [radius, concentration] value is constant) even if the radii differences are not. Given these points, one can use a simplified version of the Lamm equation to find the relationship between analogous r, c pairs on different scans and find an apparent

sedimentation coefficient

based on the equation

below, where s*i, j is the

apparent sedimentation

coefficient, rj is the radius

at the particular boundary fraction point, ti is the time of that scan relative to t0, the time

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of the “initial” scan, and w is the angular velocity. Once the s*i, j values have been determined, they are plotted against (time)^-0.5, the inverse square root of time. The reason for this is, because the vHW analysis is based on a mathematical simplification (and rightly so, an assumption of zero diffusion), the apparent sedimentation coefficients must be fitted with a line across each analogous group, which is extrapolated to 0, or infinite time (because this is 1/sqrt(time)), to rid the coefficients of the influence of diffusion. (Note that diffusion is proportional to sqrt(time) while sedimentation is proportional to time itself and thus given infinite time, [think limits! Or big O notation!] the effects caused by diffusion, a lower order contributor, are negligible.) Once these points and lines are plotted, the graph is determined and conclusions may be drawn about the whereabouts (general range) of the sedimentation coefficient. There are some shortcomings to this method, however. Because it must extrapolate to infinite time, the method assumes as well an infinitely long cell, which of course is a physical impossibility. Thus, scans were a baseline cannot be clearly determined (i.e. the actual main curve has not cleared the meniscus yet) or where the plateau region is significantly affected by back diffusion or pileup at the bottom of the cell cannot be used. This is where the enhanced vHW plot comes in-to determine the plateau concentration for scans where one cannot be determined accurately based on the current readings, the plateau concentrations for scans where one is possible to be determined are done so through another equation, and by fitting these concentrations and extrapolating to the time of the scan with the unreadable plateau one can be estimated where none was previously available.

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Also, with scans where the concentration gradient (main curve) does not fully clear the meniscus, those boundary fractions that do not intersect the meniscus are used as regular scan points and those that do are discarded. Now to determine back diffusion (and thus scans that should be partially or even fully discarded), the estimated s*i, j values are used to determine diffusion coefficients for spheres of the same sedimentation coefficient, a conservative measure then used to find (generally) the largest amount of back-diffusion that could possibly happen. With the user determining the maximum amount of tolerable back diffusion, the program subtracts the current gradient from that and when the limit is passed, stops and discards all points that would’ve been used to find the s*i, j past there. Another issue is that the correct radial dilution (the cell is sector-shaped and thus material dilutes slightly when settling to the outer edge), and thus the correct s*i, j values, is not properly accounted for in a heterogenous system due to the fact that the effects of the varying sedimentation rates on the graph is at different radius points and thus different dilutions are being made. So, given an initial boundary fraction, an s*i, j value is calculated for many points within that boundary and the baseline cutoff, to where a good estimate of the general s*i, j values in that region (species) are. This new estimation is combined with the earlier result, as well as the time, to ensure that all r, c points in an area correspond to the same species and thus keep heterogenous mixtures’ components well out of each other’s way. Finally, histograms of the extrapolated sedimentation fits can be viewed through Ultrascan. The enhanced vHW method was compared to a regular vHW algorithm in

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this study using pieces of DNA of various lengths, and results soon proved the enhanced version to be much more adept at determining number of species and clearly extrapolating a number of distinct sedimentation coefficients pointing at each specimen.