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Data | Set Initial Data

Background:  The Lamm equation does not specify concentration distribution at time zero.  In fact, it only predicts the evolution in time given an initial distribution.  Usually this is taken to be a uniform distribution.  However, it is perfectly valid to take any other distribution at any time as the starting point for modeling the evolution.  In particular, this can be an experimentally measured distribution from an actual scan (referred to here as initial data).  This has the advantage that imperfections in the sedimentation before the initial scan was taken become irrelevant. These can be, for example, artifacts from imperfect synthetic boundary experiments, from acceleration of the rotor, or from an initial temperature-driven convection.  (Please note that the effects of convection cannot be remedied by restriction of the analysis to the later scans...) This approach is described in Ref 1.  The only other rigorous method for transient convection or other imperfections is the differential second moment method.

!    Drawbacks of this approach: 1) Mathematically, we need an initial condition for each component present, therefore this approach is limited to single component (i.e. single species and self-association) models. 2) The inclusion of any noise and baseline parameters as unknowns in the initial scan would be a highly non-linear problem.  Therefore, experimental initial data are not compatible with TI and RI noise calculations, and the baseline should be set to the correct value before loading the initial scan.  This restricts this feature essentially to absorbance data, or experimentally blank-corrected interference data.

In practice, the random noise in the initial data is not translated into the later model functions, because of the diffusion term in the Lamm equation (Ref 1). However, the usable information from a scan is not complete, because the optical artifacts near the meniscus and bottom cannot be included in the calculated evolution.  This makes necessary the extrapolation from the analysis limits (green lines) to the meniscus and bottom, respectively (Ref 1).

Using this approach in Sedfit:

By default when loading files, constant initial distribution at time t = 0 is assumed, and this setting has to be switched to experimental initial condition in the parameter dialog box before loading the initial data (see Experimental Initial Distribution option in the parameter box; check this option and press Enter. A warning message may appear indicating that the correction for rotor acceleration phase will be switched off - this is OK here, but should be changed back after the analysis session). Then, chose Data | Set Initial Data and select the experimental scan that should initialize the calculated evolution (e.g., the first of the series of sedimentation velocity scans). The initial data will be shown by a green line.

The experimental data between meniscus and left analysis limit, and between the right analysis limit and the bottom, which may contain optical artifacts, will be replaced by a polynomial extrapolation. The parameters of this polynomial can be changed in the following function (see below). The results of the extrapolations should be inspected and the parameters optimized.

Extrapolation of Initial Data

An experimental scan can be used as an initial condition for the simulated sedimentation (e.g. if using synthetic boundary techniques) (see load initial data). However, the experimental scan will not yield reliable data in the regions of the optical artifacts near the meniscus and bottom of the cell. In order to prevent these optical artifacts from ‘sedimenting’ into the analysis range, an extrapolation procedure is used replacing the original data in the unreliable region, and estimating absorbance values in the region between the meniscus and the left fitting limit, and between the right fitting limit and the bottom of the cell.

The extrapolation procedure used is a polynomial extrapolation, based on a data interval within the reliable region next to the fitting limit. The user has two parameters for possible adjustment in case the default extrapolation does not generate satisfying results:

1) the polynomial order, where the default value of 1, and

2) the extrapolation distance factor, with a default value of 1.

The distance factor determines the size of the data basis that is used for the extrapolation, in multiples of the distance meniscus - left fit limit (or right fit limit - bottom, respectively). A value of 1 means that the data basis for extrapolation has the same size as the region excluded from the fit.

The polynomial order determines the highest power of the polynomial used for the extrapolation. For example, the value of 1 will calculate the best-fit straight line through the data used as basis for extrapolation, and then just extrapolates linearly into the regions of artifacts. A value of 2 would take a parabolic fit through the data basis and extrapolate with that, etc.

Reference:

1) P. Schuck, C.E. McPhee, and G.J. Howlett. (1998) Determination of sedimentation coefficients for small peptides. Biophysical Journal 74:466-474