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Parameters (keyboard shortcut ctrl-P)

This menu item invokes a parameter input dialog box, which will be slightly different dependent on the model used. Each of the parameter boxes are shown in the website of the particular model.

The following information is based on the non-interacting discrete species model, but several elements will be identical for all models.

upper section specifying model-specific parameters,

here c, s and M values of up to 4 components

middle section with experimental conditions

lower section with Lamm equation and

nonlinear regression parameters

The upper sections
specifies the parameter specific for the model (see the non-interacting
discrete species model for more details on the particular parameter box
shown). **A convention used in all parameter boxes is that a check-mark
next to a parameter field will cause this parameter to be optimized when using
the Fit command (for non-linear parameters) or
the Run command (for linear parameters).**

The middle section contains controls that depend on the experiment, which are common to many models:

1) a checkbox ‘**FIT TI Noise**’. If
checked, the boundary analysis is combined with an unknown radial-dependent
background profile that remains constant in time (**T**ime **I**nvariant).
This is calculated algebraically and explicit background profiles are used for
direct boundary modeling (see systematic
noise analysis, and ref 1).
Mostly, this function will be used when analyzing interference optical data,
although application to absorbance data can occasionally be useful, too (ref
1).
It is switched on for interference data by default. After the
time-invariant background is calculated, it can be subtracted
from the data for better inspection of the fit. Because this TI noise
consists of linear parameters, it will be calculated in both the run
and the fit command.

2) a check box ‘**FIT RI Noise**’. If
checked, this adds to the model the possibility of a baseline offset that is constant in radial direction, but different for each scan.
Like the TI noise, this is calculated algebraically (see systematic
noise analysis and ref 3),
each time when the run and the fit
command are used. It is switched on for interference data by default,
because of the small up-and-down displacement (jitter) always involved in
sequences of interference scans. Also, the integral fringe displacement
sometimes encountered in interference data can count as RI noise. **Please
note: **No correction for jitter or fringe displacement should be
performed before the analysis. The best-fit displacements will be result
of the analysis, and can be subtracted
from the data after the boundary modeling.

3) the field **Baseline** allows to enter and
optimize a constant baseline
that is common to all scans and that is constant in radial direction. If this is
checked, it will be optimized with each simulation. It is recommended to keep
the baseline parameter floated for absorbance data (except when working with
very small molecules and small sedimentation rates, when some correlation with
the molar mass can be possible if simultaneously floating the bottom
parameter).

4) the **Meniscus** position of the solution
column will generally show the radius value that has been graphically determined
when loading the files. However, the value can also be entered or changed here. The value of the meniscus
position is very important for measuring the sedimentation velocity. When
the field is marked, the meniscus is treated as a nonlinear fitting parameter,
to be optimized in the fit command. In this case, constraints for a
the lowest and highest possible values are necessary (as judged from graphical
inspection of the data), and a prompt will
automatically ask for these values when closing the parameter box. They should be carefully entered, since the
default interval could be off. The range constraints can also be set through
the fitting
options.

5) the **Bottom **position of the cell is shown here,
as graphically entered. Analogous to the meniscus field, it can be entered
or modified here. Also, the bottom value can be treated as a fitting
parameter (when checked) to be optimized in the fit
command. Also,
constraints for a the lowest and highest possible values are necessary when
floated, and a
prompt will automatically ask for these values (which can be modified through
the fitting
options). Fitting for the bottom position is very important when
back-diffusion of the species from the bottom is modeled, because the exact
bottom position is very difficult to locate graphically. Analysis with
floating bottom will mostly be required for small molecules with high diffusion
constants, at low rotor speeds, or in approach-to-equilibrium analyses. It
should be noted, though, that in approach-to-equilibrium analyses at low rotor
speed the simultaneous floating of the three parameters bottom, baseline, and
molar mass can lead to slight correlation (although generally any two will be
well-determined).

6) the radio buttons **Experimental Initial Distribution **and
**Constant Initial Distribution**. The constant initial distribution is
the default, because it corresponds to the conventional loading of the
cell. However, the numerical Lamm equation
solutions allow for any concentration distribution to be taken as a starting
point for the simulation of the evolution. Sometimes, it can be very
useful to load an experimental scan as initial distribution, for example when
using boundary forming loading techniques, or when convection occurred in the
initial parts of the experiment. A detailed description of this approach
is given here. It should be
noted that with the non-interacting species model, only a single component can
be used. (An alternative remedy for initial convection is the use of the differential
second moment method.). Please note that when switching to the
experimental initial distribution, a warning message may appear, because the corrections for rotor
acceleration phase are switched off. This is OK, but it should be
remembered that they should be switched on after the analysis session.

The lower section determines the values of parameters that control the
solution of the Lamm equation and fitting. __Please
note: The following control parameters do not have to be changed for the
majority of all problems.__

In the lower left corner is a series of parameter fields:

1) **Tolerance** governs the Simplex non-linear
regression routine: It determines the (maximum) percent change in the parameter
values below which a single Simplex is stopped (see Fit
command). The Simplex is then repeatedly restarted, until all final parameter values are
within this tolerance in two sequential simplex runs. Default value is 1.

2) **Grid Size** determines the number of radial increments (dividing the
solution column from meniscus to bottom) on which the numerical solution
of the Lamm equation is based. Usually, ~ 100 per mm solution column is a reasonable value. Higher
accuracy of the Lamm equation solution can be achieved with higher values, but
generally the experimental noise is much larger than the error at a discretization of
100/mm. Coarser grids are faster for simulation, but less precise. For
complicated situations with time-consuming Lamm simulations, it can be a good
strategy to use a coarse grid to get the floating parameter values in a good
range, and to use a very high number of grid points only in the end as a final
refinement step. This idea is automated if the fitting option of speeding
up first Simplex is used; in this case half of the grid size specified here is used for the first round of
Simplex optimization only.

3) **max dc/c (or
dt)** has two different functions, dependent on which
Lamm simulation algorithm is chosen. In a stationary frame of reference (Claverie
simulations), an adaptive time-step driver is used. In this case, the max
dc/c parameter refers to the maximum change in any of the concentration values
that is desired, and according to which the size of the time-step is
adjusted. A larger value of max dc/c effectively increases the time-steps,
while a smaller value decreases the time-steps. The detailed algorithm used is
slightly more complex, and also depends on the steepness of the simulated
boundary.

! If the desired relative change max dc/c leads to too large time-steps, it is automatically reduced.

For the moving frame of reference simulation, this field has no direct function. However, if a fixed dt is chosen, the time-steps in both the Claverie and moving hat algorithm are constrained to the value given in this field (in seconds).

In the middle of the lower section are the controls the choice of the Lamm solution algorithm. Details on these algorithms can be found here.

1) **Claverie simulation** toggles on the use of the finite element method
with stationary equidistant grid as described by Claverie. This works best for
small s or low rotor speed (i.e. in cases where diffusion influences are high
relative to sedimentation).

2) **move hat** toggles on the use of a finite element algorithm with a
moving frame of reference. This method is preferred for cases of high influence
of sedimentation versus diffusion, i.e. for high rotor speed and larger
molecules. The input field next to the radio button allows to change the
sedimentation coefficient of the frame of reference. However, this input will be
effective only if the next check box

3) **auto s hat** is not marked. The default configuration is auto s hat __on__,
which adjusts automatically the movement of the frame of reference to the
sedimentation coefficient of the simulated solute. This will reduce the
simulation on the moving frame of reference to diffusion and radial
dilution. This algorithm also works
automatically with a fixed time-step, which is determined by the movement of the
frame of reference. This size of the time-step, however, can be constrained to
smaller values (not to larger ones).

4) **fixed dt** is a checkbox that can be used to constrain the time-step
size. The effective value (in sec) will be the one entered in the field ‘max
dc/c (or dt)’ (see above).

5) **auto method** is by default __on__. This automatically switches
during an optimization from the Claverie method at low s to the moving hat
method at higher s. The transition point is by default 5 S at 30,000 rpm, with
automatic adjustment at higher and lower centrifugal field, but it can be
changed using the fitting
options.

**references**

(1)
P. Schuck and B. Demeler (1999) Direct sedimentation analysis of
interference-optical data in analytical ultracentrifugation. * Biophysical
Journal*
76:2288-2296.