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Parameters
As described in the general introduction, parameters come in three
types:
Global Parameters --> those that belong to the macromolecular system under
study, such as properties of the protein, binding constants, etc. They are
accessed using the menu function Global
Parameters. It will bring up different boxes according to the
particular selected model.
Note that they are parameters under standard conditions (i.e., s20,w,
D20,w, standard partial-specific volume),
and concentrations and binding constants are in molar units. The
transformations to experimental conditions is performed using the experimental
parameters (i.e., density, viscosity, partial-specific volume, extinction
coefficients, and optical path lengths).
Global parameters must be under standard conditions in order to permit global
analysis of data acquired under different conditions. For example, if you
have sedimentation data at different solvent densities, it is possible to fit
the partial-specific volume.
Global parameters can be floated in the analysis and optimized by non-linear
regression. This indicated by checking them in the global parameter box
(except for the partial-specific volume, which is done by menu function).
Global parameters can be saved in files (Data->Models).
Local Parameters --> those that describe properties of a particular
experiment, like loading concentration, baseline parameter, meniscus position,
but also the extinction coefficient at the particular wavelength used.
In SedPHaT, the local
parameters are subdivided in the concentration parameters, accessed in the Local
Parameters menu, and the Experiment
Parameters, which contain those related to the physical setup of the
experiment.
Some of the local parameters can be floated. The concentration
parameters can be checked in the parameter box of the model,
which causes them to be optimized in the non-linear regression. Also some
of the experimental parameters can be checked to be floated and optimized in the
non-linear regression. These are physical parameters that can carry
significant uncertainties: meniscus and bottom position of the solution
column, baseline parameters (see below), and
extinction coefficients.
Shared Local Parameters -->
parameters that are local to a data channel, but through prior knowledge can be
constrained to be the same in two or more data channels. Such shared local
parameters can be optimized in non-linear regression. Sharing
local parameters is an important concept, since it is a very safe way to
sometimes considerably simplify the non-linear regression.
Internally, this organized in the program by using for each type of parameter
an array, which redirects the access to the parameter of a particular experiment
to the parameter of another experiment. It is important, therefore, to be
aware of the Experiment Number
(the number in which it was loaded and is plotted).
If the redirection of a particular experiment points to the same experiment,
the parameter is a proper model parameter. If the redirection is to
another experiment, it will only be a copy the parameter value of the experiment
pointed to.
Four types of local parameters can be re-directed or shared:
1) Meniscus and bottom positions: If you have data acquired with
different optical systems or different wavelengths but from the same
ultracentrifugal cell, we know for sure that there is only one unique meniscus
and bottom position. Sharing is specificed in the Experimental
Parameter box.
2) Extinction coefficients: This is a property of the protein under
study, therefore cannot be different in different experiments. To share
this parameter allows to float it in non-linear regression (e.g. in
multi-wavelength analysis where one extinction coefficient is known and
concentration parameters are shared, see examples
below). Sharing is specificed in the Experimental
Parameter box.
3) Concentration parameters: are ordinarily useful to be shared always
when the same ultracentrifugal cell is scanned with different signals (i.e.
different wavelengths or optical systems). For analyses of heterogeneous
interactions with mass conservation constraints, the concentrations of the
components A or B (or their molar ratio) can also be shared. This can be
highly useful, if the concentrations in different cells are loaded as dilution
series, or by keeping the concentration of one component the same in all cells.
Note: Multi-speed equilibrium data
sets can have disadvantages when mass conservation is not used and concentration
parameters are to be shared. In this case, the concentration parameters are
shared between pairs of files (1st in exp. #1 with 1st in exp. #2, 2nd in exp.
#1 with 2nd in exp. #2, etc.). Therefore, two multi-speed equilibrium
experiments without mass conservation but with shared concentrations have to be
equivalent in the number and sequence of loaded scans. Because of these
complications, sharing in this situation is currently not enabled between
multi-speed equilibrium experiments.
4) Baseline parameters: have a special status. They can be shared only
for different sedimentation equilibrium profiles within the same 'multi-speed'
equilibrium data channel (i.e. same ultracentrifugal cell scanned at the
same wavelength (or all interference data), but acquired at different rotor
speeds.) Usually, this is the only condition under which it is safe to
assume the baselines can be the same. [Of course, the baseline can also be
shared among the data within a set of sedimentation velocity profiles.]
Sharing of the baseline parameters is indicated in the Experiment
Parameter box, not with re-direction arrays.
1) Let's say you want to characterize a self-associating protein. You
have three cells at different concentrations: cell 1 is medium
concentration, which can be scanned at 280 nm (the known extinction
coefficient), at 250 nm, and at 230 nm; cell 2 is at lower concentration,
scanned at 230 nm; cell 3 is at high concentration, scanned at 250 nm. You
acquire data at three rotor speeds.
You might load them into the following experiment data channels:
channel
1: cell 1 scanned at 280 nm, all rotor speeds are loaded as multi-speed sedimentation
equilibrium experiment
channel
2: cell 1 scanned at 230 nm, all rotor speeds are loaded as multi-speed sedimentation
equilibrium experiment
channel
3: cell 1 scanned at 250 nm, all rotor speeds are loaded as multi-speed sedimentation
equilibrium experiment
channel
4: cell 2 scanned at 230 nm (from lower loading concentration), all rotor speeds
are loaded as multi-speed sedimentation
equilibrium experiment
channel
5: cell 3 scanned at 250 nm (the highest concentration), all rotor speeds are loaded as
multi-speed sedimentation
equilibrium experiment
You could have the
following configuration of shared parameters:
--> share
concentration of 1, 2, and 3 (link concentration 2 to 1, and 3 to 1), since this
is the same cell.
--> share the
meniscus and bottom of 1, 2, and 3 (link meniscus and bottom of 2 to 1, and 3 to
1), since again this is the same cell.
--> keep the
extinction coefficient at 230 nm in channel 2 a floating parameter
--> keep the
extinction coefficient at 250 nm in channel 3 a floating parameter
--> share the
extinction coefficient of channel 4 and 2 (redirect 4 to 2)
--> share the
extinction coefficient of channel 5 and 3 (redirect 5 to 3)
--> share the
baselines of all equilibrium profiles at the same wavelength but multiple rotor
speeds: this will be done automatically since they are loaded as
multi-speed equilibrium
2) An example for hetero-associating proteins: you have loaded three cells by
diluting a stock solution of a mixture of A and B. The analysis is
performed with mass conservation constraints, floating the bottom position of
the solution columns. You can calculate the extinction coefficients for
each individual protein by running an extra cell with each component separately,
using the same multi-wavelength approach with shared concentrations as
illustrated above. For the cells of the mixture, you could share the molar
ratio B/A between the three cells of the serial dilution.
3) Another example for hetero-associating proteins: you have loaded three
cells with a mixture, but keeping the concentration of A constant and increasing
the concentration of B. You can use the same strategies as above, with
mass conservation and floating bottom position, but constrain in the
concentration of A to be the same for all cells, while floating the
concentration of B.
4) You have sedimentation equilibrium profiles of the same cell acquired with
the same wavelength, at different rotor speeds. The buffer contains some
component that changes absorbance with oxidation state, resulting in an
increasing baseline. Therefore, you cannot share the baseline
parameter. There are two options: the data could be loaded separately as
single sedimentation equilibrium profiles, sharing the concentration parameter,
and floating the baseline for each experiment. Also, of course meniscus
and bottom position, as well as extinction coefficient should be shared.
It is more efficient, however, to load the data into one multi-speed
sedimentation equilibrium experiment, and to use in the Experimental
Parameter box the Baseline option "fit
RI Noise". This will assign each profile at each speed its own
vertical offset. Also, in this way, if desired, the radial-dependent
baseline profile ("fit TI
Noise") can still be extracted from the set of equilibrium data.