Abstract

1
Comparison of Mathematical Models to Determine
Molecular Weight of Proteins A Statistical
Analysis 1Jennifer Wright, 2Edward J. Carroll,
Jr., and 1Lawrence Clevenson Departments of
1Mathematics and 2Biology California State
University Northridge NASA/PAIR Program

• 2. Test models on known protein standards.

• 4. Apply model to unknown proteins.

Abstract Accurate determination of
the molecular weight (MW) of a protein is an
important step toward its isolation, purification
and identification. Sodium Dodecyl Sulfate
Polyacrylamide Gel Electrophoresis (SDS-PAGE) in
one dimension with single percentage gels is
traditionally used for that process. Gradient
gels that incorporate a range of percentages have
been considered less accurate, in part due to a
lack of reliable mathematical models.  The
purpose of this project was to develop
statistical models to accurately predict protein
MW's on gradient gels. Six mathematical models
were applied to protein standards of previously
identified MW's to determine the best fitting
model. Relative mobility (Rm) of the protein
standards were calculated and compared to the
actual MW's to make this determination. The
"Cubic Model" was determined to be the best
fitting and will be used to identify unknown
proteins that may be involved in amphibian
fertilization.
Actual Molecular Weights vs. Predicted Molecular
Weights of Standards
Goal To determine which model provides the best
fit for determining the known protein standards

• Margin of Error

Table 1 Comparison of the 6 models and the
R-squared values produced by each model.
4 Step Procedure
1. Analysis of standards in the gels.
Fig. 5 Graph of Standards and upper/lower
predicted confidence interval at 95.
Conclusions We examined 6 mathematical models to
relate relative mobility to the molecular weights
of known protein standards. The cubic model was
determined best by examining the predicted
weights, residuals, and R-squared values for each
of the models. Then this model was used to
estimate the molecular weights of the unknown
proteins. Future The cubic model will be tested
on proteins involved in frog fertilization. Other
ways to reduce the error and improve the model
will be studied.
3. Decide on best fitting model.
Determinations 1.) The R-Squared is good
for most of the models, except for the SLIC model
for which R-squared is a little low. R-squared
is the ratio of predicted variation, ?(ûi - u)2,
to the total variation, ?(ui - u)2 where ûi is
the predicted value of ui for a particular model
and u is the mean. The Cubic model produces the
R-squared average with the closest fit of the 6
different models. Ideally, R-squared is equal to
1, meaning that the predicted values and the
actual values are equal. 2.) The
predictions of the MW are good for most of the
models but the Cubic shows a smaller amount of
variation. 3.) The residuals of the models
show the differences between the actual data
points and the predicted points. Examining the
residuals (see example above) the Cubic model
produces smaller residual values than the other 5
models.
Thanks to Carol Shubin, Virginia Latham, Larry
Clevenson, Edward Carroll, Gregory Frye, John
Handy, Jennifer Rosales, Alicia Maravilla and
Celia Smith. This work was supported by NASA
CSUN/JPL PAIR. Grant NASA-NCC5-489