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 (R m ) 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. Goal To determine which model provides the best fit for determining the known protein standards 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. 4 Step Procedure Comparison of Mathematical Models to Determine Molecular Weight of Proteins: A Statistical Analysis 1 Jennifer Wright, 2 Edward J. Carroll, Jr., and 1 Lawrence Clevenson Departments of 1 Mathematics and 2 Biology California State University Northridge NASA/PAIR Program Fig. 1 Electrophoresis Gel of Raw Data Relative Mobility vs. Molecular Weight Plot of Raw Data used in Determining the Models Fig. 2 – Graph of relative mobility of raw data vs. log molecular weights starting with two 7.5% gels, two 10%, two 12% and two gradient gels. Fig. 3 Raw Standards Actual Molecular Weights vs. Predicted Molecular Weights of Standards Residuals for Cubic Model log(MW) = a + b * R m + c * R m 2 + d * R m 3 Table 2: Residuals and R-squared values for the Cubic model. The red numbers are negative and black are positive. Comparison of 3 models with a Standard Fig. 4 One set of raw data (Gel #2 VE) is set against 3 of the models tested (Log Linear, Quad., Cubic). Fig. 5 Raw Data 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 Final Predicted Weights of Unknown Proteins Using Cubic Model Table 3: The Cubic model was applied to unknown proteins to predict their molecular weights. 1. Analysis of standards in the gels. 2. Test models on known protein standards. 3. Decide on best fitting model. 4. Apply model to unknown proteins. 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,  (û i - u) 2, to the total variation,  (u i - u) 2 where û i is the predicted value of u i 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 R-Squared Ave. 9,211 10,4729,37410,63510,267 8,0076,500 11,494 12,82012,78913,43813,618 12,27714,400 17,906 17,96321,19720,51820,514 20,93321,500 36,594 29,50628,09028,73628,822 31,64731,000 57,331 50,02844,67944,24844,271 45,51945,000 81,441 78,95572,87669,99570,111 67,68966,200 97, ,609101,04997,28096,991 94,77597, , ,416120,246117,919118, ,949116, , ,210183,306197,683197, ,028200,000 Predicted MW Molecular Weights SLICLog LinearQuad.Log-Log-LN^2CubicActual Table 1: Comparison of the 6 models and the R-squared values produced by each model. Margin of Error Fig. 5 Graph of Standards and upper/lower predicted confidence interval at 95%. Table 4: Actual and predicted molecular weights of standards with a 95% C.I.. Actual and Predicted Standards with Confidence Interval (C.I.) Table 5: The predicted molecular weights of unknown proteins involved in frog fertilization with a 95% C.I.. Unknown Predicted Weights with C.I.