(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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M is \ the sample molecular mass, ", Cell[BoxData[ \(TraditionalForm\`v\&_\)]], " and \[Rho] are the sample partial specific volume and solvent density, \ \[Omega] is the angular velocity, ", Cell[BoxData[ \(TraditionalForm\`r\)]], " is the distance from the center of rotation, ", Cell[BoxData[ \(TraditionalForm\`\(r\_m\ \)\)]], "is the radial position of the reference concentration, ", StyleBox["R", FontSlant->"Italic"], " is the Universal Gas Constant, and ", StyleBox["T", FontSlant->"Italic"], " is the absolute temperature. \nFor a simple self-associating system, \ monomer + monomer ", Cell[BoxData[ FormBox[ OverscriptBox["\[Equilibrium]", StyleBox[\(K\_12\), FontSize->14]], TraditionalForm]]], " dimer, the observed distribution will now be the sum of two exponentials, \ one for monomer and one for dimer.\n\n", Cell[BoxData[ \(TraditionalForm\`\(C\_r\ = \ C\_\(o, monomer\)\ \)\)], FontSize->24], Cell[BoxData[ \(TraditionalForm \`e\^\(\ \(( M\ \(\((1 - \ v\&_\ \[Rho])\)\ \[Omega]\^2\ \((r\^2 - r\_m\^2)\)\)\/\(2\ R\ T\))\)\)\)], FontSize->24], StyleBox[" + \n\n", FontSize->24], Cell[BoxData[ \(TraditionalForm\`\(\t\t\t\ \ \ C\_\(o, dimer\)\ \)\)], FontSize->24], Cell[BoxData[ \(TraditionalForm \`e\^\(\ \(( 2 M\ \(\((1 - \ v\&_\ \[Rho])\)\ \[Omega]\^2\ \((r\^2 - r\_m\^2)\)\)\/\(2\ R\ T\))\)\)\)], FontSize->24], StyleBox[" ", FontSize->24], "\nBy fitting the measured data to a series of aggregation models, it is \ therefore possible to determine the degree to which the protein \ self-associates. " }], "Text", FontSize->14], Cell[TextData[{ "Here we use ", StyleBox["Mathematica", FontSlant->"Italic"], " to demonstrate one possible way to fit a set of experimental data to this \ model. 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The next step is to determine the degree of \ self-association. \ \>", "Text", CellFrame->False, Background->RGBColor[0, 1, 1]], Cell["\<\ Now, try a model with components representing the monomer and dimer mass. Try \ this model next, as the average molecular weight determined previously, 39.4 \ kDa, lies between the monomer mass of 25.5 kDa and the dimer mass of 51 kDa. \ For the sake of simplicity, objects relating to the monomer-dimer model are \ identified by the suffix 12.\ \>", "Text", CellFrame->False], Cell["Fit to a monomer-dimer model.", "Commentary"], Cell[CellGroupData[{ Cell[BoxData[ \(mass = 25562; \n report12 = NonlinearRegress[P24, \n c01\ Exp[mass\ runparameters]\ + \ c02\ Exp[2\ mass\ runparameters], \n{x}, \ {{\ c01, 0.1}, \ {c02, \ 0.1}}, \ RegressionReport\ -> \ \ {BestFitParameters, \ ParameterCITable, \ EstimatedVariance, \ ANOVATable, \ AsymptoticCorrelationMatrix, \ FitResiduals, \ BestFit}\ ]; \nreport12[\([{1, \ 2, \ 3, \ 4, \ 5}]\)]\)], "InputOnly"], Cell[BoxData[ RowBox[{"{", RowBox[{ \(BestFitParameters \[Rule] {c01 \[Rule] 0.0529254204733194555`, c02 \[Rule] 0.0178503628734530295`}\), ",", RowBox[{"ParameterCITable", "\[Rule]", TagBox[GridBox[{ {"\<\"\"\>", "\<\"Estimate\"\>", "\<\"Asymptotic SE\"\>", "\<\"CI\"\>"}, {"c01", "0.0529254204733194555`", "0.00030534424657440673`", \({0.0523200458061652007`, 0.0535307951404736925`}\)}, {"c02", "0.0178503628734530295`", "0.0000694690059419972705`", \({0.0177126338124948574`, 0.0179880919344112015`}\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], ( TableForm[ #, TableDepth -> 2, TableHeadings -> {{c01, c02}, { "Estimate", "Asymptotic SE", "CI"}}]&)]}], ",", \(EstimatedVariance \[Rule] 9.7330478643543758523135737`15.0136*^-6 \), ",", RowBox[{"ANOVATable", "\[Rule]", InterpretationBox[GridBox[{ {"\<\"\"\>", "\<\"DF\"\>", "\<\"SumOfSq\"\>", "\<\"MeanSq\"\>"}, {"\<\"Model\"\>", "2", "19.2487968123836097`", "9.62439840619180486`"}, {"\<\"Error\"\>", "106", "0.00103170307362156384034523882`15.0136", "9.7330478643543758523135737`15.0136*^-6"}, {"\<\"Uncorrected Total\"\>", "108", "19.2498285154572315`", "\<\"\"\>"}, {"\<\"Corrected Total\"\>", "107", 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runparameters], \n{x}, \ {{\ c01, 0.1}, \ {c02, \ 0.1}, \ {c04, \ 0.1}}, \ RegressionReport\ -> \ \ {BestFitParameters, \ ParameterCITable, \ EstimatedVariance, \ ANOVATable, \ AsymptoticCorrelationMatrix, \ FitResiduals, \ BestFit}\ ]; \nreport3[\([{1, \ 2, \ 3, \ 4, \ 5}]\)]\)], "InputOnly"], Cell[BoxData[ RowBox[{"{", RowBox[{ \(BestFitParameters \[Rule] {c01 \[Rule] 0.0536052711171811058`, c02 \[Rule] 0.0175488858497967337`, c04 \[Rule] 6.15854304521218409`*^-6}\), ",", RowBox[{"ParameterCITable", "\[Rule]", TagBox[GridBox[{ {"\<\"\"\>", "\<\"Estimate\"\>", "\<\"Asymptotic SE\"\>", "\<\"CI\"\>"}, {"c01", "0.0536052711171811058`", "0.000596956183612861046`", \({0.0524216172785271261`, 0.0547889249558350943`}\)}, {"c02", "0.0175488858497967337`", "0.000238038842872452294`", \({0.0170768987963927347`, 0.0180208729032007326`}\)}, {"c04", "6.15854304521218409`*^-6", "4.65247665505499519`*^-6", \({\(-3.06645872740580394`*^-6\), 0.0000153835448178301703`} \)} }, RowSpacings->1, 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