(*********************************************************************** 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). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 40024, 1500]*) (*NotebookOutlinePosition[ 41077, 1534]*) (* CellTagsIndexPosition[ 41033, 1530]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox[ "The Binding of Asymmetric Ligands to an\nInfinite Anisotropic Linear \ Lattice", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontSize->14], StyleBox[" ", Editable->False, Evaluatable->False, AspectRatioFixed->True], StyleBox["by Alan R. Wolfe", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontSize->12, FontWeight->"Plain", FontSlant->"Italic"] }], "Title", Editable->False, Evaluatable->False, TextAlignment->Center, AspectRatioFixed->True, FontFamily->"New York", FontSize->14], Cell[TextData[{ StyleBox["This ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["Mathematica", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[ " notebook calculates and plots the Scatchard plot, neighbor-effect \ parameters, q, conditional probabilities, and length distribution of clusters \ of bound ligands for the anisotropic lattice, asymmetric ligand case with two \ binding modes (n1 need not equal n2). It also permits comparison of an \ experimental Scatchard plot with the calculated theoretical data. It can \ only be used after the appropriate initialization notebook has been \ evaluated. ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[ "To perform the calculations, simply set the input variables to the desired \ values and execute the \"Kernel-> Evaluation-> Evaluate Notebook\" command. \ This may be repeated with different values for the input variables. \n\n", FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[ "The notebook may also be executed in sections. To operate in this manner, \ the input parameters cell (as well as the experimental data cell, if desired) \ must be executed first. Then, the cell immediately below the first \ \"Calculate\[Ellipsis]\" heading must be executed. The Scatchard plot or any \ of the neighbor-effect parameters or conditional probabilities can then be \ displayed in any order. It's easiest to start by simply selecting the \ right-most cell grouping bracket and executing everything from the input \ parameters to the Scatchard plot. After executing the first calculation \ cell, any of the 3-D cluster length plots can be displayed by first executing \ the cell immediately below the second \"Calculate\[Ellipsis]\" heading, \ followed by the desired 3-D plot. After executing the first calculation \ cell, any of the 2-D cluster length plots can be displayed by first executing \ the cell immediately below the third \"Calculate\[Ellipsis]\" heading, \ followed by the desired 2-D plot. \n", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\n", FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["The initial value of ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["experimentalrLf", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" (= experimental r/[free ligand]) must be positive, and ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["experimentalData", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[ " must be True, in order to perform the experimental vs. theoretical \ comparison. If ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["experimentalData", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" is False, only theoretical data will be generated (over n = ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["points", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" equal intervals on the r axis). If ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["experimentalData", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" is True, and the initial value of ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["experimentalrLf", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[ " is negative, again only theoretical data will be generated, but this time \ using the list of experimental r values provided (", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["rExpArray", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox["). ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]] }], "Text", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontWeight->"Bold"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox[" ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], StyleBox["INPUT VARIABLES: ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontSize->10, FontColor->RGBColor[1, 0, 0], FontVariations->{"Shadow"->True}] }], "Subsection", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox[ "points = 10; k1 = 1; k2 = 2; n1 = 1; n2 = 1; w11 = 1; \nw22 = 2; w12 = \ 0.1; w21 = 4; experimentalData = True; \n", AspectRatioFixed->True, FontColor->RGBColor[1, 0, 0]], StyleBox["(* variables for cluster length plots: *) ", AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[ "\nrCluster2D = 0.9; maxLength2D = 6; \npoints3D = 10; maxLength3D = 5; ", AspectRatioFixed->True, FontColor->RGBColor[1, 0, 0]] }], "Input", AspectRatioFixed->True, FontFamily->"New York", FontColor->RGBColor[1, 0, 0]], Cell[TextData[StyleBox[ "rCluster2D*rSat is the r value for which 2D cluster length distribution data \ will be displayed. \npoints3D is the number of equally spaced r values \ greater than zero for which the cluster length distribution will be displayed \ in the 3D plots. \n(note - execution will be more efficient if points3D = \ points). \nmaxLength is the maximum cluster length that will be considered. \ ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Input", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Experimental Data", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontSize->10, FontColor->RGBColor[1, 0, 0], FontVariations->{"Shadow"->True}], StyleBox[" ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontSize->12, FontColor->RGBColor[1, 0, 0], FontVariations->{"Shadow"->True}], StyleBox["(* disregarded if experimentalData is False *)", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Subsection", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva"], Cell[TextData[{ StyleBox["(* experimental r values - x values of most plots *) ", Evaluatable->True, AspectRatioFixed->True, FontFamily->"Geneva", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox["\n", Evaluatable->True, AspectRatioFixed->True, FontFamily->"Chicago", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["rExpArray = {", Evaluatable->True, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox[ "0.04, 0.05, 0.06, 0.15, 0.25, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 0.96} ; \ ", Evaluatable->True, AspectRatioFixed->True, FontColor->RGBColor[1, 0, 0]] }], "Input", Editable->False, Evaluatable->True, AspectRatioFixed->True, FontFamily->"New York"], Cell[TextData[StyleBox[ "(* The number of points in the two arrays must be equal. Also, neither \ array should have values corresponding to an empty or saturated lattice. *)", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Input", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva"], Cell[TextData[{ StyleBox[ "(* experimental r/[free ligand] values - y values of Scatchard plot. \ These will be disregarded if the first value is negative *) ", AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\n", AspectRatioFixed->True, FontFamily->"Chicago", FontColor->RGBColor[1, 0, 0]], StyleBox[ "experimentalrLf = {1.35, 1.49, 1.36, 1.43, 1.28, 1.22, 1.27, 1.15, 1.0, \ 0.75, 0.39, 0.3, 0.25} ; ", AspectRatioFixed->True, FontColor->RGBColor[1, 0, 0]] }], "Input", Editable->False, AspectRatioFixed->True, FontFamily->"New York"] }, Closed]], Cell[TextData[{ StyleBox["(*", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[1, 0, 0], FontVariations->{"Shadow"->True}], StyleBox["Choose definitions *)", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", Editable->False, AspectRatioFixed->True, FontWeight->"Plain", FontColor->RGBColor[0, 0, 1]], StyleBox[ "If [ n1==n2, Def1, Def2 ] ; \nPrint [ \"initial slope = \", initialSlope \ //N, \" deltaA (dimensionless version) = \", deltaA //N ] ; ", Editable->False, CellOpen->False, AspectRatioFixed->True, FontWeight->"Plain"] }], "Input", Editable->False, CellOpen->False, AspectRatioFixed->True, FontFamily->"New York"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["(*", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[1, 0, 0], FontVariations->{"Shadow"->True}], StyleBox["Calculate the NE parameters, q, and Scatchard plot *) ", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["scroll = 1 ", Editable->False, AspectRatioFixed->True, FontSize->9, FontColor->RGBColor[0, 0, 1]] }], "Input", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva"], Cell[TextData[{ StyleBox["referencePlot = True ; ", Editable->False, CellOpen->False, AspectRatioFixed->True, FontColor->RGBColor[1, 0, 0]], StyleBox["\n\n", Editable->False, CellOpen->False, AspectRatioFixed->True], StyleBox["(* Choose definitions *)", Editable->False, CellOpen->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", Editable->False, CellOpen->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], StyleBox["\n", Editable->False, CellOpen->False, AspectRatioFixed->True], StyleBox["If [ n1==n2, Def1, Def2 ] ; \n", Editable->False, CellOpen->False, 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StyleBox[" ", Editable->False, CellOpen->False, AspectRatioFixed->True, FontWeight->"Plain", FontColor->GrayLevel[0.666667]], StyleBox[ "abscissa = xAxisInterval Join [ abscissa, abscissa2 ] ] ; \nIf [ \ experimentalData==True, \n abscissa = rExpArray ; \n points2 = Length \ [ abscissa ] +1 ; \n Do [ \n If [ abscissa[[i]] >= rSat, \ abscissa = Drop [ abscissa, {i,i} ] ], \n {i, points2-1, 1, -1} ] ; \ \n points2 = Length [ abscissa ] +1 ; \n experimentalrLf = Take [ \ experimentalrLf, points2-1 ] ] ; \nE1L = E1R = E2L = E2R = 1 ; \nQ = k1/(k1 + \ k2) ; \n\n", Editable->False, CellOpen->False, AspectRatioFixed->True, FontWeight->"Plain"], StyleBox["(* Evaluate neighbor-effect parameters and q for r < rSat *) \n", Editable->False, CellOpen->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[ "startPrint ; \ndropPoints = 0 ; \nordinate = Map [ Function [ zz, r = zz ; \ X = r/F ; \n If [ needCheck, \n If [ flag==True, \ {E1L,E1R,E2L,E2R,Q} = {1,1,1,1,0.5} ] ; \n If [ flag==False, ne ; \ checkLimits ] ; \n If [ flag==True, dropPoints = dropPoints + 1 ] , \ \n ne ] ; \n If [ flag==False, Print [ r//N, \" \", rLf//N ] \ ] ; \n {rLf,E1L,E1R,E2L,E2R,Q,X,ff} ], abscissa ] ; \nmakeReference ; \n\n\ ", Editable->False, CellOpen->False, AspectRatioFixed->True, FontWeight->"Plain"], StyleBox["(* Evaluate neighbor-effect parameters for r = rSat *) \n", Editable->False, CellOpen->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[ "PrependTo [ ordinate, {(k1 + k2)/2,1,1,1,1,k1/(k1 + k2),0,1} ] ; \n\ chooseNEandCP ; \nAppendTo [ ordinate, {0,E1L,E1R,E2L,E2R,Q,0,0} ] ; ", Editable->False, CellOpen->False, AspectRatioFixed->True, FontWeight->"Plain"] }], "Input", Editable->False, CellOpen->False, AspectRatioFixed->True, FontFamily->"New York"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["(* Indicate which equations were used *) ", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", 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Cell[CellGroupData[{ Cell[TextData[{ StyleBox["(*", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[1, 0, 0], FontVariations->{"Shadow"->True}], StyleBox["Calculate, print and plot 3D cluster length data *) ", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["scroll = 1 ", Editable->False, AspectRatioFixed->True, FontSize->9, FontColor->RGBColor[0, 0, 1]] }], "Input", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva"], Cell["\<\ clusterArray = Table [ 0, {maxLength3D} ] ; ligandArray = clusterArray ; clusterArray3D = Table [ clusterArray, {points3D+1} ] ; ligandArray3D = clusterArray3D ; maxLength = maxLength3D ; printHeadings ; Do [ rCluster = (ij/points3D) ; clusterDistribution ; clusterArray3D[[ij+1]] = clusterArray ; ligandArray3D[[ij+1]] = ligandArray , { ij, 0, points3D} ] ; 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clusterDistribution ] ; Print [ \" \" ] ; If [ (flag==False) || (rCluster2D rSat < rError) || (rCluster2D==1), Print [ \"r = \", rCluster2D rSat, \"; average cluster length = \", averageClusterLength ] ] ; If [ flag && (rCluster2D rSat >= rError) && (rCluster2D < 1), Print [ \"r = \", rCluster2D rSat ] ; Print [ \"The average cluster length could not be calculated due to a\" \ ] ; Print [ \"computational error.\" ] ] ; Print [ \"rCluster2D = \", rCluster2D, \"; maxLength2D = \", maxLength2D ] ; \ \>", "Input", Editable->False, CellOpen->False, AspectRatioFixed->True, FontFamily->"New York", FontWeight->"Plain"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["(*", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", Editable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[1, 0, 0], FontVariations->{"Shadow"->True}], StyleBox["Plot 2D cluster length data *) ", Editable->False, AspectRatioFixed->True, 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(The selection is \ executed by hitting the \"shift-return\" keys or the \"enter\" key.) ", FontColor->RGBColor[0, 0, 1]] }], "Input", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva"] }, Open ]] }, FrontEndVersion->"Macintosh 3.0", ScreenRectangle->{{0, 640}, {0, 460}}, WindowToolbars->{}, CellGrouping->Manual, WindowSize->{594, 431}, WindowMargins->{{12, Automatic}, {Automatic, -2}}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, -1}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, MacintoshSystemPageSetup->"\<\ 00<0001804P000000]P2:?oQon82n@960dL5:0?l0080001804P000000]P2:001 0000I00000400`<300000BL?00400@0000000000000006P801T1T00000000000 00000000000000000000000000000000\>" ] (*********************************************************************** Cached data follows. 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