(*********************************************************************** 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[ 46219, 1424]*) (*NotebookOutlinePosition[ 47299, 1459]*) (* CellTagsIndexPosition[ 47255, 1455]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Binding of Symmetric Ligands \nto an Infinite Linear Lattice", Editable->False, Evaluatable->False, FontFamily->"New York", FontSize->24], StyleBox["\n", Editable->False, Evaluatable->False, FontFamily->"New York"], StyleBox[ "by Alan R. Wolfe\nDepartment of Biopharmaceutical Sciences\nUniversity of \ California\nSan Francisco, CA 94143-0446", Editable->False, Evaluatable->False, FontSize->12, FontWeight->"Plain", FontSlant->"Italic"] }], "Title", Editable->False, Evaluatable->False, TextAlignment->Center, FontFamily->"New York"], Cell[TextData[{ StyleBox[ "This is the initialization notebook for the symmetic ligand case. It \ needs to be evaluated only once at the beginning of a ", 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[" session. After opening this notebook, execute the ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\"Kernel-> Evaluation-> Evaluate Initialization\"", FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" command. Then close this notebook (without quitting ", 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[") and open the corresponding output notebook. You should quit ", 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[ " and start a new session when switching to a different case. ", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]] }], "Text", Editable->False, Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontWeight->"Bold"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Turn off General::spell1 warning", Editable->False, Evaluatable->False, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Subsection", Editable->False, Evaluatable->False, FontFamily->"Geneva"], Cell[TextData[StyleBox["Off [ General::spell1 ] ; ", FontWeight->"Plain"]], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Choose whether output is to be saved", Editable->False, Evaluatable->False, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Subsection", Editable->False, Evaluatable->False, FontFamily->"Geneva"], Cell[TextData[StyleBox["saveOutput = False ; ", FontWeight->"Plain"]], "Input", Editable->False, InitializationCell->True, FontFamily->"New York", FontWeight->"Plain"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Definitions", Editable->False, Evaluatable->False, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", Editable->False, Evaluatable->False, FontColor->RGBColor[1, 0, 1]] }], "Subsection", Editable->False, Evaluatable->False, FontFamily->"Geneva"], Cell[TextData[{ StyleBox["points::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "points is the number of values to be calculated for each of the parameters \ displayed in the output. Since the values at r = 0 are not calculated, it \ equals the number of intervals on the x-axis of the plots.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["k::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["k is the binding constant for ligand-lattice interactions.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["n::usage = ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\"", Editable->False, InitializationCell->True], StyleBox["n is the number of lattice residues occupied per bound ligand.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["w::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "w is the cooperativity parameter for interactions between symmetric \ ligands bound to a lattice.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["r::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "r is the ratio of bound ligands to lattice residues (plotted on the \ abscissa of a Scatchard plot).", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["x::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "x is r/f, where f = 1 - n r is the fraction of lattice residues that are \ free.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["rLf::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "rLf is r divided by the free ligand concentration (plotted on the ordinate \ of a Scatchard plot).", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["e::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["e is the neighbor-effect parameter for free binding sites.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["rSat::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "rSat is the limiting value of r, i.e., the ratio of ligands to lattice \ residues when the lattice is saturated.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[BoxData[ \(\(rLf := k\ \((1 - n\ r)\)\ \((1 + x\/e)\)\^\(1 - n\)\ e\^2; \)\)], "Input", Editable->False, InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox[ "Expressions for the neighbor-effect parameter when r is below its maximum \ value ", Editable->False, Evaluatable->False, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Subsection", Editable->False, Evaluatable->False, FontFamily->"Geneva"], Cell[TextData[{ StyleBox["ne::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "ne gives the value of the neighbor-effect parameter when r is below its \ maximum value.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[BoxData[ \(\(ne := If[w == 1, e = 1, e := 1\/2\ \((1 - x + \((\((1 - x)\)\^2 + 4\ x\ w)\)\^0.5)\)]; \)\)], "Input", Editable->False, InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Calculation of the initial slope ", Editable->False, Evaluatable->False, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Subsection", Editable->False, Evaluatable->False, FontFamily->"Geneva"], Cell[BoxData[ \(\(initialSlope := k\ \((2\ w - 2\ n - 1)\); \)\)], "Input", Editable->False, InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Determination of the maximum value of r", Editable->False, Evaluatable->False, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Subsection", Editable->False, Evaluatable->False, FontFamily->"Geneva"], Cell[TextData[{ StyleBox["rSatDetermine::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "A routine to determine the ratio of bound ligands to lattice residues and \ the values of the conditional probabilities at at saturation.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[BoxData[ \(\(rSatDetermine := { If[w == 0, rSat = 1\/\(n + 1\); CP2, rSat = 1\/n; CP1]}; \)\)], "Input", Editable->False, InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox[ "Expressions for conditional probabilities when r is below its maximum value \ ", Editable->False, Evaluatable->False, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Subsection", Editable->False, Evaluatable->False, FontFamily->"Geneva"], Cell[TextData[{ StyleBox["ff::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "ff is the probability that a randomly chosen free lattice residue is \ bordered on a given side by another free residue.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["bf::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "bf is the probability that a randomly chosen bound ligand end is bordered \ by a free lattice residue.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["fb::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "fb is the probability that a randomly chosen free lattice residue is \ bordered on a given side by a bound ligand end.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["bb::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "bb is the probability that a randomly chosen bound ligand end is bordered \ by another bound ligand end.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[TextData[{ StyleBox[ "ff := 1 / (1 + x/e ) ; \nbf [h_] := h[[4]]/h[[2]] /; h[[1]] > 0 ;", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontWeight->"Plain"], StyleBox["(* = ff/e *)", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1]], StyleBox["\n", Editable->False, InitializationCell->True, FontWeight->"Plain", FontColor->RGBColor[0, 0, 1]], StyleBox[ "bf [h_] := bfSat /; h[[1]]==0 ; \nfb [h_] := h[[3]] h[[4]]/h[[2]] /; \ h[[1]] > 0 ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["(* = x ff/e *)", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1]], StyleBox["\n", Editable->False, InitializationCell->True, FontWeight->"Plain", FontColor->RGBColor[0, 0, 1]], StyleBox[ "fb [h_] := 1 /; h[[1]]==0 ; \nbb [h_] := h[[3]] w h[[4]]/h[[2]]^2 /; \ h[[1]] > 0 ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["(* = x w ff/e^2 *)", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontWeight->"Plain", FontColor->RGBColor[0, 0, 1]], StyleBox["\n", Editable->False, InitializationCell->True, FontWeight->"Plain", FontColor->RGBColor[0, 0, 1]], StyleBox["bb [h_] := bbSAT /; h[[1]]==0 ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox[ "Values of conditional probabilities when r is at its limit ", Editable->False, Evaluatable->False, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Subsection", Editable->False, Evaluatable->False, FontFamily->"Geneva"], Cell[TextData[{ StyleBox["bfSat::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["bfSat is the value of bf when the lattice is saturated.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["bbSAT::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["bbSAT is the value of bb when the lattice is saturated.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["CP1::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["CP1 gives conditional probability values when r = rSat = 1/n.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["CP1 := { bfSat = 0 ; bbSAT = 1 } ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["CP2::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "CP2 gives conditional probability values when r = rSat = 1/(n+1), i.e., \ when w = zero and the lattice is saturated.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True, FontColor->RGBColor[0, 0, 1]], StyleBox["CP2 := { bfSat = 1 ; bbSAT = 0 } ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Calculation of average cluster length ", Editable->False, Evaluatable->False, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Subsection", Editable->False, Evaluatable->False, FontFamily->"Geneva"], Cell[TextData[{ StyleBox["averageClusterLength::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "averageClusterLength is the average length (in ligands) of a cluster of \ bound ligands.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox[ "averageClusterLength := \"infinite\" /; bfCluster == 0 ; \n\ averageClusterLength := 1/bfCluster /; bfCluster > 0 ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Define plotting routines ", Editable->False, Evaluatable->False, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Subsection", Editable->False, Evaluatable->False, FontFamily->"Geneva"], Cell[TextData[{ StyleBox["makePlot::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["makePlot is a neighbor-effect parameter plotting routine.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox[ "makePlot [ j_, yOrigin_, yLabel_, graphLabel_ ] := { \n If [ \ saveOutput==False, \n Unprotect [ Out ] ; Clear [ Out ] ; Protect [ \ Out ] ] ; \n plotTable = Table [ {abscissa[[i]], ordinate[[i,j]]}, \ {i,points2+1} ] ; \n curvePlot = ListPlot [ plotTable, PlotJoined->True, \ \n AxesLabel->{\" r\",yLabel}, PlotLabel->graphLabel, \n \ DisplayFunction->Identity, \n PlotRange->All ] ;\n pointPlot = \ ListPlot [ plotTable, PlotStyle->PointSize[0.015], \n \ DisplayFunction->Identity, \n PlotRange->All ] ;\n Show [ \ curvePlot, pointPlot, DisplayFunction->$DisplayFunction, \n \ AxesOrigin->{0,yOrigin} ] ; \n N [ plotTable ] } ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["makePlot2::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "makePlot2 plots the theoretical r/Lf versus r curve (in black) along with \ corresponding experimental data points (in gray).", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox[ "makePlot2 := { \n If [ saveOutput==False, \n Unprotect [ Out \ ] ; Clear [ Out ] ; Protect [ Out ] ] ; \n plotTable = Table [ \ {abscissa[[i]], ordinate[[i,1]]}, {i,points2+1} ] ; \n curvePlot = \ ListPlot [ plotTable, PlotJoined->True, \n \ DisplayFunction->Identity, \n PlotRange->All ] ; \n pointPlot = \ ListPlot [ plotTable, PlotStyle->PointSize[0.015], \n \ DisplayFunction->Identity, \n PlotRange->All ] ; \n plotTable2 = \ \n Table [ {rExpArray[[i]], experimentalrLf[[i]]}, {i,points2-1} \ ]//N; \n curvePlot2 = ListPlot [ plotTable2, PlotJoined->True, \n \ DisplayFunction->Identity, \n AxesLabel->{\"r\", \"r/Lf\"}, \n \ PlotLabel->\" Scatchard Plot\", \n PlotStyle->{GrayLevel \ [0.75]}, \n PlotRange->All ] ; \n pointPlot2 = ListPlot [ \ plotTable2, \n PlotStyle->{PointSize[0.015], GrayLevel [0.75] }, \n \ DisplayFunction->Identity, \n PlotRange->All ] ; \n Show \ [ curvePlot2, pointPlot2, curvePlot, pointPlot, \n \ DisplayFunction->$DisplayFunction, \n AxesOrigin->{0,0} ] ; \n N \ [ plotTable ] } ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["makeResidualsPlot::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "makeResidualsPlot is a plotting routine for the residuals in the plot of \ the experimental versus theoretical Scatchard plots. r is plotted on the \ abscissa.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox[ "makeResidualsPlot [ dataList_, curveList_ ] := { \n residualArray = \ dataList-curveList ; \n If [ saveOutput==False, \n Unprotect [ \ Out ] ; Clear [ Out ] ; Protect [ Out ] ] ; \n xAxisList = Table [ \ abscissa[[j]], { j, 2, points2} ] ; \n plotTable = Table [ \ {xAxisList[[j]], residualArray[[j]]}, \n {j, points2-1} ] ; \n \ curvePlot := ListPlot [ plotTable, PlotJoined->True, \n AxesLabel->{\ \"r\", \"residuals\"}, \n PlotLabel->\"exp.-theoretical\", \n \ DisplayFunction->Identity, \n PlotRange->{{0, rSat}, All} ] ; \n \ pointPlot := ListPlot [ plotTable, PlotStyle->PointSize[0.015], \n \ DisplayFunction->Identity, \n PlotRange->{{0, rSat}, All} ] ; \n \ Show [ curvePlot, pointPlot, \n DisplayFunction->$DisplayFunction] ; \ \n N [ plotTable ] } ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["makeResidualsPlot2::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "makeResidualsPlot2 is a plotting routine for the residuals in the plot of \ experimental versus theoretical Scatchard plots. Point number is plotted on \ the abscissa.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox[ "makeResidualsPlot2 [ dataList_, curveList_ ] := { \n residualArray = \ dataList-curveList ; \n If [ saveOutput==False, \n Unprotect [ \ Out ] ; Clear [ Out ] ; Protect [ Out ] ] ; \n plotTable = Table [ {j, \ residualArray[[j]]}, { j, points2-1} ] ; \n curvePlot := ListPlot [ \ plotTable, PlotJoined->True, \n AxesLabel->{\"pt. #\", \ \"residuals\"}, \n PlotLabel->\"exp.-theoretical\", \n \ DisplayFunction->Identity, \n PlotRange->{{0, points2-1}, All} ] ; \n\ pointPlot := ListPlot [ plotTable, PlotStyle->PointSize[0.015], \n \ DisplayFunction->Identity, \n PlotRange->{{0, points2-1}, All} ] \ ; \n Show [ curvePlot, pointPlot, \n \ DisplayFunction->$DisplayFunction] ; \n N [ plotTable ] } ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["makeCPplot::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["makeCPplot is a plotting routine for conditional probabilities.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox[ "makeCPplot [ cpFunction_, label_ ] := { \n cpTable = Map [ cpFunction \ , ordinate ] ; \n If [ saveOutput==False, \n Unprotect [ Out ] ; \ Clear [ Out ] ; Protect [ Out ] ] ; \n plotTable = Table [ \ {abscissa[[j]], cpTable[[j]]}, { j, points2+1} ] ; \n curvePlot := \ ListPlot [ plotTable, PlotJoined->True, \n AxesLabel->{\" r\", \ label}, \n DisplayFunction->Identity, PlotRange->{-0.025,1.025} ] ; \ \n pointPlot := ListPlot [ plotTable, PlotStyle->PointSize[0.015], \n \ DisplayFunction->Identity, PlotRange->{-0.025,1.025} ] ; \n Show [ \ curvePlot, pointPlot, DisplayFunction->$DisplayFunction] ; \n N [ \ plotTable ] } ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["rCluster::usage = \"", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontWeight->"Plain"], StyleBox[ "rCluster is a number between zero and one, the fractional saturation of \ the lattice for which the calculations will be performed.", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True, AspectRatioFixed->True], StyleBox["maxLength::usage = \"", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontWeight->"Plain"], StyleBox["maxLength is the maximum cluster length to be considered.", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["twoDplot::usage = \"", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontWeight->"Plain"], StyleBox[ "twoDplot is a routine for plotting the fractions of clusters of different \ lengths, or the fractions of bound ligands in clusters of different lengths, \ at a given value of r.", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True, AspectRatioFixed->True], StyleBox[ "twoDplot [ yLabel_, maxY_, twoDarray_ ] := { \n If [ \ saveOutput==False, \n Unprotect [ Out ] ; Clear [ Out ] ; Protect [ \ Out ] ] ; \n twoDTable = Table [ {j, twoDarray[[j]]}, {j, maxLength} ] ; \ \n curvePlot = ListPlot [ twoDTable, PlotJoined->True, \n \ DisplayFunction->Identity, \n AxesLabel->{\" length\", yLabel}, \n \ PlotRange->{\n {1-0.025 (maxLength-1), maxLength+0.025 \ (maxLength-1)},\n {-0.025 maxY, 1.025 maxY}} ] ; \n \ pointPlot = ListPlot [ twoDTable, PlotStyle->PointSize[0.015], \n \ DisplayFunction->Identity, \n PlotRange->{\n {1-0.025 \ (maxLength-1), maxLength+0.025 (maxLength-1)},\n {-0.025 maxY, \ 1.025 maxY}} ] ; \n Show [ curvePlot, pointPlot, \ DisplayFunction->$DisplayFunction ] } ; ", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["printHeadings::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "printHeadings prints the column headings for the cluster length \ distribution data.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["printHeadings := { \n Print[ \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["r/ Cluster Fraction (f) Running Fraction (f) Running", Editable->False, InitializationCell->True, FontFamily->"Courier", FontWeight->"Plain"], StyleBox["\"] ; \n Print[ \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["rSat Length Clusters Sum Ligands Sum", Editable->False, InitializationCell->True, FontFamily->"Courier", FontWeight->"Plain"], StyleBox["\"] ; \n Print[ \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Courier", FontWeight->"Plain"], StyleBox["\"] } ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["clusterDistribution::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "clusterDistribution is a routine for calculating the fractions of clusters \ of different lengths, and the fractions of bound ligands in clusters of \ different lengths, at a given value of r.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox["clusterDistribution := { \n", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Geneva"], StyleBox[ "(* Calculate the conditional probabilities for r = rCluster rSat *) \n", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[ " r = rCluster rSat ; \n If [ r < rSat, x = r/(1 - n r) ; \n \ {bfCluster, bbCLUSTER} = {ff/e, x w ff/e^2}, \n {bfCluster, \ bbCLUSTER} = {bfSat,bbSAT} ] ; \n", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Geneva"], StyleBox["(* Calculate the cluster length distribution *) ", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\n", Editable->False, InitializationCell->True, FontFamily->"Geneva"], StyleBox[ " totalClusters = 0 ; maxClusters = 0 ; \n totalLigands = 0 ; \ maxLigands = 0 ; \n clusterLength =. ; \n Map [ Function [ \ clusterLength, \n If [ bbCLUSTER==0 && clusterLength==1, \ fracClusters = 1, \n fracClusters = \ bbCLUSTER^(clusterLength-1) bfCluster ] ; \n \ clusterArray[[clusterLength]] = fracClusters ; \n If [ fracClusters \ >maxClusters, maxClusters = fracClusters ] ; \n totalClusters = \ totalClusters + fracClusters ; \n fracLigands = clusterLength \ fracClusters bfCluster ; \n ligandArray[[clusterLength]] = \ fracLigands ; \n If [ fracLigands >maxLigands, maxLigands = \ fracLigands ] ; \n totalLigands = totalLigands + fracLigands ; \n \ Print [ rCluster//N, \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Courier", FontWeight->"Plain"], StyleBox["\", \n clusterLength, \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Courier", FontWeight->"Plain"], StyleBox["\", \n NumberForm [ fracClusters//N, 6], \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Courier", FontWeight->"Plain"], StyleBox["\", \n totalClusters//N,\"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Courier", FontWeight->"Plain"], StyleBox["\", \n NumberForm [ fracLigands//N, 6 ], \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[" ", Editable->False, InitializationCell->True, FontFamily->"Courier", FontWeight->"Plain"], StyleBox[ "\", \n totalLigands//N ] ], \n clusterLengthArray ] } ; \ ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["chooseTicks::usage = \"", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox[ "chooseTicks is a routine for selecting the number and position of the tick \ marks in the lattice saturation axis (r/rSat) in the 3 dimensional plots of \ cluster length distribution.", Editable->False, InitializationCell->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True], StyleBox[ "chooseTicks := { \n If [ points3D==1, tickChoice = 1, \n If [ \ points3D==2, tickChoice = 2, \n If [ Mod[points3D,5]==0, \ tickChoice = 5 ; \n tickStep = points3D/5, \n \ If [ Mod[points3D,4]==0, tickChoice = 4 ; \n \ tickStep = points3D/4, \n If [ Mod[points3D,3]==0, \ tickChoice = 3 ; \n tickStep = points3D/3, \n \ tickChoice = 6 ] ] ] ] ] ; \n If [ \ tickChoice==1, tickArray = {{1,0},{2,1}} ; \n tickArray0 = {{1,0}} \ ; tickArray1 = {{2,1}} ] ; \n If [ tickChoice==2, tickArray = \ {{1,0},{2,0.5},{3,1}} ; \n tickArray0 = {{1,0},{2,0.5}} ; \ tickArray1 = {{2,0.5},{3,1}} ] ; \n If [ tickChoice==3, \n \ tickArray = {{1,0},{1+tickStep,0.33},{1+2 tickStep,0.67}, \n \ {1+3 tickStep,1}} ; \n tickArray0 = {{1,0},{1+tickStep,0.33},{1+2 \ tickStep,0.67}} ; \n tickArray1 = {{1+tickStep,0.33},{1+2 \ tickStep,0.67}, \n {1+3 tickStep,1}} ] ; \n If [ \ tickChoice==4, \n tickArray = {{1,0},{1+tickStep,0.25},{1+2 \ tickStep,0.5}, \n {1+3 tickStep,0.75},{1+4 tickStep,1}} ; \n \ tickArray0 = {{1,0},{1+tickStep,0.25},{1+2 tickStep,0.5}, \n \ {1+3 tickStep,0.75}} ; \n tickArray1 = \ {{1+tickStep,0.25},{1+2 tickStep,0.5}, \n {1+3 \ tickStep,0.75},{1+4 tickStep,1}} ] ; \n If [ tickChoice==5, \n \ tickArray = {{1,0},{1+tickStep,0.2},{1+2 tickStep,0.4}, \n \ {1+3 tickStep,0.6},{1+4 tickStep,0.8},{1+5 tickStep,1}} ; \n \ tickArray0 = {{1,0},{1+tickStep,0.2},{1+2 tickStep,0.4}, \n \ {1+3 tickStep,0.6},{1+4 tickStep,0.8}} ; \n tickArray1 = \ {{1+tickStep,0.2},{1+2 tickStep,0.4}, \n {1+3 \ tickStep,0.6},{1+4 tickStep,0.8},{1+5 tickStep,1}} ] ; \n If [ \ tickChoice==6, \n num = 1 ; \n While [ num/points3D < \ 0.1, num = num+1 ] ; \n num2 = points3D-num ; \n While \ [ !Mod[num2,3]==0 && !Mod[num2,4]==0, \n num2 = num2-1 ] ; \n \ If [ Mod[num2,4]==0, tickChoice2 = 4 ; \n tickStep \ = num2/4, \n If [ Mod[num2,3]==0, tickChoice2 = 3 ; \n \ tickStep = num2/3 ] ] ; \n tickValue = \ tickStep/points3D ; \n If [ tickChoice2==3, \n \ tickArray = {{1,0}, \n {1+tickStep, N [ Round [ 100 \ tickValue]/100 ] }, \n {1+2 tickStep, N [ Round [ 200 \ tickValue]/100 ] }, \n {1+3 tickStep, N [ Round [ 300 \ tickValue]/100 ] }, \n {points3D+1, 1}} ; \n \ tickArray2 = { \n {1+tickStep, N [ Round [ 100 \ tickValue]/100 ] }, \n {1+2 tickStep, N [ Round [ 200 \ tickValue]/100 ] }, \n {1+3 tickStep, N [ Round [ 300 \ tickValue]/100 ] }} ; \n tickArray3 = {{points3D+1-3 \ tickStep, \n N [ Round [ 100 (1-3 tickValue)]/100 ] \ }, \n {points3D+1-2 tickStep, \n \ N [ Round [ 100 (1-2 tickValue)]/100 ] }, \n \ {points3D+1-tickStep, \n N [ Round [ 100 \ (1-tickValue)]/100 ] }} ; \n If [ tickStep > (points3D-3 \ tickStep), \n tickArray0 = tickArray2 ; tickArray1 = \ tickArray3, \n tickArray0 = tickArray3 ; tickArray1 = \ tickArray2 ] ] ; \n If [ tickChoice2==4, \n \ tickArray = {{1,0}, \n {1+tickStep, N [ Round [ 100 \ tickValue]/100 ] }, \n {1+2 tickStep, N [ Round [ 200 \ tickValue]/100 ] }, \n {1+3 tickStep, N [ Round [ 300 \ tickValue]/100 ] }, \n {1+4 tickStep, N [ Round [ 400 \ tickValue]/100 ] }, \n {points3D+1, 1}} ; \n \ tickArray2 = { \n {1+tickStep, N [ Round [ 100 \ tickValue]/100 ] }, \n {1+2 tickStep, N [ Round [ 200 \ tickValue]/100 ] }, \n {1+3 tickStep, N [ Round [ 300 \ tickValue]/100 ] }, \n {1+4 tickStep, N [ Round [ 400 \ tickValue]/100 ] }} ; \n tickArray3 = {{points3D+1-4 \ tickStep, \n N [ Round [ 100 (1-4 tickValue)]/100 ] \ }, \n {points3D+1-3 tickStep, \n \ N [ Round [ 100 (1-3 tickValue)]/100 ] }, \n \ {points3D+1-2 tickStep, \n N [ Round [ 100 (1-2 \ tickValue)]/100 ] }, \n {points3D+1-tickStep, \n \ N [ Round [ 100 (1-tickValue)]/100 ] }} ; \n \ If [ tickStep > (points3D-4 tickStep), \n tickArray0 = \ tickArray2 ; tickArray1 = tickArray3, \n tickArray0 = \ tickArray3 ; tickArray1 = tickArray2 ] ] ; \n PrependTo [ \ tickArray0, {1,0} ] ; \n AppendTo [ tickArray1, {points3D+1, 1} ] \ ] } ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, FontFamily->"New York"], Cell[TextData[{ StyleBox["threeDplot::usage = \"", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontWeight->"Plain"], StyleBox[ "threeDplot is a routine for plotting the fractions of clusters of \ different lengths, or the fractions of bound ligands in clusters of different \ lengths, as a function of r.", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox["\" ; ", Editable->False, InitializationCell->True, FontWeight->"Plain"], StyleBox["\n", Editable->False, InitializationCell->True, AspectRatioFixed->True], StyleBox[ "threeDplot [ xView_, yView_, zView_, xLabel_, yLabel_, zLabel_, \n \ threeDarray_, tickArray_ ] := { \n If [ saveOutput==False, \n \ Unprotect [ Out ] ; Clear [ Out ] ; Protect [ Out ] ] ; \n ListPlot3D [ \ threeDarray, PlotRange->{0,1}, \n BoxRatios->{1,1,1}, Lighting -> \ True, \n Ticks->{Automatic,tickArray,Automatic}, \n \ LightSources -> {{{1,0,1},RGBColor[1,0,0]}, \n \ {{1,1,1},RGBColor[0,1,0]}, {{0,1,1},RGBColor[0,0,1]}}, \n ViewPoint \ -> {xView, yView, zView}, \n AxesLabel->{xLabel, yLabel, zLabel} ] \ } ; ", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontWeight->"Plain"] }], "Input", Editable->False, InitializationCell->True, AspectRatioFixed->True, FontFamily->"New York"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox[ "Functions for calculation of correlation coefficient (R) for comparison of \ theoretical and experimental data", Editable->False, Evaluatable->False, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]]], "Subsection", Editable->False, Evaluatable->False, FontFamily->"Geneva"], Cell[BoxData[{ \(\(ssTot[ list_] := {aveY = Plus@@list\/Length[list]; Plus@@\(\((list - aveY)\)\^2\)}\[LeftDoubleBracket]1 \[RightDoubleBracket]; 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