(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 53540, 1292] NotebookOptionsPosition[ 52922, 1265] NotebookOutlinePosition[ 53333, 1283] CellTagsIndexPosition[ 53290, 1280] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Auxin influx carriers control vascular patterning and xylem differentiation \ in Arabidopsis thaliana\ \>", "Title", CellChangeTimes->{{3.596371555385809*^9, 3.596371557056796*^9}, { 3.627914999791082*^9, 3.627915037185598*^9}, {3.627915070743808*^9, 3.627915075423492*^9}, {3.637135055522574*^9, 3.637135056498361*^9}, { 3.637219632559815*^9, 3.637219673188233*^9}}], Cell[TextData[{ StyleBox["Norma F\[AGrave]bregas", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ SuperscriptBox["", RowBox[{"1", ",", " ", "\[Paragraph]"}]], TraditionalForm]], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], " ", StyleBox[", Pau Formosa-Jordan", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", RowBox[{"2", ",", " ", "\[Paragraph]", ",", "#1"}]], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[", ", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ RowBox[{"Ana", " ", "Confraria"}], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", RowBox[{"1", ",", " ", "\[Paragraph]", ",", "#2"}]], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[", Riccardo Siligato", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", RowBox[{"3", ",", "4"}]], FontColor->RGBColor[ 0.7411764705882353, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[", Jose M. Alonso", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", "5"], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[", Ranjan Swarup", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", "6"], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[", Malcolm J. Bennett", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", "6"], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[", Ari Pekka M\[ADoubleDot]h\[ODoubleDot]nen", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", RowBox[{"3", ",", "4"}]], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[", Ana I. Ca\[NTilde]o-Delgado", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", RowBox[{"1", ",", " ", "&", ",", "*"}]], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[" and Marta Iba\[NTilde]es", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", RowBox[{"2", ",", " ", "&", ",", "*"}]], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[".\n\n", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ SuperscriptBox["", "1"], TraditionalForm]], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], StyleBox[" Department of Molecular Genetics, Centre for Research in \ Agricultural Genomics (CRAG) CSIC-IRTA-UAB-UB, Barcelona E-08193, Spain.\n", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", "2"], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[" Department of Structure and Constituents of Matter, Faculty of \ Physics, University of Barcelona, Barcelona E-08028, Spain.\n", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", "3"], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[" Institute of Biotechnology, University of Helsinki, Helsinki, \ FIN-00014, Finland.\n", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", "4"], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[" Department of Biosciences, University of Helsinki, Helsinki, \ FIN-00014, Finland.\n", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", "5"], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[" Department of Plant and Microbial Biology, North Carolina State \ University, Raleigh, North Carolina 27695, USA.\n", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ SuperscriptBox["", StyleBox["6", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]]], TraditionalForm]]], StyleBox[" School of Biosciences and Centre for Plant Integrative Biology, \ University of Nottingham, LE12 5RD Nottingham, United Kingdom.\n\n", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", "#1"], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[" Current Address: Sainsbury Laboratory, University of Cambridge, \ Bateman Street, Cambridge, CB2 1LR, United Kingdom.\n", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ SuperscriptBox["", StyleBox["#2", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]]], TraditionalForm]]], StyleBox[" Current Address: Instituto Gulbenkian de Ci\[EHat]ncia, 2780-156 \ Oeiras, Portugal.\n\n* Corresponding authors\nE-mails: marta.ibanes@ub.edu \ (MI), ana.cano@cragenomica.es (AICD).\n\n", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ RowBox[{ StyleBox[ SuperscriptBox["", "\[Paragraph]"], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], " "}], TraditionalForm]]], StyleBox["These authors contributed equally to this work.\n", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["", "&"], FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], TraditionalForm]]], StyleBox[" These authors also contributed equally to this work.\n\n", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]] }], "Text", CellChangeTimes->{{3.596371555385809*^9, 3.596371557056796*^9}, { 3.627914999791082*^9, 3.627915037185598*^9}, {3.627915070743808*^9, 3.627915075423492*^9}, {3.637135055522574*^9, 3.637135056498361*^9}, { 3.637219632559815*^9, 3.637219632812065*^9}, {3.6372196636117477`*^9, 3.637219706591921*^9}, {3.6372197967615767`*^9, 3.637219798198441*^9}, 3.6372205207507973`*^9, {3.637220622658372*^9, 3.637220996710661*^9}, { 3.6372219176165867`*^9, 3.637221921991386*^9}}], Cell[CellGroupData[{ Cell["S1 Code. Simulation code for the model of auxin transport", "Subtitle", CellChangeTimes->{{3.596371555385809*^9, 3.596371557056796*^9}, { 3.627914999791082*^9, 3.627915037185598*^9}, {3.627915070743808*^9, 3.627915075423492*^9}, {3.637135055522574*^9, 3.637135056498361*^9}, { 3.637219632559815*^9, 3.637219632812065*^9}, {3.6372196636117477`*^9, 3.6372196777220716`*^9}}, FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[TextData[StyleBox["This code simulates the dynamics of Eqs S7 and S8 of \ S1 Text in a line of cells with periodic boundary conditions. By running the \ following code it appears an applet where different auxin transport \ parameters can be modified. \n\nBy default, influx levels (\[CapitalIota]), \ efflux levels (E), and apoplastic diffusion levels (D) can be modified \ through the applet slides. The output shows the cytosolic (blue) and \ apoplastic (green) auxin concentrations (left plot) and the influx (black) \ and efflux (dashed gray) carriers (right plot) at the final simulation \ time.", "Subsubsection", FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]]], "Text", CellChangeTimes->{{3.627915484134547*^9, 3.627915493391479*^9}, { 3.627915657434918*^9, 3.6279156919247*^9}, {3.627916042866741*^9, 3.627916086990303*^9}, {3.630793386323966*^9, 3.630793388487998*^9}, { 3.63079355927061*^9, 3.630793579858088*^9}, {3.630793705022719*^9, 3.630793724358481*^9}, {3.630794442760764*^9, 3.630794547633891*^9}, { 3.630795130736462*^9, 3.630795142935405*^9}, {3.630795205248719*^9, 3.630795269554661*^9}, {3.637135060695285*^9, 3.637135073544903*^9}, { 3.637135114110854*^9, 3.6371351177757883`*^9}}, FontColor->RGBColor[ 0.7490196078431373, 0.09411764705882353, 0.11372549019607843`]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "Number", " ", "of", " ", "cells", " ", "along", " ", "a", " ", "line"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"L", "=", "60"}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "Parameter", " ", "\[Delta]", " ", "sets", " ", "the", " ", "amplitude", " ", "of", " ", "the", " ", "fluctuations"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Delta]", "=", "0.1"}], ";"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "Random", " ", "number", " ", "generation", " ", "for", " ", "the", " ", "initial", " ", "conditions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"rand1", "[", "i", "]"}], "=", RowBox[{"1", "+", RowBox[{"\[Delta]", "*", RowBox[{"(", RowBox[{ RowBox[{"RandomReal", "[", "]"}], "-", "0.5"}], ")"}]}]}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "L"}], "}"}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"rand2", "[", "i", "]"}], "=", RowBox[{"1", "+", RowBox[{"\[Delta]", "*", RowBox[{"(", RowBox[{ RowBox[{"RandomReal", "[", "]"}], "-", "0.5"}], ")"}]}]}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "L"}], "}"}]}], "]"}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "Index", " ", "vector", " ", "useful", " ", "for", " ", "boundary", " ", "conditions"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ind", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"i", "-", "1"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"L", "+", "3"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ind", "[", RowBox[{"[", "1", "]"}], "]"}], "=", "L"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ind", "[", RowBox[{"[", RowBox[{"L", "+", "2"}], "]"}], "]"}], "=", "1"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ind", "[", RowBox[{"[", RowBox[{"L", "+", "3"}], "]"}], "]"}], "=", "2"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"cc", "[", "i_", "]"}], ":=", RowBox[{"ind", "[", RowBox[{"[", RowBox[{"i", "+", "1"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "Defining", " ", "the", " ", "array", " ", "of", " ", "variables"}], ",", " ", RowBox[{ "being", " ", "Ax", " ", "for", " ", "the", " ", "cytosolic", " ", "auxin", " ", "and", " ", "ax", " ", "for", " ", "the", " ", "apoplastic", " ", "auxin"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Ax", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"ToExpression", "[", RowBox[{"StringJoin", "[", RowBox[{"\"\\"", ",", RowBox[{"ToString", "[", "i", "]"}]}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "L"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ax", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"ToExpression", "[", RowBox[{"StringJoin", "[", RowBox[{"\"\\"", ",", RowBox[{"ToString", "[", "i", "]"}]}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "L"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "Setting", " ", "some", " ", "default", " ", "model", " ", "parameters"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"h", "=", "2"}], ";", RowBox[{"eps", "=", "0.05"}], ";"}], " ", RowBox[{"(*", RowBox[{"eps", " ", "is", " ", "\[Epsilon]", " ", "parameter"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dsig", "=", "2"}], ";", RowBox[{"ddeg", "=", "0.1"}], ";", RowBox[{"dca", "=", "15"}], ";"}], " ", RowBox[{"(*", " ", RowBox[{"dsig", ",", " ", RowBox[{ "ddeg", " ", "and", " ", "dca", " ", "are", " ", "the", " ", "dimensional", " ", "production"}], ",", " ", RowBox[{ "degradation", " ", "and", " ", "passive", " ", "transport", " ", "rates"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ra", "=", "10"}], ";", RowBox[{"rp", "=", "10"}], ";"}], " ", RowBox[{"(*", RowBox[{ "Auxin", " ", "thresholds", " ", "for", " ", "influx", " ", "and", " ", "efflux", " ", "production"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ha", "=", "2"}], ";", RowBox[{"hp", "=", "2"}], ";"}], " ", RowBox[{"(*", RowBox[{ RowBox[{ "Exponents", " ", "in", " ", "the", " ", "Hill", " ", "function", " ", "for", " ", "auxin"}], "-", RowBox[{ "induced", " ", "influx", " ", "and", " ", "efflux", " ", "carriers"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fc", "=", "0.003"}], ";", RowBox[{"fw", "=", "0.334"}], ";"}], " ", RowBox[{"(*", RowBox[{ "Ratios", " ", "of", " ", "protonated", " ", "auxin", " ", "in", " ", "the", " ", "cell", " ", "and", " ", "cell", " ", "wall"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"famc", "=", RowBox[{"1", "-", "fc"}]}], ";", RowBox[{"famw", "=", RowBox[{"1", "-", "fw"}]}], ";"}], " ", RowBox[{"(*", RowBox[{ "Ratios", " ", "of", " ", "anionic", " ", "auxin", " ", "in", " ", "the", " ", "cell", " ", "and", " ", "cell", " ", "wall"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"z", "=", "2"}], ";"}], RowBox[{"(*", RowBox[{ "z", " ", "is", " ", "the", " ", "number", " ", "of", " ", "nearest", " ", "neighbours", " ", "per", " ", "cell"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"tt", "=", "0"}], ";"}], RowBox[{"(*", " ", RowBox[{ RowBox[{"By", " ", "making", " ", "tt"}], "=", RowBox[{ "0", " ", "we", " ", "do", " ", "the", " ", "approximation", " ", "of", " ", "having", " ", "the", " ", "transporters", " ", "just", " ", "on", " ", "the", " ", "membrane", " ", "and", " ", "not", " ", "in", " ", "the", " ", "cytosol"}]}], "*)"}], "\n", "\[IndentingNewLine]", RowBox[{ RowBox[{"tfin", "=", "17.5"}], ";"}], RowBox[{"(*", " ", RowBox[{"Final", " ", "simulation", " ", "time"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Manipulate", "[", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"Effective", " ", "model", " ", "parameters"}], ",", " ", RowBox[{"see", " ", "Text", " ", RowBox[{"S1", ".", " ", "\"\\""}], " ", "denotes", " ", "the", " ", "tilde", " ", "appearing", " ", "on", " ", "the", " ", "variables", " ", "in", " ", "Text", " ", "S1"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"sigtild", "=", RowBox[{"dsig", "/", RowBox[{"(", "ddeg", ")"}]}]}], ";", RowBox[{"dcatild", "=", RowBox[{"dca", "/", "ddeg"}]}], ";", " ", RowBox[{"dtild", "=", RowBox[{"ddd", "/", "ddeg"}]}], ";", RowBox[{"inftild", "=", RowBox[{"dminf", "/", "ddeg"}]}], ";", " ", RowBox[{"eetild", "=", RowBox[{"e", "/", "ddeg"}]}], ";", RowBox[{"nutild", "=", RowBox[{"ddeg", "/", "ddeg"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", "Functions", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"hh", "[", "x_", "]"}], ":=", "x"}], ";", "\[IndentingNewLine]", "\n", RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", RowBox[{"x", "^", "h"}]}], ";", "\n", RowBox[{ RowBox[{"atot", "[", "x_", "]"}], ":=", RowBox[{ RowBox[{"x", "^", "ha"}], "/", RowBox[{"(", RowBox[{ RowBox[{"2", "*", RowBox[{"x", "^", "ha"}]}], "+", RowBox[{"2", "*", RowBox[{"ra", "^", "ha"}]}]}], ")"}]}]}], ";", RowBox[{"(*", RowBox[{"influx", " ", "carriers", " ", "levels"}], "*)"}], "\n", RowBox[{ RowBox[{"ptot", "[", "x_", "]"}], ":=", RowBox[{ RowBox[{"x", "^", "hp"}], "/", RowBox[{"(", RowBox[{ RowBox[{"x", "^", "hp"}], "+", RowBox[{"rp", "^", "hp"}]}], ")"}]}]}], ";", RowBox[{"(*", RowBox[{"efflux", " ", "carriers", " ", "levels"}], "*)"}], "\n", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "Homogeneous", " ", "steady", " ", "states", " ", "of", " ", "the", " ", "cytosolic", " ", "auxin", " ", "A0", " ", "and", " ", "the", " ", "apoplastic", " ", "auxin", " ", "a0"}], "*)"}], "\[IndentingNewLine]", RowBox[{"A0", "=", RowBox[{"dsig", "/", RowBox[{"(", "ddeg", ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"denh", "=", RowBox[{"(", RowBox[{ RowBox[{"dcatild", "*", "fw"}], "+", RowBox[{"inftild", "*", "famw", "*", RowBox[{"atot", "[", "A0", "]"}]}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"a0", "=", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"dcatild", "*", "fc", "*", "A0"}], "+", RowBox[{ RowBox[{"(", " ", RowBox[{"eetild", "*", RowBox[{"ptot", "[", "A0", "]"}], "*", "famc", "*", "A0", "*", RowBox[{"f", "[", "A0", "]"}]}], ")"}], "/", RowBox[{"(", RowBox[{"tt", "+", RowBox[{"2.0", "*", RowBox[{"f", "[", "A0", "]"}]}]}], ")"}]}]}], ")"}], "/", "denh"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "Terms", " ", "of", " ", "the", " ", "derivatives", " ", "in", " ", "time"}], "*)"}], "\n", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"For", " ", "the", " ", "cytosolic", " ", "auxin"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"evolA", "[", RowBox[{"A_", ",", "Am1_", ",", "AM1_", ",", "a_", ",", "am1_"}], "]"}], ":=", RowBox[{ RowBox[{"eps", "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "dcatild"}], "*", RowBox[{"(", RowBox[{ RowBox[{"z", "*", "fc", "*", "A"}], "-", RowBox[{"fw", "*", RowBox[{"(", RowBox[{"am1", "+", "a"}], ")"}]}]}], ")"}]}], "-", RowBox[{"eetild", "*", RowBox[{"hh", "[", RowBox[{"famc", "*", "A"}], "]"}], "*", RowBox[{"ptot", "[", "A", "]"}], "*", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"f", "[", "Am1", "]"}], "+", RowBox[{"f", "[", "AM1", "]"}]}], ")"}], "/", RowBox[{"(", RowBox[{"tt", "+", RowBox[{"f", "[", "Am1", "]"}], "+", RowBox[{"f", "[", "AM1", "]"}]}], ")"}]}]}], "+", RowBox[{"inftild", "*", RowBox[{"atot", "[", "A", "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{"hh", "[", RowBox[{"famw", "*", "am1"}], "]"}], "+", RowBox[{"hh", "[", RowBox[{"famw", "*", "a"}], "]"}]}], ")"}]}]}], ")"}]}], "+", "sigtild", "-", RowBox[{"nutild", "*", "A"}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"For", " ", "the", " ", "apoplastic", " ", "auxin"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"evola", "[", RowBox[{ "A_", ",", "Am1_", ",", "AM1_", ",", "AM2_", ",", "a_", ",", "am1_", ",", "aM1_"}], "]"}], ":=", RowBox[{ RowBox[{"dcatild", " ", "*", RowBox[{"(", RowBox[{ RowBox[{"fc", "*", RowBox[{"(", RowBox[{"A", "+", "AM1"}], ")"}]}], "-", RowBox[{"z", "*", "fw", "*", "a"}]}], ")"}]}], "+", RowBox[{"eetild", "*", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"f", "[", "AM1", "]"}], "*", RowBox[{"ptot", "[", "A", "]"}], "*", RowBox[{ RowBox[{"hh", "[", RowBox[{"famc", "*", "A"}], "]"}], "/", RowBox[{"(", RowBox[{"tt", "+", RowBox[{"f", "[", "Am1", "]"}], "+", RowBox[{"f", "[", "AM1", "]"}]}], ")"}]}]}], "+", RowBox[{ RowBox[{"f", "[", "A", "]"}], "*", RowBox[{"ptot", "[", "AM1", "]"}], "*", RowBox[{ RowBox[{"hh", "[", RowBox[{"famc", "*", "AM1"}], "]"}], "/", RowBox[{"(", RowBox[{"tt", "+", RowBox[{"f", "[", "A", "]"}], "+", RowBox[{"f", "[", "AM2", "]"}]}], ")"}]}]}]}], ")"}]}], "-", RowBox[{"inftild", "*", RowBox[{"hh", "[", RowBox[{"famw", "*", "a"}], "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{"atot", "[", "A", "]"}], "+", RowBox[{"atot", "[", "AM1", "]"}]}], ")"}]}], "+", RowBox[{"dtild", "*", RowBox[{"(", RowBox[{"aM1", "+", "am1", "-", RowBox[{"2", "*", "a"}]}], ")"}]}]}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Solving", " ", "the", " ", "equations"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"ss", "=", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"Flatten", "[", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", "i", "]"}], "]"}], "'"}], "[", "t", "]"}], "\[Equal]", RowBox[{"evolA", "[", RowBox[{ RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", RowBox[{"cc", "[", "i", "]"}], "]"}], "]"}], "[", "t", "]"}], ",", RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", RowBox[{"cc", "[", RowBox[{"i", "-", "1"}], "]"}], "]"}], "]"}], "[", "t", "]"}], ",", RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", RowBox[{"cc", "[", RowBox[{"i", "+", "1"}], "]"}], "]"}], "]"}], "[", "t", "]"}], ",", RowBox[{ RowBox[{"ax", "[", RowBox[{"[", "i", "]"}], "]"}], "[", "t", "]"}], ",", RowBox[{ RowBox[{"ax", "[", RowBox[{"[", RowBox[{"cc", "[", RowBox[{"i", "-", "1"}], "]"}], "]"}], "]"}], "[", "t", "]"}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"ax", "[", RowBox[{"[", "i", "]"}], "]"}], "'"}], "[", "t", "]"}], "\[Equal]", RowBox[{"evola", "[", RowBox[{ RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", RowBox[{"cc", "[", "i", "]"}], "]"}], "]"}], "[", "t", "]"}], ",", RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", RowBox[{"cc", "[", RowBox[{"i", "-", "1"}], "]"}], "]"}], "]"}], "[", "t", "]"}], ",", RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", RowBox[{"cc", "[", RowBox[{"i", "+", "1"}], "]"}], "]"}], "]"}], "[", "t", "]"}], ",", RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", RowBox[{"cc", "[", RowBox[{"i", "+", "2"}], "]"}], "]"}], "]"}], "[", "t", "]"}], ",", RowBox[{ RowBox[{"ax", "[", RowBox[{"[", RowBox[{"cc", "[", "i", "]"}], "]"}], "]"}], "[", "t", "]"}], ",", RowBox[{ RowBox[{"ax", "[", RowBox[{"[", RowBox[{"cc", "[", RowBox[{"i", "-", "1"}], "]"}], "]"}], "]"}], "[", "t", "]"}], ",", RowBox[{ RowBox[{"ax", "[", RowBox[{"[", RowBox[{"cc", "[", RowBox[{"i", "+", "1"}], "]"}], "]"}], "]"}], "[", "t", "]"}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", "i", "]"}], "]"}], "[", "0", "]"}], "\[Equal]", RowBox[{"A0", "*", RowBox[{"rand1", "[", "i", "]"}]}]}], ",", RowBox[{ RowBox[{ RowBox[{"ax", "[", RowBox[{"[", "i", "]"}], "]"}], "[", "0", "]"}], "\[Equal]", RowBox[{"a0", "*", RowBox[{"rand2", "[", "i", "]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "L"}], "}"}]}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{"ax", "[", RowBox[{"[", "i", "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "L"}], "}"}]}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"t", ",", "0", ",", "tfin"}], "}"}], ",", RowBox[{"Method", "\[Rule]", "\"\\""}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "Generating", " ", "an", " ", "array", " ", "of", " ", "the", " ", "numerical", " ", "evolution", " ", "of", " ", "the", " ", "solutions"}], "*)"}], "\[IndentingNewLine]", RowBox[{"jump", "=", "1000"}], ";", "\[IndentingNewLine]", RowBox[{"Axdata", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", "i", "]"}], "]"}], "[", "kk", "]"}]}], "}"}], "/.", "ss"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "L"}], "}"}]}], "]"}], ",", "1"}], "]"}], ",", RowBox[{"{", RowBox[{"kk", ",", "1", ",", "tfin", ",", "jump"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"axdata", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"ax", "[", RowBox[{"[", "i", "]"}], "]"}], "[", "kk", "]"}]}], "}"}], "/.", "ss"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "L"}], "}"}]}], "]"}], ",", "1"}], "]"}], ",", RowBox[{"{", RowBox[{"kk", ",", "1", ",", "tfin", ",", "jump"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"lt", "=", RowBox[{"Length", "[", "Axdata", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"jj", "=", "lt"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"tfinAx", "=", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Ax", "[", RowBox[{"[", "i", "]"}], "]"}], "[", "jj", "]"}], "/.", "ss"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "L"}], "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"influx", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"atot", "[", "#", "]"}], "&"}], ",", "tfinAx"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"efflux", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"ptot", "[", "#", "]"}], "&"}], ",", "tfinAx"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"fz", "=", "18"}], ";", RowBox[{"(*", RowBox[{"Font", " ", "Size"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Plotting", " ", "the", " ", "output"}], "*)"}], "\[IndentingNewLine]", RowBox[{"gra", "=", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Axdata", "[", RowBox[{"[", RowBox[{"Floor", "[", "jj", "]"}], "]"}], "]"}], ",", RowBox[{"axdata", "[", RowBox[{"[", RowBox[{"Floor", "[", "jj", "]"}], "]"}], "]"}]}], "}"}], ",", RowBox[{"Joined", "\[Rule]", "True"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"Directive", "[", RowBox[{"Blue", ",", "Thick"}], "]"}], ",", RowBox[{"Directive", "[", RowBox[{"Green", ",", "Thick"}], "]"}]}], "}"}]}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\\""}], "}"}]}], ",", RowBox[{"ImageSize", "\[Rule]", "450"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "L"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "200"}], "}"}]}], "}"}]}], ",", RowBox[{"LabelStyle", "\[Rule]", RowBox[{"Directive", "[", "fz", "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"grtans", "=", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"{", RowBox[{"influx", ",", "efflux"}], "}"}], ",", RowBox[{"Joined", "\[Rule]", "True"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\\""}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"Directive", "[", RowBox[{"Black", ",", "Thick"}], "]"}], ",", RowBox[{"Directive", "[", RowBox[{"Gray", ",", "Thick", ",", "Dashed"}], "]"}]}], "}"}]}], ",", RowBox[{"ImageSize", "\[Rule]", "450"}], ",", RowBox[{"LabelStyle", "\[Rule]", RowBox[{"Directive", "[", "fz", "]"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{"GraphicsGrid", "[", RowBox[{"{", RowBox[{ RowBox[{"{", "gra", "}"}], ",", RowBox[{"{", "grtans", "}"}]}], "}"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Parameters", " ", "to", " ", "vary"}], "*)"}], "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"dminf", ",", "100", ",", "\"\\""}], "}"}], ",", "0", ",", "500"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"e", ",", "105.0", ",", "\"\\""}], "}"}], ",", "0", ",", "1000"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"ddd", ",", "2.0", ",", "\"\\""}], "}"}], ",", "0", ",", "10"}], "}"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.596356686757123*^9, 3.596356700306444*^9}, { 3.596370146840703*^9, 3.5963701988006897`*^9}, {3.596370866617178*^9, 3.596370882803803*^9}, 3.596371564693346*^9, {3.596371633655637*^9, 3.5963717835986547`*^9}, {3.5963719003940907`*^9, 3.59637190113863*^9}, { 3.596371970440971*^9, 3.59637197087282*^9}, {3.596372065524816*^9, 3.596372106663968*^9}, {3.596372138446705*^9, 3.596372225279306*^9}, { 3.596372289197529*^9, 3.59637231795113*^9}, {3.5963723818276787`*^9, 3.5963723877807827`*^9}, 3.5963724197664127`*^9, {3.596372450038032*^9, 3.5963724538844957`*^9}, {3.596372544668172*^9, 3.596372585827197*^9}, { 3.596372655270412*^9, 3.596372664704295*^9}, {3.596372725355997*^9, 3.5963727430376797`*^9}, {3.5965279113258457`*^9, 3.5965280026119623`*^9}, 3.596528188278413*^9, {3.5965282525072117`*^9, 3.596528255056384*^9}, { 3.59652828674485*^9, 3.5965283110882397`*^9}, {3.5965283469105387`*^9, 3.596528352591185*^9}, {3.596528415650185*^9, 3.596528459060793*^9}, 3.5965285220550623`*^9, {3.5972114532537327`*^9, 3.5972115461177483`*^9}, { 3.597211580919416*^9, 3.59721166274938*^9}, {3.597211776797947*^9, 3.597211780601718*^9}, {3.597213539443256*^9, 3.597213546636623*^9}, { 3.597213700920439*^9, 3.597213703614574*^9}, 3.597213857240635*^9, { 3.59726702345862*^9, 3.597267024656869*^9}, 3.597267452037961*^9, { 3.597310723085669*^9, 3.5973107235684*^9}, {3.597311355688469*^9, 3.5973113586035833`*^9}, {3.597311389573514*^9, 3.5973113898360987`*^9}, { 3.5973390185929193`*^9, 3.59733902409587*^9}, {3.597339071284099*^9, 3.597339071873006*^9}, {3.597339112466578*^9, 3.5973391136192503`*^9}, { 3.597339227645871*^9, 3.5973392288443937`*^9}, 3.597345347509431*^9, { 3.597345380576662*^9, 3.597345407757944*^9}, {3.6019615848044157`*^9, 3.6019616214924183`*^9}, {3.601961761392536*^9, 3.6019617617008*^9}, { 3.601971876953454*^9, 3.601971953875678*^9}, {3.601972034050116*^9, 3.601972078404681*^9}, {3.602831331994285*^9, 3.602831339232615*^9}, { 3.6028313709884453`*^9, 3.602831412837352*^9}, {3.602831472482881*^9, 3.602831482266121*^9}, {3.602831912386475*^9, 3.6028319185344133`*^9}, { 3.602855091293502*^9, 3.6028550976292953`*^9}, {3.602855325924109*^9, 3.602855330091758*^9}, {3.602855424062578*^9, 3.6028555275210238`*^9}, { 3.60285556332901*^9, 3.602855575617236*^9}, {3.602855611442322*^9, 3.60285561396731*^9}, {3.602855656366599*^9, 3.60285566766947*^9}, { 3.602855703786315*^9, 3.6028558360791407`*^9}, {3.6028558664887943`*^9, 3.6028558757833138`*^9}, 3.602855935774392*^9, {3.6028559697507963`*^9, 3.602855973981399*^9}, {3.602856043324111*^9, 3.602856118956132*^9}, { 3.602856269845216*^9, 3.6028562705951977`*^9}, {3.6028563367317*^9, 3.602856363002309*^9}, {3.6028570006973343`*^9, 3.602857001615443*^9}, { 3.602857245156742*^9, 3.602857247077483*^9}, {3.6028573153627462`*^9, 3.602857317203272*^9}, {3.60285739784414*^9, 3.602857492505569*^9}, { 3.602874911146996*^9, 3.6028749603006477`*^9}, 3.602875042629521*^9, 3.602875100622081*^9, {3.602875147057459*^9, 3.602875147741316*^9}, { 3.6028754418996572`*^9, 3.60287547756771*^9}, {3.60287552895901*^9, 3.602875548803131*^9}, {3.602875601603986*^9, 3.602875602723702*^9}, { 3.602875654945307*^9, 3.602875655927597*^9}, {3.602875690899363*^9, 3.6028757040732927`*^9}, {3.602875767683642*^9, 3.6028757681437187`*^9}, { 3.602875809622449*^9, 3.6028758108779993`*^9}, {3.602876412760538*^9, 3.6028764131737747`*^9}, {3.608477217224106*^9, 3.608477227655962*^9}, { 3.60847726364403*^9, 3.608477302025779*^9}, {3.627914177987713*^9, 3.627914178621748*^9}, {3.62791512532168*^9, 3.62791543952975*^9}, { 3.627915559209381*^9, 3.627915630233242*^9}, {3.62791571705685*^9, 3.6279157566893787`*^9}, {3.6279157965490294`*^9, 3.6279158863078613`*^9}, 3.630792720227029*^9, {3.630792752687107*^9, 3.630792765731269*^9}, { 3.630792796695524*^9, 3.630792873913336*^9}, {3.6307929065049677`*^9, 3.630792972283853*^9}, {3.630793038205697*^9, 3.630793043594057*^9}, { 3.630793102745935*^9, 3.630793137230588*^9}, {3.6307932419833803`*^9, 3.630793277834654*^9}, {3.63079334225247*^9, 3.630793362022407*^9}, { 3.6307934031848392`*^9, 3.63079348978069*^9}, {3.630793530395928*^9, 3.6307935534316673`*^9}, {3.630793764265851*^9, 3.630793948387525*^9}, { 3.630794100304599*^9, 3.630794119897395*^9}, {3.630794153504649*^9, 3.6307941894651546`*^9}, {3.630794326469687*^9, 3.63079435327382*^9}, { 3.630794604194343*^9, 3.6307946220647697`*^9}, {3.630794783992023*^9, 3.630794802044408*^9}, {3.630794846815352*^9, 3.630794887085699*^9}, { 3.630795030488781*^9, 3.630795092132504*^9}, {3.630795280908235*^9, 3.630795309342682*^9}, {3.6307953712848797`*^9, 3.630795411452928*^9}, { 3.630795778954597*^9, 3.630795874834724*^9}, {3.631049044518079*^9, 3.631049087005117*^9}, 3.63104912123493*^9, {3.631049164585473*^9, 3.631049167613895*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`ddd$$ = 2., $CellContext`dminf$$ = 100, $CellContext`e$$ = 105., Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`dminf$$], 100, "I"}, 0, 500}, {{ Hold[$CellContext`e$$], 105., "E"}, 0, 1000}, {{ Hold[$CellContext`ddd$$], 2., "D"}, 0, 10}}, Typeset`size$$ = { 485., {300., 305.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`dminf$15552$$ = 0, $CellContext`e$15553$$ = 0, $CellContext`ddd$15554$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`ddd$$ = 2., $CellContext`dminf$$ = 100, $CellContext`e$$ = 105.}, "ControllerVariables" :> { Hold[$CellContext`dminf$$, $CellContext`dminf$15552$$, 0], Hold[$CellContext`e$$, $CellContext`e$15553$$, 0], Hold[$CellContext`ddd$$, $CellContext`ddd$15554$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`sigtild = $CellContext`dsig/$CellContext`ddeg; \ $CellContext`dcatild = $CellContext`dca/$CellContext`ddeg; $CellContext`dtild = \ $CellContext`ddd$$/$CellContext`ddeg; $CellContext`inftild = \ $CellContext`dminf$$/$CellContext`ddeg; $CellContext`eetild = \ $CellContext`e$$/$CellContext`ddeg; $CellContext`nutild = \ $CellContext`ddeg/$CellContext`ddeg; $CellContext`hh[ Pattern[$CellContext`x, Blank[]]] := $CellContext`x; $CellContext`f[ Pattern[$CellContext`x, Blank[]]] := $CellContext`x^$CellContext`h; $CellContext`atot[ Pattern[$CellContext`x, Blank[]]] := $CellContext`x^$CellContext`ha/( 2 $CellContext`x^$CellContext`ha + 2 $CellContext`ra^$CellContext`ha); $CellContext`ptot[ Pattern[$CellContext`x, Blank[]]] := \ $CellContext`x^$CellContext`hp/($CellContext`x^$CellContext`hp + \ $CellContext`rp^$CellContext`hp); $CellContext`A0 = \ $CellContext`dsig/$CellContext`ddeg; $CellContext`denh = $CellContext`dcatild \ $CellContext`fw + ($CellContext`inftild $CellContext`famw) \ $CellContext`atot[$CellContext`A0]; $CellContext`a0 = (($CellContext`dcatild \ $CellContext`fc) $CellContext`A0 + (((($CellContext`eetild \ $CellContext`ptot[$CellContext`A0]) $CellContext`famc) $CellContext`A0) \ $CellContext`f[$CellContext`A0])/($CellContext`tt + 2. $CellContext`f[$CellContext`A0]))/$CellContext`denh; \ $CellContext`evolA[ Pattern[$CellContext`A, Blank[]], Pattern[$CellContext`Am1, Blank[]], Pattern[$CellContext`AM1, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`am1, Blank[]]] := $CellContext`eps ((-$CellContext`dcatild) \ (($CellContext`z $CellContext`fc) $CellContext`A - $CellContext`fw \ ($CellContext`am1 + $CellContext`a)) - (($CellContext`eetild \ $CellContext`hh[$CellContext`famc $CellContext`A]) \ $CellContext`ptot[$CellContext`A]) (($CellContext`f[$CellContext`Am1] + \ $CellContext`f[$CellContext`AM1])/($CellContext`tt + \ $CellContext`f[$CellContext`Am1] + $CellContext`f[$CellContext`AM1])) + \ ($CellContext`inftild $CellContext`atot[$CellContext`A]) \ ($CellContext`hh[$CellContext`famw $CellContext`am1] + \ $CellContext`hh[$CellContext`famw $CellContext`a])) + $CellContext`sigtild - \ $CellContext`nutild $CellContext`A; $CellContext`evola[ Pattern[$CellContext`A, Blank[]], Pattern[$CellContext`Am1, Blank[]], Pattern[$CellContext`AM1, Blank[]], Pattern[$CellContext`AM2, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`am1, Blank[]], Pattern[$CellContext`aM1, Blank[]]] := $CellContext`dcatild ($CellContext`fc ($CellContext`A + \ $CellContext`AM1) - ($CellContext`z $CellContext`fw) $CellContext`a) + \ $CellContext`eetild (($CellContext`f[$CellContext`AM1] \ $CellContext`ptot[$CellContext`A]) ($CellContext`hh[$CellContext`famc \ $CellContext`A]/($CellContext`tt + $CellContext`f[$CellContext`Am1] + \ $CellContext`f[$CellContext`AM1])) + ($CellContext`f[$CellContext`A] \ $CellContext`ptot[$CellContext`AM1]) ($CellContext`hh[$CellContext`famc \ $CellContext`AM1]/($CellContext`tt + $CellContext`f[$CellContext`A] + \ $CellContext`f[$CellContext`AM2]))) - ($CellContext`inftild \ $CellContext`hh[$CellContext`famw $CellContext`a]) \ ($CellContext`atot[$CellContext`A] + $CellContext`atot[$CellContext`AM1]) + \ $CellContext`dtild ($CellContext`aM1 + $CellContext`am1 - 2 $CellContext`a); $CellContext`ss = NDSolve[ Flatten[ Table[{Derivative[1][ Part[$CellContext`Ax, $CellContext`i]][$CellContext`t] == \ $CellContext`evolA[ Part[$CellContext`Ax, $CellContext`cc[$CellContext`i]][$CellContext`t], Part[$CellContext`Ax, $CellContext`cc[$CellContext`i - 1]][$CellContext`t], Part[$CellContext`Ax, $CellContext`cc[$CellContext`i + 1]][$CellContext`t], Part[$CellContext`ax, $CellContext`i][$CellContext`t], Part[$CellContext`ax, $CellContext`cc[$CellContext`i - 1]][$CellContext`t]], Derivative[1][ Part[$CellContext`ax, $CellContext`i]][$CellContext`t] == \ $CellContext`evola[ Part[$CellContext`Ax, $CellContext`cc[$CellContext`i]][$CellContext`t], Part[$CellContext`Ax, $CellContext`cc[$CellContext`i - 1]][$CellContext`t], Part[$CellContext`Ax, $CellContext`cc[$CellContext`i + 1]][$CellContext`t], Part[$CellContext`Ax, $CellContext`cc[$CellContext`i + 2]][$CellContext`t], Part[$CellContext`ax, $CellContext`cc[$CellContext`i]][$CellContext`t], Part[$CellContext`ax, $CellContext`cc[$CellContext`i - 1]][$CellContext`t], Part[$CellContext`ax, $CellContext`cc[$CellContext`i + 1]][$CellContext`t]], Part[$CellContext`Ax, $CellContext`i][ 0] == $CellContext`A0 $CellContext`rand1[$CellContext`i], Part[$CellContext`ax, $CellContext`i][ 0] == $CellContext`a0 $CellContext`rand2[$CellContext`i]}, \ {$CellContext`i, 1, $CellContext`L}]], Flatten[ Table[{ Part[$CellContext`Ax, $CellContext`i], Part[$CellContext`ax, $CellContext`i]}, {$CellContext`i, 1, $CellContext`L}]], {$CellContext`t, 0, $CellContext`tfin}, Method -> "StiffnessSwitching"]; $CellContext`jump = 1000; $CellContext`Axdata = Table[ Flatten[ Table[ ReplaceAll[{$CellContext`i, Part[$CellContext`Ax, $CellContext`i][$CellContext`kk]}, \ $CellContext`ss], {$CellContext`i, 1, $CellContext`L}], 1], {$CellContext`kk, 1, $CellContext`tfin, $CellContext`jump}]; $CellContext`axdata = Table[ Flatten[ Table[ ReplaceAll[{$CellContext`i, Part[$CellContext`ax, $CellContext`i][$CellContext`kk]}, \ $CellContext`ss], {$CellContext`i, 1, $CellContext`L}], 1], {$CellContext`kk, 1, $CellContext`tfin, $CellContext`jump}]; $CellContext`lt = Length[$CellContext`Axdata]; $CellContext`jj = $CellContext`lt; \ $CellContext`tfinAx = Flatten[ Table[ ReplaceAll[ Part[$CellContext`Ax, $CellContext`i][$CellContext`jj], \ $CellContext`ss], {$CellContext`i, 1, $CellContext`L}]]; $CellContext`influx = Map[$CellContext`atot[#]& , $CellContext`tfinAx]; $CellContext`efflux = Map[$CellContext`ptot[#]& , $CellContext`tfinAx]; $CellContext`fz = 18; $CellContext`gra = ListPlot[{ Part[$CellContext`Axdata, Floor[$CellContext`jj]], Part[$CellContext`axdata, Floor[$CellContext`jj]]}, Joined -> True, Frame -> True, PlotStyle -> { Directive[Blue, Thick], Directive[Green, Thick]}, FrameLabel -> {"Cell (Apoplast) index", "Auxin [\[Mu]M]"}, ImageSize -> 450, PlotRange -> {{0, $CellContext`L}, {0, 200}}, LabelStyle -> Directive[$CellContext`fz]]; $CellContext`grtans = ListPlot[{$CellContext`influx, $CellContext`efflux}, Joined -> True, Frame -> True, FrameLabel -> {"Cell (Apoplast) index", "Normalized carriers"}, PlotStyle -> { Directive[Black, Thick], Directive[Gray, Thick, Dashed]}, ImageSize -> 450, LabelStyle -> Directive[$CellContext`fz]]; Show[ GraphicsGrid[{{$CellContext`gra}, {$CellContext`grtans}}]]), "Specifications" :> {{{$CellContext`dminf$$, 100, "I"}, 0, 500}, {{$CellContext`e$$, 105., "E"}, 0, 1000}, {{$CellContext`ddd$$, 2., "D"}, 0, 10}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{530., {372., 377.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.6028750632176943`*^9, 3.60287510360858*^9, 3.602875151695238*^9, { 3.602875451907407*^9, 3.602875480491938*^9}, {3.602875536972549*^9, 3.602875573886723*^9}, 3.602875615228848*^9, 3.602875659911249*^9, { 3.6028756992230883`*^9, 3.602875718528224*^9}, 3.602875771819889*^9, 3.602875815617082*^9, 3.602876306886694*^9, 3.6028764157372427`*^9, { 3.608477134223852*^9, 3.608477162929449*^9}, 3.608477231650839*^9, { 3.60847727289013*^9, 3.6084773100391417`*^9}, 3.627914121672628*^9, 3.6279161243910017`*^9, 3.627916182580596*^9, 3.630793006238407*^9, 3.630793048600733*^9, 3.63079320054464*^9, 3.630793288160426*^9, 3.6307933664176617`*^9, 3.630794126627878*^9, 3.6307941725854816`*^9, 3.630794363185244*^9, 3.630795095717807*^9, {3.630795788825563*^9, 3.630795818059164*^9}, {3.630795860259615*^9, 3.6307958774426947`*^9}, { 3.631049114729871*^9, 3.6310491346844273`*^9}, 3.637135103450296*^9, { 3.637221906469021*^9, 3.6372219254219513`*^9}}] }, Open ]] }, Open ]] }, Open ]] }, WindowSize->{1169, 666}, WindowMargins->{{Automatic, 5}, {36, Automatic}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, FrontEndVersion->"9.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (November 20, \ 2012)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[579, 22, 385, 7, 148, "Title"], Cell[967, 31, 8249, 232, 413, "Text"], Cell[CellGroupData[{ Cell[9241, 267, 477, 7, 51, "Subtitle"], Cell[9721, 276, 1356, 20, 167, "Text"], Cell[CellGroupData[{ Cell[11102, 300, 30719, 742, 1797, "Input"], Cell[41824, 1044, 11058, 216, 766, "Output"] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)