(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 15026873, 453062] NotebookOptionsPosition[ 15024761, 452990] NotebookOutlinePosition[ 15025204, 453008] CellTagsIndexPosition[ 15025161, 453005] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Single-molecule imaging of UEs-Cy3 nanotube", "Title", CellChangeTimes->{{3.390570189208797*^9, 3.390570221682611*^9}}], Cell[CellGroupData[{ Cell["\<\ Simulation: probability of having n fluorophores in a diffraction limited \ spot\ \>", "Subsection"], Cell[TextData[{ "The ", StyleBox["Mathematica", FontSlant->"Italic"], " code is adapted from the material and methods section of\nClate M. \ Waterman-Storer and E. E. Salmon, Fluorcent speckle microscopt of \ microtubules: how low can you go? FASEB J. 13, S225-S230 (1999)" }], "Text"], Cell[TextData[{ "The resolvability (", StyleBox["r", FontSlant->"Italic"], ") of the imaging is diffraction limited ", Cell[BoxData[ FormBox[ RowBox[{"(", FractionBox["\[Lambda]", "2"], ")"}], TraditionalForm]]], ", where \[Lambda] is the wavelength of the illumination beam (532 nm in the \ current HYscope setup)." }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{"\[Lambda]", "=", "532"}], ";", RowBox[{"r", "=", "\[Lambda]"}], ";"}]], "Input"], Cell["Declare the value for the % labeled DAO-O monomer ", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ SuperscriptBox["5", "4"], "\[IndentingNewLine]", RowBox[{"f", "=", FractionBox["1", SuperscriptBox["5", "4"]]}]}], "Input", CellChangeTimes->{{3.390560333516102*^9, 3.390560335020193*^9}, 3.390560429227014*^9, 3.3905611744017067`*^9, {3.3905612109953003`*^9, 3.390561235113426*^9}, {3.3905614429153957`*^9, 3.39056144933148*^9}, { 3.390561546460804*^9, 3.390561549322488*^9}, {3.3905707913086042`*^9, 3.390570821972815*^9}, {3.390571070591967*^9, 3.3905710792796783`*^9}}], Cell[BoxData["625"], "Output", CellChangeTimes->{ 3.3905614502240458`*^9, 3.390561549888852*^9, {3.390570783445429*^9, 3.390570822683972*^9}, {3.390571072313424*^9, 3.390571080114868*^9}}], Cell[BoxData[ FractionBox["1", "625"]], "Output", CellChangeTimes->{ 3.3905614502240458`*^9, 3.390561549888852*^9, {3.390570783445429*^9, 3.390570822683972*^9}, {3.390571072313424*^9, 3.390571080125585*^9}}] }, Open ]], Cell["\<\ Based on JACS paper, each cross section of a DNA nanotube is measured to be \ 12.5 nm and predicted to contain 7 monomers. The mean of the number of \ fluorophores in a diffraction limited spot is 3 fluorophores\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"mean", "=", RowBox[{"N", "[", RowBox[{"r", " ", RowBox[{"(", FractionBox["7", "12.5"], ")"}], "f"}], " ", "]"}]}]], "Input", CellChangeTimes->{{3.390570981855693*^9, 3.3905709854808073`*^9}}], Cell[BoxData["0.47667200000000004`"], "Output", CellChangeTimes->{ 3.3905602178771753`*^9, 3.3905603366501017`*^9, 3.3905604398258057`*^9, 3.390560777550267*^9, 3.390561176421006*^9, {3.390561213528605*^9, 3.39056123683043*^9}, 3.390561459121722*^9, 3.39056155216634*^9, { 3.3905708005243464`*^9, 3.390570825059367*^9}, {3.3905710498613462`*^9, 3.390571081861032*^9}}] }, Open ]], Cell["\<\ Assumptions: 1. The coordinate of labeled subunits follows binomial distribution 2. There is no interaction between fluorophores. The incorporation of each \ fluorophore is purely random. 3. No photobleaching\ \>", "Text", CellChangeTimes->{{3.390570266217627*^9, 3.390570282388658*^9}}, Background->GrayLevel[0.900008]], Cell["Distribution for random association of subunits", "Text"], Cell[BoxData[ RowBox[{ RowBox[{"pdist", "=", RowBox[{"BinomialDistribution", "[", RowBox[{ RowBox[{"Round", "[", RowBox[{"r", " ", RowBox[{"(", FractionBox["7", "12.5"], ")"}]}], "]"}], ",", "f"}], "]"}]}], " ", ";"}]], "Input"], Cell[TextData[{ "Probability of ", StyleBox["n", FontSlant->"Italic"], " fluorophores per diffraction limited spot. " }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{"Prob", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"n", ",", RowBox[{"PDF", "[", RowBox[{"pdist", ",", "n"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", RowBox[{"30", " ", "mean"}]}], "}"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.390560799281023*^9, 3.390560800136142*^9}}], Cell[TextData[{ "Plot the probability as a function of ", StyleBox["n", FontSlant->"Italic"] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{"Prob", ",", RowBox[{"AxesOrigin", "\[Rule]", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"PointSize", "[", "0.015`", "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"TraditionalForm", "/@", RowBox[{"{", RowBox[{"\"\<# fluorophores\>\"", ",", "\"\\""}], "}"}]}]}], ",", RowBox[{"BaseStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", "\[Rule]", "11"}]}], "}"}]}], ",", RowBox[{"ImageSize", "\[Rule]", "300"}], ",", RowBox[{"GridLines", "\[Rule]", "None"}], ",", RowBox[{"Joined", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input", CellChangeTimes->{{3.390560461481423*^9, 3.3905604778150043`*^9}, { 3.390560508929435*^9, 3.3905605272837677`*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], PointSize[0.015], LineBox[{{0., 0.6205296773503222}, {1., 0.2963426984781987}, {2., 0.07052386333976364}, {3., 0.011151209160560917`}, {4., 0.0013179514031912943`}, {5., 0.00012419157453148733`}, {6., 9.719052173537871*^-6}, {7., 6.497168577548211*^-7}, {8., 3.787411971287118*^-8}, {9., 1.95575048374869*^-9}, {10., 9.057882849413002*^-11}, {11., 3.8005102864669945`*^-12}, {12., 1.4566592577671305`*^-13}, {13., 5.1356576395636005`*^-15}, {14., 1.6754377601598285`*^-16}}]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, BaseStyle->{FontFamily -> "Lucida Sans", FontSize -> 11}, Frame->True, FrameLabel->{ FormBox[ TagBox[ FormBox["\"# fluorophores\"", TraditionalForm], TraditionalForm, Editable -> True], TraditionalForm], FormBox[ TagBox[ FormBox["\"probability\"", TraditionalForm], TraditionalForm, Editable -> True], TraditionalForm]}, ImageSize->300, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.390560527831192*^9, {3.3905607838579884`*^9, 3.3905608027709*^9}, 3.390561181426023*^9, 3.390561218949391*^9, 3.390561260637919*^9, 3.390561472993515*^9, 3.390561558754263*^9, {3.390570806143847*^9, 3.390570830918713*^9}, 3.390571088882297*^9}] }, Open ]], Cell["\<\ This is the probability distribution that we would like to have, where the \ probability of having no label is still significant while still having a lot \ of monomers with ~4 fluorophors.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["\"Experiment\"", "Subsection"], Cell["\<\ Let's conside a NAAOMi nanotube with 100 resolvable units long \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"kmax", "=", "70"}], ";", RowBox[{"tube_length", "=", RowBox[{"kmax", " ", "r"}]}]}]], "Input", CellChangeTimes->{{3.390560815335023*^9, 3.39056081705617*^9}, { 3.390560900123404*^9, 3.390560900289732*^9}}], Cell[BoxData["37240"], "Output", CellChangeTimes->{ 3.3905602328905697`*^9, 3.390560350288311*^9, 3.39056048273997*^9, 3.390560535235559*^9, {3.390560809320266*^9, 3.390560817619773*^9}, 3.390560900954692*^9, 3.39056118525191*^9, 3.390561221877996*^9, 3.39056126554018*^9, 3.3905614792124*^9, 3.39056156262925*^9, { 3.390570809623898*^9, 3.3905708347729273`*^9}, 3.390571103220343*^9}] }, Open ]], Cell["\<\ , which corresponds to 20 \[Mu]m length DNA nanotube. 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