(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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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[ 298709, 8684]*) (*NotebookOutlinePosition[ 299723, 8714]*) (* CellTagsIndexPosition[ 299679, 8710]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\( (*\ Stationary\ analysis\ of\ insulin\ clearance\ \ *) \)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\( (*\ All\ rates\ are\ in\ nmol/\((l*s)\); \ all\ concentrations\ in\ nM; \ all\ amounts\ of\ substances\ in\ nmol; \ all\ volumes\ in\ l\ \ *) \)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\(\(Param = {kins \[Rule] 10^\((\(-3\))\), kins1d \[Rule] 4*10^\((\(-4\))\), kins2d \[Rule] 4*10^\((\(-2\))\), kins1den \[Rule] 1.925*10^\((\(-3\))\), kins2den \[Rule] 3.85*10^\((\(-3\))\), kyd \[Rule] 0.00385, kyden \[Rule] 0.00722, kyp \[Rule] 0.0231, intk1 \[Rule] 5.5*10^\((\(-4\))\), intk2 \[Rule] 2*10^\((\(-4\))\), reck1 \[Rule] 1.533*10^\((\(-3\))\)};\)\[IndentingNewLine] \(Rtotal = 40;\)\[IndentingNewLine] \(ReceptorBalance = {I2Rpen \[Rule] Rtotal - R - IR - I2R - Rp - IRp - I2Rp - Ren - IRen - I2Ren - Rpen - IRpen};\)\[IndentingNewLine]\[IndentingNewLine] \(Rates = {r1 \[Rule] kins*R*Ins - kins1d*IR, r2 \[Rule] kins*Rp*Ins - kins1d*IRp, r3 \[Rule] kins*IR*Ins - kins2d*I2R, r4 \[Rule] kins*IRp*Ins - kins2d*I2Rp, r5 \[Rule] kyd*Rp, r6 \[Rule] kyp*IR - kyd*IRp, r7 \[Rule] kyp*I2R - kyd*I2Rp, i1 \[Rule] kins1den*IRen, i2 \[Rule] kins1den*IRpen, i3 \[Rule] kins2den*I2Ren, i4 \[Rule] kins2den*I2Rpen, i5 \[Rule] kyden*Rpen, i6 \[Rule] kyp*IRen - kyden*IRpen, i7 \[Rule] kyp*I2Ren - kyden*I2Rpen, f1 \[Rule] intk2*R - reck1*Ren, f2 \[Rule] intk2*IR, f3 \[Rule] intk2*I2R, f4 \[Rule] intk1*Rp - reck1*Rpen, f5 \[Rule] intk1*IRp, f6 \[Rule] intk1*I2Rp};\)\[IndentingNewLine]\[IndentingNewLine] \(Liver = {\(-r1\) + r5 - f1 \[Equal] 0, r1 - r3 - r6 - f2 \[Equal] 0, r3 - r7 - f3 \[Equal] 0, \(-r2\) - r5 - f4 \[Equal] 0, r2 - r4 + r6 - f5 \[Equal] 0, r4 + r7 - f6 \[Equal] 0, i1 + i5 + f1 \[Equal] 0, \(-i1\) + i3 - i6 + f2 \[Equal] 0, \(-i3\) - i7 + f3 \[Equal] 0, i2 - i5 + f4 \[Equal] 0, \(-i2\) + i4 + i6 + f5 \[Equal] 0\ };\)\[IndentingNewLine]\[IndentingNewLine] \(RatesParametersBalance = \(Rates /. ReceptorBalance\) /. Param;\)\[IndentingNewLine]\[IndentingNewLine] \(LiverODE = Liver /. RatesParametersBalance;\)\[IndentingNewLine]\[IndentingNewLine] \(Circulation = {k1ub -> 0.35, k2ub -> 0.2, \[IndentingNewLine]RhoLiver -> 1.051*10^3, \[IndentingNewLine]Mliver -> 0.05*bw, \[IndentingNewLine]Vhep -> \((Mliver/ RhoLiver)\)*0.78, \[IndentingNewLine]Vdisse -> 0.272*Vhep* RhoLiver*10^\((\(-3\))\), \[IndentingNewLine]Vplasma \[Rule] 0.03375*bw*10^\((\(-3\))\), \[IndentingNewLine]Mkidney -> 2*0.85*bw/230, \n Kkidney -> \((0.0225/10^3)\)* Mkidney}\ ;\)\[IndentingNewLine]\[IndentingNewLine]\ \[IndentingNewLine]\[IndentingNewLine] RateLiver = \(-\((\(-r1\) - r2 - r3 - r4)\)\)*Vhep/Vplasma //. Circulation; \ (*nmol/\((l*s)\)*) \[IndentingNewLine]RateKidney = Kkidney*Ins/Vplasma //. Circulation; \ \ (*nmol/\((l* s)\)*) \[IndentingNewLine]\[IndentingNewLine]ErgLiver = Solve[LiverODE, {R, IR, I2R, Rp, IRp, I2Rp, Ren, IRen, I2Ren, Rpen, IRpen}];\[IndentingNewLine]\n \(RateLiverFinished = \(RateLiver /. RatesParametersBalance\) /. ErgLiver (*nmol/\((l*s)\)*) ;\)\[IndentingNewLine]\n \(RateTotal = RateLiverFinished + RateKidney;\)\[IndentingNewLine] \)\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*\ Initial\ conditions\ for\ simulation\ *) \)\(\[IndentingNewLine]\)\(\ \[IndentingNewLine]\)\(ErgLiverBasal = ErgLiver /. Ins \[Rule] 0.07\n I2RpenBasal \[Rule] Rtotal - R - IR - I2R - Rp - IRp - I2Rp - Ren - IRen - I2Ren - Rpen - IRpen /. ErgLiverBasal\n\n pansec = \(\(\((RateLiverFinished + RateKidney)\)/\((1 - Ins^n/\((Ins^n + ks^n)\))\) /. Ins \[Rule] 0.07\) /. ks \[Rule] 0.5\) /. n \[Rule] 10\[IndentingNewLine]\[IndentingNewLine] \)\)\)], "Input"], Cell[BoxData[ \({{I2Ren \[Rule] 0.00012129452102194183`, IRen \[Rule] 0.1455366602250341`, Ren \[Rule] 4.88527893589525`, IRpen \[Rule] 0.492463504703932`, Rpen \[Rule] 0.12260167668272581`, R \[Rule] 31.61895216072473`, Rp \[Rule] 0.22752768990696381`, IRp \[Rule] 2.072751008823521`, IR \[Rule] 0.43000717131576927`, I2R \[Rule] 0.0006963106738637042`, I2Rp \[Rule] 0.003630120432069776`}}\)], "Output"], Cell[BoxData[ \({I2RpenBasal \[Rule] 0.000433466095105306`}\)], "Output"], Cell[BoxData[ \({0.001697604982410232`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\( (*\ Initial\ condition\ for\ Ins_ub\ as\ a\ function\ of\ k1ub\ and\ k2ub\ \ *) \)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\(\(equbstat = {0 == \ \((k1ub*Ins*Vdisse - k2ub*Insub)\)/\((Vplasma)\)};\)\[IndentingNewLine] \(InsUbstat = Flatten[Solve[equbstat, Insub]];\)\[IndentingNewLine]\n (*general\ case\ *) \[IndentingNewLine] InsUbstat /. Ins \[Rule] 0.07\[IndentingNewLine] (*for\ literature\ values\ of\ k1ub\ and\ \ k2ub*) \[IndentingNewLine] \(InsUbstat /. Ins \[Rule] 0.07\) //. Circulation\)\)\)], "Input"], Cell[BoxData[ \({Insub \[Rule] \(0.07`\ k1ub\ Vdisse\)\/k2ub}\)], "Output"], Cell[BoxData[ \({Insub \[Rule] 1.2994800000000003`*^-6\ bw}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\( (*\ Insulin\ secretion\ at\ basal\ insulin\ concentration\ [ nM/s]\ *) \)\(\[IndentingNewLine]\)\(InsSecBas = RateLiverFinished + RateKidney /. Ins \[Rule] 0.07\[IndentingNewLine] (*\ Maximal\ insulin\ secretion\ in\ 10\ minutes\ [ nM]\ *) \[IndentingNewLine] InsSecBas*60*10\ \[IndentingNewLine]\[IndentingNewLine] \)\)\)], "Input"], Cell[BoxData[ \({0.0016976049774998306`}\)], "Output"], Cell[BoxData[ \({1.0185629864998984`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\( (*\ Insulin\ removal\ rates\ *) \)\(\[IndentingNewLine]\)\(\ \[IndentingNewLine]\)\(\n\)\(\(FigRates = Plot[{RateTotal, RateLiverFinished, RateKidney}, {Ins, 0, 5}, PlotStyle \[Rule] {RGBColor[0, 0, 0], RGBColor[1, 0, 0], RGBColor[0, 0, 1]}, FrameLabel \[Rule] \ {"\", "\"}, (*\(RotateLabel \[Rule] False\)\(,\)*) \ Frame \[Rule] \ True, \ PlotRange \[Rule] \ {All, All}, ImageSize \[Rule] \ 400]\)\(\[IndentingNewLine]\) \)\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 %%ImageSize: 400 247.214 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind 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"Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*\ Clearance\ ranges\ for\ rats\ *) \)\(\[IndentingNewLine]\)\(\ \[IndentingNewLine]\)\(MinInsClearance = Limit[ClearanceLiver, Ins \[Rule] 0] + ClearanceKidney\[IndentingNewLine] MaxInsClearance = \(\(Limit[ClearanceLiver, Ins \[Rule] Infinity] + ClearanceKidney\)\(\[IndentingNewLine]\) \)\)\)\)], "Input"], Cell[BoxData[ \({10.668607300424323`}\)], "Output"], Cell[BoxData[ \({1.9956521739130428`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*\ Insulin\ binding\ at\ cell\ surface\ *) \)\(\[IndentingNewLine]\)\(\ \[IndentingNewLine]\)\(<< Graphics`MultipleListPlot`\[IndentingNewLine]\[IndentingNewLine] \(ReceptorInsBound = \(\(\(\((\((IR + 2*I2R + IRp + 2*I2Rp)\)*Vhep + Insub)\)/bw /. InsUbstat\) /. ReceptorBalance\) /. ErgLiver\) //. Circulation;\)\[IndentingNewLine]\[IndentingNewLine]\ \[IndentingNewLine] (*\ In\ silico\ reproduction\ of\ experimental\ \(data : \ \[IndentingNewLine]0.01\ nM\ labeled\ insulin\), \ varying\ concentration\ of\ unlabeled\ \(\(insulin\)\(.\)\)\ *) \n\ \[IndentingNewLine] \(ReceptorInsBoundLog = \((0.01/\((Ins)\))\)\ ReceptorInsBound /. Ins \[Rule] \((0.01 + 10^ex)\);\)\[IndentingNewLine]\[IndentingNewLine]\ \[IndentingNewLine] (*\ Data\ points\ are\ cell\ associated\ labeled\ insulin\ [ cpm/\[Micro]g\ DNA]; Background\ \((bgr)\) was\ substracted\ *) \[IndentingNewLine]\[IndentingNewLine] \(Klein2002ins = {{\(-2\), 101.04761904761904`}, {\(-1.5`\), 102.47619047619047`}, {\(-1\), 100.57142857142857`}, {\(-0.5`\), 79.6190476190476`}, {0, 47.23809523809524`}, {0.5`, 28.666666666666664`}, {1, 14.857142857142856`}, {1.5`, 5.333333333333334`}, {2, 0.9523809523809532`}, {4, 0.`}};\)\[IndentingNewLine] \(Klein2002insEB = {{{\(-2\), 101.04761904761904`}, ErrorBar[{\(-3.8095238095238098`\), 3.8095238095238098`}]}, {{\(-1.5`\), 102.47619047619047`}, ErrorBar[{\(-3.8095238095238098`\), 3.8095238095238098`}]}, {{\(-1\), 100.57142857142857`}, ErrorBar[{\(-3.8095238095238098`\), 3.8095238095238098`}]}, {{\(-0.5`\), 79.6190476190476`}, ErrorBar[{\(-2.857142857142857`\), 2.857142857142857`}]}, {{0, 47.23809523809524`}, ErrorBar[{\(-2.857142857142857`\), 2.857142857142857`}]}, {{0.5`, 28.666666666666664`}, ErrorBar[{\(-1.9047619047619049`\), 1.9047619047619049`}]}, {{1, 14.857142857142856`}, ErrorBar[{\(-2.857142857142857`\), 2.857142857142857`}]}, {{1.5`, 5.333333333333334`}, ErrorBar[{\(-1.9047619047619049`\), 1.9047619047619049`}]}, {{2, 0.9523809523809532`}, ErrorBar[{\(-1.9047619047619049`\), 1.9047619047619049`}]}, {{4, 0.`}, ErrorBar[{\(-0.9523809523809524`\), 0.9523809523809524`}]}};\)\[IndentingNewLine]\ \[IndentingNewLine]\[IndentingNewLine]\ (*\ Projection\ of\ model\ output\ on\ experimental\ data\ \ *) \[IndentingNewLine]\[IndentingNewLine] \(ReceptorInsBoundLogFit\ = \ Fit[Klein2002ins, ReceptorInsBoundLog, ex];\)\[IndentingNewLine] FigInsModel = Plot[ReceptorInsBoundLogFit, {ex, \(-3\), 4}, PlotStyle \[Rule] {RGBColor[0, 0, 0]}, FrameLabel \[Rule] \ {"\", "\"}, \ Frame \[Rule] \ True, DisplayFunction \[Rule] \ Identity, PlotRange \[Rule] \ {All, 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{271.938, 75.1875}} -> {-6.49398, \ 35.9676, 0.0219833, 0.564119}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*\ Phosphorylated\ receptors\ *) \)\(\[IndentingNewLine]\)\(\ \[IndentingNewLine]\)\(\(ReceptorPhosphorylated = \(\((Rp + IRp + I2Rp + Rpen + IRpen + I2Rpen)\)/Rtotal /. ReceptorBalance\) /. ErgLiver;\)\n \(ReceptorPhosphorylatedLog = ReceptorPhosphorylated /. Ins \[Rule] 10^ex;\)\[IndentingNewLine] (*Activity\ data\ scaled\ on\ \ fractional\ receptor\ phosphorylation*) \[IndentingNewLine] (*y - data\ [cm]\ extracted\ from\ printout\ of\ plot\ \ *) \[IndentingNewLine]\[IndentingNewLine]\[IndentingNewLine] \(Klein2002phos = {{\(-2\), 0.035398230088495575`}, {\(-1\), 0.08495575221238938`}, {0, 0.39292035398230085`}, {1, 0.6300884955752213`}, {2, 0.6725663716814159`}};\)\[IndentingNewLine]\[IndentingNewLine] \(Klein2002phosEB = {{\(-2\), 0.035398230088495575`*facphos}, {\(-1\), 0.08495575221238938`*facphos}, {{0, 0.39292035398230085`*facphos}, ErrorBar[{\(-0.035398230088495575`\)*facphos, 0.035398230088495575`*facphos}]}, {{1, 0.6300884955752213`*facphos}, ErrorBar[{\(-0.07079646017699115`\)*facphos, 0.07079646017699115`*facphos}]}, {{2, 0.6725663716814159`*facphos}, ErrorBar[{\(-0.08495575221238938`\)*facphos, 0.08495575221238938`* facphos}]}};\)\[IndentingNewLine]\[IndentingNewLine] (*\ Projection\ of\ experimental\ data\ on\ model\ output\ \ 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InsUbstat\) /. ReceptorBalance\) /. ErgLiver\) //. Circulation;\)\[IndentingNewLine]\[IndentingNewLine] \(ReceptorIns2 = \(\(\(\((I2R + I2Ren + I2Rp + I2Rpen)\)/Rtotal /. InsUbstat\) /. ReceptorBalance\) /. ErgLiver\) //. Circulation;\)\[IndentingNewLine]\[IndentingNewLine] \(ReceptorInsPM = \(\(\(\((IR + I2R + IRp + I2Rp)\)/Rtotal /. InsUbstat\) /. ReceptorBalance\) /. ErgLiver\) //. Circulation;\)\n\[IndentingNewLine] \(ReceptorIns2PM = \(\(\(\((I2R + I2Rp)\)/Rtotal /. InsUbstat\) /. ReceptorBalance\) /. ErgLiver\) //. Circulation;\)\[IndentingNewLine] \(ReceptorInsEN = ReceptorIns - ReceptorInsPM;\)\[IndentingNewLine] \(ReceptorIns2EN = ReceptorIns2 - ReceptorIns2PM;\)\)\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*\ Percentage\ of\ receptors\ with\ two\ bound\ insulin\ at\ the\ basal\ \ insulin\ concentration\ and\ at\ 100\ nM\ insulin\ *) \)\(\[IndentingNewLine]\ \)\(\[IndentingNewLine]\)\(ReceptorIns2*100 /. Ins \[Rule] 0.07\[IndentingNewLine] ReceptorIns2*100 /. 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