- Author:
- Randall Britten <r.britten@auckland.ac.nz>
- Date:
- 2013-09-13 17:17:29+12:00
- Desc:
- Initial value for HCO3 is now calculated from given initial pH and initial CO2 partial pressure, in the same way as in the Mathematica document. The system now remains at equilibrium :-)
Also, using kf = K kb, with kb=1 and K calculated from given pK = 6.1, which is apparently the accepted value in the textbooks.
Also, now actually using the initial values for CO2 concentration that was calculated from given partial pressure.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/178/rawfile/2b59edd002f0721d39e738789ddbbe9529b4de3e/pH Homeostasis.nb
(* 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[ 11551, 311]
NotebookOptionsPosition[ 10652, 280]
NotebookOutlinePosition[ 11007, 296]
CellTagsIndexPosition[ 10964, 293]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
RowBox[{
RowBox[{"initialPh", "=", "7.4"}], ";"}]], "Input",
CellChangeTimes->{{3.588028935288416*^9, 3.588028947630732*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"initialHmolar", "=",
SuperscriptBox["10",
RowBox[{"-", "initialPh"}]]}], ";"}]], "Input",
CellChangeTimes->{
3.588026866945672*^9, 3.588027345006266*^9, {3.588027526578341*^9,
3.588027528457705*^9}, {3.5880275950477552`*^9, 3.588027623943098*^9}, {
3.588028951319806*^9, 3.588028955827985*^9}, {3.588029035381466*^9,
3.5880290360526953`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"initialCO2mmHg", "=", "40"}], ";"}]], "Input",
CellChangeTimes->{{3.588028961701105*^9, 3.5880289701902637`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"solubilityMolarPerMmhg", "=", "0.03"}], ";"}]], "Input",
CellChangeTimes->{{3.588011381426174*^9, 3.5880113944215317`*^9}, {
3.588029074748098*^9, 3.588029092014204*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"initialCO2molar", "=",
FractionBox[
RowBox[{"initialCO2mmHg", " ", "solubilityMolarPerMmhg"}], "1000"]}],
";"}]], "Input",
CellChangeTimes->{
3.588026852226532*^9, 3.588026943288953*^9, {3.5880275452983923`*^9,
3.58802754682507*^9}, {3.588027627063496*^9, 3.588027635999963*^9}, {
3.588028977886209*^9, 3.588029022197158*^9}, {3.588030010813973*^9,
3.5880300116060743`*^9}, {3.588032567434842*^9, 3.58803257466298*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"pKfromTextbook", "=", "6.1"}], ";"}]], "Input",
CellChangeTimes->{{3.588028556376622*^9, 3.58802856809615*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"KfromTextbook", "=",
SuperscriptBox["10",
RowBox[{"-", "pKfromTextbook"}]]}], ";"}]], "Input",
CellChangeTimes->{{3.588012103263454*^9, 3.588012122807251*^9},
3.588012563011053*^9, 3.588029064612894*^9, {3.5880300336289062`*^9,
3.588030043062311*^9}, 3.588033492664633*^9, 3.588034881261235*^9}],
Cell[BoxData[
RowBox[{
RowBox[{"initialHCO3molar", "=",
RowBox[{"initialCO2molar", " ",
FractionBox["KfromTextbook",
SuperscriptBox["10",
RowBox[{"-", "initialPh"}]]]}]}], ";"}]], "Input",
CellChangeTimes->{{3.588035465787499*^9, 3.588035507516808*^9}, {
3.588035570662325*^9, 3.588035584396131*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{
RowBox[{"pCO2", "[",
RowBox[{"pH_", ",", "HCO3_", ",", "K_"}], "]"}], ":=",
RowBox[{
FractionBox[
SuperscriptBox["10",
RowBox[{"-", "pH"}]], "K"],
FractionBox["HCO3", "solubilityMolarPerMmhg"]}]}], ";"}]], "Input",
CellChangeTimes->{{3.588011527879652*^9, 3.588011574290142*^9}, {
3.588011605456628*^9, 3.588011648639924*^9}, {3.5880119395225277`*^9,
3.588011941657003*^9}, {3.588029099237656*^9, 3.588029102004583*^9}, {
3.588029742140643*^9, 3.588029745588648*^9}, {3.5880298638730307`*^9,
3.588029870777545*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"KbyInitial", "=",
FractionBox[
RowBox[{"initialHmolar", " ", "initialHCO3molar"}], "initialCO2molar"]}],
";"}]], "Input",
CellChangeTimes->{{3.5880276531793737`*^9, 3.5880276717256613`*^9}, {
3.588027720485572*^9, 3.588027766262341*^9}, 3.588028516161331*^9, {
3.588029040884555*^9, 3.5880290519690933`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"pKbyInitial", " ", "=", " ",
RowBox[{"-",
RowBox[{"Log10", "[", "KbyInitial", "]"}]}]}], ";"}]], "Input",
CellChangeTimes->{{3.588027774043713*^9, 3.588027798668395*^9},
3.588028524865922*^9}],
Cell[BoxData[
RowBox[{"ContourPlot", "[",
RowBox[{
RowBox[{"pCO2", "[",
RowBox[{"pH", ",", "HCO3", ",", "KfromTextbook"}], "]"}], ",",
RowBox[{"{",
RowBox[{"pH", ",", "6.8", ",", "8"}], "}"}], ",",
RowBox[{"{",
RowBox[{"HCO3", ",", "0", ",", "100"}], "}"}], ",", "\[IndentingNewLine]",
RowBox[{"Contours", "\[Rule]",
RowBox[{"{",
RowBox[{"20", ",", "40", ",", "80"}], "}"}]}]}], "\[IndentingNewLine]",
"]"}]], "Input",
CellChangeTimes->{{3.588011703454999*^9, 3.5880117174087048`*^9}, {
3.5880117501903267`*^9, 3.588011883386302*^9}, {3.588012489020569*^9,
3.588012525930511*^9}, {3.58802796882439*^9, 3.5880279848488283`*^9}, {
3.5880303452699127`*^9, 3.588030350357877*^9}, {3.5880322855350943`*^9,
3.5880322876371603`*^9}, {3.5880324327627296`*^9, 3.588032437474824*^9}, {
3.588033246047154*^9, 3.5880332502935057`*^9}}],
Cell[BoxData[
RowBox[{"ContourPlot", "[",
RowBox[{
RowBox[{"pCO2", "[",
RowBox[{"pH", ",", "HCO3", ",", "KbyInitial"}], "]"}], ",",
RowBox[{"{",
RowBox[{"pH", ",", "6.8", ",", "8"}], "}"}], ",",
RowBox[{"{",
RowBox[{"HCO3", ",", "0", ",", "100"}], "}"}], ",", "\[IndentingNewLine]",
RowBox[{"Contours", "\[Rule]",
RowBox[{"{",
RowBox[{"20", ",", "40", ",", "80"}], "}"}]}]}], "\[IndentingNewLine]",
"]"}]], "Input",
CellChangeTimes->{{3.588011703454999*^9, 3.5880117174087048`*^9}, {
3.5880117501903267`*^9, 3.588011883386302*^9}, {3.588012489020569*^9,
3.588012525930511*^9}, {3.58802796882439*^9, 3.5880279848488283`*^9}, {
3.5880303452699127`*^9, 3.5880303962599163`*^9}, {3.58803326679*^9,
3.588033269893515*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{
RowBox[{"J", "[",
RowBox[{"CO2_", ",", "H_", ",", "HCO3_", ",", "K_"}], "]"}], ":=",
"\[IndentingNewLine]",
RowBox[{"With", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"kb", "=", "1"}], ",",
RowBox[{"kf", "=", "K"}]}], "}"}], ",", "\[IndentingNewLine]",
RowBox[{
RowBox[{"kf", " ", "CO2"}], "-",
RowBox[{"kb", " ", "H", " ", "HCO3"}]}]}], "]"}]}], ";"}]], "Input",
CellChangeTimes->{{3.588018786296715*^9, 3.588018834936934*^9}, {
3.58803064993417*^9, 3.588030702244219*^9}, {3.588030736556336*^9,
3.5880307392600393`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"s2", "=",
RowBox[{"NDSolve", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"{", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"H", "'"}], "[", "t", "]"}], "\[Equal]",
RowBox[{"J", "[",
RowBox[{
RowBox[{"CO2", "[", "t", "]"}], ",",
RowBox[{"H", "[", "t", "]"}], ",",
RowBox[{"HCO3", "[", "t", "]"}], ",", "KfromTextbook"}], "]"}]}],
",", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"HCO3", "'"}], "[", "t", "]"}], "==",
RowBox[{"J", "[",
RowBox[{
RowBox[{"CO2", "[", "t", "]"}], ",",
RowBox[{"H", "[", "t", "]"}], ",",
RowBox[{"HCO3", "[", "t", "]"}], ",", "KfromTextbook"}], "]"}]}],
",", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"CO2", "'"}], "[", "t", "]"}], "\[Equal]", "0"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"H", "[", "0", "]"}], "\[Equal]", "initialHmolar"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"CO2", "[", "0", "]"}], "\[Equal]", "initialCO2molar"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"HCO3", "[", "0", "]"}], "\[Equal]", "initialHCO3molar"}]}],
"\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]",
RowBox[{"{",
RowBox[{"H", ",", "HCO3", ",", "CO2"}], "}"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "100"}], "}"}]}], "]"}]}], ";"}]], "Input",
CellChangeTimes->{{3.588018715475564*^9, 3.5880187162902117`*^9}, {
3.588018840234191*^9, 3.588018998732294*^9}, {3.588019038114986*^9,
3.5880191392578297`*^9}, {3.58801919229058*^9, 3.5880192037189703`*^9}, {
3.5880192708295116`*^9, 3.5880193124369717`*^9}, 3.588019393691187*^9, {
3.588019780866252*^9, 3.588019781165984*^9}, {3.5880267892763033`*^9,
3.588026813484517*^9}, {3.588027037873416*^9, 3.5880270428576*^9}, {
3.588027279146137*^9, 3.588027321720139*^9}, {3.5880273575433826`*^9,
3.5880273907936583`*^9}, {3.588027420862603*^9, 3.5880274750777607`*^9}, {
3.5880280434626217`*^9, 3.5880280573032427`*^9}, {3.5880291201567917`*^9,
3.588029129520361*^9}, {3.588029918088847*^9, 3.5880299189117603`*^9}, {
3.588030715718298*^9, 3.588030723876318*^9}}],
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{
RowBox[{"{",
RowBox[{"-",
RowBox[{"Log10", "[",
RowBox[{"H", "[", "t", "]"}], "]"}]}], "}"}], "/.", "s2"}], "]"}],
",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "100"}], "}"}], ",",
RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input",
CellChangeTimes->{{3.5880193595553627`*^9, 3.588019419808826*^9}, {
3.588019586814019*^9, 3.588019640555421*^9}, {3.588019692218618*^9,
3.588019694042286*^9}, {3.588019750250059*^9, 3.588019813783346*^9}, {
3.5880299242152042`*^9, 3.5880299245991173`*^9}, 3.588033297268264*^9}],
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{
RowBox[{"{",
RowBox[{"1000", " ", "solubilityMolarPerMmhg", " ",
RowBox[{"CO2", "[", "t", "]"}]}], "}"}], "/.", "s2"}], "]"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "100"}], "}"}], ",",
RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input",
CellChangeTimes->{{3.5880193595553627`*^9, 3.588019419808826*^9}, {
3.588019586814019*^9, 3.588019640555421*^9}, {3.588019692218618*^9,
3.588019694042286*^9}, {3.588019750250059*^9, 3.58801983773449*^9}, {
3.588029927447898*^9, 3.588029928206938*^9}, {3.5880332289800587`*^9,
3.5880332302508907`*^9}}],
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{
RowBox[{"{",
RowBox[{"1000", " ",
RowBox[{"HCO3", "[", "t", "]"}]}], "}"}], "/.", "s2"}], "]"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "100"}], "}"}], ",",
RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input",
CellChangeTimes->{{3.5880193595553627`*^9, 3.588019419808826*^9}, {
3.588019586814019*^9, 3.588019640555421*^9}, {3.588019692218618*^9,
3.588019694042286*^9}, {3.588019750250059*^9, 3.5880198711418*^9}, {
3.588029931103701*^9, 3.5880299319987698`*^9}}]
},
WindowSize->{1440, 852},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"9.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (January 25, \
2013)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 143, 3, 28, "Input"],
Cell[703, 25, 400, 9, 33, "Input"],
Cell[1106, 36, 149, 3, 28, "Input"],
Cell[1258, 41, 208, 4, 28, "Input"],
Cell[1469, 47, 479, 10, 49, "Input"],
Cell[1951, 59, 147, 3, 28, "Input"],
Cell[2101, 64, 348, 7, 32, "Input"],
Cell[2452, 73, 328, 8, 51, "Input"],
Cell[2783, 83, 594, 14, 53, "Input"],
Cell[3380, 99, 361, 8, 49, "Input"],
Cell[3744, 109, 241, 6, 28, "Input"],
Cell[3988, 117, 884, 18, 63, "Input"],
Cell[4875, 137, 776, 17, 63, "Input"],
Cell[5654, 156, 654, 17, 80, "Input"],
Cell[6311, 175, 2365, 52, 182, "Input"],
Cell[8679, 229, 667, 16, 28, "Input"],
Cell[9349, 247, 689, 15, 28, "Input"],
Cell[10041, 264, 607, 14, 28, "Input"]
}
]
*)
(* End of internal cache information *)