Team:Brown/Modeling/Parameters

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==Parameters==
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=Modeling Parameters=
As our circuit is relatively complex, we have many factors and thus many parameters with which to describe the function of these factors mathematically.  
As our circuit is relatively complex, we have many factors and thus many parameters with which to describe the function of these factors mathematically.  
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# K_m represents the ligand’s dissociation constant
# K_m represents the ligand’s dissociation constant
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  <title>Deterministic Modeling of a Bacterial Light Recognition Circuit</title>
 
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  <meta name="author" content="James W. Weis" />
 
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mi",output:"sinh",ttype:UNARY,func:true},{input:"\\sup",tag:"mo",output:"sup",ttype:UNDEROVER},{input:"\\tan",tag:"mi",output:"tan",ttype:UNARY,func:true},{input:"\\tanh",tag:"mi",output:"tanh",ttype:UNARY,func:true},{input:"\\gets",tag:"mo",output:"\u2190",ttype:CONST},{input:"\\leftarrow",tag:"mo",output:"\u2190",ttype:CONST},{input:"\\to",tag:"mo",output:"\u2192",ttype:CONST},{input:"\\rightarrow",tag:"mo",output:"\u2192",ttype:CONST},{input:"\\leftrightarrow",tag:"mo",output:"\u2194",ttype:CONST},{input:"\\uparrow",tag:"mo",output:"\u2191",ttype:CONST},{input:"\\downarrow",tag:"mo",output:"\u2193",ttype:CONST},{input:"\\updownarrow",tag:"mo",output:"\u2195",ttype:CONST},{input:"\\Leftarrow",tag:"mo",output:"\u21D0",ttype:CONST},{input:"\\Rightarrow",tag:"mo",output:"\u21D2",ttype:CONST},{input:"\\Leftrightarrow",tag:"mo",output:"\u21D4",ttype:CONST},{input:"\\iff",tag:"mo",output:"~\\Longleftrightarrow~",ttype:DEFINITION},{input:"\\Uparrow",tag:"mo",output:"\u21D1",ttype:CONST},{input:"\\Downarrow",tag:"mo",output:"\u21D3",ttype:CONST},{input:"\\Updownarrow",tag:"mo",output:"\u21D5",ttype:CONST},{input:"\\mapsto",tag:"mo",output:"\u21A6",ttype:CONST},{input:"\\longleftarrow",tag:"mo",output:"\u2190",ttype:LONG},{input:"\\longrightarrow",tag:"mo",output:"\u2192",ttype:LONG},{input:"\\longleftrightarrow",tag:"mo",output:"\u2194",ttype:LONG},{input:"\\Longleftarrow",tag:"mo",output:"\u21D0",ttype:LONG},{input:"\\Longrightarrow",tag:"mo",output:"\u21D2",ttype:LONG},{input:"\\Longleftrightarrow",tag:"mo",output:"\u21D4",ttype:LONG},{input:"\\longmapsto",tag:"mo",output:"\u21A6",ttype:CONST},AMsqrt,AMroot,AMfrac,AMover,AMsub,AMsup,AMtext,AMmbox,AMatop,AMchoose,{input:"\\acute",tag:"mover",output:"\u00B4",ttype:UNARY,acc:true},{input:"\\grave",tag:"mover",output:"\u0060",ttype:UNARY,acc:true},{input:"\\breve",tag:"mover",output:"\u02D8",ttype:UNARY,acc:true},{input:"\\check",tag:"mover",output:"\u02C7",ttype:UNARY,acc:true},{input:"\\dot",tag:"mover",output:".",ttype:UNARY,acc:true},{input:"\\ddot",tag:"mover",output:"..",ttype:UNARY,acc:true},{input:"\\mathring",tag:"mover",output:"\u00B0",ttype:UNARY,acc:true},{input:"\\vec",tag:"mover",output:"\u20D7",ttype:UNARY,acc:true},{input:"\\overrightarrow",tag:"mover",output:"\u20D7",ttype:UNARY,acc:true},{input:"\\overleftarrow",tag:"mover",output:"\u20D6",ttype:UNARY,acc:true},{input:"\\hat",tag:"mover",output:"\u005E",ttype:UNARY,acc:true},{input:"\\widehat",tag:"mover",output:"\u0302",ttype:UNARY,acc:true},{input:"\\tilde",tag:"mover",output:"~",ttype:UNARY,acc:true},{input:"\\widetilde",tag:"mover",output:"\u02DC",ttype:UNARY,acc:true},{input:"\\bar",tag:"mover",output:"\u203E",ttype:UNARY,acc:true},{input:"\\overbrace",tag:"mover",output:"\uFE37",ttype:UNARY,acc:true},{input:"\\overbracket",tag:"mover",output:"\u23B4",ttype:UNARY,acc:true},{input:"\\overline",tag:"mover",output:"\u00AF",ttype:UNARY,acc:true},{input:"\\underbrace",tag:"munder",output:"\uFE38",ttype:UNARY,acc:true},{input:"\\underbracket",tag:"munder",output:"\u23B5",ttype:UNARY,acc:true},{input:"\\underline",tag:"munder",output:"\u00AF",ttype:UNARY,acc:true},{input:"\\displaystyle",tag:"mstyle",atname:"displaystyle",atval:"true",ttype:UNARY},{input:"\\textstyle",tag:"mstyle",atname:"displaystyle",atval:"false",ttype:UNARY},{input:"\\scriptstyle",tag:"mstyle",atname:"scriptlevel",atval:"1",ttype:UNARY},{input:"\\scriptscriptstyle",tag:"mstyle",atname:"scriptlevel",atval:"2",ttype:UNARY},{input:"\\textrm",tag:"mstyle",output:"\\mathrm",ttype:DEFINITION},{input:"\\mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",ttype:UNARY},{input:"\\textbf",tag:"mstyle",atname:"mathvariant",atval:"bold",ttype:UNARY},{input:"\\mathit",tag:"mstyle",atname:"mathvariant",atval:"italic",ttype:UNARY},{input:"\\textit",tag:"mstyle",atname:"mathvariant",atval:"italic",ttype:UNARY},{input:"\\mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",ttype:UNARY},{input:"\\texttt",tag:"mstyle",atname:"mathvariant",atval:"monospace",ttype:UNARY},{input:"\\mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",ttype:UNARY},{input:"\\mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",ttype:UNARY,codes:AMbbb},{input:"\\mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",ttype:UNARY,codes:AMcal},{input:"\\mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",ttype:UNARY,codes:AMfrk},{input:"\\textcolor",tag:"mstyle",atname:"mathvariant",atval:"mathcolor",ttype:BINARY},{input:"\\colorbox",tag:"mstyle",atname:"mathvariant",atval:"background",ttype:BINARY}];function compareNames(s1,s2){if(s1.input>s2.input)return 1
 
-
  else return-1;}
 
-
  var AMnames=[];function AMinitSymbols(){AMsymbols.sort(compareNames);for(i=0;i<AMsymbols.length;i++)AMnames[i]=AMsymbols[i].input;}
 
-
  var AMmathml="http://www.w3.org/1998/Math/MathML";function AMcreateElementMathML(t){if(isIE)return document.createElement("m:"+t);else return document.createElementNS(AMmathml,t);}
 
-
  function AMcreateMmlNode(t,frag){if(isIE)var node=document.createElement("m:"+t);else var node=document.createElementNS(AMmathml,t);node.appendChild(frag);return node;}
 
-
  function newcommand(oldstr,newstr){AMsymbols=AMsymbols.concat([{input:oldstr,tag:"mo",output:newstr,ttype:DEFINITION}]);}
 
-
  function AMremoveCharsAndBlanks(str,n){var st;st=str.slice(n);for(var i=0;i<st.length&&st.charCodeAt(i)<=32;i=i+1);return st.slice(i);}
 
-
  function AMposition(arr,str,n){if(n==0){var h,m;n=-1;h=arr.length;while(n+1<h){m=(n+h)>>1;if(arr[m]<str)n=m;else h=m;}
 
-
  return h;}else
 
-
  for(var i=n;i<arr.length&&arr[i]<str;i++);return i;}
 
-
  function AMgetSymbol(str){var k=0;var j=0;var mk;var st;var tagst;var match="";var more=true;for(var i=1;i<=str.length&&more;i++){st=str.slice(0,i);j=k;k=AMposition(AMnames,st,j);if(k<AMnames.length&&str.slice(0,AMnames[k].length)==AMnames[k]){match=AMnames[k];mk=k;i=match.length;}
 
-
  more=k<AMnames.length&&str.slice(0,AMnames[k].length)>=AMnames[k];}
 
-
  AMpreviousSymbol=AMcurrentSymbol;if(match!=""){AMcurrentSymbol=AMsymbols[mk].ttype;return AMsymbols[mk];}
 
-
  AMcurrentSymbol=CONST;k=1;st=str.slice(0,1);if("0"<=st&&st<="9")tagst="mn";else tagst=(("A">st||st>"Z")&&("a">st||st>"z")?"mo":"mi");return{input:st,tag:tagst,output:st,ttype:CONST};}
 
-
  var AMpreviousSymbol,AMcurrentSymbol;function AMparseSexpr(str){var symbol,node,result,result2,i,st,newFrag=document.createDocumentFragment();str=AMremoveCharsAndBlanks(str,0);symbol=AMgetSymbol(str);if(symbol==null||symbol.ttype==RIGHTBRACKET)
 
-
  return[null,str,null];if(symbol.ttype==DEFINITION){str=symbol.output+AMremoveCharsAndBlanks(str,symbol.input.length);symbol=AMgetSymbol(str);if(symbol==null||symbol.ttype==RIGHTBRACKET)
 
-
  return[null,str,null];}
 
-
  str=AMremoveCharsAndBlanks(str,symbol.input.length);switch(symbol.ttype){case SPACE:node=AMcreateElementMathML(symbol.tag);node.setAttribute(symbol.atname,symbol.atval);return[node,str,symbol.tag];case UNDEROVER:if(isIE){if(symbol.input.substr(0,4)=="\\big"){str="\\"+symbol.input.substr(4)+str;symbol=AMgetSymbol(str);symbol.ttype=UNDEROVER;str=AMremoveCharsAndBlanks(str,symbol.input.length);}}
 
-
  return[AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag];case CONST:var output=symbol.output;if(isIE){if(symbol.input=="'")
 
-
  output="\u2032";else if(symbol.input=="''")
 
-
  output="\u2033";else if(symbol.input=="'''")
 
-
  output="\u2033\u2032";else if(symbol.input=="''''")
 
-
  output="\u2033\u2033";else if(symbol.input=="\\square")
 
-
  output="\u25A1";else if(symbol.input.substr(0,5)=="\\frac"){var denom=symbol.input.substr(6,1);if(denom=="5"||denom=="6"){str=symbol.input.replace(/\\frac/,"\\frac ")+str;return[node,str,symbol.tag];}}}
 
-
  node=AMcreateMmlNode(symbol.tag,document.createTextNode(output));return[node,str,symbol.tag];case LONG:node=AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output));node.setAttribute("minsize","1.5");node.setAttribute("maxsize","1.5");node=AMcreateMmlNode("mover",node);node.appendChild(AMcreateElementMathML("mspace"));return[node,str,symbol.tag];case STRETCHY:if(isIE&&symbol.input=="\\backslash")
 
-
  symbol.output="\\";node=AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output));if(symbol.input=="|"||symbol.input=="\\vert"||symbol.input=="\\|"||symbol.input=="\\Vert"){node.setAttribute("lspace","0em");node.setAttribute("rspace","0em");}
 
-
  node.setAttribute("maxsize",symbol.atval);if(symbol.rtag!=null)
 
-
  return[node,str,symbol.rtag];else
 
-
  return[node,str,symbol.tag];case BIG:var atval=symbol.atval;if(isIE)
 
-
  atval=symbol.ieval;symbol=AMgetSymbol(str);if(symbol==null)
 
-
  return[null,str,null];str=AMremoveCharsAndBlanks(str,symbol.input.length);node=AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output));if(isIE){var space=AMcreateElementMathML("mspace");space.setAttribute("height",atval+"ex");node=AMcreateMmlNode("mrow",node);node.appendChild(space);}else{node.setAttribute("minsize",atval);node.setAttribute("maxsize",atval);}
 
-
  return[node,str,symbol.tag];case LEFTBRACKET:if(symbol.input=="\\left"){symbol=AMgetSymbol(str);if(symbol!=null){if(symbol.input==".")
 
-
  symbol.invisible=true;str=AMremoveCharsAndBlanks(str,symbol.input.length);}}
 
-
  result=AMparseExpr(str,true,false);if(symbol==null||(typeof symbol.invisible=="boolean"&&symbol.invisible))
 
-
  node=AMcreateMmlNode("mrow",result[0]);else{node=AMcreateMmlNode("mo",document.createTextNode(symbol.output));node=AMcreateMmlNode("mrow",node);node.appendChild(result[0]);}
 
-
  return[node,result[1],result[2]];case MATRIX:if(symbol.input=="\\begin{array}"){var mask="";symbol=AMgetSymbol(str);str=AMremoveCharsAndBlanks(str,0);if(symbol==null)
 
-
  mask="l";else{str=AMremoveCharsAndBlanks(str,symbol.input.length);if(symbol.input!="{")
 
-
  mask="l";else do{symbol=AMgetSymbol(str);if(symbol!=null){str=AMremoveCharsAndBlanks(str,symbol.input.length);if(symbol.input!="}")
 
-
  mask=mask+symbol.input;}}while(symbol!=null&&symbol.input!=""&&symbol.input!="}");}
 
-
  result=AMparseExpr("{"+str,true,true);node=AMcreateMmlNode("mtable",result[0]);mask=mask.replace(/l/g,"left ");mask=mask.replace(/r/g,"right ");mask=mask.replace(/c/g,"center ");node.setAttribute("columnalign",mask);node.setAttribute("displaystyle","false");if(isIE)
 
-
  return[node,result[1],null];var lspace=AMcreateElementMathML("mspace");lspace.setAttribute("width","0.167em");var rspace=AMcreateElementMathML("mspace");rspace.setAttribute("width","0.167em");var node1=AMcreateMmlNode("mrow",lspace);node1.appendChild(node);node1.appendChild(rspace);return[node1,result[1],null];}else{result=AMparseExpr("{"+str,true,true);node=AMcreateMmlNode("mtable",result[0]);if(isIE)
 
-
  node.setAttribute("columnspacing","0.25em");else
 
-
  node.setAttribute("columnspacing","0.167em");node.setAttribute("columnalign","right center left");node.setAttribute("displaystyle","true");node=AMcreateMmlNode("mrow",node);return[node,result[1],null];}
 
-
  case TEXT:if(str.charAt(0)=="{")i=str.indexOf("}");else i=0;if(i==-1)
 
-
  i=str.length;st=str.slice(1,i);if(st.charAt(0)==" "){node=AMcreateElementMathML("mspace");node.setAttribute("width","0.33em");newFrag.appendChild(node);}
 
-
  newFrag.appendChild(AMcreateMmlNode(symbol.tag,document.createTextNode(st)));if(st.charAt(st.length-1)==" "){node=AMcreateElementMathML("mspace");node.setAttribute("width","0.33em");newFrag.appendChild(node);}
 
-
  str=AMremoveCharsAndBlanks(str,i+1);return[AMcreateMmlNode("mrow",newFrag),str,null];case UNARY:result=AMparseSexpr(str);if(result[0]==null)return[AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str];if(typeof symbol.func=="boolean"&&symbol.func){st=str.charAt(0);if(st=="^"||st=="_"||st==","){return[AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag];}else{node=AMcreateMmlNode("mrow",AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)));if(isIE){var space=AMcreateElementMathML("mspace");space.setAttribute("width","0.167em");node.appendChild(space);}
 
-
  node.appendChild(result[0]);return[node,result[1],symbol.tag];}}
 
-
  if(symbol.input=="\\sqrt"){if(isIE){var space=AMcreateElementMathML("mspace");space.setAttribute("height","1.2ex");space.setAttribute("width","0em");node=AMcreateMmlNode(symbol.tag,result[0])
 
-
  node.appendChild(space);return[node,result[1],symbol.tag];}else
 
-
  return[AMcreateMmlNode(symbol.tag,result[0]),result[1],symbol.tag];}else if(typeof symbol.acc=="boolean"&&symbol.acc){node=AMcreateMmlNode(symbol.tag,result[0]);var output=symbol.output;if(isIE){if(symbol.input=="\\hat")
 
-
  output="\u0302";else if(symbol.input=="\\widehat")
 
-
  output="\u005E";else if(symbol.input=="\\bar")
 
-
  output="\u00AF";else if(symbol.input=="\\grave")
 
-
  output="\u0300";else if(symbol.input=="\\tilde")
 
-
  output="\u0303";}
 
-
  var node1=AMcreateMmlNode("mo",document.createTextNode(output));if(symbol.input=="\\vec"||symbol.input=="\\check")
 
-
  node1.setAttribute("maxsize","1.2");if(isIE&&symbol.input=="\\bar")
 
-
  node1.setAttribute("maxsize","0.5");if(symbol.input=="\\underbrace"||symbol.input=="\\underline")
 
-
  node1.setAttribute("accentunder","true");else
 
-
  node1.setAttribute("accent","true");node.appendChild(node1);if(symbol.input=="\\overbrace"||symbol.input=="\\underbrace")
 
-
  node.ttype=UNDEROVER;return[node,result[1],symbol.tag];}else{if(!isIE&&typeof symbol.codes!="undefined"){for(i=0;i<result[0].childNodes.length;i++)
 
-
  if(result[0].childNodes[i].nodeName=="mi"||result[0].nodeName=="mi"){st=(result[0].nodeName=="mi"?result[0].firstChild.nodeValue:result[0].childNodes[i].firstChild.nodeValue);var newst=[];for(var j=0;j<st.length;j++)
 
-
  if(st.charCodeAt(j)>64&&st.charCodeAt(j)<91)newst=newst+
 
-
  String.fromCharCode(symbol.codes[st.charCodeAt(j)-65]);else newst=newst+st.charAt(j);if(result[0].nodeName=="mi")
 
-
  result[0]=AMcreateElementMathML("mo").appendChild(document.createTextNode(newst));else result[0].replaceChild(AMcreateElementMathML("mo").appendChild(document.createTextNode(newst)),result[0].childNodes[i]);}}
 
-
  node=AMcreateMmlNode(symbol.tag,result[0]);node.setAttribute(symbol.atname,symbol.atval);if(symbol.input=="\\scriptstyle"||symbol.input=="\\scriptscriptstyle")
 
-
  node.setAttribute("displaystyle","false");return[node,result[1],symbol.tag];}
 
-
  case BINARY:result=AMparseSexpr(str);if(result[0]==null)return[AMcreateMmlNode("mo",document.createTextNode(symbol.input)),str,null];result2=AMparseSexpr(result[1]);if(result2[0]==null)return[AMcreateMmlNode("mo",document.createTextNode(symbol.input)),str,null];if(symbol.input=="\\textcolor"||symbol.input=="\\colorbox"){var tclr=str.match(/\{\s*([#\w]+)\s*\}/);str=str.replace(/\{\s*[#\w]+\s*\}/,"");if(tclr!=null){if(IsColorName.test(tclr[1].toLowerCase())){tclr=LaTeXColor[tclr[1].toLowerCase()];}else{tclr=tclr[1];}
 
-
  node=AMcreateElementMathML("mstyle");node.setAttribute(symbol.atval,tclr);node.appendChild(result2[0]);return[node,result2[1],symbol.tag];}}
 
-
  if(symbol.input=="\\root"||symbol.input=="\\stackrel")newFrag.appendChild(result2[0]);newFrag.appendChild(result[0]);if(symbol.input=="\\frac")newFrag.appendChild(result2[0]);return[AMcreateMmlNode(symbol.tag,newFrag),result2[1],symbol.tag];case INFIX:str=AMremoveCharsAndBlanks(str,symbol.input.length);return[AMcreateMmlNode("mo",document.createTextNode(symbol.output)),str,symbol.tag];default:return[AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag];}}
 
-
  function AMparseIexpr(str){var symbol,sym1,sym2,node,result,tag,underover;str=AMremoveCharsAndBlanks(str,0);sym1=AMgetSymbol(str);result=AMparseSexpr(str);node=result[0];str=result[1];tag=result[2];symbol=AMgetSymbol(str);if(symbol.ttype==INFIX){str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMparseSexpr(str);if(result[0]==null)
 
-
  result[0]=AMcreateMmlNode("mo",document.createTextNode("\u25A1"));str=result[1];tag=result[2];if(symbol.input=="_"||symbol.input=="^"){sym2=AMgetSymbol(str);tag=null;underover=((sym1.ttype==UNDEROVER)||(node.ttype==UNDEROVER));if(symbol.input=="_"&&sym2.input=="^"){str=AMremoveCharsAndBlanks(str,sym2.input.length);var res2=AMparseSexpr(str);str=res2[1];tag=res2[2];node=AMcreateMmlNode((underover?"munderover":"msubsup"),node);node.appendChild(result[0]);node.appendChild(res2[0]);}else if(symbol.input=="_"){node=AMcreateMmlNode((underover?"munder":"msub"),node);node.appendChild(result[0]);}else{node=AMcreateMmlNode((underover?"mover":"msup"),node);node.appendChild(result[0]);}
 
-
  node=AMcreateMmlNode("mrow",node);}else{node=AMcreateMmlNode(symbol.tag,node);if(symbol.input=="\\atop"||symbol.input=="\\choose")
 
-
  node.setAttribute("linethickness","0ex");node.appendChild(result[0]);if(symbol.input=="\\choose")
 
-
  node=AMcreateMmlNode("mfenced",node);}}
 
-
  return[node,str,tag];}
 
-
  function AMparseExpr(str,rightbracket,matrix){var symbol,node,result,i,tag,newFrag=document.createDocumentFragment();do{str=AMremoveCharsAndBlanks(str,0);result=AMparseIexpr(str);node=result[0];str=result[1];tag=result[2];symbol=AMgetSymbol(str);if(node!=undefined){if((tag=="mn"||tag=="mi")&&symbol!=null&&typeof symbol.func=="boolean"&&symbol.func){var space=AMcreateElementMathML("mspace");space.setAttribute("width","0.167em");node=AMcreateMmlNode("mrow",node);node.appendChild(space);}
 
-
  newFrag.appendChild(node);}}while((symbol.ttype!=RIGHTBRACKET)&&symbol!=null&&symbol.output!="");tag=null;if(symbol.ttype==RIGHTBRACKET){if(symbol.input=="\\right"){str=AMremoveCharsAndBlanks(str,symbol.input.length);symbol=AMgetSymbol(str);if(symbol!=null&&symbol.input==".")
 
-
  symbol.invisible=true;if(symbol!=null)
 
-
  tag=symbol.rtag;}
 
-
  if(symbol!=null)
 
-
  str=AMremoveCharsAndBlanks(str,symbol.input.length);var len=newFrag.childNodes.length;if(matrix&&len>0&&newFrag.childNodes[len-1].nodeName=="mrow"&&len>1&&newFrag.childNodes[len-2].nodeName=="mo"&&newFrag.childNodes[len-2].firstChild.nodeValue=="&"){var pos=[];var m=newFrag.childNodes.length;for(i=0;matrix&&i<m;i=i+2){pos[i]=[];node=newFrag.childNodes[i];for(var j=0;j<node.childNodes.length;j++)
 
-
  if(node.childNodes[j].firstChild.nodeValue=="&")
 
-
  pos[i][pos[i].length]=j;}
 
-
  var row,frag,n,k,table=document.createDocumentFragment();for(i=0;i<m;i=i+2){row=document.createDocumentFragment();frag=document.createDocumentFragment();node=newFrag.firstChild;n=node.childNodes.length;k=0;for(j=0;j<n;j++){if(typeof pos[i][k]!="undefined"&&j==pos[i][k]){node.removeChild(node.firstChild);row.appendChild(AMcreateMmlNode("mtd",frag));k++;}else frag.appendChild(node.firstChild);}
 
-
  row.appendChild(AMcreateMmlNode("mtd",frag));if(newFrag.childNodes.length>2){newFrag.removeChild(newFrag.firstChild);newFrag.removeChild(newFrag.firstChild);}
 
-
  table.appendChild(AMcreateMmlNode("mtr",row));}
 
-
  return[table,str];}
 
-
  if(typeof symbol.invisible!="boolean"||!symbol.invisible){node=AMcreateMmlNode("mo",document.createTextNode(symbol.output));newFrag.appendChild(node);}}
 
-
  return[newFrag,str,tag];}
 
-
  function AMparseMath(str){var result,node=AMcreateElementMathML("mstyle");var cclr=str.match(/\\color\s*\{\s*([#\w]+)\s*\}/);str=str.replace(/\\color\s*\{\s*[#\w]+\s*\}/g,"");if(cclr!=null){if(IsColorName.test(cclr[1].toLowerCase())){cclr=LaTeXColor[cclr[1].toLowerCase()];}else{cclr=cclr[1];}
 
-
  node.setAttribute("mathcolor",cclr);}else{if(mathcolor!="")node.setAttribute("mathcolor",mathcolor);};if(mathfontfamily!="")node.setAttribute("fontfamily",mathfontfamily);node.appendChild(AMparseExpr(str.replace(/^\s+/g,""),false,false)[0]);node=AMcreateMmlNode("math",node);if(showasciiformulaonhover)
 
-
  node.setAttribute("title",str.replace(/\s+/g," "));if(false){var fnode=AMcreateElementXHTML("font");fnode.setAttribute("face",mathfontfamily);fnode.appendChild(node);return fnode;}
 
-
  return node;}
 
-
  function AMstrarr2docFrag(arr,linebreaks){var newFrag=document.createDocumentFragment();var expr=false;for(var i=0;i<arr.length;i++){if(expr)newFrag.appendChild(AMparseMath(arr[i]));else{var arri=(linebreaks?arr[i].split("\n\n"):[arr[i]]);newFrag.appendChild(AMcreateElementXHTML("span").appendChild(document.createTextNode(arri[0])));for(var j=1;j<arri.length;j++){newFrag.appendChild(AMcreateElementXHTML("p"));newFrag.appendChild(AMcreateElementXHTML("span").appendChild(document.createTextNode(arri[j])));}}
 
-
  expr=!expr;}
 
-
  return newFrag;}
 
-
  function AMprocessNodeR(n,linebreaks){var mtch,str,arr,frg,i;if(n.childNodes.length==0){if((n.nodeType!=8||linebreaks)&&n.parentNode.nodeName!="form"&&n.parentNode.nodeName!="FORM"&&n.parentNode.nodeName!="textarea"&&n.parentNode.nodeName!="TEXTAREA"&&n.parentNode.nodeName!="pre"&&n.parentNode.nodeName!="PRE"){str=n.nodeValue;if(!(str==null)){str=str.replace(/\r\n\r\n/g,"\n\n");str=str.replace(/\x20+/g," ");str=str.replace(/\s*\r\n/g," ");mtch=(str.indexOf("\$")==-1?false:true);str=str.replace(/([^\\])\$/g,"$1 \$");str=str.replace(/^\$/," \$");arr=str.split(" \$");for(i=0;i<arr.length;i++)
 
-
  arr[i]=arr[i].replace(/\\\$/g,"\$");if(arr.length>1||mtch){if(checkForMathML){checkForMathML=false;var nd=AMisMathMLavailable();AMnoMathML=nd!=null;if(AMnoMathML&&notifyIfNoMathML)
 
-
  if(alertIfNoMathML)
 
-
  alert("To view the ASCIIMathML notation use Internet Explorer 6 +\nMathPlayer (free from www.dessci.com)\nor Firefox/Mozilla/Netscape");else AMbody.insertBefore(nd,AMbody.childNodes[0]);}
 
-
  if(!AMnoMathML){frg=AMstrarr2docFrag(arr,n.nodeType==8);var len=frg.childNodes.length;n.parentNode.replaceChild(frg,n);return len-1;}else return 0;}}}else return 0;}else if(n.nodeName!="math"){for(i=0;i<n.childNodes.length;i++)
 
-
  i+=AMprocessNodeR(n.childNodes[i],linebreaks);}
 
-
  return 0;}
 
-
  function AMprocessNode(n,linebreaks,spanclassAM){var frag,st;if(spanclassAM!=null){frag=document.getElementsByTagName("span")
 
-
  for(var i=0;i<frag.length;i++)
 
-
  if(frag[i].className=="AM")
 
-
  AMprocessNodeR(frag[i],linebreaks);}else{try{st=n.innerHTML;}catch(err){}
 
-
  if(st==null||st.indexOf("\$")!=-1)
 
-
  AMprocessNodeR(n,linebreaks);}
 
-
  if(isIE){frag=document.getElementsByTagName('math');for(var i=0;i<frag.length;i++)frag[i].update()}}
 
-
  var inAppendix=false;var sectionCntr=0;var IEcommentWarning=true;var biblist=[];var bibcntr=0;var LaTeXCounter=[];LaTeXCounter["definition"]=0;LaTeXCounter["proposition"]=0;LaTeXCounter["lemma"]=0;LaTeXCounter["theorem"]=0;LaTeXCounter["corollary"]=0;LaTeXCounter["example"]=0;LaTeXCounter["exercise"]=0;LaTeXCounter["subsection"]=0;LaTeXCounter["subsubsection"]=0;LaTeXCounter["figure"]=0;LaTeXCounter["equation"]=0;LaTeXCounter["table"]=0;var LaTeXColor=[];LaTeXColor["greenyellow"]="#D9FF4F";LaTeXColor["yellow"]="#FFFF00";LaTeXColor["goldenrod"]="#FFE529";LaTeXColor["dandelion"]="#FFB529";LaTeXColor["apricot"]="#FFAD7A";LaTeXColor["peach"]="#FF804D";LaTeXColor["melon"]="#FF8A80";LaTeXColor["yelloworange"]="#FF9400";LaTeXColor["orange"]="#FF6321";LaTeXColor["burntorange"]="#FF7D00";LaTeXColor["bittersweet"]="#C20300";LaTeXColor["redorange"]="#FF3B21";LaTeXColor["mahogany"]="#A60000";LaTeXColor["maroon"]="#AD0000";LaTeXColor["brickred"]="#B80000";LaTeXColor["red"]="#FF0000";LaTeXColor["orangered"]="#FF0080";LaTeXColor["rubinered"]="#FF00DE";LaTeXColor["wildstrawberry"]="#FF0A9C";LaTeXColor["salmon"]="#FF789E";LaTeXColor["carnationpink"]="#FF5EFF";LaTeXColor["magenta"]="#FF00FF";LaTeXColor["violetred"]="#FF30FF";LaTeXColor["rhodamine"]="#FF2EFF";LaTeXColor["mulberry"]="#A314FA";LaTeXColor["redviolet"]="#9600A8";LaTeXColor["fuchsia"]="#7303EB";LaTeXColor["lavender"]="#FF85FF";LaTeXColor["thistle"]="#E069FF";LaTeXColor["orchid"]="#AD5CFF";LaTeXColor["darkorchid"]="#9933CC";LaTeXColor["purple"]="#8C24FF";LaTeXColor["plum"]="#8000FF";LaTeXColor["violet"]="#361FFF";LaTeXColor["royalpurple"]="#401AFF";LaTeXColor["blueviolet"]="#1A0DF5";LaTeXColor["periwinkle"]="#6E73FF";LaTeXColor["cadetblue"]="#616EC4";LaTeXColor["cornflowerblue"]="#59DEFF";LaTeXColor["midnightblue"]="#007091";LaTeXColor["navyblue"]="#0F75FF";LaTeXColor["royalblue"]="#0080FF";LaTeXColor["blue"]="#0000FF";LaTeXColor["cerulean"]="#0FE3FF";LaTeXColor["cyan"]="#00FFFF";LaTeXColor["processblue"]="#0AFFFF";LaTeXColor["skyblue"]="#61FFE0";LaTeXColor["turquoise"]="#26FFCC";LaTeXColor["tealblue"]="#1FFAA3";LaTeXColor["aquamarine"]="#2EFFB2";LaTeXColor["bluegreen"]="#26FFAB";LaTeXColor["emerald"]="#00FF80";LaTeXColor["junglegreen"]="#03FF7A";LaTeXColor["seagreen"]="#4FFF80";LaTeXColor["green"]="#00FF00";LaTeXColor["forestgreen"]="#00E000";LaTeXColor["pinegreen"]="#00BF29";LaTeXColor["limegreen"]="#80FF00";LaTeXColor["yellowgreen"]="#8FFF42";LaTeXColor["springgreen"]="#BDFF3D";LaTeXColor["olivegreen"]="#009900";LaTeXColor["rawsienna"]="#8C0000";LaTeXColor["sepia"]="#4D0000";LaTeXColor["brown"]="#660000";LaTeXColor["tan"]="#DB9470";LaTeXColor["gray"]="#808080";LaTeXColor["grey"]="#808080";LaTeXColor["black"]="#000000";LaTeXColor["white"]="#FFFFFF";var IsColorName=/^(?:greenyellow|yellow|goldenrod|dandelion|apricot|peach|melon|yelloworange|orange|burntorange|bittersweet|redorange|mahogany|maroon|brickred|red|orangered|rubinered|wildstrawberry|salmon|carnationpink|magenta|violetred|rhodamine|mulberry|redviolet|fuchsia|lavender|thistle|orchid|darkorchid|purple|plum|violet|royalpurple|blueviolet|periwinkle|cadetblue|cornflowerblue|midnightblue|navyblue|royalblue|blue|cerulean|cyan|processblue|skyblue|turquoise|tealblue|aquamarine|bluegreen|emerald|junglegreen|seagreen|green|forestgreen|pinegreen|limegreen|yellowgreen|springgreen|olivegreen|rawsienna|sepia|brown|tan|gray|grey|black|white)$/;var IsCounter=/^(?:definition|proposition|lemma|theorem|corollary|example|exercise|subsection|subsubsection|figure|equation|table)$/;var IsLaTeXElement=/^(?:displayequation|title|author|address|date|abstract|keyword|section|subsection|subsubsection|ref|cite|thebibliography|definition|proposition|lemma|theorem|corollary|example|exercise|itemize|enumerate|enddefinition|endproposition|endlemma|endtheorem|endcorollary|endexample|endexercise|enditemize|endenumerate|LaTeXMathMLlabel|LaTeXMathML|smallskip|medskip|bigskip|quote|quotation|endquote|endquotation|center|endcenter|description|enddescription|inlinemath)$/;var IsTextOnlyArea=/^(?:form|textarea|pre)$/i;var tableid=0;function makeNumberString(cntr){if(sectionCntr>0){if(inAppendix){return"A"+sectionCntr+"."+cntr;}else{return sectionCntr+"."+cntr;}}else{return""+cntr;}};function LaTeXpreProcess(thebody){var TheBody=thebody;if(TheBody.hasChildNodes()){if(!(IsLaTeXElement.test(TheBody.className)))
 
-
  {for(var i=0;i<TheBody.childNodes.length;i++){LaTeXpreProcess(TheBody.childNodes[i])}}}
 
-
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-
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-
  if(isIE&&str.match(/%/g)!=null&&IEcommentWarning){alert("Comments may not have parsed properly.  Try putting in <pre class='LaTeX><div>..</div></pre> structure.");IEcommentWarning=false;}
 
-
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-
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-
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-
  >
 
-
</head>
 
-
<body>
 
-
<h1 class="title">Deterministic Modeling of a Bacterial Light Recognition Circuit</h1>
 
-
<h1 id="players"
 
-
>Players</h1
 
-
><p
 
-
>The following are the players that are used in the modeling of our circuit:</p
 
-
><h2 id="transcription-factors"
 
-
>Transcription factors</h2
 
-
><ol
 
-
><li
 
-
  ><p
 
-
    >LovTAP</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    >LovTAP* (After light-induced conformational change)</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    >tetR</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    >Mnt</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    >AraC</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    >LacI</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    >CI</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    >CI434</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    >GAL4</p
 
-
    ></li
 
-
  ></ol
 
-
><h2 id="reporters"
 
-
>Reporters</h2
 
-
><ol
 
-
><li
 
-
  ><p
 
-
    >S1</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    >S2</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    >S3</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    >S4</p
 
-
    ></li
 
-
  ></ol
 
-
><h2 id="constants"
 
-
>Constants</h2
 
-
><p
 
-
>The following are the constants for which we need to find online or determine experimentally:</p
 
-
><ol
 
-
><li
 
-
  ><p
 
-
    ><span class="LaTeX"
 
-
      >$\delta = \left\{
 
-
    \begin{array}{ll}
 
-
        0 & \mbox{without light}\\
 
-
        1 & \mbox{with light}
 
-
    \end{array}
 
-
\right.$</span
 
-
      ></p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    ><span class="LaTeX"
 
-
      >$c$</span
 
-
      > represents the rate of conformation change from LovTAP to LovTAP* under 470nm light.</p
 
-
    ></li
 
-
  ></ol
 
-
><h2 id="parameters"
 
-
>Parameters</h2
 
-
><ol
 
-
><li
 
-
  ><p
 
-
    ><span class="LaTeX"
 
-
      >$\alpha_x$</span
 
-
      > represents the <span class="LaTeX"
 
-
      >$x$</span
 
-
      >th synthesis rate <span class="LaTeX"
 
-
      >$\left(\dfrac{\text{nanomoles}}{\text{min}}\right)$</span
 
-
      >.<br
 
-
      /> <span class="LaTeX"
 
-
      >$\alpha=\left(\text{rate of transcription}\right)\times\left(\text{rate of translation}\right)$</span
 
-
      ><br
 
-
      /> For promoters for which reliable data is not available, we assume an average <em
 
-
      >E. coli</em
 
-
      > transcription speed to be 70 nucleotides/second = 4,200 nucleotides/min, and an average translation speed of 40 amino acids/second = 2400, which is then further regulated by the appropriate ribosome binding site, represented as a normalized constant. Thus, we use the following equation to calculate unknown synthesis rates[0]: <span class="LaTeX"
 
-
      >$$\alpha = \left(\frac{4200}{\text{gene length}}\right)\times\left(\frac{2400\times\text{RBS Strength}}{\text{protein length}}\right) $$</span
 
-
      ></p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$\alpha_1$</span
 
-
      > LovTAP synthesis rate constant <span class="LaTeX"
 
-
      >$= 1.06432\times10^{-13}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_2$</span
 
-
      > tetR synthesis rate constant <span class="LaTeX"
 
-
      >$= 1.15318\times10^{-13}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_3$</span
 
-
      > Mnt synthesis rate constant <span class="LaTeX"
 
-
      >$= 6.0562\times*10^{-13}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_4$</span
 
-
      > AraC synthesis rate constant <span class="LaTeX"
 
-
      >$= 5.99989\times10^{-14}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_5$</span
 
-
      > LacI synthesis rate constant <span class="LaTeX"
 
-
      >$= 3.94791\times10^{-14}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_6$</span
 
-
      > CI synthesis rate constant <span class="LaTeX"
 
-
      >$= 8.93023\times10^{-14}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_7$</span
 
-
      > CI434 synthesis rate constant <span class="LaTeX"
 
-
      >$= 1.2236\times10^{-13}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_8$</span
 
-
      > [check]SupD synthesis rate constant <span class="LaTeX"
 
-
      >$= 1.2236\times10^{-13}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_9$</span
 
-
      > [check]T7ptag synthesis rate constant <span class="LaTeX"
 
-
      >$= 1.2236\times10^{-13}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_{10}$</span
 
-
      > [check]GAL4 synthesis rate constant <span class="LaTeX"
 
-
      >$= 1.06432\times10^{-13}$</span
 
-
      > nanomoles.</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$\alpha_{11}$</span
 
-
      > S1 synthesis rate constant <span class="LaTeX"
 
-
      >$= 9.68992\times10^{-14}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_{12}$</span
 
-
      > S2 synthesis rate constant <span class="LaTeX"
 
-
      >$= 9.68992\times10^{-14}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_{13}$</span
 
-
      > S3 synthesis rate constant <span class="LaTeX"
 
-
      >$= 9.68992\times10^{-14}$</span
 
-
      > nanomoles. <span class="LaTeX"
 
-
      >$\alpha_{14}$</span
 
-
      > S4 synthesis rate constant <span class="LaTeX"
 
-
      >$= 9.68992\times10^{-14}$</span
 
-
      > nanomoles.</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    ><span class="LaTeX"
 
-
      >$\beta_x $</span
 
-
      > represents <span class="LaTeX"
 
-
      >$x$</span
 
-
      >th basal (un-induced or un-repressed) synthesis rate of a given promoter. We assume that, for all promoters, this is equal to 1% of the synthesis rate constant. <span class="LaTeX"
 
-
      >$$\forall x \ \beta_x = 0.1\alpha_x$$</span
 
-
      ></p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    ><span class="LaTeX"
 
-
      >$\mu_x$</span
 
-
      > represents the degradation rate of a given protein. When the degredation rate is unknown, we assume a decay of 0.012 proteins/min (half-life of one hour) <span class="LaTeX"
 
-
      >$\mu_1= 0.0453$</span
 
-
      > Rate of LovTAP degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_2= 0.0453$</span
 
-
      > Rate of LovTAP* degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_3 = 0.0453$</span
 
-
      > tetR degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_4= 0.0453$</span
 
-
      > Rate of Mnt degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_5= 0.0453$</span
 
-
      > Rate of AraC degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_6= 0.0453$</span
 
-
      > Rate of LacI degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_7= 0.0453$</span
 
-
      > Rate of CI degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_8= 0.0453$</span
 
-
      > Rate of CI434 degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_9= 00453$</span
 
-
      > Rate of SupD degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_{10}= 0.0453$</span
 
-
      > Rate of T7ptag degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_{11}= 0.012$</span
 
-
      > Rate of T7 polymerase degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_{12}= 0.012$</span
 
-
      > Rate of GAL4 degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_{13}= 0.012$</span
 
-
      > Rate of S1 degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_{14}= 0.012$</span
 
-
      > Rate of S2 degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_{15}= 0.012$</span
 
-
      > Rate of S3 degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ><span class="LaTeX"
 
-
      >$\mu_{16}= 0.012$</span
 
-
      > Rate of S4 degredation <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      ></p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    ><span class="LaTeX"
 
-
      >$n_x$</span
 
-
      > represents the hill coefficient for a given protein. <span class="LaTeX"
 
-
      >$n_1 = 1$</span
 
-
      > for LovTAP*</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$n_2 = 3$</span
 
-
      > for tetR)</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$n_3 = 2$</span
 
-
      > for CI</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$n_4 = 2$</span
 
-
      > for CI434</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$n_5 = 2$</span
 
-
      > Hill coefficient of GAL4</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$n_6 = 2$</span
 
-
      > Hill coefficient of AraC</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$n_7 = 2$</span
 
-
      > Hill coefficient of T7</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$n_8 = 2$</span
 
-
      > Hill coefficient of LacI</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$n_9 = 1$</span
 
-
      > Hill coefficient of Mnt</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    ><span class="LaTeX"
 
-
      >$K_x$</span
 
-
      > represents, for a given protein, the ligand concentration producing half occupation (ligand concentration occupying half of the binding sites) in nanomoles. This is also the infamous &quot;microscopic dissociation constant&quot;. <span class="LaTeX"
 
-
      >$K_{d1} = 142$</span
 
-
      > for LovTAP*</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$K_{d2} = 0.179$</span
 
-
      > for tetR</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$K_{d3} = 50$</span
 
-
      > for CI</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$K_{d4} = 40$</span
 
-
      > for CI434</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$K_{d5} = 0.5$</span
 
-
      > for GAL4</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$K_{d6} = 14$</span
 
-
      > for AraC</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$K_{d7} = 2$</span
 
-
      > for T7</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$K_{d8} = 800$</span
 
-
      >for LacI</p
 
-
    ><p
 
-
    ><span class="LaTeX"
 
-
      >$K_{d9} = 50$</span
 
-
      > for Mnt</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    ><span class="LaTeX"
 
-
      >$c$</span
 
-
      > <span class="LaTeX"
 
-
      >$c_1 = 20.20$</span
 
-
      >, which represents the rate of light-induced LovTAP to LovTAP* conformation change <span class="LaTeX"
 
-
      >$(1/sec)$</span
 
-
      > <span class="LaTeX"
 
-
      >$c_2 = 20.20$</span
 
-
      > which represents the rate of the reaction SupD + T7ptag <span class="LaTeX"
 
-
      >$\rightarrow$</span
 
-
      > T7</p
 
-
    ></li
 
-
  ><li
 
-
  ><p
 
-
    ><span class="LaTeX"
 
-
      >$\delta = \left\{
 
-
    \begin{array}{ll}
 
-
        0 & \mbox{without light}\\
 
-
        1 & \mbox{with light}
 
-
    \end{array}\right.$</span
 
-
      ></p
 
-
    ></li
 
-
  ></ol
 
-
>
 
-
</body>
 
-
</html>
 
-
</html>
 
 +
For a complete, up-to-date list of values and sensitivities, please see our current [http://www.brownigem.com/2010_parameters.ods spreadsheet of parameters and sensitivities] (or [http://www.brownigem.com/2010_parameters.xls here] for closed source Microsoft Excel format).
-
For a complete list of values and sensitivities, please see our [http://brownigem.com/parameters_2010.ods spreadsheet of parameters and sensitivities].
+
Alternatively, please see our prettier [http://www.brownigem.com/2010_parameters.pdf typeset PDF file].
 +
 
 +
 
 +
{| {{table}}
 +
| align="center" style="background:#f0f0f0;"|'''Brown iGEM 2010 – Modeling Parameters'''
 +
| align="center" style="background:#f0f0f0;"|''''''
 +
| align="center" style="background:#f0f0f0;"|''''''
 +
| align="center" style="background:#f0f0f0;"|''''''
 +
|-
 +
| ||||||
 +
|-
 +
| Parameter Name||Value||Units||Source
 +
|-
 +
| ||||||
 +
|-
 +
| LovTAP rate of maximum synthesis||1.0643E-013||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| tatR rate of maximum synthesis||1.1532E-013||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| Mnt rate of maximum synthesis||6.0562E-013||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| AraC rate of maximum synthesis||5.9999E-014||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| LacI rate of maximum synthesis||3.9479E-014||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| CI rate of maximum synthesis||8.9302E-014||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| CI434 rate of maximum synthesis||1.2236E-013||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| SupD rate of maximum synthesis||2.7149E-012||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| T7ptag rate of maximum synthesis||7.0208E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| GAL4 rate of maximum synthesis||2.9175E-013||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| S1 rate of maximum synthesis||9.6899E-014||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| ||||||
 +
|-
 +
| LovTAP rate of basal synthesis||1.0643E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| tatR rate of basal synthesis||1.1532E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| Mnt rate of basal synthesis||6.0562E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| AraC rate of basal synthesis||5.9999E-016||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| LacI rate of basal synthesis||3.9479E-016||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| CI rate of basal synthesis||8.9302E-016||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| CI434 rate of basal synthesis||1.2236E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| SupD rate of basal synthesis||2.7149E-014||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| T7ptag rate of basal synthesis||7.0208E-017||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| GAL4 rate of basal synthesis||2.9175E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| S1 rate of basal synthesis||9.6899E-016||nanomoles/min||Determined as explained in Brown 2010 wiki
 +
|-
 +
| ||||||
 +
|-
 +
| LovTAP degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
 +
|-
 +
| LovTAP* degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
 +
|-
 +
| tetR degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
 +
|-
 +
| Mnt degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
 +
|-
 +
| AraC degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
 +
|-
 +
| LacI degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
 +
|-
 +
| CI degradation rate||5.6061E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
 +
|-
 +
| CI434 degradation rate||1.2424E-001||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
 +
|-
 +
| SupD degradation rate||6.6667E-002||1/sec||As explained in wiki
 +
|-
 +
| T7ptag degradation rate||6.6667E-002||1/sec||As explained in wiki
 +
|-
 +
| T7 polymerase degradation rate||5.8333E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
 +
|-
 +
| GAL4 degradation rate||6.6667E-002||1/sec||As explained in wiki
 +
|-
 +
| S1 degradation rate||5.0000E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
 +
|-
 +
| S2 degradation rate||5.0000E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
 +
|-
 +
| S3 degradation rate||5.0000E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
 +
|-
 +
| S4 degradation rate||5.0000E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
 +
|-
 +
| ||||||
 +
|-
 +
| LovTAP* hill coefficient||1||||Estimate
 +
|-
 +
| tetR hill coefficient||3||||https://2007.igem.org/ETHZ/Parameters
 +
|-
 +
| CI hill coefficient||2||||https://2007.igem.org/ETHZ/Parameters
 +
|-
 +
| CI434 hill coefficient||2||||PKU 2009 wiki
 +
|-
 +
| GAL4 hill coefficient||2||||PKU 2009 wiki
 +
|-
 +
| AraC hill coefficient||2||||PKU 2009 wiki
 +
|-
 +
| T7 hill coefficient||2||||PKU 2009 wiki
 +
|-
 +
| LacI hill coefficient||2||||PKU 2009 wiki
 +
|-
 +
| Mnt hill coefficient||1||||PKU 2009 wiki
 +
|-
 +
| ||||||
 +
|-
 +
| LovTAP* dissociation constant||142.000||nanomoles||Light-activated DNA binding in a designed allosteric protein,Devin Strickland, Keith Moffat, and Tobin R. Sosnick
 +
|-
 +
| tetR dissociation constant||0.179||nanomoles||https://2007.igem.org/ETHZ/Parameters
 +
|-
 +
| CI dissociation constant||50.000||nanomoles||https://2007.igem.org/ETHZ/Parameters
 +
|-
 +
| CI434 dissociation constant||40.000||nanomoles||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
 +
|-
 +
| GAL4 dissociation constant||0.500||nanomoles||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
 +
|-
 +
| AraC dissociation constant||14.000||nanomoles||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
 +
|-
 +
| T7 dissociation constant||2.000||nanomoles||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
 +
|-
 +
| LacI dissociation constant||800.000||nanomoles||https://2007.igem.org/ETHZ/Parameters
 +
|-
 +
| Mnt dissociation constant||50.000||nanomoles||Estimate
 +
|-
 +
| ||||||
 +
|-
 +
| LovTAP → LovTAP* reaction rate||0.100||1/sec||Estimate
 +
|-
 +
| SupD + T7ptag → T7 reaction rate||0.100||1/sec||Estimate
 +
|-
 +
|
 +
|}

Latest revision as of 22:14, 27 October 2010

Modeling Parameters

As our circuit is relatively complex, we have many factors and thus many parameters with which to describe the function of these factors mathematically.

These parameters are as follows:

  1. δ is a function designed to represent the presence/absence of light in a Boolean fashion. δ=0 without light and 1 with light.
  2. c_1 represents the rate of conformational change from LovTAP to LovTAP* when irradiated with 470nm light.
  3. c_2 represents the rate of SupD + T7ptag --> T7 polymerase
  4. α represents the maximum protein synthesis rate in nanomoles/sec.
  5. β represents the basal synthesis rate. We assume ∀x β_x= .01α_x
  6. μ represents the protein degradation rate.
  7. n represents a ligand’s hill coefficient.
  8. K_m represents the ligand’s dissociation constant


For a complete, up-to-date list of values and sensitivities, please see our current [http://www.brownigem.com/2010_parameters.ods spreadsheet of parameters and sensitivities] (or [http://www.brownigem.com/2010_parameters.xls here] for closed source Microsoft Excel format).

Alternatively, please see our prettier [http://www.brownigem.com/2010_parameters.pdf typeset PDF file].


Brown iGEM 2010 – Modeling Parameters ' ' '
Parameter NameValueUnitsSource
LovTAP rate of maximum synthesis1.0643E-013nanomoles/minDetermined as explained in Brown 2010 wiki
tatR rate of maximum synthesis1.1532E-013nanomoles/minDetermined as explained in Brown 2010 wiki
Mnt rate of maximum synthesis6.0562E-013nanomoles/minDetermined as explained in Brown 2010 wiki
AraC rate of maximum synthesis5.9999E-014nanomoles/minDetermined as explained in Brown 2010 wiki
LacI rate of maximum synthesis3.9479E-014nanomoles/minDetermined as explained in Brown 2010 wiki
CI rate of maximum synthesis8.9302E-014nanomoles/minDetermined as explained in Brown 2010 wiki
CI434 rate of maximum synthesis1.2236E-013nanomoles/minDetermined as explained in Brown 2010 wiki
SupD rate of maximum synthesis2.7149E-012nanomoles/minDetermined as explained in Brown 2010 wiki
T7ptag rate of maximum synthesis7.0208E-015nanomoles/minDetermined as explained in Brown 2010 wiki
GAL4 rate of maximum synthesis2.9175E-013nanomoles/minDetermined as explained in Brown 2010 wiki
S1 rate of maximum synthesis9.6899E-014nanomoles/minDetermined as explained in Brown 2010 wiki
LovTAP rate of basal synthesis1.0643E-015nanomoles/minDetermined as explained in Brown 2010 wiki
tatR rate of basal synthesis1.1532E-015nanomoles/minDetermined as explained in Brown 2010 wiki
Mnt rate of basal synthesis6.0562E-015nanomoles/minDetermined as explained in Brown 2010 wiki
AraC rate of basal synthesis5.9999E-016nanomoles/minDetermined as explained in Brown 2010 wiki
LacI rate of basal synthesis3.9479E-016nanomoles/minDetermined as explained in Brown 2010 wiki
CI rate of basal synthesis8.9302E-016nanomoles/minDetermined as explained in Brown 2010 wiki
CI434 rate of basal synthesis1.2236E-015nanomoles/minDetermined as explained in Brown 2010 wiki
SupD rate of basal synthesis2.7149E-014nanomoles/minDetermined as explained in Brown 2010 wiki
T7ptag rate of basal synthesis7.0208E-017nanomoles/minDetermined as explained in Brown 2010 wiki
GAL4 rate of basal synthesis2.9175E-015nanomoles/minDetermined as explained in Brown 2010 wiki
S1 rate of basal synthesis9.6899E-016nanomoles/minDetermined as explained in Brown 2010 wiki
LovTAP degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
LovTAP* degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
tetR degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
Mnt degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
AraC degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
LacI degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
CI degradation rate5.6061E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
CI434 degradation rate1.2424E-0011/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
SupD degradation rate6.6667E-0021/secAs explained in wiki
T7ptag degradation rate6.6667E-0021/secAs explained in wiki
T7 polymerase degradation rate5.8333E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
GAL4 degradation rate6.6667E-0021/secAs explained in wiki
S1 degradation rate5.0000E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
S2 degradation rate5.0000E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
S3 degradation rate5.0000E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
S4 degradation rate5.0000E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
LovTAP* hill coefficient1Estimate
tetR hill coefficient3https://2007.igem.org/ETHZ/Parameters
CI hill coefficient2https://2007.igem.org/ETHZ/Parameters
CI434 hill coefficient2PKU 2009 wiki
GAL4 hill coefficient2PKU 2009 wiki
AraC hill coefficient2PKU 2009 wiki
T7 hill coefficient2PKU 2009 wiki
LacI hill coefficient2PKU 2009 wiki
Mnt hill coefficient1PKU 2009 wiki
LovTAP* dissociation constant142.000nanomolesLight-activated DNA binding in a designed allosteric protein,Devin Strickland, Keith Moffat, and Tobin R. Sosnick
tetR dissociation constant0.179nanomoleshttps://2007.igem.org/ETHZ/Parameters
CI dissociation constant50.000nanomoleshttps://2007.igem.org/ETHZ/Parameters
CI434 dissociation constant40.000nanomoleshttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
GAL4 dissociation constant0.500nanomoleshttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
AraC dissociation constant14.000nanomoleshttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
T7 dissociation constant2.000nanomoleshttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
LacI dissociation constant800.000nanomoleshttps://2007.igem.org/ETHZ/Parameters
Mnt dissociation constant50.000nanomolesEstimate
LovTAP → LovTAP* reaction rate0.1001/secEstimate
SupD + T7ptag → T7 reaction rate0.1001/secEstimate
Retrieved from "http://2010.igem.org/Team:Brown/Modeling/Parameters"