Team:Duke/Modeling/Codes/Kinetic1

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(Difference between revisions)
(→Mathematical Modeling of Bistable Toggle Switch)
(→Mathematical Modeling of Bistable Toggle Switch)
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<div class="right_box">
<div class="right_box">
= '''Mathematical Modeling of Bistable Toggle Switch''' =
= '''Mathematical Modeling of Bistable Toggle Switch''' =
 +
 +
 +
Clear["Global`*"]
 +
k1 = 100;
 +
d1 = 0.007;
 +
k2 = 100;
 +
d2 = 0.007;
 +
K1 = k1/d1;
 +
K2 = k2/d2;
 +
Nns = 5*10^6;
 +
delEpd = -1.0421*10^-19;
 +
kb = 1.3806*10^-23;
 +
T = 298;
 +
P = 3000;
 +
\[Alpha] = Nns*E^(delEpd/(kb*T))/P;
 +
n = 5;
 +
(*Ksrd=;*)
 +
Knsrd = 10000;
 +
Stable1 = 0;
 +
Saddle1 = 0;
 +
Unstable1 = 0;
 +
matUp = {};
 +
matDown = {};
 +
RangeUp = {};
 +
RangeDown = {};
 +
For[Ksud = 0.01*10^-9, Ksud <= 7000*10^-9, Ksud = Ksud*1.1,
 +
Print[Ksud]
 +
 +
 +
Line 30: Line 60:
For[Ksud = 0.01*10^-9, Ksud <= 7000*10^-9, Ksud = Ksud*1.1,
For[Ksud = 0.01*10^-9, Ksud <= 7000*10^-9, Ksud = Ksud*1.1,
  Print[Ksud]
  Print[Ksud]
 +
  For[Ksvd = 0.01*10^-9, Ksvd <= 7000*10^-9, Ksvd = Ksvd*1.1,
 +
  Stable2 = 0;
 +
  Saddle2 = 0;
 +
  Unstable2 = 0;
 +
  delEud = kb*T*Log[10, Ksud/Knsrd];
 +
  delEvd = kb*T*Log[10, Ksvd/Knsrd];
 +
  xdot[x_, y_] :=
 +
    K1/(1 + \[Alpha] (1 + (y/Nns)*E^(-delEvd/(kb*T)))^n) - x;
 +
  ydot[x_, y_] :=
 +
    K2/(1 + \[Alpha] (1 + (x/Nns)*E^(-delEud/(kb*T)))^n) - y;
 +
  Jac[x_,
 +
    y_] := {{Derivative[1, 0][xdot][x, y],
 +
      Derivative[0, 1][xdot][x, y]}, {Derivative[1, 0][ydot][x, y],
 +
      Derivative[0, 1][ydot][x, y]}};
 +
  fps = NSolve[xdot[x, y] == 0 && ydot[x, y] == 0, {x, y}, Reals];
 +
  (*Print[N[fps,3]]*)
 +
  (*Print[Length[fps]-1]*)
 +
  For[i = 1, i < Length[fps] + 1, i++,
 +
    xtemp = x /. fps[[i]];
 +
    ytemp = y /. fps[[i]];
 +
    (*Print[N[xtemp,3]]*)
 +
    (*Print[N[ytemp,3]]*)
 +
    If[Im[xtemp] == 0 && Im[ytemp] == 0,
 +
      If[xtemp > 0 && ytemp > 0,
 +
      (*Print["              ",i-1,"  R1=",xtemp,"  R2=",ytemp,
 +
      "  Ksud=",Ksud,"  Ksvd=", Ksvd]*)
 +
      If[
 +
        Re[Eigenvalues[Jac[xtemp, ytemp]][[1]]] > 0 &&
 +
        Re[Eigenvalues[Jac[xtemp, ytemp]][[2]]] > 0,
 +
        Unstable2 += 1;
 +
        ];
 +
      If[
 +
        Re[Eigenvalues[Jac[xtemp, ytemp]][[1]]] < 0 &&
 +
        Re[Eigenvalues[Jac[xtemp, ytemp]][[2]]] < 0,
 +
        Stable2 += 1;
 +
        ];
 +
      If[
 +
        Re[Eigenvalues[Jac[xtemp, ytemp]][[1]]] < 0.0001 &&
 +
        Re[Eigenvalues[Jac[xtemp, ytemp]][[2]]] > 0.0001,
 +
        Saddle2 += 1;
 +
        ];
 +
      If[
 +
        Re[Eigenvalues[Jac[xtemp, ytemp]][[1]]] > 0.0001 &&
 +
        Re[Eigenvalues[Jac[xtemp, ytemp]][[2]]] < 0.0001,
 +
        Saddle2 += 1;
 +
        ];
 +
      ]
 +
      ]
 +
    ]
 +
    (*Print[Stable2, "  ", Stable1]*)
 +
    If[ (Stable2 == 2 && Stable1 == 1),
 +
    Print["Switch  (UP)"];
 +
    (*Print[{\[Alpha],\[Beta]}];*)
 +
    matUp = Insert[matUp, {Log[10, Ksud], Log[10, Ksvd]}, 1];
 +
    RangeUp = Insert[RangeUp, {Ksud, Ksvd}, 1];
 +
    ];
 +
  If[ ((Stable2 == 1 && Stable1 == 2)),
 +
    Print["Switch (DOWN)"];
 +
    (*Print[{\[Alpha],\[Beta]}];*)
 +
    matDown = Insert[matDown, {Log[10, Ksud], Log[10, Ksvd]}, 1];
 +
    RangeDown = Insert[RangeDown, {Ksud, Ksvd}, 1];
 +
    ];
 +
  If[(Stable2 == 2),
 +
    (*Print["BISTABLE ", \[Alpha], "  ",\[Beta], ",  Saddle: ",
 +
    Saddle2 ];*)
 +
    ];
 +
  If[ (Stable2 == 1),
 +
    (*Print["MONOSTABLE ",  \[Alpha],"  ",\[Beta],",  Saddle: ",
 +
    Saddle2 ];*)
 +
    ];
 +
  Saddle1 = Saddle2;
 +
  Unstable1 = Unstable2;
 +
  Stable1 = Stable2;
 +
  ]
 +
]
 +
 +
 +
 +
 +
   For[Ksvd = 0.01*10^-9, Ksvd <= 7000*10^-9, Ksvd = Ksvd*1.1,
   For[Ksvd = 0.01*10^-9, Ksvd <= 7000*10^-9, Ksvd = Ksvd*1.1,
   Stable2 = 0;
   Stable2 = 0;

Revision as of 09:10, 22 September 2013

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Mathematical Modeling of Bistable Toggle Switch

Clear["Global`*"] k1 = 100; d1 = 0.007; k2 = 100; d2 = 0.007; K1 = k1/d1; K2 = k2/d2; Nns = 5*10^6; delEpd = -1.0421*10^-19; kb = 1.3806*10^-23; T = 298; P = 3000; \[Alpha] = Nns*E^(delEpd/(kb*T))/P; n = 5; (*Ksrd=;*) Knsrd = 10000; Stable1 = 0; Saddle1 = 0; Unstable1 = 0; matUp = {}; matDown = {}; RangeUp = {}; RangeDown = {}; For[Ksud = 0.01*10^-9, Ksud <= 7000*10^-9, Ksud = Ksud*1.1, 

Print[Ksud]



Clear["Global`*"] k1 = 100; d1 = 0.007; k2 = 100; d2 = 0.007; K1 = k1/d1; K2 = k2/d2; Nns = 5*10^6; delEpd = -1.0421*10^-19; kb = 1.3806*10^-23; T = 298; P = 3000; \[Alpha] = Nns*E^(delEpd/(kb*T))/P; n = 5; (*Ksrd=;*) Knsrd = 10000; Stable1 = 0; Saddle1 = 0; Unstable1 = 0; matUp = {}; matDown = {}; RangeUp = {}; RangeDown = {}; For[Ksud = 0.01*10^-9, Ksud <= 7000*10^-9, Ksud = Ksud*1.1, 

Print[Ksud]
 For[Ksvd = 0.01*10^-9, Ksvd <= 7000*10^-9, Ksvd = Ksvd*1.1,
  Stable2 = 0;
  Saddle2 = 0;
  Unstable2 = 0;
  delEud = kb*T*Log[10, Ksud/Knsrd];
  delEvd = kb*T*Log[10, Ksvd/Knsrd];
  xdot[x_, y_] := 
   K1/(1 + \[Alpha] (1 + (y/Nns)*E^(-delEvd/(kb*T)))^n) - x; 
  ydot[x_, y_] := 
   K2/(1 + \[Alpha] (1 + (x/Nns)*E^(-delEud/(kb*T)))^n) - y; 
  Jac[x_, 
    y_] := {{Derivative[1, 0][xdot][x, y], 
     Derivative[0, 1][xdot][x, y]}, {Derivative[1, 0][ydot][x, y], 
     Derivative[0, 1][ydot][x, y]}};
  fps = NSolve[xdot[x, y] == 0 && ydot[x, y] == 0, {x, y}, Reals];
  (*Print[N[fps,3]]*)
  (*Print[Length[fps]-1]*)
  For[i = 1, i < Length[fps] + 1, i++,
    xtemp = x /. fpsi;
    ytemp = y /. fpsi;
    (*Print[N[xtemp,3]]*)
    (*Print[N[ytemp,3]]*)
    If[Im[xtemp] == 0 && Im[ytemp] == 0,
     If[xtemp > 0 && ytemp > 0,
      (*Print["              ",i-1,"  R1=",xtemp,"  R2=",ytemp, 
      "  Ksud=",Ksud,"   Ksvd=", Ksvd]*)
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] > 0 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] > 0,
       Unstable2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] < 0 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] < 0,
       Stable2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] < 0.0001 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] > 0.0001,
       Saddle2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] > 0.0001 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] < 0.0001,
       Saddle2 += 1;
       ];
      ]
     ]
    ]
   (*Print[Stable2, "  ", Stable1]*)
   If[ (Stable2 == 2 && Stable1 == 1),
    Print["Switch  (UP)"];
    (*Print[{\[Alpha],\[Beta]}];*)
    matUp = Insert[matUp, {Log[10, Ksud], Log[10, Ksvd]}, 1];
    RangeUp = Insert[RangeUp, {Ksud, Ksvd}, 1];
    ];
  If[ ((Stable2 == 1 && Stable1 == 2)),
   Print["Switch (DOWN)"];
   (*Print[{\[Alpha],\[Beta]}];*)
   matDown = Insert[matDown, {Log[10, Ksud], Log[10, Ksvd]}, 1];
   RangeDown = Insert[RangeDown, {Ksud, Ksvd}, 1];
   ];
  If[(Stable2 == 2),
   (*Print["BISTABLE ", \[Alpha], "   ",\[Beta], ",  Saddle: ",
   Saddle2 ];*)
   ];
  If[ (Stable2 == 1),
   (*Print["MONOSTABLE ",  \[Alpha],"   ",\[Beta],",  Saddle: ",
   Saddle2 ];*)
   ];
  Saddle1 = Saddle2;
  Unstable1 = Unstable2;
  Stable1 = Stable2;
  ]
]




 For[Ksvd = 0.01*10^-9, Ksvd <= 7000*10^-9, Ksvd = Ksvd*1.1,
  Stable2 = 0;
  Saddle2 = 0;
  Unstable2 = 0;
  delEud = kb*T*Log[10, Ksud/Knsrd];
  delEvd = kb*T*Log[10, Ksvd/Knsrd];
  xdot[x_, y_] := 
   K1/(1 + \[Alpha] (1 + (y/Nns)*E^(-delEvd/(kb*T)))^n) - x; 
  ydot[x_, y_] := 
   K2/(1 + \[Alpha] (1 + (x/Nns)*E^(-delEud/(kb*T)))^n) - y; 
  Jac[x_, 
    y_] := {{Derivative[1, 0][xdot][x, y], 
     Derivative[0, 1][xdot][x, y]}, {Derivative[1, 0][ydot][x, y], 
     Derivative[0, 1][ydot][x, y]}};
  fps = NSolve[xdot[x, y] == 0 && ydot[x, y] == 0, {x, y}, Reals];
  (*Print[N[fps,3]]*)
  (*Print[Length[fps]-1]*)
  For[i = 1, i < Length[fps] + 1, i++,
    xtemp = x /. fpsi;
    ytemp = y /. fpsi;
    (*Print[N[xtemp,3]]*)
    (*Print[N[ytemp,3]]*)
    If[Im[xtemp] == 0 && Im[ytemp] == 0,
     If[xtemp > 0 && ytemp > 0,
      (*Print["              ",i-1,"  R1=",xtemp,"  R2=",ytemp, 
      "  Ksud=",Ksud,"   Ksvd=", Ksvd]*)
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] > 0 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] > 0,
       Unstable2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] < 0 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] < 0,
       Stable2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] < 0.0001 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] > 0.0001,
       Saddle2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] > 0.0001 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] < 0.0001,
       Saddle2 += 1;
       ];
      ]
     ]
    ]
   (*Print[Stable2, "  ", Stable1]*)
   If[ (Stable2 == 2 && Stable1 == 1),
    Print["Switch  (UP)"];
    (*Print[{\[Alpha],\[Beta]}];*)
    matUp = Insert[matUp, {Log[10, Ksud], Log[10, Ksvd]}, 1];
    RangeUp = Insert[RangeUp, {Ksud, Ksvd}, 1];
    ];
  If[ ((Stable2 == 1 && Stable1 == 2)),
   Print["Switch (DOWN)"];
   (*Print[{\[Alpha],\[Beta]}];*)
   matDown = Insert[matDown, {Log[10, Ksud], Log[10, Ksvd]}, 1];
   RangeDown = Insert[RangeDown, {Ksud, Ksvd}, 1];
   ];
  If[(Stable2 == 2),
   (*Print["BISTABLE ", \[Alpha], "   ",\[Beta], ",  Saddle: ",
   Saddle2 ];*)
   ];
  If[ (Stable2 == 1),
   (*Print["MONOSTABLE ",  \[Alpha],"   ",\[Beta],",  Saddle: ",
   Saddle2 ];*)
   ];
  Saddle1 = Saddle2;
  Unstable1 = Unstable2;
  Stable1 = Stable2;
  ]
]


k1 = 100; d1 = 0.007; k2 = 50; d2 = 0.007; K1 = k1/d1; K2 = k2/d2; Nns = 5*10^6; delEpd = -1.0421*10^-19; kb = 1.3806*10^-23; T = 298; P = 3000; \[Alpha] = Nns*E^(delEpd/(kb*T))/P; n = 5; (*Ksrd=;*) Knsrd = 10000; Stable1 = 0; Saddle1 = 0; Unstable1 = 0; matUp1 = {}; matDown1 = {}; RangeUp1 = {}; RangeDown1 = {}; For[Ksud = 0.01*10^-9, Ksud <= 7000*10^-9, Ksud = Ksud*1.1, 

Print[Ksud]
 For[Ksvd = 0.01*10^-9, Ksvd <= 7000*10^-9, Ksvd = Ksvd*1.1,
  Stable2 = 0;
  Saddle2 = 0;
  Unstable2 = 0;
  delEud = kb*T*Log[10, Ksud/Knsrd];
  delEvd = kb*T*Log[10, Ksvd/Knsrd];
  xdot[x_, y_] := 
   K1/(1 + \[Alpha] (1 + (y/Nns)*E^(-delEvd/(kb*T)))^n) - x; 
  ydot[x_, y_] := 
   K2/(1 + \[Alpha] (1 + (x/Nns)*E^(-delEud/(kb*T)))^n) - y; 
  Jac[x_, 
    y_] := {{Derivative[1, 0][xdot][x, y], 
     Derivative[0, 1][xdot][x, y]}, {Derivative[1, 0][ydot][x, y], 
     Derivative[0, 1][ydot][x, y]}};
  fps = NSolve[xdot[x, y] == 0 && ydot[x, y] == 0, {x, y}, Reals];
  (*Print[N[fps,3]]*)
  (*Print[Length[fps]-1]*)
  For[i = 1, i < Length[fps] + 1, i++,
    xtemp = x /. fpsi;
    ytemp = y /. fpsi;
    (*Print[N[xtemp,3]]*)
    (*Print[N[ytemp,3]]*)
    If[Im[xtemp] == 0 && Im[ytemp] == 0,
     If[xtemp > 0 && ytemp > 0,
      (*Print["              ",i-1,"  R1=",xtemp,"  R2=",ytemp, 
      "  Ksud=",Ksud,"   Ksvd=", Ksvd]*)
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] > 0 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] > 0,
       Unstable2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] < 0 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] < 0,
       Stable2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] < 0.0001 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] > 0.0001,
       Saddle2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] > 0.0001 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] < 0.0001,
       Saddle2 += 1;
       (*saddlePoint2=Insert[saddlePoint2,{\[Alpha],\[Beta],Re[
       Eigenvalues[Jac[xtemp,ytemp]]2]},1];*)
       ];
      ]
     ]
    ]
   (*Print[Stable2, "  ", Stable1]*)
   If[ (Stable2 == 2 && Stable1 == 1),
    Print["Switch  (UP)"];
    (*Print[{\[Alpha],\[Beta]}];*)
    matUp1 = Insert[matUp1, {Log[10, Ksud], Log[10, Ksvd]}, 1];
    RangeUp1 = Insert[RangeUp1, {Ksud, Ksvd}, 1];
    ];
  If[ ((Stable2 == 1 && Stable1 == 2)),
   Print["Switch (DOWN)"];
   (*Print[{\[Alpha],\[Beta]}];*)
   matDown1 = Insert[matDown1, {Log[10, Ksud], Log[10, Ksvd]}, 1];
   RangeDown1 = Insert[RangeDown1, {Ksud, Ksvd}, 1];
   ];
  If[(Stable2 == 2),
   (*Print["BISTABLE ", \[Alpha], "   ",\[Beta], ",  Saddle: ",
   Saddle2 ];*)
   ];
  If[ (Stable2 == 1),
   (*Print["MONOSTABLE ",  \[Alpha],"   ",\[Beta],",  Saddle: ",
   Saddle2 ];*)
   ];
  Saddle1 = Saddle2;
  Unstable1 = Unstable2;
  Stable1 = Stable2;
  ]
]



k1 = 100; d1 = 0.007; k2 = 10; d2 = 0.007; K1 = k1/d1; K2 = k2/d2; Nns = 5*10^6; delEpd = -1.0421*10^-19; kb = 1.3806*10^-23; T = 298; P = 3000; \[Alpha] = Nns*E^(delEpd/(kb*T))/P; n = 5; (*Ksrd=;*) Knsrd = 10000; Stable1 = 0; Saddle1 = 0; Unstable1 = 0; matUp2 = {}; matDown2 = {}; RangeUp2 = {}; RangeDown2 = {}; For[Ksud = 0.01*10^-9, Ksud <= 7000*10^-9, Ksud = Ksud*1.1, 

Print[Ksud]
 For[Ksvd = 0.01*10^-9, Ksvd <= 7000*10^-9, Ksvd = Ksvd*1.1,
  Stable2 = 0;
  Saddle2 = 0;
  Unstable2 = 0;
  delEud = kb*T*Log[10, Ksud/Knsrd];
  delEvd = kb*T*Log[10, Ksvd/Knsrd];
  xdot[x_, y_] := 
   K1/(1 + \[Alpha] (1 + (y/Nns)*E^(-delEvd/(kb*T)))^n) - x; 
  ydot[x_, y_] := 
   K2/(1 + \[Alpha] (1 + (x/Nns)*E^(-delEud/(kb*T)))^n) - y; 
  Jac[x_, 
    y_] := {{Derivative[1, 0][xdot][x, y], 
     Derivative[0, 1][xdot][x, y]}, {Derivative[1, 0][ydot][x, y], 
     Derivative[0, 1][ydot][x, y]}};
  fps = NSolve[xdot[x, y] == 0 && ydot[x, y] == 0, {x, y}, Reals];
  (*Print[N[fps,3]]*)
  (*Print[Length[fps]-1]*)
  For[i = 1, i < Length[fps] + 1, i++,
    xtemp = x /. fpsi;
    ytemp = y /. fpsi;
    (*Print[N[xtemp,3]]*)
    (*Print[N[ytemp,3]]*)
    If[Im[xtemp] == 0 && Im[ytemp] == 0,
     If[xtemp > 0 && ytemp > 0,
      (*Print["              ",i-1,"  R1=",xtemp,"  R2=",ytemp, 
      "  Ksud=",Ksud,"   Ksvd=", Ksvd]*)
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] > 0 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] > 0,
       Unstable2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] < 0 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] < 0,
       Stable2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] < 0.0001 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] > 0.0001,
       Saddle2 += 1;
       ];
      If[
       Re[Eigenvalues[Jac[xtemp, ytemp]]1] > 0.0001 && 
        Re[Eigenvalues[Jac[xtemp, ytemp]]2] < 0.0001,
       Saddle2 += 1;
       (*saddlePoint2=Insert[saddlePoint2,{\[Alpha],\[Beta],Re[
       Eigenvalues[Jac[xtemp,ytemp]]2]},1];*)
       ];
      ]
     ]
    ]
   (*Print[Stable2, "  ", Stable1]*)
   If[ (Stable2 == 2 && Stable1 == 1),
    Print["Switch  (UP)"];
    (*Print[{\[Alpha],\[Beta]}];*)
    matUp2 = Insert[matUp2, {Log[10, Ksud], Log[10, Ksvd]}, 1];
    RangeUp2 = Insert[RangeUp2, {Ksud, Ksvd}, 1];
    ];
  If[ ((Stable2 == 1 && Stable1 == 2)),
   Print["Switch (DOWN)"];
   (*Print[{\[Alpha],\[Beta]}];*)
   matDown2 = Insert[matDown2, {Log[10, Ksud], Log[10, Ksvd]}, 1];
   RangeDown2 = Insert[RangeDown2, {Ksud, Ksvd}, 1];
   ];
  If[(Stable2 == 2),
   (*Print["BISTABLE ", \[Alpha], "   ",\[Beta], ",  Saddle: ",
   Saddle2 ];*)
   ];
  If[ (Stable2 == 1),
   (*Print["MONOSTABLE ",  \[Alpha],"   ",\[Beta],",  Saddle: ",
   Saddle2 ];*)
   ];
  Saddle1 = Saddle2;
  Unstable1 = Unstable2;
  Stable1 = Stable2;
  ]
]



RangeUp1; RangeDown1; ListPlot[{RangeUp1, RangeDown1}]; matUp1; matDown1; ListLinePlot[{matUp, matDown, matUp1, matDown1, matUp2, matDown2}, 

PlotStyle -> {Blue, Blue, Red, Red, Green, Green}, 
PlotRange -> {{-10, -5}, {-10, -5}}, InterpolationOrder -> 1, 
Mesh -> Full, MeshStyle -> Directive[Gray], 
AxesLabel -> {"Log(\!\(\*SubscriptBox[\(K\), \(d, Repressor\\\ \

1\)]\))", "Log(\!\(\*SubscriptBox[\(K\), \(d, Repressor\\\ 2\)]\))"}, 

PlotLabel -> 
 Style["Bistable Regions for Unbalanced Promoter Strengths", 
  Directive[Large, Bold]], LabelStyle -> Directive[Medium, Bold]]



Retrieved from "http://2013.igem.org/Team:Duke/Modeling/Codes/Kinetic1"