Bi Bi Reaction Ping Pong Mechanism ODE System

Available identifiers

system of ordinary differential equations describing a bi bi reaction with a ping pong mechanism

Defining Formula: $\begin{matrix} \frac{d c_{S_{1}}}{d t} & = k_{- 1} c_{E S_{1}} - k_{1} c_{E} c_{S_{1}} \\ \frac{d c_{S_{2}}}{d t} & = k_{- 3} c_{E * S_{2}} - k_{3} c_{E } c_{S_{2}} \\ \frac{d c_{E}}{d t} & = k_{- 1} c_{E S_{1}} + k_{4} c_{E S_{2}} - k_{1} c_{E} c_{S_{1}} - k_{- 4} c_{E} c_{P_{2}} \\ \frac{d c_{E S_{1}}}{d t} & = k_{1} c_{E} c_{S_{1}} + k_{- 2} c_{E } c_{P_{1}} - k_{- 1} c_{E S_{1}} - k_{2} c_{E S_{1}} \\ \frac{d c_{E }}{d t} & = k_{2} c_{E S_{1}} + k_{- 3} c_{E * S_{2}} - k_{- 2} c_{E } c_{P_{1}} - k_{3} c_{E } c_{S_{2}} \\ \frac{d c_{E * S_{2}}}{d t} & = k_{3} c_{E } c_{S_{2}} + k_{- 4} c_{E} c_{P_{2}} - k_{- 3} c_{E S_{2}} - k_{4} c_{E * S_{2}} \\ \frac{d c_{P_{1}}}{d t} & = k_{2} c_{E S_{1}} - k_{- 2} c_{E } c_{P_{1}} \\ \frac{d c_{P_{2}}}{d t} & = k_{4} c_{E S_{2}} - k_{- 4} c_{P_{2}} c_{E} \end{matrix}$
$\frac{d c_{E * S_{2}}}{d t}$ symbol represents Reaction Rate of Intermediate - Substrate 2 Complex
$\frac{d c_{E *}}{d t}$ symbol represents Reaction Rate of Intermediate
$\frac{d c_{E S_{1}}}{d t}$ symbol represents Reaction Rate of Enzyme - Substrate 1 Complex
$\frac{d c_{E}}{d t}$ symbol represents Reaction Rate of Enzyme
$\frac{d c_{P_{1}}}{d t}$ symbol represents Reaction Rate of Product 1
$\frac{d c_{P_{2}}}{d t}$ symbol represents Reaction Rate of Product 2
$\frac{d c_{S_{1}}}{d t}$ symbol represents Reaction Rate of Substrate 1
$\frac{d c_{S_{2}}}{d t}$ symbol represents Reaction Rate of Substrate 2
$c_{E * S_{2}}$ symbol represents Intermediate - Substrate 2 Complex Concentration
$c_{E *}$ symbol represents Intermediate Concentration
$c_{E S_{1}}$ symbol represents Enzyme - Substrate 1 Complex Concentration
$c_{E}$ symbol represents Enzyme Concentration
$c_{P_{1}}$ symbol represents Product 1 Concentration
$c_{P_{2}}$ symbol represents Product 2 Concentration
$c_{S_{1}}$ symbol represents Substrate 1 Concentration
$c_{S_{2}}$ symbol represents Substrate 2 Concentration
$k_{- 1}$ symbol represents Reaction Rate Constant
$k_{- 2}$ symbol represents Reaction Rate Constant
$k_{- 3}$ symbol represents Reaction Rate Constant
$k_{- 4}$ symbol represents Reaction Rate Constant
$k_{1}$ symbol represents Reaction Rate Constant
$k_{2}$ symbol represents Reaction Rate Constant
$k_{3}$ symbol represents Reaction Rate Constant
$k_{4}$ symbol represents Reaction Rate Constant
$t$ symbol represents Time