Bi Bi Reaction Ordered Mechanism ODE System

Available identifiers

MaRDI QIDQ6674163

system of ordinary differential equations describing a bi bi reaction with an ordered mechanism

Defining Formula: $\begin{array}{cc}\frac{d{c}_{S_1}}{dt}& =k_{-1}{c}_{E{S}_1}-k_1{c}_E{c}_{S_1}\\ \frac{d{c}_{S_2}}{dt}& =k_{-2}{c}_{E{S}_1{S}_2}-k_2{c}_{E{S}_1}{c}_{S_2}\\ \frac{d{c}_{E{S}_1}}{dt}& =k_1{c}_E{c}_{S_1}+k_{-2}{c}_{E{S}_1{S}_2}-k_{-1}{c}_{E{S}_1}-k_2{c}_{E{S}_1}{c}_{S_2}\\ \frac{d{c}_{E{S}_1{S}_2}}{dt}& =k_2{c}_{E{S}_1}{c}_{S_2}+k_{-3}{c}_{E{P}_1{P}_2}-k_{-2}{c}_{E{S}_1{S}_2}-k_3{c}_{E{S}_1{S}_2}\\ \frac{d{c}_{E{P}_1{P}_2}}{dt}& =k_3{c}_{E{S}_1{S}_2}+k_{-4}{c}_{E{P}_1}{c}_{P_2}-k_{-3}{c}_{E{P}_1{P}_2}-k_4{c}_{E{P}_1{P}_2}\\ \frac{d{c}_{E{P}_1}}{dt}& =k_4{c}_{E{P}_1{P}_2}+k_{-5}{c}_E{c}_{P_1}-k_{-4}{c}_{E{P}_1}{c}_{P_2}-k_5{c}_{E{P}_1}\\ \frac{d{c}_{P_1}}{dt}& =k_5{c}_{E{P}_1}-k_{-5}{c}_E{c}_{P_1}\\ \frac{d{c}_{P_2}}{dt}& =k_4{c}_{E{P}_1{P}_2}-k_{-4}{c}_{E{P}_1}{c}_{P_2}\\ \frac{d{c}_E}{dt}& =k_{-1}{c}_{E{S}_1}+k_5{c}_{E{P}_1}-k_1{c}_E{c}_{S_1}-k_{-5}{c}_E{c}_{P_1}\\ \end{array}$

$\frac{d{c}_{E{P}_1{P}_2}}{dt}$ symbol represents Reaction Rate of Enzyme - Product 1 - Product 2 Complex

$\frac{d{c}_{E{P}_1}}{dt}$ symbol represents Reaction Rate of Enzyme - Product 1 Complex

$\frac{d{c}_{E{S}_1{S}_2}}{dt}$ symbol represents Reaction Rate of Enzyme - Substrate 1 - Substrate 2 Complex

$\frac{d{c}_{E{S}_1}}{dt}$ symbol represents Reaction Rate of Enzyme - Substrate 1 Complex

$\frac{d{c}_E}{dt}$ symbol represents Reaction Rate of Enzyme

$\frac{d{c}_{P_1}}{dt}$ symbol represents Reaction Rate of Product 1

$\frac{d{c}_{P_2}}{dt}$ symbol represents Reaction Rate of Product 2

$\frac{d{c}_{S_1}}{dt}$ symbol represents Reaction Rate of Substrate 1

$\frac{d{c}_{S_2}}{dt}$ symbol represents Reaction Rate of Substrate 2

$c_{E{P}_1{P}_2}$ symbol represents Enzyme - Product 1 - Product 2 Complex Concentration

$c_{E{P}_1}$ symbol represents Enzyme - Product 1 Complex Concentration

$c_{E{S}_1{S}_2}$ symbol represents Enzyme - Substrate 1 - Substrate 2 Complex 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

$k_{-5}$ 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

$k_5$ symbol represents Reaction Rate Constant

$t$ symbol represents Time

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