Hi MATLAB community,
I am hoping someone can point me towards some code that I can use to solve a system of 13 equations with 12 unknowns.
All my differential equations are equal to 0 except for the last equation which is the sum of all my states.
State 0 is named S0 etc. Theres a total of 12 states.
I am solving for the values S0, S1, S2, S3, S4 , S5, S6, S7, S8. S9. S10, and S11
Here are the set of 13 equations with 12 unknowns and the model parameters below:
dS0dt = 0 = ((k_S11_S0 * S11) + (k_S1_S0 * S1)) - ((Ca_cyt_conc* k_S0_S1 + Pi_conc * k_S0_S11) * S0);dS1dt = 0 = ((Ca_cyt_conc* k_S0_S1 * S0) + (k_S2_S1 * S2)) - ((k_S1_S0 + k_S1_S2) * S1);dS2dt = 0 = ((k_S1_S2 * S1) + (k_S3_S2 * S3)) - ((k_S2_S1 + Ca* k_S2_S3) * S2);dS3dt = 0 = ((Ca_cyt_conc* k_S2_S3 * S2) + (k_S4_S3 * S4)) - ((k_S3_S2 + MgATP_conc * k_S3_S4) * S3);dS4dt = 0 = ((MgATP_conc * k_S3_S4 * S3) + (k_S5_S4 * S5)) - ((k_S4_S3 + k_S4_S5) * S4);dS5dt = 0 = ((k_S4_S5 * S4) + (k_S6_S5 * MgADP_conc * S6)) - ((k_S5_S4 + k_S5_S6) * S5);dS6dt = 0 = ((k_S5_S6 * S5) + (k_S7_S6 * S7)) - ((k_S6_S5 * MgADP_conc + k_S6_S7) * S6);dS7dt = 0 = ((k_S6_S7 * S6) + (Ca_sr_conc * k_S8_S7 * S8)) - ((k_S7_S6 * MgADP_conc + k_S7_S8) * S7);dS8dt = 0 = ((k_S7_S8 * S7) + (k_S9_S8 * S9)) - ((Ca_sr_conc * k_S8_S7 + k_S8_S9) * S8);dS9dt = 0 = ((k_S8_S9 * S9) + (Ca_sr_conc * k_S10_S9 * S10)) - ((k_S9_S8 + k_S9_S10) * S9);dS10dt = 0 = ((k_S9_S10 * S9) + (k_S11_S10 * S11)) - ((k_S10_S11 + Ca_sr_conc * k_S10_S9) * S10);dS11dt = 0 = ((k_S10_S11 * S10) + (Pi_conc * k_S0_S11 * S0)) - ((k_S11_S0 + k_S11_S10) * S11);10000 = S0 + S1 + S2 + S3 + S4 + S5 + S6 + S7 + S8 + S9 + S10 + S11; Ca_sr_conc = 1.3e-3;MgATP_conc = 5e-3; MgADP_conc = 36e-6; Pi_conc = 1e-3; Ca_cyt_conc = 140e-9; k_S0_S1 = 4e7; k_S1_S0 = 450; k_S1_S2 = 120; k_S2_S1 = 25; k_S2_S3 = 1e8; k_S3_S2 = 16; k_S3_S4 = 2e7; k_S4_S3 = 40; k_S4_S5 = 135; k_S5_S4 = 765; k_S5_S6 = 15; k_S6_S5 = 7.5e4;k_S6_S7 = 1.5; k_S7_S6 = 2.0;k_S7_S8 = 350; k_S8_S7 = 1.2e5;k_S8_S9 = 160; k_S9_S8 = 250; k_S9_S10 = 300;k_S10_S9 = 9e4; k_S10_S11 = 60; k_S11_S10 = 60; k_S11_S0 = 250; k_S0_S11 = 2.7e5;
Thanks in advance for your help!!
Best Answer