********** MODEL NAME Proteostasis ********** MODEL NOTES ********** MODEL STATES d/dt(R) = Re24-Re23-Re25+Re34+Re33 d/dt(R_T) = Re23-Re24-Re26 d/dt(T) = Re24-Re23+Re28-Re27+Re32-Re31+Re36-Re35+Re38-Re37-2*Re123+2*Re116 d/dt(T_2) = Re123-Re116 d/dt(J) = 2*Re118-2*Re117 d/dt(J2) = Re2-Re1-Re6+Re9-Re10-Re18-Re13+Re14+Re117-Re118+J2_1-J2_2-J2_3+J2_4-J2_5 d/dt(E) = 2*Re120-2*Re119 d/dt(E2) = Re12-Re11+Re119-Re120+E2_1-E2_2-E2_3+E2_4 d/dt(KT) = Re4-Re3-Re5-Re15+Re16-Re17+KT_1-KT_2-KT_3+KT_4 d/dt(GrL) = Re44-Re43+Re48-Re47 d/dt(GrLT) = Re46-Re45+Re50-Re49+Re75+Re73+Re74 d/dt(GrS) = Re82+Re75+Re83+Re84+Re73+Re85+Re86+Re74+Re87-Re53-Re54 d/dt(Dn) = Re113-Re112+Re115 d/dt(Lon) = Re106-Re105+Re110-Re109+Re108 d/dt(B) = B_1-B_2+B_3 %%Synthesis%% d/dt(R_a) = Re25+Re28-Re27-Re29 d/dt(Ra_U) = Re29+Re32-Re31-Re33 d/dt(R_a_T) = Re26+Re27-Re28-Re30 d/dt(Ra_U_T) = Re31+Re30-Re32-Re34 d/dt(U_T) = Re34-Re36+Re35 d/dt(M_T) = Re37-Re38 %%U,M,N d/dt(U) = Re22-Re21+Re2+Re4-Re1-Re3+Re33+Re36+Re40-Re35-Re39+Re44-Re43+Re46-Re45+Re84+Re73+Re85+Re106-Re105-Re76-Re78-Re80+Ud1+Ud2+Ud3+Ud4 d/dt(M) = Re21-Re22-Re37+Re38+Re14-Re13-Re15+Re16+Re48-Re47+Re50-Re49+Re86+Re74+Re87+Re110-Re109-Re77-Re79-Re81-k_a*(M)^2+ M1 d/dt(Nat) = Re39-Re40+Re82+Re75+Re83+Re113-Re112 %%DNAJ/K%% d/dt(U_J) = Re1-Re2-Re5 d/dt(U_KT) = Re3-Re4-Re6-Re7+Re12 d/dt(U_J_KT) = Re5+Re6-Re8 d/dt(U_J_KD) = Re8+Re10+Re20-Re9 d/dt(U_KD) = Re9+Re7-Re10-Re11+Re19 d/dt(U_E2_KT) = Re11-Re12 d/dt(M_J) = Re13-Re14-Re17 d/dt(M_KT) = Re15-Re16-Re18-Re19 d/dt(M_J_KT) = Re18+Re17-Re20 %%GroEL/S%% d/dt(GrL_U) = Re43-Re44-Re51 d/dt(GrLT_U) = Re51+Re45-Re46+Re52-Re53+Re82+Re83+Re84+Re85+Re86+Re87 d/dt(GrL_M) = Re47-Re48-Re52 d/dt(GrLT_M) = Re49-Re50-Re54 d/dt(GrLT_U_GrS) = Re53-Re58+Re57-Re55+Re56-Re59 d/dt(GrLT_M_GrS) = Re54-Re56+Re55-Re60 d/dt(GrLT_Nat_GrS) = Re58-Re57-Re61 d/dt(GrLD_U_GrS) = Re59-Re62+Re63-Re65+Re64-Re66-Re78-Re79 d/dt(GrLD_Nat_GrS) = Re61-Re64+Re65-Re68-Re76-Re77 d/dt(GrLD_M_GrS) = Re60+Re62-Re63-Re67-Re80-Re81 d/dt(GrLD_U_GrS_GrLT) = Re66-Re69+Re70-Re72+Re71-Re73 d/dt(GrLD_M_GrS_GrLT) = Re67-Re70+Re69-Re74 d/dt(GrLD_Nat_GrS_GrLT) = Re68-Re71+Re72-Re75 %%Degradation d/dt(U_Lon) = Re105-Re106-Re107 d/dt(U_Star_Lon) = Re107+Re111-Re108 d/dt(M_Lon) = Re109-Re110-Re111 d/dt(Nat_Dn) = Re112-Re113-Re114 d/dt(Nat_Star_Dn) = Re114-Re115 %%GroEL/S d/dt(GrLD_U_GrS_GrL_U) = Re78-Re84 d/dt(GrLD_U_GrS_GrL_M) = Re79-Re85 d/dt(GrLD_Nat_GrS_GrL_U) = Re76-Re82 d/dt(GrLD_Nat_GrS_GrL_M) = Re77-Re83 d/dt(GrLD_M_GrS_GrL_U) = Re80-Re86 d/dt(GrLD_M_GrS_GrL_M) = Re81-Re87 %%Aggregation & Disaggregation%% d/dt(A) = 0 d/dt(A) = k_a*(M)^n + k_d*A - (k_a + k_d*M)*A -k_ix_5*A*J2 + (k_ix_5/k_ix_56eq)*J2_A -k_ix_7*A*KT + (k_ix_7/k_ix_78eq)*KT_A + b_ix_17*B_A d/dt(A) = k_a*M*A + k_d*A - (k_a + k_d*M)*A -k_ix_5*A*J2 + (k_ix_5/k_ix_56eq)*J2_A -k_ix_7*A*KT + (k_ix_7/k_ix_78eq)*KT_A + b_ix_17*B_A d/dt(A) = k_a*M*A + k_d*A - (k_a + k_d*M)*A -k_ix_5*A*J2 + (k_ix_5/k_ix_56eq)*J2_A -k_ix_7*A*KT + (k_ix_7/k_ix_78eq)*KT_A + b_ix_17*B_A d/dt(A) = k_a*M*A - k_d*A -k_ix_5*A*J2 + (k_ix_5/k_ix_56eq)*J2_A -k_ix_7*A*KT + (k_ix_7/k_ix_78eq)*KT_A d/dt(J2_A) = k_ix_5*A*J2-(k_ix_5/k_ix_56eq)*J2_A-b_5*J2_A*KT d/dt(KT_A) = k_ix_7*A*KT-(k_ix_7/k_ix_78eq)*KT_A-k_ix_9*KT_A*J2-k_ix_10*KT_A+b_12*KT_E2_A d/dt(KT_A) = k_ix_7*A*KT-(k_ix_7/k_ix_78eq)*KT_A-k_ix_9*KT_A*J2-k_ix_10*KT_A+b_12*KT_E2_A d/dt(J2_KT_A) = b_5*J2_A*KT+k_ix_9*KT_A*J2-b_8*J2_KT_A d/dt(J2_KD_A) = b_8*J2_KT_A+ b_10*KD_A*J2-b_9*J2_KD_A d/dt(KD_A) = b_9*J2_KD_A-b_10*KD_A*J2+k_ix_10*KT_A-b_11*KD_A*E2-b_ix_13*KD_A*B+(b_ix_13/b_ix_1314eq)*KD_B_A d/dt(KT_E2_A) = b_11*KD_A*E2-b_12*KT_E2_A d/dt(KD_B_A) = b_ix_13*KD_A*B-(b_ix_13/b_ix_1314eq)*KD_B_A-b_15*KD_B_A*E2 d/dt(KT_E2_B_A) = b_15*KD_B_A*E2-(k_ix_7/k_ix_78eq)*KT_E2_B_A d/dt(B_A) = (k_ix_7/k_ix_78eq )*KT_E2_B_A-b_ix_17*B_A R(0) = 20 T(0) = 20 KT(0) = 30 J2(0) = 1 E2(0) = 15 GrL(0) = 42 GrS(0) = 35 Lon(0) = 0 Dn(0) = 0 B(0) = 1.8 ********** MODEL PARAMETERS N = 50 % Maximum Aggregate length - 1 min = 2 % Minimum Aggregate length that allows for growth || Constraint; min <= nucsize nucsize = 2 % Nucleus size + 1 supercrit = 0.5 % Rate constants that are protein specific k_da = 0.8 % Aggregate dissociation rate constant k_a = 1.2 km = 0.5 Km = 50 kf = 0.4 Kf = 2800 s_ix_3 = 0.000577 s_ix_9 = 0.2 s_ix_910eq = 0.25 s_ix_11 = 0.4761904762 %% 20/42 (42 = #aa) = d_ix_1 = 0.1 d_ix_12eq = 0.1 d_ix_3 = 5 d_ix_4 = 15 d_ix_8 = 0.1 d_ix_89eq = 1 d_ix_10 = 0.2 d_ix_11 = 15 k_ix_5 = 0.3 k_ix_56eq = 0.006 k_ix_7 = 1 k_ix_78eq = 0.5 k_ix_9 = 1 k_ix_10 = 1 g_ix_3 = 10 g_ix_34eq = 100 g_ix_5 = 1 g_ix_56eq = 10 p_ix_1 = 1 %% g_i15/gmacc p_ix_12eq = 1 %% g_i15/g_i16*gmstab p_ix_5 = 1 %% g_i17/*gnacc p_ix_56eq = 1 %% g_i17/g_i18*gnstab gmacc = 1 %% 1/km gmstab = 1 %% 1/Km gnacc = 1 %% 1/kf gnstab = 0.0001 %% 1/Kf b_ix_13 = 0.1 b_ix_1314eq = 50 b_ix_17 = 2 t_ix_3 = 0.3 t_ix_34eq = 6 % Rate constants for chaperone-chaperone or chaperone-ribosome interactions s_0_1 = 0.02 %% 0.02 s_0_2 = 0.05 %% 0.02/0.4 = 0.05 s_i_5 = 0.02 %% 0.02 s_i_6 = 0.05 %% 0.02/0.4 = 0.05 k_0_1 = 0.1 %% 10^-1 k_0_2 = 0.0001 %% 10^-1/10^3 = 0.0001 k_0_3 = 0.1 %% 10^-1 k_0_4 = 0.2 %% 10^-1/0.5 t_0_1 = 3 %% 3 t_0_2 = 6 %% 3/0.5 g_0_1 = 31.6227766017 %% 10^1.5 = 31.6227766017 ||[30 i interaktionsgrafen] g_0_2 = 0.1 %% 10^-1 % Rate constants for protein-chaperone interactions that will be treated as independent of the protein s_i_7 = 0.25 %%0.25 - 0.5 ||Satt till 0.25 i deras modell s_i_8 = 0.25 %%0.25 - 0.5 ||Satt till 0.25 i deras modell k11 = 0.006 k12 = 2 k13 = 1 %% 1/1 k14 = 1 k15 = 0.3 k16 = 1 k23 = 0.006 k24 = 2 b_5 = 0.006 %% 0.006||Satt till 1 i deras interaktionsgraf b_8 = 2 b_9 = 1 %% 1/1 b_10 = 1 b_11 = 0.3 b_12 = 1 b_15 = 0.3 g_i_11 = 2.5 g_i_12 = 2.5 g_i_13 = 1 g_i_14 = 1 g_i_19 = 0.1 g_i_20 = 0.1 g_i_21 = 0.1 g_i_26 = 31.6227766017 %% 10^1.5 = 10*sqrt(10) = 31.6227766017||30 i deras interaktionsgraf g_i_27 = 31.6227766017 %% 10^1.5 = 31.6227766017||30 i deras interaktionsgraf g_i_28 = 31.6227766017 %% 10^1.5 = 31.6227766017||30 i deras interaktionsgraf g_i_33 = 1 %% 10^0 = 1 g_i_34 = 1 %% 10^0 = 1 g_i_35 = 1 %% 10^0 = 1 g_ik_42 = 2.5 g_ik_43 = 2.5 g_ik_44 = 2.5 g_ik_45 = 2.5 g_ik_46 = 2.5 g_ik_47 = 2.5 ********** MODEL VARIABLES k_d = k_da/supercrit k_d = k_da M1 = arraysumIQM(k_a*M*A) Ud1 = arraysumIQM(b_ix_17*B_A*I) Ud2 = arraysumIQM(b_ix_17*B_A) Ud3 = arraysumIQM(b_12*KT_E2_A) Ud4 = arraysumIQM(b_12*KT_E2_A*I) J2_1 = arraysumIQM(k_ix_5/k_ix_56eq*J2_A) J2_2 = arraysumIQM(k_ix_5*A*J2) J2_3 = arraysumIQM(k_ix_9*KT_A*J2) J2_4 = arraysumIQM(b_9*J2_KD_A) J2_5 = arraysumIQM(b_10*KD_A*J2) KT_1 = arraysumIQM(k_ix_7/k_ix_78eq*KT_A) KT_2 = arraysumIQM(k_ix_7*A*KT) KT_3 = arraysumIQM(b_5*J2_A*KT) KT_4 = arraysumIQM(k_ix_7/k_ix_78eq*KT_E2_B_A) E2_1 = arraysumIQM(b_12*KT_E2_A) E2_2 = arraysumIQM(b_11*KD_A*E2) E2_3 = arraysumIQM(b_15*KD_B_A*E2) E2_4 = arraysumIQM(k_ix_7/k_ix_78eq*KT_E2_B_A) B_1 = arraysumIQM(b_ix_13/b_ix_1314eq*KD_B_A) B_2 = arraysumIQM(b_ix_13*KD_A*B) B_3 = arraysumIQM(b_ix_17*B_A) ********** MODEL REACTIONS %%Substrate independent reactions Re23 = s_0_1*R*T Re24 = s_0_2*R_T Re123 = t_0_1*T Re116 = t_0_2*T_2 Re117 = k_0_1*J Re118 = k_0_2*J2 Re119 = k_0_3*E Re120 = k_0_4*E2 Re121 = g_0_1*GrL Re122 = g_0_2*GrLT %%%%SYNTHESIS%%%%%%%%%%% Re25 = s_ix_3*R Re26 = s_ix_3*R_T Re27 = s_i_5*R_a*T Re28 = s_i_6*R_a_T Re29 = s_i_7*R_a Re30 = s_i_8*R_a_T Re31 = s_ix_9*Ra_U*T Re32 = (s_ix_9/s_ix_910eq)*Ra_U_T Re33 = s_ix_11*Ra_U Re34 = s_ix_11*Ra_U_T Re35 = t_ix_3*U*T Re36 = (t_ix_3/t_ix_34eq)*U_T Re37 = t_ix_3*M*T Re38 = (t_ix_3/t_ix_34eq)*M_T %%Unfolding and Msfolding Re21 = km*U Re22 = (km/Km)*M Re39 = kf*U Re40 = (kf/Kf)*Nat %%%DNAJK%%%%%% Re1 = k_ix_5*U*J2 Re2 = (k_ix_5/k_ix_56eq)*U_J Re3 = k_ix_7*U*KT Re4 = (k_ix_7/k_ix_78eq)*U_KT Re5 = k_ix_9*U_J*KT Re6 = k_ix_10*U_KT*J2 Re7 = k11*U_KT Re8 = k12*U_J_KT Re9 = k13*U_J_KD Re10 = k14*U_KD*J2 Re11 = k15*U_KD*E2 Re12 = k16*U_E2_KT Re13 = k_ix_5*M*J2 Re14 = (k_ix_5/k_ix_56eq)*M_J Re15 = k_ix_7*M*KT Re16 = (k_ix_7/k_ix_78eq)*M_KT Re17 = k_ix_9*M_J*KT Re18 = k_ix_10*M_KT*J2 Re19 = k23*M_KT Re20 = k24*M_J_KT %%%%%%%GroEL/S%%%%%%%%%%%%%%%%%%%%%%%%%%%% Re43 = g_ix_3*U*GrL Re44 = (g_ix_3/g_ix_34eq)*GrL_U Re45 = g_ix_5*U*GrLT Re46 = (g_ix_5/g_ix_56eq)*GrLT_U Re47 = g_ix_3*M*GrL Re48 = (g_ix_3/g_ix_34eq)*GrL_M Re49 = g_ix_5*M*GrLT Re50 = (g_ix_5/g_ix_56eq)*GrLT_M Re51 = g_i_11*GrL_U Re52 = g_i_12*GrL_M Re53 = g_i_13*GrLT_U*GrS Re54 = g_i_14*GrLT_M*GrS Re55 = p_ix_1*gmacc*GrLT_U_GrS Re56 = (p_ix_1/p_ix_12eq)*gmstab*GrLT_M_GrS Re57 = p_ix_5*gnacc*GrLT_Nat_GrS Re58 = (p_ix_5/p_ix_56eq)*gnstab*GrLT_U_GrS Re59 = g_i_19*GrLT_U_GrS Re60 = g_i_20*GrLT_M_GrS Re61 = g_i_21*GrLT_Nat_GrS Re62 = p_ix_1*GrLD_U_GrS Re63 = (p_ix_1/p_ix_12eq)*gmstab*GrLD_M_GrS Re64 = p_ix_5*gnacc*GrLD_Nat_GrS Re65 = (p_ix_5/p_ix_56eq)*gnstab*GrLD_U_GrS Re66 = g_i_26*GrLD_U_GrS Re67 = g_i_27*GrLD_M_GrS Re68 = g_i_28*GrLD_Nat_GrS Re69 = p_ix_1*GrLD_U_GrS_GrLT Re70 = (p_ix_1/p_ix_12eq)*gmstab*GrLD_M_GrS_GrLT Re71 = p_ix_5*gnacc*GrLD_Nat_GrS_GrLT Re72 = (p_ix_5/p_ix_56eq)*gnstab*GrLD_U_GrS_GrLT Re73 = g_i_33*GrLD_U_GrS_GrLT Re74 = g_i_34*GrLD_M_GrS_GrLT Re75 = g_i_35*GrLD_Nat_GrS_GrLT Re76 = g_ix_3*GrLD_Nat_GrS*U Re77 = g_ix_3*GrLD_Nat_GrS*M Re78 = g_ix_3*GrLD_U_GrS*U Re79 = g_ix_3*GrLD_U_GrS*M Re80 = g_ix_3*GrLD_M_GrS*U Re81 = g_ix_3*GrLD_M_GrS*M Re82 = g_ik_42*GrLD_Nat_GrS_GrL_U Re83 = g_ik_43*GrLD_Nat_GrS_GrL_M Re84 = g_ik_44*GrLD_U_GrS_GrL_U Re85 = g_ik_45*GrLD_U_GrS_GrL_M Re86 = g_ik_46*GrLD_M_GrS_GrL_U Re87 = g_ik_47*GrLD_M_GrS_GrL_M %%Degradation%% Re105 = d_ix_1*U*Lon Re106 = (d_ix_1/d_ix_12eq)*U_Lon Re107 = d_ix_3*U_Lon Re108 = d_ix_4*U_Star_Lon Re109 = d_ix_1*M*Lon Re110 = (d_ix_1/d_ix_12eq)*M_Lon Re111 = d_ix_3*M_Lon Re112 = d_ix_8*Nat*Dn Re113 = (d_ix_8/d_ix_89eq)*Nat_Dn Re114 = d_ix_10*Nat_Dn Re115 = d_ix_11*Nat_Star_Dn ********** MODEL FUNCTIONS ********** MODEL EVENTS ********** MODEL MATLAB FUNCTIONS