Model of AngII signaling and membrane electrophysiology (Makadia, Anderson, Fey et al., 2015)

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Accession:156830
We developed a novel multiscale model to bridge neuropeptide receptor-activated signaling pathway with membrane electrophysiology. The model studies the effects of Angiotensin II (AngII) on neuronal excitability changes mediated by signaling dynamics and downstream phosphorylation of ion channels. The multiscale model was implemented as a set of ordinary differential equations solved using the ode15s solver in Matlab (Mathworks, USA). The signaling reactions were modeled with either mass-action or Michaelis--Menten kinetics and ion channel electrophysiology was modeled according to the Hodgkin-Huxley formalism. These models were initially validated against their respective data domains independently and were integrated to develop a multiscale model of signaling and electrophysiology.
Reference:
1 . Makadia HK, Anderson WD, Fey D, Sauter T, Schwaber JS, Vadigepalli R (2015) Multiscale model of dynamic neuromodulation integrating neuropeptide-induced signaling pathway activity with membrane electrophysiology. Biophys J 108:211-23 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Brainstem;
Cell Type(s):
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: MATLAB;
Model Concept(s): Signaling pathways; Calcium dynamics; Neuromodulation; Multiscale;
Implementer(s): Makadia, Hirenkumar K [hiren.makadia at gmail.com]; Anderson, Warren D [warren.anderson at jefferson.edu]; Fey, Dirk [dirk.fey at ucd.ie]; Vadigepalli, Rajanikanth [Rajanikanth.Vadigepalli at jefferson.edu];
function dydt = odemodel(t, y, modelparameters, AngII)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% main odemodel function
%
% input: t - time
%        y - initial conditions (194 species)
%        modelparameters - all model parameters
%        AngII - input AngII function
%
% output: dydt - change in y at each time step t
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% parsing AngII value at time t 
y(167) = interpoln(AngII(:,1),AngII(:,2),t);

%% signaling parameters
p_1_1 = modelparameters( 1 );
p_1_2 = modelparameters( 2 );
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%% Electrophysiology parameters
ep = modelparameters(351:359);

sf=15; 
sfplcca=1;    %1, 2/3, scaling of forward reaction PLC-Gq + Ca -> PLC-Gq-Ca
sfGqbasal=0;  %1, scaling of basal activity G-GDP (38) -> betagamma (4) + G*GTP (37)

g.na=ep(1);   % maximal conductance of Na
g.kdr=ep(2);  % maximal conductance of Kdr
g.ka=ep(3);   % maximal conductance of Ka
g.kahp=ep(4); % maximal conductance of Kahp
g.cal=ep(5);  % maximal conductance of CaL
g.leak=ep(6); % maximal conductance of leak

E.na=55;         % reversal potenial of Na+ (-56 - -84)
E.kdr=-94;       % reversal potenial of K+ (-94)
E.ka=E.kdr;      % reversal potenial of K+ (-94)
E.kahp=E.kdr;    % reversal potenial of K+ (-94)
E.syne=-10;      % reversal potenial of K+ (-94)
E.leak= -41.84 ; % reversal potenial of leak (-41.31 for 1Hz; -52.57 for 2Hz; -52.56 for 3Hz)

p.Cm=0.025; % membrane capacitance 
p.taue= 3;
p.aahp=1.25e8;
p.bahp=2.5;
p.cahp=1000;

phosMK1.k_p= ep(7); % Kdr phosphorylation rate by PKC
phosMK1.n=4; % number of PKC molecule require to phosphorylate Kdr
phosMK1.k_dp=phosMK1.k_p*(1.35^phosMK1.n); % Kdr dephosphorylation rate by PKC

phosPKC1.k_p= ep(8); % Kdr phosphorylation rate by CaMKII
phosPKC1.n=4; % number of CaMKII molecule require to phosphorylate Kdr
phosPKC1.k_dp=phosPKC1.k_p*(0.5200^phosPKC1.n); % Kdr dephosphorylation rate by CaMKII

V=y(179);   % Membrane volatge from interg over Vm
mna=y(180); % activation variable of Na+
hna=y(181); % inactivation variable of Na+
mdr=y(182); % activation variable of Kdr
ma1=y(183); % activation variable of Ka1
ha1=y(184); % inactivation variable of Ka1
ma2=y(185); % activation variable of Ka2 (Ka)
ha2=y(186); % inactivation variable of Ka2 (Ka)
mahp=y(187); % activation variable of Kahp
mcal=y(188); % activation variable of CaL
gsyne=y(189); % pre synaptic excitation
Ca_ahp=y(190); 
Kv_act=y(191); % unphosphorylated Kdr channels (KU)
Kv_1=y(192); % phosphorylated Kdr channels by PKC (KP)
Kv_2=y(193); % phosphorylated Kdr channels by CaMKII (KP)
%Kv_12=y(194); % doubly phosphorylated Kdr channels by PKC and CaMKII (KP)
%Ka_act=y(5+i); % unphosphorylated Ka channels

ECa = 13.27*log(y(165)/Ca_ahp/1e3); % reversal potenial of Ca2+

% Fast Sodium Channel (see Table 3 in main text for details)
mina = ( 0.091 * (V+38)/(1-exp(-(V+38)/5)) ) / (( 0.091 * (V+38)/(1-exp(-(V+38)/5)))+ (0.062 * ((V+38)/(exp((V+38)/5)-1)) ));
hina = (0.016 * (exp(-(V+55)/15))) / ((0.016 * (exp(-(V+55)/15)))+(2.07/(1 + exp(-(V-17)/21))));
tmna = 1 / ((0.091 * (V+38)/(1-exp(-(V+38)/5)))+ (0.062 * ((V+38)/(exp((V+38)/5)-1))));
thna = 1 / ( (0.016 * (exp(-(V+55)/15))) +(2.07/(1 + exp(-(V-17)/21))));

% Delayed rectifier potassium channel (see Table 3 in main text for details)
tdr = (1/(exp((V-81)/25.6)+exp((V+132)/(-18)))+9.9)./4;
midr = (1+(2^(1/4)-1)*exp((V-2.3)/(-17)))^(-1);

% Fast activating potassium channel (see Table 3 in main text for details)
% Ka1 effects are not modeled
% Ka1
mia1 = 1/(1+exp(-(V+60)/8.5));
tma1 = 1/(exp((V+35.82)/19.69) + exp(-(V+79.69)/12.7)) + 0.37;
hia1 = 1/(1+exp((V+78)/6));
tha1 = 1/((exp((V+46.05)/5) + exp(-(V+238.4)/37.45))) - (1/((exp((V+46.05)/5)+ exp(-(V+238.4)/37.45)))-19)*(sign(V+63+abs(V+63)));
% Only Ka2 effects are modeled as Ka
% Ka2
mia2 = 1/(1+exp(-(V+36)/20));
tma2 = tma1;
hia2 = 1/(1+exp((V+78)/6));
tha2 = 1/((exp((V+46.05)/5) + exp(-(V+238.4)/37.45))) - (1/((exp((V+46.05)/5)+ exp(-(V+238.4)/37.45)))-60)*(sign(V+73+abs(V+73)));

%After hyperpolarization related calcium dependent potassium channel (see Table 3 in main text for details)
miahp= p.aahp * (Ca_ahp)^2 / (p.aahp * (Ca_ahp)^2 + p.bahp);
tahp = p.cahp/(p.aahp * (Ca_ahp)^2 + p.bahp);

% High threshold calcium channel (see Table 3 in main text for details)
mical= (1.6./(1 + exp(-0.072.*(V-5)))) / ((1.6./(1 + exp(-0.072.*(V-5)))) + (0.02.*(V-1.31)./(exp((V-1.31)./5.36)-1)));
tcal = 1/((1.6./(1 + exp(-0.072.*(V-5)))) + (0.02.*(V-1.31)./(exp((V-1.31)./5.36)-1)));

% All currents (see Table 3 in main text for details)
Ina = g.na * mna^3 * hna * (E.na - V);
IKdr = g.kdr *Kv_act* mdr^4 * (E.kdr - V);
IKa = g.ka * 0.4 * ma2^4 * ha2*(E.ka - V); % no Ka1 (0.0 * ma1^4 * ha1)
IKahp = g.kahp * mahp^2 * (E.kahp - V);
Isyne = gsyne * (E.syne - V); % 0  
Isyni = 0; % gsyni * (Esyni - V);
Ileak = g.leak * (E.leak - V);


% Calcium Epump (see Table 2 in main text for details)
P_leak1=0.26e-2*0.8;  % sa=0.8;
P_leak2=0.158e-1*0.8; % sa=0.8;
zeta=V*0.0749;
r_leak=-(P_leak1*y(31)+P_leak2*y(9)/15*sf)*zeta*(y(7)-y(165)*(exp(-zeta)))/(1-(exp(-zeta)));
r_pump=- 1800 * y(7)* y(19);

% Sodium-calcium Exchanger (NCX) (see Table 2 in main text for details)
km=2; 
Kpkcmod=0.5; % 0.5 low Ca response; 3 high Ca response
Kpkc=10; 
Dpkc=2; 
nacaactaff=0.2;
vmax=ep(9);

DFin= y(165)*5.7554*exp(2*0.5*V*0.0374); %gamma=0.5;
DFout=y(7)*562448656e-3*exp(2*(0.5-1)*V*0.0374); %gamma=0.5;
rmod=-(DFin-DFout)/(1+(0.05)*(y(7)*562448656e-3+y(165)*5.7554)); % D=0.05;
rCaNa=-(1+Kpkcmod/(1+exp((Kpkc-(y(105)*100 - 3))/Dpkc))) * (y(7)/(km+y(7)))*(y(7)/(nacaactaff + y(7)));
r_NaCa=vmax*rmod*rCaNa;

r2i=2*96480*(1.17e-11)*1e3; % z*F*v*1e3 based on soma volume v_cyt=1.17e-11;
Ical = g.cal .* mcal.^2 .* (ECa - V);
r_CaL= Ical /r2i;

r_seqmem=1.6*((2.5e-4*1e-9)/(1.17e-11))/0.0075*(-2*5.4* Ca_ahp*Ca_ahp+0.0015*(y(10)-Ca_ahp));

% NCX current
I_NaCa=-r_NaCa/2*r2i; %Netto -1 ladung: 1Ca raus 3 Na rein

% Total current
ICal=Ical+I_NaCa+(r_leak+r_CaL+r_pump)*r2i;

% phosphorylation of Kdr by PKC and CaMKII
r1=phosPKC1.k_p*Kv_act*y(175)^phosPKC1.n;
r2=phosMK1.k_p*Kv_act*y(177)^phosMK1.n;
r3=phosMK1.k_p*Kv_1*y(177)^phosMK1.n;
r4=phosPKC1.k_p*Kv_2*y(175)^phosPKC1.n;

% dephosphorylation of Kdr by PKC and CaMKII
r5=phosPKC1.k_dp*Kv_1;
r6=phosMK1.k_dp*Kv_2;
r7=phosPKC1.k_dp*(1-Kv_act-Kv_1-Kv_2);%Kv_12;
r8=phosMK1.k_dp*(1-Kv_act-Kv_1-Kv_2);%Kv_12;

% calculating reaction rates of signaling pathways

v1 =  p_1_1   * y(1)  * y(51)  - p_1_2 * y(52); %1
v2 =  p_2_1   * y(1)  * y(53)  - p_2_2 * y(54); %1
v3 =  p_3_1   * y(71) * y(1)   - p_3_2 * y(73) ; %1
v4 =  p_4_1   * y(1)  * y(77)  - p_4_2 * y(79); %1
v5 =  p_5_1   * y(1)  * y(82)  - p_5_2 * y(85); %1
v6 =  p_6_1   * y(66) * y(1)   - p_6_2 * y(147) ; %1

v7 =  p_7_1   * y(66) * y(64)  - p_7_2 * y(2) ; %2
v8 =  p_8_1   * y(53) * y(64)  - p_8_2 * y(2) ; %2

v9 =  p_9_1   * y(66) * y(63)  - p_9_2 * y(3); %3
v10 = p_10_1  * y(63) * y(53) - p_10_2 * y(3); %3

v11 =  p_11_1 * y(36) * y(4) ; %4
v12 =  p_12_1* y(117); %4
v13 =  sfGqbasal * p_13_1* y(38); %4

v14 =  p_14_1 * y(162) * y(5) * y(113) - p_14_2 * y(114); %5
v15 =  p_15_1* y(5)* y(35) - p_15_2 * y(134); %5

v16 = p_16_1 * y(118) * y(170)- p_16_2 * y(6); %6

v17 = p_17_1 * y(7) * y(107) - p_17_2 * y(108); %7
v18 = p_18_1 * y(7) * y(32) * y(7) -  p_18_2 * y(33) ; %7
v19 = p_19_1 * y(90) * y(7) - p_19_2 * y(8); %7
v20 = p_20_1 * y(22) * y(7) - p_20_2 * y(23); %7
v21 = p_21_1 * y(21) * y(7) * y(7) - p_21_2 * y(24); %7
v22 = p_22_1 * y(24) * y(7) - p_22_2 * y(22); %7
v23 = p_23_1 * y(102) * y(7)- p_23_2 * y(98); %7
v24 = p_24_1 * sfplcca* y(110) * y(7) -  p_24_2 * y(109) ; %7
v25 = p_25_1 * y(121)  ; %7
v26 = (y(10)-y(7)) * p_26_1 * y(166) ; %7
v27 = (y(10)-y(7)) * p_27_1 * y(59); %7

v28 = p_28_1 * y(18) * (y(10))^5 - p_28_2 * y(11); %10
v29 = p_29_1 * y(11) * (y(10))^5 - p_29_2 * y(12); %10
v30 = p_30_1 * y(12) * (y(10))^5 - p_30_2 * y(13); %10
v31 = p_31_1 * y(13) * (y(10))^5 - p_31_2 * y(14); %10
v32 = p_32_1 * y(14) * (y(10))^5 - p_32_2 * y(15); %10
v33 = p_33_1 * y(15) * (y(10))^5 - p_33_2 * y(16); %10
v34 = p_34_1 * y(16) * (y(10))^5 - p_34_2 * y(17); %10
v35 = p_35_1 * y(20) * (y(10))^5 - p_35_2 * y(18); %10
v36 = p_36_1 * y(10) * y(10) * y(31) - p_36_2 * y(39); %10
v37 = p_37_1 * y(33) ; %10

v38 = p_38_1 * y(7) * y(19) - p_38_2 * y(121); %19

v39 = p_39_1 * y(61) * y(23) - p_39_2  * y(64); %23
v40 = p_40_1 * y(60) * y(23) - p_40_2 * y(63) ; %23
v41 = p_41_1 * y(29) * y(23) - p_41_2 * y(30); %23
v42 = p_42_1 * y(23) * y(26)- p_42_2 * y(28) ; %23

v43 = p_43_1 * y(25)* y(115) - p_43_2 * y(131); %25
v44 = p_44_1 * y(129) ; %25

v45 = p_45_1 * y(26); %26
v46 = p_46_1 * y(131); %26
v47 = p_47_1 * y(132); %26

v48 = p_48_1 * y(27)* y(115) - p_48_2 * y(129) ; %27
v49 = p_49_1 * y(27)* y(115) - p_49_2 * y(130); %27
v50 = p_50_1 * y(120); %27
v51 = p_51_1 * y(127); %27

v52 = p_52_1 * y(28)* (y(27) + y(29)) - p_52_2 * y(119)  ; %28
v53 = p_53_1 * y(28)* (y(28) + y(30)) - p_53_2 * y(126); %28
v54 = p_54_1 * y(128); %28

v55 = p_55_1 * y(29)* (y(27) + y(29)) - p_55_2 * y(120); %29
v56 = p_56_1 * y(29)* (y(28) + y(30)) - p_56_2 * y(127); %29
v57 = p_57_1 * y(29)* y(115) - p_57_2 * y(132) ; %29
v58 = p_58_1 * y(130); %

v59 = p_59_1 * y(30)* y(115)- p_59_2 * y(128); %30
v60 = p_60_1 * y(119); %30
v61 = p_61_1 * y(126); %30

v62 = p_62_1 * y(33); %32

v63 = p_63_1 * y(33); %33

v64 = p_64_1 * y(34); %34
v65 = p_65_1 * y(34) * y(98) - p_65_2 * y(100); %34
v66 = p_66_1 * y(34) * y(102) - p_66_2 * y(103); %34
v67 = p_67_1 * y(172); %34
v68 = p_68_1 * y(155); %34
v69 = p_69_1 * y(156); %34
v70 = p_70_1 * y(157); %34
v71 = p_71_1 * y(158); %34

v72 = p_72_1 * y(35) * y(77) - p_72_2 * y(81); %35
v73 = p_73_1 * y(82) * y(35) - p_73_2 * y(84); %35
v74 = p_74_1 * y(112) * y(35) - p_74_2 * y(133); %35
v75 = p_75_1 * y(5) * y(35) - p_75_2 * y(134); %35

v76 = p_76_1 * y(37); %36
v77 = p_77_1 * y(109); %36

v78 = p_78_1 * y(108) * y(37) - p_78_2 * y(109); %37
v79 = p_79_1 * y(107) * y(37) - p_79_2 * y(110); %37

v80 = p_80_1 * y(38) * y(94) - p_80_2 * y(118); %38
v81 = p_81_1 * y(38) * y(116) - p_81_2 * y(117); %38

v82 = p_82_1 * y(40) * y(45) - p_82_2  * y(43); %40
v83 = p_83_1 * y(168); %40
v84 = p_84_1 * y(136); %40
v85 = p_85_1 * y(137); %40

v86 = p_86_1 * y(41) - p_86_2 * y(168) ; %41
v87 = p_87_1 * y(138); %41

v88 = p_88_1 * y(42) * y(45) - p_88_2 * y(44); %42
v89 = p_89_1 * y(135); %42

v90 = p_90_1 * y(168) * y(45) - p_90_2 * y(43); %43

v91 = p_91_1 * y(45) * y(168) - p_91_2 * y(44); %44

v92 = p_92_1 * y(46) * y(49) - p_92_2 * y(136); %46
v93 = p_93_1 * y(46)* y(50) - p_93_2 * y(137); %46
v94 = p_94_1 * y(143); %46

v95 = p_95_1 * y(47)* y(90) - p_95_2 * y(135); %47
v96 = p_96_1 * y(144); %47
v97 = p_97_1 * y(145); %47

v98 = p_98_1 * y(48)* y(91) - p_98_2 * y(138); %48
v99 = p_99_1 * y(142); %48

v100 = p_100_1 * y(51) * y(57)- p_100_2 * y(56) ; %51
v101 = p_101_1 * y(51)* y(90)- p_101_2 * y(142); %51
v102 = p_102_1 * y(51)* y(91)- p_102_2 * y(143); %51
v103 = p_103_1 * y(148); %51

v104 = p_104_1 * y(172); %53
v105 = p_105_1 * 0.16 * y(55)- p_105_2 * y(53); %53
v106 = p_106_1 * y(69); %53
v107 = p_107_1 * y(53)* y(60) - p_107_2 * y(139) ; %53
v108 = p_108_1 * y(53)* y(61) - p_108_2  * y(140); %53
v109 = p_109_1 * y(53)* y(62) - p_109_2  * y(141); %53
v110 = p_110_1 * y(53)* y(93) - p_110_2  * y(144); %53
v111 = p_111_1 * y(53)* y(65) - p_111_2  * y(145); %53
v112 = p_112_1 * y(147); %53

v113 = p_113_1 * y(55) - 6.25 * p_113_2 * y(53); %55
v114 = p_114_1 * y(146); %55

v115 = p_115_1 * y(66) * y(57) - p_115_2 * y(56); %56
v116 = p_116_1 * y(56); %56

v117 = p_117_1 * y(71) * y(57) - p_117_2 * y(74); %57
v118 = p_118_1 * y(77) * y(57) - p_118_2 * y(74); %57

v119 = p_119_1 * y(58) * (y(53))^3 - p_119_2 * y(59); %58

v120 = p_120_1 * y(60)* (y(28) + y(30)) - p_120_2 * y(122); %60
v121 = p_121_1 * y(60)* (y(27) + y(29)) - p_121_2 * y(124); %60
v122 = p_122_1 * y(60)* (y(105) + y(99) + y(101) + y(106) + y(97) + y(96)) - p_122_2 * y(154) ; %60

v123 = p_123_1 * y(122); %61
v124 = p_124_1 * y(124); %61

v125 = p_125_1 * y(154); %62

v126 = p_126_1 * y(63)* (y(28) + y(30)) - p_126_2 * y(123); %63
v127 = p_127_1 * y(63)* (y(27) + y(29)) - p_127_2 * y(125); %63

v128 = p_128_1 * y(123); %64
v129 = p_129_1 * y(125); %64

v130 = 0.16 * p_130_1 * y(67) - p_130_2 * y(66); %66
v131 = p_131_1 * y(66)* y(1) - p_131_2 * y(147); %66
v132 = p_132_1 * y(66)* y(93) - p_132_2 * y(148); %66
v133 = p_133_1 * y(139); %66
v134 = p_134_1 * y(140); %66
v135 = p_135_1 * y(141); %66

v136 = 6.25 * p_136_1 * y(66) - p_136_2 * y(67); %67
v137 = p_137_1 * y(67)* y(95) - p_137_2 * y(146); %67

v138 = p_138_1 * y(68); %68
v139 = p_139_1 * y(77); %68

v140 = p_140_1 * y(69) * y(72) - p_140_2 * y(75); %69
v141 = p_141_1 * y(69); %69
v142 = 0.16 * p_142_1 * y(70) - p_142_2 * y(69); %69
v143 = p_143_1 * y(77); %69

v144 = 6.25 * p_144_1* y(69) - p_144_2 * y(70); %70
v145 = p_145_1 * y(149); %70

v146 = p_146_1 * y(77); %71

v147 = p_147_1 * y(72) * y(77) - p_147_2 * y(75); %72

v148 = 6.25 * p_148_1 * y(169) - p_148_2 * y(76); %76
v149 = p_149_1 * y(153); %76

v150 = p_150_1 * y(77) * y(93) - p_150_2 * y(80); %77
v151 = p_151_1 * y(77); %77
v152 = p_152_1 * y(82); %77
v153 = p_153_1 * y(111); %77
v154 = 0.16 * p_154_1 * y(78) - p_154_2 * y(77); %77
v155 = p_155_1 * y(77)* y(86) - p_155_2 * y(150); %77
v156 = p_156_1 * y(77)* y(89) - p_156_2  * y(151); %77

v157 = 6.25 * p_157_1 * y(77) - p_157_2 * y(78); %78
v158 = p_158_1 * y(78)* y(95) - p_158_2 * y(149); %78

v159 = p_159_1 * y(82) * y(93) - p_159_2 * y(83); %82
v160 = p_160_1 * y(82) * y(163) * y(86) - p_160_2 * y(87); %82
v161 = 0.16 * p_161_1 * y(88) - p_161_2 * y(82); %82
v162 = p_162_1 * y(91) * y(82) - p_162_2 * y(92); %82
v163 = p_163_1 * y(82)* y(89) - p_163_2 * y(152); %82
v164 = p_164_1 * y(133); %82

v165 =  p_165_1 * y(112) * y(162) * y(86) - p_165_2 * y(87); %86
v166 =  p_166_1 * y(111) * y(86) - p_166_2 * y(159); %86

v167 = 6.25 * p_167_1 * y(82) - p_167_2 * y(88); %88
v168 = p_168_1 * y(88)* y(95) - p_168_2 * y(153); %88

v169 = p_169_1 * y(111) * y(89) - p_169_2 * y(160); %89

v170 = p_170_1 * y(94) * y(167) - p_170_2 * y(116); %94

v171 = p_171_1 * y(161) * y(102)- p_171_2 * y(96); %96

v172 = p_172_1 * y(102); %97
v173 = p_173_1 * y(97); %97

v174 = p_174_1 * y(98) * y(161) - p_174_2 * y(99); %98
v175 = p_175_1 * y(98); %98
v176 = p_176_1 * y(101); %98
v177 = p_177_1 * y(102) * y(7)- p_177_2 * y(98); %98

v178 = p_178_1 * y(100); %100
v179 = p_179_1 * y(106); %100

v180 = p_180_1 * y(103) * y(161) - p_180_2 * y(104); %103

v181 = p_181_1 * y(104); %104
v182 = p_182_1 * y(105); %104

v183 = p_183_1 * y(172) * y(107) - p_183_2 * y(155); %107

v184 = p_184_1 * y(109); %108
v185 = p_185_1 * y(172) * y(108) - p_185_2 * y(156); %108

v186 = p_186_1 * y(172) * y(109) - p_186_2 * y(158); %109

v187 = p_187_1 * y(172) * y(110) - p_187_2 * y(157); %110

v188 = p_188_1 * y(150); %111
v189 = p_189_1 * y(151); %111

v190 = p_190_1 * y(163) * y(112) * y(113) - p_190_2 * y(114); %112
v191 = p_191_1 * y(134); %112
v192 = p_192_1 * y(152); %112

v193 = p_193_1 * y(116); %116

v194 = p_194_1 * y(167) * y(118)- p_194_2 * y(117); %117

v195 = p_18_1 * y(7) * y(32) * y(7) -  p_195_1 * y(33) ; %33

v196 = p_92_1 * y(46) * y(49) - p_196_1 * y(136); %49

v197 = p_93_1 * y(46)* y(50) - p_197_1 * y(137); %50

v198 = p_107_1 * y(53)* y(60) - p_198_1 * y(139) ; %60

v199 = p_108_1 * y(53)* y(61) - p_199_1  * y(140); %61

v200 = p_109_1 * y(53)* y(62) - p_200_1  * y(141); %62

v201 = p_111_1 * y(53)* y(65) - p_201_1  * y(145); %65

v202 = p_155_1 * y(77)* y(86) - p_202_1 * y(150); %86

v203 = p_156_1 * y(77)* y(89) - p_203_1  * y(151); %89
v204 = p_163_1 * y(82)* y(89) - p_204_1 * y(152); %89

v205 = p_95_1 * y(47)* y(90) - p_205_1 * y(135); %90
v206 = p_101_1 * y(51)* y(90)- p_206_1 * y(142); %90

v207 = p_98_1 * y(48)* y(91) - p_207_1 * y(138); %91
v208 = p_102_1 * y(51)* y(91)- p_208_1 * y(143); %91

v209 = p_110_1 * y(53)* y(93) - p_209_1  * y(144); %93
v210 = p_132_1 * y(66)* y(93) - p_210_1 * y(148); %93

v211 = p_137_1 * y(67)* y(95) - p_211_1 * y(146); %95
v212 = p_158_1 * y(78)* y(95) - p_212_1 * y(149); %95
v213 = p_168_1 * y(88)* y(95) - p_213_1 * y(153); %95

v214 =  p_166_1 * y(111) * y(86) - p_214_1 * y(159); %111
v215 = p_169_1 * y(111) * y(89) - p_215_1 * y(160); %111

v216 = p_74_1 * y(112) * y(35) - p_216_1 * y(133); %112

v217 = p_59_1 * y(30)* y(115)- p_217_1 * y(128); %115
v218 = p_48_1 * y(27)* y(115) - p_218_1 * y(129) ; %115
v219 = p_49_1 * y(27)* y(115) - p_219_1 * y(130); %115
v220 = p_43_1 * y(25)* y(115) - p_220_1 * y(131); %115
v221 = p_57_1 * y(29)* y(115) - p_221_1 * y(132) ; %115

v222 = p_52_1 * y(28)* (y(27) + y(29)) - p_222_1 * y(119)  ; %119
v223 = p_55_1 * y(29)* (y(27) + y(29)) - p_223_1 * y(120); %120

v224 = p_120_1 * y(60)* (y(28) + y(30)) - p_224_1 * y(122); %122

v225 = p_126_1 * y(63)* (y(28) + y(30)) - p_225_1 * y(123); %123
v226 = p_121_1 * y(60)* (y(27) + y(29)) - p_226_1 * y(124); %124
v227 = p_127_1 * y(63)* (y(27) + y(29)) - p_227_1 * y(125); %125

v228 = p_53_1 * y(28)* (y(28) + y(30)) - p_228_1 * y(126); %126
v229 = p_56_1 * y(29)* (y(28) + y(30)) - p_229_1 * y(127); %127

v230 = p_131_1 * y(66)* y(1) - p_230_1 * y(147); %147

v231 = p_122_1 * y(60)* (y(105) + y(99) + y(101) + y(106) + y(97) + y(96)) - p_231_1 * y(154) ; %154

% Integrating the change in y
dydt = [ 
( - v1 - v2 - v3 - v4 - v5 - v6 )% y(1) %%-------> 1345_3pase
( v7 + v8 )% y(2) %%-------> 3kCaM*_ip3_cmplx
( v9 + v10 )% y(3) %%-------> 3kCaM_ip3_cmplx
( - v11 + v12 + v13 )% y(4) %%-------> BetaGamma
( - v14 - v15 )% y(5) %%-------> bisPP-IP4
( v16 )% y(6) %%-------> Blocked-rec-Gq
( - v17 - 2*v18 - v19 - v20 - 2 * v21 - v22 - v23 - v24 + v25 + v26 + v27 + r_NaCa + r_leak + r_pump  )% y(7) %%-------> Ca
( v19 )% y(8) %%-------> Ca-1pase-cmplx
(0 )% y(9) %%-------> Ca-leak-from-extracell
( -5*v28 - 5*v29 - 5*v30 - 5*v31 - 5*v32 - 5*v33 - 5*v34 - 5*v35 -2*6.25*v36 + 2*6.25*v37 -6.25* v26 - 6.25*v27 -6.25*r_seqmem )% y(10) %%-------> Ca-sequester
( -v29 + v28 )% y(11) %%-------> Ca10-Cal
( -v30 + v29 )% y(12) %%-------> Ca15-Cal
( -v31 + v30 )% y(13) %%-------> Ca20-Cal
( -v32 + v31 )% y(14) %%-------> Ca25-Cal
( -v33 + v32 )% y(15) %%-------> Ca30-Cal
( -v34 + v33 )% y(16) %%-------> Ca35-Cal
( v34 )% y(17) %%-------> Ca40-Cal
( -v28 + v35 )% y(18) %%-------> Ca5-Cal
( -v38 )% y(19) %%-------> CaEPump
( -v35 )% y(20) %%-------> Calseq
( -v21 )% y(21) %%-------> CaM
( -v20 + v22 )% y(22) %%-------> CaM-Ca3
( -v39 - v40 - v41 - v42 + v20  )% y(23) %%-------> CaM-Ca4
( -v22 + v21 )% y(24) %%-------> CaM-TR2-Ca2
( -v43 + v44 )% y(25) %%-------> CaMK-thr306
( -v45 - v42 + v46 + v47 )% y(26) %%-------> CaMKII
( -v48 - v49 + v50 + v51 )% y(27) %%-------> CaMKII***
( v42 - v52 -v53 + v54 )% y(28) %%-------> CaMKII-CaM
( -v41 + v45 - v55 - v56 -v57 + v58 )% y(29) %%-------> CaMKII-thr286
( v41 - v59 + v60 + v61 )% y(30) %%-------> CaMKII-thr286*-CaM
( - v36 )% y(31) %%-------> capacitive_Ca_entry*
( - v18 + v62 )% y(32) %%-------> CaTransp
( v195 - v63 )% y(33) %%-------> CaTransp-2Ca
( -v64 - v65 - v66 + v67 + v68 + v69 + v70 + v71 )% y(34) %%-------> DAG
( -v72 - v73 - v74 - v75  )% y(35) %%-------> DIPP1
( -v11 + v76 + v77 )% y(36) %%-------> G*GDP
( -v78 - v76 -v79 + v12 + v13 )% y(37) %%-------> G*GTP
( -v13 - v80 - v81 + v11 )% y(38) %%-------> G-GDP
( v36 )% y(39) %%-------> inact_cap_entry
( -v82 + v83 + v84 + v85  )% y(40) %%-------> IP1(1)
( -v86 + v87 )% y(41) %%-------> IP1(3)
( -v88 + v89 )% y(42) %%-------> IP1(4)
( v90 + v82 )% y(43) %%-------> ip1_1pase_cmplx
( v91 + v88 )% y(44) %%-------> ip1_4pase_cmplx
( -v82 - v88 - v90 - v91 )% y(45) %%-------> IP1_pase
( -v92 - v93 + v94 )% y(46) %%-------> IP2(13)
( -v95 + v96 + v97 )% y(47) %%-------> IP2(14)
( -v98 + v99 )% y(48) %%-------> IP2(34)
( -v196 )% y(49) %%-------> IP2_3pase1
( -v197 )% y(50) %%-------> IP2_3pase2
( -v1 - v100 - v101 - v102 + v103 )% y(51) %%-------> IP3(134)
( v1 )% y(52) %%-------> IP3(134)-3pase-cmplx
( -v2 - v8 - v10 + v104 + v105 + v106 - v107 - v108 - v109 - v110 - v111 + v112 + v68 + v69 + v70 + v71 )% y(53) %%-------> IP3(145)
( v2 )% y(54) %%-------> IP3(145)-3pase-cmplx
( -v113 + v114 )% y(55) %%-------> IP3(145)_ER
( v115 - v116 + v100 )% y(56) %%-------> IP3-56Kcmplx
( -v100 - v117 - v115 + v116 - v118 )% y(57) %%-------> IP3-56K_IP4-1K
( -v119 )% y(58) %%-------> IP3R
( v119 )% y(59) %%-------> IP3R*
( -v40 - v120 - v121 - v122 - v198 )% y(60) %%-------> IP3_3K
( -v39 + v123 + v124 -v199 )% y(61) %%-------> IP3_3K*
( v125 - v200 )% y(62) %%-------> IP3_3K*1
( -v10 + v40 - v9 - v126 - v127 )% y(63) %%-------> IP3_3K_CaM
( -v8 + v39 - v7 + v128 + v129 )% y(64) %%-------> IP3_3K_CaM*
( -v201 )% y(65) %%-------> IP3_5pase2
( v130 - v7 - v9 - v115 - v131 - v132 + v133 + v134 + v135 )% y(66) %%-------> IP4(1345)
( v136 - v137 )% y(67) %%-------> IP4(1345)_ER
( -v138 + v139 + v116 )% y(68) %%-------> IP4(1346)
( -v140 - v141 + v142 + v143 )% y(69) %%-------> IP4(1456)
( v144 + v145 )% y(70) %%-------> IP4(1456)_ER
( -v117 - v3 + v146 )% y(71) %%-------> IP4(3456)
( -v140 - v147 )% y(72) %%-------> IP4-3K
( v3 )% y(73) %%-------> IP4-3pase-cmplx
( v117 + v118 )% y(74) %%-------> ip4_1k_cmplx
( v147 + v140 )% y(75) %%-------> ip4_3k_cmplx
( v148 + v149 )% y(76) %%-------> IP5(12456)_ER
( -v72 - v4 - v150 - v151 - v146 - v143 + v152 + v153 - v118 - v147 + v138 - v139 + v154 - v155 - v156 )% y(77) %%-------> IP5(13456)
( v157 - v158 + v149 )% y(78) %%-------> IP5(13456)_ER
( v4 )% y(79) %%-------> IP5-3pase-cmplx
( v150 )% y(80) %%-------> IP5-5pase-cmplx
( v72 )% y(81) %%-------> IP5-DIPPcmplx
( -v73 - v5 - v159 - v160 + v161 - v162 + v151 - v152 - v163 + v164 )% y(82) %%-------> IP6
( v159 )% y(83) %%-------> IP6-5pase-inhib
( v73 )% y(84) %%-------> IP6-DIPPcmplx
( v5 )% y(85) %%-------> IP6-inhib-3pase-cmplx
( -v160 - v165 - v202 -v166 )% y(86) %%-------> IP6-K
( v165 + v160 )% y(87) %%-------> IP6-K-complex
( v167 - v168 )% y(88) %%-------> IP6_ER
( -v203 - v204 - v169 )% y(89) %%-------> IP6_K2
( -v19 - v205 - v206 )% y(90) %%-------> IP_1pase
( -v162 - v207 - v208 )% y(91) %%-------> IP_4pase
( v162 )% y(92) %%-------> IP_4pase_inact
( -v150 - v159 - v209 - v210 )% y(93) %%-------> IP_5pase1
( -v80 -v170 )% y(94) %%-------> AT1R
( -v211 - v212 - v213 )% y(95) %%-------> MIPP
( v171 )% y(96) %%-------> PKC-AA*
( v172 - v173 )% y(97) %%-------> PKC-basal*
( -v174 - v65 + v176 + v177 -v175 )% y(98) %%-------> PKC-Ca
( v174 )% y(99) %%-------> PKC-Ca-AA*
( -v178 + v179 + v65 )% y(100) %%-------> PKC-Ca-DAG
( v175 - v176 )% y(101) %%-------> KC-Ca-memb*
( -v171 - v177 - v172 + v173 - v66 )% y(102) %%-------> PKC-cytosolic
( -v180 + v66 )% y(103) %%-------> PKC-DAG
( -v181 + v182 + v180 )% y(104) %%-------> PKC-DAG-AA
( v181 - v182 )% y(105) %%-------> PKC-DAG-AA*
( v178 - v179 )% y(106) %%-------> PKC-DAG-memb*
( -v17 - v79 - v183 )% y(107) %%-------> PLC
( -v78 + v17 + v184 - v185 )% y(108) %%-------> PLC-Ca
( -v184 + v78 + v24 - v186 )% y(109) %%-------> PLC-Ca-Gq
( -v24 + v79 - v187 )% y(110) %%-------> PLC-Gq
( -v153 - v214 - v215 + v188 + v189 )% y(111) %%-------> PP-IP4
( -v190 - v165 - v216 + v191 + v192 )% y(112) %%-------> PP-IP5
( -v190 -v14 )% y(113) %%-------> PP-IP5-K
( v14 + v190 )% y(114) %%-------> PP-IP5-K-complex
( -v217 - v218 - v219 - v220 -v221 )% y(115) %%-------> PP1-active
( -v81 + v12 + v170 - v193 )% y(116) %%-------> Rec-AngII
( -v12 + v194 + v81 )% y(117) %%-------> Rec-AngII-Gq
( -v16 -v194 + v80 )% y(118) %%-------> Rec-Gq
( v222 )% y(119) %%-------> tot_autonomous_CaMKII_auton_286_complex
( v223 )% y(120) %%-------> tot_autonomous_CaMKII_auton_305_complex
( v38 )% y(121) %%-------> CaEPump_Ca-pump-out_complex
( v224 )% y(122) %%-------> tot_CaM_CaMKII_CaM-CaMK-phos_complex
( v225 )% y(123) %%-------> tot_CaM_CaMKII_CaM-CaMK-phos1_complex
( v226 )% y(124) %%-------> tot_autonomous_CaMKII_CaMK-phos_complex
( v227 )% y(125) %%-------> tot_autonomous_CaMKII_CaMK-phos1_complex
( v228 )% y(126) %%-------> tot_CaM_CaMKII_CaM_act_286_complex
( v229 )% y(127) %%-------> tot_CaM_CaMKII_CaM_act_305_complex
( v217 )% y(128) %%-------> PP1-active_Deph-thr286_complex
( v218 )% y(129) %%-------> PP1-active_Deph-thr286c_complex
( v219 )% y(130) %%-------> PP1-active_Deph-thr305_complex
( v220 )% y(131) %%-------> PP1-active_Deph-thr306_complex
( v221 )% y(132) %%-------> PP1-active_Deph_thr286b_complex
( v74 )% y(133) %%-------> DIPP1_dipp_ip7_complex
( v75 )% y(134) %%-------> DIPP1_dipp_ip8_complex
( v205 )% y(135) %%-------> IP_1pase_ip2_1pase_complex
( v196 )% y(136) %%-------> IP2_3pase1_ip2_3pase1_complex
( v197 )% y(137) %%-------> IP2_3pase2_ip2_3pase2_complex
( v207 )% y(138) %%-------> IP_4pase_ip2_4pase_complex
( v198 )% y(139) %%-------> IP3_3K_ip3-3k_complex
( v199 )% y(140) %%-------> IP3_3K*_ip3-3k*_complex
( v200 )% y(141) %%-------> IP3_3K*1_ip3-3k*1_complex
( v206 )% y(142) %%-------> IP_1pase_ip3_1pase_complex
( v208 )% y(143) %%-------> IP_4pase_ip3_4pase_complex
( v209 )% y(144) %%-------> IP_5pase1_ip3_5pase1_complex
( v201 )% y(145) %%-------> IP3_5pase2_ip3_5pase2_complex
( v211 )% y(146) %%-------> MIPP_ip4_3pase_complex
( v230 )% y(147) %%-------> 1345_3pase_ip4_3pase_complex
( v210 )% y(148) %%-------> IP_5pase1_ip4_5pase_complex
( v212 )% y(149) %%-------> MIPP_ip5_3pase_complex
( v202 )% y(150) %%-------> IP6-K_ip5_k1_complex
( v203 )% y(151) %%-------> IP6_K2_ip5_k2_complex
( v204 )% y(152) %%-------> IP6_K2_ip6_k2_complex
( v213 )% y(153) %%-------> MIPP_ip6_pase_complex
( v231 )% y(154) %%-------> PKC-active_PKC-phos_complex
( v183 )% y(155) %%-------> PLC_complex
( v185 )% y(156) %%-------> PLC-Ca_complex
( v187 )% y(157) %%-------> PLC-Gq_complex
( v186 )% y(158) %%-------> PLC-Ca-Gq_PLCb-Ca-Gq_complex
( v166 )% y(159) %%-------> IP6-K_pp-ip4-k1_complex
( v169 )% y(160) %%-------> IP6_K2_pp-ip4-k2_complex
( 0 )% y(161) %%-------> AA
( 0 )% y(162) %%-------> ADP
( 0 )% y(163) %%-------> ATP
( 0 )% y(164) %%-------> bisPP-IP3
( 0 )% y(165) %%-------> Ca-ext
( 0 )% y(166) %%-------> Ca-leak-to-cytoplasm
( 0 )% y(167) %%-------> AngII
( 0 )% y(168) %%-------> inositol
( 0 )% y(169) %%-------> IP5(12456)
( 0 )% y(170) %%-------> mGluRAntag
( 0 )% y(171) %%-------> PC
( 0 )% y(172) %%-------> PIP2
( 0 )% y(173) %%-------> total-CaMKII
( -v2 - v8 - v10 + v104 + v105 + v106 - v107 - v108 - v109 - v110 - v111 + v112 + v68 + v69 + v70 + v71 )% y(174) %%-------> IP3
( ( v181 - v182 ) + ( v174 ) + ( v175 - v176 ) + ( v178 - v179 ) + ( v172 - v173 ) + ( v171 ) )% y(175) %%-------> PKC-active
( -v48 - v49 + v50 + v51 -v41 + v45 - v55 - v56 -v57 + v58 )% y(176) %%-------> tot-autonomous-CaMKII
( ( v42 - v52 -v53 + v54 ) + ( v41 - v59 + v60 + v61 ) )% y(177) %%-------> tot-CaM-CaMKII
( 0 )% y(178) %%-------> active Kv
( 1e3*(1)*(Ina + IKdr  + IKahp +IKa+ ICal + Isyne + Isyni + Ileak)/p.Cm ) % y(179) %%-------> Membrane Voltage V % dV=1
( 1e3*( -mna + mina )/tmna ) % y(180) %%------->
( 1e3*( -hna + hina )/thna ) % y(181) %%------->
( 1e3*( -mdr + midr )/tdr ) % y(182) %%------->
( 1e3*( -ma1 + mia1 )/tma1 ) % y(183) %%------->
( 1e3*( -ha1 + hia1 )/tha1 ) % y(184) %%------->
( 1e3*( -ma2 + mia2 )/tma2 ) % y(185) %%------->
( 1e3*( -ha2 + hia2 )/tha2 ) % y(186) %%------->
( 1e3*( -mahp + miahp)/tahp ) % y(187) %%------->
( 1e3*( -mcal + mical)/tcal ) % y(188) %%------->
( 1e3*( -gsyne )/p.taue ) % y(189) %%------->  %(ICal / (2*p.vCa*p.F))*(1-P) + (p.Ca2cyt0-Ca2coni)/(17.7*exp(V/35));
( 1e3*( Ical / (2*(2.5e-4)*96480)*(1-(0.03/(0.03 + (5e-5) + 0.001))) + ((5e-5)-Ca_ahp)/(17.7*exp(V/35))) ) % y(190) %%------->  %dCa_ahpdt
( -r1-r2+r5+r6 ) % y(191) %%------->
( +r1-r3-r5+r8 ) % y(196) %%------->
( +r2-r4-r6+r7 ) % y(195) %%------->
( +r3+r4-r7-r8 ) % y(194) %%------->%-r10+r11
];

end

%
% function
function yy = interpoln( x, y, xx )
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Custom function to perform linear interpolation
%
% input x - x vector
%       y - y vector
%       xx - scaler value of x for which interpolated value of y is asked
%
% output yy - interpolated value of xx 
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  xx = floor(xx*100)/100;
  i = myfind( x, xx);
  yy = y(i) + ((xx - x(i))*y(i+1) - (xx - x(i) )*y(i))/(x(i+1) - x(i));
  yy = abs(yy);
end

%
% function
function b = myfind(x,searchfor)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Custom find function
%
% input x - x vector
%       searchfor - index value to searched on x
%
% output b - index for the lower bound value 
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
a=1;
b=numel(x);
while (a+1<b)
    lw=(floor((a+b)/2));
    if (x(lw)<searchfor)
        a=lw;
    else
        b=lw;
    end
end

end



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