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cellmodel_odes_nk02.m
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cellmodel_odes_nk02.m
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function dydt= cellmodel_odes(t, y)
%% whole cell model rates, parameters and species assigments
global a r dm kb ku thetax gamma lam;
% parameters
thetar = 426.8693338968694;
s0= 1.0e4;
gmax= 1260.0;
thetax = 4.379733394834643;
Kt= 1.0e3;
M= 1.0e8;
we= 4.139172187824451;
Km= 1.0e3;
vm= 5800.0;
nx= 300.0;
Kq= 1.522190403737490e+05;
Kp= 180.1378030928276;
vt= 726.0;
wr= 929.9678874564831;
wq= 948.9349882947897;
nq= 4;
nr= 7549.0;
ns= 0.5;
% define rate constants
dm= 0.1;
kb= 1;
ku= 1.0;
% whole cell model molecular species
rmr= y(1); % mrna-ribo complex of ribosomal proteins
em= y(2); % protein metabolic enzyme
rmq= y(3); % mrna-ribo complex of housekeeping proteins
rmt= y(4); % mrna-ribo complex of transporter enzyme proteins
et= y(5); % protein transporter enzyme
rmm= y(6); % mrna-ribo complex of metabolic enzyme proteins
mt= y(7); % mrna of transporter enzyme
mm= y(8); % mrna of metabolic enzyme
q= y(9); % protein housekeeping
si= y(10); % internal nutrients
mq= y(11); % mrna of house-keeping protein
mr= y(12); % mrna of ribosomes
r= y(13); % ribosomes
a= y(14); % ATP
%% synthetic gene circuit parameters & species assignments
% synthetic genetic circuit parameters
wp= 1000;
% synthetic gene circuit species assignments
mp= y(15); % mrna of gratuitous protein
rmp= y(16); % mrna-ribo complex of gratuitous protein
p = y(17); % gratuitous protein
%% whole cell model odes and fluxes
% fluxes
Kgamma= gmax/Kp; % translational elongation threshold [moles/cell] % essential (part equation 3)
gamma= gmax*a/(Kgamma + a); % rate of translational elongation % essential (eq. 3)
ttrate= (rmq + rmr + rmp + rmt + rmm)*gamma; % total number of ribosomes * rate of translational elongation % essential (eq.9b)
lam= ttrate/M; % growth rate % essential (eq.9b)
fr= nr*(r + rmr + rmp + rmt + rmm + rmq) / ( nr*(r + rmr + rmp + rmt + rmm + rmq) + nx * (p + q + et + em)); % ribosome fraction % equation 10 (essential???)
nucat= em*vm*si/(Km + si); % rate of metabolism of nutrients % essential (part of eq.1)
dydt(size(y,1),1)= 0;
% odes
dydt(1)= +kb*r*mr-ku*rmr-gamma/nr*rmr-lam*rmr; % d(rmr)/dt % essential (equation 6A) + non-essential terms
dydt(2)= +gamma/nx*rmm-lam*em; % d(em)/dt
dydt(3)= +kb*r*mq-ku*rmq-gamma/nx*rmq-lam*rmq; % d(rmq)/dt % essential (equation 6B) + non-essential terms
dydt(4)= +kb*r*mt-ku*rmt-gamma/nx*rmt-lam*rmt; % d(rmt)/dt % essential (equation 6C) + non-essential terms
dydt(5)= +gamma/nx*rmt-lam*et; % d(et)/dt
dydt(6)= +kb*r*mm-ku*rmm-gamma/nx*rmm-lam*rmm; % d(rmm)/dt % essential (equation 6D) + non-essential terms
dydt(7)= +(we*a/(thetax + a))+ku*rmt+gamma/nx*rmt-kb*r*mt-dm*mt-lam*mt; % d(mt)/dt % essential (eq.5D & 8)
dydt(8)= +(we*a/(thetax + a))+ku*rmm+gamma/nx*rmm-kb*r*mm-dm*mm-lam*mm; % d(mm)/dt % essential (eq.5C & 8)
dydt(9)= +gamma/nx*rmq-lam*q; % d(q)/dt
dydt(10)= +(et*vt*s0/(Kt + s0))-nucat-lam*si; % d(si)/dt nutrient import into cell % essential (eq1)
dydt(11)= +(wq*a/(thetax + a)/(1 + (q/Kq)^nq))+ku*rmq+gamma/nx*rmq-kb*r*mq-dm*mq-lam*mq; % d(mq)/dt transcription, translation and degratation of q-proteins % essential (eq.5A & 8)
dydt(12)= +(wr*a/(thetar + a))+ku*rmr+gamma/nr*rmr-kb*r*mr-dm*mr-lam*mr; % d(mr)/dt transcription, translation and degratation of ribosomal-proteins % essential (eq.5B & 8)
dydt(13)= +ku*rmr+ku*rmt+ku*rmm+ku*rmp+ku*rmq+gamma/nr*rmr+gamma/nr*rmr+gamma/nx*rmt+gamma/nx*rmm+gamma/nx*rmp+gamma/nx*rmq-kb*r*mr-kb*r*mt-kb*r*mm-kb*r*mp-kb*r*mq-lam*r; % d(r)/dt % essential (eq.7)
dydt(14)= +ns*nucat-ttrate-lam*a; % d(a)/dt % essential (eq.2)
%% synthetic gene circuit odes
% odes
dydt(15)= +transcription(wp) + ribosome_unbind(rmp) + translation(rmp,nx) - ribosome_bind(mp) - degradation(mp) - dilution(mp); % d(mp)/dt
dydt(16)= +ribosome_bind(mp) - ribosome_unbind(rmp) - translation(rmp,nx) - dilution(rmp); % d(rmp)/dt
dydt(17)= +translation(rmp,nx) - dilution(p) ; % d(p)/dt
end