function dndt = mi_araC_simplest(t,n,param) %INDUCIBLE MODEL PBAD/ARAC: % Establishes model equations for the inducible promoter pBAD/araC of % the designed circuit. It gives us back the variation of the % concentrations of the chemical species of the reactions in each % instant of time. % This model does not contemplate the presence of ribosomes. % Abbreviations: % pBAD.araC: DNA binded to araC dimer % pBAD.araC.arabi: DNA binded to (araC.arabi) transcription factor % arabe: extracellular L-arabinose % arabi: intracellular L-arabinosa (per cell) % mRNA: messenger RNA % PoI: Protein of Interest %param: model parameters %D: diffusion coefficient(min-1) %Vc ratio: cell volume(uL)/external volume(uL) %Ku: dissociation rate of DNA.araC.arabi complex(min-1) %Kd: dissociation constant of DNA.araC.arabi complex(molec^2) %Kb: association rate of DNA.araC.arabi complex(molec-2.min-1) %K: transcription rate (min-1) %alfa: constante de actividad basal del pBAD.araC(adimensional) %p: PoI translation rate (min-1) %dm: mRNA degradation rate (min-1) %darab: L-arabinose degradation rate (min-1) %dp: PoI degradation rate (min-1) %mu: Dilution rate(min-1) %cn: plamids copy number(molec) %Kmax: maximum growth capacity (cells) D = param(1); Vc = param(2); Ku = param(3); Kd = param(4); Kb = Ku/Kd; K = param(5); alfa = param(6); p = param(7); dm = param(8); darab = param(9); dp = param(10); mu = param(11); cn = param(12); Kmax = param(13); % Algebraic equations: pBAD_araC = cn - n(1); % Differential equations: %n(1): pBAD.araC.arabi concentration (molec) %n(2): Extracellular L-arabinose concentration (molec) %n(3): Intracellular L-arabinose concentration (molec) %n(4): mRNA concentration (molec) %n(5): PoI concentration(molec) %n(6): number of cells dn1 = Kb*n(3)^2*pBAD_araC - Ku*n(1); dn2 = D*n(3)*n(6) - D*Vc*n(2)*n(6) - darab*n(2); dn3 = D*Vc*n(2) - D*n(3) - 2*Kb*n(3)^2*pBAD_araC + 2*Ku*n(1) - (darab+mu)*n(3); dn4 = alfa*K*pBAD_araC + K*n(1) - (dm+mu)*n(4); dn5 = p*n(4) - (dp+mu)*n(5); dn6 = mu*n(6)*(1 - n(6)/Kmax); dndt = [dn1; dn2; dn3; dn4; dn5; dn6]; return