%pset 6 problem %E1 = Ras-GTP %E2 = RAF Phosphatase %cx = complex %P = phosphate (PO4) %PP = two phosphates %* = activated %Pase = phosphatase enzyme (so MEKPase is MEK phosphatase) %initial conditions, all from Huang & Ferrell, 1996 RAF = 0.003; %uM RAFstar = 0; %uM, initially no activated RAF RAFstar_cx = 0; %uM, initially no RAF* complex RAFstar1_cx = 0; %uM, initially no RAF* complex MEK = 1.2; %uM MEKp = 0; %uM, initially no phosphorylated MEK MEKpp = 0; %uM, initially no phosphorylated MEK MEKpp_cx = 0; %uM MEKpp1_cx = 0; %uM, initially no phosphorylated MEK complex ERK = 1.2; %uM ERKp = 0; %uM, initially no phosphorylated ERK ERKpp = 0; %uM, initially no phosphorylated ERK ERKPase = 0.12; %uM ERKPase_cx = 0; %uM, initially no complex ERKPase1 = 0.12; %uM ERKPase1_cx = 0; %uM, initially no complex MEKPase = 0.3e-3; %uM MEKPase_cx = 0; %uM, initially no complex MEKPase1 = 0.3e-3; %uM MEKPase1_cx = 0; %uM, initially no complex E2 = 0.3e-3; %uM, input stimulus, 10-fold less abundant than its substrate Mos E2_cx = 0; %uM E1 = 1e-2; %uM, will vary this input stimulus below E1_cx = 0; %uM %parameters Km = 300; %nM, Michaelis constant Vmax = 150; %nM s^-1, from Michaelis Menten E1 = logspace(-6, -1, 100); %uM params = [E2,0,ERK,ERKp,ERKpp,MEK,MEKp,MEKpp,RAF,RAFstar,MEKPase,MEKPase1,ERKPase,ERKPase1,E2_cx,E1_cx,MEKpp_cx,MEKpp1_cx,RAFstar_cx,RAFstar1_cx,MEKPase_cx,MEKPase1_cx,ERKPase_cx,ERKPase1_cx]; t = [0 100]; for j = 1:length(E1) params(2) = E1(j); [t,y] = ode23s(@KinaseCascade, t, params,[],Km,Vmax); Y1 = y(:,5); Y2 = y(:,8); Y3 = y(:,10); Activated_ERK(j) = Y1(length(t)); %just want steady state values Activated_MEK(j) = Y2(length(t)); Activated_RAF(j) = Y3(length(t)); end %normalize to get percent response Activated_ERK = Activated_ERK/(Activated_ERK(length(Activated_ERK))); Activated_MEK = Activated_MEK/(Activated_MEK(length(Activated_MEK))); Activated_RAF = Activated_RAF/(Activated_RAF(length(Activated_RAF))); semilogx(E1,Activated_RAF,'b'); hold on semilogx(E1,Activated_MEK,'g'); semilogx(E1,Activated_ERK,'r'); legend('activated RAF','activated MEK','activated ERK'); title('Predicted percent response'); xlabel ('Input stimulus (E1)'); ylabel ('predicted steady-state kinase activity'); E1 = 1e-1; %large input stimulus, uM params(2) = E1; [t,y] = ode23s(@KinaseCascade, t, params,[],Km,Vmax); activatedERK = y(:,5); figure(2) plot(t,activatedERK); title('ERK output over time for large input stimulus'); xlabel ('time'); ylabel ('predicted ERK concentration, nM');