%% 6.581 PS5 %% Qsn4 %% lambda2.m function [phi, gradPhi] = lambda2(P) %% DATA %% %% Observed Fixed points for two different trials %% obs1 = [33.71; 0.11; 1.57; 0.01]; obs2 = [0.05 ; 3.74; 0.02; 0.479]; %% Find the fixed points (x1, x2) %% Hint: this is what we did on last weeks homework x1 = ; %CHANGE ME x2 = ; %CHANGE ME %% %% Compute the Squared Error to the Data %% c = ; %CHANGE ME phi = ; %CHANGE ME %% %% Compute the Gradient of Phi with P. This part will be several steps %% you may want to compute the matrix quantites we will need here in %% a seperate function. %% gradPhi = ; %CHANGE ME %%========================================================================= %% The ODE model of the Lambda Switch %% This is implemented for you but you may want to copy and paste this code %% as a starting point for other helper methods. %% %% These are the constants that we used in PS4 %% %% p0 = [ 1.0; %DNA_TOTAL %% 0.5; %k_Cro2B_mCro %% 1.0; %k_mCro_0 %% 1.0; %k_mCro_Cro %% 1.0; %k_Cro_0 %% 10; %k_Cro_Cro2 %% 1.0; %k_Cro2_Cro %% 10; %k_Cro2_Cro2B %% 1.0; %k_Cro2B_Cro2 %% 0.5; %k_CI2B_mCI %% 1.0; %k_mCI_0 %% 1.0; %k_mCI_CI %% 1.0; %k_CI_0 %% 10; %k_CI_CI2 %% 1.0; %k_CI2_CI %% 10; %k_CI2_CI2B %% 1 %k_CI2B_CI2 %% ]; %%========================================================================= function dxdt=F(x, P) %% Indexes into x mCro = 1; Cro = 2; Cro2 = 3; Cro2B = 4; mCI = 5; CI = 6; CI2 = 7; CI2B = 8; %% Indexes into P DNA_tot = 1; k_Cro2B_mCro = 2; k_mCro_0 = 3; k_mCro_Cro = 4; k_Cro_0 = 5; k_Cro_Cro2 = 6; k_Cro2_Cro = 7; k_Cro2_Cro2B = 8; k_Cro2B_Cro2 = 9; k_CI2B_mCI = 10; k_mCI_0 = 11; k_mCI_CI = 12; k_CI_0 = 13; k_CI_CI2 = 14; k_CI2_CI = 15; k_CI2_CI2B = 16; k_CI2B_CI2 = 17; %% Don't forget to differentiate this when you are computing the Jacobian %% and the gradients DNA = P(DNA_tot) - x(Cro2B)- x(CI2B); %% The Model dxdt = [ ... P(k_Cro2B_mCro) * x(Cro2B) - P(k_mCro_0) * x(mCro); P(k_mCro_Cro) * x(mCro) + 2*P(k_Cro2_Cro) * x(Cro2) - 2*P(k_Cro_Cro2) * x(Cro)^2 - P(k_Cro_0) * x(Cro); P(k_Cro_Cro2) * x(Cro)^2 + P(k_Cro2B_Cro2) * x(Cro2B) - P(k_Cro2_Cro) * x(Cro2) - P(k_Cro2_Cro2B) * x(Cro2)*DNA; P(k_Cro2_Cro2B) * x(Cro2)*DNA - P(k_Cro2B_Cro2) * x(Cro2B); P(k_CI2B_mCI) * x(CI2B) - P(k_mCI_0) * x(mCI); P(k_mCI_CI) * x(mCI) + 2*P(k_CI2_CI) * x(CI2) - 2*P(k_CI_CI2) * x(CI)^2 - P(k_CI_0) * x(CI); P(k_CI_CI2) * x(CI)^2 + P(k_CI2B_CI2) * x(CI2B) - P(k_CI2_CI) * x(CI2) - P(k_CI2_CI2B) * x(CI2)*DNA; P(k_CI2_CI2B) * x(CI2)*DNA - P(k_CI2B_CI2) * x(CI2B)... ];