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Mass action equations

Mass action equations. E + S -(k1)  E|S E|S -(k2)  E+S E|S -(k3)  E+P OR E + S =(k1/k2) = E|S E|S -(k3)  E+P. Enzyme in matlab. Matlab code and simulation/output commands. % simulate a simple ode model tspan=[0 4]; [plott ploty]=ode15s(@enzyme,tspan,[1;1;0;0]);

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Mass action equations

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  1. Mass action equations • E + S -(k1) E|S • E|S -(k2) E+S • E|S -(k3) E+P OR • E + S =(k1/k2)= E|S • E|S -(k3) E+P

  2. Enzyme in matlab • Matlab code and simulation/output commands % simulate a simple ode model tspan=[0 4]; [plott ploty]=ode15s(@enzyme,tspan,[1;1;0;0]); plot(plott,ploty)

  3. Enzyme simulation here… function dydt = enzyme(t,y) %----------------------------------------------------------------------- % Specify the ODE %----------------------------------------------------------------------- % Get rate constants from outside this function global xk1 xki xk2 xk1=3; xki=4; xk2=4; % Work in a more comprehensible set of variables E = y(1); S = y(2); ES = y(3); P = y(4); % Dynamic equations dydt(1) = -xk1*E*S + xki*ES + xk2*ES ; % dE/dt dydt(2) = -xk1*E*S + xki*ES ; % dS/dt dydt(3) = xk1*E*S - xki*ES - xk2*ES ; % dES/dt dydt(4) = xk2*ES ; % dP/dt dydt = dydt'; %MATLAB v5 wants a column vector

  4. Model analysis techniques • Parameter scanning • Multiple simulations at a range of values for one parameter • Bifurcation analysis • For example, identifying the point where oscillations start • Sensitivity analysis • How do the concentrations depend on one specific rate?

  5. Sensitivity analysis • Sensitivity analysis investigates the changes in the system outputs or behavior with respect to the parameter variations. It is a general technique for establishing the contribution of individual parameter values to the overall performance of a complex system. • Sensitivity analysis is an important tool in the studies of the dependence of a system on external parameters, and sensitivity considerations often play an important role in the design of control systems. • Parameter sensitivity analysis can also be utilised to validate a model’s response and iteratively, to design experiments that support the estimation of parameters Slide from Xuan Liu

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