Conor Keith Week 7

Purpose

• The purpose of this assignment was to complete my project on nitrogen metabolism in yeast.

Workflow

• Most of the work I did was done on paper. Most of my time consisted of me reading different fermentation models and methods of optimal control and changing them around to simplify them.
• Notes
• Once I constructed system of equations, I created a cost function and derived the Hamiltonian. I first attempted to solve it directly and find a transversality condition, but I quickly realized that wasn't feasible and decided to let matlab handle the solutions for me.

toms t toms tfs tf = 100*tfs; tfg = 50; x1g = 5; x2g = 80-80*t/tf; x3g = 50; x4g = 200*t/tf; ug = 3; n = [ 20 60 60 60]; e = [0.01 0.002 1e-4 0]; for i = 1:3

   p = tomPhase('p', t, 0, tf, n(i));
   setPhase(p);
   tomStates x1s x2s x3s x4s
   if e(i)
       tomStates u
   else
       tomControls u
   end
   x1 = 10*x1s;
   x2 = 1*x2s;
   x3 = 100*x3s;
   x4 = 100*x4s;
   x0 = {tf == tfg
       icollocate({
       x1 == x1g
       x2 == x2g
       x3 == x3g
       x4 == x4g
       })
       collocate({u==ug})};
       cbox = {
       0.1 <= tf <= 100
       mcollocate({
       0    <= x1
       0    <= x2
       0    <= x3
       1e-8 <= x4  
       })
       0 <= collocate(u) <= 12};
   cbnd = {initial({
       x1 == 1;
       x2 == 80;
       x3 == 0;
       x4 == 20})
       final(0 <= x4 <= 200)};
   g1 = (0.408/(1+x3/16))*(x2/(x2+0.22));
   g2 = (1/(1+x3/71.5))*(x2/(0.44+x2));    
   ceq = collocate({
       dot(x1) == g1*x1 - u*x1/x4
       dot(x2) == -10*g1*x1 + u*(150-x2)/x4
       dot(x3) == g2*x1 - u*x3/x4
       dot(x4) == u});   
   J = final(x3*x4);
   if e(i)
       objective = -J/4900 + e(i)*integrate(dot(u)^2);
   else
       objective = -J/4900;
   end
  options = struct;
   options.name = 'EtOH Production';
   solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);
   subplot(2,1,1)
   ezplot([x1 x2 x3 x4]);
   legend('Biomass','Glucose Concentration','EtOH Concentratino','Volume');
   title(['EtOH Production state variables. J = ' num2str(subs(J,solution))]);
   subplot(2,1,2)
   ezplot(u);
   legend('Feed Rate');
   title('EtOH Production control');
   drawnow     
   tfg = subs(tf,solution);
   x1g = subs(x1,solution);
   x2g = subs(x2,solution);
   x3g = subs(x3,solution);
   x4g = subs(x4,solution);    

end

Presentation

• Presentation Power Point
• Updated Version of Slideshow
• PDF Version of Presentation

Acknowledgements

• This assignment was completed by me without help from an outside source.

References

• Brauer, M. J., Saldanha, A. J., Dolinski, K., & Botstein, D. (2005). Homeostatic adjustment and metabolic remodeling in glucose-limited yeast cultures. Molecular biology of the cell, 16(5), 2503-2517.
• Van den Brink, J., Canelas, A. B., Van Gulik, W. M., Pronk, J. T., Heijnen, J. J., De Winde, J. H., & Daran-Lapujade, P. (2008). Dynamics of glycolytic regulation during adaptation of Saccharomyces cerevisiae to fermentative metabolism. Applied and environmental microbiology, 74(18), 5710-5723.
• Wang, F. S., & Cheng, W. M. (1999). Simultaneous Optimization of Feeding Rate and Operation Parameters for Fed‐Batch Fermentation Processes. Biotechnology Progress, 15(5), 949-952.
• Vázquez-Lima, F., Silva, P., Barreiro, A., Martínez-Moreno, R., Morales, P., Quirós, M., ... & Ferrer, P. (2014). Use of chemostat cultures mimicking different phases of wine fermentations as a tool for quantitative physiological analysis. Microbial cell factories, 13(1), 85.
• Gabriel, E., & Carrillo, U. (1999). Optimal control of fermentation processes (Doctoral dissertation, PhD Thesis, City University, London).
• Banga, J. R., Balsa-Canto, E., Moles, C. G., & Alonso, A. A. (2005). Dynamic optimization of bioprocesses: Efficient and robust numerical strategies. Journal of Biotechnology, 117(4), 407-419.

Conor Keith 02:48, 2 March 2017 (EST)