Multi-Enzyme Pathway Optimisation Through Star-Shaped Reachable Sets

1. Carbonell, P., Parutto, P., Herisson, J., Pandit, S.B., Faulon, J.L.: XTMS: pathway design in an eXTended metabolic space. Nucleic Acids Res. 42(W1), W389–W394 (2014)

   Article  Google Scholar 

2. Klipp, E., Heinrich, R., Holzhütter, H.G.: Prediction of temporal gene expression. Eur. J. Biochem. 269(22), 5406–5413 (2002)

   Article  Google Scholar 

3. Mazurenko, S.: Partial differential equation for evolution of star-shaped reachability domains of differential inclusions. Set-Valued Variational Anal. 24(2), 333–354 (2016)

   Article  MathSciNet  MATH  Google Scholar 

4. Filippov, A.: On certain questions in the theory of optimal control. J. Soc. Ind. Appl. Math. Ser. A Control 1(1), 76–84 (1962)

   Article  MathSciNet  MATH  Google Scholar 

5. Aubin, J.P., Cellina, A.: Differential Inclusions: Set-Valued Maps and Viability Theory, vol. 264. Springer, Heidelberg (1984)

   MATH  Google Scholar 

6. Bayon, L., Otero, J.A., Ruiz, M.M., Suárez, P.M., Tasis, C.: Sensitivity analysis of a linear and unbranched chemical process with n steps. J. Math. Chem. 53(3), 925–940 (2015)

   Article  MathSciNet  MATH  Google Scholar 

7. Dvorak, P., Kurumbang, N.P., Bendl, J., Brezovsky, J., Prokop, Z., Damborsky, J.: Maximizing the efficiency of multienzyme process by stoichiometry optimization. ChemBioChem 15(13), 1891–1895 (2014)

   Article  Google Scholar 

8. Llorens, M., Nuño, J.C., Rodríguez, Y., Meléndez-Hevia, E., Montero, F.: Generalization of the theory of transition times in metabolic pathways: a geometrical approach. Biophys. J. 77(1), 23–36 (1999)

   Article  Google Scholar 

9. Bartl, M., Li, P., Schuster, S.: Modelling the optimal timing in metabolic pathway activation – use of Pontryagin’s Maximum Principle and role of the Golden section. Biosystems 101(1), 67–77 (2010)

   Article  Google Scholar 

10. Oyarzun, D.A., Ingalls, B.P., Middleton, R.H., Kalamatianos, D.: Sequential activation of metabolic pathways: a dynamic optimization approach. Bull. Math. Biol. 71(8), 1851–1872 (2009)

    Article  MathSciNet  MATH  Google Scholar 

11. Hijas-Liste, G.M., Klipp, E., Balsa-Canto, E., Banga, J.R.: Global dynamic optimization approach to predict activation in metabolic pathways. BMC Syst. Biol. 8(1), 1 (2014)

    Article  Google Scholar 

12. Kurzhanski, A.B., Varaiya, P.: Dynamics and Control of Trajectory Tubes. Theory and Computation. Birkhauser, Basel, (2014)

    Book  MATH  Google Scholar 

13. Mitchell, I.M., Bayen, A.M., Tomlin, C.J.: A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games. IEEE Trans. Autom. Control 50(7), 947–957 (2005)

    Article  MathSciNet  MATH  Google Scholar 

14. Panasyuk, A.I., Panasyuk, V.I.: An equation generated by a differential inclusion. Math. Notes Acad. Sci. USSR 27(3), 213–218 (1980)

    MathSciNet  MATH  Google Scholar 

15. Althoff, M., Stursberg, O., Buss, M.: Computing reachable sets of hybrid systems using a combination of zonotopes and polytopes. Nonlinear Anal. Hybrid Syst. 4(2), 233–249 (2010)

    Article  MathSciNet  MATH  Google Scholar 

16. Mazurenko, S.S.: Viscosity Solutions to Evolution of Star-Shaped Reachable Sets (2016). Submitted and is currently under review

    Google Scholar 

17. Kurzhanski, A.B., Filippova, T.F.: On the theory of trajectory tubes - a mathematical formalism for uncertain dynamics, viability and control. In: Advances in Nonlinear Dynamics and Control, pp. 122–188. Birkhauser, Boston (1993)

    Google Scholar 

18. Crandall, M.G., Lions, P.L.: Two approximations of solutions of Hamilton-Jacobi equations. Math. Comput. 43(167), 1–19 (1984)

    Article  MathSciNet  MATH  Google Scholar 

19. Souganidis, P.E.: Approximation schemes for viscosity solutions of Hamilton-Jacobi equations. J. Differ. Eqn. 59(1), 1–43 (1985)

    Article  MathSciNet  MATH  Google Scholar 

Download references