Semi-deterministic and genetic algorithms for global optimization of microfluidic protein-folding devices

International Journal for Numerical Methods in Engineering

Volumn 66, Issue 2, 2006, Pages 319-333

  Ivorra, Benjamin ^a   Hertzog, David E ^b   Mohammadi, Bijan ^a   Santiago, Juan G ^b  

^a UNIV MONTPELLIER   (France)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Boundary value problem; Dynamical systems; Global optimization; Microfluidic mixers; Shape optimization

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; GENETIC ALGORITHMS; MIXING; PROTEINS; SENSITIVITY ANALYSIS;

COMPUTATIONAL TIME APPROXIMATE STATE; MICROFLUIDIC MIXERS; OPTIMIZATION ALGORITHMS;

GLOBAL OPTIMIZATION;

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; GENETIC ALGORITHMS; GLOBAL OPTIMIZATION; MIXING; PROTEINS; SENSITIVITY ANALYSIS;

EID: 33645469408     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1562     Document Type: Article

References (33)

1. Goldberg D. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley: Reading, MA, 1989.
2. Fonseca CM, Fleming J. An overview of evolutionary algorithms in multi-objective optimization. Evolutionary Computation 1995; 3(1):1-16.
3. Mohammadi B, Saiac J-H. Pratique de la simulation numérique. Dunod: Paris, 2002.
4. Attouch H, Cominetti R. A dynamical approach to convex minimization coupling approximation with the steepest descent method. Journal of Differential Equations 1996; 128(2):519-540.
5. Ivorra B, Mohammadi B, Redont P. Low-complexity global optimization by solution of BVP. Journal of Global Optimization 2005, submitted.
6. Mohammadi B, Santiago J, Molho J. Incomplete sensitivities in the design of minimal dispersion fluidic channels. Computer Methods in Applied Mechanics and Engineering 2003; 192:4131-4145.
7. Mohammadi B, Bharadwadj R, Santiago J. Design and optimization of on-chip capillary electrophoresis. Electrophoresis Journal 2002; 23(16):2729-2744.
8. Mohammadi B, Molho J, Herr A, Santiago J, Kenny T, Brennen R, Gordon G. Optimization of turn geometries for on-chip electrophoresis. Analytical Chemistry 2001; 73(6):1350-1360.
9. Hertzog DE, Michalet X, Jager M, Kong X, Santiago JG, Weiss S, Bakajin O. Femtomole mixer for microsecond kinetic studies of protein folding. Analytical Chemistry 2004; 75(24):7169-7178.
10. Roder H. Stepwise helix formation and chain compaction during protein folding. Proceedings of the National Academy of Sciences of the USA 2004; 101:1793-1794.
11. Jones CM, Henry ER, Hu Y, Chan C-K, Luck SD, Bhuyan A, Roder H, Hofrichter J, Eaton WA. Fast events in protein folding initiated by nanosecond laser photolysis. Proceedings of the National Academy of Sciences of the USA 1993; 90:11860-11864.
12. Hagen SJ, Eaton WA. Two-state expansion and collapse of a polypeptide. Journal of Molecular Biology 2000; 301:1037-1045.
13. Pryse KM, Bruckman TG, Maxfield BW, Elson EL. Kinetics and mechanism of the folding of cytochrome c. Biochemistry 1992; 31(22):5127-5136.
14. Jacob M, Holtermann G, Perl D, Reinstein J, Schindler T, Geeves MA, Schmid FX. Microsecond folding of the cold shock protein measured by a pressure jump technique. Biochemistry 1999; 38:2882-2891.
15. Chan CK, Hu Y, Takahashi S, Rousseau DL, Eaton WA. Submillisecond protein folding kinetics studied by ultrarapid mixing. Proceedings of the National Academy of Sciences of the USA 1997; 94:1779-1784.
16. Pollack L, Tate MW, Darnton NC, Knight JB, Gruner SM, Eaton WA, Austin RH. Compactness of the denatured state of a fast-folding protein measured by submillisecond small angle X-ray scattering. Proceedings of the National Academy of Sciences of the USA 1999; 96:10115-10117.
17. Park S-H, Shastry MCR, Roder H. Folding dynamics of the b1 domain of protein g explored by ultrarapid mixing. Nature, Structural Biology 1999; 6:943-947.
18. Brody JP, Yager P, Goldstein RE, Austin RH. Biotechnology at low Reynolds numbers. Biophysical Journal 1996; 71(6):3430-3441.
19. Russell R, Millet IS, Tate MW, Kwok LW, Nakatani B, Gruner SM, Mochrie SGJ, Pande VS, Doniach S, Herschlag D, Pollack L. Rapid compaction during RNA folding. Proceedings of the National Academy of Sciences of the USA 2002; 99:4266-4271.
20. Knight JB, Vishwanath A, Brody JP, Austin RH. Hydrodynamic focusing on a silicon chip: mixing nanoliters in microseconds. Physical Review Letters 1998; 80:3863-3866.
21. Shastry MCR, Luck SD, Roder H. A continuous-flow capillary mixer to monitor reactions on the microsecond time scale. Biophysical Journal 1998; 74:2714-2721.
22. Dumas L, Herbert V, Muyl F. Hybrid method for aerodynamic shape optimization in automotive industry. Computers and Fluids 2004; 33(5):849-858.
23. Ivorra B. Semi-deterministic global optimization. Ph.D. Thesis, University of Montpellier 2, 2006.
24. Mohammadi B, Pironneau O. Applied Shape Optimization for Fluids. Oxford University Press: Oxford, 2001.
25. Vanderplaats GN. Numerical Optimization Techniques for Engineering Design. McGraw-Hill: New York, 1990.
26. Debiane L, Ivorra B, Mohammadi B, Nicoud F, Ern A, Poinsot T, Pitsch H. Temperature and pollution control in flames. Proceedings of the Summer Program, Vol. 5. Center for Turbulence Research, NASA AMES/Stanford University, USA, 2004; 367-375.
27. Mohammadi B, Pironneau O. Shape optimization in fluid mechanics. Annual Review of Fluid Mechanics 2004; 36:255-279.
28. Ottino JM. The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press: Cambridge, 1989.
29. Darnton N, Bakajin O, Huang R, North B, Tegenfeldt J, Cox E, Sturn J, Austin RH. Condensed matter. Journal of Physics 2001; 13:4891-4902.
30. Deen WM. Analysis of Transport Phenomena. Oxford University Press: New York, 1998.
31. Hughes T, Brooks A. A multi-dimensional upwind scheme with no crosswind diffusion. In Finite Element Methods for Convection Dominated Flows, Vol. 34, Hughes T (ed.). ASME: New York 1979; 19-35.
32. Deuflhard P. A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting. Numerical Mathematics 1974; 32:289-315.
33. Hertzog DE, Ivorra B, Mohammadi B, Bakajin O, Santiago JG. Optimization of fast microfluidic mixers for protein folding, in press.