Publication: Two- and three-dimensional modeling and optimization applied to the design of a fast hydrodynamic focusing microfluidic mixer for protein folding
Loading...
Full text at PDC
Publication Date
2013
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Institute of Physics
Citations
Exportar
Abstract
We present a design of a microfluidic mixer based on hydrodynamic focusing which is used to initiate the folding process (i.e., changes of the molecular structure) of a protein. The folding process is initiated by diluting (from 90% to 30%) the local denaturant concentration (initially 6 M GdCl solution) in a short time interval we refer to as mixing time. Our objective is to optimize this mixer by choosing suitable shape and flow conditions in order to minimize this mixing time. To this end, we first introduce a numerical model that enables computation of the mixing time of a mixer. This model is based on a finite element method approximation of the incompressible Navier-Stokes equations coupled with the convective diffusion equation. To reduce the computational time, this model is implemented in both full three-dimensional (3D) and simplified two-dimensional (2D) versions; and we analyze the ability of the 2D model to approximate the mixing time predicted by the 3D model. We found that the 2D model approximates the mixing time predicted by the 3D model with a mean error of about 15%, which is considered reasonable. Then, we define a mixer optimization problem considering the 2D model and solve it using a hybrid global optimization algorithm. In particular, we consider geometrical variables and injection velocities as optimization parameters. We achieve a design with a predicted mixing time of 0.10 μs, approximately one order of magnitude faster than previous mixer designs. This improvement can be in part explained by the new mixer geometry including an angle of π/5 radians at the channel intersection and injections velocities of 5.2 m s−1 and 0.038 m s−1 for the side and central inlet channels, respectively. Finally, we verify the robustness of the optimized result by performing a sensitivity analysis of its parameters considering the 3D model. During this study, the optimized mixer was demonstrated to be robust by exhibiting mixing time variations of the same order than the parameter ones. Thus, the obtained 2D design can be considered optimal also for the 3D model.
Description
UCM subjects
Unesco subjects
Keywords
Citation
1 J. M. Berg, J. L. Tymoczko, and L. Stryer, Biochemistry, 5th ed. (W. H. Freeman, New York, 2002).
2 H. Roder, “Stepwise helix formation and chain compaction during protein folding,” Proc. Natl. Acad. Sci. U.S.A. 101, 1793–1974 (2004).
3 M. Gaudet, N. Remtulla, S. E. Jackson, E. R. G. Main, D. G. Bracewell, G. Aeppli, and P. A. Dalby, “Protein denaturation and protein: Drugs interactions from intrinsic protein fluorescence measurements at the nanolitre scale,” Protein Sci. 19(8), 1544–1554 (2010).
4 J. A. Infante, B. Ivorra, A. M. Ramos, and J. M. Rey, “On the modeling and simulation of high pressure processes and inactivation of enzymes in food engineering,” Math. Models Meth. Appl. Sci. 19(12), 2203–2229 (2009).
5 R. Russell, I. S. Millett, M. W. Tate, L. W. Kwok, B. Nakatani, S. M. Gruner, S. G. Mochrie, V. Pande, S. Doniach, D. Herschlag, and L. Pollack, “Rapid compaction during RNA folding,” Proc. Natl. Acad. Sci. U.S.A. 99(7), 4266–4271 (2002).
6 C. M. Jones, E. R. Henry, Y. Hu, C. Chan, S. D. Luck, A. Bhuyan, H. Roder, J. Hofrichter, and W. A. Eaton, “Fast events in protein folding initiated by nanosecond laser photolysis,” Proc. Natl. Acad. Sci. U.S.A. 90(24), 11860–11864 (1993).
7 M. Jacob, G. Holtermann, D. Perl, J. Reinstein, T. Schindler, M. A. Geeves, and F. X. Schmid, “Microsecond folding of the cold shock protein measured by a pressure-jump technique,” Biochemistry 38(10), 2882–2891 (1999).
8 S. H. Park, M. C. Shastry, and H. Roder, “Folding dynamics of the B1 domain of protein G explored by ultrarapid mixing,” Nat. Struct. Biol. 6(10), 943–947 (1999).
9 H. Yamaguchi, M. Miyazaki, M. Portia Briones-Nagata, and H. Maeda, “Refolding of difficult-to-fold proteins by a gradual decrease of denaturant using microfluidic chips,” J. Biochem. 147(6), 895–903 (2010).
10 M. B. Kerby, J. Lee, J. Ziperstein, and A. Tripathi, "Kinetic measurements of protein conformation in a microchip,” Biotechnol. Prog. 22(5), 1416–1425 (2006).
11 E. Mansur, M. Ye, Y. Wang, and Y. Dai, “A state-of-the-art review of mixing in microfluidic mixers,” Chin. J. Chem. Eng. 16(4), 503–516 (2008).
12 J. P. Brody, P. Yager, R. E. Goldstein, and R. H. Austin, “Biotechnology at low Reynolds numbers,” Biophys. J. 71(6),3430–3441 (1996).
13 J. Dunbar, H. P. Yennawar, S. Banerjee, J. Luo, and G. K. Farber, “The effect of denaturants on protein structure,” Protein Sci. 6(8), 1727–1733 (1997).
14 D. E. Hertzog, B. Ivorra, B. Mohammadi, O. Bakajin, and J. G. Santiago, “Optimization of a microfluidic mixer for studying protein folding kinetics,” Anal. Chem. 78(13), 4299–4306 (2006).
15 D. E. Hertzog, X. Michalet, M. Jager, X. Kong, J. G. Santiago, S. Weiss, and O. Bakajin, “Femtomole mixer for microsecond ¨kinetic studies of protein folding,” Anal. Chem. 76(24), 7169–7178 (2004).
16 S. Yao and O. Bakajin, “Improvements in mixing time and mixing uniformity in devices designed for studies of proteins folding kinetics,” Anal. Chem. 79(1), 5753–5759 (2007).
17 B. Ivorra, B. Mohammadi, J. G. Santiago, and D. E. Hertzog, “Semi-deterministic and genetic algorithms for global optimization of microfluidic protein folding devices,” Int. J. Numer. Method Eng. 66(2), 319–333 (2006).
18 N. Darnton, O. Bakajin, R. Huang, B. North, J. O. Tegenfeldt, E. C. Cox, J. Sturm, and R. H. Austin, "Hydrodynamics in 2 1 2 dimensions: Making jets in a plane,” J. Phys.: Condens. Matter 13, 4891–4902 (2001).
19 H. Y. Park, X. Qiu, E. Rhoades, J. Korlach, L. Kwok, W. R. Zipfel, W. W. Webb, and L. Pollack, “Achieving uniform mixing in a microfluidic device: Hydrodynamic focusing prior to mixing,” Anal. Chem. 78(13), 4465–4473 (2006).
20 A. J. M. Ferreira, MATLAB Codes for Finite Element Analysis, Solid Mechanics and its Applications, Vol. 157 (Springer, Dordrecht, Netherlands, 2009).
21 B. Massey and J. Ward-Smith, Mechanics of Fluids, 8th ed. (Taylor & Francis, New York, 2005).
22 C.-W. Tsaoa and D. L. DeVoe, Lab on a Chip Technology: Volume 1: Fabrication and Microfluidics (Caister Academic, Norfolk, UK, 2009).
23 J. B. Knight, A. Vishwanath, J. P. Brody, and R. H. Austin, “Hydrodynamic focusing on a silicon chip: Mixing nanoliters in microseconds,” Phys. Rev. Lett. 80(17), 3863–3866 (1998).
24 S. A. Berger, L. Talbot, and L. S. Yao, “Flow in curved pipes,” Annu. Rev. Fluid Mech. 15(1), 461–512 (1983).
25 W. R. Dean, “The stream-line motion of fluid in a curved pipe (second paper),” Philos. Mag. 5(30), 673–695 (1928).
26 Y. Gambin, V. VanDelinder, A. C. Ferreon, E. A. Lemke, A. Groisman, and A. Deniz, “Visualizing a one-way protein encounter complex by ultrafast single-molecule mixing,” Nat. Methods 8(3), 239–41 (2011).
27 Y. Gambin, C. Simonnet, V. VanDelinder, A. Deniz, and A. Groisman, “Ultrafast microfluidic mixer with three-dimensional flow focusing for studies of biochemical kinetics,” Lab Chip 10, 598–609 (2010).
28 M. S. Munson and P. Yager, “Simple quantitative optical method for monitoring the extent of mixing applied to a novel microfluidic mixer,” Anal. Chim. Acta 507, 63–71 (2004).
29 J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge University Press, Cambridge, UK, 1989).
30 R. Glowinski and P. Neittaanmaki, ¨ Partial Differential Equations: Modelling and Numerical Simulation, Computational Methods in Applied Sciences, Vol. 16 (Springer, Dordrecht, Netherlands, 2008).
31 K. Kawahara and C. Tanford, “Viscosity and density of aqueous solutions of urea and guanidine hydrochloride,” J. Biol. Chem. 241(13), 3228–3232 (1966).
32 S. Nishida, N. Tomokazu, and M. Terazima, “Hydrogen bonding dynamics during protein folding of reduced cytochrome c: Temperature and denaturant concentration dependence,” Biophys. J. 89, 2004–2010 (2005).
33 R. F. Ismagilov, A. D. Stroock, P. J. A. Kenis, G. Whitesidesa, and H. A. Stonea, “Experimental and theoretical scaling laws for transverse diffusive broadening in two-phase laminar flows in microchannels,” Appl. Phys. Lett. 76(17), 2376–2378 (2000).
34 J. L. Redondo, J. Fernandez, I. García, and P. M. Ortigosa, “A robust and efficient global optimization algorithm for planar competitive location problems,” Ann. Oper. Res. 167(1), 87–105 (2009).
35 J. L. Redondo, J. Fernandez, I. García, and P. M. Ortigosa, “Solving the multiple competitive location and design problem on the plane,” Evol. Comput. 17(1), 21–53 (2009).
36 J. L. Redondo, J. Fernandez, I. García, and P. M. Ortigosa, “Parallel algorithms for continuous competitive location problems,” Optim. Methods Software 23(5), 779–791 (2008).
37 D. E. Goldberg, Genetic Algorithms in Search, optimization, and Machine Learning (Addison-Wesley, Boston, Massachusetts, 1989).
38 L. Debiane, B. Ivorra, B. Mohammadi, F. Nicoud, T. Poinsot, A. Ern, and H. Pitsch, “A low complexity global optimization algorithm for temperature and pollution control in flames with complex chemistry,” Int. J. Comput. Fluid Dyn. 20(2),93–98 (2006).
39 B. Ivorra, A. M. Ramos, and B. Mohammadi, "Semideterministic global optimization method: Application to a control problem of the burgers equation,” J. Optim. Theory Appl. 135(3), 549–561 (2007).
40 S. Gomez, B. Ivorra, and A. M. Ramos, “Optimization of a pumping ship trajectory to clean oil contamination in the open sea,” Math. Comput. Modell. 54(1), 477–489 (2011).
41 D. Isebe, F. Bouchette, P. Azerad, B. Ivorra, and B. Mohammadi, “Shape optimization of geotextile tubes for sandy beach protection,” Int. J. Numer. Method Eng. 174(8), 1262–1277 (2008).
42 B. Ivorra, D. Mohammadi, L. Dumas, O. Durand, and P. Redont, “Semi-deterministic vs. genetic algorithms for global optimization of multichannel optical filters,” Int. J. Comput. Sci. Eng. 2(3), 170–178 (2006).
43 B. Ivorra, B. Mohammadi, and A. M. Ramos, “Optimization strategies in credit portfolio management,” J. Glob. Optim. 43(2), 415–427 (2009)