Biospecific Affinity Chromatography: Computational Modelling via Lattice Boltzmann Method and Influence of Lattice-Based Dimensionless Parameters

Dayane C.G. Okiyama; Eliana S. Kamimura; José A. Rabi

doi:10.6000/1927-3037.2015.04.01.5

Authors

Dayane C.G. Okiyama Faculty of Animal Science and Food Engineering, University of São Paulo Av. Duque de Caxias Norte 225, Pirassununga, SP, 13635-900, Brazil
Eliana S. Kamimura Faculty of Animal Science and Food Engineering, University of São Paulo Av. Duque de Caxias Norte 225, Pirassununga, SP, 13635-900, Brazil
José A. Rabi Faculty of Animal Science and Food Engineering, University of São Paulo Av. Duque de Caxias Norte 225, Pirassununga, SP, 13635-900, Brazil

DOI:

https://doi.org/10.6000/1927-3037.2015.04.01.5

Keywords:

Biospecific affinity chromatography, phenomenological modelling, numerical simulation, lattice Boltzmann method.

Abstract

Based on a dynamic (i.e. time-dependent) one-dimensional approach, this work applied lattice Boltzmann method (LBM) to computationally model biospecific affinity chromatography (BAC). With governing equations expressed in lattice-based dimensionless form, LBM was implemented in D1Q2 lattice by assigning particle distribution functions to adsorbate concentration in both fluid and solid phases. The LBM simulator was firstly tested in view of a classic BAC work on lysozyme and the streaming step relating to adsorbate concentration in the solid-phase was suppressed from the LBM code with no loss of functionality. Expected behaviour of breakthrough curves was numerically reproduced and the influence of lattice-based dimensionless parameters was examined. The LBM simulator was next applied so as to assess lattice-based dimensionless parameters regarding an experimental BAC work on lipase.

References

Souza-Santos ML. Solid Fuels Combustion and Gasification: Modeling, Simulation, and Equipment Operation. 2nd ed. New York: CRC Press; 2010. Print ISBN 978-1-4200-4749-3, eBook ISBN: 978-1-4200-4750-9.

Diaz MS, Brignole EA. Modeling and optimization of supercritical fluid processes. J Supercrit Fluids 2009; 47: 611-8. http://dx.doi.org/10.1016/j.supflu.2008.09.006

Brannock M, Leslie G, Wang Y, Buetehorn S. Optimising mixing and nutrient removal in membrane bioreactors: CFD modelling and experimental validation. Desalination 2010; 250: 815-8. http://dx.doi.org/10.1016/j.desal.2008.11.048

Głuszcz P, Petera J, Ledakowicz S. Mathematical modeling of the integrated process of mercury bioremediation in the industrial bioreactor. Bioproc Biosyst Eng 2011; 34: 275-85. http://dx.doi.org/10.1007/s00449-010-0469-8

Parco V, Du Toit G, Wentzel M, Ekama G. Biological nutrient removal in membrane bioreactors: denitrification and phosphorus removal kinetics. Water Sci Technol 2007; 56: 125-34. http://dx.doi.org/10.2166/wst.2007.642

Ching CB, Wu YX, Lisso M, Wozny G, Laiblin T, Arlt W. Study of feed temperature control of chromatography using computational fluid dynamics simulation. J Chromatogr A 2002; 945: 117-31. http://dx.doi.org/10.1016/S0021-9673(01)01479-0

Özdural AR, Alkan A, Kerkhof PJAM. Modeling chromatographic columns: non-equilibrium packed-bed adsorption with non-linear adsorption isotherm. J Chromatogr A 2004; 1041: 77-85. http://dx.doi.org/10.1016/j.chroma.2004.05.009

Vidal-Madjar C, Cañada-Cañada F, Jaulmes A, Pantazaki A, Taverna M. Numerical simulation of the chromatographic process for direct ligand-macromolecule binding studies. J Chromatogr A 2005; 1087: 95-103. http://dx.doi.org/10.1016/j.chroma.2005.01.008

Leickt L, Månsson A, Ohlson S. Prediction of affinity and kinetics in biomolecular interactions by affinity chromatography. Anal Biochem 2001; 291: 102-8. http://dx.doi.org/10.1006/abio.2001.5019

Datta AK, Sablani SS. Mathematical modeling techniques in food and bioprocess: an overview. In: Sablani SS, Rahman MS, Datta AK, Mujumdar AR, editors. Handbook of Food and Bioprocess Modeling Techniques. Boca Raton: CRC Press 2007; p. 1-11. ISBN13: 978-0-8247-2671-3.

Norton T, Sun D-W. An overview of CFD applications in the food industry. In: Sun D-W, editor. Computational Fluid Dynamics in Food Processing. Boca Raton: CRC Press 2007; p. 1-41. ISBN 978-0-8493-9286-3.

Puri VM, Anantheswaran RC. The finite-element method in food processing: a review. J Food Eng 1993; 19: 247-74. http://dx.doi.org/10.1016/0260-8774(93)90046-M

Scott G, Richardson P. The application of computational fluid dynamics in the food industry. Trends Food Sci Technol 1997; 8: 119-24. http://dx.doi.org/10.1016/S0924-2244(97)01028-5

Xia B, Sun D-W. Applications of computational fluid dynamics (CFD) in the food industry: a review. Comput Electron Agric 2002; 34: 5-24. http://dx.doi.org/10.1016/S0168-1699(01)00177-6

Wang L, Sun D-W. Recent developments in numerical modelling of heating and cooling processes in the food industry - a review. Trends Food Sci Technol 2003; 14: 408-23. http://dx.doi.org/10.1016/S0924-2244(03)00151-1

Yun J, Lin D-Q, Yao S-J. Predictive modeling of protein adsorption along the bed height by taking into account the axial nonuniform liquid dispersion and particle classification in expanded beds. J Chromatogr A 2005; 1095: 16-26. http://dx.doi.org/10.1016/j.chroma.2005.07.120

Alper HE, Stouch TR. Orientation and diffusion of a drug analogue in biomembranes: Molecular Dynamics simulations. J Phys Chem 1995; 99: 5724-31. http://dx.doi.org/10.1021/j100015a065

Bemporad D, Luttman C, Essex JW. Behaviour of small solutes and large drugs in a lipid bilayer from computer simulation. Biochem Biophys Acta 2005; 1718: 1-21. http://dx.doi.org/10.1016/j.bbamem.2005.07.009

Henneré G, Prognon P, Brion F, Rosilio V, Nicolis I. Molecular Dynamics simulation of a mixed lipid emulsion: influence of the triglycerides on interfacial phospholipid organization. Teochem J Mol Struct 2009; 901: 174-85. http://dx.doi.org/10.1016/j.theochem.2009.01.020

Xiang T-X, Anderson BD. Lipossomal drug transport: a molecular perspective from Molecular Dynamics simulations in lipid bilayers. Adv Drug Deliv Rev 2006; 58: 1357-78. http://dx.doi.org/10.1016/j.addr.2006.09.002

Rothman DH, Zaleski S. Lattice-Gas Cellular Automata: Simple Models of Complex Hydrodynamics. Cambridge: Cambridge University Press; 1997. ISBN-13: 978-0-5216-0760-5. http://dx.doi.org/10.1017/CBO9780511524714

Wolf-Gladrow DA. Lattice-Gas Cellular Automata and Lattice Boltzmann Models: an Introduction. Berlin: Springer; 2000. ISBN: 978-3-540-66973-6. http://dx.doi.org/10.1007/b72010

Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford: Oxford University Press; 2001. ISBN: 978-0-19-850398-9.

McNamara GR, Zanetti G. Use of the Boltzmann equation to simulate lattice-gas automata. Phys Rev Lett 1988; 61: 2332-5. http://dx.doi.org/10.1103/PhysRevLett.61.2332

van der Sman RGM. Lattice Boltzmann simulation of microstructures. In: Sablani SS, Rahman MS, Datta AK, Mujumdar AR, editors. Handbook of Food and Bioprocess Modeling Techniques. Boca Raton: CRC Press 2007; p. 15-39. ISBN13: 978-0-8247-2671-3.

Mantle MD, Bijeljic B, Sederman AJ, Gladden LF. MRI velocimetry and lattice-Boltzmann simulations of viscous flow of a Newtonian liquid through a dual porosity fiber array. Magn Reson Imaging 2001; 19: 527-9. http://dx.doi.org/10.1016/S0730-725X(01)00285-5

Ladd AJC, Verbeg RJ. Lattice-Boltzmann simulations of particle-fluid suspensions. J Stat Phys 2001; 104: 1191-1251. http://dx.doi.org/10.1023/A:1010414013942

Zhang XX, Bengough AG, Deeks LK, Crawford JW, Young IM. A novel three-dimensional lattice Boltzmann model for solute transport in variably saturated porous media. Water Resour Res 2002; 38: 1167-76. http://dx.doi.org/10.1029/2001WR000982

Zhang XX, Ren LJ. Lattice Boltzmann model for agrochemical transport in soils. J Contam Hydrol 2003; 67: 27-42. http://dx.doi.org/10.1016/S0169-7722(03)00086-X

Migliorini C, Qian Y, Chen H, Brown EB, Jain RK, Munn LL. Red blood cells augment leukocyte rolling in a virtual blood vessel. Biophys J 2002; 83: 1834-41. http://dx.doi.org/10.1016/S0006-3495(02)73948-9

Sun C, Migliorini C, Munn LL. Red blood cells initiate leukocyte rolling in postcapillary expansions: a lattice Boltzmann analysis. Biophys J 2003; 85: 208-22. http://dx.doi.org/10.1016/S0006-3495(03)74467-1

Sukop MC, Or D. Lattice Boltzmann method for modeling liquid-vapor interface configurations in porous media. Water Resour Res 2004; 40: W01509. http://dx.doi.org/10.1029/2003WR002333

Agarwal S, Verma N, Mewes D. A lattice Boltzmann model for adsorption breakthrough. Heat Mass Transf 2005; 41: 843-54. http://dx.doi.org/10.1007/s00231-005-0625-x

Schure MR, Maier RS, Kroll DM, Davis HT. Simulation of ordered packed beds in chromatography. J Chromatogr A 2004; 1031: 79-86. http://dx.doi.org/10.1016/j.chroma.2003.12.030

Okiyama DCG, Rabi JA. Lattice-Boltzmann Simulation of Transport Phenomena in Agroindustrial Biosystems. In: Kora AB, editor. Advances in Computational Modeling Research: Theory, Developments and Applications. Hauppauge: Nova Science Publishers 2013; p. 79-104. ISBN: 978-1-62618-065-9.

Golshan-Shirazi S, Guiochon G. Modeling of preparative liquid chromatography. J Chromatogr A 1994; 658: 149-71. http://dx.doi.org/10.1016/0021-9673(94)80013-8

Guiochon G, Golshan-Shirazi S. A retrospective on the solution of the ideal model of chromatography. J Chromatogr A 1994; 658: 173-7. http://dx.doi.org/10.1016/0021-9673(94)80014-6

Chase HA. Prediction of the performance of preparative affinity chromatography. J Chromatogr 1984; 297: 179-202. http://dx.doi.org/10.1016/S0021-9673(01)89041-5

Mendieta-Taboada O, Kamimura ES, Maugeri Filho F. Modelling and simulation of the adsorption of the lipase from Geotrichum sp on hydrophobic interactions columns. Biotechnol Lett 2001; 23: 781-6. http://dx.doi.org/10.1023/A:1010302416897

Mohamad AA. Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes. London: Springer-Verlag; 2011. ISBN: 9780857294548. http://dx.doi.org/10.1007/978-0-85729-455-5

Cowan GH, Gosling IS, Laws JF, Sweetenham WP. Physical and mathematical modeling to aid scale-up of liquid chromatography. J Chromatogr 1986; 363: 37-56. http://dx.doi.org/10.1016/S0021-9673(00)88990-6

Kempe H, Axelsson A, Nilsson B, Zacchi G. Simulation of chromatographic processes applied to separation of proteins. J Chromatogr A 1999; 846: 1-12. http://dx.doi.org/10.1016/S0021-9673(98)01079-6

Sridhar P, Sastri NVS, Modak JM, Mukherjee AK. Mathematical simulation of bioseparation in an affinity packed column. Chem Eng Technol 1994; 17: 422-9. http://dx.doi.org/10.1002/ceat.270170610

Nield DA, Bejan A. Convection in Porous Medium. New York: Springer-Verlag; 1992. ISBN: 0-387-97651-5. http://dx.doi.org/10.1007/978-1-4757-2175-1

Sanchez FJM, del Valle EM, Serrano MAG, Cerro RL. Modeling of monolith supported affinity chromatography. Biotechnol Prog 2004; 20: 811-7. http://dx.doi.org/10.1021/bp034343n

Okiyama DCG, Rabi JA. Dirichlet versus Danckwerts inlet condition for bioaffinity chromatography part 2: comparing results from lattice-Boltzmann simulations. In: Proceedings of the XIX SINAFERM - X SHEB; 2013: Iguassu Falls, Brazil: UFSCar / UNICAMP / UEM / ABEQ; 2013: CD-ROM.

Qian YH, D’Humières D, Lallemand P. Lattice BGK models for Navier-Stokes equation. Europhys Lett 1992; 17: 479-84. http://dx.doi.org/10.1209/0295-5075/17/6/001

Karlin IV, Ansumali S, Frouzakis CE, Chikatamarla SS. Elements of the lattice Boltzmann method I: linear advection equation. Commun Comput Phys 2006; 1: 1-45. Available from: http://65.54.113.26/Publication/7038361/elements-of-the-lattice-boltzmann-method-i-linear-advection-equation.

Maier RS, Bernard RS, Daryl WG. Boundary conditions for the lattice Boltzmann method. Phys Fluids 1996; 8: 1788-1801. http://dx.doi.org/10.1063/1.868961

Rabi JA, Mohamad AA. Simulation of zero-order transport problems using lattice-Boltzmann method: imposition of periodic boundary conditions or suppression of streaming step. In: Proceedings of the 17th Discrete Simulation of Fluids Dynamics; 2008: Florianopolis, Brazil: UFSC; 2008: p. 25.

Patankar SV. Numerical Heat Transfer and Fluid Flow. New York: Hemisphere; 1980. ISBN-13: 978-0891165224.

Rabi JA. Numerical simulation of mass transfer aiming at food processes and bioprocesses in fixed-bed equipment: a comparison between finite-differences and lattice-Boltzmann method. WSEAS Trans Heat Mass Transf 2012; 7: 69-78. Available from: http://www.wseas.org/wseas/cms.action? id=6941.

Kamimura ES, Mediata O, Rodrigues MI, Maugeri Filho F. Studies on lipase-affinity adsorption using response-surface analysis. Biotechnol Appl Biochem 2001; 33: 153-9. http://dx.doi.org/10.1042/BA20000081