Abstract
Recent rapid development of single molecule analysis highly demands the trapping of molecular objects. In this study, we present how stability and random motions vary depending on dielectrophoretic and electrophoretic descriptions for a molecular object in planar quadrupole electrical traps. The object is modeled as a molecular dipole surrounded by a cavity (“molecular dipole cavity”) to introduce the solvent accessible surface of a solute molecule, and the instantaneous electrophoretic and dielectrophoretic force formulations are employed for the rigorous estimation of the deterministic stability which is identified by the equation of motion without random impulse and the random fluctuation that is compared with the trap size for the identification of random stability. The deterministic stability is analyzed with the universal Mathieu equation based theories for Paul trap while the random fluctuation is computed by averaging the multiple trajectories with different random seeds. The results show that the deterministic stabilities are quite similar in dielectrophoretic and electrophoretic descriptions, whereas the random fluctuation is significantly influenced by the type of force description. This study is expected to provide fundamental information in designing a quadrupole trap for molecular objects which is essential in single molecule analysis.
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References
H. A. Pohl, The motion and precipitation of suspensions in divergent electric fields, Journal of Applied Physics, 22 (1951) 869–871.
M. P. Hughes, AC electrokinetics: applications for nanotechnology, Nanotechnology, 11 (2) (2000) 124–132.
M. P. Hughes and H. Morgan, Dielectrophoretic trapping of single sub-micrometre scale bioparticles, Journal of Physics D: Applied Physics, 31 (17) (1998) 2205-2010.
J. Voldman, R. A. Braff, M. Toner, M. L. Gray and M. A. Schmidt, Holding forces of single-particle dielectrophoretic traps, Biophysical Journal, 80 (1) (2001) 531-454.
W. Guan, S. Joseph, J. H. Park, P. S. Krstic and M. A. Reed, Paul trapping of charged particles in aqueous solution, Proceedings of the National Academy of Sciences of the United States of America, 108 (23) (2011) 9326–9330.
J. H. Park, W. Guan, M. A. Reed and P. S. Krstic, Tunable aqueous virtual micropore, Small, 8 (6) (2012) 907–912.
J. Voldman, Electrical forces for microscale cell manipulation, Annual Review of Biomedical Engineering, 8 (2006) 425–454.
W. Paul, Electromagnetic traps for charged and neutral particles, Reviews of Modern Physics, 62 (1990) 531–540.
G. Fuhr, W. M. Arnold, R. Hagedorn, T. Müller, W. Benecke, B. Wagner and U. Zimmermann, Levitation, holding, and rotation of cells within traps made by high-frequency fields. Biochimica et Biophysica Acta, 1108 (2) (1992) 215–223.
L. F. Hartley, K. V. I. S. Kaler and R. Paul, Quadrupole levitation of microscopic dielectric particles, Journal of Electrostatics, 46 (4) (1999) 233–246.
R. Pethig, Review article - dielectrophoresis: status of the theory, technology, and applications, Biomicrofluidics, 4 (2) (2010) 022811.
P. K. Gupta, Single-molecule DNA sequencing technologies for future genomics research, Trends in Biotechnology, 26 (11) (2008) 602–611.
N. G. Walter, C.-Y. Huang, A. J. Manzo and M. A. Sobhy, Do-it-yourself guide: How to use the modern singlemolecule toolkit, Nature Methods, 5 (2008) 475–489.
A. Einstein, Investigation on the Theory of the Brownian Movement, Dover publication, Mineola, NY, USA (1956).
S. Arnold, L. M. Folan and A. Korn, Optimal imaging of a charged microparticle in a Paul trap near STP: stochastic calculation and experiment, Journal of Applied Physics, 74 (7) (1993) 4291–4297.
T. Hasegawa and K. Uehara, Dynamics of a single particle in a Paul trap in the presence of the damping force, Applied Physics B, 61 (2) (1995) 159–163.
F. G. Major, V. N. Gheorghe and G. Werth, Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement, Springer, Berlin, Germany (2005).
M. Krone, K. Bidmon and T. Ertl, Interactive visualization of molecular surface dynamics, IEEE Transactions on Visualization and Computer Graphics, 15 (6) (2009) 1391–1398.
B. Lee and F. M. Richards, The interpretation of protein structures: estimation of static accessibility, Journal of Molecular Biology, 55 (3) (1971) 379–400.
X. Xuan, Joule heating in electrokinetic flow, Electrophoresis, 29 (1) (2008) 33–43.
B. J. Kirby, Micro- and Nanoscale Fluid Mechanics, Cambridge University Press, New York, USA (2010).
M. Washizu and T. B. Jones, Generalized multipolar dielectrophoretic force and electrorotational torque calculation, Journal of Electrostatics, 38 (1996) 199-121.
J. H. Park, Non-ponderomotive stability and random motion in micro-/nano-scale quadrupole dielectrophoretic traps, Journal of Physics D: Applied Physics, 47 (43) (2014) 435501.
H. Fischer, I. Polikarpov and A. F. Craievich, Average protein density is a molecular-weight-dependent function, Protein Science, 13 (10) (2004) 2825–2828.
H. P. Erickson, Size and shape of protein molecules at the nanometer level determined by sedimentation, gel filtration, and electron microscopy, Biological Procedures Online, 11 (1) (2009) 32–51.
P. Nelson, Biological Physics: with New Art by David Goodsell, Updated Ed., W.H. Freeman and Company, New York, USA (2004).
R. M. Robertson, S. Laib and D. E. Smith, Diffusion of isolated DNA molecules: Dependence on length and topology, Proceedings of National Academy of Science of U.S.A., 103 (19) (2006) 7310–7314.
J. Snijder and A. J. R. Heck, Analytical approaches for size and mass analysis of large protein assemblies, Annual Review of Analytical Chemistry, 7 (2014) 43–64.
J.-H. He, Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B, 20 (10) (2006) 1141–1199.
J. D. Jackson, Classical Electrodynamics, Third Ed., John Wiley & Sons, Inc., Hoboken, NJ, USA (1999).
S. Earnshaw, On the nature of the molecular forces which regulate the constitution of the luminferous ether, Transactions of the Cambridge Philosophical Society, 7 (1842) 97–112.
D. Cohen, On the numerical discretisation of stochastic oscillators, Mathematics and Computers in Simulation, 82 (8) (2012) 1478–1495.
C. Yuan and X. Mao, Convergence of the Euler-Maruyama method for stochastic differential equations with Markovian switching, Mathematics and Computers in Simulation, 64 (2) (2004) 223–235.
J. H. Park and P. S. Krstic, Stability of an aqueous quadrupole micro-trap, Journal of Physics: Condensed Matter, 24 (16) (2012) 164208.
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Recommended by Associate Editor Won Hyoung Ryu
Ramki Murugesan received his B.E. degree in Aeronautical Engineering from Kumaraguru College of Technology and his M.E. degree from the Graduate School of Mechanical and Aerospace Engineering at Gyeongsang National University in 2012 and 2014, respectively. He is currently a Ph.D. student in the Graduate School of Mechanical and Aerospace Engineering at Gyeongsang National University.
Jae Hyun Park received his B.S., M.S. and Ph.D. degrees from the Department of Aerospace Engineering at KAIST in 1996, 1998, and 2002, respectively. He is currently an Associate Professor in the Department of Aerospace and Software Engineering at Gyeongsang National University.
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Murugesan, R., Park, J.H. Electrophoretic and dielectrophoretic trapping of molecular objects in planar quadrupole electrode configuration at room temperature. J Mech Sci Technol 31, 1331–1339 (2017). https://doi.org/10.1007/s12206-017-0233-y
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DOI: https://doi.org/10.1007/s12206-017-0233-y