Piecewise-linear approximation of the potential relief of a brownian motors
Abstract
The review of the piecewise linear potential reliefs approximation of actual and model nanodevices (Brownian motors) rectifying chaotic Brownian motion in systems with broken reflexion symmetry under the action of an external fluctuation perturbation in the absence of macroscopic driving forces is given. Relations are derived to carry out this approximation.
References
1. Reimann P. Brownian Motors: Noisy Transport far from Equilibrium. Phys. Rep. 2002. 361(2–4): 57. https://doi.org/10.1016/S0370-1573(01)00081-3
2. Astumian R.D. Adiabatic theory for fluctuation-induced transport on a periodic potential. J. Phys. Chem. 1996. 100(49): 19075. https://doi.org/10.1021/jp961614m
3. Astumian R.D. Thermodynamics and kinetics of a Brownian motor. Science. 1997. 276(5314): 917. https://doi.org/10.1126/science.276.5314.917
4. Hanggi P. Organic electronics: Harvesting randomness. Nat. Mat. 2011. 10(1): 6. https://doi.org/10.1038/nmat2925
5. Squires T.M., Quake S.R. Microfluidics: Fluid physics at the nanoliter scale. Rev. Mod. Phys. 2005. 77(3): 977. https://doi.org/10.1103/RevModPhys.77.977
6. Pamme N. Continuous flow separations in microfluidic devices. Lab Chip. 2007. 7(12): 1644. https://doi.org/10.1039/b712784g
7. Faucheux L.P., Libchaber A. Selection of Brownian particles. J. Chem. Soc., Faraday Trans. 1995. 91(18): 3163. https://doi.org/10.1039/ft9959103163
8. Gorre-Talini L., Jeanjean S., Silberzan P. Sorting of Brownian particles by pulsed application of an asymmetric potential. Phys. Rev. E. 1997. 56: 2025. https://doi.org/10.1103/PhysRevE.56.2025
9. Grimm A., Stark H., Van der Maarel J.R.C. Model for a Brownian ratchet with improved characteristics for particle separation. Phys. Rev. E. 2009. 79(6): 061102. https://doi.org/10.1103/PhysRevE.79.061102
10. Linke H., Humphrey T., Lofgren A., Sushkov A.O., Newbury R., Taylor R.P., Omling P. Experimental tunneling ratchets. Science. 1999. 286(5448): 2314. https://doi.org/10.1126/science.286.5448.2314
11. Kharpai V.S., Ludwig S., Kotthaus J.P., Tranitz H.P., Wegscheider W. A double-dot quantum ratchet driven by an independently biased quantum point contact. Phys. Rev. Lett. 2006. 97: 176803. https://doi.org/10.1103/PhysRevLett.97.176803
12. Roeling E.M, Germs W.Ch., Smalbrugge B., Geluk E.J., de Vries T., Janssen R.A.J., Kemerink M. Organic electronic ratchets doing work. Nat. Mater. 2011. 10: 51. https://doi.org/10.1038/nmat2922
13. Cheetham M.R., Bramble J.P., McMillan D.G.G., Bushby R.J., Olmsted P.D., Jeuken L.J.C., Evans S.D. Manipulation and sorting of membrane proteins using patterned diffusion-aided ratchets with AC fields in supported bilayers. Soft Matter. 2012. 8(20): 5459. https://doi.org/10.1039/c2sm25473e
14. Krogh A., Larsson B., von Heijne G., Sonnhammer E. Predicting transmembrane protein topology with a hidden Markov model. Application to complete genomes. J. Mol. Biol. 2001. 305: 567. https://doi.org/10.1006/jmbi.2000.4315
15. Overington J.P., Al-Lazikani B., Hopkins A.L. How many drug targets are there? Nat. Rev. Drug Discov. 2006. 5(12): 993. https://doi.org/10.1038/nrd2199
16. Bader J.S., Hammond R.W., Henck S.A., Deem M.W., McDermott G.A., Bustillo J.M., Simpson J.W., Mulhern G.T., Rothberg J.M. DNA Transport by a micromachined Brownian ratchet device. Proc. Nat. Acad. Sci. USA. 1999. 96(23): 13165. https://doi.org/10.1073/pnas.96.23.13165
17. Vale R.D. The molecular motor toolbox for intracellular transport. Cell. 2003. 112(4): 467. https://doi.org/10.1016/S0092-8674(03)00111-9
18. Finer J.T., Simmons R.M., Spudich J.A. Single myosin molecule mechanics–piconewton forces and nanometre steps. Nature. 1994. 368(6467): 113. https://doi.org/10.1038/368113a0
19. Hirokawa N. Kinesin and dynein superfamily proteins and the mechanism of organelle transport. Science. 1998. 279(5355): 519. https://doi.org/10.1126/science.279.5350.519
20. Howard J., Hudspeth A.J., Vale R.D. Movement of microtubules by single kinesin molecules. Nature. 1989. 342: 154. https://doi.org/10.1038/342154a0
21. Bath J., Green S.J. Turberfield A.J. A Free-running DNA motor powered by a nicking enzyme. Angew. Chem. Int. Ed. 2005. 44(28): 4358. https://doi.org/10.1002/anie.200501262
22. Yin P., Choi H.M.T., Calvert C.R., Pierce N.A. Programming biomolecular self-assembly pathways. Nature. 2008. 451: 318. https://doi.org/10.1038/nature06451
23. Omabegho T., Sha R., Seeman N.C. A bipedal DNA Brownian motor with coordinated legs. Science. 2009. 324(5923): 67. https://doi.org/10.1126/science.1170336
24. He Y., Liu D.R. Autonomous multistep organic synthesis in a single isothermal solution mediated by a DNA walker. Nat. Nanotechnol. 2010. 5: 778. https://doi.org/10.1038/nnano.2010.190
25. Lund K., Manzo A.J., Dabby N., Michelotti N., Johnson-Buck A., Nangreave J., Taylor S., Pei R., Stojanovic M.N., Walter N.G., Winfree E., Yan H. Molecular robots guided by prescriptive landscapes. Nature. 2010. 465(7295): 206. https://doi.org/10.1038/nature09012
26. Wickham S.F.J., Endo M., Katsuda Y., Hidaka K., Bath J., Sugiyama H., Turberfield A.J. Direct observation of stepwise movement of a synthetic molecular transporter. Nat. Nanotechnol. 2011. 6: 166. https://doi.org/10.1038/nnano.2010.284
27. Cha T.G., Pan J., Chen H., Salgado J., Li X., Mao Ch., Choi J.H. A synthetic DNA motor that transports nanoparticles along carbon nanotubes. Nat. Nanotechnol. 2013. 9(1): 39. https://doi.org/10.1038/nnano.2013.257
28. Preda C.E., Ségard B., Glorieux P. Weak temporal ratchet effect by asymmetric modulation of a laser. Opt. Lett. 2006. 31(15): 2347. https://doi.org/10.1364/OL.31.002347
29. Cousins T.R., Goldstein R.E., Jaworski J.W., Pesci A.I. A ratchet trap for Leidenfrost drops. J. Fluid Mech. 2012. 696: 215. https://doi.org/10.1017/jfm.2012.27
30. Adachi K., Takaki T. Vibration of a flattened drop. 1. Observation. J. Phys. Soc. Jpn. 1984. 53(12): 4184. https://doi.org/10.1143/JPSJ.53.4184
31. Linke H., Alem’An B.J., Melling L.D., Taormina M.J., Francis M.J., Dow-Hygelund C.C., Narayanan V., Taylor R.P., Stout A. Self-propelled Leidenfrost droplets. Phys. Rev. Lett. 2006. 96: 154502. https://doi.org/10.1103/PhysRevLett.96.154502
32. Magnasco M.O. Forsed thermal ratchets. Phys. Rev. Lett. 1993. 71(10): 1477. https://doi.org/10.1103/PhysRevLett.71.1477
33. Sokolov M. Irreversible and reversible modes of operation of deterministic ratchets. Phys. Rev. E. 2001. 63(2): 021107. https://doi.org/10.1103/PhysRevE.63.021107
34. Rozenbaum V.M., Korochkova T.Ye., Chernova A.A., Dekhtyar M.L. Brownian motor with competing spatial and temporal asymmetry of potential energy. Phys. Rev. E. 2011. 83(5): 051120. https://doi.org/10.1103/PhysRevE.83.051120
35. Korochkova T.Ye., Shkoda N.G., Chernova A.A., Rozenbaum V.M. Exact analytical solutions in the theory of brownian motors and pumps. Surface. 2012. 4(19): 19. [in Russian].
36. Korochkova T.E., Rozenbaum V.M., Shapochkina I.V. Sawtooth potential model in the theory of a brownian motors. Surface. 2015. 7(22): 12. [in Russian].
37. Rozenbaum V.M. Low -temperature operational regime of an adiabatic Brownian motor. Low Temperature Physics. 2014. 40(5): 604. [in Russian]. https://doi.org/10.1063/1.4876230
38. Korochkova T.E., Rosenbaum V.M., Chuyko O.O. Brownian particle drift due to orientational structuring of the adsorbate. Reports of the National Academy of Sciences of Ukraine. 2004. 8: 93. [in Russian].
39. Kharchenko V.O., Goychuk I. Subdiffusive rocking ratchets in viscoelastic media: Transport optimization and thermodynamic efficiency in overdamped regime. Phys. Rev. E. 2013. 87(5): 052119. https://doi.org/10.1103/PhysRevE.87.052119
40. Son W.-S., Ryu J.-W., Hwang D.-U., Lee S.-Y., Park Y.-J., Kim C.M. Transport control in a deterministic ratchet system. Phys. Rev. E. 2008. 77(6): 066213. https://doi.org/10.1103/PhysRevE.77.066213
41. Rozenbaum V.M., Makhnovskii Yu.A., Shapochkina I.V., Sheu S.-Y., Yang D.-Y., Lin S.H. Inertial effects in adiabatically driven flashing ratchets. Phys. Rev. E. 2014. 89(1): 052131. https://doi.org/10.1103/PhysRevE.89.052131
