Hydrodynamic Interactions Introduce Differences in the Behaviour of a Ratchet Dimer Brownian Motor
Author(s)
José A. Fornés*
Affiliation(s)
Departamento de Fsica Aplicada I, Facultad de Ciencias Físicas, Universidad Complutense, Madrid, Spain.
Departamento de Fsica Aplicada I, Facultad de Ciencias Físicas, Universidad Complutense, Madrid, Spain.
ABSTRACT
We use the Brownian dynamics with hydrodynamic interactions simulation in order to describe the movement of an elastically coupled dimer Brownian motor in a ratchet potential. The only external forces considered in our system were the load, the random thermal noise and an unbiased thermal fluctuation. We observe differences in the dynamic behaviour if hydrodynamic interactions are considered as compared with the case without them. In conclusion, hydrodynamic interactions influence substantially the dynamics of a ratchet dimer Brownian motor; consequently they have to be considered in any theory where the molecular motors are in a liquid medium.
We use the Brownian dynamics with hydrodynamic interactions simulation in order to describe the movement of an elastically coupled dimer Brownian motor in a ratchet potential. The only external forces considered in our system were the load, the random thermal noise and an unbiased thermal fluctuation. We observe differences in the dynamic behaviour if hydrodynamic interactions are considered as compared with the case without them. In conclusion, hydrodynamic interactions influence substantially the dynamics of a ratchet dimer Brownian motor; consequently they have to be considered in any theory where the molecular motors are in a liquid medium.
KEYWORDS
Hydrodynamic Interactions, Motor Proteins, Molecular Dynamics, Brownian Dynamics, Fluctuation Phenomena, Random Processes, Noise, Brownian Motion
Hydrodynamic Interactions, Motor Proteins, Molecular Dynamics, Brownian Dynamics, Fluctuation Phenomena, Random Processes, Noise, Brownian Motion
Cite this paper
Fornés, J. (2015) Hydrodynamic Interactions Introduce Differences in the Behaviour of a Ratchet Dimer Brownian Motor. Journal of Biomaterials and Nanobiotechnology, 6, 81-90. doi: 10.4236/jbnb.2015.62008.
Fornés, J. (2015) Hydrodynamic Interactions Introduce Differences in the Behaviour of a Ratchet Dimer Brownian Motor. Journal of Biomaterials and Nanobiotechnology, 6, 81-90. doi: 10.4236/jbnb.2015.62008.
References
[1] Reimann, P. and Hanggi, P. (2002) Introduction to the Physics of Brownian Motors. Applied Physics A: Materials Science & Processing, 75, 169-178.
http://dx.doi.org/10.1007/s003390201331 [2] Wang, H.Y. and Bao, J.D. (2004) The Roles of Ratchet in Transport of Two Coupled Particles. Physica A: Statistical Mechanics and Its Applications, 337, 13-26.
http://dx.doi.org/10.1016/j.physa.2004.01.031 [3] Wang, H.Y. and Bao, J.D. (2005) Cooperation Behavior in Transport Process of Coupled Brownian Motors. Physica A: Statistical Mechanics and Its Applications, 357, 373-382.
http://dx.doi.org/10.1016/j.physa.2005.01.059 [4] Wang, H.Y. and Bao, J.D. (2007) Transport Coherence in Coupled Brownian Ratchet. Physica A: Statistical Mechanics and Its Applications, 374, 33-40.
http://dx.doi.org/10.1016/j.physa.2006.07.005 [5] Fornés, J.A. (2005) An Oscillating Electric Field with Thermal Noise Increases the Rotational Diffusion and Drives Rotation in a Dipole. Journal of Colloid and Interface Science, 281, 236-239.
http://dx.doi.org/10.1016/j.jcis.2004.08.088 [6] von Gehlen, S., Evstigneev, M. and Reimann, P. (2008) Dynamics of a Dimer in a Symmetric Potential: Ratchet Effect Generated by an Internal Degree of Freedom. Physical Review E, 77, Article ID: 031136.
http://dx.doi.org/10.1103/PhysRevE.77.031136 [7] Lipowsky, R., Chai, Y., Klumpp, S., Liepelt, S. and Müller, M.J.I. (2006) Molecular Motor Traffic: From Biological Nanomachines to Macroscopic Transport. Physica A: Statistical Mechanics and Its Applications, 372, 34-51.
http://dx.doi.org/10.1016/j.physa.2006.05.019 [8] Taoa, Y.G. and Kapralb, R. (2008) Design of Chemically Propelled Nanodimer Motors. Journal of Chemical Physics, 128, Article ID: 164518.
http://dx.doi.org/10.1063/1.2908078 [9] Howard, J. (2001) Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Massachusetts. [10] Block, S.M. (1995) Nanometres and Piconewtons: The Macromolecular Mechanics of Kinesin. Trends in Cell Biology, 5, 169-175.
http://dx.doi.org/10.1016/S0962-8924(00)88982-5 [11] Visscher, K., Schnitzer, M.J. and Block, S.M. (1999) Single Kinesin Molecules Studied with a Molecular Force Clamp. Nature, 400, 184-189.
http://dx.doi.org/10.1038/22146 [12] Schnitzer, M.J., Visscher, K. and Block, S.M. (2000) Force Production by Single Kinesin Motors. Nature Cell Biology, 2, 718-723.
http://dx.doi.org/10.1038/35036345 [13] Speer, D., Eichhorn, R., Evstigneev, M. and Reimann, P. (2012) Dimer Motion on a Periodic Substrate: Spontaneous Symmetry Breaking and Absolute Negative Mobility. Physical Review E, 85, Article ID: 061132.
http://dx.doi.org/10.1103/PhysRevE.85.061132 [14] Zimmermann, E. and Seifert, U. (2012) Efficiencies of a Molecular Motor: A Generic Hybrid Model Applied to the F1- ATPase. New Journal of Physics, 14, Article ID: 103023. http://dx.doi.org/10.1088/1367-2630/14/10/103023 [15] Pinkoviezky, I. and Gov, N.S. (2013) Modelling Interacting Molecular Motors with an Internal Degree of Freedom. New Journal of Physics, 15, Article ID: 025009.
http://dx.doi.org/10.1088/1367-2630/15/2/025009 [16] Ermak, D.L. and Mc Cammon, J.A. (1978) Brownian Dynamics with Hydrodynamic Interactions. The Journal of Chemical Physics, 69, 1352-1360.
http://dx.doi.org/10.1063/1.436761 [17] Kemps, J.A.L. and Bhattacharjee, S. (2009) Particle Tracking Model for Colloid Transport near Planar Surfaces Covered with Spherical Asperities. Langmuir, 25, 6887-6997.
http://dx.doi.org/10.1021/la9001835 [18] Günther, S. and Kruse, K. (2008) A Simple Self-Organized Swimmer Driven by Molecular Motors. Europhysics Letters, 84, Article ID: 68002.
http://dx.doi.org/10.1209/0295-5075/84/68002 [19] Ramia, M., Tullock, D.L. and Phan-Thien, N. (1993) The Role of Hydrodynamic Interaction in the Locomotion of Microorganisms. Biophysical Journal, 65, 755-778.
http://dx.doi.org/10.1016/S0006-3495(93)81129-9 [20] Kim, M.J. and Powers, T.R. (2004) Viscous Hydrodynamics of Rotating Helices. Physical Review E, 69, Article ID: 061910. [21] Fornés, J.A. (2010) Hydrodynamic Interactions Induce Movement against an External Load in a Ratchet Dimer Brownian Motor. Journal of Colloid and Interface Science, 341, 376-379. http://dx.doi.org/10.1016/j.jcis.2009.09.057 [22] Machura, L., Kostur, M., Marchesoni, F., Talkner, P., H?nggi, P. and Luczka, J. (2005) Optimal Strategy for Controlling Transport in Inertial Brownian Motors. Journal of Physics: Condensed Matter, 17, S3741-S3752. [23] Grimm, A. and Stark, H. (2011) Hydrodynamic Interactions Enhance the Performance of Brownian Ratchets. Soft Matter, 7, 3219-3227.
http://dx.doi.org/10.1039/C0SM01085E [24] Polson, J.M., Bylhouwer, B., Zuckermann, M.J., Horton, A.J. and Scott, W.M. (2010) Dynamics of a Polymer in a Brownian Ratchet. Physical Review E, 82, Article ID: 051931.
http://dx.doi.org/10.1103/PhysRevE.82.051931 [25] Dickinson, E. (1985) Brownian Dynamic with Hydrodynamic Interactions: The Application to Protein Diffusional Problems. Chemical Society Reviews, 14, 421-455.
http://dx.doi.org/10.1039/cs9851400421 [26] Doi, M. and Edwards, S.F. (1986) The Theory of Polymer Dynamics. Claredon Press, Oxford. [27] Freund, J.A. and Schimansky-Geier, L. (1999) Diffusion in Discrete Ratchets. Physical Review E, 60, 1304.
http://dx.doi.org/10.1103/PhysRevE.60.1304 [28] Houtman, D., Pagonabarraga, I., Lowe, C.P., Esseling-Ozdoba, A., Emons, A.M.C. and Eiser, E. (2007) Hydrodynamic Flow Caused by Active Transport along Cytoskeletal Elements. Europhysics Letters, 78, Article ID: 18001.
http://dx.doi.org/10.1209/0295-5075/78/18001
[1] Reimann, P. and Hanggi, P. (2002) Introduction to the Physics of Brownian Motors. Applied Physics A: Materials Science & Processing, 75, 169-178.
http://dx.doi.org/10.1007/s003390201331 [2] Wang, H.Y. and Bao, J.D. (2004) The Roles of Ratchet in Transport of Two Coupled Particles. Physica A: Statistical Mechanics and Its Applications, 337, 13-26.
http://dx.doi.org/10.1016/j.physa.2004.01.031 [3] Wang, H.Y. and Bao, J.D. (2005) Cooperation Behavior in Transport Process of Coupled Brownian Motors. Physica A: Statistical Mechanics and Its Applications, 357, 373-382.
http://dx.doi.org/10.1016/j.physa.2005.01.059 [4] Wang, H.Y. and Bao, J.D. (2007) Transport Coherence in Coupled Brownian Ratchet. Physica A: Statistical Mechanics and Its Applications, 374, 33-40.
http://dx.doi.org/10.1016/j.physa.2006.07.005 [5] Fornés, J.A. (2005) An Oscillating Electric Field with Thermal Noise Increases the Rotational Diffusion and Drives Rotation in a Dipole. Journal of Colloid and Interface Science, 281, 236-239.
http://dx.doi.org/10.1016/j.jcis.2004.08.088 [6] von Gehlen, S., Evstigneev, M. and Reimann, P. (2008) Dynamics of a Dimer in a Symmetric Potential: Ratchet Effect Generated by an Internal Degree of Freedom. Physical Review E, 77, Article ID: 031136.
http://dx.doi.org/10.1103/PhysRevE.77.031136 [7] Lipowsky, R., Chai, Y., Klumpp, S., Liepelt, S. and Müller, M.J.I. (2006) Molecular Motor Traffic: From Biological Nanomachines to Macroscopic Transport. Physica A: Statistical Mechanics and Its Applications, 372, 34-51.
http://dx.doi.org/10.1016/j.physa.2006.05.019 [8] Taoa, Y.G. and Kapralb, R. (2008) Design of Chemically Propelled Nanodimer Motors. Journal of Chemical Physics, 128, Article ID: 164518.
http://dx.doi.org/10.1063/1.2908078 [9] Howard, J. (2001) Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Massachusetts. [10] Block, S.M. (1995) Nanometres and Piconewtons: The Macromolecular Mechanics of Kinesin. Trends in Cell Biology, 5, 169-175.
http://dx.doi.org/10.1016/S0962-8924(00)88982-5 [11] Visscher, K., Schnitzer, M.J. and Block, S.M. (1999) Single Kinesin Molecules Studied with a Molecular Force Clamp. Nature, 400, 184-189.
http://dx.doi.org/10.1038/22146 [12] Schnitzer, M.J., Visscher, K. and Block, S.M. (2000) Force Production by Single Kinesin Motors. Nature Cell Biology, 2, 718-723.
http://dx.doi.org/10.1038/35036345 [13] Speer, D., Eichhorn, R., Evstigneev, M. and Reimann, P. (2012) Dimer Motion on a Periodic Substrate: Spontaneous Symmetry Breaking and Absolute Negative Mobility. Physical Review E, 85, Article ID: 061132.
http://dx.doi.org/10.1103/PhysRevE.85.061132 [14] Zimmermann, E. and Seifert, U. (2012) Efficiencies of a Molecular Motor: A Generic Hybrid Model Applied to the F1- ATPase. New Journal of Physics, 14, Article ID: 103023. http://dx.doi.org/10.1088/1367-2630/14/10/103023 [15] Pinkoviezky, I. and Gov, N.S. (2013) Modelling Interacting Molecular Motors with an Internal Degree of Freedom. New Journal of Physics, 15, Article ID: 025009.
http://dx.doi.org/10.1088/1367-2630/15/2/025009 [16] Ermak, D.L. and Mc Cammon, J.A. (1978) Brownian Dynamics with Hydrodynamic Interactions. The Journal of Chemical Physics, 69, 1352-1360.
http://dx.doi.org/10.1063/1.436761 [17] Kemps, J.A.L. and Bhattacharjee, S. (2009) Particle Tracking Model for Colloid Transport near Planar Surfaces Covered with Spherical Asperities. Langmuir, 25, 6887-6997.
http://dx.doi.org/10.1021/la9001835 [18] Günther, S. and Kruse, K. (2008) A Simple Self-Organized Swimmer Driven by Molecular Motors. Europhysics Letters, 84, Article ID: 68002.
http://dx.doi.org/10.1209/0295-5075/84/68002 [19] Ramia, M., Tullock, D.L. and Phan-Thien, N. (1993) The Role of Hydrodynamic Interaction in the Locomotion of Microorganisms. Biophysical Journal, 65, 755-778.
http://dx.doi.org/10.1016/S0006-3495(93)81129-9 [20] Kim, M.J. and Powers, T.R. (2004) Viscous Hydrodynamics of Rotating Helices. Physical Review E, 69, Article ID: 061910. [21] Fornés, J.A. (2010) Hydrodynamic Interactions Induce Movement against an External Load in a Ratchet Dimer Brownian Motor. Journal of Colloid and Interface Science, 341, 376-379. http://dx.doi.org/10.1016/j.jcis.2009.09.057 [22] Machura, L., Kostur, M., Marchesoni, F., Talkner, P., H?nggi, P. and Luczka, J. (2005) Optimal Strategy for Controlling Transport in Inertial Brownian Motors. Journal of Physics: Condensed Matter, 17, S3741-S3752. [23] Grimm, A. and Stark, H. (2011) Hydrodynamic Interactions Enhance the Performance of Brownian Ratchets. Soft Matter, 7, 3219-3227.
http://dx.doi.org/10.1039/C0SM01085E [24] Polson, J.M., Bylhouwer, B., Zuckermann, M.J., Horton, A.J. and Scott, W.M. (2010) Dynamics of a Polymer in a Brownian Ratchet. Physical Review E, 82, Article ID: 051931.
http://dx.doi.org/10.1103/PhysRevE.82.051931 [25] Dickinson, E. (1985) Brownian Dynamic with Hydrodynamic Interactions: The Application to Protein Diffusional Problems. Chemical Society Reviews, 14, 421-455.
http://dx.doi.org/10.1039/cs9851400421 [26] Doi, M. and Edwards, S.F. (1986) The Theory of Polymer Dynamics. Claredon Press, Oxford. [27] Freund, J.A. and Schimansky-Geier, L. (1999) Diffusion in Discrete Ratchets. Physical Review E, 60, 1304.
http://dx.doi.org/10.1103/PhysRevE.60.1304 [28] Houtman, D., Pagonabarraga, I., Lowe, C.P., Esseling-Ozdoba, A., Emons, A.M.C. and Eiser, E. (2007) Hydrodynamic Flow Caused by Active Transport along Cytoskeletal Elements. Europhysics Letters, 78, Article ID: 18001.
http://dx.doi.org/10.1209/0295-5075/78/18001