On Application of Langevin Dynamics in Logarithmic Potential to Model Ion Channel Gate Activity
-
Agata Wawrzkiewicz-Jałowiecka
,
Przemysław Borys
Abstract
We model the activity of an ion channel gate by Langevin dynamics in a logarithmic potential. This approach enables one to describe the power-law dwell-time distributions of the considered system, and the long-term correlations between the durations of the subsequent channel states, or fractal scaling of statistical characteristics of the gate’s movement with time. Activity of an ion channel gate is described as an overdamped motion of the reaction coordinate in a confining logarithmic potential, which ensures great flexibility of the model. Depending on the chosen parameters, it allows one to reproduce many types of gate dynamics within the family of non-Markovian, anomalous conformational diffusion processes. In this study we apply the constructed model to largeconductance voltage and Ca2+-activated potassium channels (BKCa). The interpretation of model assumptions and parameters is provided in terms of this biological system. Our results show good agreement with the experimental data.
References
1. Metzler, R., Klafter, J. and Jortner, J. Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems. Proc. Natl. Acad. Sci. USA 96 (1999) 11085-11089.Search in Google Scholar
2. Dechant, A., Lutz, E., Barkai, E. and Kessler, D.A. Solution of the Fokker- Planck equation with a logarithmic potential. J. Stat. Phys. 145 (2011) 1524-1545.Search in Google Scholar
3. Dechant, A., Lutz, E., Kessler, D.A. and Barkai, E. Fluctuations of time averages for Langevin dynamics in a binding force field. Phys. Rev. Lett. 107 (2011) 240603.Search in Google Scholar
4. Kessler, D.A. and Barkai, E. Infinite covariant density for diffusion in logarithmic potentials and optical lattices. Phys. Rev. Lett. 105 (2010) 120602.Search in Google Scholar
5. Dechant, A., Lutz, E., Kessler, D.A. and Barkai, E. Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials. Phys. Rev. E 85 (2012) 051124.Search in Google Scholar
6. Goychuk, I. and Hänggi, P. Fractional diffusion modeling of ion channel gating. Phys. Rev. E 70 (2004) 051915. Search in Google Scholar
7. Fuliński, A., Grzywna, Z.J., Mellor, I., Siwy, Z. and Usherwood, P.N.R. Non-Markovian character of ionic current fluctuations in membrane channels. Phys. Rev. E 58 (1998) 919-924.Search in Google Scholar
8. Cox, D.H., Cui, J. and Aldrich, R.W. Allosteric gating of a large conductance Ca-activated K+ channels. J. Gen. Physiol. 110 (1997) 257-281.Search in Google Scholar
9. Goychuk, I. and Hänggi, P. The role of conformational diffusion in ion channel gating. Physica A 325 (2003) 9-18.Search in Google Scholar
10. Horrigan, F.T. and Aldrich, R.W. Coupling between voltage sensor activation, Ca2+ binding and channel opening in large conductance (BK) potassium channels. J. Gen. Physiol. 120 (2002) 267-305.Search in Google Scholar
11. Millhauser, G.L., Salpeter, E.E. and Oswald, R.E. Diffusion models of ionchannel gating and the origin of power-law distributions from single-channel recording. Proc. Natl. Acad. Sci. USA 85 (1988) 1503-1507.Search in Google Scholar
12. Rothberg, B.S. and Magleby, K.L. Voltage and Ca2+ activation of single large-conductance Ca2+-activated k+ channels described by a two-tiered allosteric gating mechanism. J. Gen. Physiol. 116 (2000) 75-99.Search in Google Scholar
13. Wawrzkiewicz, A., Pawelek, K., Borys, P., Dworakowska, B. and Grzywna, Z.J. On the simple random walk models of ion channel gate dynamics reflecting long-term memory. Eur. Biophys. J. 41 (2012) 505-526.Search in Google Scholar
14. Borys, P. The role of passive calcium influx through the cell membrane in galvanotaxis. Cell. Mol. Biol. Lett. 18 (2013) 187-199.Search in Google Scholar
15. Lindahl, E. and Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys. J. 79 (2000) 426-433.Search in Google Scholar
16. Bandeira, H.T., Barbosa, C.T.F., Campos De Oliveira R.A., Aguiar J.F. and Nogueira R.A. Chaotic model and memory in single calcium-activated potassium channel kinetics. Chaos 18 (2008) 033136.Search in Google Scholar
17. Campos de Oliveira, R.A., Barbosa, C.T.F., Consoni, L.H.A., Rodrigues, A.R.A., Varanda, W.A. and Nogueira, R.A. Long-term correlation in single calciumactivated potassium channel kinetics. Physica A 364 (2006) 13-22.Search in Google Scholar
18. Varanda, W.A., Liebovitch, L.S., Figueiroa, J.N. and Nogueira, R.A. Hurst analysis applied to the study of single calcium-activated potassium channel kinetics. J. Theor. Biol. 206 (2000) 343-353.Search in Google Scholar
19. Liebovitch, L.S. and Krekora, P. The physical basis of ion channel kinetics: the importance of dynamics. in: Institute for Mathematics and its Applications Volumes in Mathematics and its Applications, Membrane Transport and Renal Physiology. (Layton, H.E. and Weinstein A.M., Eds.) 129 (2002) 27-52.Search in Google Scholar
20. Cui, J., Yang, H. and Lee, U.S. Molecular mechanism of BK channel activation. Cell. Mol. Life Sci. 66 (2008) 852-875.Search in Google Scholar
21. Zwanzig, R. Diffusion past an entropy barrier. J. Phys. Chem. 96 (1992) 3926-3930.Search in Google Scholar
22. Reguera, D. and Rubi, J.M. Kinetic equations for diffusion in the presence of entropic barriers. Phys. Rev. E 64 (2001) 061106-1-061106-8. Search in Google Scholar
23. Kosińska, I.D. and Fuliński, A. Asymmetric nanodiffusion. Phys. Rev. E 72 (2005) 011201-1-011201-7.10.1103/PhysRevE.72.011201Search in Google Scholar PubMed
24. Siwy, Z., Kosińska, I.D., Fuliński A. and Martin, C.R. Asymmetric diffusion through synthetic nanopores. Phys. Rev. Lett. 94 (2005) 048102-1-048102-4.Search in Google Scholar
25. Fuliński, A., Kosińska I. and Siwy, Z. Transport properties of nanopores in electrolyte solutions: the diffusional model and surface currents New J. Phys. 7 (2005) 1-19.Search in Google Scholar
26. Fuliński, A., Kosińska I. and Siwy, Z. On the validity of continuous modelling of ion transport through nanochannels Europhys. Lett. 67 (2004) 683-689.Search in Google Scholar
27. Risken, H. The Fokker-Planck Equation: Methods of Solutions and Applications, 2nd ed. Springer - Verlag, Berlin, 1996, 32-62.10.1007/978-3-642-61544-3_3Search in Google Scholar
28. Fowler, P.W. and Sansom, M.S.P. The pore of voltage-gated potassium ion channels is strained when closed. Nat. Commun. 4 (2013) 1872.Search in Google Scholar
29. Cox, D.H. BKCa-Channel Structure and Function. in: Biological Membrane Ion Channels. Dynamics, Structure and Application, (Chung, S.-H., Andersen, O.S. and Krishnamorthy, V., Eds.) Springer, New York, 2007, 171-210.10.1007/0-387-68919-2_5Search in Google Scholar
30. Läuger, P. Internal motions in proteins and gating kinetics of ionic channels. Biophys. J. 53 (1988) 877-884.Search in Google Scholar
31. Kloeden, P.E. and Platen, E. Numerical Solution of Stochastic Differential Equations. Springer, Berlin, 1995, 395-426.Search in Google Scholar
32. Mercik, S., Weron, K. and Siwy, Z. Statistical analysis of ionic current fluctuations in membrane channels. Phys. Rev. E 60 (1999) 7343-7348.Search in Google Scholar
33. Hurst, H.E. Long-term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng. 116 (1951) 770-808.Search in Google Scholar
34. Hurst, H.E., Black, R.P. and Simaika, Y.M. Long-Term Storage, An Experimental Study, Constable, London, 1965, 1-145.Search in Google Scholar
35. Bouchaud, J.-P. and Georges, A. Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys. Rep. 195 (1990) 127-293.Search in Google Scholar
36. Metzler, R. and Klafter, J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339 (2000) 1-77.Search in Google Scholar
37. Goychuk, I. and Hänggi, P. Ion channel gating: A first-passage time analysis of the Kramers type. Proc. Natl. Acad. Sci. USA 99 (2002) 3552-3556.10.1073/pnas.052015699Search in Google Scholar PubMed PubMed Central
38. Grzywna, Z.J., Borys, P. and Kruczek, B. On the well-posed problems for diffusion with time dependent boundary condition. Separ. Sci. Technol. 46 (2011) 2427-2435.Search in Google Scholar
39. Cherstvya, A.G. and Metzler, R. Population splitting, trapping, and nonergodicity in heterogeneous diffusion processes Phys. Chem. Chem. Phys. 15 (2013) 20220-20235. 10.1039/c3cp53056fSearch in Google Scholar PubMed
© 2015
Articles in the same Issue
- Elevated pressure enhanced TRAIL-induced apoptosis in hepatocellular carcinoma cells via ERK1/2-inactivation
- HsOrc4-dependent DNA remodeling of the ori-β DHFR replicator
- Is Iron Chelation Important in Preventing Glycation of Bovine Serum Albumin in Vitro?
- The transition of the 37-kDa laminin receptor (RPSA) to higher molecular weight species: SUMOylation or artifact?
- Mechanical strain affects some microRNA profiles in pre-oeteoblasts.
- Sphingosine-1-phosphate induces the migration and angiogenesis of EPCs through the Akt signaling pathway via sphingosine-1-phosphate receptor 3/platelet-derived growth factor receptor-β
- Bioinformatics-based molecular classification of Arthrobacter plasmids
- Ras Transformation Overrides a Proliferation Defect Induced by Tpm3.1 Knockout
- The advanced lipoxidation end product precursor malondialdehyde induces IL-17E expression and skews lymphocytes to the Th17 subset
- On Application of Langevin Dynamics in Logarithmic Potential to Model Ion Channel Gate Activity
- Superoxide Dismutase 2 Polymorphisms and Osteoporosis in Asian Indians: A Genetic Association Analysis
Articles in the same Issue
- Elevated pressure enhanced TRAIL-induced apoptosis in hepatocellular carcinoma cells via ERK1/2-inactivation
- HsOrc4-dependent DNA remodeling of the ori-β DHFR replicator
- Is Iron Chelation Important in Preventing Glycation of Bovine Serum Albumin in Vitro?
- The transition of the 37-kDa laminin receptor (RPSA) to higher molecular weight species: SUMOylation or artifact?
- Mechanical strain affects some microRNA profiles in pre-oeteoblasts.
- Sphingosine-1-phosphate induces the migration and angiogenesis of EPCs through the Akt signaling pathway via sphingosine-1-phosphate receptor 3/platelet-derived growth factor receptor-β
- Bioinformatics-based molecular classification of Arthrobacter plasmids
- Ras Transformation Overrides a Proliferation Defect Induced by Tpm3.1 Knockout
- The advanced lipoxidation end product precursor malondialdehyde induces IL-17E expression and skews lymphocytes to the Th17 subset
- On Application of Langevin Dynamics in Logarithmic Potential to Model Ion Channel Gate Activity
- Superoxide Dismutase 2 Polymorphisms and Osteoporosis in Asian Indians: A Genetic Association Analysis
