Research PapersNo Access

Properties of sodium-driven bacterial flagellar motor: A two-state model approach

Yunxin Zhang

Shanghai Key Laboratory for Contemporary Applied Mathematics, Centre for Computational Systems Biology, School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Shanghai Center for Mathematical Sciences, Shanghai 200433, China

Search for more papers by this author

https://doi.org/10.1142/S0217984914502704Cited by:0 (Source: Crossref)

Abstract

Bacterial flagellar motor (BFM) is one of the ion-driven molecular machines, which drives the rotation of flagellar filaments and enable bacteria to swim in viscous solutions. Understanding its mechanism is one challenge in biophysics. Based on previous models and inspired by the idea used in description of motor proteins, in this study one two-state model is provided. Meanwhile, according to corresponding experimental data, mathematical relationship between BFM membrane voltage and pH value of the environment, and relationship between internal and external sodium concentrations are given. Therefore, with model parameter values obtained by fitting theoretical results of torque-speed relation to recent experimental data, many biophysical properties of bacterial flagellar motor can be obtained for any pH values and any external sodium concentrations, including the rotation speed, stall torque (i.e. the torque generated by BFM), rotation dispersion, and rotation randomness. In this study, the single-stator BFM will be firstly analyzed, and then properties of multiple-stator BFM are addressed briefly.

Keywords:

PACS: 87.16.Nn, 87.16.A-, 82.39.Jn, 05.40.Jc

References

B. Hille , Ionic Channels of Excitable Membranes , 3rd edn. ( Sinauer Associates , Sunderland, MA , 2001 ) . Google Scholar
D. Bray , Cell Movements: From Molecules to Motility , 2nd edn. ( Garland , New York , 2001 ) . Google Scholar
J. Howard , Mechanics of Motor Proteins and the Cytoskeleton ( Sinauer Associates , Sunderland, MA , 2001 ) . Google Scholar
M. Schliwa , Molecular Motors ( Wiley-VCH , Weinheim , 2003 ) . Google Scholar
D. D. Shultis et al. , Science 312 , 1396 ( 2006 ) . Crossref, Web of Science, ADS, Google Scholar
Y. Sowa and R. M. Berry , Q. Rev. Biophys. 41 , 103 ( 2008 ) . Crossref, Web of Science, Google Scholar
D. Okuno , R. Iino and H. Noji , J. Biochem. 149 , 655 ( 2008 ) . Crossref, Web of Science, Google Scholar
P. Mitchell , BBA-Bioenergetics 1807 , 1507 ( 2011 ) . Crossref, Web of Science, Google Scholar
R. Yasuda et al. , J. Bioenerg. Biomembr. 93 , 1117 ( 1998 ) . Google Scholar
G. Oster and H. Wang , Nature 32 , 459 ( 2000 ) . Google Scholar
K. Kinosita et al. , Philos. Trans. R. Soc. B 355 , 473 ( 2000 ) . Crossref, Web of Science, Google Scholar
S. Toyabe et al. , Proc. Natl. Acad. Sci. USA 108 , 17951 ( 2011 ) . Crossref, Web of Science, ADS, Google Scholar
S. Mukherjee and A. Warshel , Proc. Natl. Acad. Sci. USA 108 , 20550 ( 2011 ) . Crossref, Web of Science, ADS, Google Scholar
S. Mukherjee and A. Warshel , Proc. Natl. Acad. Sci. USA 109 , 14876 ( 2012 ) . Crossref, Web of Science, ADS, Google Scholar
K. Adachi et al. , Cell 130 , 309 ( 2007 ) . Crossref, Web of Science, Google Scholar
K. M. Davies et al. , Proc. Natl. Acad. Sci. USA 109 , 13602 ( 2012 ) . Crossref, Web of Science, ADS, Google Scholar
H. Bouvrais et al. , Proc. Natl. Acad. Sci. USA 109 , 18442 ( 2012 ) . Crossref, Web of Science, ADS, Google Scholar
J. Xing et al. , Biophys. J. 87 , 2148 ( 2004 ) . Crossref, Web of Science, Google Scholar
M. Diez et al. , Nat. Struct. Mol. Biol. 11 , 135 ( 2004 ) . Crossref, Web of Science, Google Scholar
R. M. Berry , Curr. Biol. 15 , R386 ( 2005 ) . Crossref, Web of Science, Google Scholar
H. Sielaff et al. , Proc. Natl. Acad. Sci. USA 105 , 17760 ( 2008 ) . Crossref, Web of Science, ADS, Google Scholar
W. Junge , H. Sielaff and S. Engelbrecht , Nature 459 , 364 ( 2009 ) . Crossref, Web of Science, ADS, Google Scholar
K. Hayashi et al. , Phys. Rev. Lett. 104 , 218103 ( 2010 ) . Crossref, Web of Science, ADS, Google Scholar
S. Toyabe et al. , Phys. Rev. Lett. 104 , 198103 ( 2010 ) . Crossref, Web of Science, ADS, Google Scholar
R. Shimo-Kon et al. , Biophys. J. 98 , 1227 ( 2010 ) . Crossref, Web of Science, Google Scholar
M. A. Little et al. , Biophys. J. 101 , 477 ( 2011 ) . Crossref, Web of Science, Google Scholar
B. N. Goldstein , A. M. Aksirov and D. T. Zakrjevskaya , Biosystems 104 , 9 ( 2011 ) . Crossref, Web of Science, Google Scholar
A. Kohori et al. , Biophys. J. 101 , 188 ( 2011 ) . Crossref, Web of Science, Google Scholar
M. Sugawa et al. , Biophys. J. 101 , 2201 ( 2011 ) . Crossref, Web of Science, Google Scholar
R. Iino and H. Noji , Biochimica et Biophysica Acta 1817 , 1732 ( 2012 ) . Crossref, Web of Science, Google Scholar
M. Tanigawara et al. , Biophys. J. 103 , 970 ( 2012 ) . Crossref, Web of Science, Google Scholar
K. Okazaki and G. Hummer , Proc. Natl. Acad. Sci. USA 110 , 16468 ( 2013 ) . Crossref, Web of Science, ADS, Google Scholar
T. Choua , J. Chem. Phys. 110 , 606 ( 1999 ) . Crossref, Web of Science, ADS, Google Scholar
A. M. Berezhkovskii , M. A. Pustovoit and S. M. Bezrukov , J. Chem. Phys. 116 , 9952 ( 2002 ) . Crossref, Web of Science, ADS, Google Scholar
A. M. Berezhkovskii , M. A. Pustovoit and S. M. Bezrukov , J. Chem. Phys. 119 , 3943 ( 2003 ) . Crossref, Web of Science, ADS, Google Scholar
A. M. Berezhkovskii and S. M. Bezrukov , Chem. Phys. 319 , 342 ( 2005a ) . Crossref, Web of Science, ADS, Google Scholar
A. M. Berezhkovskii and S. M. Bezrukov , Biophys. J.: Biophys. Lett. 88 , L17 ( 2005b ) . Crossref, Web of Science, Google Scholar
S. M. Bezrukov , A. M. Berezhkovskii and A. Szabo , J. Chem. Phys. 127 , 115101 ( 2007 ) . Crossref, Web of Science, ADS, Google Scholar
A. B. Kolomeisky , Phys. Rev. Lett. 98 , 048105 ( 2007 ) . Crossref, Web of Science, ADS, Google Scholar
A. B. Kolomeisky and S. Kotsev , J. Chem. Phys. 128 , 085101 ( 2008 ) . Crossref, Web of Science, Google Scholar
A. Zilman , Biophys. J. 96 , 1235 ( 2009 ) . Crossref, Web of Science, Google Scholar
D. Stock , K. Namba and L. K. Lee , Curr. Opin. Biotechnol. 23 , 545 ( 2012 ) . Crossref, Web of Science, Google Scholar
H. C. Berg , Annu. Rev. Biochem. 72 , 19 ( 2003 ) . Crossref, Web of Science, Google Scholar
D. R. Thomas et al. , J. Bacteriol. 188 , 7039 ( 2006 ) . Crossref, Web of Science, Google Scholar
G. Meacci and Y. Tu , Proc. Natl. Acad. Sci. USA 106 , 3746 ( 2009 ) . Crossref, Web of Science, ADS, Google Scholar
F. Bai et al. , Phys. Rev. Lett. 108 , 178105 ( 2012 ) . Crossref, Web of Science, ADS, Google Scholar
W. S. Ryu , R. M. Berry and H. C. Berg , Nature 403 , 444 ( 2000 ) . Crossref, Web of Science, ADS, Google Scholar
X. Chen and H. C. Berg , Biophys. J. 78 , 1036 ( 2000 ) . Crossref, Web of Science, Google Scholar
C. Gabel and H. C. Berg , Proc. Natl. Acad. Sci. USA 100 , 8748 ( 2003 ) . Crossref, Web of Science, ADS, Google Scholar
Y. Sowa et al. , J. Mol. Biol. 327 , 1043 ( 2003 ) . Crossref, Web of Science, Google Scholar
Y. Asai et al. , J. Mol. Biol. 327 , 453 ( 2003 ) . Crossref, Web of Science, Google Scholar
J. Yuan and H. C. Berg , Proc. Natl. Acad. Sci. USA 105 , 1182 ( 2008 ) . Crossref, Web of Science, ADS, Google Scholar
Y. Inoue et al. , J. Mol. Biol. 376 , 1251 ( 2008 ) . Crossref, Web of Science, Google Scholar
S. Nakamura et al. , J. Mol. Biol. 386 , 332 ( 2009 ) . Crossref, Web of Science, Google Scholar
J. Yuan et al. , Proc. Natl. Acad. Sci. USA 107 , 12846 ( 2010 ) . Crossref, Web of Science, ADS, Google Scholar
R. Schmitt , Biophys. J. 85 , 843 ( 2003 ) . Crossref, Web of Science, Google Scholar
J. Xing et al. , Proc. Natl. Acad. Sci. USA 103 , 1260 ( 2006 ) . Crossref, Web of Science, ADS, Google Scholar
T. Mora , H. Yu and N. S. Wingreen , Phys. Rev. Lett. 103 , 248102 ( 2009 ) . Crossref, Web of Science, ADS, Google Scholar
F. Bai et al. , Biophys. J. 96 , 3154 ( 2009 ) . Crossref, Web of Science, Google Scholar
C. J. Lo et al. , Proc. Natl. Acad. Sci. USA 110 , E2544 ( 2013 ) . Crossref, Web of Science, ADS, Google Scholar
M. E. Fisher and A. B. Kolomeisky , Proc. Natl. Acad. Sci. USA 98 , 7748 ( 2001 ) . Crossref, Web of Science, ADS, Google Scholar
Y. Zhang , Physica A 383 , 3465 ( 2009a ) . Crossref, Web of Science, ADS, Google Scholar
Y. Zhang , J. Biol. Chem. 286 , 39439 ( 2011 ) . Crossref, Web of Science, Google Scholar
A. B. Kolomeisky and M. E. Fisher , Annu. Rev. Phys. Chem. 58 , 675 ( 2007 ) . Crossref, Web of Science, ADS, Google Scholar
Y. Zhang , Phys. Lett. A 373 , 2629 ( 2009b ) . Crossref, Web of Science, ADS, Google Scholar
B. Derrida , J. Stat. Phys. 31 , 433 ( 1983 ) . Crossref, Web of Science, ADS, Google Scholar
M. E. Fisher and A. B. Kolomeisky , Physica A 274 , 241 ( 1999 ) . Crossref, Web of Science, ADS, Google Scholar
S. Klumpp and R. Lipowsky , Proc. Natl. Acad. Sci. USA 102 , 17284 ( 2005 ) . Crossref, Web of Science, ADS, Google Scholar
M. J. I. Müller , S. Klumpp and R. Lipowsky , Proc. Natl. Acad. Sci. USA 105 , 4609 ( 2008 ) . Crossref, Web of Science, ADS, Google Scholar
Y. Zhang , Phys. Rev. E 79 , 061918 ( 2009c ) . Crossref, Web of Science, ADS, Google Scholar
S. Toyabea et al. , Proc. Natl. Acad. Sci. USA 108 , 17951 ( 2011 ) . Crossref, Web of Science, ADS, Google Scholar
X. Meng , M. Yu and Y. Zhang , J. Phys.: Condens. Matter 25 , 374102 ( 2013 ) . Crossref, Web of Science, Google Scholar
K. Visscher , M. J. Schnitzer and S. M. Block , Nature 400 , 184 ( 1999 ) . Crossref, Web of Science, ADS, Google Scholar
Y. Zhang , J. Stat. Phys. 134 , 669 ( 2009d ) . Crossref, Web of Science, ADS, Google Scholar