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Mathematical modeling of bacterial track-altering motors: Track cleaving through burnt-bridge ratchets

Blerta Shtylla

James P. Keener

  • Department of Mathematics, Pomona College, Claremont, California 91711, USA

  • Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA

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Phys. Rev. E 91, 042711 – Published 20 April, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.042711

Abstract

The generation of directed movement of cellular components frequently requires the rectification of Brownian motion. Molecular motor enzymes that use ATP to walk on filamentous tracks are typically involved in cell transport, however, a track-altering motor can arise when an enzyme interacts with and alters its track. In Caulobacter crescentus and other bacteria, an active DNA partitioning (Par) apparatus is employed to segregate replicated chromosome regions to specific locations in dividing cells. The Par apparatus is composed of two proteins: ParA, an ATPase that can form polymeric structures on the nucleoid, and ParB, a protein that can bind and destabilize ParA structures. It has been proposed that the ParB-mediated alteration of ParA structures could be responsible for generating the directed movement of DNA during bacterial division. How precisely these actions are coordinated and translated into directed movement is not clear. In this paper we consider the C. crescentus segregation apparatus as an example of a track altering motor that operates using a so-called burnt-bridge mechanism. We develop and analyze mathematical models that examine how diffusion and ATP-hydrolysis-mediated monomer removal (or cleaving) can be combined to generate directed movement. Using a mean first passage approach, we analytically calculate the effective ParA track-cleaving velocities, effective diffusion coefficient, and other higher moments for the movement a ParB protein cluster that breaks monomers away at random locations on a single ParA track. Our model results indicate that cleaving velocities and effective diffusion constants are sensitive to ParB-induced ATP hydrolysis rates. Our analytical results are in excellent agreement with stochastic simulation results.

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References (35)

  1. J. Howard, Nature (London) 389, 561 (1997).
  2. F. Jülicher, A. Ajdari, and J. Prost, Rev. Mod. Phys. 69, 1269 (1997).
  3. A. Gennerich and R. D. Vale, Curr. Opin. Cell Biol. 21, 59 (2009).
  4. S. Saffarian, I. E. Collier, B. L. Marmer, E. L. Elson, and G. Goldberg, Science 306, 108 (2004).
  5. S. Saffarian, H. Qian, I. Collier, E. Elson, and G. Goldberg, Phys. Rev. E 73, 041909 (2006).
  6. T. Antal and P. L. Krapivsky, Phys. Rev. E 72, 046104 (2005).
  7. A. Y. Morozov, E. Pronina, A. B. Kolomeisky, and M. N. Artyomov, Phys. Rev. E 75, 031910 (2007).
  8. A. Y. Morozov and A. B. Kolomeisky, J. Stat. Mech. (2007) P12008.
  9. J. Mai, I. M. Sokolov, and A. Blumen, Phys. Rev. E 64, 011102 (2001).
  10. A. Lakhanpal and T. Chou, Phys. Rev. Lett. 99, 248302 (2007).
  11. T. Omabegho, R. Sha, and N. C. Seeman, Science 324, 67 (2009).
  12. J. H. Schulz, A. B. Kolomeisky, and E. Frey, Europhys. Lett. 95, 30004 (2011).
  13. M. N. Artyomov, A. Y. Morozov, E. Pronina, and A. B. Kolomeisky, J. Stat. Mech. (2007) P08002.
  14. M. N. Artyomov, A. Y. Morozov, and A. B. Kolomeisky, Phys. Rev. E 77, 040901 (2008).
  15. T. Antal, P. L. Krapivsky, and S. Redner, Phys. Rev. E 72, 036121 (2005).
  16. J. L. Ptacin, S. F. Lee, E. C. Garner, E. Toro, M. Eckart, L. R. Comolli, W. Moerner, and L. Shapiro, Nat. Cell Biol. 12, 791 (2010).
  17. W. B. Schofield, H. C. Lim, and C. Jacobs-Wagner, EMBO J. 29, 3068 (2010).
  18. S. Ringgaard, J. van Zon, M. Howard, and K. Gerdes, Proc. Natl. Acad. Sci. U.S.A. 106, 19369 (2009).
  19. K. Gerdes, M. Howard, and F. Szardenings, Cell 141, 927 (2010).
  20. A. G. Vecchiarelli, L. C. Hwang, and K. Mizuuchi, Proc. Natl. Acad. Sci. U.S.A. 110, E1390 (2013).
  21. A. G. Vecchiarelli, Y.-W. Han, X. Tan, M. Mizuuchi, R. Ghirlando, C. Biertümpfel, B. E. Funnell, and K. Mizuuchi, Mol. Microbiol. 78, 78 (2010).
  22. B. Shtylla and J. P. Keener, J. Theor. Biol. 307, 82 (2012).
  23. E. J. Banigan, M. A. Gelbart, Z. Gitai, N. S. Wingreen, and A. J. Liu, PLoS computational biology 7, e1002145 (2011).
  24. B. Derrida, J. Stat. Phys. 31, 433 (1983).
  25. B. Shtylla and J. P. Keener (unpublished).
  26. A. G. Vecchiarelli, K. C. Neuman, and K. Mizuuchi, Proc. Natl. Acad. Sci. U.S.A. 111, 4880 (2014).
  27. G. Laloux and C. Jacobs-Wagner, J. Cell Biol. 201, 827 (2013).
  28. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, 1992), Vol. 1.
  29. D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977).
  30. H. C. Tijms, A first Course in Stochastic Models (Wiley, New York, 2003).
  31. R. Wolff, Stochastic Modeling and the Theory of Queues (Prentice Hall, Englewood Cliffs, 1989).
  32. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 3rd ed. (Springer, Berlin, 2004).
  33. C. R. Doering, K. V. Sargsyan, L. M. Sander, and E. Vanden-Eijnden, J. Phys.: Condens. Matter 19, 065145 (2007).
  34. J. Helenius, G. Brouhard, Y. Kalaidzidis, S. Diez, and J. Howard, Nature (London) 441, 115 (2006).
  35. L. Quarmby, J. Cell Sci. 113, 2821 (2000).

Outline

Information

Phys. Rev. E 91, 042711– Published 20 April, 2015
  • Received 6 May 2014
  • Revised 6 January 2015
Article part of CHORUS

©2015 American Physical Society

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