Predictions from a stochastic polymer model for the MinDE protein dynamics in Escherichia coli

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 80, Issue 4, 2009, Pages

  Borowski, Peter ^a,b   Cytrynbaum, Eric N ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b PACIFIC INSTITUTE FOR THE MATHEMATICAL SCIENCES   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

FIXED POINTS; IN-CELL; MIN PROTEINS; NUMERICAL TECHNIQUES; OSCILLATORY SYSTEM; POLYMER LENGTH; POLYMER MODELS; PROTEIN DYNAMICS; SPATIO-TEMPORAL OSCILLATIONS; STOCHASTIC EVOLUTION; STOCHASTIC FORMULATION; STOCHASTIC HYBRID SYSTEMS; THEORETICAL PREDICTION;

BIOCHEMISTRY; CELL MEMBRANES; CELL PROLIFERATION; ESCHERICHIA COLI; HYBRID SYSTEMS; POLYMERS; PROBABILITY DISTRIBUTIONS;

STOCHASTIC MODELS;

EID: 70350215725     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.041916     Document Type: Article

References (42)

1. X. C. Yu and W. Margolin, Mol. Microbiol. 32, 315 (1999). 10.1046/j.1365-2958.1999.01351.x
2. P. A. J. de Boer, R. E. Crossley, A. R. Hand, and L. I. Rothfield, EMBO J. 10, 4371 (1991).
3. Z. Hu and J. Lutkenhaus, Mol. Cell 7, 1337 (2001). 10.1016/S1097-2765(01) 00273-8
4. D. M. Raskin and P. A. J. de Boer, J. Bacteriol. 181, 6419 (1999).
5. Z. Hu, A. Mukherjee, S. Pichoff, and J. Lutkenhaus, Proc. Natl. Acad. Sci. U.S.A. 96, 14819 (1999). 10.1073/pnas.96.26.14819
6. D. M. Raskin and P. A. de Boer, Proc. Natl. Acad. Sci. U.S.A. 96, 4971 (1999). 10.1073/pnas.96.9.4971
7. J. Lutkenhaus, Adv. Exp. Med. Biol. 641, 49 (2009). 10.1007/978-0-387- 09794-7-4
8. Z. Hu, E. P. Gogol, and J. Lutkenhaus, Proc. Natl. Acad. Sci. U.S.A. 99, 6761 (2002). 10.1073/pnas.102059099
9. K. Suefuji, R. Valluzzi, and D. RayChaudhuri, Proc. Natl. Acad. Sci. U.S.A. 99, 16776 (2002). 10.1073/pnas.262671699
10. Y.-L. Shih, T. Le, and L. Rothfield, Proc. Natl. Acad. Sci. U.S.A. 100, 7865 (2003). 10.1073/pnas.1232225100
11. J. Szeto, N. F. Eng, S. Acharya, M. D. Rigden, and J.-A. R. Dillon, Res. Microbiol. 156, 17 (2005). 10.1016/j.resmic.2004.07.009
12. H. Meinhardt and P. A. de Boer, Proc. Natl. Acad. Sci. U.S.A. 98, 14202 (2001). 10.1073/pnas.251216598
13. G. Meacci and K. Kruse, Phys. Biol. 2, 89 (2005). 10.1088/1478-3975/2/2/ 002
14. K. C. Huang, Y. Meir, and N. S. Wingreen, Proc. Natl. Acad. Sci. U.S.A. 100, 12724 (2003). 10.1073/pnas.2135445100
15. M. Howard, A. D. Rutenberg, and S. de Vet, Phys. Rev. Lett. 87, 278102 (2001). 10.1103/PhysRevLett.87.278102
16. M. Howard and A. D. Rutenberg, Phys. Rev. Lett. 90, 128102 (2003). 10.1103/PhysRevLett.90.128102
17. R. Kerr, H. Levine, T. Sejnowski, and W. Rappel, Proc. Natl. Acad. Sci. U.S.A. 103, 347 (2006). 10.1073/pnas.0505825102
18. D. Fange and J. Elf, PLoS Comput. Biol. 2, e80 (2006). 10.1371/journal.pcbi.0020080
19. K. Kruse, Biophys. J. 82, 618 (2002). 10.1016/S0006-3495(02)75426-X
20. D. A. Drew, M. J. Osborn, and L. I. Rothfield, Proc. Natl. Acad. Sci. U.S.A. 102, 6114 (2005). 10.1073/pnas.0502037102
21. N. Pavin, H. C. Paljetak, and V. Krstic, Phys. Rev. E 73, 021904 (2006). 10.1103/PhysRevE.73.021904
22. E. N. Cytrynbaum and B. D. L. Marshall, Biophys. J. 93, 1134 (2007). 10.1529/biophysj.106.097162
23. F. Tostevin and M. Howard, Phys. Biol. 3, 1 (2006). 10.1088/1478-3975/3/ 1/001
24. B. P. B. Downing, A. D. Rutenberg, A. Touhami, and M. Jericho, PLoS ONE 4, e7285 (2009). 10.1371/journal.pone.0007285
25. E. Mileykovskaya, A. C. Ryan, X. Mo, C. C. Lin, K. I. Khalaf, W. Dowhan, and T. A. Garrett, J. Biol. Chem. 284, 2990 (2009). 10.1074/jbc.M805189200
26. S. Mazor, T. Regev, E. Mileykovskaya, W. Margolin, W. Dowhan, and I. Fishov, Biochim. Biophys. Acta 1778, 2505 (2008). 10.1016/j.bbamem.2008.08.004
27. A. Touhami, M. Jericho, and A. D. Rutenberg, J. Bacteriol. 188, 7661 (2006). 10.1128/JB.00911-06
28. G. Meacci, J. Ries, E. Fischer-Friedrich, N. Kahya, P. Schwille, and K. Kruse, Phys. Biol. 3, 255 (2006). 10.1088/1478-3975/3/4/003
29. A. R. Champneys and M. di Bernardo, Scholarpedia 3, 4041 (2008).
30. E. Mileykovskaya, I. Fishov, X. Fu, B. Corbin, W. Margolin, and W. Dowhan, J. Biol. Chem. 278, 22193 (2003). 10.1074/jbc.M302603200
31. F. Oosawa and S. Asakura, Thermodynamics of the Polymerization of Protein (Molecular Biology) (Academic Press Inc., New York, 1975).
32. Y.-L. Shih, X. Fu, G. F. King, T. Le, and L. Rothfield, EMBO J. 21, 3347 (2002). 10.1093/emboj/cdf323
33. C. Hale, H. Meinhardt, and P. de Boer, EMBO J. 20, 1563 (2001). 10.1093/emboj/20.7.1563
34. P. de Boer, R. Crossley, and L. Rothfield, Cell 56, 641 (1989). 10.1016/0092-8674(89)90586-2
35. J. Derr, J. T. Hopper, A. Sain, and A. D. Rutenberg, Phys. Rev. E 80, 011922 (2009). 10.1103/PhysRevE.80.011922
36. To simplify the notation, we use the term monomer throughout this paper, even though the original model as well as experiments suggests a polymer formed of dimers.
37. Derr recently examined an alternate model for MinE "ring" formation that does not require MinE polymerization. Although testing it in the full MinD polymer model is still required, this might remove the requirement of assuming MinE polymerization.
38. For high total MinD concentrations, lmax can come close to L, i.e., the D-polymer would cover the whole cell from pole to pole. To avoid further assumptions on what happens if a polymer hits the opposite cell wall, we restrict ourselves here to total MinD concentrations that make these events very unlikely or impossible. With the parameters from Table, this means we consider maximal total MinD concentrations of around 5μM. In the simulations, the polymer simply stops growing in the unlikely case that it reaches the opposite cell wall.
39. A simple Euler-forward routine (time step 10-4 s) was used to solve the differential equations. To reduce error in averages and to get smooth distributions, typically, simulations were run for 106 - 108 s of simulated time (i.e., roughly 2× 104 -2× 106 capping events).
40. If the capping occurs while the E-polymer on the opposite side still has its steady state length lE,ss, our model predicts a second E-ring of length zero. According to our model equations, the E-polymer could nucleate (stochastically) but the deterministic growth equation does not support an elongation because cE is at the critical concentration for elongation due to the presence of the other E-ring. A more detailed model would incorporate stochastic effects in the growth and shrinking of the E- (and DE-) polymer.
41. In the opposite case (stochastic nucleation and deterministic capping), the transitions are not observed. In this case, if the regular oscillation pattern is violated and a D-polymer nucleates very late, cE > cE,th, and the D-polymer as well as all following D-polymers will be capped right away.
42. To numerically compute the integrals, 5000 discrete mesh points were used over the interval 0...L. After each integration, the distribution is normalized.