More Realistic Model for Simulating Min Protein Dynamics: Lattice Boltzmann Method Incorporating the Role of Nucleoids
The dynamics of Min proteins plays a center role in
accurate cell division. Although the nucleoids may presumably play
an important role in prokaryotic cell division, there is a lack of
models to account for its participation. In this work, we apply the
lattice Boltzmann method to investigate protein oscillation based on a
mesoscopic model that takes into account the nucleoid-s role. We
found that our numerical results are in reasonably good agreement
with the previous experimental results On comparing with the other
computational models without the presence of nucleoids, the
highlight of our finding is that the local densities of MinD and MinE
on the cytoplasmic membrane increases, especially along the cell
width, when the size of the obstacle increases, leading to a more
distinct cap-like structure at the poles. This feature indicated the
realistic pattern and reflected the combination of Min protein
dynamics and nucleoid-s role.
[1] P. de Boer, R. Crossley and L. Rothfield, A division inhibitor and a
topological specificity factor coded for by the minicell locus determine
proper placement of the division septum in E. coli, Cell, 56 (4), 641-
649, 1989.
[2] P. de Boer, R. Crossley and L. Rothfield, Central role for the
Escherichia coli minC gene product in two different cell divisioninhibition
systems, Proceedings of the National Academy of Sciences,
87 (3), 1129, 1990.
[3] P. De Boer, R. Crossley, A. Hand and L. Rothfield, The MinD protein is
a membrane ATPase required for the correct placement of the
Escherichia coli division site, The EMBO journal, 10 (13), 4371, 1991.
[4] J. Huang, C. Cao and J. Lutkenhaus, Interaction between FtsZ and
inhibitors of cell division, Journal of Bacteriology, 178 (17), 5080-5085,
1996.
[5] Z. Hu and J. Lutkenhaus, Topological regulation of cell division in
Escherichia coli involves rapid pole to pole oscillation of the division
inhibitor MinC under the control of MinD and MinE, Molecular
Microbiology, 34 (1), 82-90, 1999.
[6] D. Raskin and P. de Boer, MinDE-dependent pole-to-pole oscillation of
division inhibitor MinC in Escherichia coli, Journal of Bacteriology,
181 (20), 6419, 1999.
[7] X. Fu, Y. Shih, Y. Zhang and L. Rothfield, The MinE ring required for
proper placement of the division site is a mobile structure that changes
its cellular location during the Escherichia coli division cycle,
Proceedings of the National Academy of Sciences of the United States
of America, 98 (3), 980-985, 2001.
[8] D. Raskin and P. de Boer, Rapid pole-to-pole oscillation of a protein
required for directing division to the middle of Escherichia coli,
Proceedings of the National Academy of Sciences of the United States
of America, 96 (9), 4971, 1999.
[9] S. Rowland, X. Fu, M. Sayed, Y. Zhang, W. Cook and L. Rothfield,
Membrane redistribution of the Escherichia coli MinD protein induced
by MinE, Journal of Bacteriology, 182 (3), 613-619, 2000.
[10] C. Hale, H. Meinhardt and P. de Boer, Dynamic localization cycle of the
cell division regulator MinE in Escherichia coli, The EMBO journal, 20
(7), 1563-1572, 2001.
[11] D. Drew, M. Osborn and L. Rothfield, A polymerizationdepolymerization
model that accurately generates the self-sustained
oscillatory system involved in bacterial division site placement,
Proceedings of the National Academy of Sciences of the United States
of America, 102 (17), 6114, 2005.
[12] M. Howard and A. Rutenberg, Pattern formation inside bacteria:
fluctuations due to the low copy number of proteins, Physical Review
Letters, 90 (12), 128102, 2003.
[13] M. Howard, A. Rutenberg and S. de Vet, Dynamic
compartmentalization of bacteria: accurate division in E. coli, Physical
Review Letters, 87 (27), 278102, 2001.
[14] K. Huang and N. Wingreen, Min-protein oscillations in round bacteria,
Physical Biology, 1 229-235, 2004.
[15] K. Kruse, A dynamic model for determining the middle of Escherichia
coli, Biophysical Journal, 82 (2), 618-627, 2002.
[16] H. Meinhardt and P. de Boer, Pattern formation in Escherichia coli: a
model for the pole-to-pole oscillations of Min proteins and the
localization of the division site, Proceedings of the National Academy of
Sciences of the United States of America, 98 (25), 14202, 2001.
[17] C. Modchang, P. Kanthang, W. Triampo, W. Ngamsaad, N. Nuttawut, I.
Tang and Y. Lenbury, Modeling of the dynamic pole-to-pole
oscillations of the min proteins in bacterial cell division: The effect of
an external field, Journal of Korean Physical Society, 46 1031-1036,
2005.
[18] W. Ngamsaad, W. Triampo, P. Kanthang, I. Tang, N. Nuttawut, C.
Modjung and Y. Lenbury, A lattice Boltzmann method for modeling the
dynamic pole-to-pole oscillations of Min proteins for determining the
position of the midcell division plane, Journal of Korean Physical
Society, 46 (4), 1025-1030, 2005.
[19] C. Woldringh, E. Mulder, J. Valkenburg, F. Wientjes, A. Zaritsky and
N. Nanninga, Role of the nucleoid in the toporegulation of division,
Research in Microbiology, 141 (1), 39, 1990.
[20] C. Woldringh, The role of co-transcriptional translation and protein
translocation(transertion) in bacterial chromosome segregation,
Molecular Microbiology, 45 (1), 17-29, 2002.
[21] S. Dawson, S. Chen and G. Doolen, Lattice Boltzmann computations for
reaction diffusion equations, The Journal of Chemical Physics, 98 1514,
1993.
[22] S. Chen, H. Chen, D. Martnez and W. Matthaeus, Lattice Boltzmann
model for simulation of magnetohydrodynamics, Physical Review
Letters, 67 (27), 3776-3779, 1991.
[23] P. Lallemand and L. Luo, Theory of the lattice Boltzmann method:
Dispersion, dissipation, isotropy, Galilean invariance, and stability,
Physical Review E, 61 (6), 6546-6562, 2000.
[24] X. Zhang, J. Crawford, A. Glyn Bengough and I. Young, On boundary
conditions in the lattice Boltzmann model for advection and anisotropic
dispersion equation, Advances in Water Resources, 25 (6), 601-609,
2002.
[25] J. A. Valkenburg and C. L. Woldringh, Phase separation between
nucleoid and cytoplasm in Escherichia coli as defined by immersive
refractometry, Journal of Bacteriology, December; 160(3), 1151-
1157, 1984.
[26] U. Junthorn, S. Unai, P. Kanthang, W. Ngamsaad, C. Modchang, W.
Triampo, C. Krittanai, D. Wtriampo and Y. Lenbury, Single-Particle
Tracking Method for Quantitative Tracking and Biophysical Studies of
the MinE Protein, Journal of the Korean Physical Society, 52 (3), 639-
648, 2008.
[27] S. Unai, P. Kanthang, U. Junthon, W. Ngamsaad, W. Triampo, C.
Modchang and C. Krittanai, Quantitative analysis of time-series
fluorescence microscopy using a spot tracking method: application to
Min protein dynamics, Biologia, 64 (1), 27-42, 2009.
[28] Z. Hu, A. Mukherjee, S. Pichoff and J. Lutkenhaus, The MinC
component of the division site selection system in Escherichia coli
interacts with FtsZ to prevent polymerization, Proceedings of the
National Academy of Sciences, 96 (26), 14819-14824, 1999.
[1] P. de Boer, R. Crossley and L. Rothfield, A division inhibitor and a
topological specificity factor coded for by the minicell locus determine
proper placement of the division septum in E. coli, Cell, 56 (4), 641-
649, 1989.
[2] P. de Boer, R. Crossley and L. Rothfield, Central role for the
Escherichia coli minC gene product in two different cell divisioninhibition
systems, Proceedings of the National Academy of Sciences,
87 (3), 1129, 1990.
[3] P. De Boer, R. Crossley, A. Hand and L. Rothfield, The MinD protein is
a membrane ATPase required for the correct placement of the
Escherichia coli division site, The EMBO journal, 10 (13), 4371, 1991.
[4] J. Huang, C. Cao and J. Lutkenhaus, Interaction between FtsZ and
inhibitors of cell division, Journal of Bacteriology, 178 (17), 5080-5085,
1996.
[5] Z. Hu and J. Lutkenhaus, Topological regulation of cell division in
Escherichia coli involves rapid pole to pole oscillation of the division
inhibitor MinC under the control of MinD and MinE, Molecular
Microbiology, 34 (1), 82-90, 1999.
[6] D. Raskin and P. de Boer, MinDE-dependent pole-to-pole oscillation of
division inhibitor MinC in Escherichia coli, Journal of Bacteriology,
181 (20), 6419, 1999.
[7] X. Fu, Y. Shih, Y. Zhang and L. Rothfield, The MinE ring required for
proper placement of the division site is a mobile structure that changes
its cellular location during the Escherichia coli division cycle,
Proceedings of the National Academy of Sciences of the United States
of America, 98 (3), 980-985, 2001.
[8] D. Raskin and P. de Boer, Rapid pole-to-pole oscillation of a protein
required for directing division to the middle of Escherichia coli,
Proceedings of the National Academy of Sciences of the United States
of America, 96 (9), 4971, 1999.
[9] S. Rowland, X. Fu, M. Sayed, Y. Zhang, W. Cook and L. Rothfield,
Membrane redistribution of the Escherichia coli MinD protein induced
by MinE, Journal of Bacteriology, 182 (3), 613-619, 2000.
[10] C. Hale, H. Meinhardt and P. de Boer, Dynamic localization cycle of the
cell division regulator MinE in Escherichia coli, The EMBO journal, 20
(7), 1563-1572, 2001.
[11] D. Drew, M. Osborn and L. Rothfield, A polymerizationdepolymerization
model that accurately generates the self-sustained
oscillatory system involved in bacterial division site placement,
Proceedings of the National Academy of Sciences of the United States
of America, 102 (17), 6114, 2005.
[12] M. Howard and A. Rutenberg, Pattern formation inside bacteria:
fluctuations due to the low copy number of proteins, Physical Review
Letters, 90 (12), 128102, 2003.
[13] M. Howard, A. Rutenberg and S. de Vet, Dynamic
compartmentalization of bacteria: accurate division in E. coli, Physical
Review Letters, 87 (27), 278102, 2001.
[14] K. Huang and N. Wingreen, Min-protein oscillations in round bacteria,
Physical Biology, 1 229-235, 2004.
[15] K. Kruse, A dynamic model for determining the middle of Escherichia
coli, Biophysical Journal, 82 (2), 618-627, 2002.
[16] H. Meinhardt and P. de Boer, Pattern formation in Escherichia coli: a
model for the pole-to-pole oscillations of Min proteins and the
localization of the division site, Proceedings of the National Academy of
Sciences of the United States of America, 98 (25), 14202, 2001.
[17] C. Modchang, P. Kanthang, W. Triampo, W. Ngamsaad, N. Nuttawut, I.
Tang and Y. Lenbury, Modeling of the dynamic pole-to-pole
oscillations of the min proteins in bacterial cell division: The effect of
an external field, Journal of Korean Physical Society, 46 1031-1036,
2005.
[18] W. Ngamsaad, W. Triampo, P. Kanthang, I. Tang, N. Nuttawut, C.
Modjung and Y. Lenbury, A lattice Boltzmann method for modeling the
dynamic pole-to-pole oscillations of Min proteins for determining the
position of the midcell division plane, Journal of Korean Physical
Society, 46 (4), 1025-1030, 2005.
[19] C. Woldringh, E. Mulder, J. Valkenburg, F. Wientjes, A. Zaritsky and
N. Nanninga, Role of the nucleoid in the toporegulation of division,
Research in Microbiology, 141 (1), 39, 1990.
[20] C. Woldringh, The role of co-transcriptional translation and protein
translocation(transertion) in bacterial chromosome segregation,
Molecular Microbiology, 45 (1), 17-29, 2002.
[21] S. Dawson, S. Chen and G. Doolen, Lattice Boltzmann computations for
reaction diffusion equations, The Journal of Chemical Physics, 98 1514,
1993.
[22] S. Chen, H. Chen, D. Martnez and W. Matthaeus, Lattice Boltzmann
model for simulation of magnetohydrodynamics, Physical Review
Letters, 67 (27), 3776-3779, 1991.
[23] P. Lallemand and L. Luo, Theory of the lattice Boltzmann method:
Dispersion, dissipation, isotropy, Galilean invariance, and stability,
Physical Review E, 61 (6), 6546-6562, 2000.
[24] X. Zhang, J. Crawford, A. Glyn Bengough and I. Young, On boundary
conditions in the lattice Boltzmann model for advection and anisotropic
dispersion equation, Advances in Water Resources, 25 (6), 601-609,
2002.
[25] J. A. Valkenburg and C. L. Woldringh, Phase separation between
nucleoid and cytoplasm in Escherichia coli as defined by immersive
refractometry, Journal of Bacteriology, December; 160(3), 1151-
1157, 1984.
[26] U. Junthorn, S. Unai, P. Kanthang, W. Ngamsaad, C. Modchang, W.
Triampo, C. Krittanai, D. Wtriampo and Y. Lenbury, Single-Particle
Tracking Method for Quantitative Tracking and Biophysical Studies of
the MinE Protein, Journal of the Korean Physical Society, 52 (3), 639-
648, 2008.
[27] S. Unai, P. Kanthang, U. Junthon, W. Ngamsaad, W. Triampo, C.
Modchang and C. Krittanai, Quantitative analysis of time-series
fluorescence microscopy using a spot tracking method: application to
Min protein dynamics, Biologia, 64 (1), 27-42, 2009.
[28] Z. Hu, A. Mukherjee, S. Pichoff and J. Lutkenhaus, The MinC
component of the division site selection system in Escherichia coli
interacts with FtsZ to prevent polymerization, Proceedings of the
National Academy of Sciences, 96 (26), 14819-14824, 1999.
@article{"International Journal of Biological, Life and Agricultural Sciences:53382", author = "J.Yojina and W. Ngamsaad and N. Nuttavut and D.Triampo and Y. Lenbury and W. Triampo and P. Kanthang and S.Sriyab", title = "More Realistic Model for Simulating Min Protein Dynamics: Lattice Boltzmann Method Incorporating the Role of Nucleoids", abstract = "The dynamics of Min proteins plays a center role in
accurate cell division. Although the nucleoids may presumably play
an important role in prokaryotic cell division, there is a lack of
models to account for its participation. In this work, we apply the
lattice Boltzmann method to investigate protein oscillation based on a
mesoscopic model that takes into account the nucleoid-s role. We
found that our numerical results are in reasonably good agreement
with the previous experimental results On comparing with the other
computational models without the presence of nucleoids, the
highlight of our finding is that the local densities of MinD and MinE
on the cytoplasmic membrane increases, especially along the cell
width, when the size of the obstacle increases, leading to a more
distinct cap-like structure at the poles. This feature indicated the
realistic pattern and reflected the combination of Min protein
dynamics and nucleoid-s role.", keywords = "lattice Boltzmann method, cell division, Minproteins oscillation, nucleoid", volume = "4", number = "7", pages = "451-6", }
