Simple membrane-based model of the Min oscillator
Min proteins in E. coli bacteria organize into a dynamic pattern oscillating between the two cell poles. This process identifies the middle of the cell and enables symmetric cell division. In an experimental model system consisting of a flat membrane with effectively infinite supply of proteins and...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2015-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/17/4/043023 |
| _version_ | 1797751240863514624 |
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| author | Zdeněk Petrášek Petra Schwille |
| author_facet | Zdeněk Petrášek Petra Schwille |
| author_sort | Zdeněk Petrášek |
| collection | DOAJ |
| description | Min proteins in E. coli bacteria organize into a dynamic pattern oscillating between the two cell poles. This process identifies the middle of the cell and enables symmetric cell division. In an experimental model system consisting of a flat membrane with effectively infinite supply of proteins and energy source, the Min proteins assemble into travelling waves. Here we propose a simple one-dimensional model of the Min dynamics that, unlike the existing models, reproduces the sharp decrease of Min concentration when the majority of protein detaches from the membrane, and even the narrow MinE maximum immediately preceding the detachment. The proposed model thus provides a possible mechanism for the formation of the MinE ring known from cells. The model is restricted to one dimension, with protein interactions described by chemical kinetics allowing at most bimolecular reactions, and explicitly considering only three, membrane-bound, species. The bulk solution above the membrane is approximated as being well-mixed, with constant concentrations of all species. Unlike other models, our proposal does not require autocatalytic binding of MinD to the membrane. Instead, it is assumed that two MinE molecules are necessary to induce the dissociation of the MinD dimer and its subsequent detachment from the membrane. We investigate which reaction schemes lead to unstable homogeneous steady states and limit cycle oscillations, and how diffusion affects their stability. The suggested model qualitatively describes the shape of the Min waves observed on flat membranes, and agrees with the experimental dependence of the wave period on the MinE concentration. These results highlight the importance of MinE presence on the membrane without being bound to MinD, and of the reactions of Min proteins on the membrane. |
| first_indexed | 2024-03-12T16:45:41Z |
| format | Article |
| id | doaj.art-8cf8c9f76ecb4bc5b4f8ae5460631cc5 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:45:41Z |
| publishDate | 2015-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-8cf8c9f76ecb4bc5b4f8ae5460631cc52023-08-08T14:15:31ZengIOP PublishingNew Journal of Physics1367-26302015-01-0117404302310.1088/1367-2630/17/4/043023Simple membrane-based model of the Min oscillatorZdeněk Petrášek0Petra Schwille1Department of Cellular and Molecular Biophysics, Max-Planck-Institute of Biochemistry , Am Klopferspitz 18, 82152 Martinsried, Germany; Institut für Biotechnologie und Bioprozesstechnik, Technische Universität Graz , Petersgasse 10-12/I, 8010 Graz, AustriaDepartment of Cellular and Molecular Biophysics, Max-Planck-Institute of Biochemistry , Am Klopferspitz 18, 82152 Martinsried, GermanyMin proteins in E. coli bacteria organize into a dynamic pattern oscillating between the two cell poles. This process identifies the middle of the cell and enables symmetric cell division. In an experimental model system consisting of a flat membrane with effectively infinite supply of proteins and energy source, the Min proteins assemble into travelling waves. Here we propose a simple one-dimensional model of the Min dynamics that, unlike the existing models, reproduces the sharp decrease of Min concentration when the majority of protein detaches from the membrane, and even the narrow MinE maximum immediately preceding the detachment. The proposed model thus provides a possible mechanism for the formation of the MinE ring known from cells. The model is restricted to one dimension, with protein interactions described by chemical kinetics allowing at most bimolecular reactions, and explicitly considering only three, membrane-bound, species. The bulk solution above the membrane is approximated as being well-mixed, with constant concentrations of all species. Unlike other models, our proposal does not require autocatalytic binding of MinD to the membrane. Instead, it is assumed that two MinE molecules are necessary to induce the dissociation of the MinD dimer and its subsequent detachment from the membrane. We investigate which reaction schemes lead to unstable homogeneous steady states and limit cycle oscillations, and how diffusion affects their stability. The suggested model qualitatively describes the shape of the Min waves observed on flat membranes, and agrees with the experimental dependence of the wave period on the MinE concentration. These results highlight the importance of MinE presence on the membrane without being bound to MinD, and of the reactions of Min proteins on the membrane.https://doi.org/10.1088/1367-2630/17/4/043023Min oscillationspattern formationself-organizationdynamic instability |
| spellingShingle | Zdeněk Petrášek Petra Schwille Simple membrane-based model of the Min oscillator New Journal of Physics Min oscillations pattern formation self-organization dynamic instability |
| title | Simple membrane-based model of the Min oscillator |
| title_full | Simple membrane-based model of the Min oscillator |
| title_fullStr | Simple membrane-based model of the Min oscillator |
| title_full_unstemmed | Simple membrane-based model of the Min oscillator |
| title_short | Simple membrane-based model of the Min oscillator |
| title_sort | simple membrane based model of the min oscillator |
| topic | Min oscillations pattern formation self-organization dynamic instability |
| url | https://doi.org/10.1088/1367-2630/17/4/043023 |
| work_keys_str_mv | AT zdenekpetrasek simplemembranebasedmodeloftheminoscillator AT petraschwille simplemembranebasedmodeloftheminoscillator |