dorsal/arxiv
View SchemaModeling oscillatory Microtubule--Polymerization
| Authors | Martin Hammele, Walter Zimmermann |
|---|---|
| Categories | |
| ArXiv ID | physics/0210030 |
| URL | https://arxiv.org/abs/physics/0210030 |
| DOI | 10.1103/PhysRevE.67.021903 |
Abstract
Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates as well as typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold a so--called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.
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"abstract": "Polymerization of microtubules is ubiquitous in biological cells and under\ncertain conditions it becomes oscillatory in time. Here simple reaction models\nare analyzed that capture such oscillations as well as the length distribution\nof microtubules. We assume reaction conditions that are stationary over many\noscillation periods, and it is a Hopf bifurcation that leads to a persistent\noscillatory microtubule polymerization in these models. Analytical expressions\nare derived for the threshold of the bifurcation and the oscillation frequency\nin terms of reaction rates as well as typical trends of their parameter\ndependence are presented. Both, a catastrophe rate that depends on the density\nof {\\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay\nreaction, such as the depolymerization of shrinking microtubules or the decay\nof oligomers, support oscillations. For a tubulin dimer concentration below the\nthreshold oscillatory microtubule polymerization occurs transiently on the\nroute to a stationary state, as shown by numerical solutions of the model\nequations. Close to threshold a so--called amplitude equation is derived and it\nis shown that the bifurcation to microtubule oscillations is supercritical.",
"arxiv_id": "physics/0210030",
"authors": [
"Martin Hammele",
"Walter Zimmermann"
],
"categories": [
"physics.bio-ph",
"q-bio.OT"
],
"doi": "10.1103/PhysRevE.67.021903",
"title": "Modeling oscillatory Microtubule--Polymerization",
"url": "https://arxiv.org/abs/physics/0210030"
},
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