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摘要翻译：
微管聚合在生物细胞中普遍存在，在一定条件下，微管聚合随时间呈振荡变化。这里分析了捕捉这种振荡以及微管长度分布的简单反应模型。我们假设反应条件在许多振荡周期内是稳定的，在这些模型中，是Hopf分支导致了持续振荡的微管聚合。导出了分叉阈值和振荡频率随反应速率的解析表达式，并给出了它们参数依赖的典型趋势。突变率依赖于{鸟苷三磷酸}(GTP)连接微管蛋白二聚体的密度，而延迟反应，如收缩微管的解聚或低聚体的衰变，都支持振荡。当微管蛋白二聚体浓度低于阈值时，振荡微管聚合会在到达稳态的过程中发生，如模型方程的数值解所示。在接近阈值的情况下，导出了振幅方程，证明了微管振荡的分叉是超临界的。
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英文标题：
《Modeling oscillatory Microtubule--Polymerization》
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作者：
Martin Hammele and Walter Zimmermann
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最新提交年份：
2002
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分类信息：
一级分类：Physics 物理学
二级分类：Biological Physics 生物物理学
分类描述：Molecular biophysics, cellular biophysics, neurological biophysics, membrane biophysics, single-molecule biophysics, ecological biophysics, quantum phenomena in biological systems (quantum biophysics), theoretical biophysics, molecular dynamics/modeling and simulation, game theory, biomechanics, bioinformatics, microorganisms, virology, evolution, biophysical methods.
分子生物物理、细胞生物物理、神经生物物理、膜生物物理、单分子生物物理、生态生物物理、生物系统中的量子现象（量子生物物理）、理论生物物理、分子动力学/建模与模拟、博弈论、生物力学、生物信息学、微生物、病毒学、进化论、生物物理方法。
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一级分类：Quantitative Biology 数量生物学
二级分类：Other Quantitative Biology 其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
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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PDF链接：
https://arxiv.org/pdf/physics/0210030
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