We investigate an idealized model of microtubule dynamics that involves: (i) attachment of guanosine triphosphate (GTP) at rate λ, (ii) conversion of GTP to guanosine diphosphate (GDP) at rate 1, and (iii) detachment of GDP at rate μ. As a function of these rates, a microtubule can grow steadily or its length can fluctuate wildly. For μ = 0, we find the exact tubule and GTP cap length distributions, and power-law length distributions of GTP and GDP islands. For μ = ∞, we argue that the time between catastrophes, where the microtubule shrinks to zero length, scales as e(λ). We also discuss the nature of the phase boundary between a growing and shrinking microtubule.

中文翻译：

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微管不稳定性的动力学

我们研究了一个理想化的微管动力学模型，包括：（i）以 λ 速率附着三磷酸鸟苷（GTP），（ii）以速率 1 将 GTP 转化为二磷酸鸟苷（GDP），以及（iii）以速率 λ 分离 GDP μ。作为这些速率的函数，微管可以稳定生长或其长度可以剧烈波动。对于 μ = 0，我们找到了精确的小管和 GTP 帽长度分布，以及 GTP 和 GDP 岛的幂律长度分布。对于 μ = ∞，我们认为灾难之间的时间，其中微管收缩到零长度，按 e(λ) 缩放。我们还讨论了生长和收缩微管之间相界的性质。