Nelson Anna C, McKinley Scott A, Rolls Melissa M, Ciocanel Maria-Veronica
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA.
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA.
J Theor Biol. 2025 Aug 30;616:112254. doi: 10.1016/j.jtbi.2025.112254.
Microtubules (MTs) are dynamic protein filaments essential for intracellular organization and transport, particularly in long-lived cells such as neurons. The plus and minus ends of neuronal MTs switch between growth and shrinking phases, and the nucleation of new filaments is believed to be regulated in both healthy and injury conditions. We propose stochastic and deterministic mathematical models to investigate the impact of filament nucleation and length-regulation mechanisms on emergent properties such as MT lengths and numbers in living cells. We expand our stochastic continuous-time Markov chain model of filament dynamics to incorporate MT nucleation and capture realistic stochastic fluctuations in MT numbers and tubulin availability. We also propose a simplified partial differential equation (PDE) model, which allows for tractable analytical investigation into steady-state MT distributions under different nucleation and length-regulating mechanisms. We find that the stochastic and PDE modeling approaches show good agreement in MT length distributions, and that both MT nucleation and the catastrophe rate of large-length MTs regulate MT length distributions. In both frameworks, multiple mechanistic combinations achieve the same average MT length. The models proposed can predict parameter regimes where the system is scarce in tubulin, the building block of MTs, and suggest that low filament nucleation regimes are characterized by high variation in MT lengths, while high nucleation regimes drive high variation in MT numbers. These mathematical frameworks have the potential to improve our understanding of MT regulation in both healthy and injured neurons.
微管（MTs）是细胞内组织和运输所必需的动态蛋白质细丝，在诸如神经元等长寿命细胞中尤为重要。神经元微管的正端和负端在生长和收缩阶段之间切换，并且新细丝的成核被认为在健康和损伤条件下均受到调节。我们提出随机和确定性数学模型，以研究细丝成核和长度调节机制对活细胞中诸如微管长度和数量等涌现特性的影响。我们扩展了细丝动力学的随机连续时间马尔可夫链模型，以纳入微管成核并捕捉微管数量和微管蛋白可用性中的实际随机波动。我们还提出了一个简化的偏微分方程（PDE）模型，该模型允许对不同成核和长度调节机制下的微管稳态分布进行易于处理的分析研究。我们发现随机和偏微分方程建模方法在微管长度分布上显示出良好的一致性，并且微管成核和大长度微管的灾变率均调节微管长度分布。在这两个框架中，多种机制组合可实现相同的平均微管长度。所提出的模型可以预测微管构建块微管蛋白稀缺的参数范围，并表明低细丝成核范围的特征是微管长度变化大，而高成核范围导致微管数量变化大。这些数学框架有可能增进我们对健康和受损神经元中微管调节的理解。
