基于偏微分方程约束优化的神经元物质运输调节和交通阻塞模型
Modeling material transport regulation and traffic jam in neurons using PDE-constrained optimization
摘要：
细胞内转运过程在将必需物质递送通过神经元的分支几何结构以使其存活和发挥功能方面起着重要作用。许多神经退行性疾病与运输中断有关。因此，研究神经元如何控制物质的运输过程，使其定位于所需的位置是非常必要的。在这里，我们开发了一种新的优化模型来模拟交通管制机制的物质运输的复杂几何形状的神经元。通过最小化预定义的目标函数，控制运输以避免物料的交通堵塞。优化受一组偏微分方程（PDE）的约束条件，描述的材料运输过程的基础上的宏观分子马达辅助运输模型的细胞内颗粒。提出的偏微分方程约束优化模型求解复杂的树结构，通过使用等几何分析（IGA）。使用不同的模拟参数来引入交通堵塞，并研究神经元如何处理交通问题。具体来说，我们成功地建模和解释的微管（MT）和MT漩涡的数量减少所造成的交通堵塞。总之，我们的模型有效地模拟了健康神经元中的物质运输过程，也解释了异常神经元中交通堵塞的形成。我们的研究结果表明，几何形状和MT结构在实现神经元的最佳传输过程中起着重要的作用。
英文摘要：
The intracellular transport process plays an important role in delivering essential materials throughout branched geometries of neurons for their survival and function. Many neurodegenerative diseases have been associated with the disruption of transport. Therefore, it is essential to study how neurons control the transport process to localize materials to necessary locations. Here, we develop a novel optimization model to simulate the traffic regulation mechanism of material transport in complex geometries of neurons. The transport is controlled to avoid traffic jam of materials by minimizing a pre-defined objective function. The optimization subjects to a set of partial differential equation (PDE) constraints that describe the material transport process based on a macroscopic molecular-motor-assisted transport model of intracellular particles. The proposed PDE-constrained optimization model is solved in complex tree structures by using isogeometric analysis (IGA). Different simulation parameters are used to introduce traffic jams and study how neurons handle the transport issue. Specifically, we successfully model and explain the traffic jam caused by reduced number of microtubules (MTs) and MT swirls. In summary, our model effectively simulates the material transport process in healthy neurons and also explains the formation of a traffic jam in abnormal neurons. Our results demonstrate that both geometry and MT structure play important roles in achieving an optimal transport process in neuron.
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