Karamched Bhargav R, Bressloff Paul C
Department of Mathematics, University of Utah, Salt Lake City, Utah.
Department of Mathematics, University of Utah, Salt Lake City, Utah.
Biophys J. 2015 May 5;108(9):2408-19. doi: 10.1016/j.bpj.2015.03.055.
A fundamental question in cell biology is how the sizes of cells and organelles are regulated at various stages of development. Size homeostasis is particularly challenging for neurons, whose axons can extend from hundreds of microns to meters (in humans). Recently, a molecular-motor-based mechanism for axonal length sensing has been proposed, in which axonal length is encoded by the frequency of an oscillating retrograde signal. In this article, we develop a mathematical model of this length-sensing mechanism in which advection-diffusion equations for bidirectional motor transport are coupled to a chemical signaling network. We show that chemical oscillations emerge due to delayed negative feedback via a Hopf bifurcation, resulting in a frequency that is a monotonically decreasing function of axonal length. Knockdown of either kinesin or dynein causes an increase in the oscillation frequency, suggesting that the length-sensing mechanism would produce longer axons, which is consistent with experimental findings. One major prediction of the model is that fluctuations in the transport of molecular motors lead to a reduction in the reliability of the frequency-encoding mechanism for long axons.
细胞生物学中的一个基本问题是，细胞和细胞器的大小在发育的各个阶段是如何被调控的。大小稳态对神经元来说尤其具有挑战性，因为其轴突在人类中可以从数百微米延伸到数米。最近，一种基于分子马达的轴突长度感知机制被提了出来，其中轴突长度由振荡逆行信号的频率编码。在本文中，我们建立了这种长度感知机制的数学模型，其中双向马达运输的平流扩散方程与一个化学信号网络相耦合。我们表明，由于通过霍普夫分岔的延迟负反馈，化学振荡出现了，从而产生了一个作为轴突长度单调递减函数的频率。驱动蛋白或动力蛋白的敲低会导致振荡频率增加，这表明长度感知机制会产生更长的轴突，这与实验结果一致。该模型的一个主要预测是，分子马达运输中的波动会导致长轴突频率编码机制的可靠性降低。
