White Diana, Honoré Stéphane, Hubert Florence
Department of Mathematics, Clarkson University, New York, USA.
Aix-Marseille Université, INSERM UMR S 911, CRO2, Marseille, France.
J Theor Biol. 2017 Sep 21;429:18-34. doi: 10.1016/j.jtbi.2017.06.014. Epub 2017 Jun 20.
Microtubules (MTs) play a key role in normal cell development and are a primary target for many cancer chemotherapy MT targeting agents (MTAs). As such, understanding MT dynamics in the presence of such agents, as well as other proteins that alter MT dynamics, is extremely important. In general, MTs grow relatively slowly and shorten very fast (almost instantaneously), an event referred to as a catastrophe. These dynamics, referred to as dynamic instability, have been studied in both experimental and theoretical settings. In the presence of MTAs, it is well known that such agents work by suppressing MT dynamics, either by promoting MT polymerization or promoting MT depolymerization. However, recent in vitro experiments show that in the presence of end-binding proteins (EBs), low doses of MTAs can increase MT dynamic instability, rather than suppress it. Here, we develop a novel mathematical model, to describe MT and EB dynamics, something which has not been done in a theoretical setting. Our MT model is based on previous modeling efforts, and consists of a pair of partial differential equations to describe length distributions for growing and shortening MT populations, and an ordinary differential equation (ODE) system to describe the time evolution for concentrations of GTP- and GDP-bound tubulin. A new extension of our approach is the use of an integral term, rather than an advection term, to describe very fast MT shortening events. Further, we introduce an ODE system to describe the binding and unbinding of EBs with MTs. To compare simulation results with experiment, we define novel mathematical expressions for time- and distance-based catastrophe frequencies. These quantities help to define MT dynamics in in vivo and in vitro settings. Simulation results show that increasing concentrations of EBs work to increase time-based catastrophe while distance-based catastrophe is less affected by changes in EB concentration, a result that is consistent with experiment. We further describe how EBs and MTAs alter MT dynamics. In the context of this modeling framework, we show that it is likely that MTAs and EBs do not work independently from one another. Thus, we propose a mechanism for how EBs can work synergistically with MTAs to promote MT dynamic instability at low MTA dose.
微管（MTs）在正常细胞发育中起关键作用，并且是许多癌症化疗微管靶向剂（MTAs）的主要作用靶点。因此，了解在这些药剂存在的情况下微管的动力学，以及其他改变微管动力学的蛋白质，极其重要。一般来说，微管生长相对缓慢，缩短速度非常快（几乎瞬间完成），这一事件被称为灾变。这些被称为动态不稳定性的动力学，已在实验和理论环境中进行了研究。在微管靶向剂存在的情况下，众所周知这些药剂通过抑制微管动力学起作用，要么通过促进微管聚合，要么通过促进微管解聚。然而，最近的体外实验表明，在存在末端结合蛋白（EBs）的情况下，低剂量的微管靶向剂会增加微管动态不稳定性，而不是抑制它。在这里，我们开发了一个新的数学模型来描述微管和末端结合蛋白的动力学，这在理论环境中尚未做到。我们的微管模型基于先前的建模工作，由一对偏微分方程组成，用于描述生长和缩短的微管群体的长度分布，以及一个常微分方程（ODE）系统，用于描述结合GTP和GDP的微管蛋白浓度的时间演变。我们方法的一个新扩展是使用一个积分项，而不是平流项，来描述非常快速的微管缩短事件。此外，我们引入一个常微分方程系统来描述末端结合蛋白与微管的结合和解离。为了将模拟结果与实验进行比较，我们为基于时间和距离的灾变频率定义了新的数学表达式。这些量有助于定义体内和体外环境中的微管动力学。模拟结果表明，增加末端结合蛋白的浓度会增加基于时间的灾变，而基于距离的灾变受末端结合蛋白浓度变化的影响较小，这一结果与实验一致。我们进一步描述了末端结合蛋白和微管靶向剂如何改变微管动力学。在这个建模框架的背景下，我们表明微管靶向剂和末端结合蛋白可能并非彼此独立起作用。因此，我们提出了一种机制，说明末端结合蛋白如何能与微管靶向剂协同作用，在低剂量微管靶向剂的情况下促进微管动态不稳定性。
