Electro-Acoustic Behavior of the Mitotic Spindle: A Semi-Classical Coarse-Grained Model

The regulation of chromosome separation during mitosis is not fully understood yet. Microtubules forming mitotic spindles are targets of treatment strategies which are aimed at (i) the triggering of the apoptosis or (ii) the interruption of uncontrolled cell division. Despite these facts, only few physical models relating to the dynamics of mitotic spindles exist up to now. In this paper, we present the first electromechanical model which enables calculation of the electromagnetic field coupled to acoustic vibrations of the mitotic spindle. This electromagnetic field originates from the electrical polarity of microtubules which form the mitotic spindle. The model is based on the approximation of resonantly vibrating microtubules by a network of oscillating electric dipoles. Our computational results predict the existence of a rapidly changing electric field which is generated by either driven or endogenous vibrations of the mitotic spindle. For certain values of parameters, the intensity of the electric field and its gradient reach values which may exert a not-inconsiderable force on chromosomes which are aligned in the spindle midzone. Our model may describe possible mechanisms of the effects of ultra-short electrical and mechanical pulses on dividing cells—a strategy used in novel methods for cancer treatment.目前学界对有丝分裂过程中染色体分离的调控机制尚未完全阐明。构成有丝分裂纺锤体（mitotic spindle）的微管（microtubules），是两类治疗策略的作用靶点：一是触发细胞凋亡，二是阻断失控的细胞增殖。尽管如此，迄今为止针对有丝分裂纺锤体动力学特性的物理模型仍为数不多。本文提出首个可计算与有丝分裂纺锤体声振动耦合的电磁场（electromagnetic field）的机电模型（electromechanical model）。该电磁场源于构成有丝分裂纺锤体的微管的电极性（electrical polarity）。本模型以共振振动微管的振荡电偶极子（oscillating electric dipoles）网络近似为核心构建思路。我们的计算结果预测，存在一类由有丝分裂纺锤体受迫振动（driven vibrations）或内源振动（endogenous vibrations）所产生的快速交变电场。当参数取特定取值时，该电场及其电场梯度（electric field gradient）的强度足以对纺锤体中区（spindle midzone）排列的染色体施加不可忽视的作用力。本模型可用于阐释超短电脉冲与机械脉冲（ultra-short electrical and mechanical pulses）对分裂细胞的作用机制——这也是新型癌症治疗方法所采用的策略之一。