Title: Stochastic Analysis of Taxis and Kinesis Properties of Colonial Protozoa Show Chinese title

Title: 共生原生动物的 taxis 和 kinesis 特性的随机分析

Abstract: Protozoan colonies undergo stimulus driven motion for purposes such as nutrient acquisition. Colonial response to a stimulus is mediated through a mechanical aggregation of the response properties of members of the colony. We develop and apply asymptotic analysis to a stochastic model for the integration of two classes of stimulus responses of the constituent cells -- taxis and kinesis. We investigate in particular the maintenance of effectiveness of taxis and kinesis in the transition from unicellular to multicellular organisms, using experimental observations of chemotaxis and aerotaxis of protozoa as a reference. Our taxis model based on a steering response of individual cells actually leads to a counterproductive drift of the colony down the stimulus gradient, together with a constructive drift up the gradient which is proportional to a measure of asymmetry of the flagellar placement. The strength of taxis drift up the stimulus gradient decreases with colony size while the counterproductive term does not, indicating a failure for colonial taxis based on a steering response of individual cells. Under a kinesis response of the cellular flagellar motion, enhancing the noise as the cell is facing away from the stimulus gradient, the colony does drift up the gradient with a speed independent of colony size, even under a completely symmetric placement of flagella. Show Chinese abstract

Abstract: 原生动物群落通过刺激驱动的运动来实现诸如获取营养等目的。 群落对刺激的反应是通过群落成员的反应特性的机械聚集来介导的。 我们开发并应用渐近分析，对两种刺激反应类型的细胞整合进行随机模型研究——趋性与趋动性。 我们特别研究了从单细胞生物到多细胞生物的转变中，趋性与趋动性的有效性维持问题，并以原生动物的趋化性和趋氧性的实验观察作为参考。 基于个体细胞转向反应的趋性模型实际上会导致群落沿着刺激梯度向下产生有害的漂移，同时也会产生有益的向上漂移，这种向上漂移与鞭毛位置的不对称性程度成正比。 趋性沿刺激梯度的漂移强度随着群落大小的增加而减小，而有害的漂移项则不会，这表明基于个体细胞转向反应的群落趋性存在失效。 在细胞鞭毛运动的趋动性反应下，当细胞朝向远离刺激梯度的方向时增强噪声，群落仍会沿着梯度向上漂移，其速度与群落大小无关，即使鞭毛的放置完全对称也是如此。