Flagellar length control in monoflagellates by motorized transport: growth kinetics and correlations of length fluctuations

Abstract

How does a cell self-organize so that its appendages attain specific lengths that are convenient for their respective functions? What kind of 'rulers' does a cell use to measure the length of these appendages? How does a cell transport structure building materials between the cell body and distal tips of these appendages so as to regulate their dynamic lengths during various stages of its lifetime? Some of these questions are addressed here in the context of a specific cell appendage called flagellum (also called cilium). A "time of flight" (ToF) mechanism, adapted from the pioneering idea of Galileo, has been used successfully very recently to explain the length control of flagella by a biflagellate green algae. Using the same ToF mechanism, here we develop a stochastic model for the dynamics of flagella in two different types of monoflagellate unicellular organisms. A unique feature of these monoflagellates is that these become transiently multi-flagellated during a short span of their life time. The mean length of the flagella in our model reproduce the trend of their temporal variation observed in experiments. Moreover, for probing the intracellular molecular communication between the dynamic flagella of a given cell, we have computed the correlation in the fluctuations of their lengths during the multiflagellated stage of the cell cycle by Monte Carlo simulation. I. DEDICATIONDietrich Stauffer (DS) was the external examiner of the Ph.D. thesis of the senior author (DC) of this paper in 1984. DS was also his first post-doc mentor (host professor during DC's visit to Cologne as an Alexander von Humboldt fellow) and then a long-time collaborator. DC had the privilege of writing more than 30 papers and a book with DS over the twenty year period 1985-2005. DS deserved to be co-author of several other papers of DC, but DS refused to put his name on those papers because he had not himself computed any of the results reported in those despite supplying some of the key ideas. Outside science, DS and DC shared a common interest in history on which their discussion and debate continued for thirty-five years till January 2019 although their views did not necessarily converge on the causes and consequences of many historical events. This paper is dedicated to the memory of DS with whom DC wrote his first paper on theoretical biology.