  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.
