The functional consequences of convenient size of subcellular structures have been analysed in the past and currently the questions regarding the underlying physical mechanisms for their genesis, the sensing of their size by the cell and maintenance of their convenient size in the steady state are receiving much attention. Long cell protrusions, which are effectively one-dimensional, are highly dynamic subcellular structures and their length keep fluctuating about the mean length even in the the steady state. For proper functioning, particularly as sensors, the length of a specific protrusion must not cross a narrow band bounded by two thresholds. However, fluctuations may drive the length beyond these thresholds. We study generic stochastic models of length control of long cell protrusions; the special cases of this model correspond to specific examples of different types of cell appendages . Exploiting the techniques of level crossings developed for random excursions of stochastic process, we have derived analytical expressions of passage times for hitting various thresholds, sojourn times of random excursions beyond the threshold and the extreme lengths attained during the lifetime of these protrusions. As a concrete example, we apply our general formulae to flagella(also called cilia) of eukaryotic cells thereby getting estimates of the typical length scales and time scales associated with the various aspects of random fluctuations. Since most of the earlier works investigated only the mean length of cell protrusions, our study of the fluctuations opens a new horizon in the field of subcellular size control .
 Long cell protrusions, which are effectively one-dimensional, are highly dynamic subcellular structures . Length of many such protrusions keep fluctuating about the mean value even in the the steady state. We develop here a stochastic model motivated by length fluctuations of a type of appendage of an eukaryotic cell called flagellum (also called cilium) . Exploiting the techniques developed for the calculation of level-crossing statistics of random excursions of stochastic process, we have derived analytical expressions of passage times for hitting various thresholds, sojourn times of random excursions beyond the threshold and the extreme lengths attained during the lifetime of these model flagella. We identify different parameter regimes of this model flagellum that mimic those of the wildtype and mutants of a well known flagellated cell. By analysing our model in these different parameter regimes, we demonstrate how mutation can alter the level-crossing statistics even when the steady state length remains unaffected by the same mutation. Comparison of the theoretically predicted level crossing statistics, in addition to mean and variance of the length, in the steady state with the corresponding experimental data can be used in near future as stringent tests for the validity of the models of flagellar length control. The experimental data required for this purpose, though never reported till now, can be collected, in principle, using a method developed very recently for flagellar length fluctuations .
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The functional consequences of convenient size of subcellular structures have been analysed in the past and currently the questions regarding the underlying physical mechanisms for their genesis, the sensing of their size by the cell and maintenance of their convenient size in the steady state are receiving much attention.
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For proper functioning, particularly as sensors, the length of a specific protrusion must not cross a narrow band bounded by two thresholds. However, fluctuations may drive the length beyond these thresholds. We study generic stochastic models of length control of long cell protrusions; the special cases of this model correspond to specific examples of different types of cell appendages
We develop here a stochastic model motivated by length fluctuations of a type of appendage of an eukaryotic cell called flagellum (also called cilium)
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of level crossings developed for
developed for the calculation of level-crossing statistics of
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protrusions. As a concrete example, we apply our general formulae to flagella(also called cilia) of eukaryotic cells thereby getting estimates of the typical length scales and time scales associated with the various aspects of random fluctuations. Since most of the earlier works investigated only the mean length of cell protrusions, our study of the fluctuations opens a new horizon in the field of subcellular size control
model flagella. We identify different parameter regimes of this model flagellum that mimic those of the wildtype and mutants of a well known flagellated cell. By analysing our model in these different parameter regimes, we demonstrate how mutation can alter the level-crossing statistics even when the steady state length remains unaffected by the same mutation. Comparison of the theoretically predicted level crossing statistics, in addition to mean and variance of the length, in the steady state with the corresponding experimental data can be used in near future as stringent tests for the validity of the models of flagellar length control. The experimental data required for this purpose, though never reported till now, can be collected, in principle, using a method developed very recently for flagellar length fluctuations