No Arabic abstract
Every organism has a size that is convenient for its function. Not only multicellular organisms but also uni-cellular organisms and even subcellular structures have convenient sizes. Flagella of eukaryotic cells are long dynamic cell protrusions. Because of their simple linear geometry, these cell appendages have been popular system for experimental investigation of the mechanisms of size control of organelles of eukaryotic cells. In the past most of the attention have been focussed on mono-flagellates and bi-flagellates. By extending our earlier model of bi-flagellates, here we develop a theoretical model for flagellar length control in {it Giardia} which is an octo-flagellate. It has four pairs of flagella of four different lengths. Analyzing our model we predict the different sizes of the four pairs of flagella . This analysis not only provide insight into the physical origins of the different lengths but the predicted lengths are also consistent with the experimental data.
Flagella of eukaryotic cells are transient long cylindrical protrusions. The proteins needed to form and maintain flagella are synthesized in the cell body and transported to the distal tips. What `rulers or `timers a specific type of cells use to strike a balance between the outward and inward transport of materials so as to maintain a particular length of its flagella in the steady state is one of the open questions in cellular self-organization. Even more curious is how the two flagella of biflagellates, like Chlamydomonas Reinhardtii, communicate through their base to coordinate their lengths. In this paper we develop a stochastic model for flagellar length control based on a time-of-flight (ToF) mechanism. This ToF mechanism decides whether or not structural proteins are to be loaded onto an intraflagellar transport (IFT) train just before it begins its motorized journey from the base to the tip of the flagellum. Because of the ongoing turnover, the structural proteins released from the flagellar tip are transported back to the cell body also by IFT trains. We represent the traffic of IFT trains as a totally asymmetric simple exclusion process (TASEP). The ToF mechanism for each flagellum, together with the TASEP-based description of the IFT trains, combined with a scenario of sharing of a common pool of flagellar structural proteins in biflagellates, can account for all key features of experimentally known phenomena. These include ciliogenesis, resorption, deflagellation as well as regeneration after selective amputation of one of the two flagella. We also show that the experimental observations of Ishikawa and Marshall are consistent with the ToF mechanism of length control if the effects of the mutual exclusion of the IFT trains captured by the TASEP are taken into account. Moreover, we make new predictions on the flagellar length fluctuations and the role of the common pool.
Organelles of optimum size are crucial for proper functioning of a living cell. The cell employs various mechanisms for actively sensing and controlling the size of its organelles. Recently Bauer et al have opened a new research frontier in the field of subcellular size control by shedding light on the noise and fluctuations of organelles of controlled size. Taking eukaryotic flagellum as a model organelle, which is quite popular for such studies because of its linear geometry and dynamic nature, Bauer et al have analysed the nature of fluctuations of its length. Here we summarize the key questions and the fundamental importance of the recent developments. Although our attention is focussed here mainly on the experimental and theoretical works on eukaryotic flagellum, the ideas are general and applicable to wide varieties of cell organelle.
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.
The flexibility of the bacterial flagellar hook is believed to have substantial consequences for microorganism locomotion. Using a simplified model of a rigid flagellum and a flexible hook, we show that the paths of axisymmetric cell bodies driven by a single flagellum in Stokes flow are generically helical. Phase-averaged resistance and mobility tensors are produced to describe the flagellar hydrodynamics, and a helical rod model which retains a coupling between translation and rotation is identified as a distinguished asymptotic limit. A supercritical Hopf bifurcation in the flagellar orientation beyond a critical ratio of flagellar motor torque to hook bending stiffness, which is set by the spontaneous curvature of the flexible hook, the shape of the cell body, and the flagellum geometry, can have a dramatic effect on the cells trajectory through the fluid. Although the equilibrium hook angle can result in a wide variance in the trajectorys helical pitch, we find a very consistent prediction for the trajectorys helical amplitude using parameters relevant to swimming P. aeruginosa cells.
Groups of beating flagella or cilia often synchronize so that neighboring filaments have identical frequencies and phases. A prime example is provided by the unicellular biflagellate Chlamydomonas reinhardtii, which typically displays synchronous in-phase beating in a low-Reynolds number version of breaststroke swimming. We report here the discovery that ptx1, a flagellar dominance mutant of C. reinhardtii, can exhibit synchronization in precise antiphase, as in the freestyle swimming stroke. Long-duration high-speed imaging shows that ptx1 flagella switch stochastically between in-phase and antiphase states, and that the latter has a distinct waveform and significantly higher frequency, both of which are strikingly similar to those found during phase slips that stochastically interrupt in-phase beating of the wildtype. Possible mechanisms underlying these observations are discussed.