A systematic comparison of mathematical models for inherent measurement of ciliary length: how a cell can measure length and volume

Chlamydomonas as a model system to study cilia and flagella using genetics, biochemistry, and microscopy

The unicellular green alga, Chlamydomonas reinhardtii, has played a central role in discovering much of what is currently known about the composition, assembly, and function of cilia and flagella. Chlamydomonas combines excellent genetics, such as the ability to grow cells as haploids or diploids and to perform tetrad analysis, with an unparalleled ability to detach and isolate flagella in a single step without cell lysis. The combination of genetics and biochemistry that is possible in Chlamydomonas has allowed many of the key components of the cilium to be identified by looking for proteins that are missing in a defined mutant. Few if any other model organisms allow such a seamless combination of genetic and biochemical approaches. Other major advantages of Chlamydomonas compared to other systems include the ability to induce flagella to regenerate in a highly synchronous manner, allowing the kinetics of flagellar growth to be measured, and the ability of Chlamydomonas flagella to adhere to glass coverslips allowing Intraflagellar Transport to be easily imaged inside the flagella of living cells, with quantitative precision and single-molecule resolution. These advantages continue to work in favor of Chlamydomonas as a model system going forward, and are now augmented by extensive genomic resources, a knockout strain collection, and efficient CRISPR gene editing. While Chlamydomonas has obvious limitations for studying ciliary functions related to animal development or organ physiology, when it comes to studying the fundamental biology of cilia and flagella, Chlamydomonas is simply unmatched in terms of speed, efficiency, cost, and the variety of approaches that can be brought to bear on a question.

The purpose and ubiquity of turnover

Turnover-constant component production and destruction-is ubiquitous in biology. Turnover occurs across organisms and scales, including for RNAs, proteins, membranes, macromolecular structures, organelles, cells, hair, feathers, nails, antlers, and teeth. For many systems, turnover might seem wasteful when degraded components are often fully functional. Some components turn over with shockingly high rates and others do not turn over at all, further making this process enigmatic. However, turnover can address fundamental problems by yielding powerful properties, including regeneration, rapid repair onset, clearance of unpredictable damage and errors, maintenance of low constitutive levels of disrepair, prevention of stable hazards, and transitions. I argue that trade-offs between turnover benefits and metabolic costs, combined with constraints on turnover, determine its presence and rates across distinct contexts. I suggest that the limits of turnover help explain aging and that turnover properties and the basis for its levels underlie this fundamental component of life.

Distribution and bulk flow analyses of the intraflagellar transport (IFT) motor kinesin-2 support an "on-demand" model for Chlamydomonas ciliary length control

Most cells tightly control the length of their cilia. The regulation likely involves intraflagellar transport (IFT), a bidirectional motility of multi-subunit particles organized into trains that deliver building blocks into the organelle. In Chlamydomonas, the anterograde IFT motor kinesin-2 consists of the motor subunits FLA8 and FLA10 and the nonmotor subunit KAP. KAP dissociates from IFT at the ciliary tip and diffuses back to the cell body. This observation led to the diffusion-as-a-ruler model of ciliary length control, which postulates that KAP is progressively sequestered into elongating cilia because its return to the cell body will require increasingly more time, limiting motor availability at the ciliary base, train assembly, building block supply, and ciliary growth. Here, we show that Chlamydomonas FLA8 also returns to the cell body by diffusion. However, more than 95% of KAP and FLA8 are present in the cell body and, at a given time, just ~1% of the motor participates in IFT. After repeated photobleaching of both cilia, IFT of fluorescent kinesin subunits continued indicating that kinesin-2 cycles from the large cell-body pool through the cilia and back. Furthermore, growing and full-length cilia contained similar amounts of kinesin-2 subunits and the size of the motor pool at the base changed only slightly with ciliary length. These observations are incompatible with the diffusion-as-a-ruler model, but rather support an "on-demand model," in which the cargo load of the trains is regulated to assemble cilia of the desired length.

Lithium-induced ciliary lengthening sparks Arp2/3 complex-dependent endocytosis

Ciliary length is highly regulated, but can be disrupted by lithium, which causes ciliary elongation across cell types and organisms. We used the algal system Chlamydomonas reinhardtii to investigate the mechanism behind lithium-induced ciliary elongation. Protein synthesis is not required for lengthening, and the target of lithium, GSK3, has substrates that can influence membrane dynamics. Further, ciliary assembly requires a supply of ciliary membrane as well as protein. Lithium-treated cilia elongate normally with brefeldin treatment, but dynasore treatment produced defective lengthening suggesting a source of membrane from the cell surface rather than the Golgi. Genetic or chemical perturbation of the Arp2/3 complex or dynamin, required for endocytosis, blocks lithium-induced ciliary lengthening. Finally, we found an increase in Arp2/3 complex- and endocytosis-dependent actin filaments near the ciliary base upon lithium treatment. Our results identify a mechanism for lithium-mediated cilium lengthening and demonstrate the endocytic pathway for cilium membrane supply in algae is likely a conserved mechanism given lithium's conserved effects across organisms.

The flagellar length control system: exploring the physical biology of organelle size

How cells build and maintain dynamic structures of defined size is currently an important unsolved problem in quantitative cell biology. The flagella of the unicellular green algaChlamydomonasprovide a highly tractable model system to investigate this general question, but while the powerful genetics of this organism have revealed numerous genes required for proper flagellar length, in most cases we do not understand their mechanistic role in length control. Flagellar length can be viewed as the steady state solution of a dynamical system involving assembly and disassembly of axonemal microtubules, with assembly depending on an active transport process known as intraflagellar transport (IFT). The inherent length dependence of IFT gives rise to a family of simple models for length regulation that can account for many previously described phenomena such as the ability of flagella to maintain equal lengths. But these models requires that the cell has a way to measure flagellar length in order to adjust IFT rates accordingly. Several models for length sensing have been modeled theoretically and evaluated experimentally, allowing them to be ruled out. Current data support a model in which the diffusive return of the kinesin motor driving IFT provides a length dependence that ultimately is the basis for length regulation. By combining models of length sensing with a more detailed representation of cargo transport and availability, it is now becoming possible to formulate concrete hypotheses to explain length altering mutants.

Testing the ion-current model for flagellar length sensing and IFT regulation

Eukaryotic cilia and flagella are microtubule-based organelles whose relatively simple shape makes them ideal for investigating the fundamental question of organelle size regulation. Most of the flagellar materials are transported from the cell body via an active transport process called intraflagellar transport (IFT). The rate of IFT entry into flagella, known as IFT injection, has been shown to negatively correlate with flagellar length. However, it remains unknown how the cell measures the length of its flagella and controls IFT injection. One of the most-discussed theoretical models for length sensing to control IFT is the ion-current model, which posits that there is a uniform distribution of Ca2+ channels along the flagellum and that the Ca2+ current from the flagellum into the cell body increases linearly with flagellar length. In this model, the cell uses the Ca2+ current to negatively regulate IFT injection. The recent discovery that IFT entry into flagella is regulated by the phosphorylation of kinesin through a calcium-dependent protein kinase has provided further impetus for the ion-current model. To test this model, we measured and manipulated the levels of Ca2+ inside of Chlamydomonas flagella and quantified IFT injection. Although the concentration of Ca2+ inside of flagella was weakly correlated with the length of flagella, we found that IFT injection was reduced in calcium-deficient flagella, rather than increased as the model predicted, and that variation in IFT injection was uncorrelated with the occurrence of flagellar Ca2+ spikes. Thus, Ca2+ does not appear to function as a negative regulator of IFT injection, hence it cannot form the basis of a stable length control system.

Biosynthesis of Linear Protein Nanoarrays Using the Flagellar Axoneme

Applications in biotechnology and synthetic biology often make use of soluble proteins, but there are many potential advantages of anchoring enzymes to a stable substrate, including stability and the possibility for substrate channeling. To avoid the necessity of protein purification and chemical immobilization, there has been growing interest in bio-assembly of protein-containing nanoparticles, exploiting the self-assembly of viral capsid proteins or other proteins that form polyhedral structures. However, these nanoparticles are limited in size, which constrains the packaging and the accessibility of the proteins. An axoneme, the insoluble protein core of the eukaryotic flagellum or cilium, is a highly ordered protein structure that can be several microns in length, orders of magnitude larger than other types of nanoparticles. We show that when proteins of interest are fused to specific axonemal proteins and expressed in living Chlamydomonas reinhardtii cells, they become incorporated into linear arrays, which have the advantages of high protein loading capacity and single-step purification with retention of biomass. The arrays can be isolated as membrane-enclosed vesicles or as exposed protein arrays. The approach is demonstrated for both a fluorescent protein and an enzyme (beta-lactamase), showing that incorporation into axonemes retains protein function in a stable, easily isolated array form.

The short flagella 1 (SHF1) gene in Chlamydomonas encodes a Crescerin TOG-domain protein required for late stages of flagellar growth

Length control of flagella represents a simple and tractable system to investigate the dynamics of organelle size. Models for flagellar length control in the model organism, Chlamydomonas reinhardtii have focused on the length-dependence of the intraflagellar transport (IFT) system which manages the delivery and removal of axonemal subunits at the tip of the flagella. One of these cargoes, tubulin, is the major axonemal subunit, and its frequency of arrival at the tip plays a central role in size control models. However, the mechanisms determining tubulin dynamics at the tip are still poorly understood. We discovered a loss-of-function mutation that leads to shortened flagella, and found that this was an allele of a previously described gene, SHF1, whose molecular identity had not previously been determined.  We found that SHF1 encodes a Chlamydomonas ortholog of Crescerin, previously identified as a cilia-specific TOG-domain array protein that can bind tubulin via its TOG domains and increase tubulin polymerization rates. In this mutant, flagellar regeneration occurs with the same initial kinetics as wild-type cells, but plateaus at a shorter length. Using a computational model in which the flagellar microtubules are represented by a differential equation for flagellar length combined with a stochastic model for cytoplasmic microtubule dynamics, we found that our experimental results are best described by a model in which Crescerin/SHF1 binds tubulin dimers in the cytoplasm and transports them into the flagellum. We suggest that this TOG-domain protein is necessary to efficiently and preemptively increase intra-flagella tubulin levels to offset decreasing IFT cargo at the tip as flagellar assembly progresses.

Analysis of biological noise in the flagellar length control system

Any proposed mechanism for organelle size control should be able to account not only for average size but also for the variation in size. We analyzed cell-to-cell variation and within-cell variation of length for the two flagella in Chlamydomonas, finding that cell-to-cell variation is dominated by cell size, whereas within-cell variation results from dynamic fluctuations. Fluctuation analysis suggests tubulin assembly is not directly coupled with intraflagellar transport (IFT) and that the observed length fluctuations reflect tubulin assembly and disassembly events involving large numbers of tubulin dimers. Length variation is increased in long-flagella mutants, an effect consistent with theoretical models for flagellar length regulation. Cells with unequal flagellar lengths show impaired swimming but improved gliding, raising the possibility that cells have evolved mechanisms to tune biological noise in flagellar length. Analysis of noise at the level of organelle size provides a way to probe the mechanisms determining cell geometry.

Functional exploration of heterotrimeric kinesin-II in IFT and ciliary length control in Chlamydomonas

Heterodimeric motor organization of kinesin-II is essential for its function in anterograde IFT in ciliogenesis. However, the underlying mechanism is not well understood. In addition, the anterograde IFT velocity varies significantly in different organisms, but how this velocity affects ciliary length is not clear. We show that in Chlamydomonas motors are only stable as heterodimers in vivo, which is likely the key factor for the requirement of a heterodimer for IFT. Second, chimeric CrKinesin-II with human kinesin-II motor domains functioned in vitro and in vivo, leading to a ~ 2.8 fold reduced anterograde IFT velocity and a similar fold reduction in IFT injection rate that supposedly correlates with ciliary assembly activity. However, the ciliary length was only mildly reduced (~15%). Modeling analysis suggests a nonlinear scaling relationship between IFT velocity and ciliary length that can be accounted for by limitation of the motors and/or its ciliary cargoes, e.g. tubulin.

Scaling of Subcellular Structures

As cells grow, the size and number of their internal organelles increase in order to keep up with increased metabolic requirements. Abnormal size of organelles is a hallmark of cancer and an important aspect of diagnosis in cytopathology. Most organelles vary in either size or number, or both, as a function of cell size, but the mechanisms that create this variation remain unclear. In some cases, organelle size appears to scale with cell size through processes of relative growth, but in others the size may be set by either active measurement systems or genetic programs that instruct organelle biosynthetic activities to create organelles of a size appropriate to a given cell type.

Nanobody-directed targeting of optogenetic tools to study signaling in the primary cilium

Compartmentalization of cellular signaling forms the molecular basis of cellular behavior. The primary cilium constitutes a subcellular compartment that orchestrates signal transduction independent from the cell body. Ciliary dysfunction causes severe diseases, termed ciliopathies. Analyzing ciliary signaling has been challenging due to the lack of tools to investigate ciliary signaling. Here, we describe a nanobody-based targeting approach for optogenetic tools in mammalian cells and in vivo in zebrafish to specifically analyze ciliary signaling and function. Thereby, we overcome the loss of protein function observed after fusion to ciliary targeting sequences. We functionally localized modifiers of cAMP signaling, the photo-activated adenylyl cyclase bPAC and the light-activated phosphodiesterase LAPD, and the cAMP biosensor mlCNBD-FRET to the cilium. Using this approach, we studied the contribution of spatial cAMP signaling in controlling cilia length. Combining optogenetics with nanobody-based targeting will pave the way to the molecular understanding of ciliary function in health and disease.

Speed and Diffusion of Kinesin-2 Are Competing Limiting Factors in Flagellar Length-Control Model

Flagellar length control in Chlamydomonas is a tractable model system for studying the general question of organelle size regulation. We have previously proposed that the diffusive return of the kinesin motor that powers intraflagellar transport can play a key role in length regulation. Here, we explore how the motor speed and diffusion coefficient for the return of kinesin-2 affect flagellar growth kinetics. We find that the system can exist in two distinct regimes, one dominated by motor speed and one by diffusion coefficient. Depending on length, a flagellum can switch between these regimes. Our results indicate that mutations can affect the length in distinct ways. We discuss our theory's implication for flagellar growth influenced by beating and provide possible explanations for the experimental observation that a beating flagellum is usually longer than its immotile mutant. These results demonstrate how our simple model can suggest explanations for mutant phenotypes.

Cutting off ciliary protein import: intraflagellar transport after dendritic femtosecond-laser ablation

Primary cilia, organelles protruding from the surface of eukaryotic cells, act as cellular antennae to detect and transmit signals from the extracellular environment. They are built and maintained by continuous cycles of intraflagellar transport (IFT), where ciliary proteins are transported between the ciliary base and tip. These proteins originate from the cell body because cilia lack protein synthesis machinery. How input from the cell body affects IFT and ciliary function is not well understood. Here, we use femtosecond-laser ablation to perturb the dendritic input of proteins to chemosensory cilia in living Caenorhabditis elegans. Using fluorescence microscopy, we visualize and quantify the real-time response of ciliary proteins to dendritic ablation. We find that the response occurs in three distinct stages. First, IFT dynein is activated within seconds, redistributing IFT components toward the ciliary base; second, the ciliary axoneme shortens and motors slow down; and third, motors leave the cilium. Depletion of ATP by adding azide also results in IFT slowdown and IFT components leaving the cilium, but not in activation of retrograde IFT. These results indicate that laser ablation triggers a specific mechanism important for IFT regulation that allows the cilium to rapidly adapt to changes in the outside environment.

Testing the role of intraflagellar transport in flagellar length control using length-altering mutants of Chlamydomonas

Cilia and flagella are ideal model organelles in which to study the general question of organelle size control. Flagellar microtubules are steady-state structures whose size is set by the balance of assembly and disassembly. Assembly requires intraflagellar transport (IFT), and measurements of IFT have shown that the rate of entry of IFT particles into the flagellum is a decreasing function of length. It has been proposed that this length dependence of IFT may be the basis for flagellar length control. Here, we test this idea by showing that three different long-flagella mutations in Chlamydomonas all cause increased IFT injection, thus confirming that IFT can influence length control. However, quantitative comparisons with mathematical models suggest that the increase in injection is not sufficient to explain the full increase in length seen in these mutants; hence, some other mechanism may be at work. One alternative mechanism that has been proposed is length-regulated binding of tubulin to the IFT particles. However, we find that the apparent length dependence of tubulin loading that has previously been reported may actually reflect length-dependent organization of IFT trains.

This article is part of the Theo Murphy meeting issue ‘Unity and diversity of cilia in locomotion and transport’.

Length-dependent disassembly maintains four different flagellar lengths in Giardia

With eight flagella of four different lengths, the parasitic protist Giardia is an ideal model to evaluate flagellar assembly and length regulation. To determine how four different flagellar lengths are maintained, we used live-cell quantitative imaging and mathematical modeling of conserved components of intraflagellar transport (IFT)-mediated assembly and kinesin-13-mediated disassembly in different flagellar pairs. Each axoneme has a long cytoplasmic region extending from the basal body, and transitions to a canonical membrane-bound flagellum at the 'flagellar pore'. We determined that each flagellar pore is the site of IFT accumulation and injection, defining a diffusion barrier functionally analogous to the transition zone. IFT-mediated assembly is length-independent, as train size, speed, and injection frequencies are similar for all flagella. We demonstrate that kinesin-13 localization to the flagellar tips is inversely correlated to flagellar length. Therefore, we propose a model where a length-dependent disassembly mechanism controls multiple flagellar lengths within the same cell.

Assembly, Functions and Evolution of Archaella, Flagella and Cilia

Cells from all three domains of life on Earth utilize motile macromolecular devices that protrude from the cell surface to generate forces that allow them to swim through fluid media. Research carried out on archaea during the past decade or so has led to the recognition that, despite their common function, the motility devices of the three domains display fundamental differences in their properties and ancestry, reflecting a striking example of convergent evolution. Thus, the flagella of bacteria and the archaella of archaea employ rotary filaments that assemble from distinct subunits that do not share a common ancestor and generate torque using energy derived from distinct fuel sources, namely chemiosmotic ion gradients and FlaI motor-catalyzed ATP hydrolysis, respectively. The cilia of eukaryotes, however, assemble via kinesin-2-driven intraflagellar transport and utilize microtubules and ATP-hydrolyzing dynein motors to beat in a variety of waveforms via a sliding filament mechanism. Here, with reference to current structural and mechanistic information about these organelles, we briefly compare the evolutionary origins, assembly and tactic motility of archaella, flagella and cilia.

LF4/MOK and a CDK-related kinase regulate the number and length of cilia in Tetrahymena

The length of cilia is controlled by a poorly understood mechanism that involves members of the conserved RCK kinase group, and among them, the LF4/MOK kinases. The multiciliated protist model, Tetrahymena, carries two types of cilia (oral and locomotory) and the length of the locomotory cilia is dependent on their position with the cell. In Tetrahymena, loss of an LF4/MOK ortholog, LF4A, lengthened the locomotory cilia, but also reduced their number. Without LF4A, cilia assembled faster and showed signs of increased intraflagellar transport (IFT). Consistently, overproduced LF4A shortened cilia and downregulated IFT. GFP-tagged LF4A, expressed in the native locus and imaged by total internal reflection microscopy, was enriched at the basal bodies and distributed along the shafts of cilia. Within cilia, most LF4A-GFP particles were immobile and a few either diffused or moved by IFT. We suggest that the distribution of LF4/MOK along the cilium delivers a uniform dose of inhibition to IFT trains that travel from the base to the tip. In a longer cilium, the IFT machinery may experience a higher cumulative dose of inhibition by LF4/MOK. Thus, LF4/MOK activity could be a readout of cilium length that helps to balance the rate of IFT-driven assembly with the rate of disassembly at steady state. We used a forward genetic screen to identify a CDK-related kinase, CDKR1, whose loss-of-function suppressed the shortening of cilia caused by overexpression of LF4A, by reducing its kinase activity. Loss of CDKR1 alone lengthened both the locomotory and oral cilia. CDKR1 resembles other known ciliary CDK-related kinases: LF2 of Chlamydomonas, mammalian CCRK and DYF-18 of C. elegans, in lacking the cyclin-binding motif and acting upstream of RCKs. The new genetic tools we developed here for Tetrahymena have potential for further dissection of the principles of cilia length regulation in multiciliated cells.

Diffusion as a Ruler: Modeling Kinesin Diffusion as a Length Sensor for Intraflagellar Transport

An important question in cell biology is whether cells are able to measure size, either whole cell size or organelle size. Perhaps cells have an internal chemical representation of size that can be used to precisely regulate growth, or perhaps size is just an accident that emerges due to constraint of nutrients. The eukaryotic flagellum is an ideal model for studying size sensing and control because its linear geometry makes it essentially one-dimensional, greatly simplifying mathematical modeling. The assembly of flagella is regulated by intraflagellar transport (IFT), in which kinesin motors carry cargo adaptors for flagellar proteins along the flagellum and then deposit them at the tip, lengthening the flagellum. The rate at which IFT motors are recruited to begin transport into the flagellum is anticorrelated with the flagellar length, implying some kind of communication between the base and the tip and possibly indicating that cells contain some mechanism for measuring flagellar length. Although it is possible to imagine many complex scenarios in which additional signaling molecules sense length and carry feedback signals to the cell body to control IFT, might the already-known components of the IFT system be sufficient to allow length dependence of IFT? Here we investigate a model in which the anterograde kinesin motors unbind after cargo delivery, diffuse back to the base, and are subsequently reused to power entry of new IFT trains into the flagellum. By mathematically modeling and simulating such a system, we are able to show that the diffusion time of the motors can in principle be sufficient to serve as a proxy for length measurement. We found that the diffusion model can not only achieve a stable steady-state length without the addition of any other signaling molecules or pathways, but also is able to produce the anticorrelation between length and IFT recruitment rate that has been observed in quantitative imaging studies.

Ciliary Length Sensing Regulates IFT Entry via Changes in FLA8/KIF3B Phosphorylation to Control Ciliary Assembly

The length of cilia is robustly regulated [1]. Previous data suggest that cells possess a sensing system to control ciliary length [2-5]. However, the details of the mechanism are currently not known [6, 7]. Such a system requires a mechanism that responds to ciliary length, and consequently, disruption of that response system should alter ciliary length [1]. The assembly rate of cilium mediated by intraflagellar transport (IFT) gradually decreases as the cilium elongates and eventually is balanced by the constant rate of disassembly, at which point cilium elongation stops [8, 9]. Because the rate of IFT entry into the cilium also decreases as the cilium elongates [10], regulation of IFT entry could provide the mechanism for length control. Previously, we showed that phosphorylation of the FLA8/KIF3B subunit of the anterograde kinesin-II IFT motor blocks IFT entry and flagellar assembly in Chlamydomonas [11]. Here, we show in Chlamydomonas that cellular signaling in response to alteration of flagellar length regulates phosphorylation of FLA8/KIF3B, which restricts IFT entry and, thus, flagellar assembly to control flagellar length. Cellular levels of phosphorylated FLA8 (pFLA8) are tightly linked to flagellar length: FLA8 phosphorylation is reduced in cells with short flagella and elevated in cells with long flagella. Depletion of the phosphatases CrPP1 and CrPP6 increases the level of cellular pFLA8, leading to short flagella due to decreased IFT entry. The results demonstrate that ciliary length control is achieved by a cellular sensing system that controls IFT entry through phosphorylation of the anterograde IFT motor.

Stochastic Dynamics of Eukaryotic Flagellar Growth

We study the dynamics of flagellar growth in eukaryotes where intraflagellar transporters (IFT) play a crucial role. First we investigate a stochastic version of the original balance point model where a constant number of IFT particles move up and down the flagellum. The detailed model is a discrete event vector-valued Markov process occurring in continuous time. First the detailed stochastic model is compared and contrasted with a simple scalar ordinary differential equation (ODE) model of flagellar growth. Numerical simulations reveal that the steady-state mean value of the stochastic model is well approximated by the ODE model. Then we derive a scalar stochastic differential equation (SDE) as a first approximation and obtain a "small noise" approximation showing flagellar length to be Gaussian with mean and variance governed by simple ODEs. The accuracy of the small noise model is compared favorably with the numerical simulation results of the detailed model. Secondly, we derive a revised SDE for flagellar length following the revised balance point model proposed in 2009 in which IFT particles move in trains instead of in isolation. Small noise approximation of the revised SDE yields the same approximate Gaussian distribution for the flagellar length as the SDE corresponding to the original balance point model.

Dynamics of the IFT machinery at the ciliary tip

Intraflagellar transport (IFT) is essential for the elongation and maintenance of eukaryotic cilia and flagella. Due to the traffic jam of multiple trains at the ciliary tip, how IFT trains are remodeled in these turnaround zones cannot be determined by conventional imaging. Using PhotoGate, we visualized the full range of movement of single IFT trains and motors in Chlamydomonas flagella. Anterograde trains split apart and IFT complexes mix with each other at the tip to assemble retrograde trains. Dynein-1b is carried to the tip by kinesin-II as inactive cargo on anterograde trains. Unlike dynein-1b, kinesin-II detaches from IFT trains at the tip and diffuses in flagella. As the flagellum grows longer, diffusion delays return of kinesin-II to the basal body, depleting kinesin-II available for anterograde transport. Our results suggest that dissociation of kinesin-II from IFT trains serves as a negative feedback mechanism that facilitates flagellar length control in Chlamydomonas.

Testing the time-of-flight model for flagellar length sensing

A combination of quantitative imaging, modeling, and genetics has been used to test a proposed mechanism for measuring the size of an organelle. One way to measure distance is to send a clock out on a train and measure the elapsed time when the train returns. We tested a molecular version of this model as a possible regulator of intraflagellar transport by altering the return speed of the transport machinery and probing the effect on a known length-dependent process.

Cilia and flagella are microtubule-based organelles that protrude from the surface of most cells, are important to the sensing of extracellular signals, and make a driving force for fluid flow. Maintenance of flagellar length requires an active transport process known as intraflagellar transport (IFT). Recent studies reveal that the amount of IFT injection negatively correlates with the length of flagella. These observations suggest that a length-dependent feedback regulates IFT. However, it is unknown how cells recognize the length of flagella and control IFT. Several theoretical models try to explain this feedback system. We focused on one of the models, the “time-of-flight” model, which measures the length of flagella on the basis of the travel time of IFT protein in the flagellar compartment. We tested the time-of-flight model using Chlamydomonas dynein mutant cells, which show slower retrograde transport speed. The amount of IFT injection in dynein mutant cells was higher than that in control cells. This observation does not support the prediction of the time-of-flight model and suggests that Chlamydomonas uses another length-control feedback system rather than that described by the time-of-flight model.

Intraflagellar transport: mechanisms of motor action, cooperation, and cargo delivery

Intraflagellar transport (IFT) is a form of motor-dependent cargo transport that is essential for the assembly, maintenance, and length control of cilia, which play critical roles in motility, sensory reception, and signal transduction in virtually all eukaryotic cells. During IFT, anterograde kinesin-2 and retrograde IFT dynein motors drive the bidirectional transport of IFT trains that deliver cargo, for example, axoneme precursors such as tubulins as well as molecules of the signal transduction machinery, to their site of assembly within the cilium. Following its discovery in Chlamydomonas, IFT has emerged as a powerful model system for studying general principles of motor-dependent cargo transport and we now appreciate the diversity that exists in the mechanism of IFT within cilia of different cell types. The absence of heterotrimeric kinesin-2 function, for example, causes a complete loss of both IFT and cilia in Chlamydomonas, but following its loss in Caenorhabditis elegans, where its primary function is loading the IFT machinery into cilia, homodimeric kinesin-2-driven IFT persists and assembles a full-length cilium. Generally, heterotrimeric kinesin-2 and IFT dynein motors are thought to play widespread roles as core IFT motors, whereas homodimeric kinesin-2 motors are accessory motors that mediate different functions in a broad range of cilia, in some cases contributing to axoneme assembly or the delivery of signaling molecules but in many other cases their ciliary functions, if any, remain unknown. In this review, we focus on mechanisms of motor action, motor cooperation, and motor-dependent cargo delivery during IFT.

Cell Cycle-Related Kinase (CCRK) regulates ciliogenesis and Hedgehog signaling in mice

The Hedgehog (Hh) signaling pathway plays a key role in cell fate specification, proliferation, and survival during mammalian development. Cells require a small organelle, the primary cilium, to respond properly to Hh signals and the key regulators of Hh signal transduction exhibit dynamic localization to this organelle when the pathway is activated. Here, we investigate the role of Cell Cycle Related kinase (CCRK) in regulation of cilium-dependent Hh signaling in the mouse. Mice mutant for Ccrk exhibit a variety of developmental defects indicative of inappropriate regulation of this pathway. Cell biological, biochemical and genetic analyses indicate that CCRK is required to control the Hedgehog pathway at the level or downstream of Smoothened and upstream of the Gli transcription factors, Gli2 and Gli3. In vitro experiments indicate that Ccrk mutant cells show a greater deficit in response to signaling over long time periods than over short ones. Similar to Chlamydomonas mutants lacking the CCRK homolog, LF2, mouse Ccrk mutant cells show defective regulation of ciliary length and morphology. Ccrk mutant cells exhibit defects in intraflagellar transport (the transport mechanism used to assemble cilia), as well as slowed kinetics of ciliary enrichment of key Hh pathway regulators. Collectively, the data suggest that CCRK positively regulates the kinetics by which ciliary proteins such as Smoothened and Gli2 are imported into the cilium, and that the efficiency of ciliary recruitment allows for potent responses to Hedgehog signaling over long time periods.

The importance of cilia in development and disease has become broadly appreciated in recent years due in part to their roles in signal transduction. Despite this attention, crucial aspects of ciliary assembly and function, such as the mechanisms controlling ciliary assembly and the signal transduction events occurring in cilia, remain unclear. Cilia play a central role in sensing and transducing Hedgehog signals in the context of mammalian embryogenesis and in a variety of cancers. Here, we investigate the functions of Cell Cycle Related Kinase (CCRK), which plays an evolutionarily conserved function in the assembly of cilia and flagella. We find that mouse CCRK positively and negatively regulates ciliary length. We show that CCRK controls multiple aspects of Hedgehog signaling in vivo and in vitro by regulating the processing and activities of the Gli transcription factors. Our data suggest that CCRK controls Hedgehog signaling by promoting the efficient ciliary import of core signaling components.

Protein transport in growing and steady-state cilia

Cilia and eukaryotic flagella are threadlike cell extensions with motile and sensory functions. Their assembly requires intraflagellar transport (IFT), a bidirectional motor-driven transport of protein carriers along the axonemal microtubules. IFT moves ample amounts of structural proteins including tubulin into growing cilia likely explaining its critical role for assembly. IFT continues in non-growing cilia contributing to a variety of processes ranging from axonemal maintenance and the export of non-ciliary proteins to cell locomotion and ciliary signaling. Here, we discuss recent data on cues regulating the type, amount and timing of cargo transported by IFT. A regulation of IFT-cargo interactions is critical to establish, maintain and adjust ciliary length, protein composition and function.

Intraflagellar Transport and Ciliary Dynamics

Cilia and flagella are microtubule-based organelles whose assembly requires a motile process, known as intraflagellar transport (IFT), to bring tubulin and other components to the distal tip of the growing structure. The IFT system uses a multiprotein complex with components that appear to be specialized for the transport of different sets of cargo proteins. The mechanisms by which cargo is selected for ciliary import and transport by IFT remain an area of active research. The complex dynamics of cilia and flagella are under constant regulation to ensure proper length control, and this regulation appears to involve regulation at the stage of IFT injection into the flagellum, as well as regulation of flagellar disassembly and, possibly, of cargo binding. Cilia and flagella thus represent a convenient model system to study how multiple motile and signaling pathways cooperate to control the assembly and dynamics of a complex cellular structure.

Cell Geometry: How Cells Count and Measure Size

The cell represents a highly organized state of living matter in which numerous geometrical parameters are under dynamic regulation in order to match the form of a cell with its function. Cells appear capable of regulating not only the total quantity of their internal organelles, but also the size and number of those organelles. The regulation of three parameters, size, number, and total quantity, can in principle be accomplished by regulating the production or growth of organelles, their degradation or disassembly, and their partitioning among daughter cells during division. Any or all of these steps could in principle be under regulation. But if organelle assembly or disassembly is regulated by number or size, how would the cell know how many copies of an organelle it has, or how big they are?

Screen-based identification and validation of four new ion channels as regulators of renal ciliogenesis

To investigate the contribution of ion channels to ciliogenesis, we carried out a small interfering RNA (siRNA)-based reverse genetics screen of all ion channels in the mouse genome in murine inner medullary collecting duct kidney cells. This screen revealed four candidate ion channel genes: Kcnq1, Kcnj10, Kcnf1 and Clcn4. We show that these four ion channels localize to renal tubules, specifically to the base of primary cilia. We report that human KCNQ1 Long QT syndrome disease alleles regulate renal ciliogenesis; KCNQ1-p.R518X, -p.A178T and -p.K362R could not rescue ciliogenesis after Kcnq1-siRNA-mediated depletion in contrast to wild-type KCNQ1 and benign KCNQ1-p.R518Q, suggesting that the ion channel function of KCNQ1 regulates ciliogenesis. In contrast, we demonstrate that the ion channel function of KCNJ10 is independent of its effect on ciliogenesis. Our data suggest that these four ion channels regulate renal ciliogenesis through the periciliary diffusion barrier or the ciliary pocket, with potential implication as genetic contributors to ciliopathy pathophysiology. The new functional roles of a subset of ion channels provide new insights into the disease pathogenesis of channelopathies, which might suggest future therapeutic approaches.

How Cells Measure Length on Subcellular Scales

Cells are not just amorphous bags of enzymes, but precise and complex machines. With any machine, it is important that the parts be of the right size, yet our understanding of the mechanisms that control size of cellular structures remains at a rudimentary level in most cases. One problem with studying size control is that many cellular organelles have complex 3D structures that make their size hard to measure. Here we focus on linear structures within cells, for which the problem of size control reduces to the problem of length control. We compare and contrast potential mechanisms for length control to understand how cells solve simple geometry problems.

Crescerin uses a TOG domain array to regulate microtubules in the primary cilium

Primary cilia are critical organelles involved in development, sensation, and signaling. Crescerin, a conserved protein family in ciliated and flagellated eukaryotes, uses a TOG domain array with tubulin polymerization activity to regulate cilia microtubules and facilitate proper cilia length, ultrastructure, and function.

Eukaryotic cilia are cell-surface projections critical for sensing the extracellular environment. Defects in cilia structure and function result in a broad range of developmental and sensory disorders. However, mechanisms that regulate the microtubule (MT)-based scaffold forming the cilia core are poorly understood. TOG domain array–containing proteins ch-TOG and CLASP are key regulators of cytoplasmic MTs. Whether TOG array proteins also regulate ciliary MTs is unknown. Here we identify the conserved Crescerin protein family as a cilia-specific, TOG array-containing MT regulator. We present the crystal structure of mammalian Crescerin1 TOG2, revealing a canonical TOG fold with conserved tubulin-binding determinants. Crescerin1's TOG domains possess inherent MT-binding activity and promote MT polymerization in vitro. Using Cas9-triggered homologous recombination in Caenorhabditis elegans, we demonstrate that the worm Crescerin family member CHE-12 requires TOG domain–dependent tubulin-binding activity for sensory cilia development. Thus, Crescerin expands the TOG domain array–based MT regulatory paradigm beyond ch-TOG and CLASP, representing a distinct regulator of cilia structure.

Calculation of a fluctuating entropic force by phase space sampling

A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.