Skip to main content
NCBI home page
UKPMC Funders Author Manuscripts logoLink to UKPMC Funders Author Manuscripts
. Author manuscript; available in PMC: 2012 Jul 4.
Published in final edited form as: Cell Rep. 2012 Jun 21;1(6):608–616. doi: 10.1016/j.celrep.2012.05.013

A Motor Driven Mechanism for Cell Length Sensing

Ida Rishal 1,#, Naaman Kam 1,#, Rotem Ben-Tov Perry 1, Vera Shinder 2, Elizabeth MC Fisher 3, Giampietro Schiavo 4, Mike Fainzilber 1,*
PMCID: PMC3389498  EMSID: UKMS48899  PMID: 22773964

Summary

Size homeostasis is fundamental in cell biology but it is not clear how large cells such as neurons can assess their own size or length. We examined a role for molecular motors in intracellular length sensing. Computational simulations suggest that spatial information can be encoded by the frequency of an oscillating retrograde signal arising from a composite negative feedback loop between bidirectional motor-dependent signals. The model predicts that decreasing either or both anterograde or retrograde signals should increase cell length, and this prediction was confirmed upon application of siRNAs for specific kinesin and/or dynein heavy chains in adult sensory neurons. Heterozygous dynein heavy chain 1 mutant sensory neurons also exhibited increased lengths both in vitro and during embryonic development. Moreover, similar length increases were observed in mouse embryonic fibroblasts upon partial downregulation of dynein heavy chain 1. Thus, molecular motors critically influence cell length sensing and growth control.

Keywords: cell size, cell length, molecular motor, dynein, kinesin, axonal transport, neuronal growth, oscillatory signal, frequency encoded

Introduction

Size homeostasis is one of the most fundamental aspects of biology, with distinct size limitations for individual cell types (Hall et al., 2004). Neurons exhibit the most marked size differences of any class of cells, having process lengths ranging from a few microns in central interneurons up to a meter in human peripheral neurons. Early work suggested that the intrinsic growth rates of embryonic sensory neurons in vivo differ according to the distances they must cross in order to reach their specific targets (Davies, 1994), and that neurons modulate protein biosynthesis and degradation rates to maintain size homeostasis (Franklin and Johnson, 1998). Individual axonal growth rates can vary considerably at different stages of elongating growth in the embryo (Rossi et al., 2007), and interstitial growth rates of axons that have connected to their targets can be remarkably enhanced by stretch growth along with the organism (Smith, 2009). How then can a neuron coordinate between the output of transcriptional and metabolic programs controlled by the nucleus and differential growth and maintenance needs of different lengths of axons?

A fundamental prerequisite for intracellular coordination on axonal scales should be an intrinsic capacity to monitor process lengths. Indeed, intrinsic length sensors in neurons are supported by observations on axonal initiation in hippocampal neurons (Goslin and Banker, 1989), sprouting capacity in motor neurons (Pestronk and Drachman, 1988), mitochondrial content of Drosophila medial neurons (O’Toole et al., 2008), dendritic arbor length in cortical neurons (Samsonovich and Ascoli, 2006), myosin effects on soma and minor process size (Kollins et al., 2009; van Diepen et al., 2009), and distance sensing of axotomy sites in a wide variety of neurons (Kam et al., 2009). Theoretical analyses also support the existence of intrinsic constraints on maximal lengths of neuronal arbors (Brown et al., 2008). Thus, both modeling and experimental approaches support the existence of intrinsic length sensors in neurons, but the underlying mechanisms are largely unknown.

Recent studies have proposed length-sensing mechanisms based on diffusion gradients in cell division control in fission yeast (Martin and Berthelot-Grosjean, 2009; Moseley et al., 2009) and in polarity determination in hippocampal neurons (Toriyama et al., 2010). Although such diffusion-based mechanisms may allow length sensing over restricted distances, the range limits of intracellular gradients fall far short of those needed for process lengths of more than 100 μm (Stelling and Kholodenko, 2009). Intrinsic “molecular rulers” based on microtubule dynamics or length-dependent modulators have also been described (Picone et al., 2010; Varga et al., 2009), but given the plasticity and lengths involved, a simple microtubule ‘ruler’ is not a likely length sensing mechanism for large cells. Active transport on molecular motors allows rapid translocation of signals between neurite tip and cell body (Ibanez, 2007). We therefore examined the possibility that motor-based signaling might enable distance sensing between cell center and axon endings on a continuous basis.

Results

A Motor-Dependent Frequency-Encoded Length Sensing Mechanism

Models were constructed using a previously described approach (Kam et al., 2009), representing motor transported signals (MTS) as moving units in a computer simulation. Each such MTS moves in simulation space according to a velocity assigned to it on the basis of known velocity distributions for molecular motors (Fig. S1). We first attempted to model a gradient generating mechanism that would be similar in principle to the diffusion gradient mechanism in yeast, by simulating active transport of length encoding signals by the dynein motor from axon tip to cell body, with a constant rate of signal loss en route. In this scenario, signal levels at the cell body remain high as long as axons are relatively short. Upon sufficient axonal extension the accumulating loss along longer tracts will reduce signal levels in the cell body (Fig. 1A). Simulations of this model predict that reducing levels of the dynein motor, hence reducing amounts of transported signal, should result in shorter axon lengths (Fig. 1B). One limitation of this gradient generating model is that it does not consider the source of the axonal tip signal, and we therefore examined a second family of models wherein a cell body signal is anterogradely transported by kinesin motors to the neurite end, where it activates dynein-mediated retrograde transport of another cargo (or a modified version of itself) to the cell center. Different versions of this latter model were tested by simulation, including single and dual positive feedback loops (Fig. S1), and a composite negative feedback configuration wherein the retrograde signal represses the original anterograde entity, thus periodically resetting the system (Fig. 1C and Movie S1). The latter configuration generates an oscillating retrograde signal, with frequencies that decrease as a function of increasing cell length (Figs 1D and S1). It is noteworthy that this frequency-encoded model showed much greater robustness in repetitive runs of the simulations than the gradient model or previous quantity-dependent models for sensing injury distance (Kam et al., 2009). Interestingly, frequency encoded signals are utilized for distance determination in radar technology, where they are commonly termed “chirp” signals (Bloch, 1973). Reducing levels of either anterograde or retrograde motors (thereby reducing signal levels in each phase of the mechanism) causes a slowing in frequency reduction with growth time in the system (Fig. 1E). If elongation rates are correlated with retrograde signal frequency, this leads to the counter-intuitive prediction that an increase in axon length should occur in both cases (Fig. 1F). Thus, cell lengthening or shortening upon partial knockdown of a candidate motor provides a way to discriminate the alternative models shown in Fig. 1.

Figure 1. Motor Based Models for Cell Length Sensing.

Figure 1

Open in a new tab

(A) A gradient-based model wherein length encoding signals are actively transported by dynein from axon tip to cell body, with a constant rate of signal loss en route. At an early time point (T1) axons are short and signal levels at the cell body are high. At later time points (T2, T3) the accumulating signal loss along longer tracts will reduce signal levels in the cell body. (B) Retrograde signal levels at the cell body during axon elongation from simulations of the gradient model at high (blue), medium (red) and low (green) dynein levels, respectively. Reduced dynein levels result in shorter axon lengths (e.g. inset, using threshold indicated by horizontal line in main graph). (C) A bidirectional mechanism wherein anterograde signals are transported by a kinesin from cell body to axon tip, where they activate dynein-dependent retrograde signaling to the cell body, which then represses the anterograde signal via negative feedback. (D) The model configuration of (C) generates an oscillating retrograde signal, the frequency of which decreases with axon elongation. (E) If axons stop growing once the signal drops below a certain frequency threshold, the simulations predict that decreasing levels of either kinesin, dynein, or both motors together will lead to longer axons, as shown in (F) for growth arrest at a normalized frequency threshold of 0.02. See also Figure S1 and Movie S1.

A Targeted siRNA Screen Reveals Motors Affecting Sensory Neuron Length

Adult sensory neurons from the dorsal root ganglia (DRG) extend axonal-type processes in culture with a unidirectional microtubule cytoskeleton (Zheng et al., 2001). All anterograde transport in these processes is kinesin-based, while retrograde transport is dynein-based, thus providing an appropriate system for testing of the models outlined above. We used siRNA transfection of YFP transgenic sensory neurons followed by automated live cell fluorescence microscopy to assess the effects of partial knockdown of 36 microtubule motor heavy chains. These experiments revealed clear axon length increases upon transfection with siRNA against five kinesin heavy chains, including the three Kif5 isoforms, and dynein heavy chain 1 (Dync1h1), without significant effects on soma size (Fig. 2A, B). These effects are in accordance with the predictions of the frequency-dependent model. Strikingly, combined down-regulation of Kif5B and Dync1h1 caused a greater length increase than with each siRNA alone (Fig. 2C, D), as predicted by the frequency-dependent model in the case of partial down-regulation of both motors. Validation of the siRNA effects for Kif5B and for dynein confirmed reductions of 40-60% in levels of the targeted proteins in neuronal cultures exhibiting the observed length increases (Fig. 2E-H). Since dynein is a potential cargo of Kif5 complexes we quantified the degree of reduction in both Kif5B and Dync1h1 after treatment with siRNAs against Kif5B. siRNA treatment leading to 40% reduction in Kif5B levels had no effect on Dync1h1 expression (Fig. 2I, J). Thus, the increase in axon length observed upon Kif5B reduction is not due to an indirect effect on dynein levels.

Figure 2. Partial downregulation of certain microtubule motor heavy chains increases neurite length.

Figure 2

Open in a new tab

(A, B) siRNA screen for 34 kinesin and two dynein heavy chains (n>100). Positive hits were validated in at least three independent experiments (n>500), showing that partial downregulation of KIF5A, KIF5B, KIF5C, KIF1B, KIF23 or DYNC1H1 increases process length up to 50%. *, p < 0.05; **, p < 0.01, ***, p < 0.001 (Student’s t-test and One way ANOVA). (C) Fluorescence images of cultured DRG neurons from adult Thy1-YFP mice treated with the indicated siRNAs. Neurons were re-plated one day after siRNA transfection and images were acquired 48 hours after re-plating. Scale bar 200 μm. (D) Combined down-regulation of both KIF5B and DYNC1H1 causes a greater increase in axon length than observed upon down-regulation of each motor separately (n=80, p < 0.01, ***, p < 0.001, Student’s t-test and One way ANOVA). (E) Immunostaining for endogenous DYNC1H1 in DRG neurons treated with control or anti-DynHC1 siRNAs. Scale bar 60 μm. (F) Quantification of the immunostaining over six independent experiments reveals partial downregulation of DYNC1H1 (***, p < 0.0005). (G) Immunostaining for endogenous KIF5B in DRG neurons treated with control or anti-KIF5B siRNAs. Scale bar 60 μm. (H) Quantification of the immunostaining over three independent experiments reveals partial downregulation of KIF5B (***, p < 0.0005). (I, J) Immunostaining for endogenous Dynein HC1 in DRG neurons treated with control or anti-KIF5B siRNAs does not show any difference in endogenous levels of Dynein HC1 after siKIF5B treatment. See also Figure S2.

The length increase observed upon reduction of Dync1h1 is striking, since this ATP-binding subunit is indispensable for all dynein-based axonal transport processes. Importantly, microtubule network and growth cone morphology were normal in neurons treated with Dync1h1-siRNA using this protocol (Fig. S2). Greater depletion of Dync1h1 by longer siRNA treatment was previously shown to disrupt microtubules, cause aberrant growth cone morphology, and reduce neurite outgrowth (Ahmad et al., 2006). Partial depletion of the motor as achieved here does not cause these drastic effects, thus enabling detection of the length increase phenotype.

Increased Process Lengths in Sensory Neurons from a Dynein Mutant Mouse

To verify the siRNA results by an independent approach, we then carried out experiments on sensory neuron cultures from the Loa mouse, which harbors an F508Y mutation in Dync1h1 which is lethal in homozygotes but tolerated in the heterozygous background over normal lifespan (Hafezparast et al., 2003). Adult Loa heterozygote sensory neurons reveal a reduction in Dync1h1 levels specifically in axons, while overall cell body levels are not affected (Fig. 3A, B). Transport velocities for both retrograde and anterograde transport do not differ significantly between wild type and Loa heterozygous neurons (Fig. S3), thus for our purposes sensory neurons from the Loa heterozygote mouse provide a model with specific dynein reduction in the axon, that does not significantly impact housekeeping transport requirements. Again, the frequency-dependent model prediction for this case is that cultured mutant neurons should extend longer neurites than the wild type. Indeed, neurite lengths in cultured adult sensory neurons from heterozygous Loa mice are significantly longer than those observed from wild type littermates (Fig. 3C, D). Moreover, there is a greater length increase in Loa heterozygous neurons than in wild type neurons upon treatment with Kif5B siRNA (Fig. 3E, F). This finding corroborates the result obtained with dual siRNAs treatment (Fig. 2C, D), and is in complete accordance with the frequency-dependent model prediction for concomitant reduction of both motors.

Figure 3. Increased process length in sensory neurons from a Dynein Heavy Chain 1 mutant mouse.

Figure 3

Open in a new tab

(A) Immunostaining of endogenous DYNC1H1 in cultured DRG neurons from wild type (wt) and Loa/+ heterozygous mice. Scale bar 100 μm. (B) Reduced levels of DYNC1H1 in processes of Loa/+ neurons. (C) Loa/+ DRG neurons exhibit markedly increased process length in culture when compared to wild type neurons, as visualized by NFH staining. Scale bar 100 μm. (D) Quantification of process lengths revealed significant differences between wild type and Loa/+ DRG neurons in culture. ***, p < 0.001 (n = 600, Student’s t-test). (E) Down-regulation of KIF5B in Loa/+ DRG neurons causes a greater increase in process length in culture than observed upon KIF5B down-regulation in wild type neurons. Scale bar 200 μm. (F) Quantification of the effects of KIF5B down-regulation in Loa/+ background compared to wild type (n=100, *, p < 0.05; **, p < 0.01, ***, p < 0.001, Student’s t-test and One way ANOVA). (G) Electron micrographs showing immunogold labeling for DYNC1H1 on ultrathin sciatic nerve cross-sections from +/+ (left panel) and Loa/+ (right panel) mice. Scale bar 200nm. (H) DYNC1H1 associated gold particles within axon cytoplasm are decreased in Loa/+ mice. (I) Wholemount neurofilament staining in E11 limbs in wild type (+/+, left panel) and Loa/+ (right panel) mice. Scale bar 100 μm. (J) Quantification of total nerve branch lengths reveals significant increase in total outgrowth. *, p < 0.05 (n = 15, Student’s t-test). (K) Wholemount neurofilament staining in E12 limbs in wild type (+/+, left panel) and Loa/+ (right panel) mice. Scale bar 200 μm. (L) Quantification of the total length of nerve branches reveals significant increase in total outgrowth. *, p < 0.05 (n = 14, Student’s t-test). See also Figure S3.

The axon length data summarized above are based on in vitro cultures of adult neurons that were axotomized upon excision from the ganglia. To test whether the length increases are replicated in vivo in neurons in the normal elongating phase of outgrowth without any injury, we first verified the reduction in dynein levels in Loa heterozygote axons within the sciatic nerve by immunoelectron microscopy. Loa heterozygote axons revealed approximately 30% reduction in the levels of Dync1h1 positive puncta as compared to wild type axons (Fig. 3G, H). We then examined axon lengths in forepaws of mouse embryos by whole mount immunostaining. The dorsal surfaces were imaged for quantification of total outgrowth of the neurofilament-positive processes. Loa heterozygote embryos had over 50% more forepaw innervation than wild type littermates at E11 (Fig. 3I, J), and approximately 30% more at E12 (Fig. 3K, L). Interestingly, there were no apparent differences between the genotypes by E13 (data not shown), indicating that the role of dynein in axon length control is most prominent during the elongating phase of growth in early embryonic development, and is likely compensated by other mechanisms after axons reach their targets.

Dynein Downregulation Increases Fibroblast Cell Dimensions

Finally, we sought to determine whether these observations are of relevance to other cell types. Fibroblasts are amongst the largest non-neuronal cells, and are used as a model for cell length studies (Kharitonova and Vasiliev, 2008). We therefore tested the effects of dynein downregulation in NIH 3T3 cells treated with anti-Dync1hi siRNA, or in mouse embryonic fibroblasts (MEFs) from Loa versus wild type mice. Dync1h1 siRNA-treated 3T3 cells revealed highly significant increases in cell area and in cell size in comparison with control siRNA-treated cells (Figs 4A-C and S4). Furthermore, heterozygous Loa MEFs revealed highly significant increases in cell area versus their respective controls (Fig. 4D, E). Measurement of the longest axis from nucleus to cell periphery (Fig. 4F) in Loa versus wild type MEFs revealed clear and significant length increase in the Loa MEF population (Fig. 4G). Thus, the effects of dynein downregulation on cell dimensions are seen in both neurons and fibroblasts, and are likely to be shared by other large cell types.

Figure 4. Partial downregulation of Dynein HC1 increases fibroblast cell dimensions.

Figure 4

Open in a new tab

(A) Downregulation of Dynein HC1 by siDynC1h1 in 3T3 cell cultures. (B) Quantification of 3T3 cell area over three independent experiments reveals a significant increase upon dynein downregulation, p<0.001. (C) Quantification of cell size over three independent FACS measurements (Fig. S4) revealed significant increase in total size of 3T3 cells treated with Dync1h1 siRNA. (D) Phalloidin and DAPI stained cultures of E14 MEFs from wild type and Loa/+ embryos. Scale bar 40 μm. (E) Quantification of four independent MEF cohorts reveals a significant increase in cell area in the Loa/+ cells. ***, p<0.001. (F) Longest axis (yellow line) measurements of the same MEF populations show (G) a significant increase in cell length in Loa/+ MEFs as compared to wild-type. **, p<0.01. See also Figure S4.

Discussion

We have used modeling approaches to examine ways in which molecular motors might enable length sensing over cellular dimensions that are beyond the effective range of diffusion-based mechanisms. Mechanisms based on either quantity or frequency readouts of signal could be formulated in silico, however the experimental results clearly rule out a quantity-based mechanism and support frequency-encoded signaling as a basis for cell length sensing. This is most strikingly revealed in the length increase phenotypes for dynein or kinesin alone, and for both together. Since these motors transport in opposite directions in axons, reduction in motor levels should lead to opposite effects in a quantity based mechanism, while the frequency-based model predicts these counterintuitive results. Although direct confirmation of this mechanism will eventually require identification of the signals and feedback processes involved, the data presented here clearly show that modulating levels of microtubule motors influences cell length, and set the stage for future work to elucidate the mechanistic details of the system.

Negative feedback loops with a time delay generate oscillating signals, enabling robust encoding of temporal information in biological systems (Mengel et al., 2010; Paszek et al., 2010). Our findings extend this concept by showing that if the time delay in such a feedback loop is provided by motor-dependent transport, such systems can also encode spatial information. The exponentially decaying signal frequency observed in our model should suffice to account for lengths of most non-neuronal cell types, and for axon lengths required during initial embryonic development and innervation of targets. Once targets are innervated neurons switch to a distinct mode of stretch-induced interstitial growth (Smith, 2009), concomitantly with transition to scales requiring length sensing mechanisms with less marked frequency decay. This might be achieved by utilizing wave-type signaling (Munoz-Garcia and Kholodenko, 2010) instead of motors. The motor-dependent mechanism proposed here might therefore explain the slow pace of axon regeneration in adult neurons, which could be constrained in their growth rates by an intrinsic length-sensing mechanism evolved for the embryonic scale.

An intriguing future question will be the identity of the signaling molecules in motor-dependent length sensing. Frequency-dependent modulation of transcription factor nuclear import was recently shown to coordinate the regulation of gene expression in yeast (Cai et al., 2008). Transcription factors can be retrogradely transported in axons by importins linked to dynein (Ben-Yaakov et al., 2012), hence frequency encoding of dynein transported signals might feed directly into frequency modulation of nuclear translocation. Perturbations of such mechanisms in the embryo might manifest in disease onset later in life, as indeed has been described for dynein (Hafezparast et al., 2003; Weedon et al., 2011).

Experimental Procedures

Modeling and Simulations

Movement of signals on kinesin and dynein molecular motors was simulated based on published motor velocity distributions (Deinhardt et al., 2006; Seitz and Surrey, 2006), as previously described (Kam et al., 2009). Models represented MTS as moving units with a spatial location and an assigned velocity. At the beginning of the simulation, batches of anterograde MTS are generated in the soma for every time step. Retrograde MTS batches are generated once anterograde signal above a designated threshold reaches the axon tip, and in turn anterograde MTS production is repressed once retrograde signal above a designated threshold reaches the cell soma. MTS are removed from the simulation at the time step following their arrival at the soma (for retrograde MTS) or at the tip (for anterograde MTS). For further details on modeling see Movie S1, Fig. S1, and Supplementary Experimental Procedures. A wide range of model configurations were examined, including a range of 20-400 MTS per batch, and activation or inhibition thresholds between 10-100 accumulated MTS. Axons elongate at each time step throughout the simulation at a fixed rate of 4 μm/hour. All simulation scripts were written in MATLAB, and simulation executions were performed on the Weizmann Wiccopt cluster.

DRG Neuron Cultures and siRNA Screen

Wild type C57BL/6 and Loa heterozygote mice were bred with C57BL/6 YFP16 mice (Feng et al., 2000). Adult mouse DRG cultures were transfected with siGenome siRNAs using DharmaFect 4 (Dharmacon), replated 24 hr later, and imaged 72 hr after transfection. Images were captured at X10 magnification on an ImageXpress Micro (Molecular Devices), followed by determination of morphological parameters by MetaXpress2 (Molecular Devices) and WIS-Neuromath (Weizmann Institute) softwares. The parameters reported include total outgrowth, defined as the sum of lengths of all processes and branches per cell; and maximal process length, defined as the sum of length of the longest process of a cell including all its branches. When neurite growth extended beyond the maximal field of view compatible with automated analysis, montage images were analyzed manually in random sequence by an observer blinded to the details of the experiment. This parameter is reported as the longest axon, defined as the length of the longest process extending from the cell body without secondary branching. Statistical analyses were carried out using Student’s t-test and One Way ANOVA.

Electron Microscopy

DRG neurons were grown on sapphire disks and fixed 48 hr after plating using high pressure freezing (HPF) in a Bal-Tec HPM10, followed by freeze substitution, washing, embedding, and ultrathin sectioning (70–90 nm). Sciatic nerves were fixed in 4% paraformaldehyde and 0.1% glutaraldehyde, washed, cut to 1 mm segments and impregnated by 2.3 M sucrose before rapid freeze in liquid nitrogen, and ultrathin sectioning (70–90 nm). Sections were collected on nickel grids. For immunostaining, grids were first reacted with anti-dynein HC1, followed by anti-GFP when required for double-labeling, and secondary anti-rabbit IgG with different sizes of gold particles. The grids were then stained in uranyl acetate and lead citrate and analyzed under 120 kV on a Tecnai 12 (FEI) Transmission Electron Microscope with a EAGLE (FEI) CCD camera using TIA software.

Fibroblast Cultures and siRNA treatment

NIH 3T3 cells grown in DMEM medium with 10% FBS were transfected with siGenome using DharmaFect 1. Mouse embryonic fibroblasts (MEF) were isolated from E14 mouse embryos, passage 2 MEF were collected and imaged. Images of 3T3 or MEF cultures were captured at X10 and X40 magnification on an ImageXpress Micro (Molecular Devices). Nucleus and cell body area were determined using MetaXpress2 software (Molecular Devices). Statistical analyses were carried out using Student’s t-test and One Way ANOVA.

Supplementary Material

Movie 1

Supplementary Movie S1. Illustration of a simulation run for the frequency-based model (Supplementary information for Figure 1C, D). The cell soma is shown on the left as a green ellipse and the axon tip on the right. Motor-transported signals (MTS) are represented as blue circles for kinesin transported anterograde signals or red circles for dynein transported retrograde signals. Blue arrows represent activation, while red lines represent inhibition. “Spreading” of MTS batches en route is due to the velocity distribution range of each motor.

Download video file (9.2MB, mov)
01

Acknowledgements

We thank Vladimir Kiss for microscopy expertise, and Shelly Tzlil and Shlomo Sklarz for helpful comments. This work was supported by the Kahn Family Research Center for Systems Biology, the Harris Foundation and the Dr. Miriam and Sheldon G. Adelson Medical Research Foundation (to M.F.), the Wellcome Trust (to E.M.C.F.), Cancer Research UK (to G.S.), and the Weizmann-UK Making Connections program (to M.F. and G.S.). M.F. is the incumbent of the Chaya Professorial Chair in Molecular Neuroscience at the Weizmann Institute of Science.

References

  1. Ahmad FJ, He Y, Myers KA, Hasaka TP, Francis F, Black MM, Baas PW. Effects of dynactin disruption and dynein depletion on axonal microtubules. Traffic. 2006;7:524–537. doi: 10.1111/j.1600-0854.2006.00403.x. [DOI] [PubMed] [Google Scholar]
  2. Ben-Yaakov K, Dagan SY, Segal-Ruder Y, Shalem O, Vuppalanchi D, Willis DE, Yudin D, Rishal I, Rother F, Bader M, et al. Axonal transcription factors signal retrogradely in lesioned peripheral nerve. EMBO J. 2012;31:1350–1363. doi: 10.1038/emboj.2011.494. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Bloch SC. Introduction to Chirp Concepts with a cheap Chirp Radar. Am J Phys. 1973;41:857–864. [Google Scholar]
  4. Brown KM, Gillette TA, Ascoli GA. Quantifying neuronal size: summing up trees and splitting the branch difference. Semin Cell Dev Biol. 2008;19:485–493. doi: 10.1016/j.semcdb.2008.08.005. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Cai L, Dalal CK, Elowitz MB. Frequency-modulated nuclear localization bursts coordinate gene regulation. Nature. 2008;455:485–490. doi: 10.1038/nature07292. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Davies AM. Intrinsic programmes of growth and survival in developing vertebrate neurons. Trends Neurosci. 1994;17:195–199. doi: 10.1016/0166-2236(94)90104-x. [DOI] [PubMed] [Google Scholar]
  7. Deinhardt K, Salinas S, Verastegui C, Watson R, Worth D, Hanrahan S, Bucci C, Schiavo G. Rab5 and Rab7 control endocytic sorting along the axonal retrograde transport pathway. Neuron. 2006;52:293–305. doi: 10.1016/j.neuron.2006.08.018. [DOI] [PubMed] [Google Scholar]
  8. Feng G, Mellor RH, Bernstein M, Keller-Peck C, Nguyen QT, Wallace M, Nerbonne JM, Lichtman JW, Sanes JR. Imaging neuronal subsets in transgenic mice expressing multiple spectral variants of GFP. Neuron. 2000;28:41–51. doi: 10.1016/s0896-6273(00)00084-2. [DOI] [PubMed] [Google Scholar]
  9. Franklin JL, Johnson EM. Control of neuronal size homeostasis by trophic factor-mediated coupling of protein degradation to protein synthesis. J Cell Biol. 1998;142:1313–1324. doi: 10.1083/jcb.142.5.1313. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Goslin K, Banker G. Experimental observations on the development of polarity by hippocampal neurons in culture. J Cell Biol. 1989;108:1507–1516. doi: 10.1083/jcb.108.4.1507. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Hafezparast M, Klocke R, Ruhrberg C, Marquardt A, Ahmad-Annuar A, Bowen S, Lalli G, Witherden AS, Hummerich H, Nicholson S, et al. Mutations in dynein link motor neuron degeneration to defects in retrograde transport. Science. 2003;300:808–812. doi: 10.1126/science.1083129. [DOI] [PubMed] [Google Scholar]
  12. Hall MN, Raff M, Thomas J, editors. Cell Growth: Control of Cell Size. CSHL Press; New York: 2004. [Google Scholar]
  13. Ibanez CF. Message in a bottle: long-range retrograde signaling in the nervous system. Trends Cell Biol. 2007;17:519–528. doi: 10.1016/j.tcb.2007.09.003. [DOI] [PubMed] [Google Scholar]
  14. Kam N, Pilpel Y, Fainzilber M. Can molecular motors drive distance measurements in injured neurons? PLoS Comput Biol. 2009;5:e1000477. doi: 10.1371/journal.pcbi.1000477. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Kharitonova MA, Vasiliev JM. Controlling cell length. Semin Cell Dev Biol. 2008;19:480–484. doi: 10.1016/j.semcdb.2008.07.008. [DOI] [PubMed] [Google Scholar]
  16. Kollins KM, Hu J, Bridgman PC, Huang YQ, Gallo G. Myosin-II negatively regulates minor process extension and the temporal development of neuronal polarity. Dev Neurobiol. 2009;69:279–298. doi: 10.1002/dneu.20704. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Martin SG, Berthelot-Grosjean M. Polar gradients of the DYRK-family kinase Pom1 couple cell length with the cell cycle. Nature. 2009;459:852–856. doi: 10.1038/nature08054. [DOI] [PubMed] [Google Scholar]
  18. Mengel B, Hunziker A, Pedersen L, Trusina A, Jensen MH, Krishna S. Modeling oscillatory control in NF-kappaB, p53 and Wnt signaling. Curr Opin Genet Dev. 2010;20:656–664. doi: 10.1016/j.gde.2010.08.008. [DOI] [PubMed] [Google Scholar]
  19. Moseley JB, Mayeux A, Paoletti A, Nurse P. A spatial gradient coordinates cell size and mitotic entry in fission yeast. Nature. 2009;459:857–860. doi: 10.1038/nature08074. [DOI] [PubMed] [Google Scholar]
  20. Munoz-Garcia J, Kholodenko BN. Signalling over a distance: gradient patterns and phosphorylation waves within single cells. Biochem Soc Trans. 2010;38:1235–1241. doi: 10.1042/BST0381235. [DOI] [PubMed] [Google Scholar]
  21. O’Toole M, Latham R, Baqri RM, Miller KE. Modeling mitochondrial dynamics during in vivo axonal elongation. J Theor Biol. 2008;255:369–377. doi: 10.1016/j.jtbi.2008.09.009. [DOI] [PubMed] [Google Scholar]
  22. Paszek P, Jackson DA, White MR. Oscillatory control of signalling molecules. Curr Opin Genet Dev. 2010;20:670–676. doi: 10.1016/j.gde.2010.08.004. [DOI] [PubMed] [Google Scholar]
  23. Pestronk A, Drachman DB. Motor nerve outgrowth: reduced capacity for sprouting in the terminals of longer axons. Brain Res. 1988;463:218–222. doi: 10.1016/0006-8993(88)90394-0. [DOI] [PubMed] [Google Scholar]
  24. Picone R, Ren X, Ivanovitch KD, Clarke JD, McKendry RA, Baum B. A polarised population of dynamic microtubules mediates homeostatic length control in animal cells. PLoS Biol. 2010;8:e1000542. doi: 10.1371/journal.pbio.1000542. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Rossi F, Gianola S, Corvetti L. Regulation of intrinsic neuronal properties for axon growth and regeneration. Prog Neurobiol. 2007;81:1–28. doi: 10.1016/j.pneurobio.2006.12.001. [DOI] [PubMed] [Google Scholar]
  26. Samsonovich AV, Ascoli GA. Morphological homeostasis in cortical dendrites. Proc Natl Acad Sci U S A. 2006;103:1569–1574. doi: 10.1073/pnas.0510057103. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Seitz A, Surrey T. Processive movement of single kinesins on crowded microtubules visualized using quantum dots. EMBO J. 2006;25:267–277. doi: 10.1038/sj.emboj.7600937. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Smith DH. Stretch growth of integrated axon tracts: extremes and exploitations. Prog Neurobiol. 2009;89:231–239. doi: 10.1016/j.pneurobio.2009.07.006. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Stelling J, Kholodenko BN. Signaling cascades as cellular devices for spatial computations. J Math Biol. 2009;58:35–55. doi: 10.1007/s00285-008-0162-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Toriyama M, Sakumura Y, Shimada T, Ishii S, Inagaki N. A diffusion-based neurite length-sensing mechanism involved in neuronal symmetry breaking. Mol Syst Biol. 2010;6:394. doi: 10.1038/msb.2010.51. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. van Diepen MT, Parsons M, Downes CP, Leslie NR, Hindges R, Eickholt BJ. MyosinV controls PTEN function and neuronal cell size. Nat Cell Biol. 2009;11:1191–1196. doi: 10.1038/ncb1961. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Varga V, Leduc C, Bormuth V, Diez S, Howard J. Kinesin-8 motors act cooperatively to mediate length-dependent microtubule depolymerization. Cell. 2009;138:1174–1183. doi: 10.1016/j.cell.2009.07.032. [DOI] [PubMed] [Google Scholar]
  33. Weedon MN, Hastings R, Caswell R, Xie W, Paszkiewicz K, Antoniadi T, Williams M, King C, Greenhalgh L, Newbury-Ecob R, et al. Exome sequencing identifies a DYNC1H1 mutation in a large pedigree with dominant axonal Charcot-Marie-Tooth disease. Am J Hum Genet. 2011;89:308–312. doi: 10.1016/j.ajhg.2011.07.002. [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. Zheng JQ, Kelly TK, Chang B, Ryazantsev S, Rajasekaran AK, Martin KC, Twiss JL. A functional role for intra-axonal protein synthesis during axonal regeneration from adult sensory neurons. J Neurosci. 2001;21:9291–9303. doi: 10.1523/JNEUROSCI.21-23-09291.2001. [DOI] [PMC free article] [PubMed] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Movie 1

Supplementary Movie S1. Illustration of a simulation run for the frequency-based model (Supplementary information for Figure 1C, D). The cell soma is shown on the left as a green ellipse and the axon tip on the right. Motor-transported signals (MTS) are represented as blue circles for kinesin transported anterograde signals or red circles for dynein transported retrograde signals. Blue arrows represent activation, while red lines represent inhibition. “Spreading” of MTS batches en route is due to the velocity distribution range of each motor.

Download video file (9.2MB, mov)
01
NIHMS48899-supplement-01.pdf (343KB, pdf)

RESOURCES