The size of a cell’s internal parts are scaled to its overall size. This size-scaling behavior has been demonstrated for organelles as well as large macromolecular assemblies, illustrating the broad importance of adapting the size of internal structures to the geometric dimensions of the cell (Rafelski et al., 2012; Levy and Heald, 2010; Hazel et al., 2013; Good et al., 2013; Weber and Brangwynne, 2015; Greenan et al., 2010; Jorgensen et al., 2007; Decker et al., 2011; Neumann and Nurse, 2007; Lacroix et al., 2018). A popular model of cellular scaling is the limiting pool mechanism, wherein maintaining a constant concentration of molecular components enables the subcellular structure to increase in size proportionally with cell volume (Goehring and Hyman, 2012; de Godoy et al., 2008) This allows larger cells to assemble larger structures, since the total number of molecular building blocks increases proportionally with cell volume. Additionally, this mechanism is biochemically simple because it does not require active processes that dynamically tune concentrations or activity levels of proteins involved in the construction . Indeed, cells appear to use a limiting pool mechanism to scale the size of their nucleoli, centrosomes, and mitotic spindles (Hazel et al., 2013; Good et al., 2013; Weber and Brangwynne, 2015; Greenan et al., 2010; Decker et al., 2011; Lacroix et al., 2018). However, limiting pool models cannot explain how the size of a linear subcellular structure scales with the linear dimensions of a cell, rather than its volume. Namely, these mechanisms predict that a two fold increase in the radius of a spherical cell will increase the length of a linear structure eight fold, following the eight fold increase in cell volume. This suggests that other mechanisms must account for how some subcellular structures are scaled with the linear dimensions of a cell.

Polarized actin cables in S. cerevisiae are an example of a linear structure that appear to grow to match the linear dimensions of the cell in order to effectively deliver secretory vesicles (Moseley and Goode, 2006). These cables are linear bundles of crosslinked actin filaments assembled by formins, which extend along the cell cortex and serve as tracks for intracellular transport of cargo from the mother cell to the growing bud, or daughter cell. Complementary sets of cables are assembled by two formins, Bni1 at the bud tip and Bnr1 at the bud neck (Pruyne et al., 2004). Throughout the cell cycle, cables are continuously polymerized, turn over at high rates, and appear to grow until they reach the back of the mother cell (Yu et al., 2011; Yang and Pon, 2002; Eskin et al., 2016). This prompted us to more rigorously investigate the relationship between cable length and cell size.

We started by comparing cable lengths to the lengths of the mother cells in which they grew. Cables were imaged in fixed wild-type haploid cells using super-resolution microscopy. Cable lengths were measured from their site of assembly (the bud neck) to their distal tip in the mother cell (note that mother cell and cell are synonymous and used interchangeably from this point on) (Figure 1—figure supplement 1A). Average cable length and average cell length were remarkably similar (4.5 ± 0.3 µm and 4.5 ± 0.2 µm, respectively), suggesting a scaling relationship. However, we note that there was a wider range in cable lengths (2.0–8.7 µm) compared to cell lengths (3.7–5.5 µm), presumably because cables in fixed cells are at different stages of growth. Further, because cables grow along the cortex of an ellipsoid shaped cell, their length can exceed the length of the cell while not growing past the back of the cell. Therefore, a cable that grows from the bud neck to the back of the cell is expected to be slightly longer than the direct distance between these two points.

The observations above led us to ask whether the relationship between cable length and cell length is maintained as cell size increases. To address this, we compared cable lengths in haploid and diploid cells, and cdc28-13^ts temperature-sensitive mutants that grow abnormally large. Diploid mother cells had an ~2-fold increase in volume compared to haploid mother cells (81.8 ± 6.3 µm³ and 44.9 ± 4.7 µm³, respectively) (Figure 1A,B and E), consistent with previous studies (Jorgensen et al., 2002). The cdc28-13^ts strain exhibited a normal haploid mother cell size at the permissive temperature. However, this strain displayed a ~ 5-fold increase in volume (198.3 ± 5.5 µm³ versus 40.9 ± 2.3 µm³) after growth at the restrictive temperature (37°C) for 8 hr, followed by 1 hr of growth at the permissive temperature (25°C) to allow cell polarization and bud growth (Figure 1C,D and E; and Figure 1—figure supplement 1B and C; Allard et al., 2018). Accordingly, cell length increased with cell volume (Figure 1F). Cable length was greater in diploids (6.3 ± 0.7 µm) compared to haploids (4.5 ± 0.3 µm), and greater in induced (8.2 ± 0.4 µm) compared to uninduced (4.3 ± 0.1 µm) cdc28-13^ts cells (Figure 1G). However, the distribution of cable lengths for all strains collapsed when we divided the lengths of cables by the lengths of the cells in which they grew (Figure 1H and I). These results strongly suggest that cables grow to a length that matches cell length.

Figure 1 with 2 supplements see all

Download asset Open asset

Figure 1—source data 1

Complete results from statistical tests performed in this study.

The p-value is indicated for student’s t-test used to compare the data presented in Figure 1 and Figure 1—figure supplement 1.

https://cdn.elifesciences.org/articles/68424/elife-68424-fig1-data1-v2.xlsx

Download elife-68424-fig1-data1-v2.xlsx

Next, we used a power law analysis to rigorously test the scaling relationships of cable length with cell length and volume (Figure 1J and K). Generally, scaling relations can be described by the power law $y=A{x}^a$, where $a$ is the scaling exponent that reflects the relationship between the two measured quantities, $x$ and $y$ (Reber and Goehring, 2015). This analysis revealed isometric scaling (${\displaystyle a_L=0.91\pm 0.03,R^2=0.50}$) between cable length and cell length (Figure 1J), whereas scaling between cable length and cell volume was hypoallometric (${\displaystyle a_V=0.36\pm 0.01,R^2=0.46}$) (Figure 1K).

To uncouple cell length from cell volume, we compared the length of cables in cells of different morphology. We computed the aspect ratio (the ratio of cell length to cell width) for the same cells analyzed above. This revealed that while some cells had nearly spherical morphologies, others had highly elongated morphologies (Figure 1—figure supplement 2A and B). Despite these differences in cell shape, the ratio of cable length to cell length, and the scaling exponents were similar for all cells (Figure 1—figure supplement 2C–G). Therefore, in cells of vastly different size and shape, the cable length directly scales with cell length, rather than with other dimensions such as cell surface area or volume.

We considered two distinct models to explain the control of cable length. In both models, the length of a cable is determined by competing rates of actin assembly $\left(k_{+}\right)$ at the barbed ends of cables and disassembly $\left(k_{-}\right)$ at the pointed ends of cables (Figure 2A and B). Therefore, at any given time, the extension rate of a cable is determined by the difference in its assembly and disassembly rates (Figure 2B). In the boundary-sensing model, the assembly rate is greater than the disassembly rate until the extending cable physically encounters the rear of the cell, causing one or both rates to abruptly change (Figure 2C, and Figure 2—figure supplement 1A; Reber and Goehring, 2015). This model predicts that the cable extension rate will be constant until the cable tip encounters the back of the cell. In contrast, the balance-point model requires that either the assembly rate, the disassembly rate, or both rates are length-dependent, and defines steady state cable length as the point at which these two rates are balanced (Figure 2D, and Figure 2—figure supplement 1B; Mohapatra et al., 2016). In clear contrast to the boundary-sensing model, this model predicts that the cable extension rate will steadily decrease as the cable lengthens.

Figure 2 with 2 supplements see all

Download asset Open asset

To directly test the predictions of the two models, we used live imaging to track the tips of cables as they grew from the bud neck into the mother cell (Figure 2E, Video 1, and Figure 2—figure supplement 2A–C). Initially cables extended at 0.36 ± 0.02 µm s⁻¹, and as they grew longer their extension rates steadily decreased (Figure 2F, Figure 2—figure supplement 2D). Accordingly, we observed greater changes in cable length during earlier phases of cable growth (Figure 2G, Figure 2—figure supplement 2E). Thus, as cables lengthen their growth rate decelerates.

Video 1

Download asset

Note that we detected cables that were very short (<2 µm) by live imaging, which were not seen in our analysis of fixed cells. We expect that this is because shorter cables extend at a faster rate compared to longer cables and are therefore less prevalent in fixed cell populations.

Our experimental observations above support a balance-point model in which steady state cable length is reached when the assembly and disassembly rates are balanced. In this model, the rate of cable extension at any given time is given by the difference between the assembly and disassembly rates, which we call the feedback function, $f=k_{+}-k_{-}.$ To account for the observed scaling of cable length with cell length (Figure 1H and I), we assume that $f$ depends on the cable length ($L_{cable}$) scaled by the cell length ($L_{cell}$), that is $f\left(L_{cable}{,L}_{cell}\right)=f(L_{cable}/L_{cell})$. The steady state cable length $\left(L_{cable}^{*}\right)$ is reached when the feedback function equals zero, $f(L_{cable}^{*}/L_{cell})=0$. Therefore, the scale-invariant feedback function leads to the scaling of $L_{cable}^{*}$ with $L_{cell}$ seen in Figure 1J. (Further mathematical details in Materials and methods.)

Smy1 is a factor implicated in cable length control, and therefore we considered whether it might be required for cable deceleration. It has been reported that cables are longer in smy1∆ compared to wildtype cells, and that Smy1 directly inhibits Bnr1-mediated actin assembly (Eskin et al., 2016; Chesarone-Cataldo et al., 2011). Further, Smy1 is transported by myosin along cables to the bud neck where Bnr1 is anchored. Based on these observations, an ‘antenna mechanism’ has been proposed in which longer cables deliver more Smy1 to slow cable extension and limit cable length (Mohapatra et al., 2015). We confirmed the increase in cable length in smy1∆ cells (Figure 3A, and Figure 3—figure supplement 1A and B; Eskin et al., 2016), but found that cables continued to decelerate in the absence of Smy1 (Figure 3B and C). Furthermore, we observed an increase in the initial cable extension rate in smy1Δ (0.42 ± 0.04 µm s⁻¹) compared to wild-type cells (0.35 ± 0.02 µm s⁻¹) (Figure 3D and E). Interestingly, the initial extension rate in smy1Δ cells increased by the same magnitude (1.2-fold ± 0.2) as the measured increase in cable length (1.2-fold ± 0.1). Thus, Smy1 affects cable length by limiting the initial cable growth rate (Figure 3F) but does not provide the feedback that results in cable deceleration. Importantly, this does not rule out the possibility of other cellular factors acting through an antenna mechanism to control cable growth in a length-dependent manner.

Figure 3 with 1 supplement see all

Download asset Open asset

Our model makes an interesting quantitative prediction for cables that have abnormally fast initial extension rates, such as those measured in smy1Δ cells above. Specifically, our model predicts that this increase in initial extension rate will lead to a proportional increase in the initial deceleration (see Equation 7 in Materials and methods). Thus, the measured 1.2-fold increase in initial extension rate seen in smy1∆ cells is expected to lead to a 1.2-fold increase in initial deceleration of cables, shortly after they emerge from the bud neck. Indeed, linear fits to the cable extension rate, as a function of time over the first 10 s (i.e. the first few microns of cable extension), yield, $d_o^{smy1\mathrm{\Delta }}=-0.018\pm 0.010\mu m/s^2$ and $d_o^{wt}=-0.015\pm 0.005\mu m/s^2$, for smy1∆ and wild-type cells, respectively (Figure 3B and C). The ratio of these two, $d_0^{smy1\mathrm{\Delta }}/d_0^{wt}=1.2\pm 0.7$, matches the ratio of the initial extension rates, $f{\left(0\right)}^{smy1\mathrm{\Delta }}/f{\left(0\right)}^{wt}=1.2\pm 0.2$. Therefore, these data lend additional quantitative support for our model.

A key prediction of our balance-point model is that cable extension rates should depend on cell length, that is a cable of a given length should grow faster (or slow down more gradually) in longer cells compared to shorter cells (Figure 4A, top). Further, it predicts that the cable extension rate profiles from cells of different lengths will collapse when cable length is normalized to cell length (Figure 4A, bottom; predictions of model derived in Materials and methods). To test these predictions, we compared cable extension dynamics in uninduced and induced cdc28-13^ts cells (Figure 4B and C, Figure 4—figure supplement 1A and B, and Videos 2, 3, 4). When cables began to grow, they extended at similar rates in shorter and longer cells (Figure 4—figure supplement 1C). However, as the cables grew longer, they decelerated more gradually in the longer cells (Figure 4D–F). This led to longer cables in longer cells (Figure 4—figure supplement 1D). Linear regression analysis revealed that there is a nearly 2-fold greater initial deceleration in the shorter, uninduced cdc28-13^ts cells ($d_0^{uninduced}=-0.019\pm 0.005\mu m/s^2$) compared to the longer, induced cdc28-13^ts cells ($d_0^{induced}=-0.010\pm 0.003\mu m/s^2$). To determine how deceleration changes with respect to cell length, we compared the ratio of initial deceleration and cell length in induced ${\displaystyle \left(L_{induced}=8.2\pm 0.4\mu \mathrm{m}\right)}$ and uninduced ${\displaystyle \left(L_{uninduced}=4.3\pm 0.1\mu \mathrm{m}\right)}$ cdc28-13^ts cells. We found that the initial deceleration rate is inversely proportional to cell length ($d_0^{uninduced}/d_0^{induced}=2\pm 1$; ${(L_{uninduced}/L_{induced})}^{-1}=1.9\pm 0.1$), consistent with the predictions of our balance-point model (Figure 4D and E and Equation 7 in Materials and methods). Further, once cable length was normalized to cell length, cables extended with similar dynamics (Figure 4G), as predicted by our model.

Figure 4 with 1 supplement see all

Download asset Open asset

Video 2

Download asset

Video 3

Download asset

Video 4

Download asset

Collectively, our observations demonstrate that cables grow until their length matches the length of the cell, and that this is achieved by length-dependent deceleration of cable extension. The precise mechanism providing the feedback to enable cable deceleration is not yet clear. One possibility is that it is controlled by a gradient of actin disassembly-promoting activity that is highest at the rear of the cell. Such a gradient could be established by the retrograde transport of disassembly factors on cables, leading to their release at the rear of the cell. This would produce a higher concentration of disassembly factors, and greater disassembly rate for cables, at the back of the cell. An alternative possibility is a reaction-diffusion mechanism, achieved by anchoring an activator of disassembly factors (such as a kinase) at the rear of the cell while having an inhibitor (such as a phosphatase) in the cytosol. This would be similar conceptually to how Ran GTPase gradients form around chromatin (Kalab et al., 2002), although it would require additional features to produce the scaling that we observe (Ben-Zvi et al., 2011). Either of these two mechanisms (retrograde transport or modified reaction-diffusion) has the potential to create a gradient that is shallower in longer cells compared to shorter cells, accounting for the cell-length-sensitive cable deceleration (Figure 2—figure supplement 1D). This mechanism also would allow cables to sense the rear of the cell without requiring physical interactions with that boundary. A third possibility, which is not mutually exclusive with either mechanism above, would be length-dependent inhibition of cable assembly, that is an antenna mechanism, albeit one that is dependent on cellular factors other than Smy1 (Mohapatra et al., 2015).

It has recently been shown for other subcellular structures (e.g. nucleus, spindle, centrosome, and nucleolus) that their sizes scale with cell volume, and this scaling is explained by limiting pool models (Hazel et al., 2013; Good et al., 2013; Weber and Brangwynne, 2015; Decker et al., 2011; Neumann and Nurse, 2007; Lacroix et al., 2018). However, we found that polarized actin cables scale with cell length rather than volume. This length control cannot be explained by a limiting pool mechanism, and instead is explained, both theoretically and experimentally, by a balance-point model. These results reveal a new strategy by which cells solve engineering challenges, enabling them to scale internal structures with the linear dimensions of the cell (Kirschner et al., 2000). Similar principles may underlie the length control of other polarized, linear actin structures, such as filopodia and stereocilia. Further, related strategies may be used to control the growth of radial microtubule arrays that reach the cell periphery (Lacroix et al., 2016; Wühr et al., 2010), and may explain the scaling relationships observed between flagellar length and cell length (Bauer et al., 2021) and between contractile ring diameter and cell diameter (Kukhtevich et al., 2020). Ultimately, the model of size control that we have presented here expands our understanding of the mechanisms used by cells to sense specific aspects of their geometry, including length, surface area, and volume, to assemble structures that scale with these different dimensions (Rieckhoff et al., 2020; Brownlee and Heald, 2019).

All data points are shown in the main figures and figure supplements, and all cell images and source code are archived at Zenodo.

1. 1. Allard CAH
   2. Decker F
   3. Weiner OD
   4. Toettcher JE
   5. Graziano BR

   (2018) A size-invariant bud-duration timer enables robustness in yeast cell size control

   PLOS ONE 13:e0209301.

   https://doi.org/10.1371/journal.pone.0209301

   • PubMed
   • Google Scholar
2. 1. Bauer D
   2. Ishikawa H
   3. Wemmer KA
   4. Hendel NL
   5. Kondev J
   6. Marshall WF

   (2021) Analysis of biological noise in the flagellar length control system

   iScience 24:102354.

   https://doi.org/10.1016/j.isci.2021.102354

   • PubMed
   • Google Scholar
3. 1. Ben-Zvi D
   2. Shilo BZ
   3. Barkai N

   (2011) Scaling of morphogen gradients

   Current Opinion in Genetics & Development 21:704–710.

   https://doi.org/10.1016/j.gde.2011.07.011

   • PubMed
   • Google Scholar
4. 1. Brownlee C
   2. Heald R

   (2019) Importin α partitioning to the plasma membrane regulates intracellular scaling

   Cell 176:805–815.

   https://doi.org/10.1016/j.cell.2018.12.001

   • PubMed
   • Google Scholar
5. 1. Chesarone-Cataldo M
   2. Guérin C
   3. Yu JH
   4. Wedlich-Soldner R
   5. Blanchoin L
   6. Goode BL

   (2011) The myosin passenger protein Smy1 controls actin cable structure and dynamics by acting as a formin damper

   Developmental Cell 21:217–230.

   https://doi.org/10.1016/j.devcel.2011.07.004

   • PubMed
   • Google Scholar
6. 1. de Godoy LM
   2. Olsen JV
   3. Cox J
   4. Nielsen ML
   5. Hubner NC
   6. Fröhlich F
   7. Walther TC
   8. Mann M

   (2008) Comprehensive mass-spectrometry-based proteome quantification of haploid versus diploid yeast

   Nature 455:1251–1254.

   https://doi.org/10.1038/nature07341

   • PubMed
   • Google Scholar
7. 1. Decker M
   2. Jaensch S
   3. Pozniakovsky A
   4. Zinke A
   5. O'Connell KF
   6. Zachariae W
   7. Myers E
   8. Hyman AA

   (2011) Limiting amounts of centrosome material set centrosome size in C. elegans embryos

   Current Biology 21:1259–1267.

   https://doi.org/10.1016/j.cub.2011.06.002

   • PubMed
   • Google Scholar
8. 1. Eskin JA
   2. Rankova A
   3. Johnston AB
   4. Alioto SL
   5. Goode BL

   (2016) Common formin-regulating sequences in Smy1 and Bud14 are required for the control of actin cable assembly in vivo

   Molecular Biology of the Cell 27:828–837.

   https://doi.org/10.1091/mbc.E15-09-0639

   • PubMed
   • Google Scholar
9. 1. Goehring NW
   2. Hyman AA

   (2012) Organelle growth control through limiting pools of cytoplasmic components

   Current Biology 22:R330–R339.

   https://doi.org/10.1016/j.cub.2012.03.046

   • PubMed
   • Google Scholar
10. 1. Good MC
    2. Vahey MD
    3. Skandarajah A
    4. Fletcher DA
    5. Heald R

    (2013) Cytoplasmic volume modulates spindle size during embryogenesis

    Science 342:856–860.

    https://doi.org/10.1126/science.1243147

    • PubMed
    • Google Scholar
11. 1. Greenan G
    2. Brangwynne CP
    3. Jaensch S
    4. Gharakhani J
    5. Jülicher F
    6. Hyman AA

    (2010) Centrosome size sets mitotic spindle length in Caenorhabditis elegans embryos

    Current Biology 20:353–358.

    https://doi.org/10.1016/j.cub.2009.12.050

    • PubMed
    • Google Scholar
12. 1. Gregor T
    2. Bialek W
    3. van Steveninck RRdR
    4. Tank DW
    5. Wieschaus EF

    (2005) Diffusion and scaling during early embryonic pattern formation

    PNAS 102:18403–18407.

    https://doi.org/10.1073/pnas.0509483102

    • Google Scholar
13. 1. Hazel J
    2. Krutkramelis K
    3. Mooney P
    4. Tomschik M
    5. Gerow K
    6. Oakey J
    7. Gatlin JC

    (2013) Changes in cytoplasmic volume are sufficient to drive spindle scaling

    Science 342:853–856.

    https://doi.org/10.1126/science.1243110

    • PubMed
    • Google Scholar
14. 1. Jorgensen P
    2. Nishikawa JL
    3. Breitkreutz BJ
    4. Tyers M

    (2002) Systematic identification of pathways that couple cell growth and division in yeast

    Science 297:395–400.

    https://doi.org/10.1126/science.1070850

    • PubMed
    • Google Scholar
15. 1. Jorgensen P
    2. Edgington NP
    3. Schneider BL
    4. Rupes I
    5. Tyers M
    6. Futcher B

    (2007) The size of the nucleus increases as yeast cells grow

    Molecular Biology of the Cell 18:3523–3532.

    https://doi.org/10.1091/mbc.e06-10-0973

    • PubMed
    • Google Scholar
16. 1. Kalab P
    2. Weis K
    3. Heald R

    (2002) Visualization of a Ran-GTP gradient in interphase and mitotic Xenopus egg extracts

    Science 295:2452–2456.

    https://doi.org/10.1126/science.1068798

    • PubMed
    • Google Scholar
17. 1. Kirschner M
    2. Gerhart J
    3. Mitchison T

    (2000) Molecular “Vitalism”

    Cell 100:79–88.

    https://doi.org/10.1016/S0092-8674(00)81685-2

    • Google Scholar
18. 1. Kukhtevich IV
    2. Lohrberg N
    3. Padovani F
    4. Schneider R
    5. Schmoller KM

    (2020) Cell size sets the diameter of the budding yeast contractile ring

    Nature Communications 11:2952.

    https://doi.org/10.1038/s41467-020-16764-x

    • Google Scholar
19. 1. Lacroix B
    2. Ryan J
    3. Dumont J
    4. Maddox PS
    5. Maddox AS

    (2016) Identification of microtubule growth deceleration and its regulation by conserved and novel proteins

    Molecular Biology of the Cell 27:1479–1487.

    https://doi.org/10.1091/mbc.E16-01-0056

    • PubMed
    • Google Scholar
20. 1. Lacroix B
    2. Letort G
    3. Pitayu L
    4. Sallé J
    5. Stefanutti M
    6. Maton G
    7. Ladouceur AM
    8. Canman JC
    9. Maddox PS
    10. Maddox AS
    11. Minc N
    12. Nédélec F
    13. Dumont J

    (2018) Microtubule dynamics scale with cell size to set spindle length and assembly timing

    Developmental Cell 45:496–511.

    https://doi.org/10.1016/j.devcel.2018.04.022

    • PubMed
    • Google Scholar
21. 1. Levy DL
    2. Heald R

    (2010) Nuclear Size Is Regulated by Importin α and Ntf2 in Xenopus

    Cell 143:288–298.

    https://doi.org/10.1016/j.cell.2010.09.012

    • Google Scholar
22. 1. Longtine MS
    2. McKenzie A
    3. Demarini DJ
    4. Shah NG
    5. Wach A
    6. Brachat A
    7. Philippsen P
    8. Pringle JR

    (1998) Additional modules for versatile and economical PCR-based gene deletion and modification in Saccharomyces cerevisiae

    Yeast 14:953–961.

    https://doi.org/10.1002/(SICI)1097-0061(199807)14:10<953::AID-YEA293>3.0.CO;2-U

    • PubMed
    • Google Scholar
23. Software

    1. McInally SG

    (2021a) Source Code for “Scaling of Subcellular Structures with Cell Length Through Decelerated Growth

    Zenodo.

    https://doi.org/10.5281/zenodo.4812981
24. Software

    1. McInally SG
    2. Kondev J
    3. Goode BL

    (2021b) Data and imaging files for: “Scaling of subcellular structures with cell length through decelerated growth

    Zenodo.

    https://doi.org/10.5281/zenodo.4791679
25. 1. Mohapatra L
    2. Goode BL
    3. Kondev J

    (2015) Antenna mechanism of length control of actin cables

    PLOS Computational Biology 11:e1004160.

    https://doi.org/10.1371/journal.pcbi.1004160

    • PubMed
    • Google Scholar
26. 1. Mohapatra L
    2. Goode BL
    3. Jelenkovic P
    4. Phillips R
    5. Kondev J

    (2016) Design principles of length control of cytoskeletal structures

    Annual Review of Biophysics 45:85–116.

    https://doi.org/10.1146/annurev-biophys-070915-094206

    • PubMed
    • Google Scholar
27. 1. Moseley JB
    2. Goode BL

    (2006) The yeast actin cytoskeleton: from cellular function to biochemical mechanism

    Microbiology and Molecular Biology Reviews 70:605–645.

    https://doi.org/10.1128/MMBR.00013-06

    • PubMed
    • Google Scholar
28. 1. Neumann FR
    2. Nurse P

    (2007) Nuclear size control in fission yeast

    Journal of Cell Biology 179:593–600.

    https://doi.org/10.1083/jcb.200708054

    • Google Scholar
29. 1. Pruyne D
    2. Gao L
    3. Bi E
    4. Bretscher A

    (2004) Stable and dynamic axes of polarity use distinct formin isoforms in budding yeast

    Molecular Biology of the Cell 15:4971–4989.

    https://doi.org/10.1091/mbc.e04-04-0296

    • PubMed
    • Google Scholar
30. 1. Rafelski SM
    2. Viana MP
    3. Zhang Y
    4. Chan YH
    5. Thorn KS
    6. Yam P
    7. Fung JC
    8. Li H
    9. Costa LF
    10. Marshall WF

    (2012) Mitochondrial network size scaling in budding yeast

    Science 338:822–824.

    https://doi.org/10.1126/science.1225720

    • PubMed
    • Google Scholar
31. 1. Reber S
    2. Goehring NW

    (2015) Intracellular scaling mechanisms

    Cold Spring Harbor Perspectives in Biology 7:a019067.

    https://doi.org/10.1101/cshperspect.a019067

    • PubMed
    • Google Scholar
32. 1. Rieckhoff EM
    2. Berndt F
    3. Elsner M
    4. Golfier S
    5. Decker F
    6. Ishihara K
    7. Brugués J

    (2020) Spindle scaling is governed by cell boundary regulation of microtubule nucleation

    Current Biology 30:4973–4983.

    https://doi.org/10.1016/j.cub.2020.10.093

    • PubMed
    • Google Scholar
33. 1. Slubowski CJ
    2. Funk AD
    3. Roesner JM
    4. Paulissen SM
    5. Huang LS

    (2015) Plasmids for C-terminal tagging in Saccharomyces cerevisiae that contain improved GFP proteins, envy and ivy

    Yeast 32:379–387.

    https://doi.org/10.1002/yea.3065

    • PubMed
    • Google Scholar
34. 1. Weber SC
    2. Brangwynne CP

    (2015) Inverse size scaling of the nucleolus by a concentration-dependent phase transition

    Current Biology 25:641–646.

    https://doi.org/10.1016/j.cub.2015.01.012

    • PubMed
    • Google Scholar
35. 1. Wühr M
    2. Tan ES
    3. Parker SK
    4. Detrich HW
    5. Mitchison TJ

    (2010) A model for cleavage plane determination in early amphibian and fish embryos

    Current Biology 20:2040–2045.

    https://doi.org/10.1016/j.cub.2010.10.024

    • PubMed
    • Google Scholar
36. 1. Yang HC
    2. Pon LA

    (2002) Actin cable dynamics in budding yeast

    PNAS 99:751–756.

    https://doi.org/10.1073/pnas.022462899

    • PubMed
    • Google Scholar
37. 1. Yu JH
    2. Crevenna AH
    3. Bettenbühl M
    4. Freisinger T
    5. Wedlich-Söldner R

    (2011) Cortical actin dynamics driven by formins and myosin V

    Journal of Cell Science 124:1533–1541.

    https://doi.org/10.1242/jcs.079038

    • PubMed
    • Google Scholar

Acceptance summary:

This manuscript will be of interest to researchers in the fields of cell size control and the cytoskeleton. A combination of modelling and experimental data show that actin cables, which extend in budding yeast cells from the bud tip and bud neck, display an average length similar to the length of the cell, likely due to progressive decrease in their extension rate up to cell length. The distinct scaling relationship with cell length rather than volume may be a new paradigm that drives new investigations in related phenomena in other organisms.

Decision letter after peer review:

Thank you for submitting your article "Scaling of subcellular structures with cell length through decelerated growth" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Jonathan Cooper as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Arjun Raj (Reviewer #1).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission. The vast majority of points raised can be addressed by rewriting and reanalyzing data already generated. However, a single new experiment has been sought by one of the referees, which I agree will further sharpen the models you are trying to advance.

Essential Revisions:

1. I'm not as familiar with the details of the models, but it seems that a key assumption is that f(L_cable,L_cell) = f(L_cable/L_cell), which allows for the cells to scale length appropriately. Can the authors speculate on potential mechanisms underlying this length scaling? If there is a gradient, what could form it with such a property?

2. The effect of Smy1 KO on initial elongation rate is modest. I think it would be useful to quantify the effect size and put it in the main text. Also, does the degree of increase quantitatively match the increased cable length observed? If not, can the authors speculate on the source of the discrepancy?

3. To uncouple cell length and cell volume, the authors could use mutants with abnormal cell shape (for instance using more ellipsoid or more rounded cells). Many such mutants have been described over the years in S. cerevisiae, so this should be a technically straightforward approach to take. This would allow to probe whether actin cable length indeed correlates better with cell length than the cubic root of volume (or other shape measurements).

4. An indication of how cables were selected for tracking and their number amongst how many cells would help better explain the extension rate measurements and increase confidence in the data. Extending this comparison to other mutants with altered cell shape as suggested above would also strengthen the conclusions.

5. Measurement of cable length and steady state length. The study depends heavily on the ability to measure actin cable length. But how cable length was measured in 3D is not presented with sufficient detail. I think it is essential to show convincing 3D images of cable end identification for the majority of actin cables in a cell. I am suggesting this since cables that reach the cell back may "turn around" and/or form bundles or unbundle through interactions with other cables.

6. The extension rate of actin cables that grow from the bud neck to the cell back is shown in movies and quantified in the figures. However, it's not clear if these cables eventually *stop* elongating. For example, in Figure 4D the extension rate does not decay to zero at the longest times. That seems to me to be an essential point since I would expect that if one is able to measure the length of most actin cables in the cell, then one should be able to see most of these cables stop extending.

7. I found the contrast between the two models, "boundary-sensing" and "balance-point" was not so sharp: the difference is on whether the extension rate decays more or less abruptly with distance along the cell. I also don't see if either of these models as presented is excluded by the data. The authors convincingly show that the cable extension rate decays with cable length, as would be expected from a balance-point model. However, as mentioned in comment 1, it is not clear where the extension rate decays to zero in graphs such as Figure 1F, 3B, 4D. If cable elongation ends abruptly at the longest time in these graphs, then this would indicate a boundary-sensing mechanism (so overall a combination/intermediate model).

8. I feel that the mechanism by which the actin cable system reaches a steady state needs to be clarified. We see a few cables that start from the bud neck and grow to the whole cell. Is this typical or are these rare cases? If rare, are they still representative? Do cables disappear to allow for new cable growth? Such processes change cable length so they are linked to the central theme of cable length regulation.

9. There is a lack of discussion and experimentation of known regulators of actin assembly and disassembly. Perhaps it's ok to leave the precise mechanism providing the feedback of cable deceleration for future work, however I feel that at least some discussion should be provided. For example, cofilin might sever filaments in age-dependent manner and cofilin-decorated filaments might be prone to breaking when buckled. Myosin motors are also known to regulate the extension rate of cables.

10. The authors don't measure cables shorter than 2 microns in Figure 1G, yet such cables should exist from the movies of cable growth versus time. I wonder if their measurement was biased towards the longest cables. In Figure 1D (cdc28-13 induced) there may be several short cables in addition to the long one. Perhaps a plot of total actin cable intensity vs distance would help.

Reviewer #1:

In this manuscript, the authors evaluate models for length determination of actin cables in yeast. The problem they pose is that actin cables must scale with the length of a cell, but given that length is a one dimensional measure, it cannot use "limiting pool" or "limiting factor" mechanisms in order to achieve such scaling. They first show that actin cables do indeed scale with cell length over a variety of cell cycle stages and perturbations. They then propose two models: a boundary sensing model and a balance-point model, the latter of which they show to be more consistent with the data. In line with their model, the rate of cable extension scaled with distance scaled by total cell length.

I found this manuscript to be a really nice example of quantitative cell biology. I think the problem of scaling of various cell components is fundamental and of great interest, and this work has framed an interesting example of the 1D scaling required for a linear component (actin cables). The paper is well written, the data is very solid with strong image analysis, and the claims are well supported.

Reviewer #2:

This is an interesting manuscript examining how the length of actin cables is set in budding yeast cells. The authors show that the average length of actin cables from bud neck to the distal pole of the mother cell is very similar to the length of the cell. The cable length appears to scale linearly with cell length in cells of diverse sizes (haploid, diploid, and cells artificially enlarged by a cell-cycle block), but cable length also scales with cell volume (with a power law – roughly with the cubic root of volume). The authors then propose a couple of possible models that would account for this scaling behaviour and show data that is in agreement with the idea that either assembly or disassembly rates are dependent on cable length, leading to a balance point at length equal that of the cell. The underlying molecular mechanism of this balance-point model is not examined, except for the finding that Smy1, which the authors previously proposed serves to limit cable length in an "antenna model" (Mohapatra et al., PLoS Comput Biol 2015), is not involved.

The correlation between cable length and cell length is very intriguing and suggestive that cell length is the relevant measure used by cells to set the length of their actin cytoskeleton. However, the presented data do not exclude that the relevant measure may be cell volume, with which actin cable length scales with cell volume using a more complex hypoallometric power law. To rigorously test whether cell length rather than cell volume is the relevant parameter, it would be necessary to decouple length from volume and test how actin cables length scales with these measurements.

The authors propose a balance-point model in which cable assembly and disassembly rates are balanced when the cable has the length of the cell due to either rate being cable length-dependent. They contrast this to a boundary model in which cable growth would abruptly stop when reaching the model cell distal pole. The experimental data to discriminate between these model focuses on measured cable extension rates in WT haploids, and normal-sized and enlarged cdc28-13 mutants. These measurements of actin cable extension by fluorescence microscopy are very challenging, and the authors should be commended for attempting it. However, they also raise uncertainty. Looking at the movies and the time-lapses, there are clearly many actin cables that do not behave as a simple birth at the neck followed by extension towards the opposite cell pole. Some of the tracking is also not certain – see for instance 17 to 18 s in movie 2: it looks like a big jump to a structure that was actually already present in the first of these two timepoints. This reduces somewhat the confidence in the conclusion that rate extension deceleration scales with cell length.

In summary, the finding of linear scaling between actin cable length and cell length is interesting, but whether cell length is the relevant parameter for this scaling is not fully established. There is a significant degree of uncertainty associated with the measurements of cable extension. While the current data is in agreement with a model in which cable extension diminishes with cable length, the mechanism of how this may be coupled to cell length is unknown.

Reviewer #3:

In this paper the authors find that the length of yeast actin cables scales with cell length. Cable length is studied using haploid, diploid, and cdc28-13 cells that grow abnormally large. Cable length extension rate is found to decrease with extension distance, at a different rate depending on cell size, supporting a "balance-point" mechanism of length regulation. The ratio between the shortest and longest cables in this work is a factor of order 2 (Figure 1F). This factor is significant to make this work interesting in the context of size regulation (though one can also be somewhat skeptical if a factor of 2 is large enough to unambiguously determine scaling mechanisms, given the multitude of actin regulators in cells that can provide such a change). Overall, this is a nicely written paper. However, I have several concerns as described below.

1) Measurement of cable length and steady state length. The study depends heavily on the ability to measure actin cable length. But how cable length was measured in 3D is not presented with sufficient detail. I think it is essential to show convincing 3D images of cable end identification for the majority of actin cables in a cell. I am suggesting this since cables that reach the cell back may "turn around" and/or form bundles or unbundle through interactions with other cables.

The extension rate of actin cables that grow from the bud neck to the cell back is shown in movies and quantified in the figures. However, it's not clear if these cables eventually *stop* elongating. For example, in Figure 4D the extension rate does not decay to zero at the longest times. That seems to me to be an essential point since I would expect that if one is able to measure the length of most actin cables in the cell, then one should be able to see most of these cables stop extending.

2) I found the contrast between the two models, "boundary-sensing" and "balance-point" was not so sharp: the difference is on whether the extension rate decays more or less abruptly with distance along the cell. I also don't see if either of these models as presented is excluded by the data. The authors convincingly show that the cable extension rate decays with cable length, as would be expected from a balance-point model. However, as mentioned in comment 1, it is not clear where the extension rate decays to zero in graphs such as Figure 1F, 3B, 4D. If cable elongation ends abruptly at the longest time in these graphs, then this would indicate a boundary-sensing mechanism (so overall a combination/intermediate model).

3) I feel that the mechanism by which the actin cable system reaches a steady state needs to be clarified. We see a few cables that start from the bud neck and grow to the whole cell. Is this typical or are these rare cases? If rare, are they still representative? Do cables disappear to allow for new cable growth? Such processes change cable length so they are linked to the central theme of cable length regulation.

4) There is a lack of discussion and experimentation of known regulators of actin assembly and disassembly. Perhaps it's ok to leave the precise mechanism providing the feedback of cable deceleration for future work, however I feel that at least some discussion would need to be provided. For example, cofilin might sever filaments in age-dependent manner and cofilin-decorated filaments might be prone to breaking when buckled. Myosin motors are also known to regulate the extension rate of cables.

Essential Revisions:

1. I'm not as familiar with the details of the models, but it seems that a key assumption is that f(L_cable,L_cell) = f(L_cable/L_cell), which allows for the cells to scale length appropriately. Can the authors speculate on potential mechanisms underlying this length scaling? If there is a gradient, what could form it with such a property?

The manuscript now has been edited to include two potential molecular mechanisms leading to a scale-invariant gradient of actin depolymerizing activity (see end of main text).

In addition, how scale-invariant gradients are potentially established is discussed in more depth in a new theory manuscript on BioRxiv (see: https://doi.org/10.1101/2021.05.18.444733). This theory paper proposes that regulatory proteins diffuse in the cytoplasm and are captured and transported to the cell pole by motors moving along the cell cortex (a form of the ‘antenna’ mechanism – see minor comment #4 below), producing a scale-invariant gradient of these regulatory proteins. The simple idea is that upon release at the pole, proteins diffuse a typical distance $\lambda \approx \sqrt{\mathrm{\text{Dτ}}}$ , until they are captured by the motor proteins at the cell surface; here D is the protein diffusion constant in the cytoplasm and τ is the time until a protein is captured at the surface by a motor protein. In a spherical cell of radius $L_{\mathrm{\text{cell}}},\tau \approx L_{{\mathrm{\text{cell}}}^2}/D$, which leads to $\lambda \approx \sqrt{\mathrm{\text{Dτ}}}\approx L_{\mathrm{\text{cell}}}$. In other words, the combined action of cytoplasmic diffusion and motor transport at the cell surface, leads to a spatial protein gradient with a decay length to $\lambda \approx L_{\mathrm{\text{cell}}}$. Assuming this is a gradient of depolymerizing activity, and further assuming that the cable assembly rate is length-independent, leads to the scaling of the cable extension rate with the assumed scaling property. While no such gradient of cytoskeletal depolymerizing activity has been described in yeast thus far, its existence and role in regulating lengths of flagella in Giardia have been demonstrated (see: 10.7554/eLife.48694).

2. The effect of Smy1 KO on initial elongation rate is modest. I think it would be useful to quantify the effect size and put it in the main text. Also, does the degree of increase quantitatively match the increased cable length observed? If not, can the authors speculate on the source of the discrepancy?

The manuscript has been edited to include the direct comparison of the effect size for the increased cable length and cable extension rates measured in smy1Δ cells. As indicated in the edited text, the effect size of these phenotypes is similar, and thus we conclude that the observed increase in cable length is likely due to the initial increase in cable extension rate. Additionally, this comment inspired us to move the experimental test of our quantitative model (using smy1∆) from the supplement to the main text; these data previously appeared in the supplemental mathematics section, but we realized that they could be easily overlooked in that location. While the Smy1 data do not identify the molecular mechanism controlling cable deceleration, they confirm that increased initial cable extension rate will lead to a proportional increase in the initial deceleration of the cable, a specific prediction of our model in Equation 7. We believe that moving this section to the main text will strengthen our paper and be helpful to readers in light of the reviewer’s comment.

3. To uncouple cell length and cell volume, the authors could use mutants with abnormal cell shape (for instance using more ellipsoid or more rounded cells). Many such mutants have been described over the years in S. cerevisiae, so this should be a technically straightforward approach to take. This would allow to probe whether actin cable length indeed correlates better with cell length than the cubic root of volume (or other shape measurements).

To address this, we have performed an analysis of cable lengths in cells of different shape, as indicated by their different aspect ratios (ratio of cell length to width). This analysis allows us to compare cables in cells of the same length but with different volumes. These data (see new ‘Figure 1 —figure supplement 2’) show that cable length is not affected by differences in cell shape, supporting our conclusion that cable length scales with cell length, rather than other dimensions such as surface area or cell volume.

4. An indication of how cables were selected for tracking and their number amongst how many cells would help better explain the extension rate measurements and increase confidence in the data. Extending this comparison to other mutants with altered cell shape as suggested above would also strengthen the conclusions.

We have revised the methods to provide additional information regarding the inclusion criteria for cables used in live cell imaging analyses. Briefly, cables were only included in our analysis if we could observe their extending tips emerge from the bud neck, and track their tips until they stopped growing. The number of cables analyzed, and the number of independent experiments is indicated in each figure legend. The typical number of cables tracked in an individual cell (by live imaging) is ~1-2 due to technical constraints, such as the relatively short time (~2 minutes) that we can acquire images before the signal begins to bleach, and before there is substantial drift in the z-dimension that prevents accurate cable tip tracking. With future methodological improvements, it may become possible to track larger numbers of cables per cell, and for longer periods of time.

5. Measurement of cable length and steady state length. The study depends heavily on the ability to measure actin cable length. But how cable length was measured in 3D is not presented with sufficient detail. I think it is essential to show convincing 3D images of cable end identification for the majority of actin cables in a cell. I am suggesting this since cables that reach the cell back may "turn around" and/or form bundles or unbundle through interactions with other cables.

We revised the methods to provide additional information about how cable lengths were measured. We clarify that cables were not measured in 3D, but that the 3D stack was used to reliably determine where cables emerged from the bud neck and where their tips were in the mother cell. In addition, we have included annotated maximum intensity projects (see ‘Figure 1 —figure supplement 1A’) that display all of the cables traced in example cells. Additional annotated cell images are available in our imaging dataset uploaded to Zenodo (10.5281/zenodo.4791679).

To address the possibility that cables ‘turn around’, we have computed cable end-to-end distance and tortuosity. The end-to-end distance of a cable is the distance between the distal tip of the cable and its starting point back at the bud neck. Tortuosity is the ratio of cable length (obtained from the trace) to its end-to-end distance, where a perfectly straight cable has a value of one. This analysis shows that the majority of cables do not turn around or make sharp turns, and have a mean cable tortuosity of 1.2-1.3 (see ‘Figure 1 —figure supplement 1’). In our live imaging experiments, we have never observed individual cables interacting and dynamically bundling or unbundling with each other, although our data do not exclude the possibility that this could occur.

6. The extension rate of actin cables that grow from the bud neck to the cell back is shown in movies and quantified in the figures. However, it's not clear if these cables eventually *stop* elongating. For example, in Figure 4D the extension rate does not decay to zero at the longest times. That seems to me to be an essential point since I would expect that if one is able to measure the length of most actin cables in the cell, then one should be able to see most of these cables stop extending.

When we “measure the length of most actin cables in the cell” we are using super-resolution imaging of chemically fixed cells. In contrast, when we perform live imaging of cables we are only able track a subset of the cables in a cell for technical reasons stated earlier (see comment #4; also see comment #8 below). That said, we expect that the reason cable extension rates (by live imaging) do not decay to zero is a consequence of tracking the tips of cables, which can ‘wiggle’ or diffuse laterally while their length does not change. Additionally, all of the cable deceleration profiles we have measured stop at ~0.1um/sec, which is close to the size of a single pixel (0.133um/pixel) in our videos. Thus, we expect that this represents the limit of detection in our assays and should be interpreted as cables no longer extending.

7. I found the contrast between the two models, "boundary-sensing" and "balance-point" was not so sharp: the difference is on whether the extension rate decays more or less abruptly with distance along the cell. I also don't see if either of these models as presented is excluded by the data. The authors convincingly show that the cable extension rate decays with cable length, as would be expected from a balance-point model. However, as mentioned in comment 1, it is not clear where the extension rate decays to zero in graphs such as Figure 1F, 3B, 4D. If cable elongation ends abruptly at the longest time in these graphs, then this would indicate a boundary-sensing mechanism (so overall a combination/intermediate model).

As stated above, we do not think that the final cable extension rate falls to zero (see response to comment #6). Further, cable tips were not observed to abruptly stop. With these clarifications in mind, we believe that the difference between the ‘boundary-sensing’ and ‘balance-point’ models is fairly sharp. In one model, cables exhibit a constant rate of extension until they physically encounter the cell boundary and then they halt. In the other model, cable extension rate is constantly changing, starting out fast as the cable emerges from the bud neck and then slowing as a function of cell length – until the cable length matches the length of the cell (see ‘Figure 2C and 2D’).

8. I feel that the mechanism by which the actin cable system reaches a steady state needs to be clarified. We see a few cables that start from the bud neck and grow to the whole cell. Is this typical or are these rare cases? If rare, are they still representative?

As mentioned above, due to technical limitations we are only able to track a subset of the cables in a cell by live imaging (see response to comment #6). However, given our analysis of cables in fixed cells, where the majority of cables grow to reach the back of the cell, we are fairly confident that our live tracking of cables extending to reach the rear of the cell are representative of typical cable behavior.

Do cables disappear to allow for new cable growth? Such processes change cable length so they are linked to the central theme of cable length regulation.

How cables disappear to allow for new cable growth is an important question that we hope to address in the future. Little is known about how cables are disassembled in vivo once they reach the back of the cell. To date, these questions have been difficult to approach experimentally, in part due to the same technical limitations mentioned above (e.g., our imaging is limited to ~2 minutes before photobleaching and drift prevent accurate image acquisition). We anticipate that improvements in fluorescent tags (to mark cables) and better control of the microscope stage will allow for longer analyses in the future, and make it possible to begin answering these types of questions.

9. There is a lack of discussion and experimentation of known regulators of actin assembly and disassembly. Perhaps it's ok to leave the precise mechanism providing the feedback of cable deceleration for future work, however I feel that at least some discussion should be provided. For example, cofilin might sever filaments in age-dependent manner and cofilin-decorated filaments might be prone to breaking when buckled. Myosin motors are also known to regulate the extension rate of cables.

We have revised our Discussion to include several possible molecular mechanisms controlling cable deceleration (see response to comment #1). This includes the possibility of an activity gradient of cofilin and/or other actin disassembly factors, where their activity is higher at the rear of the cell. We also acknowledge that actin filament aging could play a role in the observed scaling relationship (cable length with cell length). However, this would require filament aging (in cables) to be cell length dependent, given that initial cable extension rates are similar in cells of different length. As such, cells would need to have a mechanism for slowing π release (from the F-actin in cables) in longer cells, or alternatively, accelerating π release from cables in shorter cells.

10. The authors don't measure cables shorter than 2 microns in Figure 1G, yet such cables should exist from the movies of cable growth versus time. I wonder if their measurement was biased towards the longest cables. In Figure 1D (cdc28-13 induced) there may be several short cables in addition to the long one. Perhaps a plot of total actin cable intensity vs distance would help.

We fully expect that there are cables smaller than 2 µm, but they are also growing much faster than longer cables, and are therefore less frequently observed. Additionally, as touched upon above (see response to comment #8) we don’t know what fraction of all the cables in a cell are undergoing de novo assembly at any given time.

Author details

1. Shane G McInally

   1. Department of Biology, Brandeis University, Waltham, United States
   2. Department of Physics, Brandeis University, Waltham, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-6145-4581

2. Jane Kondev

   Department of Physics, Brandeis University, Waltham, United States

   Contribution

   Conceptualization, Supervision, Funding acquisition, Methodology, Writing - original draft, Project administration, Writing - review and editing

   For correspondence

   kondev@brandeis.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-7522-7144

3. Bruce L Goode

   Department of Biology, Brandeis University, Waltham, United States

   Contribution

   Conceptualization, Supervision, Funding acquisition, Writing - original draft, Project administration, Writing - review and editing

   For correspondence

   goode@brandeis.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-6443-5893

• 2,506

  Page views

• 275

  Downloads

• 5

  Citations

Article citation count generated by polling the highest count across the following sources: Crossref, PubMed Central, Scopus.