Flagellar energy costs across the tree of life

  1. Paul E Schavemaker  Is a corresponding author
  2. Michael Lynch
  1. Biodesign Center for Mechanisms of Evolution, Arizona State University, United States
4 figures, 1 table and 1 additional file


Figure 1 with 2 supplements
Construction costs of flagella in bacteria and eukaryotes as a function of cell volume.

Each point denotes a species. The costs are the sum over all flagella present on a single cell. (A) The absolute construction cost. The lines are power law fits to bacteria, eukaryotic flagellates (euglenids, kinetoplastids, and ‘other eukaryotes’), and ciliates and parabasalids. The equations are: cabs=1.1×109V0.81±0.14 , cabs=2.6×1010V0.31±0.03 , and cabs=2.8×109V0.86±0.10 , respectively (exponent ± SE). (B) The construction costs of flagella relative to the construction costs of the entire cell. The line is a power law fit to the eukaryotic flagellates: crel=0.98V-0.66±0.03 . The grey-shaded triangle is explained in the Discussion. In both panels the asterisk marks Opalina ranarum, which resembles ciliates in its flagellar distribution but does not belong to the ciliate clade. Data in Figure 1—source data 1.

Figure 1—source data 1

Table of flagellar and cellular properties for bacterial and eukaryotic species.

Figure 1—figure supplement 1
Overview of flagellar and cellular properties of eukaryotic species.

(A) Distribution of flagellum lengths for cells with less than eight flagella and cells with eight or more flagella. Only unique flagellar lengths for each species are included (also for B–E), otherwise ciliate and parabasalid data would overwhelm the plot. (B) Distribution of flagellum length for cells with or without a rod in their flagellum. (C) Flagellum length plotted against cell volume. The legend in Figure E holds for C–F. (D) Flagellum length plotted against number of flagella. (E) Number of flagella plotted against cell volume. (F) Cell aspect ratio plotted against cell volume. The aspect ratio is calculated by dividing the cell length by the cell width (or the geometric mean of the width and depth). The dashed line is a power law fit to all species: 1.57V0.052±0.016 . Data in Figure 1—figure supplement 1—source data 1 and 2.

Figure 1—figure supplement 1—source data 1

Table of flagellar numbers and lengths of eukaryotic species.

Figure 1—figure supplement 1—source data 2

Table of cell aspect ratios for eukaryotic species.

Figure 1—figure supplement 2
Relative flagellar construction costs of special cases plotted against cell volume.

The blue points show Anaeramoeba ignava, Anaeramoeba gargantua, Dinematomonas valida, and Psammosa pacifica, before correcting for their real flagellum shape. The red points show the same species after correction. The grey points represent other eukaryotic species, shown for comparison. Data in Figure 1—figure supplement 2—source data 1.

Figure 1—figure supplement 2—source data 1

Table of alternative flagellar construction costs.

The cost and benefits of flagellar motility.

Each point denotes a species. (A) Swimming speed plotted against cell volume. Plotted are all species from the cost dataset for which the swimming speed is known. This includes bacteria, eukaryotic flagellates, and ciliates. The continuous line is the fit to all species: v=37V0.13±0.03 (exponent ± SE). The dashed line is a fit to the eukaryotic flagellates: v=95V-0.02±0.09 . The legend holds for the entire Figure 2. (B) Swimming speed plotted against the absolute flagellar construction cost. The line is the fit: v=1.2cabs0.16±0.03 . (C) Swimming speed (in cell lengths s−1) per ATP of construction cost plotted against cell volume. The solid blue line is the fit to the bacterial data: vATP=2.7×10-8V-1.13±0.16 . The solid black line is the fit to the eukaryotic data (both flagellates and ciliates): vATP=3.1×10-8V-1.06±0.11 . The dashed lines are extrapolations. (D) Comparison of the swimming power, or operating cost, calculated from Stokes’ law with empirical values. This gives an indication of the efficiency of converting chemical energy into swimming power. The line indicates equality. (E) The relative growth rate as a function of cell volume for cells in a medium with a homogenous distribution of small molecule nutrients, comparing cells with flagella to cells without flagella. In all panels the asterisk marks Opalina ranarum, which resembles ciliates in its flagellar distribution but does not belong to the ciliate clade. Data in Figure 2—source data 1.

Figure 2—source data 1

Table with swimming speeds, swimming power, and cell growth rate.

The population-genetic environment of different flagellar proteins for bacteria and eukaryotes.

The different distributions are for different proteins, with varying copy numbers, within the same flagellum. The spread within each distribution reflects the variation of relative flagellar construction costs over all bacterial or eukaryotic species in our construction cost dataset. The points on the top show the effective population sizes, Ne , of different species of bacteria and eukaryotes (Lynch and Trickovic, 2020) (the vertical spread of the datapoints is for visualisation). The bacterial flagellar protein names were taken from Escherichia coli. Inner arm dyneins are present in 94 copies per µm of flagellum, for FAP20, etc., this number is 1125, and for tubulins it is 29,125. The vertical dashed line is explained in the main text. Data in Figure 3—source data 1.

Figure 3—source data 1

Table with relative costs of adding an amino acid to flagellar proteins in various species.

The cost of eukaryotic flagella compared to bacterial cell and flagellar budgets.

(A) Histograms comparing the total cellular cost (excluding maintenance) for bacterial species to the cost of constructing flagella in eukaryotic species. (B) Histograms comparing the total eukaryotic flagellum length of bacteria and eukaryotes, where for the bacteria we have taken the absolute flagellar construction cost for each bacterial species and divided that by the per µm construction cost of the eukaryotic flagellum, to obtain the hypothetical length of the eukaryotic flagellum affordable to each bacterial species. Data in Figure 4—source data 1.

Figure 4—source data 1

Table with flagellum lengths, flagellum construction costs, and cell construction costs.



Table 1
Energy costs of flagella in the three domains of life.
SpeciesEscherichia coliPyrococcus furiosus*Chlamydomonas reinhardtii
Construction cost per µm (ATP)3.02 × 1071.28 × 1072.80 × 109
Construction cost per flagellum (ATP)2.32 × 1082.15 × 1073.08 × 1010
Number of flagella per cell3.4502
Construction cost of all flagella (ATP cell–1)7.88 × 1081.07 × 1096.15 × 1010
Cell volume (µm3)1.00.22122
Cell division time (hr)
Total cost of cell (construction + operating; ATP)1.59 × 10106.50 × 1095.32 × 1012
Relative construction cost, all flagella (%)
Operating cost per flagellum (ATP s–1)6.6 × 1042.64 × 102 9.7 × 105
Operating cost per cell cycle, all flagella (ATP)8.08 × 1084.75 × 107 †6.39 × 1010
Relative operating cost, all flagella (%)5.20.73 1.2
Relative total cost, all flagella (%)10.217.2 2.6
  1. *

    Due to gaps in knowledge of P. furiosus flagella, some data were taken from other archaea (see main text).

  2. This estimate for the operating cost is probably too low as the flagellar rotation rate that it is based on was recorded with a bead attached, which slows down flagellar rotation.

Table 1—source data 1

Breakdown of flagellar construction costs for bacteria, archaea, and eukaryotes.


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  1. Paul E Schavemaker
  2. Michael Lynch
Flagellar energy costs across the tree of life
eLife 11:e77266.