Actin is one of the most abundant proteins in eukaryotic cells [1, 5]. In S. pombe, the concentration of Act1p has been measured by quantitative immuno-blotting and is indeed very high relative to other cytoplasmic proteins - roughly 65 uM (see Table 1 and ref 2). Actins are also among the 10 most abundant proteins in X. laevis, zebrafish and rat cells when their proteomes are measured (see www.paxdb.org). In cells where actin is required for motility (keratocytes) or for cell division (S. pombe) experiments have demonstrated that a dramatic turnover of the actin cytoskeleton coordinates these processes. Since actin is an ATPase, one wonders: how much ATP is required to sustain these levels of actin polymerization?
Actin is a very well-studied protein and a lot is known about its structure, enzymatic activity and interaction with other proteins. The helical structure of F-actin has been derived by docking monomer crystal structures into cryo-EM structures of actin filaments (Figure 1, adapted from ref ). These studies show that actin filaments have a repeated helical structure with a period of ~36 nm and about 13 monomers per helix (Figure 1). Not only does this present an awfully pretty picture of F-actin, but it also gives us a useful number about actin filaments: that there is 1 actin monomer for every ~2.7 nm of filament. Alternatively: 2 monomers for every 5.4 nm of filament. This makes lots of sense because each G-actin monomer is roughly 5.5 nm long (longest axis) and F-actin is composed of actin dimers repeating along the longest axis of the filament . For reference, a G-actin monomer is roughly rectangular in shape and has dimensions of 5.5 x 5.5 x 3.5 nm .
Figure 1: the structure of an F-actin filament, adapted from Dominquez & Holmes 2011.
From studies of actin dynamics and enzymatic activity, we now know several useful things about actin:
- ATP-actin is the polymerizing species of actin monomer, but G-actin is not a very good ATPase.
- ADP-actin is the depolymerizing species within F-actin filaments.
- Polymerization induces a conformational shift in actin, which increases its ATPase activity [1,3].
Going forward, I’ll assume that every monomer in F-actin has an ATP or ADP bound and that only ADP actin dissociates. As a first approximation, therefore, we can assume that the rate of actin depolymerization is equal to the rate of actin-dependent ATP hydrolysis. In a steady-state (no net production or destruction of actin filaments, called treadmilling ), the rates of actin polymerization and depolymerization will be equal, so we can use either number to estimate the rate of actin-dependent ATP hydrolysis. This is, of course, a huge simplification because it ignores many other ATP-dependent proteins involved in the nucleation, movement and regulation of the actin cytoskeleton. Most notably, this simplification ignores any ATP-driven interaction between F-actin and myosin. Nonetheless, since the concentration of actin monomers is dramatically higher than than other cytoskeletal proteins (in S. pombe, see Table 1 from ref ) this approximation is a reasonable lower bound and hopefully accurate within an order of magnitude. Caveat emptor.
Let’s suppose that, in steady-state, a single actin fibril turns over at a rate of 2 monomer per second (2 /s). That is, two monomers associate with the barbed end and two dissociate from the pointed end each second. By our assumptions above, this would entail the hydrolysis of 2 ATP per second per filament and the extension of the barbed end by 5.4 nm/s. It’s worth noting that it’s irrelevant how long the fibrils are - we are only interested in how much ATP they hydrolyze and that’s purely a function of the rate of turnover.
Now I’ll estimate the ATP requirement of the actin cytoskeleton in four scenarios for which there is reasonable data available.
- ATP required by the actin cytoskeleton in a keratocyte to generate forces for movement at typical speeds.
- ATP required by S. pombe during cytokinesis to coordinate the contractile ring at the cell center.
- ATP required by S. cerevisiae to support turnover of its actin cytoskeleton during normal growth.
- ATP drained by Listeria and Rickettsia “comet tails” during infection of a macrophage.
Finally, I will try to put these numbers in context by estimating the ATP budgets of these cells, i.e. how much ATP they make per unit time, and compare the budget with the ATP cost of maintaining the actin cytoskeleton (again per unit time).
Goldfish Keratocyte Locomotion
First things first: you should definitely watch this video of a zebrafish keratocyte swimming along all happy-like.
I’m tackling the motion of a keratocyte first because it is possible to estimate the amount of actin cycling required for movement from the size and motion of the cell. Julie Theriot and Tim Mitchison famously used labeled actin in a pulse-chase microscopy experiment to show that actin filaments move at the same rate that a locomoting goldfish keratocyte moves , about 0.05 microns / s (at 15 C, see Figure 5 of ref 4). The Arp2/3 complex nucleates branching actin fibrils at an angle of roughly 70 degrees , and so we will assume that actin fibrils are incident to the lamellipodium membrane at an angle of ~ 110 / 2 = 55 degrees on average. If the membrane itself moves at 0.05 um/s, then the incident actin filament grows at a rate of 0.05 / sin(55) ~ 0.061 um/s. As there are 2 monomers per ~5.4 nm of filament, then each filament must grow by ~22.6 monomers/s to support this rate of movement. If we assume steady-state (no net growth of actin fibrils at the lamellipodium) this would entail hydrolysis of ~20 ATP per F-actin fibril per second (using an angle of 35 degrees as in ref  gives a slightly higher rate of elongation of ~30 monomers/s). Also, the steady-state assumption is pretty reasonable: if there was net growth of fibrils, we’d still be locking up ATP in actin, ATP which would eventually be hydrolyzed to free the actin monomers.
How many fibrils are required to support this movement? The lamellipodium of a goldfish keratocyte is roughly 20 um long (Figure 3 of ref ) and it is estimated that there are 100 actin filaments per micron of leading edge (0.1-0.2 um wide, see ref ). If the lamellipodium is the only part of the cell where locomotion-powering actin turnover takes place (a conservative assumption since there is a dense network of actin throughout the cell), then 100 x 20 x 22.6 = 45.2e3 ATP/s must be hydrolyzed to support a velocity of 0.05 um/s.
However, Theriot and Mitchison note in their 1991 paper that their measurements are inconsistent with an assumption that there is actin turnover only in the leading edge. Rather, when they injected fluorescent actin monomers into keratocytes, they observed that the signal from the fluorescent bar weakens continuously and at a roughly constant rate as it migrates away from the leading edge. This implies that there is actin turnover not just on the leading edge but throughout the lamellipodium (see Figure 2 below, reproduced from ref ). They note that the rate of turnover is roughly constant throughout the lamellipodium, which appears to be ~10 microns wide (Figure 2). If we assume that the actin network is equally dense throughout the lamellipodium (Figure 3 of ref ), then there are ~10 filaments per 0.1 square microns of lamellipodium and about 100 square microns of lamellipodium area total, implying 10 x 100 / 0.1 = 1e4 filaments in the lamellipodium. This gives an order-of-magnitude higher estimate for the ATP flux required to support a velocity of 0.05 um/s - 45.2e4 ATP/s.
As a sanity check, we can compare our estimates with those given by other studies. In refs [6,7] Miyoshi and Watanabe use speckle analysis results to estimate that actin filaments at the leading edge of Xenopus XTC fibroblasts must elongate at a rate of 66 monomers/s, which is only 2 to 3-fold more than our estimates above. In another study, Abraham et al. give an estimate of ~1500 um of F-actin per cubic micron of lamellipodia in fibroblasts migrating at 13.8 um/minute (0.23 um/s, about 5x the speed of the goldfish keratocytes). From this, they calculate that 23e3 actin monomers must assemble every second for every micron of leading edge. Using the same leading-edge length as above, this would imply the hydrolysis of ~20x23e3 = 46e4 ATP/s, which nearly identical to our higher estimate above (though supporting a 5x faster speed). The consonance of these independent estimates, which differ by much less than an order-of-magnitude, provides a modicum of confidence in our work.
Cytokinesis in S. pombe
Schizosaccharomyces pombe (S. pombe) is a popular model system for studying actin dynamics because it undergoes an actin-mediated symmetric fission event (cytokinesis) during cell division [2, 9]. Indeed, inhibition of actin polymerization by Latrunculin prevents mitotic cell division in S. pombe . Robert Pelham and Fred Chang measured the dynamics of the actin cytoskeleton during S. pombe cell division using fluorescent fusion proteins and found that F-actin in the contractile ring turns over complete in roughly 1 minute . Combining this observation with measurements of local F-actin concentrations in S. pombe during cytokinesis from ref , we can come to a reasonable estimate of the amount of ATP required to drive this beautiful process (here’s a video just for kicks).
Table 1 below gives local concentration and copy number measurements of actin and actin-related proteins taken in S. pombe during cytokinesis. These indicate that there are ~76e3 actin monomers congregating around the site of cell division. For simplicity, let’s assume that all of these monomers turn over every minute (i.e. during one turnover of the contractile ring). That is, they all attach to a filament and dissociate during a 1 minute window. This is perhaps a liberal estimate because it assumes that none of the G-actin monomers are held in reserve, but it will give an upper bound on the ATP expenditure associated with the contractile ring. In this case, S. pombe would need ~76e3 ATP/minute or ~1.2e3 ATP/s to drive cytokinesis.
Cytoskeletal Maintenance in S. Cerevisiae
Using Latrunculin inhibition, Ayscough and pals showed that ~95% of the F-actin in S. cerevisiae turns over within 1 minute and more than 99% turn over within 2 minutes (figure 1 of ref ). So let’s assume that all the cytosolic G-actin monomers in S. cerevisiae polymerize and depolymerize within 120 seconds so that we can upper-bound the amount of ATP hydrolysis required to sustain this turnover from the cytoplasmic G-actin concentration. The concentration of G-actin in S. cerevisiae is estimated to be ~12 uM . Given a cell volume of ~50 cubic um (characteristic of a haploid cell BNID 100430), this entails the turnover of 50e-15 liters x 12e-6 mol / liter x 6.02e23 molecules/mol = 3.6e5 actin monomers every 120 seconds. As such, S. cerevisiae must burn about 3e3 ATP/s to sustain it’s actin cytoskeleton. As DNA takes up a large fraction of the cellular volume, diploid S. cerevisiae cells are about 1.5 times as big as haploid cells (in volume; BNID 109473), which predicts a somewhat higher ATP requirement for diploids of 4.5e3 ATP/s.
Comet Tails of Listeria
In 1992, Julie Theriot and Tim Mitchison that Listeria zips around macrophages it infects at a rate of ~0.2 um/s by forming actin “comet-tails” (see Figure 3 of ). They also showed that the rate of movement is equal to the rate of actin polymerization by showing a correlation between the speed of bacterial movement and the length of the comet tail (as would be expected from a steady-state turnover of actin at the bacterial tail). It has since been shown in Matt Welch’s lab that Rickettsia performs a similar trick using two different mechanisms, one co-opting the Arp2/3 pathway and another co-opting formin-like actin nucleation .
Lisa Cameron and friends measured the density of F-actin on the surface of beads that could induce comet-tail like locomotion . They found that 12-35% of the bead surface was attached to actin filaments and that the speed of movement did not depend very much on the length of the tail. Listeria is a rod-shaped bacterium roughly 0.5 um wide (Figure 3 reproduced from ref  below). If we model the tail of a Listeria cell the as a half-sphere of radius 0.25 um, then the half-sphere has surface area 2 π r^2 = 0.39 um^2. If 35% of this area (0.13 square micrometers) has incident actin filaments (who have an area of at most 2x3.5 nm * 5.5nm = 35 square nm = 35e-6 square um), then ~3000 actin filaments will be incident to the tail end of the moving bacterium. If we assume that only these filaments are elongating (since the bacterium induces elongation using proteins on its surface) then Listeria must elongate 3000 filaments at a rate 0.2 um per second in the direction of movement to account for the observed comet-like movement.
Assuming, as above, that the filaments are incident to the cell at ~55 degrees on average (i.e. due to Arp2/3 branching), then each filament must grow at 0.2/sin(55) = 0.24 um/s or 90.3 monomers/s to support the observed rate of movement (0.2 um/s). So rocketing a single Listeria cell around a macrophage at 0.2 um/s requires 2.7e5 polymerizations/s, which (assuming steady state as before) implies hydrolysis of 2.7e5 ATP/s per Listeria cell.
Comparison to Cellular ATP Budget
It’s all well and good to estimate how much ATP it takes to maintain a certain rate of actin turnover. But how much ATP does the cell even have? The flux to ATP is most straightforward to estimate in cells where metabolic fluxes have been measured extensively, and S. cerevisiae is one such system. During aerobic growth on glucose, wild-type S. cerevisiae takes up 16 mmol glucose / (gDW h) . About 75% of these glucose molecules make it through glycolysis  and, thus, lead to the production of 2 x 16 x 0.75 = 24 mmol ATP / (gDW h). S. cerevisiae being a famous fermentor, only 12% of the glucose molecules makes it to the TCA cycle and less than 2% makes it all the way through . Presuming an intermediate value of roughly 7% and a standard ATP yield of roughly 25 ATP/glucose from the TCA cycle and oxidative phosphorylation gives 25 x 16 x 0.07 = 28 mmol ATP / (gDW h). So the total flux to ATP is roughly 42 mmol ATP / (gDW h) or ~12 umol ATP / (gDW s).
Assuming yeast has roughly the same density as E. coli, then the dry weight should scale with cell volume. Since cerevisiae is ~50x the size of E. coli (volumetrically) and a single E. coli cell has a dry mass of ~280 femtograms (BNID 100008), we estimate the per cell dry mass of S. cerevisiae at ~15 picograms. This gives a flux to ATP of ~ 12e-6 x 15e-12 x 6.02e23 = 1e8 ATP per cell per second.
We can calculate the flux to ATP in yeast in a different fashion to check ourselves (before we wreck ourselves). Verduyn et al. measured the yield of S. cerevisiae biomass per unit ATP in chemostat cultures . At a dilution rate of 0.3 (doubling-time of ~3.3 hours) the yield was ~ 10 g biomass / mol ATP (see Figure 1 of ref  reproduced as Figure 4 below). Using the same dry mass value as above, we calculate that there are 6.7e10 cells per gram of biomass and, therefore, it takes 1.5e-12 mol ATP = 9e11 ATP molecules to make a single S. cerevisiae cell at this somewhat lackluster doubling-time of 3.3 hours. So a single cell must make 9e11 ATP in 3.3 hours = 11880 seconds and so the ATP flux in single cells must be at least 7.6e7 ATP/s. Importantly, this estimate includes only the ATP flux that leads to the creation of biomass and excludes any ATP production associated with homeostasis, so it is, by necessity, an under-estimate. It may even be a gross under-estimate. But we take comfort in the fact that both our estimates are in the same order of magnitude.
Importantly, these estimates of ATP production flux are 3-5 orders of magnitude higher than our estimates of the ATP flux required to sustain the actin polymerization in S. cerevisiae (~3000 ATP/s), macrophages infected with listeria (~300,000 ATP/listeria cell/s), S. pombe and goldfish keratocytes (at most 50,000 ATP/s). Moreover, the other cells we considered - S. pombe, keratocytes and macrophages - are at least as large as S. cerevisiae (if not dramatically larger) and they primarily consume glucose aerobically through the TCA cycle. It stands to reason that they make at least as much ATP as S. cerevisiae, if not much more. Indeed, macrophages are ~100x the size of S. cerevisiae (BNID 103566) and larger cells have much more room for metabolic enzymes and mitochondria with which to generate ATP. But the absolute ATP fluxes we estimated for these actin-dependent processes all lie in the range of 1e3-1e5 ATP/s, several orders of magnitude less than the presumptive ATP production flux. Even in the case of Listeria, where multiple bacteria might infect the same macrophage, it would take the simultaneous infection of a macrophage by hundreds or thousands of bacteria for the ATP required by comet tails to reach the same order-of-magnitude as our most conservative estimate of ATP flux in S. cerevisiae (which remains ~100x smaller than a macrophage). So actin polymerization likely demands a negligible fraction (less than 1%) of cellular ATP production, even during very dramatic and dynamic actin-related processes like locomotion, cytokinesis and comet-like movement of infectious bacteria.
Table 1, from Wu & Pollard 2005. Concentrations of actin cytoskeletal proteins and proteins involved in spindle pole formation and cytokinesis. Measurements performed by calibrating fluorescence measurements of functional YFP fusions under the control of endogeonous promoters to results from quantitative immuno-blotting. Note that Act1p has a global concentration 1-2 orders of magnitude higher than all other proteins listed.
Figure 2: reproduced from Theriot and Mitchison, 1991. Shows the migration of injected bar of fluorescent actin and the intensity of fluorescence as a function of time.
Figure 3: EM of comet-tails on Listeria. Reproduced from Tilney & Portnoy, 1989.
Figure 4: Yield of cells per mol ATP formed. Measured as a function of dilution rate in chemostat cultures of S. cerevisiae.
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