ATP Synthase F1

F-ATPase 3.6.1.34 A review of: “Stepping rotation of F1-ATPase visualized through angle-resolved single-fluorophore imaging” By Adachi, et al.

Cory Camasta

From Glucose to Gold (Biologically) From here on, we will have to make some lofty assumptions. The first of many is that we can get 3 ATP/NADH and 2 ATP/FADH2. Those are generally considered to be valid assumptions, but they may be high-ball estimates.

16e-

8

2

4e-

2

H+ 2 2

H+

Tri-Carboxylic Acid Cycle

Glycolysis

10 2 10 2

2

20e-

Net Gain: ~36 ATP/Glucose

Respiratory Chain H+

~32

Lesson of the Day: Question Everything!

[ATP] ~ 1 mM [ADP] ~ 10 μM [Pi] ~ 1 mM ΔG’° ~ -32.5 kJ/mole T = 37 C = 310 K

• Assuming we can get a maximum of 36 ATP/Glucose and provided concentrations in reference 1 (above) are somewhat close to real concentrations in mitochondria, we can calculate the phosphorylation potential: ΔGp = ΔG’° + RT × ln(Q) ΔGp ≈ -32.5 kJ/mol + (8.314 J/(K mol))(310 K) × ln([10μM][1mM]/[1mM]) ΔGp ≈ -32.5 – 29.7 = -62.2 kJ/mole Molar mass of glucose ≈ 6(12.01 g/mol C) + 12(1.01 g/mol H) + 6(16.00 g/mol O) = 180.18 g/mole So, theoretically… (omitting intermediate units for brevity)

Bioenergy per 1 gram of glucose ≈ 36 × (62.2/180.18) ≈ 12.4 kJ/gram ≈ 3.0 kcal/gram • The calculated number does not reasonably match the conventional value on our food labels (≲4 kcal/gram of sugar), and using the numbers from reference 1 gives a slightly more reasonable (?) value than using numbers extracted from a more recent textbook, reference 2 (~2.5 kcal/gram), but both use numbers taken from some other textbook that was published in the 70’s anyway. Whatever the case, when thinking critically about the free energy equation, one may notice that the energy we can obtain from the hydrolysis of ATP actually largely depends on the intercellular concentrations of all relevant species, which fluctuate faster than we can comprehend and are also extremely difficult to calculate simultaneously. One thing we can say for sure is that everything is relative. • Note that the reaction quotient, Q, does not appear unitless because, in a real experiment, we would have to measure the activities of each species rather than simply their concentrations. Activity is a unitless “effective concentration” that reflects non-ideality. The equation also lacks a term(s) for magnesium, which is usually chelated to ATP and thus likely plays a large role in the process. In the spirit of this slide: Why are textbooks so expensive? 1 2

Johnathon Howard. Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Inc., Sunderland, MA. (2001) David Nelson, Michael Cox. Principles of Biochemistry, Fifth Edition. W.H. Freeman and Company, New York, NY. (2008)

ATPase – Involution at its Finest

C-ring

• In most organisms, ATPase is used to generate ATP from ADP and Pi.

Fo

• The passive force that drives ATP synthesis is usually a transmembrane proton gradient, but other ions (Na+, K+, etc.) are also employed. • Protons diffuse through outer-membrane portion of a and bond to conserved glutamate in the c-ring. Brownian ratchet rotation of the c-ring rotates the γ-stalk by side-chain interactions (likely with ε) while depositing protons through the inner-membrane portion of a.1,2 Deprotonated Lewis residue forces rotation in one direction due to its charge.2

ε γ

• γ-stalk rubs against β-subunits as it rotates in order to induce conformational changes necessary to open and close the ATP/ADP binding pocket. • In bacteria that do not have aerobic respiration machinery to generate the acidic transmembrane space, the reaction is reversed and hydrolysis of ATP fuels active proton transport against the concentration gradient, often resulting in flagellar motion.3

F1

• The image at right is a picture of the whole complex, obtained from cryo-EM Bos taurus imaging of an Escherichia coli cell expressing Bos taurus ATPase. ATP-synthase • α-subunits also bind ATP, but are not catalytically-active. 1

George Oster, Hongyun Wang. “ATP synthase: two motors, two fuels”, Structure, 7, R67-R72. (1999) Anna Zhou, et al. “Structure and conformational states of the bovine mitochondrial ATP synthase by cryo-EM”, eLife. (2015) 3 Boris A. Feniouk. “ATP synthase – a splendid molecular machine”. Available from: www.atpsynthase.info. (2012) 2

a

complex 5ARA Image credit2

PDB ID: 5ARA (and others)

α β δ

b

H2O β - Lys α - Arg β - Arg

Mg Jan Pieter Abrahams, et al. “Structure at 2.8 Å of F1-ATPase from bovine heart mitochondria”, Nature, 370, 621-628. (1994)

PDB ID: 1BMF

Hydrolysis Coordinate

Image credit1

• Free-energy diagram at right shows the energy state as a function of rotation during the (reverse) hydrolysis reaction in units of kBT. • Opening the catalytic pocket is the rate-limiting step in both binding and release. • The “switches” are at points in the rotation where γ unfavorably interacts with β. • Kinetic barriers (not to scale) are decreased by conformational changes in β upon passing the switch gate that facilitate rate-limiting steps. • Though α is usually regarded as being non-catalytic, the binding pocket is located at the interface between α and β, thus residues from both subunits may participate, whether directly or not, in the reaction. • Another (somewhat) unique feature of ATPase is hydrogen bonding of amide H’s to the substrate. 1

George Oster, Hongyun Wang. “ATP synthase: two motors, two fuels”, Structure, 7, R67-R72. (1999)

Step One: Mutation • Obtained F1-ATPase from Bacillus (sp.) PS3 strain

• Since ATPase wasn’t designed by a lab technician for use in experiments, modifications are necessary in order to tailor the protein for query. The final modifications are indicated below:

• α(Cys193→Ser)3 Similar properties, doesn’t bond to maleimide

• β(N-terminal His10)3 Used to attach the protein to glass surface

• γ(Iso210→Cys) Bonds to maleimide 1

Gibbons C, et al., “The structure of the central stalk in bovine F(1)-ATPase at 2.4 Å resolution”, Nat. Struct. Biol., 7(11), 1055-1061. (2000)

Picture:1 Bos taurus F1-ATPase, PDB ID: 1E79

Fluorophore Tethering • Cyanine 3 (Cy3)-maleimide covalently attached to mutant γ cysteine (210) through electrophilic maleimide tail.1 • Anisotropy measurements indicate that the Cy3 “wobble” was within a cone of semiangle < 25°. • Since Cy3 was attached opposite the surface tethers, on the empty Fo side of F1, it theoretically should not obstruct anything as it wobbles. Error check: • Extinction coefficients at 555 and 280 nm were extracted from older literature rather than calculated de novo, thus concentration data may be slightly inaccurate.

Photophillic conjugated π-system

Maleimide tether 1

Wikipedia. “Maleimide”, Wikimedia Foundation, Inc. (Accessed 10/2015)

Partial geometry optimization @ B3LYP/3-21+G*

F1-ATPase Surface Tethering • Ni(II)-Nitrilotriacetic acid (NTA) covalently attached to glass surface • F1-ATPase tethered to nickel by modified His10 N-termi on β • Only a small portion of F1-ATPase remained attached for the duration of the experiment, but it was enough to collect results. • May be due to short His tag or (probably) pre-wash with imidazole At right: One distorted octahedral nickel site in a roughly optimized conformation (RPM6/ZDO)

Ni(II)

ATPase Activity • Kinetics probed with a Malachite Green Pi assay in 2mM [ATP]. • Product solution absorbance @ 650 nm (for Malachite Green complex) was approximately proportional to reaction time after 10 minutes, indicating that a steady-state was reached. • Obtained first-order rate constant for steady-state ATP hydrolysis of 19 s-1 with Cy3-F1 tethered to glass surface; about 30% of free solution rate (67 s-1). Initial free solution rate constant was 239 s-1.

• Less than 10% of surface molecules are expected to be active. • Relatively low activity could be due to unnatural tethering by the opposite end – sufficiently far from the active site or no?

• In addition, the His10 tail could have favorable intermolecular attractions that compete with chelation to Ni(II)-NTA surface. • The viscous drag force is also greater near the surface.

3x

Perspective: (almost to scale, tethers not optimized) Bos taurus F1-ATPase, PDB ID: 1E79

Results: ATPase Activity • • • • • • • •

Large symbol = ensemble average Small symbol = single-molecule measurement Blue = hydrolysis rate Green = step rate Red = rotation rate Black = previously measured rotation rates with actin and streptavidin linker1

Apparent drop in rate at high [ATP] could be due to limited temporal resolution. Hydrolysis rate (in turnovers/second) was fit to the following second-order Michaelis-Menten-like equation:

𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = For independent variables:

𝑘𝑐𝑎𝑡𝑎𝐾𝑀𝑏 𝐴𝑇𝑃 + 𝑘𝑐𝑎𝑡𝑏 𝐴𝑇𝑃 2 𝐴𝑇𝑃 2 + 𝐾𝑀𝑏 𝐴𝑇𝑃 + 𝐾𝑀𝑎𝐾𝑀𝑏 𝐾𝑀 =

𝑘𝑑 + 𝑘𝑐𝑎𝑡 𝑘𝑏

Error check: • Why are the stepping and rotation rates the same at the first sample concentration? 1

𝑘𝑐𝑎𝑡𝑎 = 89 s-1 𝑘𝑐𝑎𝑡𝑏 = 292 s-1 𝐾𝑀𝑎 = 6.3 μM 𝐾𝑀𝑏 = 680 μM

Ryohei Yasuda, et al. “F1-ATPase Is a Highly Efficient Molecular Motor that Rotates with Discreet 120° Steps”, Cell, 93, 1117-1124. (1998)

Feed Me Chemistry! • In the ATPase and rotation assays, different enzyme-substrate systems were formulated to fill different in vitro niches. Relevant reactions in the rotation assay are shown at left and in the activity assay at right.

Methods – Rotation and Fluorescence Assays • • • • • •

532 nm green laser attached to an inverted IX70 epifluorescence microscope. Laser was circularly polarized by a quarter-wave plate. Rotating sheet polarizer inserted after the QWP in order to rotate the excitation polarization. Fluorescence collected through oil-immersion objective lens, then amplified and sent to CCD. Images captured on Hi8 camcorder and analyzed on a computer. Data collected at 23±1°C. Results are based upon the fact that only incident photons with Ē coplanar to a molecule’s transition dipole(s) are absorbed; the rest of the light is reflected, refracted, or transmitted. • Orientations of individual fluorophores were assessed by two methods: i. ii.

Absorption efficiency of polarized excitation (rotation) Polarization of emitted fluorescence (fluorescence) Image Credit1

1

Douglas Murphy, Kenneth Spring, Michael Davidson. “Introduction to Polarized Light”, Available from: http://www.microscopyu.com/articles/polarized/polarizedlightintro.html. (Accessed 10/2015)

Fluorescence Anisotropy • Anisotropy and polarization are essentially analogous, the difference being that anisotropy takes the other perpendicular axis into account (the 2 in the denominator), thus the value is always less than or equal to that of the polarization.1 • Cy3 was chosen as the fluorophore because its covalent attachment to F1 resulted in the highest fluorescence anisotropy, calculated by: 𝑟=

𝐼 ∥−𝐼 ⊥ 𝐼 ∥ + 2𝐼 ⊥

• The equation returned a value of 0.32 for the Cy3-labeled F1, which is among the highest values that experimenters hope for. • Cy3 absorbs the most light at around 550 nm λ and emits at 590 nm. Though the actual λ fall into continua, analysis is easier when only one value, near the peak, is selected. 1

TRACES. “Anisotropy”, AnalyzingIT Inc., Available from: http://www.utsc.utoronto.ca/~traceslab/FLD_Anisotropy.pdf. (Accessed 10/2015)

Mathematics • Malus’ Law states that the observed amplitude of the electric field wave of plane-polarized light is proportional to the cosine of the angle between the polarizer and analyzer axes.1 Since one typically measures intensity:

𝐼(𝜃) = 𝐼0 cos 2 𝜃 which is equivalent to:

1 1 𝐼(𝜃) = 𝐼0 ( + cos 2𝜃) 2 2 • Thus the researchers fit the observed intensity to:

360° × 2𝑡 𝐼(𝑡) ∝ cos( − 2𝜃0) 𝑇 in order to obtain 𝜃 (𝑡), the angular coordinate of γ as a function of time.

• Notice that the plot of the calculated intensity (black) matches the phase of the Malus curve (red) about 1/3 of the time, in support of 120° phase shifts. 1 Physics

Handbook.com. “Malus’s Law”. Available from: http://www.physicshandbook.com/laws/maluslaw.htm. (accessed 10/2015)

𝐼 𝜃 = Observed intensity ∝ E2 (magnitude) 𝐼(𝑡) = Relative observed intensity 𝐼0 = Incident light intensity 𝑇 = Period of excitation rotation (1s) 𝜃0 = Initial angular position

Results: Rotation Assay

1.7 x 1.7 μm2

In this assay, the excitation was circularly polarized and rotated at 1 revolution/sec. • •

•

• •

A: Fluorescence of active F1 B: Fluorescence of inactive F1 • Time-lapse images collected at 33 ms/frame intervals C: Integrated intensity plotted and overlain on a Malus curve (above); relative calculated fluorophore orientation and revolutions (below) D: Revolution plots for different fluorophores, all assayed at the same [ATP] ~ 20 nm E: Histogram of apparent dwell times, fit to an exponential: 𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟𝑠 = 𝑒 −𝑘𝑜𝑛 ATP 𝑡

For:

𝑘𝑜𝑛 = 3.1×107 M-1s-1 @ [20 nM]

t = 2 seconds

Switching Gears

Image Credit1

Image Credit2

• In fluorescence assays, the rotating sheet polarizer was removed from the microscope, resulting in incident light that was then only subjected to a QWP, or circular polarization filter. • When the QWP retards linearly polarized light by circularly polarized and left-handed.

𝜋 exactly 2

radians, the resulting light is

• When the phase difference between the slow and fast components is not a multiple of light exiting the wave-plate is elliptically-polarized.

𝜋 , 2

• Emitted fluorescence was decomposed into its vertical and horizontal components by the CCD for further analysis. 1 2

Douglas Murphy, Kenneth Spring, Michael Davidson. “Introduction to Polarized Light”, Available from: http://www.microscopyu.com/articles/polarized/polarizedlightintro.html. (Accessed 10/2015) Tino L. Riethmüller. “Investigations of small-scale magnetic features on the solar surface”, Dissertation, Technischen Universität Carolo-Wilhelmina zu Braunschweig. (2013)

Results: Fluorescence Assay • A: Time-lapse images spaced at 167 ms intervals of vertically (V) and horizontally (H) polarized fluorescence • B: Intensity plot for V (red) and H (black) polarized fluorescence – points were derived from image integration, median-filtered over 8 video frames (0.27 s) • C: Plots of polarization (blue) and total intensity (green) • Data indicates that the molecule in this dataset photobleached at t ~ 55 seconds. 𝑃=

𝐼𝑉− 𝐼𝐻 𝐼𝑉+ 𝐼𝐻

𝐼tot = 𝐼𝑉 + 𝐼𝐻

• The blue dotted lines are given by: 𝑃 = 0.4 × [sin2 𝜃 + 18° − cos2 𝜃 + 18° ] evaluated at the three orientations of Cy3 shown in D, for 𝜃 = 0°, 120° and 240° in a, b and c, respectively.

1.5 x 1.5 μm2

Results: Fluorescence vs. Concentration • A: Polarization (blue) and total intensity (green) plotted over time, until Cy3 photobleached, for three different ATP concentrations – complete rotations indicated by vertical red lines • B: Calculated full-rotation timelapse histograms for each [ATP] with exponential fits according to: 𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟𝑠 = 𝑡2𝑒 −𝑘𝑜𝑛 ATP 𝑡 For: 𝑘𝑜𝑛 = 1.9×107 M-1s-1 @ [200 nM] 𝑘𝑜𝑛 = 2.3×107 M-1s-1 @ [60 nM] 𝑘𝑜𝑛 = 2.9×107 M-1s-1 @ [20 nM]

Discussion • One notices that the rate is largely dependent on the choice of the fluorescent tag, meaning that either the “no-load” estimation could be slightly inaccurate or (more likely) the mechanism is just that stochastic, especially when the proton pump is decoupled. • The fluorescent areas analyzed were much larger than the size of the F1 complex, thus we also must consider the possibility that multiple complexes were analyzed per fluorescent spot. Given the total number of spots observed (59,149), we assume that the researchers picked 76 good ones. • Future experiments may yield better results by taking advantage of electron-beam lithography and/or nucleic acid tethering to construct a more adequate reaction vessel. • Also worth noting is that the measurement was obtained from one modified ATPase that is meant to represent a collection of species’ protein products. • Recent experiments have found evidence for substeps that add up to the full 120° step size, providing evidence for choreographed intermediate steps in the reaction (i.e. explicit hydrolysis/condensation, phosphate binding/release).

• Commercial sources of Malachite Green reagent suggest that 620 nm is the absorbance peak,1 as opposed to 650 nm, as mentioned in the text. This could have offset the rate constant of steady-state ATP hydrolysis, but not hugely. The product, as available from Iantron Labratories, could not be found with a quick internet search. 1

Eschelon, Inc. Available from: https://echelon-inc.com/index.php?module=Products&func=view&category_id=10058. (Accessed 11/2015)

Conclusions • The average concentration of ATP in an E. coli cell was recently measured using FRET biosensors at around 1.54±1.22 mM.1 • Given that these ballpark results apply to all or most ATPases (and that the modifications had no effect on their fidelity – an okay assumption), the data presented suggests that the in vivo single-molecule hydrolysis rate is on the order of 10 ATP/sec. • Data obtained in this study once again elucidates the stochastic nature of nanoscale chemistry; none of it appears to be periodic. • However, as usual, the distribution can still be fit to an exponential curve, thus providing more evidence that Euler’s number is God.

𝓮 = (1 + 1

Hideyuki Yaginuma, et al., “Diversity in ATP concentrations in a single bacterial cell population revealed by single-cell imaging”, Sci Rep., 4 : 6522, 1-7. (2014)

1 ∞ ) ∞

Global References & Acknowledgements • Kengo Adachi, et al. “Stepping of F1-ATPase visualized through angle-resolved single-fluorophore imaging”, PNAS, 97(13), 7243-7247. (2000)

•

ACD/Structure Elucidator, Freeware Version, Advanced Chemistry Development, Inc., Toronto, ON, Canada, www.acdlabs.com. (2015)

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Swiss Institute of Bioinformatics. Available from: http://www.expasy.org/. (Accessed 2015)

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