ATP hydrolysis 1 1 1

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1 ATP hydrolysis 1 1 1

2 ATP hydrolysis 2 2 2

3 The binding zipper 1 3 3

ATP hydrolysis/synthesis is coupled to a torque Yasuda, R., et al (1998). Cell 93:1117 1124.

4 ATP hydrolysis/synthesis is coupled to a torque Yasuda, R., et al (1998). Cell 93: Abrahams, et al (1994). Nature 370: Stock, Leslie, & Walker (1999) Science 286:1700. Wang & Oster (1998). Nature 369:

5 Which step of the hydrolysis cycle generates the force? ATP Hydrolysis cycle in solution: ATP Hydrolysis ADP +P i ATP Hydrolysis cycle at a catalytic site: ATP binding F + ATP F ATP 1 1 Product Hydrolysis release F ADP P 1 i F 1 + ADP + P i 5

6 The catalytic sites lie in the seam between the α and β subunits mostly in β, but with a critical residue in α TOP β SIDE γ α β α The nucleotide is held in the grip of loops emanating from the β- sheet 6 6

7 A hinge bending motion is associated with ATP binding Abrahams, et al (1994). Nature 370: Wang & Oster (1998). Nature 369:

8 The hinge bending motion is capable of driving the rotation of γ Wang & Oster (1998). Nature 369:

Binding transition is an efficient force generator (Binding zipper) Diffusion to catalytic site Binding Transition ( Zipper ) The binding rate k on [ATP] measures this

9 Binding transition is an efficient force generator (Binding zipper) Diffusion to catalytic site Binding Transition ( Zipper ) The binding rate k on [ATP] measures this step. Zipping up the hydrogen bonds generates force. This process is independent of [ATP]. ATP binding free energy is utilized gradually to generate a constant force. 9

10 The power stroke takes place as the P-loop slides over the nucleotide Stereo MD Corrected Interpolation Sun, Chandler, Dinner, & Oster (2003) 10 10

solvent lubricated sliding with: Matching surface geometries Solvent-solvent

11 The Binding Zipper principle Aqueous Solvent F MD Simulation Eide, Chakraborty, & Oster (2003) Binding Surface The best way to extract work from binding is a smooth, solvent lubricated sliding with: Matching surface geometries Solvent-solvent interaction solvent-enzyme which is how the P-Loop slides over ATP to generate the power stroke 11 11

ATP binding affinity of a conformation vs ATP binding affinity of a catalytic site Misconception: The ATP binding affinity of β E is too low. Therefore ATP binding cannot generate a significant force.

12 ATP binding affinity of a conformation vs ATP binding affinity of a catalytic site Misconception: The ATP binding affinity of β E is too low. Therefore ATP binding cannot generate a significant force. The affinity of the rest conformation of β E is low. If β E is fixed at its rest conformation, then the affinity of the site is low. ATP binding involves conformational changes. If β E is allowed to bend, then the ATP will proceed from weak binding to tight binding and drive the bending of β. 12

13 Hydrolysis releases products so that the cycle can repeat Breaking covalent bonds Binding is weakened and distributed over ADP and Pi ( H ~ 8.5 k B T) Hydrolysis breaks the γ covalent bond, distributing the binding over two products. Electrostatic repulsion weakens the binding of two products. 13

14 Summary of the binding zipper model The binding zipper transduces free energy gradually. In the hydrolysis cycle, ATP binding free energy is utilized efficiently to generate a constant force. Bonds form sequentially between ATP and catalytic site. Conformational change is coupled continuously to binding affinity. Hydrolysis resets the cycle. In the synthesis cycle, the force generated in the Fo is used to decrease gradually the binding affinity of newly formed ATP. Diffusion to catalytic site Binding Transition ( Zipper ) 14

15 Elastic Energy is stored in the curvature of the β-sheet ~ 6 kb T Free Energy computed from MD & the interpolated structures 15 15

16 The β-sheet is the elastic recoil element Primary Power Stroke Binding Zipper Recoil Stroke β-sheet Elastic recoil of the β-sheet Primary Power Stroke Recoil Power Stroke 16 16

The catalytic sites communicate via mechanical stress to coordinate the hydrolysis cycles helps product release from the next site Stress is

17 The catalytic sites communicate via mechanical stress to coordinate the hydrolysis cycles helps product release from the next site Stress is transmitted asymmetrically through the α-subunits & γ-shaft. Binding of ATP This results in a multisite enhancement of ~ 105 over the unisite rates! 17 17

attraction and brownian motion Flash an electric field to switch

18 Ion Driven Motors Bacterial Flagellar Motor: Driven by ion-triggered conformation change Fo motor of ATP Synthase: Driven by coulomb attraction and brownian motion Flash an electric field to switch protein conformation Flash an electric field to switch Coulomb attraction 18

19 ATP synthase is composed of two reversible motors Proton Turbine c 9-14 = rotor γ,ε = shaft Hydrolysis Motor α 3 β 3 = hexamer γ,ε = shaft a,b,δ = stator 19 19

20 The Na + F o ATPase MEMBRANE ROTOR STATOR Top F o c 11 a γ b Side c 11 F 1 α 3 β 3 Ion binding site δ Rotor 20 20

21 The Sodium Fo Motor Na+ Torque generating interface The flow of ions through the motor generates > 45 pn. nm of torque in the rotor-stator interface Balmooth, et. al. (2002), J. Biol. Chem, 277,

22 The total driving potential for the rotor has 4 components: Electrostatic + membrane potential + hydration + Steric Outlet Arg227 Front Side V Steric Hydration Coulomb Membrane Potential Xing, Wang, Dimroth & Oster (2004) 22 22

Operating principle of the F o motor Binds Na+ from

stator charge exit channel next site Occupied site

2 rotor sites inside the stator, both sites alternately

23 Operating principle of the F o motor Binds Na+ from Captured Loses by Na+ to Pushed out input by channel stator charge exit channel next site Occupied site enters stator hydration well Pull-push principle: With 2 rotor sites inside the stator, both sites alternately provide torque (high duty ratio). Including steric potential 23 23

24 The bacterial flagellar motor K. Namba 24 24

25 Torque ~ pn. nm Rotate ~ 1700 Hz D. Thomas, N. Francis, and D. DeRosier, unpublished 25 25

26 Structure of the motor Torque: ~ 4000 pn.nm; Speed: ~ 1700 Hz Lloyd et al. (1999) Nature 400: Blair (2003), FEBS Lett. 545: Braun, Blair (2001), Biochemistry 40:

The power stroke is driven by a conformational transition in the stator that is triggered by the protons hopping onto

27 Properties sufficient to fit the data The rotation of the motor is observed through a soft elastic linkage between the motor and the viscous load. Motor rotation and ion transport are tightly coupled: ~ 1 step/ion pair. The power stroke is driven by a conformational transition in the stator that is triggered by the protons hopping onto and off the stator charges. T. Pollard Cell Biology The ion channel through the stator is gated by the motion of the rotor. D. Goodsell 27 27

A model illustrating the operating principle The power stroke is driven by a conformational transition in the stator that is triggered by the protons hopping onto and off the MotB charges.

28 A model illustrating the operating principle The power stroke is driven by a conformational transition in the stator that is triggered by the protons hopping onto and off the MotB charges. Elastic coupling Tight coupling The stator is bistable D. Blair The rotation of the motor is observed through a soft elastic linkage between the motor and the viscous load. Motor rotation and ion transport are tightly coupled. The ion channel through the stator is gated by the motion of the rotor. 28

29 The stator power stroke Ion triggered conformational change in the stator drives the power stroke. Peptidoglycan Rotor-stator interaction has duty ratio ~ 1 Ion flux is tightly coupled to rotation Stator Inner Membrane Rotor Rotor-stator interaction is steric/electrostatic 29 29

Thermodynamic efficiency Efficiency A motor working against a conservative force: η TD = Rate of potential energy increase in the external agent Rate of energy consumption in motor system

30 Thermodynamic efficiency Efficiency A motor working against a conservative force: η TD = Rate of potential energy increase in the external agent Rate of energy consumption in motor system External agent Motor system Visscher, K., et al (1999) A laser trap has the same effect as a spring on the motor. η TD = If tightly coupled f v ( ΔG) r, ƒ = cont. v = L r, η TD = f L ΔG Step size ( ) 30

, et al (1994) η Stokes = ζ v 2 ( ΔG) r If tightly coupled

31 Stokes efficiency A motor working against a viscous drag: Yasuda, R., et al (1998) The Stokes efficiency: Hunt, A., et al (1994) η Stokes = ζ v 2 ( ΔG) r If tightly coupled v = L r, η Stokes = ζ v L ΔG ( ) Question: η Stokes 100%? 31

32 Stokes efficiency vs thermodynamic efficiency ψ B and ψ C : High thermodynamic efficiency High Stokes efficiency ψ A : High thermodynamic efficiency Low Stokes efficiency A special case of ψ A : ΔG v 2D L η Stokes = ζ v L ΔG ( ) 0 At stall, η TD = 100% 32

33 What does a high efficiency tell us about the motor mechanism? High thermodynamic efficiency the motor is tightly coupled near stall. High Stokes efficiency the driving potential has a nearly constant slope. 33

ATP synthase: two motors, two fuels George Oster* and Hongyun Wang

Minireview R67 ATP synthase: two motors, two fuels George Oster* and Hongyun Wang F o F 1 ATPase is the universal protein responsible for ATP synthesis. The enzyme comprises two reversible rotary motors: