Linear Motors. Nanostrukturphysik II, Manuel Bastuck

Transcription

1 Molecular l Motors I: Linear Motors Nanostrukturphysik II, Manuel Bastuck

2 Why can he run so fast? Usain Bolt 100 m / 9,58 s Usain Bolt: muscle: slide 2

3 Actin & Myosin muscle contraction transport of cell organelles myosin/actin: slide 3

4 Dynein, Kinesin & Microtubule microtubule to cell nucleus to cell membrane dynein kinesin flagella movement (dynein) transport of cell organelles slide 4

5 Mnemonic ( Eselsbrücke ) DNAH2 Kinesin-8 Kinesin-1 DNAL4 Kinesin-4 Myosin II Myosin V Myosin X slide 5

6 Example: Structure of Kinesin slide 6

7 Kinesin walking slide 7

8 Some famous names Langevin equation (overdamped) stochastic force, uncorrelated in time Fokker-Planck equation free diffusion slide 8

9 Directed motion why? Richard P. Feynman ( ) M. Smoluchowski ( ) Feynman: Smoluchowski: slide 9

10 Brownian ratchet Experimentally realized! T.R. Kelly, I. Tellitu, J.P. Sestelo, In search of molecular ratchets, Angew. Chem. Int. Ed. Engl. 36 (1997) T.R. Kelly, I. Tellitu, J.P. Sestelo,Angew. Chem. Int. Ed. Engl. 36 (1997) 1866 slide 10

11 Brownian ratchet (linear) U 0 x R. D. Vale and F. Oosawa, Adv. Biophys., Vol. 26, pp (1990) slide 11

12 Brownian ratchet ε energy to withdraw the pawl δf energy needed to raise weight without external load (F = 0) and at T 1 = T 2 : image: The Feynman Lectures on Physics, Vol. 1, ch. 46 slide 12

13 Brownian ratchet Otherwise, it would violate the 2 nd Law of Thermodynamics: No process is possible whose sole result is the absorption of heat from a reservoir and the conversion of this heat into work. Planck s formulation slide 13

14 Kramer s theory A more mathematical approach to obtain the same result: U 0 E a x slide 14

15 The solution: switched potential P(x,t>0) U 0 x slide 15

16 Conformational change by ATP adsorption of ATP alters protein structure protein binding sites don t see the filament potential switch-off ATP is catalysed to ADP + P, desorbs protein binding sites exposed to filament potential switch-on Planck s formulation slide 16

17 Model: Poisson stepper master equation (neglecting backwards steps): solution is Poisson distribution Prof. Dr. Ulrich Gerland, lecture Stochastic Processes, Uni München slide 17

18 Model: Poisson stepper Prof. Dr. Ulrich Gerland, lecture Stochastic Processes, Uni München slide 18

19 Experimental results Bormuth et al., SCIENCE 2009, doi /science / trap bead with kinesin with optical tweezers pull it over fixed microtubule deflection ~ force determination of maximum force, friction, step size, Bormuth et al., SCIENCE 2009, doi /science slide 19

20 Experimental results movement easier in plus-direction asymmetric potential ti speed limited by protein friction (i.e. rate of bond detachment) t) Bormuth et al., SCIENCE 2009, doi /science slide 20

21 Experimental results ntial poten position slide 21

22 Experimental results Kramer s theory / free diffusion: U 0 = 13 k B T random walk with step rates fit to speed-friction-curve: curve: Δ = 0.3 nm δ = 7.8 nm Bormuth et al., SCIENCE 2009, doi /science slide 22

23 Mechanisms of movement dynein kinesin myosin (both) image: Munárriz et al., Phys. Rev. E, 2008, doi /PhysRevE slide 23

24 Experimental evidence Yildiz et al., SCIENCE 2003, doi /science / tag one hand with dye (red) 0 nm detect alternating step sizes of 0 and 16.6 nm 16.6 nm kinesin step size known: 8.3 nm image: Munárriz et al., Phys. Rev. E, 2008, doi /PhysRevE Yildiz et al., SCIENCE 2003, doi /science slide 24

25 (More) Efficiency Munárriz et al., Phys. Rev. E, 2008, doi /PhysRevE /Ph kinesin s energy efficiency is 50% increase to almost 100% by shorter link probably instable in nature (chemical bonds) but possible for artificial i motors? Munárriz et al., Phys. Rev. E, 2008, doi /PhysRevE slide 25

26 And the winner is Usain Bolt 100 m / 9.58 s 1.95 m v = 5.4 m/s / m myosin 1.2 µm/s 150 nm v = 8 m/s / m slide 26

27 Thank you for your attention! slide 27