Molecular l Motors I: Linear Motors Nanostrukturphysik II, Manuel Bastuck
Why can he run so fast? Usain Bolt 100 m / 9,58 s Usain Bolt: http://www.wallpaperdev.com/stock/fantesty-usain-bolt.jpg muscle: http://www.apotheken-umschau.de/multimedia/106/134/108/70463676433.jpg slide 2
Actin & Myosin muscle contraction transport of cell organelles myosin/actin: http://www.embl.de/~guenther/project_muscleoscillations.html slide 3
Dynein, Kinesin & Microtubule microtubule to cell nucleus to cell membrane dynein kinesin flagella movement (dynein) transport of cell organelles http://drugline.org/img/term/microtubule-motor-protein-9586_1.jpg slide 4
Mnemonic ( Eselsbrücke ) DNAH2 Kinesin-8 Kinesin-1 DNAL4 Kinesin-4 Myosin II Myosin V Myosin X slide 5
Example: Structure of Kinesin http://www.uic.edu/classes/bios/bios100/summer2006/kinesin.jpg slide 6
Kinesin walking http://www.youtube.com/watch?v=y-uuk4pr2i8 slide 7
Some famous names Langevin equation (overdamped) stochastic force, uncorrelated in time Fokker-Planck equation free diffusion slide 8
Directed motion why? Richard P. Feynman (1918-1988) M. Smoluchowski (1872-1917) Feynman: http://www.aps.org/publications/apsnews/201305/images/feynman-web.jpg Smoluchowski: http://www.cyfronet.krakow.pl/~ncadamcz/smolucho.jpg slide 9
Brownian ratchet Experimentally realized! T.R. Kelly, I. Tellitu, J.P. Sestelo, In search of molecular ratchets, Angew. Chem. Int. Ed. Engl. 36 (1997) 1866 http://www.manuel-strehl.de/thesis/thesis.xhtml T.R. Kelly, I. Tellitu, J.P. Sestelo,Angew. Chem. Int. Ed. Engl. 36 (1997) 1866 slide 10
Brownian ratchet (linear) U 0 x R. D. Vale and F. Oosawa, Adv. Biophys., Vol. 26, pp. 97-134 (1990) slide 11
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: http://www.manuel-strehl.de/thesis/thesis.xhtml The Feynman Lectures on Physics, Vol. 1, ch. 46 slide 12
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
Kramer s theory A more mathematical approach to obtain the same result: U 0 E a x http://www.uni-ulm.de/fileadmin/website_uni_ulm/nawi.inst.251/lehre/tapc/kramers.pdf slide 14
The solution: switched potential P(x,t>0) U 0 x slide 15
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
Model: Poisson stepper master equation (neglecting backwards steps): solution is Poisson distribution Prof. Dr. Ulrich Gerland, lecture Stochastic Processes, Uni München slide 17
Model: Poisson stepper Prof. Dr. Ulrich Gerland, lecture Stochastic Processes, Uni München slide 18
Experimental results Bormuth et al., SCIENCE 2009, doi. 10.1126/science.11749231126/ 1174923 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. 10.1126/science.1174923 slide 19
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. 10.1126/science.1174923 slide 20
Experimental results ntial poten position slide 21
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. 10.1126/science.1174923 slide 22
Mechanisms of movement dynein kinesin myosin (both) image: Munárriz et al., Phys. Rev. E, 2008, doi. 10.1103/PhysRevE.77.031915 slide 23
Experimental evidence Yildiz et al., SCIENCE 2003, doi. 10.1126/science.10937531126/ 1093753 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. 10.1103/PhysRevE.77.031915 Yildiz et al., SCIENCE 2003, doi. 10.1126/science.1093753 slide 24
(More) Efficiency Munárriz et al., Phys. Rev. E, 2008, doi. 10.1103/PhysRevE.77.0319151103/Ph 031915 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. 10.1103/PhysRevE.77.031915 slide 25
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
Thank you for your attention! slide 27