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Brownian(Mo*On( Brownian(Mo*on( Reem(Mokhtar( What(is(a(Ratchet?( A(device(that(allows(a(sha9(to(turn(only(one(way( hLp://www.hpcgears.com/products/ratchets_pawls.htm( Feynman,(R.(P.,(Leighton,(R.(B.,(&(Sands,(M.(L.((1965).(The$Feynman$Lectures$on$Physics:$ Mechanics,$radia7on,$and$heat((Vol.(1).(AddisonKWesley.( Thermodynamics( 2nd(law,(by(Sadi(Carnot(in(1824.( ( • Zeroth:(If(two(systems(are(in(thermal(equilibrium(with( a(third(system,(they(must(be(in(thermal(equilibrium( with(each(other.(( • First:(Heat(and(work(are(forms(of(energy(transfer.( • Second:(The(entropy(of(any(isolated(system(not(in( thermal(equilibrium(almost(always(increases.( • Third:(The(entropy(of(a(system(approaches(a(constant( value(as(the(temperature(approaches(zero.( ( hLp://en.wikipedia.org/wiki/Laws_of_thermodynamics( Why(is(there(a(maximum(amount(of(work( that(can(be(extracted(from(a(heat(engine?( • Why(is(there(a(maximum(amount(of(work(that( can(be(extracted(from(a(heat(engine?( • Carnot’s(theorem:(heat(cannot(be(converted( to(work(cyclically,(if(everything(is(at(the(same( temperature(!(Let’s(try(to(negate(that.( The(Ratchet(As(An(Engine( Ratchet,(pawl(and(spring.( The(Ratchet(As(An(Engine( Forward rotation Backward rotation ε energy to lift the pawl ε energy to lift the pawl ε Lθ work done on load θ ε + Lθ energy to rotate wheel θ Lθ work provided by load by one tooth f 1 L / − −(ε+ θ ) τ1 ε + Lθ energy given to vane L fB = Z e Boltzmann factor for work provided by vane b −1 −ε /τ2 f fB = Z e Boltzmann factor for ν fB ratching rate with ν T2 T2 attempt frequency tooth slip ν f b slip rate with f fL power delivered B ν B θ attempt frequency ν ε energy provided to ratchet T1 T1 Equilibrium and reversibility Ratchet Brownian motor b f ε+ Lθ ε ratching rate = slip rate f f τ1 − − B = B f b Leq θε= −1 τ1 τ2 Angular velocity of ratchet: Ω =θν (fB − fB )= θν e − e τ 2 Reversible process by increasing the ε ε load infinitesimally from equilibrium − − ΩL=0 →θν e τ1 − e τ 2 Leq. This forces a rotation leading to Without load: heating of reservoir 1 with τ2 ε Lθ dq1=ε+Leq ? and cooling of − − Ω(L)τ1=τ 2=τ→θν e τ e τ −1 reservoir 2 as dq2=−ε: Equal temperatures: L dq1 ε + eq θ τ1 = = τ1 − dq 2 ε τ 2 τ Ω 1 rectification dq dq 12dS dS 0 +=+=12 L ττ12 τ isentropic process 2 Escherichia coli ATP synthase H. Wang and G. Oster (Nature 396:279-282 1998) 2 Forward rotation Backward rotation ε energy to lift the pawl ε energy to lift the pawl ε Lθ work done on load θ ε + Lθ energy to rotate wheel θ Lθ work provided by load by one tooth f 1 L / − −(ε+ θ ) τ1 ε + Lθ energy given to vane L fB = Z e Boltzmann factor for work provided by vane b −1 −ε /τ2 f fB = Z e Boltzmann factor for ν fB ratching rate with ν T2 T2 attempt frequency tooth slip ν f b slip rate with f fL power delivered B ν B θ attempt frequency ν ε energy provided to ratchet T1 T1 Equilibrium and reversibility Ratchet Brownian motor b f ε+ Lθ ε ratching rate = slip rate f f τ1 − − B = B f b Leq θε= −1 τ1 τ2 Angular velocity of ratchet: Ω =θν (fB − fB )= θν e − e τ 2 Reversible process by increasing the ε ε load infinitesimally from equilibrium − − ΩL=0 →θν e τ1 − e τ 2 Leq. This forces a rotation leading to Without load: heating of reservoir 1 with τ2 ε Lθ dq1=ε+Leq ? and cooling of − − Ω(L)τ1=τ 2=τ→θν e τ e τ −1 reservoir 2 as dq2=−ε: Equal temperatures: L dq1 ε + eq θ τ1 = = τ1 − dq 2 ε τ 2 τ Ω 1 rectification dq dq 12dS dS 0 +=+=12 L ττ12 τ isentropic process 2 Escherichia coli ATP synthase H. Wang and G. Oster (Nature 396:279-282 1998) 2 Forward rotation Backward rotation energy to lift the pawl ε ε energy to lift the pawl ε Lθ work done on load θ ε + Lθ energy to rotate wheel θ Lθ work provided by load by one tooth f 1 L / − −(ε+ θ ) τ1 ε + Lθ energy given to vane L fB = Z e Boltzmann factor for work provided by vane b −1 −ε /τ2 f fB = Z e Boltzmann factor for ν fB ratching rate with ν T2 T2 attempt frequency tooth slip ν f b slip rate with f fL power delivered B ν B θ attempt frequency ν ε energy provided to ratchet T1 T1 Equilibrium and reversibility Ratchet Brownian motor b f ε+ Lθ ε ratching rate = slip rate f f τ1 − − B = B f b Leq θε= −1 τ1 τ2 Angular velocity of ratchet: Ω =θν (fB − fB )= θν e − e τ 2 Reversible process by increasing the ε ε load infinitesimally from equilibrium − − ΩL=0 →θν e τ1 − e τ 2 Leq. This forces a rotation leading to Without load: heating of reservoir 1 with τ2 ε Lθ dq1=ε+Leq ? and cooling of − − Ω(L)τ1=τ 2=τ→θν e τ e τ −1 reservoir 2 as dq2=−ε: Equal temperatures: L dq1 ε + eq θ τ1 = = τ1 − dq 2 ε τ 2 τ Ω 1 rectification dq dq 12dS dS 0 +=+=12 L ττ12 τ isentropic process 2 Escherichia coli ATP synthase H. Wang and G. Oster (Nature 396:279-282 1998) 2 Forward rotation Backward rotation energy to lift the pawl ε ε energy to lift the pawl ε Lθ work done on load θ ε + Lθ energy to rotate wheel θ Lθ work provided by load by one tooth f 1 L / − −(ε+ θ ) τ1 ε + Lθ energy given to vane L fB = Z e Boltzmann factor for work provided by vane b −1 −ε /τ2 f fB = Z e Boltzmann factor for ν f ratching rate with ν T2 T2 B tooth slip attempt frequency ν f b slip rate with f fL power delivered B ν B θ attempt frequency ν ε energy provided to ratchet T1 T1 Equilibrium and reversibility Ratchet Brownian motor b f ε+ Lθ ε ratching rate = slip rate f f τ1 − − B = B f b Leq θε= −1 τ1 τ2 Angular velocity of ratchet: Ω =θν (fB − fB )= θν e − e τ 2 Reversible process by increasing the ε ε load infinitesimally from equilibrium − − ΩL=0 →θν e τ1 − e τ 2 Leq. This forces a rotation leading to Without load: heating of reservoir 1 with τ2 ε Lθ dq1=ε+Leq ? and cooling of − − Ω(L)τ1=τ 2=τ→θν e τ e τ −1 reservoir 2 as dq2=−ε: Equal temperatures: L dq1 ε + eq θ τ1 = = τ1 − dq 2 ε τ 2 τ Ω 1 rectification dq dq 12dS dS 0 +=+=12 L ττ12 τ isentropic process 2 Escherichia coli ATP synthase H. Wang and G. Oster (Nature 396:279-282 1998) 2 ATP synthase, H. Wang and G. Oster (Nature 396, 279, 1998) Myosin Muscle myosin is a dimerof two identical motor heads that are anchored to the thick filament (top) by a coiled-coil (gray rod extending to the upper right). The helicalactin filament is shown at the bottom (gray). Myosin's catalytic core is blue and its mechanical elements (converter, lever arm helix and surrounding light chains) are colored yellow or red. In the beginning of the movie, the myosin heads are in the prestroke ADP-Pi state (yellow) and the catalytic cores bind weakly to actin . Once a head docks properly onto an actinsubunit (green), phosphate (Pi) is released from the active site. Phosphate release increases the affinity of the myosin head for actin and swings the converter/lever arm to the poststroke, ADP state (transition from yellow to red). The swing of the lever arm moves theactin filament by ~100 Å the exact distance may vary from cycle to cycle depending upon the initial prestroke binding configuration of the myosin onactin . After completing the stroke, ADP dissociates and ATP binds to the empty active site, which causes the catalytic core to detach from actin. The lever arm thenrecocks back to its prestroke state (transition from red to yellow). The surface features of the myosin head and the actin filament were rendered from X-ray crystal structures by Graham Johnson (fiVth media: www.fiVth.com) using the programs MolView, Strata Studio Pro and Cinema 4D. PDB files used were ADP-AlF4-smooth muscle myosin (prestroke, yellow: #1BR2) and nucleotide-free chicken skeletal myosin (poststroke, red: #2MYS). Transitions between myosin crystal structure states were performed by computer coordinated extrapolations between the knownprestroke and poststrokepositions. http://www.sciencemag.org/feature/data/1049155.shl Kinesin Molecular gears The two heads of the kinesindimer work in a coordinated manner to move processivelyalong the microtubule. The catalytic core (blue) is bound to a tubulinheterodimer (green, b-subunit; white, a-subunit) along a microtubule protofilament (the cylindrical microtubule is composed of 13 protofilament tracks). In solution, both kinesinheads contain ADP in the active site (ADP release is rate-limiting in the absence of microtubules). The chaotic motion of the kinesinmolecule reflects Brownian motion. One kinesinhead makes an initial weak binding interaction with the microtubule and then rearranges to engage in a tight binding interaction. Only one kinesinhead can readily make this tight interaction with the microtubule, due to restrai nts imposed by the coiled -coil and pre-stroke conformation of the neck linker in the bound head.
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