Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Motor proteins and mechano-chemistryMartin LindénI. A mini-zoo of some motors, their biological functions, and some important experiments.II.Qualitative (toy) models, and ingredients in quantitative models.III.First passage time calculations(Bias: single motors and single molecule experiments)Part I: a small zoo of motor proteins.●Motors in intracellular transport.●The flagella rotary motor.●Translocation through a pore,and the ratchet effect.Motors in intracellullar transportLever arms~8 nm~36 nm+-microtubuleActin filamentMotors in intracellullar transportLever arms●Driven by ATP●Specific molecular track and direction●Processive (in vitro)kinesin: ~100 steps/runmyosin V: ~ 10 steps/run●Works in small groups in vivoWatching single motors in vitroNishiyama, Higuchi & YanagidaNature Cell Biol 4:790 (2002)How does it walk?Actin filamentMyosin VHand over hand motion●Flourophore attached to one of the heads of Myosin V: step size indicates hand-over-hand motion.Ahmet Yildiz, UC Berkeley“How Microtubular motors move”March 9, 4 PM, 106 SpaldingE coli swimming is driven by a rotary motor●Rotating filaments (flagella) form screw-like bundles●up to ~300 Hz rotation rate, v ~ few tens of m/s ●switch between runs (CCW) and tumbles(CW): biased random walk in search of good conditionsSwimming E. coliDarnton et alJ. Bact. 189:1756 (2007)Swimming E coliSteps in the flagellar motor(slow mutant version):Sowa et al, Nature 437:916(2005) (H C Berg)Translocation: the ratchet effectPart II: Qualitative (toy) models, and ingredients in quantitative models.(Pun on a classic paper/talk by Purcell).Motor proteins (and all other proteins) work under very noisy conditions.How noisy...?Trajectories of motors:The one-state model●Simple, captures randomness and molecular discreteness of motors. ●Rationale: one transition (often) slowest●Steps map to many examples●Mean velocity●Effective diffusion constant●Waiting time distribution: exponential (known?)●Maximal forceδ'Effective' diffusion? What does it look like?Energy and force●Energy content of molecular fuel●Maximum force?●Principle of detailed balance●Force dependence of transition rates●Free energy landscape, and what it means to understand the 'mechanism' of a motor protein.●Force-velocity and [fuel]-velocity curves●Calculation of first passage timesFree energy from ATPc0, G0: standard conditions.∆G: distance from equilibriumBionumbers.com: ∆G0=-11 kBTHuman muscle:[ATP]~8.2 mM [ADP]~9 .4 µM[Pi]~3.7 mM∆G ~ -24 kBTCanonical value: -20 kBTComplications: several species (ATP, ATP-Mg2+, ...)Maximal force from a single motor ●Kinesin: δ = 8.2 nm, Fmax ~ 10 pNFstall~ 6-8 pN (in vitro)●Myosin V: δ = 36 nm, Fmax~ 2.3 pNFstall ~ 2-3 pN (in vitro)●Many in vitro experiments are done far from physiological conditions (e.g., [ADP]~0).●Why are these numbers so good...?(rough estimate of upper limit)Principle of detailed balanceConsistency requirement: how to not model a perpetuum mobile.Applications●Consistency check●Motion implies force dependent rates●Detect free energy transduction.Motion implies force dependenceDetailed balance:(If the wells have equal width...).For a single rate●Detailed balance only constrains the ratio.●Common choice (quick&dirty): transition state theoryxtransGtrans.Reaction free energy under opposing loadDetailed balance in action∆z ~ 70 nmMeiners' labU MichiganDNA looping:Binding and unbinding of looping protein is an equilibrium process.Free energy landscape●Keep track of position and fuel consumption independently.●Direction of motion is not parallell to applied forces: some kinetic “mechanism” is at work.●Backward steps are (somtimes) not reversed forward steps: no detailed balance in that case.●Most useful for models with many states.●Direction of motion is not sum of applied forces: some kinetic “mechanism” is needed.●Stall force is pretty well described by the physiological ∆GATP, even far from physiological conditions. Why?Speculation:●Force is limited by kinetic mechanism, which is optimized for physiological conditions.Free energy landscapeEscher and detailed balance...?If the free energy change along a closed path is non-zero, then there is a 'hidden' driving force in the model. (This might be OK, just do not put it there by mistake.)Beyond the 1-state model:●Complex force-velocity relations●Diffusion constant too low. 1-state prediction●Non-exponential waiting time distributionsIII. First passage time calculations●Workhorse: 2 state model.●Non-exponential waiting times.●Absorbing boundary vs adjoint equation.●Moment generating functions.●Several exits, . . ., (no time).Ahmet Yildiz, UC Berkeley“How Microtubular motors move”March 9, 4 PM, 106
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