Sophie Dumont BP204 March

Transcription

1 Sophie Dumont BP204 March

2 Molecules Mechanics What can we learn? Tools? Framework? Challenges? Looking ahead? structure, chemistry Cells 2

3 What biological activities are associated with force? Examples Protein/RNA folding Replication, transcription, translation Viral infection Cytoskeletal organization Intracellular transport Cell signaling and adhesion Muscle movement Tissue development and morphology nm µm mm What biological activities are not associated with force? 3

4 1 Spring: 2 Drag: 3 Inertia: F F = k x (k is spring constant) F = γ v = γ = m a dx dt (γ is drag coefficient) 2 d x = m 2 dt (m is mass) Process Single motors Myosin Kinesin Dynein Cell regulation Transcription Translation Replication Force 3-5 pn 5-7 pn 7 pn 15 pn 1-20 pn pn Cells and tissue Muscle contraction N Blood pressure 0.01 pn/nm 2 energy = force x distance 1 k B T = 4 pn-nm 1 ATP = pn-nm at 37C v( t) = t / τ v0e, τ = m γ sec for ribosome mass normally irrelevant 4

5 Types of processes Elementary processes Electronic transition Bond vibration Conformational change Intermediate processes Bimolecular dissociation Bond formation or breaking Motor movements Kinesin stepping at Vmax Myosin stepping at Vmax Bacteriophage stepping rate Enzyme turnover Chymotrypsin ATP synthase Time s s 10-9 to 10-6 s 10-6 to 10-3 s 10-6 to 10-3 s 10 ms 5 ms 10 ms/bp 10 ms 5 ms Average out elementary processes Can generally probe mechanics of molecules at ms to min range Gene expression Prokaryotic replication (E. coli) Eukaryotic replication (X. laevis) RNA transcription Translation 2 ms/bp 2 ms/bp 40 ms/bp ms/aa 5

6 Measuring & exerting forces Generating force (active forces) Responding to force (passive forces) Integrating forces (molecules to cells, self-organization) Linear forces Torque 6

7 Goal: measure how forces affect the dynamics of molecules under force. Dulin et al., Nature Reviews Genetics

8 Neuman et al., Nature Methods

9 Distributions Information! Mechanics: force output, step sizes, energy efficiency force-dependent kinetic step (coupling of ATP with force generation) Different reaction pathways Different folding & unfolding trajectories 9

10 Examples of biomolecules probed with optical tweezers: Fazal & Block, Nature Photonics

11 Microscope objective focuses laser light to diffraction-limited spot Conservation of momentum As force, trapped bead moves linearly out of equilibrium position: F = k x Block lab website, Stanford 11

12 Measuring bead position x Measuring trap stiffness k thermal fluctuations on spring Gaussian noise Quadrant PhotoDiode (QPD) probability x = 0 V y = V x = (A + B) (C + D) A + B + C + D (B + D) (A + C) A + B + C + D voltage reports on bead position x 1 p( x) = exp σ 2π σ = kbt k ( x 2 2 2σ ) fluctuations report on trap stiffness k 12

13 Signal-to-noise ratio (SNR) limited by thermal fluctuations (and experimental noise): SNR k 4 k tether B T x B γ k tether : stiffness of biomolecule x: size of physical displacement (e.g. step size) B: rate of data collection/ averaging (lower limit imposed by speed of reaction!) γ: drag coefficient of bead Inverse relationship between spatial and temporal resolution 13

14 Magnetic tweezers: can make parallel measurements on a field of molecules and can measure and apply torque! Need to know distance to measure force: measure distance with bead imaging Dekker and coworkers 14

15 Transcription: Viscous drag Replication: Optical tweezers + twisting pipette ATP synthase: Magnetic tweezers Forth et al., Annual Reviews

16 Short filament Long filament Calculate frictional torque: Angular velocity (ω) Medium viscosity (η) Filament length (L) and radius (r) F 1 -ATPase: nearly 100% efficient motor that rotates with discrete 120 steps Kinosita Lab: Nohi et al., Nature 1997, Yasuda et al., Cell

17 Looking ahead: Combining mechanical measurements with other observables (fluorescence, etc.) Purified macromolecular complexes from cells Measurements inside cells Comstock et al., Nat Meth

18 (energy consumed) Measuring & exerting forces Generating force (active forces) Responding to force (passive forces) Integrating forces (molecules to cells, self-organization) Translocation motor Polymerization motor 18

19 Distance (nm) 8 nm steps 19

20 How is chemical potential converted to mechanical force? Substrate binding v = V mmm[s] K M + [S] Hydrolysis Product release Force affects V max /K M, but not V max Force affects V max, but not V max /K M Force affects both V max and V max /K M 20

21 φ29 viral packaging motor: v = V mmm[aaa] K M + [AAA] Low ATP Capsid pressure: High ATP Force affects V max, but not V max /K M : force generation at product release Minimal mechanochemical cycle proposed: Chemla et al., Cell

22 Purified yeast kinetochores: Catch bond: Detaches less under higher force! Question: How do you know you re holding on to a single molecule? Akiyoshi et al., Nature

23 40nm Number of motors affects run length and time, but not velocity Derr et al., Science

24 Dynamic polymers can move objects, without needing translocation motors Dogterom et al., Current Opinion Cell Biology

25 0.5pN 5pN if consider lever arm 30-65pN if consider all protofilaments optical trap What s coupling cellular objects to depolymerizing microtubules? Grishchuk et al., Nature

26 (no energy consumed) Measuring & exerting forces Generating force (active forces) Responding to force (passive forces) Integrating forces (molecules to cells, self-organization) Elasticity, folding/unfolding Molecular friction 26

27 Short length scale: deform elastic beam cosθ P = = exp π E a 4 k T B 4 ( L / P) L = distance P = Persistence length a = radius E = Young s modulus (1GPa for most proteins = plexiglass) a 2 nm for actin P 3 µm (unbundled) a 10 nm for microtubules P 2 mm (compared to P 50 nm for DNA!) Reasonable agreement with experiment Gittes et al. JCB 1993 Longer length scale: extend random coil to overcome entropy (next slide) 27

28 Wuite et al. Nature 2000 Force to extend DNA against entropic elasticity: Worm-like chain model (WLC) F = kb T P x L 1 4 ( ) 2 x L F = force P = Persistence length x = extension L = contour length Why do we care about the elasticity biomolecules? For DNA, for example Predicting DNA conformations in vivo Thermodynamics of protein:dna interactions with DNA distortion Quantitative design when using DNA as a building material DNA as a model system to test polymer physics theories 28

29 unfold fold dissipated work unfolded folded new reaction coordinate Can get: Position of mechanical barriers Position of transition state ( x * ): small = brittle, large = compliant G if equilibrium pulling Dependence on sequence, Mg 2+ buffer, etc. Liphardt et al., Science

30 unfolded folded K eq ( F) = Thermodynamics: G = G 0 F x k k forw rev Keq ( F) = ( F) ( F) K k = k 0 eq e 0 forw 0 rev e ( F x) k T B ( F x) k T B k k forw rev G kbt ki = Ai e 0* * ( G F xforw = A e ) forw 0* * ( G F xrev ) kbt = A e k k forw rev rev Kinetics: = k = k 0 forw 0 rev e e F x 0* F x * rev * forw k B T k B T k B T Force has a larger effect on reactions with large x s (and x * ) discussion paper #1! 30

31 Jarzynski s equality: 2 nd law of thermodynamics in small systems G e Equilibrium info k B T = < e W i k B T > N Non-equilibrium data The secret: left tail! Liphardt et al., Science

32 T. thermophila ribozyme self-splicing intron: How to assign mechanical rips to molecular features? truncation mutants positional mutants oligos to prevent postulated interactions Secondary and tertiary structure assignment Onoa et al., Science

33 Microtubulebinding protein called NuMA: lower friction to minus-ends than plus-ends! Forth et al., Cell

34 Measuring & exerting forces Generating force (active forces) Responding to force (passive forces) Integrating forces (molecules to cells, self-organization) 34

35 Need tools to: 1measure 2perturb 3control.. forces in cellular context 35

36 AFM Actin network Actin networks stiffen then soften under load: Stress Stiffening Softening Chaudhuri et al., Nature

37 Use micropatterning to assemble geometrically controlled and polarized actin networks: Myosin VI contracts antiparallel, but not parallel, actin network Motor activity Network architecture Reymann et al., Science

38 SPRING DASHPOT Solid-like ( stiffness) Liquid-like ( viscosity) How do molecular properties give rise to these cell-scale properties? Kasza et al., Curr. Opinion Cell Biology

39 Summary: Poke and/or track! Kasza et al., Curr. Opinion Cell Biology

40 FRET-based force sensor: molecular measurements inside cells In vivo FRET sensor In vitro force-fret calibration optical trap use in cells ( but different FRET pair ) Grashoff et al., Nature

41 Low force High force Where to insert FRET sensor? How to interpret FRET sensor data? Forces in new focal adhesions are higher than at old focal adhesions (probably) Grashoff et al., Nature

42 easy hard Adhesion via integrin has a sharp threshold (33-43 pn) Other conclusions: 1Formation of focal adhesions requires a higher tension tolerance than adhesion 2Notch signaling does not have a detectable minimum tension tolerance Wang and Ha, Science

43 Fuel (ATP, GTP) Chemistry Mechanics Mechanical signals: -fast signal propagation -orientation specific signal -global info from local cues Mechanotransduction Enzyme-substrate displacement Unfolding of protein New binding site exposed 43

44 How to integrate forces over length scales and time scales? nm µm mm m ms min-days years Hierarchical thread 44

45 Biological structures: 1. Material properties of individual building blocks (e.g. titin stiffness muscle stiffness) 2. Basic architecture: orientation of blocks, etc. (e.g. microtubule orientation in spindle) 3. Density of building blocks and crosslinks (e.g. cytoskeletal networks) 4. Shape of structure and internal geometry (e.g. shape of tissue where cells proliferate) 5. Affinity of interactions (e.g. cell-cell junction affinity tissue integrity) Genentech Hall: 1. Elastic moduli of materials 2. Support beam orientations 3. Support beam densities 4. Anchor point geometrical distributions 5. Anchor point strengths? What mechanics emerge? Why is this hard?? 45

46 Self-assembly: Order arises from local interactions between passive parts. No energy is consumed, and structures typically reach a steady-state. Self-organization: Order arises from self-driven active parts that consume energy (from metabolism), bringing biological processes out of equilibrium. Karsenti Nat. Rev. Mol. Cell Bio

47 Biological structures: 1. Change their own structure over time 2. Building blocks come on and off 3. Building blocks actively generate force (i.e. consume energy) No traditional mechanics framework Emergent structures: Tornadoes and sand dunes exhibit properties that their smallest parts do not, arising from collective behavior of parts. Biological emergent structures can be even more complex: spatially heterogeneous, and made from great diversity of parts and interactions (e.g. cytoskeleton, active membranes, repairing tissue). 47

48 How do forces generated by individual molecules affect larger scale structures? How do stresses across the whole structure flow through individual molecules? Need to be able to externally control and tune 1. architecture 2. on-and-off kinetics 3. active force-generation ability of the structure s building blocks in real-time! 48

49 Design of cytoskeletal motors that reversibly change gears (speed up, slow down, change direction) when exposed to blue light Nakamura et al. Nature Nanotechnology

50 Measuring & exerting forces Generating force (active forces) Responding to force (passive forces) Integrating forces (molecules to cells, self-organization) Challenges: 1. How to measure and perturb forces inside cells? 2. How do mechanics of cellular structures emerge from those of molecules? 50

51 What is the basis of friction asymmetry? How could it be tuned? Implications on cellular structures? What do these motors test about our understanding? What would you do with these motors? How to control other motors? 51