Biophysics Master Course, Fall 2002

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Biophysics Master Course, Fall 2002 Some of
the physics cells have to deal with Random
walks, diffusion and Brownian motion
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Background reading Frederick Reif
Statistical and Thermal Physics, Chpt. 1 (random
walks), Chpt. 15 (fluctuations, Brownian
motion) Howard Berg Random Walks in Biology,
Chpts. 1, 2 (diffusion), Appendix A
(distributions) Jonathon Howard, Mechanics of
Motor Proteins and the Cytoskeleton, Chpt. 4
(diffusion), Chpt. 16 (motor models) Richard
Feynman, Feynman Lectures I, Chpt 41 (Brownian
motion), Chpt. 46 (thermal ratchet) Landau,
Lifschitz, Volume V, Statistical Physics, Chpt.
12 (fluctuations, pretty advanced) Frederick
Gittes, Christoph Schmidt, Signals and noise in
micromechanical measurements. In Laser Tweezers
in Cell Biology. Methods in Cell Biology, 55
129-156, Academic Press, San Diego, CA, 1998
(power spectral analysis). Gittes, F.,
Schmidt, C.F. (1998), Thermal Noise Limitations
on Micromechanical Experiments, Eur. Biophys.
J., 27 75-81 (spectral analysis, other noise)
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Optical trapping of 0.2 µm silica beads in water
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Bacterial motility, E. coli from Howard Berg
lab, courtesy Linda Turner
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Intracellular transport in Reticulomyxa, video
M. Schliwa, M. Koonce
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(No Transcript)
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2D random walk, 18050 steps
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Intracellular Transport on Cytoskeletal Tracks
1 m
Axon
Cell Body
Synapse
Vesicles with motors
Microtubules
Active transport v 1µm/s, T 10
days Diffusion T x2/6D 26,000 years
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The Main Motor Protein Families
Cargo Vesicles, Organelles
Motors myosins, kinesins, dyneins
Fuel ATP
(asymmetric) track actin filaments, microtubules
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The Feynman Thermal Ratchet
Pforwardexp(-De/kT1) Pbackwardexp(-De/kT2) work
s only if T1gtT2 !!
trel Cl2/(4p2k)
wrong model
motor protein conformational change µs decay of
temperature gradient over 10 nm ns
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Brownian Ratchet (A.F. Huxley 57)
Cargo
Net transport
Thermal motion
Motor
Track
perpetuum mobile? Not if ATP is used to switch
the off-rate.
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Three-bead assay with ncd
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Myosin averaged power strokes (Veigel et al.
Nature 99, 398, 530)
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Myosin Power Stroke
ADP Pi
Mechano-chemical cycle
attach
MATP
working stroke
myosin
MADPPi
actin
ADP
detach
M
recovery stroke
Pi
15
Conformational Change of Single ncd Molecule
7 nm
ADPPi
ADP
release
ADP
DeCastro, Fondecave, Clarke, Schmidt, Stewart,
Nature Cell Biology (2000), 2724
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(No Transcript)
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Stepping and Stalling of a Single Kinesin
Molecule
6 pN stall force
8 nm steps
Svoboda, Schmidt, Schnapp, Block, Nature (1993),
365 721
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Dtconst. clockwork
Randomness parameter
r 0
k
k
k
k
k
1 -gt 2 -gt 3 -gt 4 -gt 5 -gt 6
ltx2(t)gt - ltx(t) gt 2
r lim
d ltx(t)gt
t -gt 8
Dt exponentially distributed Poisson process
r 1
k
1 -gt 2
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Randomness parameter for single
kinesin (Visscher,Schnitzer, Block (99), Nature
400, 184)
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Time series
Spectrum
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Efficiency, Invertability andProcessivity of
Molecular Motors
F. Jülicher, Institut Curie, Paris
A. Parmeggiani L. Peliti (Naples) A. Ajdari
(Paris) J. Prost (Paris)
http//www.curie.fr/julicher
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Mechano-chemical coupling
4
M-ATP
3
M-ADP-P
M-ADP
2
x
M
1
mean velocity
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Example weakly bound state
weakly bound
strongly bound
ATP
ADP-P
ADP
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Example identical shifted states
U
l
a
chemical free energy of hydrolysis
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Dissipation rates
motion within a state
chemical transitions
total internal dissipation of the motor
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Efficiency of energy transduction
force
velocity
Energy conservation
chemical energy
chemical rate
mechanical work
chemical work
total internal dissipation
A. Parmeggiani, F. Jülicher, A. Ajdari and J.
Prost, PRE 60, 2127 (1999)