1: Life, free energy and Brownian motion

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Section 2 Bioenergetics and Molecular Machines
7 topics in 8 lectures
1 Life, free energy and Brownian motion 2
Swimming at Low Reynolds Number Guest Lecture
by Ard Louis. 3 Transition theory and the single
molecule 4 Biological membranes 5
Bioenergetics 6 Molecular motors I linear
motors 7 Molecular motors II rotary motors
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Topic 1 Life, Free Energy and Brownian Motion
Introduction to this section Bioenergetics and
Molecular machines
Single molecules, kT, fluctuations
Brownian Motion
Fluctuation-dissipation theorem(Einstein
Relation)
Biological examples
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Reading for Topic 1

• Nelson, Chapter 4
• Howard, Chapter 4
• Berg, H.C.
• Random Walks in Biology 152pp Princeton
  University Press,

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Thermodynamics of life
Heat (high entropy)
sun
Photons (low entropy)
Life (low entropy)
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An overview of bioenergetics Free Energy flow in
living things
food eg) glucose
NADH
Essential processes of life, including
reproduction
growth
photons
ATP
pmf
transport
movement
Main topics in this section of the course
Biological Free energy Protonmotive force,
(biological membranes), ATP
Movement, transport Molecular Motors
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G U - TS
Free energy
(Gibbs Free energy only if U H Uo PV)
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Length Scales
Organskin
1 mm 10-3
Organism human
1 m 100
Tissue epidermis
100 mm 10-4
Molecular machine F1-ATPase
10 nm 10-8
Cell basal cell
10 mm 10-5
Molecular assembly Mitochondrial membrane
Organelle mitochondrion
1 mm 10-6
10 nm 10-8
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Examples of molecular machines
Bacterial flagellar motor
Myosin V
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The ribosome
F1-ATPase
kinesin
Bacterial flagellar motor
myosin II
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Energy scales
Boltzmanns constant the amount of thermal
energy per molecule per degree k 1.38 x 10-23
J/K (sometimes kB)
kT 4.1 x 10-21 J 4 pN nm (at 25o C)
1 eV 160 pN nm 40 kT (or kT 25 meV)
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Principle of Equipartition of Energy ½ kT per
degree of freedom
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DemosBrownian motion livecomputer
simulation of random walk
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1-D random walk
kn gives the direction of the last step, Dx is
the step size
This is a recurrence relation combined with
ltx20gt 0 we get
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Diffusion Equation
One solution

(Test it by substitution)
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A random walk under a constant force F
Here ltDxgt is the average distance travelled, due
to the force, on top of the thermal motion, and
ltvgt is the average or drift velocity
This is the definition of g
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Drift velocity due to external force (Low
Reynolds Number)
Viscous Drag coefficient
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Molecules are real!
Measurements of the displacements in successive
30s Intervals of a 0.37 mm particle in water.
Rings of radius n x 1.96 mm. Jean Perrin 1948
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Diffusive transport examples
So
12 min
23 yrs
goldfish
2x10-6
8200 yrs
8 bn yrs
108
2.8 days