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Lecture 10. Background for cell propulsion Fluid dynamics Enzyme kinetics How do animals swim?: 1. pushing fluid backward by limb action; 2. pushing fluid forward by resistance of body.

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lecture 10
Lecture 10
  • Background for cell propulsion
  • Fluid dynamics
  • Enzyme kinetics
  • How do animals swim?:
  • 1. pushing fluid backward by limb action;
  • 2. pushing fluid forward by resistance of body.
  • I.e fish starting from release will accelerate until the backward & forward momentum (of the fluid) balance. Viscosity is only significant at the boundary layer.
cell propulsion
Cell Propulsion
  • Small scale phenomenon: slow velocities driven by surface forces: pressure and viscous stress. Fluid resistance is significant, and balances propulsive force.
  • Motion of a body depends on the ratio of viscous and inertial effects: Reynold’s number: Small for cells, large for almost all animals. Cellular world is ruled by friction.
cellular motors
Cellular Motors
  • Molecular motors must move (swim) in fluids, where most of the work is dissipated
  • What forces must they overcome?
  • Where do the motors get their fuel?
  • How do they exhaust spent fuel?
  • What is the efficiency?
oscillatory muscles
Oscillatory muscles

Stretch activation

Synchronous Asynchronous

myosin
Myosin
  • 5.3 pN for each myosin molecule
  • 100 molecules per filament.
  • Each filament has c.s.a. of 1.8 X 10 –15 m2 in the relaxed muscle.
sample fluid properties
Sample fluid properties

When f > fcrit- inertial forces dominate

swimming is it worth it
Swimming: is it worth it?
  • Cilium with velocity, v, length, d, time scale:
  • Diffusion time scale :
  • Swimming time, ts should be < tD
viscous flow

A

vo f

d

Viscous flow
  • Newtonian fluids are isotropic
  • What is a viscous fluid?
  • When f< fcrit

Shear

Planar geometry

slide20
I.e., 1 mm cilium, D = 10-5 cm2/sec,
  • so v> 103mm /sec:
  • stirring and swimming is not energetically favorable for nutrition.
rotary cellular motors
Rotary Cellular Motors
  • The rotary mechanism of ATP synthase , Stock D, Gibbons C, Arechaga I, Leslie AGW, Walker JECURRENT OPINION IN STRUCTURAL BIOLOGY ,10 (6): 672-679 DEC 2000
  • 2. ATP synthase - A marvellous rotary engine of the cell, Yoshida M, Muneyuki E, Hisabori TNATURE REVIEWS MOLECULAR CELL BIOLOGY 2 (9): 669-677 SEP 2001
  • 3. The gamma subunit in chloroplast F-1-ATPase can rotate in a unidirectional and counter-clockwise manner Hisabori T, Kondoh A, Yoshida M FEBS LETTERS 463 (1-2): 35-38 DEC 10 1999
  • 4. Constructing nanomechanical devices powered by biomolecular motors.C. Montemagno, G Bachand, Nanotechnology 10: 225-2312, 1999.
f1 atpase a rotary motor
F1 ATPase: A rotary motor
  • Can either make or break ATP, hence is reversible
  • Torque of 40 pN-nM; work in 1/3 rev. is 80 pn-nM (40 * 2p/3) equivalent to free energy from ATP hydrolysis
  • Can see rotation by attaching an actin filament
slide30

Nature Reviews Molecular Cell Biology2; 669-677 (2001)ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL

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elasticity
Elasticity

Nano versus macro elasticity

Behaviour relative to kT: Stretch a rubber band and a string of paper clips.

Significant for The nanometer-scale monomers of a macromolecule, but not for a string of paper clips. The retracting force exerted by a stretched rubber band is entropic. It increases disorder.

Do most polymers have persistence lengths longer than their total (contour) length?

slide35
When L>> x, the chain has many bends and is always crumpled in solution – the FJC model applies, with each link approximated as 2 x, and perfectly flexible joints.
  • To count all possible curved states in a smooth-bending rod in solution- it’s a WLC- supercoiling is possible.
slide36
Promoters have different abilities to uncoil
  • Twisting DNA torsional buckling instability
  • Unwinding and causes local denaturation
  • Many motors are needed: RNA plymerase, DNA polymerase: 100 nucleotides/sec.
  • Forces (pN) can stop transcription
mechano regulation
Mechano - regulation
  • Growth, proliferation, protein synthesis, gene expression, homeostasis.
  • Transduction process- how?
  • Single cells do not provide enough material.
  • MTC can perturb ~ 30,000 cells and is limited.
  • MTS is more versatile- more cells, longer periods, varied waveforms..
markov chains
Markov Chains
  • A dynamic model describing random movement over time of some activity
  • Future state can be predicted based on current probability and the transition matrix
transition probabilities
Transition Probabilities

Today’s Game Outcome

Need a P for

Today’s game

Tomorrow’s

Game Outcome

grades transition matrix

Good

Bad

Good

3/4

1/2

Bad

1/4

1/2

Sum

1

1

Grades Transition Matrix

This Semester

Grade

Tendencies

To predict future:

Start with now:

What are the grade

probabilities for this

semester?

Next Semester

slide47

Markov Chain

Intial Probability

Set independently

computing markov chains
Computing Markov Chains

% A is the transition probability

A= [.75 .5

.25 .5]

% P is starting Probability

P=[.1

.9]

for i = 1:20

P(:,i+1)=A*P(:,i)

end