D.J.C. MacKay and R.S. MacKay: Ergodic pumping: Useful numbers

·	Summary

Abstract

Further observations
·	Hamiltonian models
·	Unequal masses
·	Multiple drivers
·	Thermalize
·	Changing shape
·	Two particles
·	Modified volume
·	Control experiment
·	Theory 1
·	Theory 2
·	Nonlinear potentials
·	16kT of work
·	Movies
·	More results
·	Niggles
·	Simple One-D
·	More One-D
·	Yet More One-D
·	Charged exit-path trick
·	Complication with simulations
·	Discussion of 1-6 potential
·	Details
·	Pressure paradox
·	Useful numbers «

Useful numbers

Hydrogen bond

20 kJ/mol

= 8 kT

2.5 kJ/mol

Maximum speed of myosin past actin

4 microns per sec

Maximum Myosin cycling frequency

40 Hz

Length of one myosin/actin filament

2 micron

Stress sustained by muscle

30 tons per m^2 = 43 psi

Muscle concentrations

[ATP] =8.1 mM

[ADP] = 0.93 mM

[Pi] = 8.1 mM

Diffusion coefficient: ATP in cytoplasm

1.5 x 10^-12 m²/sec

0.15 x 10^-5 cm²/sec

D: PO₄ in water

~10 x 10^-12 m²/sec

~1 x 10^-5 cm²/sec

D: O₂ in water:

20 x 10^-12 m²/sec

2 x 10^-5 cm²/sec

D: CO₂ in water:

16 x 10^-12 m²/sec

1.6 x 10^-5 cm²/sec

the diffusion coefficient for a sphere is:

D = kT/(6 pi eta r )

For a sphere of one micron diameter in water at room temperature

D = 4.4e-9 cm^2/sec = 4.4e-13 m^2/sec

Drag coefficient (in f = phi v) is

phi = 6 pi eta r = 9.5e-6 g/sec = 9.5e-9 Kg/sec

Drag coefficient for a 5 nm sphere is

phi = 6 pi eta r = 5e-8 g/sec = 5e-12 Kg/sec

Dissipation produced by one 5nm sphere moving at 4 microns per sec

= phi v^2 = 5e-12 Kg/sec * 4e-6 m/sec * 4e-6 m/sec = 8e-23 J/sec

Dissipation per mole

= 48J/sec = 1J per (Myosin cycle) (c.f. 40kJ or so free energy liberated)

Lengthscale of cell

20 micron