Energetic consumption of mitochondrial movement

Hydrodynamic calculation:

Use Stokes' drag formula (http://en.wikipedia.org/wiki/Stokes%27_law) to calculate with velocity from question 15

Stokes' formula: F = 6*pi*mu*R*V; dynamic viscosity mu, radius R, velocity V

mu ~ 12 mPa, R ~ 0.5 um, V ~ 1 um s^-1

Gives drag force of ~ 0.1 pN, smaller than molecular motor stall forces of ~ 2.5 pN

Power dissipation P = Fv = 1e-19 W

ATP consumption of kinesin:

Kinesin cycles ~ 100 times per second, consumes 1 ATP per cycle gives 100 ATP per kinesin per second.

Each phosphate bond hydrolysis liberates approximately 1e-19 J giving Kinesin power consumption for movement of approx 1e-17 W

Why might these two be different? Molecular motors are ~50% efficient, so inefficiency of the motor cannot account for such a discrepancy. Perhaps the stochastic behaviour of a molecular walker may have something to do with it - the Stokes' drag formula calculation assumes constant velocity forwards, whereas molecular motors drop off tracks and re-attach, thus wasting energy. Equally, this assumes a small, spherical mitochondrion, whereas in reality they are ovoid and may not be dragged with the semiminor axis parallel to the direction of travel, thus increasing the Stokes drag.

Geometric mean: ~ 1e-18 W