Single molecule measurements and biological motors

Damping

The preceding sections give a rather static picture of the behaviour of a trapped object. However, if we want to describe the motion of an object over time, we need to consider the damping of the object's motion, which is proportional to its velocity. This damping is due to the viscous drag of the object moving through the medium, and is given by the term γ(dx/dt) above. γ, the drag coefficient, is, for a spherical object, given by Stoke's Law:

γ = 6·π·η·r

where η is the viscosity of the medium, and r is the radius of the object. For example, for a 1 μm diameter bead in water (η = 0.001 N·s·m^-2), γ = 9.4 × 10^-9 N·s·m^-1. A correction to this relationship, known as Faxen's law, is required in close proximity to surfaces (such as the cover slip). Because the damping effect is dependent on the velocity of the bead, rather than its position, it does not affect the distribution of positions mentioned above. However, it does affect the behaviour of the bead over time, and therefore also the power spectrum of bead motion.

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