Sedimentation Coefficient
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Sedimentation Coefficient

The sedimentation coefficient (s) of a particle characterizes its sedimentation during centrifugation. It is defined as the ratio of a particle's sedimentation velocity to the applied acceleration causing the sedimentation.

${\displaystyle s={\frac {v_{t}}{a}}}$

The sedimentation speed ${\displaystyle v_{t}}$ (in m/s) is also the terminal velocity. It is constant because the force applied to a particle by gravity or by a centrifuge (typically in multiples of tens of thousands of gravities in an ultracentrifuge) is balanced by the viscous resistance of the fluid (normally water) through which the particle is moving. The applied acceleration a (in m/s2) can be either the gravitational acceleration g, or more commonly the centrifugal acceleration ${\displaystyle \omega ^{2}r}$. In the latter case, ${\displaystyle \omega }$ is the angular velocity of the rotor and r is the distance of a particle to the rotor axis (radius).

The viscous resistance is given by Stokes' law: 6r0v, where ? is the viscosity of the medium, r0 is the radius of the particle and v is the velocity of the particle. Stokes' law applies only for large spheres in an infinite amount of fluid.

The centrifugal force is given by the equation: mr?2, where r is the distance of the particle from the axis of rotation. When the two opposite viscous and centrifugal forces balance, the particle moves at constant (terminal) velocity. The terminal velocity is given by the equation:

${\displaystyle {v_{t}}={\frac {mr\omega ^{2}}{6\pi \eta r_{0}}}}$

Rearranging this equation gives the final formula:

${\displaystyle s={\frac {v_{t}}{r\omega ^{2}}}={\frac {m}{6\pi \eta r_{0}}}}$

The sedimentation coefficient has units of time, expressed in svedbergs. One svedberg is exactly 10-13 s. The sedimentation coefficient normalizes the sedimentation rate of a particle to its applied acceleration. The result no longer depends on acceleration, but only on the properties of the particle and the fluid in which it is suspended. Sedimentation coefficients quoted in literature usually pertain to sedimentation in water at 20°C.

Heavier particles sediment faster and have higher svedberg, or s values. Sedimentation coefficients are, however, not additive. When two particles bind together, they have reduced surface area. Thus, when measured separately they may have svedberg values that do not total that of the bound particle. This is the case with the ribosome. Ribosomes are typically identified by their sedimentation coefficient. For instance, the 70 S ribosome from bacteria has a sedimentation coefficient of 70 svedberg, although it is composed of a 50 S subunit and a 30 S subunit.