Sedimentation coefficient
Encyclopedia
The sedimentation coefficient s of a particle is used to characterize its behaviour in sedimentation
processes, notably centrifugation
. It is defined as the ratio of a particle's sedimentation velocity
to the acceleration
that is applied to it (causing the sedimentation).
The sedimentation speed
(in ms−1
) is also known as the terminal velocity
. It is constant because the force applied to a particle by gravity or by a centrifuge (measuring typically in multiples of tens of thousands of gravities
in an ultracentrifuge
) is cancelled by the viscous resistance of the medium (normally water
) through which the particle is moving. The applied acceleration a (in ms−2
) can be either the gravitational acceleration
g, or more commonly the centrifugal acceleration
. In the latter case, 
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 the Stokes' law: 6πηr0v where η is the viscosity of the medium, r0 is the radius of the particle and v is the velocity of the particle. This law applies only for large spheres in an infinite sea of the fluid.
The centrifugal force is given by the familiar equation: mrω2. Here r is the distance of the particle from the axis of rotation. When the two forces (viscous force and the centrifugal force) balance (they are oppositely directed), the particle moves with constant velocity called the terminal velocity. Hence the terminal velocity is given by the following equation.
Rearranging this equation we get the final formula:
The sedimentation coefficient has the dimension
s of a unit of time
and is expressed in svedberg
s. One svedberg is defined as exactly 10−13 s
. Essentially the sedimentation coefficient serves to normalize the sedimentation rate of a particle by the acceleration applied to it. The resulting value is no longer dependent on the acceleration, but depends only on the properties of the particle and the medium in which it is suspended. Sedimentation coefficients quoted in literature usually pertain to sedimentation in water at 20°C.
Bigger particles sediment faster and have higher sedimentation coefficients (svedberg, or S values). Sedimentation coefficients are, however, not additive. Sedimentation rate does not depend only on the mass or volume of a particle, and when two particles bind together there is inevitably a loss of surface area. Thus when measured separately they will have svedberg values that may not add up to that of the bound particle.
This is notably the case with the ribosome
. Ribosomes are most often identified by their sedimentation coefficient. For instance, the 70 S ribosome that comes from bacteria
actually has a sedimentation coefficient of 70 svedberg. It is composed of a 50 S subunit and a 30 S subunit.
Sedimentation
Sedimentation is the tendency for particles in suspension to settle out of the fluid in which they are entrained, and come to rest against a barrier. This is due to their motion through the fluid in response to the forces acting on them: these forces can be due to gravity, centrifugal acceleration...
processes, notably centrifugation
Centrifugation
Centrifugation is a process that involves the use of the centrifugal force for the sedimentation of mixtures with a centrifuge, used in industry and in laboratory settings. More-dense components of the mixture migrate away from the axis of the centrifuge, while less-dense components of the mixture...
. It is defined as the ratio of a particle's sedimentation velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
to the acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
that is applied to it (causing the sedimentation).
The sedimentation speed
(in ms−1Metre per second
Metre per second is an SI derived unit of both speed and velocity , defined by distance in metres divided by time in seconds....
) is also known as the terminal velocity
Terminal velocity
In fluid dynamics an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving....
. It is constant because the force applied to a particle by gravity or by a centrifuge (measuring typically in multiples of tens of thousands of gravities
Standard gravity
Standard gravity, or standard acceleration due to free fall, usually denoted by g0 or gn, is the nominal acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely , or about...
in an ultracentrifuge
Ultracentrifuge
The ultracentrifuge is a centrifuge optimized for spinning a rotor at very high speeds, capable of generating acceleration as high as 2,000,000 g . There are two kinds of ultracentrifuges, the preparative and the analytical ultracentrifuge...
) is cancelled by the viscous resistance of the medium (normally water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...
) through which the particle is moving. The applied acceleration a (in ms−2
Metre per second squared
The metre per second squared is the unit of acceleration in the International System of Units . As a derived unit it is composed from the SI base units of length, the metre, and the standard unit of time, the second...
) can be either the gravitational acceleration
Gravitational acceleration
In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....
g, or more commonly the centrifugal acceleration
. In the latter case, is the angular velocityAngular velocity
In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...
of the rotor
Turbine
A turbine is a rotary engine that extracts energy from a fluid flow and converts it into useful work.The simplest turbines have one moving part, a rotor assembly, which is a shaft or drum with blades attached. Moving fluid acts on the blades, or the blades react to the flow, so that they move and...
and r is the distance of a particle to the rotor axis (radius
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
).
The viscous resistance is given by the Stokes' law: 6πηr0v where η is the viscosity of the medium, r0 is the radius of the particle and v is the velocity of the particle. This law applies only for large spheres in an infinite sea of the fluid.
The centrifugal force is given by the familiar equation: mrω2. Here r is the distance of the particle from the axis of rotation. When the two forces (viscous force and the centrifugal force) balance (they are oppositely directed), the particle moves with constant velocity called the terminal velocity. Hence the terminal velocity is given by the following equation.
Rearranging this equation we get the final formula:
The sedimentation coefficient has the dimension
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
s of a unit of time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
and is expressed in svedberg
Svedberg
A svedberg is a non-SI physical unit used for sedimentation coefficients. It characterizes the behaviour of a particle type in sedimentation processes, notably centrifugation. The svedberg is technically a measure of time, and is defined as exactly 10-13 seconds A svedberg (symbol S, sometimes...
s. One svedberg is defined as exactly 10−13 s
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
. Essentially the sedimentation coefficient serves to normalize the sedimentation rate of a particle by the acceleration applied to it. The resulting value is no longer dependent on the acceleration, but depends only on the properties of the particle and the medium in which it is suspended. Sedimentation coefficients quoted in literature usually pertain to sedimentation in water at 20°C.
Bigger particles sediment faster and have higher sedimentation coefficients (svedberg, or S values). Sedimentation coefficients are, however, not additive. Sedimentation rate does not depend only on the mass or volume of a particle, and when two particles bind together there is inevitably a loss of surface area. Thus when measured separately they will have svedberg values that may not add up to that of the bound particle.
This is notably the case with the ribosome
Ribosome
A ribosome is a component of cells that assembles the twenty specific amino acid molecules to form the particular protein molecule determined by the nucleotide sequence of an RNA molecule....
. Ribosomes are most often identified by their sedimentation coefficient. For instance, the 70 S ribosome that comes from bacteria
Bacteria
Bacteria are a large domain of prokaryotic microorganisms. Typically a few micrometres in length, bacteria have a wide range of shapes, ranging from spheres to rods and spirals...
actually has a sedimentation coefficient of 70 svedberg. It is composed of a 50 S subunit and a 30 S subunit.
External links
- Introduction to Cell Fractionation in the Cell Biology Laboratory Manual
- Analysis of sedimentation velocity data
- An article on sedimentation velocities on the Alliance Protein Laboratories website
- Modern Analytical Ultracentrifugation in Protein Science: A tutorial review