## Monday, 24 December 2012

### Centrifugation

Centrifugation – the basics
A centrifuge produces a centrifugal force many times greater than the earth’s gravity, by spinning the sample about a central axis.
Centrifugation is the process of separating mixtures suspended in a liquid by applying centrifugal force.

A very slow centrifuge….

A rather faster centrifuge…

Particles of different size, shape, or density will sediment at different rates, depending on the speed of rotation and distance from the central axis.

Centrifugal field G, operating on a particle P, spinning at a distance r from the central axis of a centrifuge.

Centrifugal force
Is centrifugal force real?
For our purposes:
Centrifugal force acts in an outward direction when a particle or object moves in a curved or circular path.

Exploded view of a centrifuge
A centrifuge:
a piece of equipment that rapidly spins a number of tubes which contain a suspension of particles in a liquid

A typical centrifuge

The force which causes particles to move down in a centrifuge tube:
Applied Centrifugal Field
G = ω2 x r                             [ω is the Greek omega]
where G is the applied centrifugal field (in cm per second squared: units of acceleration)
ω is the angular velocity of the rotor (in radians per second)
r is the radial distance of the particle from the axis of rotation (in centimetres)

Applied Centrifugal Field and  revolutions per minute (revs.)
The angular velocity ω is more easily understood in terms of revolutions per minute:
ω = 2π  x (revolutions per minute) / 60
Therefore since G = ω2 x r,                               the applied centrifugal field becomes:
G = 4π2 x r x (revolutions per minute)2 / 3600

Equation to apply
for G in cm/s2

A pilot in a fast aircraft executing a sharp turn or climb will experience a ‘g force’ several times that of gravity.
We can also express Applied Centrifugal Force in a centrifuge as a ‘g force’

Relative Centrifugal Field (RCF)
The centrifugal field is more commonly expressed in multiples of the gravitational field of the earth (981 cm per second squared)
Known as the Relative Centrifugal Field (RCF) and the units are in g:
RCF = 4π2  x r x (revolutions per minute)2
/ (3600 x 981)
This simplifies to
Relative Centrifugal Field (RCF) = 1.118 x r x
(revolutions per minute)2  x  10 -5
[ where the radius r is in centimetres (cm)]
1g = 981cm/s2

Equation to apply for RCF units of g

Applied and Relative Centrifugal Field
The Applied Centrifugal Field G                                                 G= 4π2 x r x (revolutions per minute)2 / 3600
[in units of cm per second squared]
and the Relative Centrifugal Field (RCF)                      RCF= 1.118 x r x (revolutions per minute)2  x  10 -5                                      [in units of multiples of gravity]
[NOTE: G = RCF x g]
[the radius r is in centimetres (cm)]

Relative Centrifugal Field (RCF)
QUESTION:
A fixed angle centrifuge spins at 20 000 revolutions per minute.  The distance from the centre of the liquid suspension in the centrifuge tube to the axis of rotation is 35 mm.  What is the Relative Centrifugal Field experienced by the particle?
RCF= 1.118 x r x (revolutions per minute)2  x  10 -5

Example: calculation of RCF
Spins at 20 000 revolutions per minute.  Distance from the centre of the liquid to axis of rotation is 35 mm (remember to convert this to centimetres = 3.5 cm).
RCF = 1.118 x r x (revolutions per minute)2  x  10 -5
RCF = 1.118 x 3.5 x (20000)2 x  10 -5
= 1.118 x 3.5 x (4 x 108)  x 10 -5
= 1.118 x 3.5 x 4 x 103
RCF = 15652 g [where g means times the force of gravity]

Nomogram
Columns are (left to right): Radius (cm); RCF (g); Speed (rev/min)

The line gives an RCF of 100,000 or 1000g for a centrifuge radius of 10 cm and speeds of 30,000 and 3,000 rev/min respectively.

Types of centrifuge
Low-speed centrifuges   Swing-out rotors are used in low-speed centrifuges (3000-6000 r.p.m.) for harvesting cells and larger organelles (e.g. nuclei).
Microcentrifuges   Fixed-angle rotors are used (up to 12 000 r.p.m) for higher-speed operation, for cells and precipitates.
Ultracentrifuges (speeds greater than 30 000 r.p.m.) are used for very small particles e.g. biological macromolecules.

Swing-out low-speed centrifuge and sample tube
Swing-out centrifuges are used at speeds of 4000-10000 revs. per minute, with RCFs of 3000 – 7000g.
Mainly used to collect material that sediments rapidly
eg PEI resin from HCl

Table-top microcentrifuge
One of the most commonly used centrifuge types. Can reach speeds of 12000-15000 rpm (RCF about 12000g).
Mainly used to harvest small volumes of cells, or isolate microgram quantities of (for example) proteins and nucleic acids.

Microcentrifuge has a fixed-angle rotor and uses microcentrifuge tubes
Eppendorf’ tube
capacity 1.5ml

Smaller (0.5 ml or 0.2 ml) tubes require use of different rotors

Floor-standing large centrifuge
For centrifuging large volumes of a mixture at one time.

Centrifuge for 96-well plates

An ultracentrifuge

Ø  Refrigeration
Ø  Operates under vacuum

Ultracentrifuges
Refrigeration is needed to counteract the heat generated during centrifugation at high speed, to keep clinical and biological specimens stable.
Evacuation also reduces air friction.
Analytical centrifugation uses an ultracentrifuge with an optical system to observe the settling of the particles.

Different types of centrifuges

Rotor types

Centrifuge with swing-out rotor
When the rotor is in motion and the tubes are horizontal, why doesn’t the liquid drain away?

Angled rotor
This is the type most often used with microcentrifuge tubes. Another version is used with very high speed centrifuges
Solid construction; heavy; sample tubes have tops fixed in place during spinning.

Fixed angle rotors
Are ideal for pelleting during differential centrifugation to separate biological particles with different sedimentation rates.
The pellet is the name given to the material which collects at the bottom of the centrifuge tube. The liquid left above the pellet is the supernatant.

Vertical rotor
Ø  Vertical rotors use sealed centrifuge tubes  (diagram is not accurate!). Why?
Ø  Samples sediment across the diameter of the tube – short run times.

Centrifuge: application at UEL
Sample preparation for HPLC high performance liquid chromatography:
example
Analysis of herbal medicine tincture solutions and dried plants for active ingredients

HPLC column. Can be blocked by small particles. Remedy: microcentrifuge the sample solutions before analysis and use the clear solution above the pellet for analysis.

Centrifugal force
Centrifugal force acts in an outward direction when a particle or object moves in a curved or circular path.
A centrifuge is a piece of
equipment that rapidly spins
a number of tubes which contain
a suspension of particles in a liquid

Sedimentation
Sedimentation is the settling of solid particles through a liquid under the influence of a gravitational or centrifugal field.
The speed at which a particle will settle in a liquid is related to the size, shape and density of the particle.
The size of the particle is the major determining factor in the settling (or sedimentation) rate of a particle, but its density and weight also make a difference to the speed.

Sedimentation of different-sized particles

Factors controlling the sedimentation of a particle
The denser a particle, the faster it will sediment
The heavier the particle, the faster it will sediment
The denser the solution in which it is suspended, the slower a particle will sediment
If the particle and solution are of equal density the particle will not sediment
The greater the centrifugal force, the faster it will sediment

Sedimentation and particle size
Particles of different sizes can be separated by the difference in their sedimentation rate.

Centrifugation is a convenient method of increasing the speed of sedimentation of all the particles in a mixture.
But the relative rates of sedimentation of different size particles are not affected by the speed of the centrifuge.
For example if particles of size A sediment ten times faster than those of size B at 1000 revs per minute (centrifuge speed), A also sediments 10 times faster than B at 10,000rpm.

Rate of sedimentation
The rate of sedimentation of a particle in a solution (medium) is given by Stoke’s Law:
V= 2  x R 2p - ρm) x g x RCF
9                            η
V = sedimentation rate in cm per second;
R is the radius of the particle in cm;
ρp and ρm are the densities of the particle and medium (solution) in gm/cm3
g is the gravitational field in cm/sec2, which should be multiplied by the Relative Centrifugal Field (RCF)
η is the viscosity of the medium (units are gm/sec.cm).
V= 2  x R 2p - ρm) x g x RCF
9                            η
where V = sedimentation rate in cm per second
QUESTION: what if ρp and ρm are equal?
- the densities of the particle and the medium (the solution).

calculation of rate of sedimentation
V= 2  x R 2p - ρm) x g x RCF
9                            η
For a particle of radius R  0.02 cm (diameter 400 microns)                                              [1cm=10mm=10,000microns]
particle density ρp of 1.2 gm/cm3 in a liquid of density ρm 1.0 gm/cm3
liquid viscosity η of 1.00
g= 980 gm/cm2 in a centrifugal field with RCF=1000g:
What is the Sedimentation rate (v)  in cm/sec?
V= 2  x R 2p - ρm) x g      [1cm=10mm=10,000microns]
9                            η
Particle radius R  0.02 cm (diameter 400 microns)
particle density ρp of 1.2 gm/cm3 in a liquid of density ρm 1.0 gm/cm3
liquid viscosity η of 1.00
g= 980 gm/cm2 in a centrifugal field with RCF=1000:
Sedimentation rate (v) is calculated as
= 2 x (0.02)2 x (1.2 – 1.0) x 980 x 1000 /( 9 x 1)
= 2 x 4 x 10-4 x 0.2 x 980 x 1000 / 9
= 17.42 cm/sec

We may wish to calculate not the rate of sedimentation (in cms per second), but the time taken for a particle to settle – this is more useful to know.

Distances needed to calculate time for a particle to settle :
rt (radial distance to top of liquid)
rb (distance to bottom of tube)

Settling out time for a particle
t = 9 x  η  x  (ln rb/rt) x 3600
8     π2     p - ρm)   (rev/min)2 x R2
η is the viscosity of the medium (units are gm, sec and cm).
rb and rt are the radial distance to bottom and top of liquid
ρp and ρm are the densities of the particle and medium (solution) in gm/cm3
R is the radius of the particle in cm;

Centrifugation is used for two main applications: Preparative and Analytical
Preparative is the separation of components of cells etc into their components
Analytical produces information on the quantities of components present.
Preparative also divides into two types:           1) Differential (this week) and

Preparative centrifugation
1. Differential Centrifugation
uses differences in sedimentation rate
selectively sediment out particles with particular properties
applied centrifugal field is increased step-wise
at each stage different types/sizes of particles can be collected
Differential centrifugation

The longer a solution is centrifuged, the more the particles separate by size.
In Differential centrifugation, the centrifuge is run for long enough for all the particles of a certain size to pellet out, leaving the smaller sizes suspended in the supernatant.

Differential centrifugation: separates into different particle sizes
Largest particles separate out first (into the pellet)
A suspension of particles is centrifuged just long enough to pellet the largest types.
The supernatant liquid is poured off into another centrifuge tube.
But some small particles also ended up in the pellet. What to do about it?

Sedimentation – getting clear separation into particle sizes
Particles of small size ‘trapped’ in the pellet.
Answer: remix the pellet with liquid to get another suspension; re-centrifuge until all the large particles are in the pellet.
After this second stage, an even smaller number of small particles are ‘trapped’.
The supernatant liquid is added to the first supernatant liquid for centrifuging out the next (smaller) size particles.

A useful rule for differential separation:
It has been shown in practice:
to achieve an effective separation between particles of two different sizes, they must differ by an order of magnitude
ie – one must have a diameter 10 times that of the other.

Angled rotor
Sedimentation patterns in different
centrifuge
rotors

Practical example of Differential centrifugation
Differences in sedimentation rate are used to selectively sediment out particles with particular properties: example - fractionation of skeletal muscle homogenate.      (see K.Wilson and J.Walker, Principles and Techniques of Practical Biochemistry)
applied centrifugal field is increased step-wise
at each stage different types/sizes of particles can be collected.

Example of a step-wise separation of a skeletal muscle homogenate
Differential centrifugation Stage 1
centrifuge the  mixture of 10% (w/v) of the homogenate at 1000g (RCF) for 10 mins: pellet = cell nuclei plus debris

Differential centrifugation Stage 2
supernatant from stage 1 is then re-centrifuged at 10,000g for 10 min; pellet = contractile apparatus.
Stage 3
supernatant from 2 re-centrifuged at 20000g for 20 min; pellet = mitochondria
Stage 4
supernatant re-centrifuged at 100 000g for 60 min; pellet = crude microsomes; supernatant contains cytosol.   [ultracentrifuge required]
Ribosome from E.Coli.
[Microsomes are rich in ribosomes]

Centrifugation is used for two main applications
Preparative and Analytical.
Preparative is the separation of components of cells etc into their components.
Analytical produces information on the quantities of components present.

Preparative centrifugation
also divides into:
1:Differential
The centrifugation field is increased in stages.
1. Rate zonal (particle size separation)
2. Isopycnic (particle density separation)

1: Differential centrifugation
Differential Centrifugation uses differences in sedimentation rate to selectively sediment out particles of different sizes.

BUT: Differential Centrifugation is not very good at separating particles which are only slightly different in size.

divides into:
1. Rate zonal (particle size separation)
2. Isopycnic (particle density separation)

In Density Gradient centrifugation, the density of the solution in the centrifuge tube increases from the top to the bottom of the solution.

RATE ZONAL centrifugation
Particles are separated by size
Different sizes of particles move at different speeds down through the density gradient.

• RATE ZONAL centrifugation is like a race: the particles travel at different speeds towards the bottom of the centrifuge tube. Their size controls their speed.
• Particles which differ is size by 10% or more can be separated.

RATE ZONAL centrifugation:
how it works
• layer a mixed sample in solution onto the top of a shallow pre-formed density gradient
• centrifuge
• larger particles will move faster through the gradient than the smaller
• distinct zones (bands) of different size particles
• Centrifugation is stopped before any band reaches the bottom of the tube.

2: Density Gradient RATE ZONAL (particle size separation) – THEORY
If two types of particle are very similar in density, but of different mass (that is, radius, or size) the two types will sediment at different rates.
Sedimentation rate (Stoke’s Law) depends on the radius squared (R is the radius):
V= 2  x R 2p - ρm) x g x RCF
9                            η

Rate-Zonal Density Centrifugation
The density gradient does not change very much down the tube
Antibody classes all have very similar densities, but different masses.  Separation based on mass will separate the different classes, but separation based on density will not be able to resolve these antibody classes

Criteria for successful rate-zonal centrifugation
Density of the sample particle must be greater than that of the highest density portion of the gradient
The pathlength must be enough for separation to occur
Time is important.  Too long a run, and all particles may pellet at the bottom of the tube.

Rate-zonal centrifugation

2: b. Density Gradient  ISOPYCNIC centrifugation
If a particle and solution are of equal density the particle will not sediment.
Samples are added to solutions in which the liquid density increases towards the bottom of the centrifuge tube (and the solutions are then centrifuged).

Isopycnic (from the Greek: isos: equal, pyknos: dense)
Requires a steep density gradient (the density increases fairly rapidly down the centrifuge solution)
During centrifugation, once a particle reaches a part of the solution with the same density as itself, it will not sink further.

Rate Zonal vs Isopycnic density gradient centrifugation

2: Applications of density gradient centrifugation
where there is more difficulty in separating out a mixture – for example where there are several kinds of large molecules or particles which must be separated from one another.
to obtain fractions enriched in individual proteins from the supernatant obtained from a low-speed centrifugation of broken cells.
for separation of protein molecules, high rotor speeds (often up to 70000 rpm) are required.

Solutions used in forming a density gradient
Sucrose - a sugar
Glycerol
Ficoll – a polysaccharide
Percoll – a colloidal silica
Caesium Chloride – an alkali metal salt Disadvantage: may damage biological structures

for either Rate-Zonal or Isopycnic

With a special mixing instrument (will form linear, concave and convex gradients).
Or
A self-forming gradient (a solution which forms a gradient just by centrifuging it).

Percoll will spontaneously form a LINEAR gradient when a solution is centrifuged
Percoll solutions contain colloidal silica particles coated with a thin layer of plastic.  Centrifuging a solution will spontaneously form a LINEAR gradient –known as a self-forming gradient. The Percoll colloid settles to the bottom of the tube, making the solution denser from the top to the bottom

Laboratory practical is on isopycnic density gradient
1. A gradient has been pre-formed in a centrifuge tube using Percoll
2. Carefully pipette/layer the density marker beads (coloured) on top of the Percoll solution

1. Centrifuge the solution. The beads will settle in coloured layers. Each colour represents one density.
2. Measure the distance that each coloured layer has moved from the top of the solution.

Rf = (distance travelled by a layer of beads/total distance)
distance travelled by a layer
total distance

Analytical Centrifugation
Analytical produces information on the quantities of components present.
It usually requires the use of an ultracentrifuge – high speeds are required.
A spectrometer is used to monitor changes in the optical absorbance of the solution as the particles sediment.

Uses of analytical centrifugation
Determination of the purity of macromolecules
Determination of the Relative Molecular Mass of molecules in solution
Changes in Relative Molecular Mass of molecules
Study of the binding sites (receptors) on proteins for cell signalling

Analytical rotor and absorption cell

Analytical ultracentrifugation

Analytical centrifugation:
measuring changes in optical characteristics.
The rate of movement of a concentration boundary gives information on the biomolecule.

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