Post on 08-Oct-2020
Hydrodynamic methods
Viscosity
Diffusion
Sedimentation
CENTRIFUGTIAN
viscosity
Centrifuges are used for • Preparation of biological materials
• Analytical studies for hydrodynamic
properties of macromolecules or
organelles (shape, size, density)
• It done through exposing biological
materials for strong force (moving sample
at high speed)
• Sedimentation of biological material
depends on the mass or volume or density
• Analytical method where molecules move
along the centrifugation axis aims to
determine the sedimentation velocity in
order to find the sedimentation coefficient
• Sedimentation coefficient is a number
which give information about molecular
weight and shape of the molecule
• Upon measuring concentrations
distribution under experimental conditions,
in which is not changing with time, thus,
molecules reach a sedimentation
equilibrium state
• This type of measurement gives
information about molecular weigh, density
at formation (composition)
Basic principles of centrifugation • Revolving the molecule around central axis will
generate a centrifugal force on the body
• If this molecule represents a precipitate or
particles or organelles with molecular weigh (M),
the intensity of centrifugal force (F) will be:
• F = M w2 x , (1)
• Where:
• w: angular velocity in radians / second
(red/sec)
• x: distance from central axis of rotation
• When molecule are large, or speed of
centrifugation is high, or distance from axis
is large, the intensity of centrifugation will
be high and therefore, precipitation of
molecule will be high
• Since biochemical experiments undergo in
aquous solvents, therefore, there are two
forces working against the centrifugal
force namely:
Buoyant force
• Since molecule will displace the liquid
medium to precipitate, then
Buoyant force = Mw2 x v-p (2)
• V-: partial specific volume; a change in
volume resulted when putting 1 gm of
molecule (dry weight) in large quantity of
solvent Centrifugal force
• For most proteins dissolved/ at 20oc, v- will
be 0.73 cm3/g
• Whenever the partial specific volume for
solute is high or whenever density of
solvent is high, the rate of precipitation of
molecule will be low
Frictional force • Molecule will generate friction as it moves
through the solvent
Frictional force = f v = f (dx/dt) (3)
• Where:
f: frictional coefficients
v or (dx/dt): rate of precipitation (change in
axis of rotation per time)
• Frictional coefficient depends on the solvent viscosity
• Equation 1,2 and 3 can be used to establish a relation between rate of sedimentation (dx/dt) and molecular weight (M) of molecule
• Molecule moves form speed to speed in central centrifugation, unless:
Centrifugal force= buoyant force + frictional force (4)
• This happens because frictional force increases with increasing of sedimentation whereas centrifugal force and buoyant force stayed constant for any molecules
and for any rotor speed.
• Practically, this type of equilibrium for these force happened quickly since molecule sediment under constant rate (dx/dt)
• by replacing equation 1 and 3 in equation 4 and by rearrangement, the following equations will be obtained:
Mw2 x = Mw2 X v-p+ f (dx) / (dt) (5)
M (1 – v- p) w2 x = f (dx/dt) (6)
M = f / (1- v- p) ((dx/dt) / w2 x) (7)
Therefore, sedimentation coefficient (s) can
be defined as:
s = (dx/dt) / w2 x
by replacing this definition in equation (7)
M = (f) (s) / (1 – v- p) (8)
frictional coefficient (f) can be determined
through experiments determination for
diffusion constant (D) and its unit cm2 / sec
D = RT / f (9)
Where:
R: gas constant (8.3*107gcm2/sec/deg/mol)
T: absolute temperature
F = RT / D
By replacing equation (9) in equation (8) gives:
M = RTs / D (1 – v- p) (10)
Or:
s = M (1 – v- p) D / RT
• Equation 10 is the basis in analysis of speed of precipitation, where rate of sedimentation coefficient (s) which can be used for determination of molecular weight (M) of molecules under experiment, and T,R,P,V and D are all constant
• Sedimentation coefficient, is a quantity
similar to electrophoretic mobility where
both are speed per unit force
• Molecular weight of macromolecules can
be determined by measuring
sedimentation coefficient, distribution
coefficient and partial specific volume
• Since these measurement are tiredsome,
take long time and need very expensive
instruments, therefor it replaced by
Polyacrylamide gel electrophoresis or
Gel permeation chromatography
• s is defined under standard conditions such as
temperature (20oC), water as solvent media and
written as s20,w
• s value represents a physical property, and used
for classification of macromolecules
• s for most macromolecules are in the range of
10-13 to 10-11 seconds
• For simplicity, s can be expressed in Svedberg
units (s)
1s = 1*10-13 seconds
Ribonucleasa A has s =1.85*10-13 seconds,
which abbreviated as 1.85 s
• s for proteins range between 1s to 10s.
• s for nucleic acid range between 30s to
50s.
• s for subcellular organelles range between
50s to 100s
• The aim of most of experiments using
centrifuges is to determine s
• Measuring RPM is through the relative
centrifugal force (RCF) which is defined as
RCF = (1.119 * 10-5 ) (rpm)2 . (x)
where:
X: distance of molecule precipitation from axis of rotation
rpm: revolution of molecule per minute
• RCF can be also determined through the
mammogram
• RCF is changing with the change of x
therefore, it is important to determine x for
each experiment published in scientific
journal
• Average RCF is determined by using the
value of x (represents half the distance
between the upper and the
lower distance in the test
tube from the axis of rotation)
Instrumentation for centrifugation
• Centrifuges are consist of two parts:
Drive shaft
Rotor
• Centrifuges are classified into:
Bench top centrifuges
High speed centrifuges
Ultra speed centrifuges
Bench top centrifuges
• Used for normal precipitation for heavy
materials
• Low speed between 4,000 – 15,000 rpm
• Can not control temperature
• Two rotors; fixed angle and swinging
bucket
• Tubes range from 1- 50 ml
• Pellet vs supernatant
High speed centrifuges
• Used for most biochemical applications
such as preparation of organelles
• Speed up to 25,000 – 30,000 rpm
• Temperature are controlled up to 4ºC
• Two rotors: fixed angle and swinging
bucket
• Speed breaks
Ultra speed centrifuges • Speed up to 500,000 x g
• Temperature are controlled
• Rotor chamber is vacuumed
• Fixed angle rotor made of aluminum or
titanium
• Chamber is covered
with steel armor
• Used for preparative
and analytical
measurements
• For analytical measurement, sample of 0.1
to 1 ml was put into the rotor and
centrifuged and light shine through the
sample was paralled to the axis of rotation
• Absorbance or transmittance for sample
will be accomplished right away
• The optical system detect and measure
the moving boundary of precipitating
molecules
Applications of centrifugation Preparative techniques:
- velocity sedimentation centrifugation
Separate molecules with different volumes from coarse
precipitates to
cellular ribosomes
- differential
centrifugation
• Sequential centrifugation processes with increasing the speed of the rotor
• It used to separate cellular components
• Primary centrifugation ranges from 600 x g to 20,000 x g
• After centrifugation, supernatant is poured into another centrifugal speed
• Last centrifugation uses 100,000 x g centrifugation contains the cytosol which consists of the soluble part of the cell (dissolved proteins and small molecules)
Analytical measurements:
Analytical measurements used to determine molecular weight, density and purity of biological sample
- Differential centrifugation
• Precipitation of molecules in homogenous media of density in order to measure the sedimentation coefficient
• During centrifugation, moving boundary will be generated between pure solvent and precipitating molecules
• Ultra speed centrifuge has the boundary, therefore, sedimentation velocity can be measured experimentally, thus determination of sedimentation coefficient, subsequently determining the molecular weight
• Can be used also to analyze the purity of macromolecules. If only one layer of moving boundary was detected in centrifugal tube this indicate that sample has one component, and therefore it is pure
- density gradient centrifugation
• Sample is centrifuged in liquid medium that density increased from top to bottom. This technique allows to separate a mixture containing different components of macromolecules and measure their sedimentation coefficients
Two methods depends on the same idea are:
- zonal centrifugation
• Sample is centrifuges in prepared media
with density gradient
• The media is prepared prior to
centrifugation using automatic gradient
mixer using solution of low molecular
weight solvent such as sucrose or glycerol
to fill the centrifuge tubes
• Sample is put over this solution in
swinging bucket rotor
• Centrifugation in ultra speed centrifuges allows
the molecules to move with rate depending on
singles values for each macromolecules
• Different macro molecules will separate as
zones and stay separated from each other
• Centrifugation will be stopped before any
molecules reach the bottom of the centrifugal
tube
• Zones will be separated by collecting fractions
• Sucrose concentration can be reach up to 60 %
with density reaching to 1.28 g/cm3
- isopyenic centrifugation or equilibrium density gradient ultracentrifugation
• In this method, density gradient will be formed during centrifugation
• Molecules will be separated according to their densities
• The sample is dissolved in a solution containing salt with high density such as cesium chloride or cesium sulfate
• Cesium salt can be used to establish density gradient up 1.8 g/cm3
• Under the force of centrifugation, cesium
salt will be redistributed to form media with
optional density from top to bottom
• Macromolecules will move to a zone in
centrifugal tube where their densities are
equivalent to that zone density, e.g.
macromolecules move to a zone where
total force is equal to zero
• At least two days needed to establish
cesium gradient
• Used to separate pure macromolecules in
addition it used to measure S