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