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Sedimentation, electrophoresis and mass spectrometry

Tibor G. Szántó

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Related book chapters:

VI./1. Sedimentation and Electrophoretic Methods (pp. 379-387)

VI/1.1. Sedimentation techniques:

Sedimentation velocity method

Sedimentation equilibrium method

VI/1.2. Electrophoresis and Isoelectric focusing

Gel electrophoresis

Isoelectric focusing

X/7.Mass spectrometry (pp. 611-612)

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Physical methods in molecular and cellular diagnostics

Previous knowledge (high school physics):• Description of circular motion e.g. angular speed• Centripetal acceleration and centrifugal force• Bouyant force, Archimedes’ principle• Motion of a charged particle in electric field, the Coulomb force. The work done by the electric

field.• Motion of a charged particle in a magnetic field (Lorentz’ force)

Why are these methods necessary?• Macromolecules, cell organelles etc. have several physical properties that enable the use of

physical methods to explore the molecular background of their structural distortion in certaindiseases

What do we learn today? The principles of…• sedimentation techniques (sedimentation velocity method, density gradient centrifugation etc.) • gel electrophoresis (agarose, SDS-PAGE) and isoelectric focusing• mass spectrometry

Aim: to learn and understand the basics of principles behind those physical/biological methods thatare widely used to…• separate and identify proteins and nucleic acids based on their mass and charge• determine the composition of biologically important macromolecules (e.g. amino acid sequence of

proteins etc.)

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Sedimentation techniques• In biophysics and cell / molecular biology it is often required to

• separate molecules based on their size

• characterize the size and density

of molecules.

• Sedimentation techniques achieve these aims by examining the sedimentation of molecules in

strong „gravitational” field in centrifuges.

analytical ultracentrifugation

preparative ultracentrifugation

Eg

Why do we need a strong gravitational field for this?

522

26 23

23 21

10 9.81 0.1 1.6 10 J

6 10 6 10

1.38 10 293 4 10 J

g

t

ME m g h g h

E kT

h=0.1 m

Room temperature: 20 C = 293 K

M – molecular mass (g/mole)

Mass of a moleculein g: in kg:

236 10

M

266 10

M

Molecules don’t sediment in the earth’s gravitational field since the gravitational energy is similar in magnitude to the thermal energy (Et).

How to generate a strong gravitational field?

2

22 2 260

c

RPMa r f r r

RPM – revolutions per minuteIf RPM = 1000 1/min, r = 0.1 m

2

2

2

1097 1097 112

9.81 c

msma g

s ms

112-times standard gravity

!

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Sedimentation techniques

Name of technique Property to be determined

sedimentation velocity sedimentation constant

density gradient centrifugation density

sedimentation equilibrium molecular weight

Sedimentation velocity method

axis of rotation

Fc

Fb

Ff

In equilibrium the net force is zero.

The particle doesn’t accelerate, it sediments at constant speed. (The speed only increases as it gets farther away from the axis of rotation)

Fc – centrifugal forceFb – bouyant forceFf – frictional force

0 c b fF F F F 2

2 2

0 0

c

b

f

F m r

mF V r r

F fv

, 0 – density of the particle and the medium, respectively

!

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Sedimentation velocity method

2 2

0

c b fF F F

mm r r fv

2 0

0

2

1

1

m r fv

mv

Sr f

equilibrium condition

rearranging to find the sedimentation velocity upon unit acceleration, i.e. the

sedimentation coefficient (S).The unit of the sedimentation coefficient is

1 S (Svedberg) = 10-13 s.

Using the above equation one can determine the molecular mass of a molecule (M)

0 0

1 1

f S k T Sm

D

0

1

R T SM

D

kTD

f 236 10R k

Equations used in the derivation

Theodor SvedbergNobel prize in chemistry in 1926 for “his work on

disperse systems” (sedimentation and

diffusion)

!

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Sedimentation velocity method

• Very strong gravitational fields can be generated (up to 1,000,000 g)

• Molecules can be separated according to their sedimentation coefficient.

• Since the sedimentation coefficient depends on the molecular weight and

size, molecules are separated based on these parameters.

Co

nce

ntr

ation

Antibody (IgG) monomers and oligomers separated by centrifugation based on their

sedimentation coefficient

The larger a particle, the larger its sedimentation coefficient is.

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Sedimentation equilibrium method

• Usually performed • at lower revolutions per minute• for a long time (several hours or more than a day)to achieve equilibrium between• sedimentation and• thermal motion or diffusion

In the long run sedimentation would concentrate all molecules at the bottom.

• This is counteracted by diffusion.• The smaller a molecule is, the farther away it can diffuse

from the bottom.

no

rmal

ized

co

nce

ntr

atio

n

radius

MW2

MW1

bottom of the tube

• Since molecule # 1 is lighter than molecule # 2, it

can get farther away from the bottom.

• The molecular weight can be determined from the

slope of the curve: the slope is proportional to the

molecular weight.

• The molecular weight can be determined

independent of the form factor or the diffusion

coefficient.

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Density gradient centrifugationAIM• To determine the density of a molecule or particle (cells, organelles) • To separate molecules or particles based on their density

METHOD• Perform the centrifugation in a density gradient until equilibrium is reached

increasing density of the medium (0)

axis of rotation

FcFb 2 2

0

c bF F

mm r r

In equilibrium:

rearranging

2 00 1 0 m r if

• The particle experiences zero net force if it is in a

medium whose density is equal to its own density.• The particles will accumulate in this layer.

FcFb

FcFb

equilibrium position ( = 0)

net force

net forceIf the particle is above or below its equilibrium position, it will experience a net force such that it is accelerated toward its equilibrium position.

!

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Density gradient centrifugation

BIOLOGICAL AND MEDICAL APPLICATIONS• Separation of cells based on their density

Before centrifugation

Blood

Separation fluid Red blood cells +

granulocytes

Separation fluid

Mononuclear cells (lymphocytes,

monocytes)

Serum

Cells and the serum are separated according to their densities:

RBC > separation fluid > mono > serum

After centrifugation

Blood is layered on top of the separation fluid.

Red blood cells + granulocytes

Separation fluid

Serum

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The physical principles of electrophoresis

• Electrophoresis is the migration of charged electrical species when dissolved, or suspended, in an electrolyte through which an electric current is passed.

+ –

direction of electrophoresis

FqFf

In equilibrium (when the particle moves at constant speed):

0

0f q

F

F F

Fq – Coulomb forceFf – frictional force Only considering their magnitude:

f qF F

f v E Q

f v E z e

f – form factorv – speedE – electric field strengthe – elementary chargez – charge number

v Q z eu

E f f

u – electrophoretic mobility: electrophoretic velocity in unit electric field• The form factor depends on the size, and consequently the molecular weight of molecules• Since electrophoretic mobility depends on the charge (Q) and the size (molecular weight) of

molecules, electrophoresis is used for separating molecules based on their charge and size.

!

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Free vs. gel electrophoresis

Free electrophoresis: • matrix-free electrophoresis in which charged particles move in a solution• due to the low viscosity of the medium (aqueous solution) diffusion is not negligible

• Diffusion complicates the separation of molecules based on their charge or molecular weight• Therefore, it is rarely used nowadays

Gel electrophoresis: • electrophoresis takes place in a matrix (or gel)• the gel eliminates / slows down diffusion

• separation won’t be complicated by diffusion• the gel serves as an anti-diffusive and sieving medium• widely used for the separation of

• nucleic acids• proteinsaccording to their molecular weight

gel is usually made of agarose

gel is usually made of polyacrylamide

!

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Agarose gel electrophoresis

A little bit of chemistry:Agar is a polysaccharide isolated from algae.Agar is mixture of two components:• agarose: linear polysaccharide • agaropectin: heterogeneous mixture of smaller

oligosaccharides

• Nucleic acid is loaded into a well close to the negative electrode with a pipette

• Negatively-charged nucleic acid migrates toward the positive electrode

+

–

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Agarose

Agarose gel electrophoresis

+–

well

– –

– ––

– –

–

–

–––

–

• Nucleic acids are negatively charged at neutral pH due to the presence of phosphate groups• Long nucleic acids have lower electrophoretic mobility they migrate more slowly• Explanation: it is increasingly difficult for long nucleic acids to migrate across the pores of

agarose (“sieving effect”)

slow electrophoresis

fast electrophoresis

( )

z eu

f MW

!

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Agarose gel electrophoresis: biological applications

• Both single-stranded and double-stranded DNA and RNA can be separated according to their size.

• The gel is soaked with the fluorescent dye ethidium bromide.

• Nucleic acid-bound ethidium bromide fluoresces strongly under UV exposure.

• Each fluorescent band corresponds to nucleic acid with a certain size.

Determination of molecular weight:

• a calibration sample (“marker”) containing a mixture of DNA with known sizes is run in parallel

• the size of DNA is given in bp (base pair)

• the length of DNA in the experimental sample is compared to the known length of DNA in the marker

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Electrophoresis of proteins: SDS-PAGE

PROBLEM• While nucleic acids have a uniform negative charge at physiological pH, the charge of proteins

depends on their amino acid composition.

• Electrophoretic separation of native proteins not only depends on their size.

SOLUTION• Proteins are denatured with the charged detergent SDS (sodium dodecyl sulphate)

• it denatures proteins (removes their secondary and tertiary structure) all kinds of proteins will have a similar shape

• on average one SDS molecule binds to every 2 amino acid the protein will be uniformly negatively charged

heat + SDS–

– –––

–

– SDS

• SDS-coated proteins are electrophoresed in a gel made of polyacrylamide • The technique is called SDS-polyacrylamide gel electrophoresis (SDS-PAGE)

!

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Electrophoresis of proteins: SDS-PAGE

• The mobility of SDS-denatured proteins is approximately inversely proportional to the logarithm of their molecular weight.

1

lgu

MW

• Visualization: • with radioactivity (autoradiography)• chemiluminescence

protein

mixture

poly-

acrylamide

electro-

phoresis

• Proteins are separated according to their molecular weight.

• Markers are used like in agarose electrophoresis of nucleic acids for determining molecular weight

+ +

– –

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Electrophoretic separation based on charge: isoelectric focusing

• Proteins are amphoteric (do not confuse with amphipathic!!!)• they contain both acidic and basic functional groups• their charge is pH dependent

• There is a specific pH at which the number of positive and negative charges is equal. At this pH, called the isoelectric point, the protein is neutral.

• Aim of the technique: find the isoelectric point of the protein.

!

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Electrophoretic separation based on charge: isoelectric focusing

METHOD• A polyacrylamide gel is prepared in which there is a stable pH gradient.• Electrophoresis of native proteins (IN THE ABSENCE OF SDS) is carried out in the pH gradient.

pH 4 pH 5 pH 6 pH 7 pH 8 pH 9 pH 10

Isolectric point: pH 8 Isolectric point: pH 6

++ + – – –0

–electrode

+ electrode

++ + – – –0

forceforce

forceforce

• At a pH above their isoelectric point proteins are negatively charged• At a pH below their isoelectric point proteins are positively charged• If the negative electrode is at the high pH part of the gel, the proteins will move toward

the pH range equal to their isoelectric point.• At their isoelectric point they will stop moving since they do not have charge.

!

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Electrophoretic separation based on size and charge:Two-dimensional electrophoresis

• Isoelectric focusing in the first dimension is followed by SDS-PAGE in the second one.• Biological application: separation of thousands of different proteins from cells and tissues

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Mass spectrometryAIM• to determine the constituents of a molecule (e.g. what kind of amino acids are present in a protein)• from the mass / charge (m / q or m / z) ratio

PROCEDURE1-2. Introduce the molecules of interest into the gas phase AND ionize them3. Accelerate the ions in an electric field4. Analyze the accelerated ions, i.e. somehow separate them according to their m / z ratio5. Detect the ions (won’t be discussed)

1-2. Transfer of molecules to the gas phase and their ionizationTwo techniques are used in the biological applications of mass spectrometry

MALDI (matrix-assisted laser desorption/ionization)

ESI (electrospray ionization)

solid matrix

protein molecules of interest

laser shone on the surface• Both proteins and matrix molecules enter

the gas phase.• The matrix is ionized first.• Ionized matrix molecules ionize proteins.

Role of the matrix: to soften the ionization process to prevent fragmentation of the proteins

solution in a capillary

vacuu

m

• droplets are formed when the fluid enters the vacuum• they are ionized by an electric field

+–

!

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Mass spectrometry

3-4. Accelerate and analyze the ions

Classical mass spectrometer

ion source

magnet

magnetic field (outward toward

viewer)

circular path of charged,accelerated particle

position of particles is

determined by the m/q ratio.

Elec

tric

fie

ldAcceleration by the electric field:

21. 1:

2Eq q U mv

2 . 2 :

v m r BEq m Bqv

r q v

From equations 1 and 2:

2 2

2

m B r

q U

large m/q ratio

small m/q ratio

Step 1

Step 2

!

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Mass spectrometry

3-4. Accelerate and analyze the ions

Time-of-flight (TOF) mass spectrometer

Electric field

Drift region (neither electric,

nor magnetic field) L

Time required to cover the drift region:

2 2 1 2

2

Lt

v mt L

q Uq Uq U mv v

m

21. 1:

2Eq q U mv

The m/q ratio can be determined from the time of flight.

5*

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Take-home message

Ask yourself:

• What kind of forces are acting on a molecule in a centrifuge upon sedimentation?

• How can the density or the isoelectric point of an unknown macromolecule be determined?

• What are the similarities and differences of the electrophoresis of proteins and nucelic

acids?

• What is the aim and principle of mass spectrometry?

Medical relevance:

• Physical methods are more and more frequently used in diagnostics to explore the

molecular background of structural distortions.

• Density gradient centrifugation is widely used to separate the different cell types from the

blood

• Modern spectrometers are a fast way of obtaining molecular fingerprints and are widely

used to identify genetic diseases and for detecting polluting, poisonous or performance

enhancing substances.