Ch 24pages 650-652

Lecture 12 – Electrophoresis

The rate at which equilibrium is reached depends on hydrodynamic properties such as the diffusion coefficient

The equilibrium concentration profile only depends on thermodynamic properties of the system and we derived that equation using either Boltzmann distribution function or imposing that the chemical potential does not depend on r

Summary of Lecture 11

Equilibrium sedimentation can be used to separate, purify and analyze all kind of cellular components and to measure the absolute molecular weight of biological molecules

The concentration profile at equilibrium is determined by the balancing of diffusion and concentration and is described by the following expression:

Summary of Lecture 11

20

2222

0 2

1)(ln rr

RT

VM

C

rC

(from the homework)

Summary of Lecture 11

20

2222

0 2

1)(ln rr

RT

VM

C

rC

ln(C) versus r^2

0

0.5

1

1.5

2

2.5

3

46 47 48 49 50 51

r*r

ln(C

)

(from the homework)

Summary of Lecture 11

20

2222

0 2

1)(ln rr

RT

VM

C

rC

C versus r at equilibrium

05

10152025303540

1 2 3 4 5 6 7 8

distance

Co

nce

ntr

atio

n (

arb

u

nit

s)

small protein(x5)

large protein

sum

Sedimentation in a density gradient is a common technique used to separate biomoleculesA salt solution is spun at very high speed to generate a density gradient (the density of the solution increases with the salt concentration); the concentration of CsCl will reach equilibrium as described by the equilibrium centrifugation equation:

Summary of Lecture 11

20

22

0, 2

1ln rr

RT

VM

C

C CsClCsCl

CsCl

CsCl

The biomolecule (e.g. DNA) will sediment at a point r’ where the density of the solution matches the partial specific volume of the DNA. The concentration profile around r’ is given by:

2

2

''2

exp)'()( rrrdr

d

RT

VMrCrC DNADNA

DNADNA

Summary of Lecture 11

The biomolecule (e.g. DNA) will sediment at a point r’ where the density of the solution matches the partial specific volume of the DNA. The concentration profile around r’ is given by:

2

2

''2

exp)'()( rrrdr

d

RT

VMrCrC DNADNA

DNADNA

This is a bell-shaped curve with standard deviation:

drdVMr

RT

DNADNA /'2

2

Electrophoresis

Electrophoresis is a primary technique to separate and analyze biological molecules

It takes advantage of the fact that proteins and nucleic acids are generally charged and therefore move in an electric field towards the positive or negative electrode depending on their charge

The velocity of motion can be derived in complete analogy to what was done for sedimenation by ultracentrifugation, i.e. by imposing that all the forces acting on the molecule, under steady state conditions, balance each other out

Electrophoresis

The velocity of motion can be derived in complete analogy to what was done for sedimentation by ultracentrifugation, i.e. by imposing that all the forces acting on the molecule, under steady state conditions, balance each other out

0 fe FF

0 fuZeE f

ZeEu

Where E is the electric field applied externally, e the electron charge and f the frictional coefficient. The quantity:

f

Ze

E

u

is called electrophoretic mobility.

Electrophoresis

This expression was used to measure the electron charge at the turn of the century, but biological molecules have complex electrostatic properties, because they are surrounded by counterions (e.g. mono and divalent ions for nucleic acids) that shields the electrostatic field in a complex way. As it moves, the molecule also drags its ionic atmosphere along with it, thereby affecting the frictional coefficient that depends in complex ways on the shape and charge of the molecule and on the nature of the electrophoretic medium. For these reasons, it is very difficult to measure absolute properties of biological molecules by electrophoresis. However, because the technique is so sensitive, it is used very effectively to separate molecules that differ very little in charge and/or mass

Gel electrophoresis of nucleic acids

Gels are three-dimensional polymer networks dissolved in a solvent. In acrylamide gel electrophoresis, the main technique for nucleic acids separation, the network is generated by cross-linking a copolymer of acrylamide and bisacrylamide to form a net-like structure. The degree of cross-linking can be controlled by the ratio of the bis-compound (the cross-linker) and acrylamide (that forms long linear polymers). Although most of the matrix is occupied by aqueous buffered medium, the presence of the network prevents diffusion and convectional forces and allows the separation of DNA molecules that differ even by a single base

Gel electrophoresis of nucleic acids

The path traveled by the molecule through the porous gel is very long, much greater than the length of the gel

The gel imposes additional frictional forces on the molecule

The macromolecules interact with charged groups on the gel network

The pore size may be too small for certain molecules to penetrate the gel matrix

All of these factors allow separation to be conducted with exquisite sensitivity to very small differences in mass, charge and shape

DNA sequencing

The most impressive application of gel electrophoresis concerns the ability to determine the sequence of single-stranded nucleic acids by fractionating DNA based on its size under denaturing conditions

The electrophoretic mobility of nucleic acids is determined by the number of phosphate groups

Each phosphate groups carries one negative charge at and around neutral pH, though this is largely shielded by positive ions so that the effective charge is more like 0.24e per phosphate)

DNA sequencing

High concentrations of a denaturant (like urea) and temperature (the power at which the gel is run) are used to break all secondary structure (disrupts W-C base pairs)

Because gel mobility is so sensitive to differences in charge of even one e (or 0.24e), polynucleotides chains that differ by even a single base can be separated by running gels at different concentrations of acrylamide depending on the size of the molecule one wishes to separate

DNA sequencing

How does one then apply this technique to the problem of DNA sequencing?

One could either use a chemical reaction selective for each type of base (e.g. G) to modify the polynucleotide chain so that it is broken after every guanine (Gilbert)

Alternatively, one could use an enzymatic procedure based on a DNA polymerase and 4 nucleotide analogues (ddN’s) that cause termination of chain elongation by a polymerase (Sanger)

DNA sequencing

The enzyme adds dNTPs as the chain elongates, but if the nucleotide has been modified to include H instead of OH at the 3’-position, where polymerization takes place, then the chain will terminate

This is done only a fraction of the time: the solution will contain 90% of dNTPs (which can be elongated) and 10% of ddNTPs (which cannot) so that not all chains are stopped at the first G (for example) in the sequence

DNA sequencing

If you run 4 separate reactions with analogues of A, C, T and G, each will contain a mixture of molecule that will terminate after each base, and by running the four lanes side by side, one can sequence DNA by labeling each chain with 32P and monitoring the position of the electrophoretic band on the gel by autoradiography

If one wants to be clever, it is possible to avoid using radioactivity by using ddNTP analogues that carry a fluorescent group, a different chemical group fluorescing at a different color for each of the 4 bases, so that a single reaction and single lane (instead of 4) can be used to completely sequence a DNA molecule

Electrophoresis of DNA

Electrophoresis under native conditions in either agarose (a mixture of a polysaccharide derived from algae) or acrylamide can be used not only to separate nucleic acids based on their size but also based on their conformation

Double stranded DNA - can be separated according to their size under native conditions; in water, the elecrophoretic mobility of DNA is independent of molecular weight because the charge density is constant); however, as the molecules wander through the pores of the gel, their mobility strongly depends on molecular weight for sizes of 10 (ten!)-100,000 base pairs

Electrophoresis of DNA

Topoisomers - Nucleic acids with the same molecular weight but different shape will also migrate differently under electrophoretic conditions; for example, DNA can be linear or circular: the circular DNA is more compact than its linear topoisomer and therefore travels faster. Different DNA’s can have different topologies (think of a figure 8) and they can be separated on a gel according to their topological properties (shape). This is used to study enzymes such as topoisomerase I and II which play critical roles in DNA replication and are targets of anticancer drugs

Electrophoresis of DNA

DNA bending - DNAs of a few hundred base pairs behave essentially as rigid rods; however, certain sequences (AT-rich sequences), certain chemical modifications induced by drugs that covalently modify DNA (e.g. platinated compounds used to cure various forms of cancer), induce bending in the DNA itself. These can be separated on a gel under native conditions

RNA structure - RNA molecules are synthesized as single strands, but then, like proteins, fold into complex secondary and tertiary structures that are essential for its function. These structures can be studied and separated by gel electrophoresis (acrylamide in this case)

Electrophoresis of DNA

Nucleic acid-protein interactions – gels can be used to study protein-DNA or protein-RNA interactions. Under native conditions, the mobility of a DNA differs depending on whether a protein is bound to it or not; if the exchange is slow compared to the time needed for separation, the two species will migrate with different mobility and the equilibrium constant can be measured by estimating the amount of DNA in each band. This technique can be used to study all sort of kinetic and thermodynamic properties of the interaction of proteins with nucleic acids.

Gel electrophoresis of proteins

Unlike nucleic acids, proteins are not uniformly charged and their net charge depends not just on the sequence of the proteins, but also on the pH of the solution

Furthermore, like RNA molecules or topoisomers, proteins will adopt different structures and therefore shapes, which will determine the mobility of the protein under electrophoretic conditions

One could use these properties to study the shape of proteins but, most often, electrophoresis of proteins is used to determine the molecular weight of protein samples and is therefore conducted under conditions where proteins are not structured (high concentrations of a surfactant, SDS, that causes proteins to denature)

Gel electrophoresis of proteins

An additional advantage of having SDS is that at concentrations higher than mM, most proteins will bind a nearly constant amount of SDS per amino acid (approximately 0.5 molecules of SDS per amino acid, on average)

Under these conditions, the charge of the SDS/protein complex is determine primarily by the surfactant itself, making the charge per unit weight independent of the protein sequence and therefore the same for every protein. Under these conditions, the mobility of SDS-treated proteins is determined only by the protein molecular weight; experimentally, there is a linear relationship between the Log of molecular weight and distance x traveled in the gel:

Gel electrophoresis of proteins

The mobility of SDS-treated proteins is determined only by the protein molecular weight; experimentally, there is a linear relationship between the Log of molecular weight and distance x traveled in the gel:

bxaM log

Where a and b are constant determined by the electric field strength and gel matrix

Gel electrophoresis of proteins

bxaM log

This property can be used to analyze protein molecular masses, although for some proteins that are highly charged (e.g. histones) or that binds unusual amounts of SDS (glycoproteins) or heavily modified (phosphorylated or methylated or acetylated proteins), this relationship is not true. Deviations from this behavior can therefore be used to monitor the modification state of a protein (e.g. its phosphorylation!).

Gel electrophoresis of proteins

Under native conditions, the mobility of a protein depends on its charge, which in turn depends in most cases on pH (ionizable groups on the surface of a protein have different charges at different pH)

At low pH, all proteins are positively charged bacuse the carboxy groups of Asp and Glu are neutral (COOH) while the amino groups of Lys and Arg are charged (NH3+), and so on for His and other ionizable groups

At high pH, all proteins are negatively charged instead (Lys and Arg are neutral, Asp and Glu are negatively charged). Thus, for each protein, there will be a pH value at which the protein is neutral (isoelectric point)

Gel electrophoresis of proteins

By creating a pH gradient in a gel, proteins can be separated not only based on their size but also based on their isoelectric properties

At the isoelectric point, the charge is zero and therefore the electrophoretic mobility is also zero

If one establishes a pH gradient so that the pH is high towards the negative electrode and low at the positive electrode, then proteins will move until they find their isoelectric point

If we then perform SDS-PAGE at a right angle, we will separate each spot on the gel composed of proteins of similar charge (but different mass) according to their mass. This is exploited in two-dimensional gel electrophoresis to separate even hundreds of proteins on a single gel.