Electrophoresis

J = ∑ LiXi (1.3)

where:

• external forces Electric fields• internal forces i.e. diffusional force

XDi, which describes the tendency of Brownianmotion to restore a uniform concentration of all componentsthroughout a system.

i=1

N

CHEM 305

CHEM 305

e.g. Monitor levels of proteinexpression, purification protocols,or the time course of protein degradation (pulse chase experiment)

C. Ma et al., Prot. Sci., 11, 546 (2002)

CHEM 305

2. Electrophoresis

A solute in a solution will migrate from a region of high concentrationto low concentration

What should we expect if the macromolecule has a net charge qand we apply an electric field?

+

+

J2

+

+

E

?

CHEM 305

+

+

+

+

E

The ion will feel an electrical force:

Felectric = qE

and a frictional force

Ffriction = vf ,

where f =6πηa. In a constant electric field, the forces will balance out, thus wecan define a steady-state velocity as

v = qE (1)f

CHEM 305

We can also define an ion’s electrophoretic mobility, µ, as

µ = v = q (2)E f

For a spherical molecule of charge ze and radius a

µ = ze (3)6πηa

with e being the charge of an electron. The equations given up this pointare quite straightforward. Unfortunately, they cannot be used to describeelectrophoresis of biomolecules. Why?

CHEM 305

+

E

+

E

-- -

- -

or

?

+

E

?

Elocal

Reality: A biomolecule with a net chargeq will be surrounded by a cloudof counterions in solution.

Ideal: Ions at infinite dilution in anon-conducting solvent

++

+

+

CHEM 305

More specifically

e.g. 1.5 Å resolution structure of a water soluble fragment of the “Rieske” iron-sulfur protein of the bovine heart mitochondrial cytochromebc1 complex by S. Iwata, M. Saynovits, T.A. Link, and H. Michel(Structure, 4, 567-579, 1996)

CHEM 305

Applying an electric field:

net effect CHANGE IN CHARGE DISTRIBUTION

CHEM 305

Note that there will not be a complete charge separation as this is much tooenergetically unfavourable. Instead the ions and the biopolymer will only moveby a small amount. Let us determine what the mobility would be under thesecircumstances.

Let us begin by treating the charged atmosphere around the biopolymer as a continuous distribution (i.e. ignore individual charges). The electrostaticpotential Φ at a distance r away from a uniformly charged sphere of radius ain a medium of dielectric constant ε is

Φ = ze/ εr for r > a (4)

ε

a

z

CHEM 305

By solving an approximate form of the Poison-Boltzmann equation, it can beshown that

Φ = ze expκ(a-r) (5)εr (1+κa)

where κ a screening parameter (units = length-1) and is given by

κ = 8πNAe2 I ½1,000 εkT

with I being the ionic strength. This latter parameter is defined as

I = ½ ∑ Cizi2

where Ci is the molar concentration.

The equation for the screening parameter clearly indicates that the higher theionic strength, the higher the screening.

( )½

i

If the screening potential is constant in an electric field, then it can beshown that the electrophoretic mobility for a spherical particle of radius a is given by

µ = ze X1(κa) (6)6πηa (1+ κa)

where X1(κa) is a tabulated function (by D.C. Henry).

This equation still does not adequately describe electrophoretic mobilitybecause it does not account of the mobility of the ions.

How would mobility of the ions and the motions of the macromoleculeschange things?

CHEM 305

CHEM 305

CHEM 305

This is too complex to describe analytically. In addition, macromolecules cannotbe easily approximated as spherical charges.

Thus mobility is simply taken to be proportional to charge on the macromolecule.And electrophoresis is used as a qualitative method in the analysis and separation of proteins and nucleic acids.

Use electrophoresis to obtain information about relative charge(for molecules of the same size and shape)

Use electrophoresis to obtain information about relative size(for molecules of the same charge)

CHEM 305

Practical applications of electrophoresis

In practice, solid supports which are permeated with buffer are used inelectrophoresis, e.g.

paper, thin layer cellulose, cellulose acetate,

• polyacrylamide gels, • agarose gels (mol. weight >200kDa),

• ion-exchange papers (which selectively retardcharged molecules)

weak or non-speficicinteraction with macromolecules

retard the motion ofmacromolecules

There is NO quantitative analysis of electrophoretic mobility possible insolid supports. Why?

CHEM 305

Electrophoresis using paper as a solid support

posi

tive

char

ge

refe

renc

e

nega

tive

char

ge+ -

Ref: Voet and Voet, Biochemistry, New York: John Wiley and Sons, 1995, p.90

Protocol:

- The paper is saturated with a buffering solution.- Sample is introduced in the middle.- A DC potential of 100-1000V is applied.- The band migrates.- The paper is removed, dried and treated with a

color producing agent so that thebands can be observed.

CHEM 305

e.g. Ninhydrin is used to visualise amino acids bands

CHEM 305

Applications

1) Determination of the isoelectric point of a macromolecule

The charge on a protein or other macromolecule depends on pH. At the isoelectric point [pI = ½ (pKa1 + pKa2)], the mobility of themacromolecule is zero.

N Cα C

O

HH

H

H

OHH

+N Cα C

O

HH

H

H

OH

+

-

N Cα C

O

HH

HOH -

pH=1 pH=7 pH=14

CHEM 305

+ -

+ -

+ -

N Cα C

O

HH

H

H

OHH

+

N Cα C

O

HH

H

H

OH

+

-

N Cα C

O

HH

HOH -

CHEM 305

N Cα C

O

RH

H

H

OH

+

-

What do you expect will happen for different R groups?

e.g. alaninehistidinelysineglutamic acid

CHEM 305

Isoelectric points of proteins

The isoelectric point is the pH at which the net charge of the proteinis zero. It can be calculated using a number of tools on the web.

e.g. http://www.expasy.org/tools/protparam.html

or can be determined experimentally using isoelectric focusing (IEF). With thepresence of a pH gradient in the IEF technique, the protein will migrate to theposition in the gradient where its charge is zero. Proteins with a positive netcharge will migrate toward the cathode until it meets its pI. Proteins with anegative net charge will migrate toward the anode until it meets its pI. If theprotein diffuses away from its pI, it will regain its charge and migrate back.This focusing effect allows proteins to be separated based on very small charge differences. IEF is performed under high voltages (> 1000 V) until the proteins have reachedtheir final position in the pH gradient. If IEF isperformed under denaturing conditions very highresolution and cleanliness of sample can

be obtained.

http://www.protein.iastate.edu/ief.html

CHEM 305

Protocol:- Place polyacrylamide gel in box with buffer solution(pH ~ 9 such that net negative charges and migratedownwards to the anode)

- Load the sample (protein + dye in SDS) in wells- Connect top electrode and run DC current (300V)- Bands will migrate- Remove gel and develop with stain

For proteins:

Electrophoresis using gels

+

-

CHEM 305

2) SDS-PAGE gels to determine molecular weight

SDS = sodium dodecylsulfate CH3(CH2)11SO3- Na+

PAGE = polyacrylamide

http://www.davidson.edu/academic/biology/courses/Molbio/SDSPAGE/SDSPAGE.html

CHEM 305

Why is SDS needed?

To denature the protein

To convert all proteins to similar rod-like structures.

Most proteins bind 1.4 g SDS/g amino acids – overall charge is proportionalto the molecular weight of the protein

Why do we need to denature the protein?

18 Å

M

Rf =relative distancetravelled

d = diameter of the hydrated polymer(10 Å)

CHEM 305

Fixes the protein in thegel by denaturing it and

complexes the dye to theprotein. Excess dye is

washed.

Protein quantities ≥ µg

Fixes the protein in thegel by denaturing it. A silver-protein complex

is formed.

~ 50 times more sensitivethan the Coomassie dye

Gel is dried or coveredwith plastic wrap and

clamped over a sheet of x-ray film. The film is

developed.

Protein quantities ≥ µg

Visualization of proteins on a gel

Coomassie blue Silver staining Radioactive labelling(e.g. 35S-Met)

CHEM 305

Electrophoretic mobility vs gel concentration

If we were to run gels of increasing concentration for a number of proteinsand determine the relative mobility, we would observe the following:

ln(R

elat

ive

mob

ility)

Gel concentration (% acrylamide)5 10 15 20

Increasingmolecular

weight

ln µ(c) = -kc + ln µ(0) (7)

c: concentration in % acrylamideµ: apparent mobilityk: constant which depends on

extent of cross-linking of gel &shape and molecular weight of proteins

Ferguson plot

CHEM 305

It may come as a surprise that at zero concentration, µ(0) is a constant for a set of similar kinds of molecules. This can be explained by looking at theequations for electrophoretic mobility.

protein-SDS complexes have a constant weight percent of SDS

protein charge can be neglected

net charge z is proportional to molecular weight M, but

18 Å

l = M

therefore z α l (8)

CHEM 305

The frictional coefficient is also roughly linear in molecular weight, i.e.

f = 6πηa= 6πη Vh

⅓ F

where Vh is the hydrated volume which is directly proportional to length l, and F is the shape factor. For a rod shaped molecule, we canapproximate the shape by a prolate ellipsoid:

It can be shown that the shape factor, F, for large a/b is

F = (a/b)⅔ /ln(a/b)

ab

CHEM 305

18 Å

l = M

ab

a/b l

Thus,

f α l⅓ l⅔ /ln l ~ l (9)

for large l. Finally, the mobility is

µ(0) α z = constant * lf l

i.e. the mobility at zero concentration is independent of molecular weight (sincel=M).

CHEM 305

Equation 7 shows that the mobility decreases as the amount of solvent in thegel support decreases, i.e.

This equation also shows that moleculesof different sizes will have differentmobilities, due to pore size.

= polymer

ln(R

elat

ive

mob

ility)

Gel concentration (% acrylamide)5 10 15 20

Increasingmolecular

weight

CHEM 305

IMPLICATION:

Many pores will accommodate the smallmolecules.

The large molecules will have to travellarger distances.

Agarose gels of nucleic acids

CHEM 305Ethidium bromide

CHEM 305

Summary

- Electrophoresis is a transport process. Equations for flux and mobility aredifficult to derive in the “real” case because biomolecules are not pointcharges and are surrounded by a “mobile” local electric field.

- Electrophoresis can be described qualitatively.

- A number of supports exists: paper, SDS-PAGE, agarose.