Biophysics II By A/Prof. Xiang Yang Liu Biophysics Lab Department of Physics, NUS

Announcement Term Test – Mar 2, 2007, Fri Venue: S Time: 8:30-9:30am (1 hr) Closed book. One A4 “cheat sheet” is allowed.

Outline ELECTROPHORESIS Discussion: you are supposed to prepare your questions to be discussed in the lecture.

Example

If the temperature of the dissolution of sugar crystals in water is not very far from the melting temperature (T m ), the solubility (x i mole fraction) of sugar can be described in terms of the dissolution enthalpy (  H m ). Treat the dissolution equilibrium as a special chemical equilibrium. Derive the relationship between x i and  H m.

ELECTROPHORESIS Most of the remarkable advances in molecular biology over the past few decades would have been impossible without electrophoretic methods

ELECTROPHORESIS The great majority of the polymers of biological interest are electrically charged. Polyelectrolytes are somewhat arbitrarily classified as “strong” or “weak,” depending on the ionization constants of the acidic or basic groups. They may be strong polyacids, such as the nucleic acids; weak polybases, such as poly- l-lysine; or polyampholytes, such as the proteins.

ELECTROPHORESIS electric charge differences can be used to separate and analyze mixtures of biopolymers: electrophoretic methods are used in every area of biochemistry and molecular charged: most important physical technique available to scientists working in these fields.

Electrophoresis: General Principles Electrophoresis: The transport of particles by an electrical field. The charged molecule is not alone, but in the presence of many other charged particles, and these will both influence the local field and interact with the macromolecule, making analysis difficult.

Diffusion through a solvent The Diffusion coefficient and the fraction coefficient  Diffusion coefficient introduced Albert Einstein: D = kT/f f: friction coefficient-measures the resistance encountered by the molecule in moving through the solvent. Stokes’ Law for a sphere of radius a f o = 6  a  : the viscosity of the solvent D o = kT/6  a

Electrophoresis: General Principles An idealized, simplified situation: an isolated charged particle in a nonconducting medium. The force experienced by a particle in an electrical field is given by Coulomb’s law, F = ZeE (E-electric field: potential per unit length) The viscous resistance of the medium to the motion: -fv (f: the frictional factor) The viscous resistance of the medium just balances the driving force. fv = F = ZeE

Electrophoresis: General Principles Electrophoretic mobility U (the ratio of velocity to the strength of the driving field) U = v/E = Ze/f If the particle happens to be spherical, Stokes’s law applies U = Ze/6  a The zonal techniques: In these methods, a thin layer or zone of the macromolecule solution is electrophoresed through some kind of matrix. The matrix provides stability against convection. In addition, in many cases the matrix acts as a molecular sieve to aid in the separation of molecules on the basis of size.

Electrophoresis: General Principles The kind of supporting matrix used depends on the type of molecules to be separated and on the desired basis for separation: charge, molecular weight, or both. Almost all electrophoresis of biological macromolecules is at present carried out on either polyacrylamide or agarose gels

Electrophoresis Each macromolecular solution is applied in a thin layer in one well. If several components of different mobility are present, they will separate during electrophoresis, just as the zones of molecules of different sedimentation rate separate in zonal centrifugation. Usually, a dye of high mobility is added; its migration serves to mark the progress of the experiment.

Electrophoresis The dye also serves as a convenient measure of mobility; the relative mobility U ri of each component i is defined by U d is the dye mobility and d i and d d are the distances that component i and dye, respectively, have moved by the conclusion of the experiment

Ferguson plots A very simple relationship between relative mobility and gel concentration, logU ri = logU ri o - k i C where C is the gel concentration and is the relative mobility of component i when C = 0, that is, the relative mobility in free electrophoresis. The constant k i: large molecules will have large values of k, whereas very small molecules will have small values, and hence will behave almost the same way in a gel as they do in free electrophoresis.

Electrophoresis Ferguson plots for a number of commonly encountered solutions.

Example

Analysis of multisubunit structures by SDS gel electrophoresis a very widely used technique for the estimation of the molecular weights of polypeptide chains. the protein to be studied is first heated in a dilute solution of a detergent such as sodium dodecyl sulfate (SDS). This breaks down all native quaternary, tertiary, and secondary structures in the protein.  Usually, a reducing agent such as  -mercaptoethanol is also added to reduce any disulfide bonds.  The protein is then electrophoresed in the presence of SDS.  The separation proceeds on the basis of polypeptide-chain weight, and is nearly independent of the charge on the polypeptide.

Analysis of multisubunit structures by SDS gel electrophoresis General principles: First, SDS at a given solution concentration binds to many different proteins at a constant weight-weight ratio: there is a defined number of bound SDS charges per amino acid residue; therefore, the charge contributed by SDS is proportional to protein molecular weight. the complexes between SDS and proteins are extended structures: molecules with both charge and friction proportional to molecular weight. As in that case, this predicts that the free mobility will be essentially independent of molecular weight, and that separation will be by the effect of sieving.

Analysis of multisubunit structures by SDS gel electrophoresis As in the case of DNA, there exists, for each particular gel type and concentration, an approximately linear relationship between the logarithm of the protein molecular weight and mobility. logU ri = logU ri o - k i C DNA samples (open squares) are restriction fragments from a bacterial plasmid. Proteins are polymers of the globular domain of histone H5, cross- linked with either glutaraldehyde (squares) or dithiobis (succinimidyl propionate) (circles).

References Section 5.4 in Principles of Physical Biochemistry