Lecture 17: Application of Sedimentation concept and EpilogueReviewDiffusion o Collisions amongst molecules o Model of random Walk o Friction and it’s relation to molecular structure o Fick’s laws o SedimentationToday o Sedimentation in centrifuge o Density gradient centrifugation (application to DNA problems) o Concept of viscosity o Electrophoresis o Gel electrophoresis o DNA sequence analysis o Pulsed field gradient electrophoresis o Application to DNA and Proteins
Density Gradient CentrifugationUsing salt or sucrose solution where it’s difficult toovercome effects due diffusion it is possible to createdensity gradient across a tube in a centrifuge. Sincesedimentation coefficient depends on: s ∝ (1 − ρ v )and ρ(x)=≈ρ top+(dρ/dx)x, it is possible to find a locationwhere ρν =1. At this location forces due buoyancy andcentrifugation exactly cancel leading to zero mobility.This is where the molecular migration stops and can beused to achieve separation as shown below +
ViscosityConsider laminar flow, generated in figure below.Liquid in contact with moving wall will move withvelocity of the wall while the liquid at the bottom wallwill be stationary. This creates a momentum gradientalong y.The consequence of the momentum gradient is thatthere is net momentum flux transferred in the oppositedirection. Each of these laminar layers creates aneffective friction amongst layer whose magnitudedepends on the pressure gradient along the x direction.The viscosity is therefore defined as, du yJ mu = −η dyNote that the frictional coefficient f is directlyproportional to the viscosity coefficient.
Viscosity (Continued)To measure viscosity coefficient, we can determine theterminal velocity of sphere and relate it to the viscosity ofthe fluid. Generally, same sphere can be used to compareviscosities of different fluids. However, more commonly anOswald viscometer is used. Here a fixed volume of liquid isallowed to run through a glass capillary and time required is measured. The viscosity of the fluid is calculated by comparing it to the fluid of known viscosity. Measured viscosity also depends on the density of the fluid, since the pressure difference is directly related to it. η ρ t . This method is generally 1 =1 1 η ρt 2 1 1 suitable for reasonably low viscosity fluids. However, for a highly viscous fluid, a cone viscometer is commonly used. In thismethod, a spindle is immersed in viscous fluid and theforce required to maintain certain rotational frequency ismeasured. This allows measurement of the viscosity as afunction of rotational speed. Generally, polymer solutionsshow a dramatic dependence on the rotational speed. Hence they are termed as non-Newtonian fluids. By measuring the viscosity as a function of concentration one can attempt to relate the structural changes occurring under dynamicconditions.
Gel-electrophoresis Just as insedimentation processes, we exploited the balancingof forces involving gravity and friction. It is possibleto extend this idea where we replace mechanicalforces with electrical forces. In this way, moleculesthat have charge can be imparted with differentterminal velocity, ZeE ZeE = fu u = f
The quantify u/E is termed as an electrophoreticmobility and the method is called as electrophoresis.Since DNA molecules have negatively charged PO4groups, single strands of DNA molecules weresequenced using a clever technique. Gel ElectrophoresisActually, most of the electrophoresis studies use gelmedia as opposed to solutions. Gels can be made withspecial polymers such as gelatin, agar, or poly-acrylamide. The common features of gel that makesthem valuable for these studies are: 1. Convection or accidental mixing is avoided. 2. Owing to their micro-porous structure they slow the speed of migration significantly depending on the size of the protein or DNA. 3. Polymer-bio-molecule interactions can be influenced by selecting the size of the network mesh (concentration) and/or charges on the gel forming polymer 4. Owing to the obstructive nature of the of polymer, the actual path taken by bio-molecules is much longer than the length of the gel allowing for better separation. (Think about the resolution obtained on a chromatographic column)As shown before, one of the clever methods to sequenceDNA in seventies was to subject single stranded DNA tospecific enzymes that cleave a specific base in DNA. Asthere are only 4 bases, this method allowed structuralsequence of DNA to be determined using radio-labeled
DNA. The trick here was to use 7m urea. It disables thebase pairing interactions and leaves the chargedphosphate groups unaffected. So the DNA migrateselectrophoretically. To improve resolution and extendthe range of the technique to higher molecular weights,a pulsed field gradient electrophoresis was invented. Applications to ProteinsFundamentally, the same ideas can be used to separateand identify new proteins. The frictional coefficients ofthe proteins depend on their size and shape. Also chargeon the proteins is dependent on their basic amino acidsequence. The net charge depends on the PK andtherefore on the pH of the buffer solution. Sincedifferent proteins have different isoelectric points (i.e.where the net charge on the protein is zero), a methodof isoelectric focusing has been developed. Differentbuffers are used to establish a pH gradient in a gel. So,when a protein enters a region of pH corresponding toits isoelectric point, its mobility vanishes allowing forseparation based on the net charge on the protein.Conceptually, this is similar to the density gradientmethod employed in sedimentation.
Protein Molecular weight Unlike DNA, which has fixed charge per base pairdue to phosphate group, proteins can have variablecharges depending on the amino acid configuration. Tocreate a uniform charge density, proteins are denaturedand treated with Sodium dodecyl sulphate andmercapto-ethanol. The latter cleaves the S-S thiolbonds. The former, when used in concentrations of 1mM or above, binds strongly to the denatured protein(1SDS per two amino acid groups) leading to a uniformcharge density per unit length. This SDS-PAGE methodallows one determine molecular weight of the proteinsbased on their electrophoretic mobility as shown above.