A report on an experiment I did of doing electrophoresis with proteins

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The key equation behind this is called the “Kohlrausch Regulating Function” which will be explored to some extent in the next section. The point to remember is that the following analysis ignores the effect of the gel and considers only a solution of ions of different mobilities in the presence of a constant potential difference. 18 B. Kohlrausch Regulating Function Some basic equations and definitions that is needed to make the above concept precise are as follows, • If a charged ion moves a distance d in time t in an electric field E then one defines mobility = µ = d tE • If a solution contains many species of mobile ions labelled by i each of concentration [i] and mobility µ i and charge ez i where e is the charge of an electron, then the conductivity σ of the solution is, σ = e ∑ i [i]µ i z i • If x i is the dissociation fraction of the species i compared to its undissociated form then the average velocity of migration of this species is given as, v i = Eµ i x i • For the current purpose one can restrict to dilute solutions where one can use the definition of pH as pH = −log([H + ]) where [H + ] is the numerical value of the concentration of [H + ] measured in molarity. For the dilute solutions used in electrophoresis one can keep approximating the activity of the ions by the numerical values of their concentrations expressed in molarity. For this purpose the same shall be done with regard to other similar quantities like pK a , pK b and pK w . In the context of the electrophoresis set-up that is used in this laboratory the important features that need to be kept in view are the following, • There is a gel on the top which has a pH of 6.8. • There is a gel at the bottom which has a pH of 8.8. • There are Cl −1 ions in both the layers of the gel and in the conducting buffer. • Glycine ions are present only in the buffer. • The mobilities of the relevant ions in increasing order of mobilities is glycine < proteins < Cl −1 Let the ions in the upper layer be labelled as u i and the ones in the lower layers are l i . Let the mobility of u i be µ iu and have a charge z iu . Let the electric field in the upper gel be E u and the field in the lower gel be E l . Let the cross-sectional area of the gels through which the current flows be A and since the two gels are in series the current through them is the same and hence equating the currents in the two layers using the definition of conductivity given earlier one has, E u Ae ∑ i [u i ]µ iu z iu = E l Ae ∑ i [l i ]µ il z il which can be re-written as,
19 E l ∑i [u i]µ iu z iu = E u ∑ i [l i]µ il z il Earlier it was argued that the velocities of the ions in the two gels have to be the same because of continuity and hence here one uses that for the upper ion whose parameters are subscripted with u and for the lower ions whose corresponding parameters are subscripted with l. Then one has from the velocity equality, Substituting this back in the earlier equation we have, E u µ u x u = E l µ l x l µ u x u ∑i [u i]µ iu z iu = µ l x ∑ l i [l i]µ il z il The above is known as the Kohlrausch Regulating Function One of ways to see what this function does is to consider a situation when µ l x l > µ u x u and in that case one can see that if an upper ion finds itsel in the lower gel then it will move slower than the surroundings and will be eventually be overtakn by the boundary and it will return to its original location. Similarly if a lower ion inds itself in the upper gel it will move faster than the boundary and will soon overtake it and get back to its original point. Thus the system maintains a clear separating layer between the two regions. Let µ p and x p be the mobility and the dissociation fraction of the proteins and µ g and x g be for the glycine. From the experimental set-up one knows that glycines will be in the upper layer and the proteins will be in the lower layer and the chloride ions are common to both the layers but has different concentrations and hence Kohlrausch Regulating function for this case says that, µ g x g [g]µ g z g + [cu]µ c z c = µ p x p [p]µ p z p + [cl]µ c z c (using c to denote the chloride ions) By microscopic charge neutrality one has [g]z g = −[cu]z c and [p]z p = −[cl]z c . Using that the crucial equation that emerges is that, ( cg x g ) ( cp x p ) = ( µg ) z g ( ) µp z p ( ) µp − µ c µ g − µ c If the effects of the gel are not included then the above equation explains why a system of ions of different mobilities should maintain distinct separating boundaries while flowing in the presence of a constant potential difference. The analysis of the gel on this above effect is a further comlicated phenomenon which in someway can be thought of as providing a viscous drag force which imepedes the motion. But the modelling of that effect runs into complications ofthe fact that denatured protein molecules in the system tend to be cylindrical in shape and hence the direction of their approach becomes a crucial factor after a certain molecular mass number. This is what is dubbed as “Non- Newtonian” viscosity. Further also needs to model the effect that the static pH boundary in the gel does not disrupt the moving pH boundary of the ion solution. C. Some comment about the polymerization It is a still harder problem to model how doe the pore size of the gel vary as a function of the concentration of the polymer. As a minimal model consider that the gel consists of n × n × n cubical cells for evey unit cube in it and network be formed of polymer chains of unit length. Then one can approximate the pore diameter by the length of a side of the cell (say r) and then one can see that r = 1 n − ( 1 + 1 n) d and the number of polymer chains in each such cube is 3(n + 1) 2 . Then simple calculation gives that if the concentration of the polymer is increased by J then number of squares per edge would becme (n + 1) √ J − 1 and hence from that one can calculate by how much the r changes with J.
Page 1 and 2: SDS-PAGE Electrophoresis Anirbit De
Page 3 and 4: 3 To make Staining Solution one mix
Page 5 and 6: 5 D. Making BSA dilution solution T
Page 7 and 8: • The voltage is maintained till
Page 9 and 10: 9 FIG. 7: The basic idea is of two
Page 11 and 12: 11 H. Image analysis on the gel Aft
Page 13 and 14: 13 FIG. 14: A pot of the points (1
Page 15 and 16: 15 FIG. 18: The above graph shows t
Page 17: But for a fixed protein if m 0 and

A report on an experiment I did of doing electrophoresis with proteins

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