SDS-PAGE Electrophoresis

Transcription

1 SDS-PAGE Electrophoresis Anirbit Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai , India (Dated: February 15, 2010) In this report I shall explain the steps involved in doing an electrophoresis experiment on proteins and eventual analysis of the data to study how best one can predict the mass of a protein from the intensity of the dye stains. The particular version of electrophoresis that will be used is called SDS-PAGE in literature because of the essential use of the chemical Sodium Dodecyle Sulphate and Polyacrylamide in the process. En route one shall unravel many subtleties of the prediction process and realize the intrinsic problems of doing a simple intensity-mass plots as compared to more robust power law behaviour that will be be seen to emerge in variation of intensity with logarithm of fractional masses. I. INTRODUCTION To start off one can imagine the electrophoresis as a method by which a solution of proteins is passed through a gel in the presence of a constant potential difference such that the proteins of various sizes flow through it at different speeds and hence one can tell the constituents of the solution based on the positions of a dye stain which binds to the proteins. In the future experiments that will be done in this laboratory it will be important that one can monitor fractional changes of a certain protein during the run of an experiment. In most of these proteins knowing the exact amount of protein in the solution is very hard. In this experiment the attempt shall be to try to extend the applicability of electrophoresis to see if given a pure protein solution one can predict the total mass of protein in it by correlating the intensity of the dye stain with the mass of the protein. II. SDS-PAGE ELECTROPHORESIS In the given electrophoresis set-up of Bio-Rad one can set up 2 gels to run simultaneously. One prepares the solutions of chemicals in volumes slightly larger than what is required to account for the spill-overs that are very common. To run 2 gels together I found it convenient to make 15ml of 8% solution for Separating Gel and 5ml of solution for Stacking Gel. FIG. 1: The upper part (the darker part after staining) of the gel is called the Stacking Gel and the lower part is called the Separating Gel. There is also a conducting electrolyte in the system which completes the circuit externally between these two parts of the gel.

2 2 A. A note on the chemical solutions used Some of the standard acronyms for chemicals that are used are, Acrylamide Mix is a 1 : 29 mixture of N, Nmethylene bis-acrylamide and Acrylamide SDS is Sodium Dodecyl Sulphate APS is Ammonium per-sulphate (always stored at 20 C) TEMED is N,N,N,N -Tetramethylethyl-enediamine (always stored at 4 C) All the autoclaving in this experiment are done at 121 C for 15minutes at 103kP a of pressure in an autoclaving apparatus made by Hospharma. The mixture of chemicals required to make 15ml of Separating Gel are, H 2 O 6.9ml 30%Acrylamide M ix 4.0ml 1.5M T ris Hcl(pH 8.8) 3.8ml 10% SDS 0.15ml 10% AP S 0.15ml T EMED 0.009ml The mixture of chemicals required to make 5ml of Stacking Gel are, H 2 O 3.4ml 30%Acrylamide M ix 0.83ml 1M T ris Hcl(pH 8.8) 0.63ml 10% SDS 0.05ml 10% AP S 0.05ml T EMED 0.005ml To make 2l of the Electrophoresis Buffer that will act as the conductor for the current during electrophoresis one uses the following mixture, Trizma Base (a.k.a Tris), which is mainly C 4 H 11 NO 3 12g Glycine 57.6g SDS 2g Autoclaved water is added to make up the volume to 2l and ph adjustment is not done. To make 50ml of the Sample Buffer (DTT dye) one has to mix the following, 0.6M solution of Tris in HCl at ph 6.8 5ml SDS 0.5g Sucrose 5g β Mercaptoethanol 0.25ml 0.5% Bromophenol Blue 5ml Autoclaved water is added to make up the solution to 50ml

3 3 To make Staining Solution one mixes, 0.1%(v/v) Coomassie brilliant blue R250 50%(v/v) Methanol 10%(v/v) Glacial Acetic acid. To make the Destaining Solution one mixes, 10% Methanol 7% Glacial Acetic acid To make many of these solutions the masses of the chemicals needed to be measured and they were done on these two machines manufactured by Sartorius, One was the model CP 1245 and it had a maximum load capacity of 120g with a least count of 10 4 g The other was of model BL1500S and it had a maximum load capacity of 1500g with a least count of 10 2 g The following are the steps in setting the gels, B. Setting the gels Before one starts making the solutions one sets up the two pairs of glass plates on the rack in a particular orientation as marked on the plates. Each of these glass plates is about 1mm think and specially made to be as smooth as possible and are very fragile. The larger plat is of dimensions about 10cm 8.2cm and the smaller one is of size about 10cm 7.3cm. There are two about 1mm thick strips of opaque glass of sizes almost 8.2cm 9mm stuck on the two sides of the larger glass. This ensures a gap of 1mm between the two glass plates in which the gel will be polymerized. One makes the solutions of the separating and the stacking gel in separate containers. I made them in discarded 50ml aliquots manufactured by Falcon. Except APS and TEMED one mixes in all the chemicals in the two compositions given above. APS needs to be freshly prepared or one that has been stored at 20 C and just taken out. Since the separating gel will be made first hence for now one puts the APS in the separating solution only and mixes the TEMED also in only that one. As soon as the APS and TEMED are poured into the separating solution one immediately transfers them between one of the pairs of glass-plates through a pipette tip and the tip should be moved all along the edge through out to ensure that the fluid flows in uniformly between the glass plates. Any non-uniformity will result in nucleation centers for the polymerization process and make the gel non-homogeneous. One stops pouring the solution when it reaches an height of about 1cm below the edge of the plates (such that the gap is larger than the depth of the comb so that the protein solutions have to pass through some stacking gel before entering the separating gel andin the process they undergo isoelectric focussing through the process of isotacphoresis.) One pours butanol on the top of it through another pipette. This is immiscible with the rest of the solution and floats on the top helping to smoothen the gel surface and also acts as a protecting layer from the oxidation effects of the atmosphere. Now one waits for about 30mins for the gel to form. It can sometimes take an hour or a little more depending on humidity and temperature conditions. After about 30mins I keep checking for the formation of the gel by tilting the whole set up at times to see if the butanol layer is hitting a hard boundary on its lower surface. Once the separating gel is formed one washes out the butanol layer by tilting the container and gently flowing in autoclaved water through the gap and absorbing any further remnant butanol by gently inserting a tissue paper in the gap.

4 4 FIG. 2: The above photograph shows green frames in which the gel is set and the transparent rack in which the green frames are clamped to keep them stable during the polymerization process. Now one mixes the APS and the TEMED in the stacking solution and pours it into the gap between the pairs of plates through a pipette in a similar fashion. Now one has to quickly insert the comb into the gap which will demarcate the wells that will form inside the stacking gel. This comb is not to be taken out untill the protein loading starts. This set up should be left undisturbed till it is necessary to install the gels into the electrophoresis tank. Generally during this time one starts making the chemicals that will be loaded into the gel. Like the dilution series of Actin and BSA to be described below. C. Making Actin dilution solution When Actin is extracted it is not known as to how much Actin is present in the solution. It is estimated from indirect methods that the concentration is 2µg/mul. The various steps in preparing the Actin dilution are as follows, I took 5 aliquots of the Actin solution which gave me about 43µl of Actin solution. I added 117µl of H2 O to it and hence made up the solution to 160µl. Call this solution A0 I took 80µl of A0 and added 80µl of H2 O to it and made 160µl of another solution. Lets name it A1 Again I took 80µl of A1 and added 80µl of H2 O to it and made 160 of another solution. Lets name it A2. Thus iterating the process about 5 times one makes solutions of 80µl each till A5. In the making of A5 the 80µl of A4 that remains is preserved separately for future experiments and not used in the dyeing and heating in the next steps. In each of the 80µl solutions from A0 to A5 of Actin, 20µl of the 5X DTT dye is added (so that in the final solution the dye is in concentration of 1X ) and then each of these 100µl solutions is sent for heating for 5mins at 100 C. Post heating one loads 20µl of each solution in each of the wells of the gel. Hence the amounts of protein in the wells of the gel fall in inverse powers of two.

5 5 D. Making BSA dilution solution The steps to prepare the BSA sample that will be loaded in the gel, 1. 5mg of BSA is mixed in 1ml of water. (call this solution A 0 ) ml of A 0 is taken in another aliquot and 0.5ml of water is mixed in it (call it solution A 1 ) ml of A 1 is taken in another aliquot and 0.5mk of water is mixed in it (call it solution A 2 ). 4. In this way solutions till A 5 are made µl of A 0 is taken in an aliquot and 7.5µl of the 5X dye is mixed in it. (This choice is explained in the last point) 6. So the aliquout now contains 150µg of BSA in a solution of volume 37.5µl. 7. To denature the proteins boil this 37.5µl of solution for 5min at 100 C (call this B 0 ) 8. The steps 5,6 and 7 are repeated for A 1, A 2, A 3, A 4, A 5 and call the corresponding 37.5µl solutions B 1, B 2, B 3, B 4, B µl of each B i is taken and loaded into each of the wells. 10. Then the mass of the BSA loaded in each of the wells are respectively 12µg, 6µg, 3µg, 1.5µg, 0.75µg and 0.375µg. 11. The 5X dye is a solution of the dye made and stored in such a way that it has concentration 5 times more than what it should be in the final solution. Then one can see that adding 7.5µl of such a 5X dye to 30µl of fluids results in the correct concentration of the dye in the final mixture. The steps are as follows, E. Loading, running, staining and destaining the gel One generally needs to have about 500ml of the electrophoresis buffer as a conductor for running the gel. 50ml of the available 10X buffer is mixed with 450ml of autoclaved water to make the required solution. First the two glass framed gels are slid into the slots on the two sides of the frame that goes into the tank. The glass frames are positioned so that the shorter plate faces inward. Checking for snug fitting one locks them by the plastic hinges on the frame. Then the frame is inserted into the tank and the electrophoresis buffer is poured into the volume between the two glass frames. One checks if the buffer is leaking out into the tank. If it does then one has to diamantle the frame and reset it again. Then one pours the rest of the prepared buffer in the volume surrounding the frame inside the tank. Now one should pull out the combs taking care that the jerk does not break the wells inside the gel that would have formed. At certain angles the wells will be visibile to the naked eye because of the refractive index difference between air and the transparent gel. To reduce chances of loading the protein at regions other than the gel one can mark the positions of the wells on the wall of the tank using some marker. The proteins are loaded into the micropipettes from the aliquots and the pippete is lightly inserted into the well from the side of the shorter glass plate and the protein pushed in. One can see the coloured protein settled into the well. Care should be taken to push in the protein in one shot since doing a suction can contaminate the protein by the buffer solution. After all the gels are loaded, the top cover is closed and it is connected to the D.C source that comes with the instrument. It is generally run at about 100V. This D.C source has ratings of delivering 2.5A current at 500V delivering a maximum power of 500W.

6 6 FIG. 3: The above photograph shows the electrophoresis set-up while it is running. FIG. 4: The top-view of the electrophoresis set-up while it is running.

7 7 The voltage is maintained till the blue line in the gel (formed due to the accumulation of the dye) hits the lower edge of the gel. As a thumb rule the protein is generally behind dye. One shouldn t leave the process unattended for long at this stage since the proteins can very well run out of the gel into the solution if kept for long. FIG. 5: The faint blue line towards the bottom of the gel indicating the distance through which the dye has run. After the gel running is complete, the apparantus is dismantled and the glass plates taken out. The two glass plates in every pair will stick to each other very strongly because of surface tension and just trying to pull them apart runs the risk of breaking the fragile glass and also the gel. In general water is lighly run through the upper edge and then softly one can pry them apart using a plastic wedge. Using the same wedge the gel is lighly detached from the glass plate and this thin film that is formed is transferred to a tray. Now one can either use this gel to do staining with Coomassie blue dye or use it for Western Blotting. The next steps of Coomassie blue staining are relatively simple which are listed below and Western Blotting is a longer sequence of steps which was unsuccessfully tried and shall not be explained here. The steps of staining and destaining are as follows, On the gels which are transferred into the tray, Coomassie Blue dye solution is poured and the set up is put on a rocker for overnight staining. This is staining is generally done for about 10 12hours and during this time the oscillations of the rocker ensure that the dye keeps flowing across the gel uniformly without clustering anywhere and hence stains the gel uniformly. After the staining is over the remaining staining solution is recovered for reuse. The destaining solution is is then pourd in and set on a rocker. As the stain dissolves into the destaining solution the solution will keep becoming blue and then one decants out the solution and pours in fresh solution. This change has to be done almost every minutes for about 5hours. During this destaining process care must be taken not to overdo the process since it can eventually start dissolving out the dye stuck to the protein bands also. Initially the gel looks uniformly blue after about 2 rounds of destaining the protein bands become visible in contrast with the lighter background.

8 8 Some general dimensions of the gel are, F. Some measurements of the gel The separating gel is generally about 5.5cm 8.2cm in size and the stacking gel is 1.5cm 8.2cm with wells along one edge. The wells in the stacking gel are about 1cm deep and 0.5cm in width, so the proteins pass through about 0.6cm of stacking gel before hitting the separating gel. The gel is generally 0.1cm in thickness. The separating gel is about 4.26g in mass and is typically at a density of 0.91g/cc. The stacking gel is about 0.83g in mass and is typically at a density of 1.03g/cc G. A short note about the chemicals The precise utility of each of the chemicals in the experiment is a extensive question in chemistry and the rational behind the quatities of each to be used is hard to theoretically justiy. Some of the essential physical ideas that go behind it shall be explained at the end in the section on background theory. A basic list of use of the important chemicals are, Sodium Dodecyle Sulphate is basically a soap which when heated with the protein binds to the amino acids in the protein and hence destabilizes the hydrogen-bonding which renders the protein its structure. This denatures the protein by making all of them more or less cylindrical in shape. This ensures that the proteins s mobility which determines their stacking sequence depends less on the structure and more on the molecular mass. Also, anions of SDS bind to the main peptide chain at a ratio of one SDS anion for every two amino acid residues. This effectively imparts a negative charge on the protein that is proportional to the mass of that protein (about 1.4gSDS/gprotein). This negative charging is essential for the migration of the proteins (precisely the protein- SDS complex) towards the anode during electrophoresis. FIG. 6: SDS β Mercaptoethanol, HO (CH 2 ) 2 SH is mixed in the protein solution mainly to break the di-sulphide bonds in the protein which also help keep the protein conformation.

9 9 FIG. 7: The basic idea is of two amino acids bonding to form a peptide. This will exist mostly as a zwitterion in solution and SDS when heated at 100 C for 5 minutes with proteins will bind at the rate of one SDS anion for every two amino acid residues or approximately as 1.4gSDS/g protein. This not only breaks the hydrogen bonding responsible for the protein conformation but will also give a net negative charge to the protein essential for its migration towards the anode during electrophoresis. FIG. 8: The above is the typical reaction by which β Mercaptoethanol cleaves the disulphide bond in proteins The steps in the polymerization are as follows, TEMED catalyzes the decomposition of the persulphate ion S to give a free radical as, S e 1 SO4 2 + SO4 1 If M is the acylamide monomer then polymerization proceeds by iterating the following, R + M RM RM + M RMM RMM + M RMM The dissolved 0 2 mops up the free-radical. and so on...

10 The Glycine provides the ion with the slowest mobility which helps in stacking the proteins during the transport in the presence of the electric field. The Chloride ions provide the background conducting medium and is the leading ion being the ion around with the highest mobility. Hence the proteins being of intermediate mobility get stacked between the chloride and the glycine ions. Bromophenol Blue is employed tracking dye mixed in the protein solution, because it is viable in alkali and neutral ph, it is a small molecule, it is negatively charged above ph 4.6 and hence moves towards the anode. Being a small molecule it moves ahead of most proteins and nucleic acids. As it reaches the anodic end of the electrophoresis medium electrophoresis is stopped. It can bind with proteins weakly and give blue colour. 10 FIG. 9: Structure of Bromophenol Blue Coomassie Blue R-250 is an anionic dye used in the staining solution.this binds with proteins non-specifically. As SDS is also anionic, it may interfere with staining process. Therefore large volume of staining solution is recommended for use. FIG. 10: Structure of Coomassie Blue

11 11 H. Image analysis on the gel After the gel has been destained the objective is to quantify the mass of the proteins from the instensity of the dye that is stuck to it. An exact quantification has its own complications and I shall explain how far one can go in this goal. Basically the idea is to see how the intensity of the gel varies as a function of the protein mass and this requires a way of quantifying the intensity. For this the gel is photographed and the sum of the pixel values is taken as a proxy for the intensity since one knows that bighter points in the picture have higher pixel values. Then all analysis can be done using this set of numbers as obtained by the following process of digitizing the gel. The exact steps in the process are as follows, The last destaining solution is not transferred out of the tray. A pair of soft smooth transparent plastic sheets is cut out of the size little bigger than the gel and these are joint at one edge. Usually this is made by cutting out from the edge of plastic packets. Keeping the gel dipped inside the solution a hard plastic is slid underneath it and the gel is lifted out of the solution on it. This method ensures that no air bubbles are trapped between the gel and the plastic. Then gently the gel is slipped on to one of the pair of soft palstic sheets from the hard plastic by sliding it onto it keeping the leading edge always in touch with a thin film of water. This ensures that no air bubbles get trapped in this stage. The second plastic film is covered over it in a similar way ensuring that no air bubbles are trapped. FIG. 11: The gel as it looks just after taking out of the destaining process This setup of the gel trapped between pairs of soft tranparent plastic sheets is gently put on a scanner and the image is taken at a resolution of 600dpi. From the image the relevant part is cut out (generally a thin rectangular strip corresponding to the dilution series) and rotated if necessary. FIG. 12: The strip of the scanned image of the gel along the dilution series

12 12 The software ImageJ is used to invert the contrast of the image and convert this inverted picture into a matrix of numbers which gets saves as a text file. FIG. 13: Inverted image of the strip of the scanned image of the gel along the dilution series Inversion is done to make the numerical analysis more intuitive so that places in the image which are brighter because of the dye attaching to the protein have higher numerical values. By looking at this picture the rectangular regions are selected in the strip which correspond to the protein spots and a C++ program was written which takes this text file as input, stores it as a matrix and sums the numbers in every rectangular region corresponding to each protein spot. I. The data analysis So at the end of the data extraction one has a set of pairs of numbers {m i, I i } where I i is the intensity of of the spot corresponding to m i mass of the protein and m i+1 = 1 2 m i. Using Mathematica7 the following two graphs are plotted, I i vs m i I i vs i The graph I i vs m i shows somewhat of a linear behaviour if the extreme values are dropped. At the higher mass end (i.e > 6µg) the intesity seems to stall and at the very low mass (i.e < 0.75µg) the intensity seems to drop sharply most likely because of being very close to the lowest detection limits of this staining procedure. At a protein mass of about 0.375µg the stain is just barely visible. A typical running of a dilution gel has 6 dilutions as shown in the photographs of the strips and the intensities as defined earlier as the sum of the matrix entries in the sub-rectangles look like, { , , , , , } corresponding to {12µg, 6µg, 3µg, 1.5µg, 0.75µg, 0.375µg}. This data can be analyzed in the following ways, One can plot the points {(1, ), (2, ), (3, ), (4, ), (5, ), (6, )} and fit the function I = A x n to it and find the optimum value of A and n for that. The way to think of this graph is that given the set of points {(m i, I i ) i {1, 2,..., 6}} one is constructing from it a set {(i, I i ) i {1, 2,..., 6}} such that i = 1 + log 2 ( m 1 m i ). Here which is m 1 and which is m 2 etc is unambiguous since we know precisely in the making of the dilution series that m i+1 = 1 2 m i. So m 1 is always the highest mass sent through the gel.

13 13 FIG. 14: A pot of the points (1 + log 2 m1 m i Mathematica7 as A and n , I i) and fitted to it is the function I = A x n with the best fit values given by FIG. 15: A plot of the points (m iµg, I i) for the same rectangular strip from the same run with BSA as above FIG. 16: A plot of the points (m iµg, I i) for another run of a dilution gel with BSA which showed the typical problems of the intensities stalling for larger masses and showing sharp drops for lower masses. These are issues with the sensitivity of the detection technique. For a fixed protein the above analysis is repeated on multiple gels by taking multiple rectangles around the stained strip and the values of intensities and the coeffcients A and n are averaged over them and the standard deviation of them is taken as a proxy for the error in their measurements. Displayed below are the values for the protein Actin. Actin that was used was extracted in-house and hence the exact amount of the concentration of the protein solution is not known. But we can still do a dilution series gel using it since not knowing the exact concentration is not a hindrance in taking half of the mass inserted into the first gel ans so on. Hence for such cases we scale the mass unit and consider the highest mass lane to have 1 unit mass Actin and the lane to the right of it has 0.5 unit mass Actin and so forth. Then the similar image analysis can be done as explained before.

14 14 Run and selection Actin Gel 1, rectangle Actin Gel 1, rectangle Actin Gel 2, rectangle Actin Gel 2, rectangle Mean Standard Deviation TABLE I: Intensities and the averages and the standard deviations for the same scaled masses of Actin in various trials Fitting the function A x on the above averaged points for Actin the values gotten are A = and n n = The relevant dependencies can be seen in the graphs below. FIG. 17: The above plot shows the fall of the intensity with 1+ logarithm of the fracional mass along with an estimate of the errors in the intensities and the curve I = is fitted to that. x

15 15 FIG. 18: The above graph shows the intensities of the Coomassie stains as a function of the scaled protein mass in arbitrary units along with an estimate of the errors in the intensities. This shows the problems of stalling at higher masses and a sharp drop of the sensitivity at the lower ends. It also shows the best-fit straight line of x that one gets on dropping the lowest mass from the data. A similar experiment as above was done with the protein BSA (Bovine Serum Albumin) and this was commercially bought. Hence in this case can know with greater confidence the amount of protein present in the sample but running of the gel gave spurious bands and hence brought in the doubt that the commercial protein isn t so pure. Further the staining data on BSA seemed to show some unnaturalness. Under the expectation that the efficency of doing the experiment increases with time only the last 2 runs of doing electrophoresis on a dilution series with the BSA are reported in the follwing table and taking two rectangles from each gel as for Actin. Run and selection 12µg 6µg 3µg 1.5µg 0.75µg 0.375µg BSA Gel 1, rectangle BSA Gel 1, rectangle BSA Gel 2, rectangle BSA Gel 2, rectangle Mean Standard Deviation TABLE II: Intensities and the averages and the standard deviations for the same masses of BSA in various trials Fitting the function A x n n = on the above averaged points for BSA the values gotten are A = and

16 16 FIG. 19: The above plot shows the fall of the intensity with 1+ logarithm of the fracional mass along with an estimate of the errors in the intensities and the curve I = is fitted to that. x FIG. 20: The above graph shows the intensities of the Coomassie stains as a function of the mass of the protein in micrograms in the BSA sample along with an estimate of the errors in the intensities. This shows the problems of stalling at higher masses and sharp drop of the sensitivity at the lower ends. It also shows the best-fit straight line of m that one gets on dropping the lowest mass from the data. J. Using the results of the analysis If the largest mass of the protein used in the dilution gel is m 0 (with respect to which the other masses are scaled) then the result of the above calculation states that there exists constants A and n such that the intensity (I) of a stain goes with mass of the protein (m) as, A I = [ ( m0 ) ] n log2 m + 1 But one must be cautious of the interpretation of this result as it stands now. One should take note that the constants A and n are NOT intrinsic to the protein but depend on m 0 as can be easily checked by doing the fit on the same set of data with the current highest mass removed and scaling everything with respect to the current second highest mass. But obviously for the same m 0, A and n will be different for different proteins.

17 But for a fixed protein if m 0 and its corresponding A and n are known then one can treat the result as a standardization such that it can now be used to predict masses of other samples of the same protein from their staining intensities. But the prediction can have two different forms as follows, Like for standardization with BSA where m 0 is known, given an unknown sample of stain intensity I its mass can be predicted to be m = 2 m 0 1 A n I 1 1 Like for standardization with Actin where m 0 is not known, given two samples of proteins of stain intensities I 1 and I 2 one can predict the ratio of the masses of the proteins as, 17 m 1 m 2 = 2 A I 1 1 n 1 A n I 2 K. Some findings/observations of my own I started filtering the destaining solution twice to ensure greater efficieny of the chemical on reuse. I devised this method of transferring the gel on the scanner by using plastic supports while keeping it always submeged in the destaining solution. This practically eliminates the risk of air bubbles getting trapped. The image analysis technique described here is of my own and I have not found that in any reference. I wondered if the staining/destaining step could be avoided by sending into the gel, protein mixed with Coomassie Blue. But then this does not work as I found out that Coomassie Blue happens to have higher mobility than the proteins and hence inside the gel it moves faster ahead without causing any staining effect. III. SOME THEORETICAL BACKGROUND The entire physics and chemistry of the process of electrophoresis is a very complicated mix of phenomenon and much of the numbers like the amount of each chemical to be used is very hard to rationalize by pure theoretical calculation and are obtained by experimental optimization. A. A basic overview of the idea One of the key ideas behind electrophoresis is that if 2 solutions of different ph and different densities containing charged molecules of different mobility can be stabilized against convective instabilities then the boundary between the two fluids can be robustly maintained in an electric field. In that case the two fluids can move maintaining the boundary or if the boundary is somehow made rigid (like through polymerization) then the charged ions can flow through it in a predictable sequence without disturbing the boundary. This predictability of the sequence gives the quite essential stacking effect in gel electrophoresis which holds the key to identification of the different protein components in the initial solution. The convective instabilities are generally avoided by either having the two fluids to be immiscible and of different densities or by polymerization like here so that convection is prohibited simply due to structural rigidity. If the boundary is moveable then the crucial observation is that inspite of the difference in mobilities of the mobile ions on the two sides the velocities at which they move have to be the same since otherwise a gap gets created at the interface through which electricity cannot conduct. Since in most situations the electric field and the mobilities are given constants the formation of the gap is prevented by the rigid polymer matrix, the system attains this dynamic quilibrium by dissociating the correct number of ions on either side. Eventually it wll be seen that whether the system can dissociate to this optimal extent depends on whether the experimentalist has chosen the right dissociation reactions and ph. And much of these optimal values have been established over years of standardization of the experiment and only some order of magnitude esimates can be gotten from pure theoretical arguments.

18 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 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 ( µg ) ) ( ) x g z g µp µ ( ) = ( ) c cp µp µ g µ c x p z p 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 ( 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.

20 20 IV. CONCLUSION This experiment and the associated analysis shows a careful analysis of the limitations of being able predict mass of a protein in a given sample by looking at intensitities of dye stains. In the process the use of running a serial dilution of the protein solution through an SDS-PAGE electrophoresis set-up is found to be helpful to find out the dependence of the intensity of the stain on the mass. Analysis of that shows that though intensities of stain seem to show not so regular behaviour with the mass of the protein the intensities show a power-law fall with masses of the protein with exponents and pre-factors which seem robust across experiments. Hence as an end result one can get standardization curves which can be used to either predict masses of proteins in a random solution if in one sample the mass is exactly known or ratios of masses in different samples in any case. Doing of the experiment also introduced me to new experimental skills involved in handling microliters of fluids and doing image analysis. V. ACKNOWLEDGEMENT I would like to express my deep gratitude for Prof.Roop Mallick for letting me intern in his laboratory for these 2 months and for giving me immense freedom to explore various possibilities and suggesting crucial checks and cautions while analyzing the results. I was fortunate to receive and extraordinary amount of help from Pradeep. It was heartening to see him even compromise on his examination peparations and his own research to help me with every experiment that I tried and especially for patiently teaching me all the basic techniques. For every problem in the laboratory I found Pradeep s kind help to save the day. Further I would like to thank Ashim for helping me through a Western Blotting experiment and also for his timely and sharp insights with feasibility of experiments. I would like to thank Ravi for letting me use some of the solutions of Actin protein which he along with the others had painstakingly extracted and purified. I would like to thank members of Prof.Ulhas Kolthur s lab for letting me use their water heater and antibodies ever so often. Once I also had to use the water bath in Prof.Shubha Tole s lab. Thanks are also due to Prof. Gotam. K. Jarori s lab for letting me use their 30% Acrylamide solutions. Lastly I would like to thank the Suject Board of Physics at TIFR for providing this enriching experience. 5 Electrobloting of proteins from polyacrylamide gels by Michael.J.Dunn, published in Protein Purification Protocols edited by Paul Cutler 5 Using Antibodies by Ed Harlow and David Lane 5 Disc Electrophoresis-I by Leonard Ornstein 5 Isotachophoresis-Some fundamental aspects by Jozef Leonardus Beckers 5 Wikipedia