Jisnuson Svasti' and Bhinyo Panijpan Department of Biochemistry Mahidol University Rama VI Road Bangkok, Thailand
SDS-Polyacrylamide Gel Electrophoresis A simple explanation of why it works
SDS (Sodium dodecvlsulfate)-nolvacwlamide eel electro, ~ ~ , phoresis is a technique b d e l y used fur the effective-separation of oroteins and fur determining their molecular weiehts (I-JI. ln'this technique, proteins are denatured by theudeteigeit SDS and the SDS-oolvacrvlamide eel eauilibrated with buffered SDS solurio~.~ ~ o n ~ a ~ ~ l i of c aant ielectrical on field the nerativelv charred SDS-oolvueotides move towards the anodeat a rate dependent on-the molecular weight. A plot of the electrophoretic mobility of the protein relative to a marker substance against the logarithm of the molecular weight gives, over a certain range, a straight line as shown in Figure 1.Although this fact is known to our students and the technique is constantly used by them, we find them usually unable to explain why they get this relationship. In this brief communication, we attempt to provide a simple explanation and answer some of the more common questions raised. Proteinsand polypeptides are made up of amino acids covalently linked by peptide bonds, regularly arranged on the backbone; the larger the molecular weight the larger the number of nentide bonds. In their native state. the nentide chains of giodu~arproteins are tightly folded to'form a compact three-dimensional structure. Treatment with SDS in the presence of reducing agent causes the polypeptide chains to unfold and assume a rod-like structure (Fig. 2) in which the polypeptide core is coated by SDS-molecules (4).Proteins of hirher molecular weieht bind more SDS than those of lower molecular weight. since the SDS molecule has one net negative charge at neutral pH, larger SDS-polypeptides will be more negatively charged than smaller SDS-polypeptides. In fact, the SDS molecule binds to the polypeptide with a constant weight ratio ( 5 ) ,corresponding to about one SDS molecule bound per three peptide bonds. In other words, in SDS-polypeptides, the charge per unit weight is constant. Since the electrical force acting on a particle is directly proportional to its net charge, the above relationship means that the electrical force per unit weight is also constant. Force is eoual to the nroduct of mass and acceleration (force . = mass ----~X acceleration). Thus force + mass or, in this case, force + w e i ~ his t eaual to acceleration. So in SDS-uolvacrvlamide pel elec%opho;esis all molecules a t the same position are unier a constant acceleratine null bv the electrical field. If all ~ D ~ - ~ o l ~are ~ under e ~ ~the d same e s acceleration, why do smaller molecules travel faster than larger molecules? The answer is provided by the sieving properties of polyacrylamide gel, which has a distribution of pore sizes ofthe same order of magnitude as the sizes of proteins normally found in s the nature ( 6 ) .The averaee Dore size of the eel d e ~ e n d on concentration of the ac&amide and methilene-bisacrylamide monomers used during polymerization. At the start of the electrophoretic run, the SDS-polypeptides are a t the same position and begin to move under the same acceleration, when the electrical field is applied. Small molecules can travel thnugh some of the polyacrylamide pores more easily than big molecules (Fig. 2). Granted that there are other physical barriers to the movement of all molerules, after having cone through a sufficient number of pores, the distance covered by the molecules will differ enough to effect a clear separation. ~
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Figwe 1. Hypotheticalgraphshowing the linear relationshipbetween me electrmhwetic mobiliw of standard orateins (relativeto a marker dvel and the looarnthms of tne r molecJlar uetgnls The ootted lone snows m w memo ecJlar we ght 01 an ,nknown may oe estnmated from its relet ve moblllty usmg ~ u c n a graph
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560 1 Journal of Chemical Education
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Figure 2. The binding of SDS to alobular rotei ins. (a1 The structure of SDS isodium dodecvl sulfate1. fbl . . Schematic diaoram showino the denaturation of a globuler protein by 1 ° n SDS ,n the presence of .l-mercaptoelnano LIME) me tqhtly loloeo po ypcptde cnam unlolar to l a m an exlsnoedrod. w In ma polypeptide at the core being coated by negatively charged SDS molecules.
Such a situation would allow the separation of polypeptides of different molecular weight, provided that these molecules have similar shapes, so that molecular weight differences are reflected in size differences. SDS-polypeptides all have similar rigid rod-like shapes, which have a constant minor axis (18A) and a major axis dependent on the molecular weight ( 4 ) . Why is the plot semi-logarithmic? This can be explained by thinking of the sieve pores as perfect circles of various diameters. The molecules could be imagined as spheres occupying the same effective space as that described by their constant tumbling. The ease with which a molecule goes through the pores is then dependent on the cross-sectional area, which is directly proportional to the square of its diameter. The molecular weight is proportional to volume and hence to the cube of the diameter of the equivalent sphere.
Figwe 3. Schsmatic representation of a cross-section of a polyacrylamide gal. This diagram shows only a fewpores oul ol an extended network and fewerintercannectionr than probably exist in r e d i i . In addition,fw simplicihl,only two sires of pores and two sires of protein are shown. The smaller proteins move fasterbecause they can penetrate both large and small pores, while the large proteins can only penetrate lhe larger pores.
F i e 4. SchwMticrepresentationsofsmall sectionsof: (a) Gels used lor gel libation. Particier of gel are shown as circles snclosed by a broken line. in which gaps rewesent pmes. Each particle mnsists of two regions: the gel mahix (faint
solid line)and imernal solvent space (the remaining space).The space outside and in between particles (dotled areas) is a n u p i g l by solvent faming Ux! mabile ohase. lbl . . Gels used for electraoharesis.A small oortion of Fioure 3 1s shown. representmg a network ol V e s (clear regions).through which proteins mdrt pass hatched areas ndicale reglans wilh too hlgh s density of poiyaerylam~de chains for proteins to penetrate. Takine loearithms of the molecular weieht should thus helo ' linearGe i'is relationship to the e~ectro~ohoretic mobility. Whv do we eet the o n ~ o s i t results e to eel filtration? In the lattermethoi(7, 8), column is packei with cross-linked dextran or wlvacrvlamide particles of defined w r e size ranees and protein molecules are'eluted through the column unier the constant initial acceleration of gravity. Thus, although the principles of separation are similar, large molecules emerge from the column before small molecules. This apparent discrepancy may he explained by recognizing the fact that due to their geometry and their low compressibility, the particles cannot he sufficiently tightly packed to exclude solvent. Thus the space within the column can be considered t o consist of thrke components: the space occupied by the gel matrix. the space within each particle occupied hv solvent, and the apace orrupied hy solvenioutside (and between) par;icles \Fie. 40). The latter two spaces are accessihle to molecules of solite which are sufficiently small to be able to penetrate through the pores of the particle. Thus proteins and other s d u molecules ~ will disthhute themselvbs between the solvent spaces inside and outside the particles: these solvent spacesform the stationary and mobile phases of the chromatographic system, respectively. At equilibrium, the partition function, represented by the ratio of the concentration of solute in the internal solvent space to that in the external solvent space, will he of higher magnitude for small molecules
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than for large molecules. In other words, as the solutes to be separated are of similar size to the particle pores used, small molecules may pass into the particle more easily than large molecules. Therefore, since the internal solvent space is the stationary phase, small molecules will be eluted out more slowly than large molecules. In SDS-polyacrylamide gel electrophoresis, the gel is a continuous network of pores (Fie. 46) and contains no equivalent of the accessihle external solvent space. Thus, unlike gel filtration, all molecules in gel electrophoresis have no option but to travel through the pores. In this model, i t would be predicted that if electrophoresis of SDS-polypeptides was carried out in the gels used for gel filtration, large molecules would move faster than small ones. Won't the intrinsic charge of the protein, from its amino acid side chains, have any effect? In most cases, the intrinsic charge has little effect, because it is an order of magnitude smaller than the negative charge gained from binding SDS molecules. However. in the case of hiehlv chareed proteins = l l ) , deviations from linearity on the such as the histones log - .(molecular weieht) - . versus mobilitv" .lot are observed. unless proteins of a similar intrinsic charge density are used as standards. But. for some reason. no deviation is apparent .. for the highly acidic protein, pepsin ( p l = 1 ) . W ~ d the d methorl work if all proteins had a different shape, say were spheres instead? The answer is yes, as long as all proteins had a similar s h a ~ and e densitv. so that the hvdrodynamic properties of all the proteins &dependent ontheir molecular weight. This explains why, using the same electrophoretic conditions, proteins of molecular weight less than 10,000-15,000 daltons give a line of different slope to those of larger proteins (9).This anomalous behavior arises from the fact that, in these small proteins, the dimensions of the minor and major axes are not sufficiently different, so that their hydrodynamic behavior approaches that of a sphere instead of a cvlinder. C& other detergents he used instead of SDS? Yes,provided that the two important conditions discussed ahove are fulfilled, namely that all proteins have the same electrical force per unit weight (or initial acceleration) and hydrodynamic properties that are a function of molecular weight. Such conditions appear to be fulfilled by the positively charged detergents N-hexadecylpyridinium chloride (10) and cetyltrimethylammonium bromide (II), which also give straight line plots between electrophoretic mobility and log (molecular weieht). In fact, no detercents are required for macromolecules which, in theirnatural state, show constant net charge per unit weight and have hydrodynamic properties which are identical functions of their molecular weight. Thus plots of the electrophoretic mobility of rihonucleic acids in tris-borate buffer, pH 8.3 against log (molecular weight) yield straight lines, in the absence of detergents (12). Is the molecular seiving effect of pdyacrylamide vssential for separation? In theory, it 1s not. The elertricul force is directly proportional to the molecular weight. On the other hand, the frictional force is a direct function of the radius of the equivalent sphere, which depends on the dimensions of both the minor and major axes. Since the minor axis is relativelv small compared to the maior axis. the radius of the equivalent sphere approximates t o but does not equal the length of the major axis, which in turn is directly proportional to the molecular weight. So under ideal conditions, molecules of different molecular weieht should reach slizhtlv different terminal velocities and aker a sufficient d&a&e should separate, even in the absence of molecular sieving. But in effective separation cannot be achievedwithout molecular sieving because of the disruptive effects of diffusion and convection-Separation should aiso be possible in other supporting media, such as starch or azarose. if the concentr&ons ofthese gels were made high enough produce pore sizes small enough to he within the size ranges . of the protein molecules to he separated.
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Volume 54, Number 9, September 1977 / 561
We realize that our attempt to explain this phenomenon makes several assumptions &d simplifications,such as on the structure of polyacrylamide gel (13).But we believe that this article mav brine some d e e m of satisfaction to the non-exmrt and student inYtheir visGalization of the'mechanics of'the separation technique.
Acknowledgment
Fimrres 1. 2. and 3 and some of the ideas nre.sented here
562 i J m l of Chemical Educ~tion
Literature Cned (11 Shapiro,A. h.Vinucla,E..and M a i d J.V.,Jr.. Bioehim. Biophhys.Re*. Commun.. 28, 815 (19671. 121 Weber, %and aibarn.M . . J Biol Chsm., 244,4406 119691. (3) W.bcr.X.. PringIe,* R , , d Osbobobo,M.,MMM~thalaliiE66rmor~)..A~dsdmi"P~~~, New York and London. 1912, Vol. 26. pp. 3-27. 141 Reynolds.J. A.,andTsnford,C., J. B i d Chem.. 245.5166(19701. ( 5 ) Reynolds, J. A.,and Tsnford, C., Proc Not. Acod. Sei., U S A . , 66,1002 (19101. (61 Gordon, A. H., "Laboratmy Techniques in Biahemktv and Molecular Biolw," North Holland Publishing Co.. Amsterdam and London, Vol I, pp. 9-13. 1968. (71 Determsnn, H., "Gel Chromatography." Sprinser-Verlag. NewYork. Inc. 1968. (81 Ackers. G. K.. "Advances in Protein Chemistry," Academic Press. New York and London. VoL 24.1910, pp. 34M46. (91 Swsnk,R.T.,andMunkres,K. D.,Anol. Biocham., 39.462 l19711. I101 Schick. M..Anol. Bmchern.. 63.345 11975).
