- Email: [email protected]
Mobility-molecular weight relationships of small proteins and peptides in acrylamide-gel electrophoresis
,ANALYTICAL
20,
BIOCHEMISTRY
Mobility-Molecular and
24-29
Weight
Peptides
Research
Relationships
in Acrylamide-Gel
L. INGRAM, Unilever
(1007)
M. P. TOMBS,
Laboratory,
Colworth
Received
House,
November
of Small
Proteins
Electrophoresis AND
A. HURST’
Sharnbrook,
Bedford,
England
28, 1966
Previous results have shown that the mobility of proteins and peptides in acrylamide-gel electrophoresis is strongly dependent on the concentration of the gel (1, 2). Generally, the more concentrated the gel, the lower is the mobility. In presenting our earlier results (2) for proteins of molecular weight 10,000 to 700,000 we tried to arrive at a relationship between mobility and molecular weight in this range. A reasonably good empirical relationship was found, though it did not agree with that suggested by a theoretical approach. Calculations of the diameters of peptides of the order of 1000 molecular weight suggested that they were of the same order as the pore sizes in acrylamide gels and could be expected to show some retardation, especially at high gel concentration. This paper presents some data for peptides of molecular weight 1200 upward and derives an empirical relationship similar to that previously described (2). EXPERIMENTAL
Chemicals: Polymyxin and bacitracin were purchased from Burroughs Wellcome & Co., London. Gramicidin S was a gift from Astra Laboratories, Sweden. Subtilin was a gift from Dr. J. C. Lewis, Western Regional Laboratories. Nisin was a gift from Dr. J. Tramer, United Dairies Central Laboratory, London. Saramycetine was obtained from Hoffmann-La Roche, New Jersey. Insulin was obtained from British Drug Houses Ltd., Poole, England, ribonuclease from L. Light & Co., Colnbrook, England, lysozyme from Armour Pharmaceutical Co. Ltd., Eastbourne, England, and trypsin from Seravac Laboratories (Pty.) Ltd., Maidenhead, England. Other reagents were of A. R. grade. Methods: Acrylamide gels were made from Cyanogum 41 obtained from British Drug Houses Ltd. A batch to batch variation of this product was observed. Gels were made in distilled water according to Tombs (2) and with the exception of saramycetine all the peptides were run in a pH 2.2 1 Formerly
A. Hirsch. 24
SMALL
PROTEINS
IN
ACRYLAMIDE
2; ‘i
GELS
glycine + HCl buffer (50 ml 1.0 M glycine + 44 ml 1.0 M HCl made up to 1 liter) in a cold room at 2”. Saramycetine was run in a Tris-citrate/sodium borate discontinuous buffer, pH 8.6 (2). Each substance was run in nine gel concentrations ranging from 5 to 307$ (w/v) and the mobility expressed as cm’/ntin-17. The potential gradient was separately determined on each gel. Zones were detected with naphthalene black and measurements of mobilit)y made to the center of the zone. Duplicate and in some cases triplicate determinations were made at, each gel concentration, and the mean value used for calculation. Plots of mobility against reciprocal of gel concentration were then made. They always showed a flat part at low gel concentrations and this was used to estimate the mobility at zero gel concent,ration. Then the gel concen-
60
20-
I I
IO-/(
i/
I I
0.01
cl05
01
I 015
I c7
‘k
Variation of mobility with gel concentration (expressed as concentration (w/v) of monomer used to make gel) for bacitracin, two forms of nisin, and insulin. An estimate of error is shown for bacitracin, and t(he nisin points. They are omitt,ed for the sake of FIG.
clarity
1.
from
the insulin
curve.
26
INGRAM,
TOMES,
AND
HUFtST
tration (c’) required to give half of this mobility was found graphically. Some typical plots are shown in Figure 1, as well as an estimate of the error of individual determinations. RESULTS
AND
DISCUSSION
Our previous theories (2) on the relationship between the mobility of a protein and the gel concentration introduced the concept of a limiting pore size in the gel, PL, which the protein molecule could not quite enter. By assuming : that there is a normal distribution of pore sizes in the gel, of mean pore size @ and standard deviation u, that there is a limiting pore size PL, and that the mobility is proportional to the fraction of pores that the molecule can penetrate, we derived the following equation:
6)
($
where Q is a standard normal probability integral, M is the mobility and Msol the mobility in free solution (i.e., zero gel concentration). One important consequence of this result is that, when the mobility is half that in free solution, then PL = 15, where p is the average pore size of the gel at the concentration (c’) required to produce 50% retardation. In order to make use of this result we also need the relationship between pore size and gel concentration, since the gel concentration is the quantity actually measured. We obtained previously (2) the relation:
where d is the diameter of the strands making up the gel. It is assumed that the strands are in a regular rectangular array. Clearly if c in the above equation is c’, then p becomes PL. It is also possible to obtain PL in another way. Thus, if we assume that the molecules are spherical and of density 1.3, the (unsolvated) diameter of the molecule can be cakulated from the molecular weight (2). The approximate molecular diameters are shown in Table 1. Even peptides of quite low molecular weight have diameters of the order of the pore sizes to be expected in the acrylamide gels used in practice. Thus polymyxin has a diameter of about 15 1 while lysozyme with about ten times its molecular weight has a diameter of only 34 b. This is, of course, a consequence of the dependence of diameter on the cube root of molecular weight and suggests that the
SMALL
PROTEINS
IN
ACRYLAMIDE
<” 2l
GELS
filtration effect of polyacrylamide gels should be observable with compounds having a molecular weight of the order of 1000. The limiting pore size, that is the “diameter” of a pore which the protein cannot quit,e enter, can be equated w&h the molecular diameter. Figure 2 shows the relationship between molecular diameters and 1 lIc’. A st,raight TABLE 1 Calculated Molecular Diameters and Determined Values of l/c’ (molecular diameters were calculated as described in reference 2 from the molecular weights given in the references)
Protein
Arachin Dimer Monomer a-Chain -j-Chain Glycinin 158 11s 7s Albumin Dimer Monomer Ovalbumin @Lactoglobulin Trypsin Lysozyme Saramycetine Ribonurlease Nisin Insulin Subt,ilin Bacitrscin Gramicidin S Polymyxin B
M.W.
340,000 170,000 35,000
10,000
Ref.
10 10 10 10
AppPX. molecul r diam. f (equal to limi$:pplqre
96 74
41 ::o
700,000 350,000 175,000
11 I1 I1
100
132,000
12
66,000
12
66 53
44,000
12 12 12 13 s 12 7
35,000 24,000 15,000 14,000 13,000 7,000 5,700
3,200 1,400 1,350
1,225
12 s x s 8
96
76
44
41 38 34
1 /e’
0, 170 0.138 0.085 0 ,056 0 1% 0.170 0.144 0 “20 1
0.10s 0.09X 0. 11x 0.084 0.077
3” 30 ‘2X
0.0&i
26
0 06:!
24 20 16 15
0.05s
0.073 0.06r;
0.053
0.053 0.048
line describes it well over the wide molecular weight range tested (1.2 X lo” to 7 X 105). We can also calculate a possible theoretical relationship between molecular diameter and l/c’, for example by using equation 2, providing some assumption of the value of d is made. Figure 2 shows two curves, for d = 10 i and d = 18 A. It is clear that these lines are not in agreement with the experimental data. This is the same conclusion as reached previously for a narrower range of molecular weights (2) Thrs
28
INGRAM,
TOMBS,
AMI
HGRST
FIG. 2. Plot of PL (in h;), calculated from molecular weight, against l/c’. The two curves are calculated from equation 2 by assuming, for the upper curve cl = 10 A and for the lower d = 18 A. The straight line through the points (data from Table 1) was fitted to a regression equation:
PL = -8.84 + 540 (l/c’) where PL is the calculated molecular diameter, and c’ is the gel concentrat(ion required to reduce mobility to half its value in free solution.
reasons for the failure of equation 2 to fit the experimental data are not clear. It may be that the assumptions underlying equation 1 are not valid, although some equation of this form must be used to explain the sigmoid M vs. l/c plots. (Equation 1 predicts a sigmoid relationship between mobility and l/c. Several examples of this were described previously (2) and the smaller peptides gave very similar results, though higher gel concentrations were needed to produce significant retardation and the full sigmoid shape for the smaller molecules could not be obtained (Fig. l).) It seemsmore likely that the various models used for the gel structure, leading to results such as equation 2, are inadequate. No direct evidence on
t,he structure of acrylamide gels is available: the mechanism of polymerization is complex (3) and it is likely that the gel structure becomes qualitatively different, apart from the simple concentration effect predicted by equation 2, as monomer concentration increases. For example if d is not’ caonstant, and varies with gel strength, some approximat,ion to the experimental data could be made. The empirical relationship shown in Figure 2 permits an approximate estimat,e of molecular weight, perhaps to about of: 207,. If we bear in mind the necessary simplifying assumption made, such as that the molecules are spherical, this is as good as can be expected. Recently, there was much work on the relationship between excluded volume and log molecular weight in gel filtration (4). Theoretical treatments (5) are available based on an approach similar to that used here, and suffering from similar difficulties. For esample all protein molecules are caertainly not spherical, so that only approximate molecular weights can be dctcrminrd by either method. Some improvement can be made by using Stokes radii (6) but this involves collecting much exutra data from other techniques. Electrophoresis has a greater resolving power than gel filtration and thr general approach described here can be used, for example, in assigning molec*ular weights to the components of a complex mixture, and particularly in studying monomer-polymer systems. both of which can be difficult, by gel filt,rat,ion methods. l’hc usefulness of the method is illustrated by the estimation of the molecular weight) of nisin, which was thought to be about 7000 (7). This ligure was challenged by Bodansky and Perlman (S), who suggested that the molec~ular n-eight of nisin was one-third of the original value. However, a value of 7000 fits the st’raight line of Figure 2, support’ing this estimate; t.his x&ill corresponds with the “fast nisin” component. recent’ly described in a similar preparation (9). The “slow nisin” (Fig. 1) component has an apparent molecular weight, of 14,000 and could be a dimer of “fast, nisirr.” REFERENCES 1. k%YMOSD,
&, -13-D -\IAKAMICHI,
M.,~~U~.&OChCm.&23
(I$?@).
2. TOMBS, RI. P., And. Biochem. 13, 121 (1965). 3. DAVIS. B. J., A/r,,. i\-. I’. Acad. Sci. 121, 421 (1964). 4. Ah~~~~~s, P.. Biociiem. J. 96, 595 (1965). 5. IA~URENT, T. C., ASD KILLANDER, J., J. Chromatog. 14, 317 (1965). 6. SIEGEL, L., AND MONTY, K., Biochim. Biophys. Ada 112, 346 (1966) 7. CHEESEMAN, G. C., AND BERRIDGE, N. J., Biochem. J. 71, 185 (1959). S. BODANSKY, M., AND PERLMAN, D., Nature (London) 204, 840 (1964). 9. HURST, A., J. Gen. Microbial. 45, 503 (1966). 10. TOMBS, M. P., Biochem. J. 96, 119 (1965). Il. WOLF, W. J., AND BRIGGS, D. R., Arch. Biochem. Biophys. 85, 186 (1957). 12. “The Proteins” (H. Neurath, ed.). Academic Press, Sew York-London, 19%.
20,
BIOCHEMISTRY
Mobility-Molecular and
24-29
Weight
Peptides
Research
Relationships
in Acrylamide-Gel
L. INGRAM, Unilever
(1007)
M. P. TOMBS,
Laboratory,
Colworth
Received
House,
November
of Small
Proteins
Electrophoresis AND
A. HURST’
Sharnbrook,
Bedford,
England
28, 1966
Previous results have shown that the mobility of proteins and peptides in acrylamide-gel electrophoresis is strongly dependent on the concentration of the gel (1, 2). Generally, the more concentrated the gel, the lower is the mobility. In presenting our earlier results (2) for proteins of molecular weight 10,000 to 700,000 we tried to arrive at a relationship between mobility and molecular weight in this range. A reasonably good empirical relationship was found, though it did not agree with that suggested by a theoretical approach. Calculations of the diameters of peptides of the order of 1000 molecular weight suggested that they were of the same order as the pore sizes in acrylamide gels and could be expected to show some retardation, especially at high gel concentration. This paper presents some data for peptides of molecular weight 1200 upward and derives an empirical relationship similar to that previously described (2). EXPERIMENTAL
Chemicals: Polymyxin and bacitracin were purchased from Burroughs Wellcome & Co., London. Gramicidin S was a gift from Astra Laboratories, Sweden. Subtilin was a gift from Dr. J. C. Lewis, Western Regional Laboratories. Nisin was a gift from Dr. J. Tramer, United Dairies Central Laboratory, London. Saramycetine was obtained from Hoffmann-La Roche, New Jersey. Insulin was obtained from British Drug Houses Ltd., Poole, England, ribonuclease from L. Light & Co., Colnbrook, England, lysozyme from Armour Pharmaceutical Co. Ltd., Eastbourne, England, and trypsin from Seravac Laboratories (Pty.) Ltd., Maidenhead, England. Other reagents were of A. R. grade. Methods: Acrylamide gels were made from Cyanogum 41 obtained from British Drug Houses Ltd. A batch to batch variation of this product was observed. Gels were made in distilled water according to Tombs (2) and with the exception of saramycetine all the peptides were run in a pH 2.2 1 Formerly
A. Hirsch. 24
SMALL
PROTEINS
IN
ACRYLAMIDE
2; ‘i
GELS
glycine + HCl buffer (50 ml 1.0 M glycine + 44 ml 1.0 M HCl made up to 1 liter) in a cold room at 2”. Saramycetine was run in a Tris-citrate/sodium borate discontinuous buffer, pH 8.6 (2). Each substance was run in nine gel concentrations ranging from 5 to 307$ (w/v) and the mobility expressed as cm’/ntin-17. The potential gradient was separately determined on each gel. Zones were detected with naphthalene black and measurements of mobilit)y made to the center of the zone. Duplicate and in some cases triplicate determinations were made at, each gel concentration, and the mean value used for calculation. Plots of mobility against reciprocal of gel concentration were then made. They always showed a flat part at low gel concentrations and this was used to estimate the mobility at zero gel concent,ration. Then the gel concen-
60
20-
I I
IO-/(
i/
I I
0.01
cl05
01
I 015
I c7
‘k
Variation of mobility with gel concentration (expressed as concentration (w/v) of monomer used to make gel) for bacitracin, two forms of nisin, and insulin. An estimate of error is shown for bacitracin, and t(he nisin points. They are omitt,ed for the sake of FIG.
clarity
1.
from
the insulin
curve.
26
INGRAM,
TOMES,
AND
HUFtST
tration (c’) required to give half of this mobility was found graphically. Some typical plots are shown in Figure 1, as well as an estimate of the error of individual determinations. RESULTS
AND
DISCUSSION
Our previous theories (2) on the relationship between the mobility of a protein and the gel concentration introduced the concept of a limiting pore size in the gel, PL, which the protein molecule could not quite enter. By assuming : that there is a normal distribution of pore sizes in the gel, of mean pore size @ and standard deviation u, that there is a limiting pore size PL, and that the mobility is proportional to the fraction of pores that the molecule can penetrate, we derived the following equation:
6)
($
where Q is a standard normal probability integral, M is the mobility and Msol the mobility in free solution (i.e., zero gel concentration). One important consequence of this result is that, when the mobility is half that in free solution, then PL = 15, where p is the average pore size of the gel at the concentration (c’) required to produce 50% retardation. In order to make use of this result we also need the relationship between pore size and gel concentration, since the gel concentration is the quantity actually measured. We obtained previously (2) the relation:
where d is the diameter of the strands making up the gel. It is assumed that the strands are in a regular rectangular array. Clearly if c in the above equation is c’, then p becomes PL. It is also possible to obtain PL in another way. Thus, if we assume that the molecules are spherical and of density 1.3, the (unsolvated) diameter of the molecule can be cakulated from the molecular weight (2). The approximate molecular diameters are shown in Table 1. Even peptides of quite low molecular weight have diameters of the order of the pore sizes to be expected in the acrylamide gels used in practice. Thus polymyxin has a diameter of about 15 1 while lysozyme with about ten times its molecular weight has a diameter of only 34 b. This is, of course, a consequence of the dependence of diameter on the cube root of molecular weight and suggests that the
SMALL
PROTEINS
IN
ACRYLAMIDE
<” 2l
GELS
filtration effect of polyacrylamide gels should be observable with compounds having a molecular weight of the order of 1000. The limiting pore size, that is the “diameter” of a pore which the protein cannot quit,e enter, can be equated w&h the molecular diameter. Figure 2 shows the relationship between molecular diameters and 1 lIc’. A st,raight TABLE 1 Calculated Molecular Diameters and Determined Values of l/c’ (molecular diameters were calculated as described in reference 2 from the molecular weights given in the references)
Protein
Arachin Dimer Monomer a-Chain -j-Chain Glycinin 158 11s 7s Albumin Dimer Monomer Ovalbumin @Lactoglobulin Trypsin Lysozyme Saramycetine Ribonurlease Nisin Insulin Subt,ilin Bacitrscin Gramicidin S Polymyxin B
M.W.
340,000 170,000 35,000
10,000
Ref.
10 10 10 10
AppPX. molecul r diam. f (equal to limi$:pplqre
96 74
41 ::o
700,000 350,000 175,000
11 I1 I1
100
132,000
12
66,000
12
66 53
44,000
12 12 12 13 s 12 7
35,000 24,000 15,000 14,000 13,000 7,000 5,700
3,200 1,400 1,350
1,225
12 s x s 8
96
76
44
41 38 34
1 /e’
0, 170 0.138 0.085 0 ,056 0 1% 0.170 0.144 0 “20 1
0.10s 0.09X 0. 11x 0.084 0.077
3” 30 ‘2X
0.0&i
26
0 06:!
24 20 16 15
0.05s
0.073 0.06r;
0.053
0.053 0.048
line describes it well over the wide molecular weight range tested (1.2 X lo” to 7 X 105). We can also calculate a possible theoretical relationship between molecular diameter and l/c’, for example by using equation 2, providing some assumption of the value of d is made. Figure 2 shows two curves, for d = 10 i and d = 18 A. It is clear that these lines are not in agreement with the experimental data. This is the same conclusion as reached previously for a narrower range of molecular weights (2) Thrs
28
INGRAM,
TOMBS,
AMI
HGRST
FIG. 2. Plot of PL (in h;), calculated from molecular weight, against l/c’. The two curves are calculated from equation 2 by assuming, for the upper curve cl = 10 A and for the lower d = 18 A. The straight line through the points (data from Table 1) was fitted to a regression equation:
PL = -8.84 + 540 (l/c’) where PL is the calculated molecular diameter, and c’ is the gel concentrat(ion required to reduce mobility to half its value in free solution.
reasons for the failure of equation 2 to fit the experimental data are not clear. It may be that the assumptions underlying equation 1 are not valid, although some equation of this form must be used to explain the sigmoid M vs. l/c plots. (Equation 1 predicts a sigmoid relationship between mobility and l/c. Several examples of this were described previously (2) and the smaller peptides gave very similar results, though higher gel concentrations were needed to produce significant retardation and the full sigmoid shape for the smaller molecules could not be obtained (Fig. l).) It seemsmore likely that the various models used for the gel structure, leading to results such as equation 2, are inadequate. No direct evidence on
t,he structure of acrylamide gels is available: the mechanism of polymerization is complex (3) and it is likely that the gel structure becomes qualitatively different, apart from the simple concentration effect predicted by equation 2, as monomer concentration increases. For example if d is not’ caonstant, and varies with gel strength, some approximat,ion to the experimental data could be made. The empirical relationship shown in Figure 2 permits an approximate estimat,e of molecular weight, perhaps to about of: 207,. If we bear in mind the necessary simplifying assumption made, such as that the molecules are spherical, this is as good as can be expected. Recently, there was much work on the relationship between excluded volume and log molecular weight in gel filtration (4). Theoretical treatments (5) are available based on an approach similar to that used here, and suffering from similar difficulties. For esample all protein molecules are caertainly not spherical, so that only approximate molecular weights can be dctcrminrd by either method. Some improvement can be made by using Stokes radii (6) but this involves collecting much exutra data from other techniques. Electrophoresis has a greater resolving power than gel filtration and thr general approach described here can be used, for example, in assigning molec*ular weights to the components of a complex mixture, and particularly in studying monomer-polymer systems. both of which can be difficult, by gel filt,rat,ion methods. l’hc usefulness of the method is illustrated by the estimation of the molecular weight) of nisin, which was thought to be about 7000 (7). This ligure was challenged by Bodansky and Perlman (S), who suggested that the molec~ular n-eight of nisin was one-third of the original value. However, a value of 7000 fits the st’raight line of Figure 2, support’ing this estimate; t.his x&ill corresponds with the “fast nisin” component. recent’ly described in a similar preparation (9). The “slow nisin” (Fig. 1) component has an apparent molecular weight, of 14,000 and could be a dimer of “fast, nisirr.” REFERENCES 1. k%YMOSD,
&, -13-D -\IAKAMICHI,
M.,~~U~.&OChCm.&23
(I$?@).
2. TOMBS, RI. P., And. Biochem. 13, 121 (1965). 3. DAVIS. B. J., A/r,,. i\-. I’. Acad. Sci. 121, 421 (1964). 4. Ah~~~~~s, P.. Biociiem. J. 96, 595 (1965). 5. IA~URENT, T. C., ASD KILLANDER, J., J. Chromatog. 14, 317 (1965). 6. SIEGEL, L., AND MONTY, K., Biochim. Biophys. Ada 112, 346 (1966) 7. CHEESEMAN, G. C., AND BERRIDGE, N. J., Biochem. J. 71, 185 (1959). S. BODANSKY, M., AND PERLMAN, D., Nature (London) 204, 840 (1964). 9. HURST, A., J. Gen. Microbial. 45, 503 (1966). 10. TOMBS, M. P., Biochem. J. 96, 119 (1965). Il. WOLF, W. J., AND BRIGGS, D. R., Arch. Biochem. Biophys. 85, 186 (1957). 12. “The Proteins” (H. Neurath, ed.). Academic Press, Sew York-London, 19%.