HHS Public Access
`Author manuscript
`Curr Protoc Protein Sci. Author manuscript; available in PMC 2016 April 01.
`
`Published in final edited form as:
`Curr Protoc Protein Sci. 2001 May ; APPENDIX 3: Appendix–3F. doi:10.1002/0471140864.psa03fs13.
`
`Protein Precipitation Using Ammonium Sulfate
`
`Paul T. Wingfield
`Protein Expression Laboratory (HNB-27), National Institute of Arthritis and Musculoskeletal and
`Skin Diseases (NIAMS) - NIH, Bldg 6B, Room 1B130, 6 Center Drive, Bethesda MD 20814, Tel:
`301-594-1313
`
`Paul T. Wingfield: paul.wingfield2@nih.gov
`
`Abstract
`The basic theory of protein precipitation by addition of ammonium sulfate is presented and the
`most common applications are listed, Tables are provided for calculating the appropriate amount
`of ammonium sulfate to add to a particular protein solution.
`
`Key terms for indexing
`Ammonium sulfate; ammonium sulfate tables; protein concentration; protein purification
`
`BASIC THEORY
`
`The solubility of globular proteins increases upon the addition of salt (<0.15 M), an effect
`termed salting-in. At higher salt concentrations, protein solubility usually decreases, leading
`to precipitation; this effect is termed salting-out ((Green and Hughes, 1955). Salts that
`reduce the solubility of proteins also tend to enhance the stability of the native conformation.
`In contrast, salting-in ions are usually denaturants.
`
`The mechanism of salting-out is based on preferential solvation due to exclusion of the
`cosolvent (salt) from the layer of water closely associated with the surface of the protein
`(hydration layer). The hydration layer, typically 0.3 to 0.4 g water per gram protein (Rupley
`et al., 1983), plays a critical role in maintaining solubility and the correctly folded native
`conformation. There are three main protein-water interactions: ion hydration between
`charged side chains (e.g., Asp, Glu, Lys), hydrogen bonding between polar groups and water
`(e.g., Ser, Thr, Tyr, and the main chain of all residues), and hydrophobic hydration (Val, Ile,
`Leu, Phe). In hydrophobic hydration, the configurational freedom of water molecules is
`reduced in the proximity of apolar residues. This ordering of water molecules results in a
`loss of entropy and is thus energetically unfavorable. When salt is added to the solution, the
`surface tension of the water increases, resulting in increased hydrophobic interaction
`between protein and water. The protein responds to this situation by decreasing its surface
`area in an attempt to minimize contact with the solvent—as manifested by folding (the
`folded conformation is more compact than the unfolded one) and then self-association
`leading to precipitation. Both folding and precipitation free up bound water, increasing the
`entropy of the system and making these processes energetically favorable. Timasheff and his
`colleagues provide a detailed discussion of these complex effects (e.g., Kita et al., 1994;
`Timasheff and Arakawa, 1997).
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`KASHIV EXHIBIT 1059
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`It should be mentioned that the increase in surface tension of water by salt follows the well-
`known Hofmeister series, shown below (see Parsegian, 1995, and references therein). Hence,
`as an approximation, those salts that favor salting-out raise the surface tension of water the
`highest. As (NH4)2SO4 has much a higher solubility than any of the phosphate salts, it is the
`reagent of choice for salting-out.
`
`TIPS AND GUIDELINES
`
`• With solid ammonium sulfate, a mortar and pestle can be used to break up any
`lumps.
`
`•
`
`•
`
`•
`
`•
`
`•
`
`•
`
`Use analytical grade as lower grade material is often contaminated with heavy
`metals.
`
`Addition of ammonium sulfate acidifies the solution so use at least a 50 mM
`HEPES or Tris buffer etc., 5mM EDTA can also be included.
`
`Add solid ammonium sulfate slowly with gentle stirring; allow to dissolve before
`adding more solid, try to prevent foaming.
`
`On-line calculators can be accessed to conveniently determine the amounts of solid
`ammonium sulfate required to reach a given saturation. For example, EnCor
`Biotechnology Inc., has an on-line calculator based on the equations given in this
`appendix: http://www.encorbio.com/protocols/AM-SO4.htm.
`
`Ammonium sulfate solution, 4.1M saturated at 25 °C can be purchased from
`Sigma-Aldrich and other suppliers.
`
`Note: In the literature sulfate is often referred to by UK spelling: sulphate.
`
`COMMON APPLICATION
`
`Concentration of Proteins
`
`Because precipitation is due to reduced solubility and not denaturation, pelleted protein can
`be readily resolubilized using standard buffers. After concentration, the protein is well suited
`for gel filtration (UNIT 8.3) whereby the buffer can be exchanged and the remaining
`ammonium sulfate removed. Alternately, the protein can be dissolved in a nonprecipitating
`concentration of (NH4)2SO4 (e.g., 1 M) and then applied to a hydrophobic interaction matrix
`(UNIT 8.4).
`
`Protein Purification
`
`Practical details of selective precipitation are presented in UNIT 4.5, and an example in the
`purification of interleukin 1β is given in UNIT 6.2 where the protein is fractionated between
`~50 – 77% saturation. Low molecular weight proteins, like interleukin-1β, as a rule require
`higher salt concentration for precipitation than larger molecular proteins, for example, large
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`multiprotein complexes can often be salted out with < 20% saturation. Another example
`(classic) is the precipitation of IgG from blood sera. The addition of 40 – 45% ammounium
`sulfate precipitates IgG which can be further purified by anion exchange chromatography.
`Salt precipitation has been widely used to fractionate membrane proteins (Schagger, 1994).
`Due to bound lipid and/or detergents, ammonium sulfate precipitates have lower density
`than protein-only precipitates. During centrifugation, these precipitates will often float to the
`top of tube rather than pelleting; the use of swing-out rotors is recommended. Crystallization
`is a traditional method of protein purification. Jakoby (1971) describes a general method that
`involves extracting (NH4)2SO4-precipitated protein with successively dilute (NH4)2SO4
`solutions at low temperature. Although there are several methods for removing
`contaminating nucleic acids from protein solutions including, for example, addition of 0.1%
`(w.v) polyethyleneimine, a simple and effective approach is to apply the protein to a small
`anion exchange column equilibriated with 0.4M ammonium sulfate, where the nucleic acids
`binds to the column and the protein is collected in the flow-through.
`
`Folding and Stabilization of Protein Structure
`
`As mentioned above, (NH4)2SO4 and other neutral salts stabilize proteins by preferential
`solvation (Timasheff and Arakawa, 1997). Proteins are often stored in (NH4)2SO4, which
`inhibits bacterial growth and contaminating protease activities. Protein unfolded by
`denaturants such as urea can be pushed into native conformations by the addition of
`(NH4)2SO4 (Mitchinson and Pain, 1986). A practical application is the folding of
`recombinant proteins. For example, HIV-1 Rev expressed in E. coli was solubilized using
`urea, purified by ion-exchange chromatography in the presence of urea, then folded by the
`addition of 0.5 to 1.0 M (NH4)2SO4 (Wingfield et al., 1991).
`
`Basic Calculations
`Basic definitions—Percentage (%) saturation concentration of (NH4)2SO4 in solution as
`% of maximum solubility at the given temperature. For example, at 0°C, a 100% saturated
`solution is 3.9 M.
`
`Specific volume (sp. vol.) volume occupied by 1 g of (NH4)2SO4 (ml/g) = inverse of density.
`At 0°C, if 706.8 g of (NH4)2SO4 is added to 1 L of water the volume = 1000 ml + volume
`occupied by the salt (706.8 × 0.5281 ml) = total volume of 1373.26 ml. The molarity = 3.9
`M.
`
`Calculating quantities of (NH4)2SO4 to be added—By weight. The following
`equation is used to calculate the weight of solid (NH4)2SO4 to be added to 1 liter of solution
`of initial concentration S1 to produce final saturation S2:
`
`where:
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`Gsat = grams of (NH4)2SO4 contained in 1 liter of saturated solution. For example, at 0°C,
`Gsat = 515.35 (see Table A.3F.1).
`
`S1 and S2 are fractions of complete saturation; for example, a 20% saturation is expressed as
`0.2.
`
`For example, P = 0.2722 and 0.2945 at 0°C and 25°C, respectively.
`
`By volume. The following equation is used to calculate volume of saturated (NH4)2SO4
`solution to be added to 100 ml of solution to increase saturation from S1 to S2:
`
`For example, to raise 100 ml of 0.2 saturated solution to 0.70 saturation:
`
`Hence, 166.66 ml of saturated solution is added to 100 ml of 20% saturated solution to give
`266.66 ml of 70% saturated solution.
`
`AMMONIUM SULFATE TABLES
`
`The tables shown are taken from Wood (1976). Table A.3F.2 gives the weight of (NH4)2SO4
`to be added to a solution to obtain the desired concentration. Table A.3F.3 gives the volume
`of a 3.8 M solution to add to obtain a desired concentration. Tables A.3F.4 and A.3F.5 give
`the final volumes after the addition of the solid salt or a 3.8 M solution, respectively. The
`concentration of (NH4)2SO4 is expressed in molarity (corresponding % saturation is
`indicated in Table A.3F.2). The data is valid for solutions at 0°C, and the variation of
`specific volume with concentration is taken into account. For a table referring to solutions at
`25°C, see Green and Hughes (1955).
`
`LITERATURE CITED
`
`Dawson, RMC.; Elliot, DC.; Elliot, WH.; Jones, KM. Data for Biochemical Research. 3rd. Oxford:
`Oxford Science Publications, Clarendon Press; 1986. p. 537
`Green AA, Hughes WL. Protein solubility on the basis of solubility in aqueous solutions of salts and
`organic solvents. Methods Enzymol. 1955; 1:67–90.
`Jakoby WB. Crystallization as a purification technique. Methods Enzymol. 1971; 22:248–252.
`
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`Kita Y, Arakawa T, Lin T-Y, Timasheff S. Contribution of the surface free energy perturbations to
`protein-solvent interactions. Biochemistry. 1994; 33:1517–1589.
`Mitchinson C, Pain RH. The effect of sulphate and urea on the stability and reversible unfolding of β-
`lactamase from Staphylococcus aureus. J. Mol. Biol. 1986; 184:331–342. [PubMed: 3875732]
`Parsegian VA. Hopes for Hofmeister. Nature. 1995; 378:335–336.
`Rupley JA, Gratton E, Careri G. Water and globular proteins. Trend Biochem. Sci. 1983; 8:18–22.
`Schagger, H. Chromatographic techniques and basic operations in membrane protein purification. In:
`von Jagow, G.; Schagger, H., editors. A Practical Guide to Membrane Protein Purification. San
`Diego: Academic Press; 1994. p. 23-57.
`Timasheff, SN.; Arakawa, T. membrane protein purification Stabilization of protein structure by
`solvents. In: Creighton, TE., editor. Protein Structure: A Practical Approach. 2nd. Oxford: IRL
`Press at Oxford University Press; 1997. p. 349-364.
`Wingfield PT, Stahl SJ, Payton MA, Vankatesan S, Misra M, Steven AC. HIV-1 Rev expressed in
`recombinant Escherichia coli: Purification, polymerization and conformational properties.
`Biochemistry. 1991; 30:7527–7534. [PubMed: 1854752]
`Wood WI. Tables for the preparation of ammonium sulfate solutions. Anal. Biochem. 1976; 73:250–
`257. [PubMed: 942105]
`
`KEY REFERENCE
`
`Wood. 1976. See above.
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`Table A.3F.1
`Density and Molarity of Ammonium Sulfate Solutionsa,b
`
`Temperature (°C)
`
`0
`
`10
`
`20
`
`25
`
`(NH4)2SO4 (g) added to 1 liter of water to give saturated solution
`
`706.8
`
`730.5
`
`755.8
`
`766.8
`
`(NH4)2SO4 (g) per liter saturated solution
`
`Molarity of saturated solution
`
`Density (g/ml)
`
`515.35
`
`524.60
`
`536.49
`
`541.80
`
`3.90
`
`3.97
`
`4.06
`
`4.10
`
`1.2428
`
`1.2436
`
`1.2447
`
`1.2450
`
`Specific volume in saturated solution (ml/g)
`
`0.5281
`
`0.5357
`
`0.5414
`
`0.5435
`
`a
`Molecular weight of (NH4)2SO4 = 132.14.
`
`b
`Adapted from Dawson et al. (1986).
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`
`0.00
`
`18.1
`
`56.1
`
`94.0
`
`132
`
`169
`
`207
`
`244
`
`281
`
`318
`
`355
`
`391
`
`428
`
`464
`
`499
`
`535
`
`570
`
`605
`
`639
`
`673
`
`707
`
`0.00
`
`37.6
`
`75.0
`
`112
`
`150
`
`187
`
`224
`
`260
`
`297
`
`333
`
`369
`
`405
`
`441
`
`477
`
`512
`
`546
`
`581
`
`615
`
`649
`
`682
`
`0.00
`
`36.7
`
`73.2
`
`110
`
`146
`
`182
`
`218
`
`254
`
`290
`
`325
`
`360
`
`395
`
`430
`
`465
`
`499
`
`533
`
`566
`
`599
`
`632
`
`0.00
`
`35.8
`
`282
`
`317
`
`351
`
`386
`
`420
`
`486
`
`519
`
`552
`
`585
`
`3.90
`
`3.80
`
`3.60
`
`3.40
`
`71.5
`
`107
`
`142
`
`178
`
`213
`
`248
`
`453
`
`0.00
`
`35.0
`
`69.8
`
`104
`
`139
`
`174
`
`208
`
`242
`
`276
`
`310
`
`343
`
`376
`
`409
`
`442
`
`475
`
`507
`
`539
`
`0.00
`
`34.2
`
`68.2
`
`102
`
`136
`
`170
`
`203
`
`236
`
`270
`
`303
`
`335
`
`368
`
`400
`
`432
`
`464
`
`495
`
`0.00
`
`33.4
`
`66.7
`
`99.8
`
`133
`
`166
`
`199
`
`231
`
`264
`
`296
`
`328
`
`359
`
`391
`
`422
`
`453
`
`0.00
`
`32.7
`
`65.2
`
`97.7
`
`130
`
`162
`
`194
`
`226
`
`258
`
`289
`
`321
`
`352
`
`383
`
`413
`
`221
`
`3.20
`
`3.00
`
`2.80
`
`2.60
`
`2.40
`
`Author Manuscript
`
`0.00
`
`32.0
`
`63.9
`
`95.7
`
`127
`
`159
`
`190
`
`252
`
`283
`
`314
`
`344
`
`375
`
`0.00
`
`31.3
`
`62.6
`
`93.7
`
`125
`
`156
`
`186
`
`217
`
`247
`
`278
`
`308
`
`338
`
`0.00
`
`30.7
`
`61.4
`
`91.9
`
`122
`
`153
`
`183
`
`213
`
`243
`
`272
`
`302
`
`0.00
`
`30.2
`
`60.2
`
`90.2
`
`120
`
`150
`
`179
`
`209
`
`238
`
`267
`
`0.00
`
`29.6
`
`59.1
`
`88.5
`
`118
`
`147
`
`176
`
`205
`
`234
`
`0.00
`
`29.1
`
`58.1
`
`87.0
`
`116
`
`144
`
`173
`
`202
`
`0.00
`
`57.1
`
`85.5
`
`114
`
`142
`
`170
`
`2.20
`
`2.00
`
`1.80
`
`1.60
`
`1.40
`
`1.20
`
`Final molarity
`
`Table A.3F.2
`
`Author Manuscript
`
`28.6
`
`0.00
`
`28.1
`
`56.2
`
`84.2
`
`112
`
`140
`
`0.00
`
`27.7
`
`55.4
`
`83.0
`
`111
`
`1.00
`
`0.80
`
`0.00
`
`27.4
`
`54.7
`
`81.9
`
`0.60
`
`0.00
`
`27.0
`
`54.0
`
`0.40
`
`0.00
`
`26.7
`
`0.20
`
`0.00
`
`0.00
`
`3.90
`
`3.80
`
`3.60
`
`3.40
`
`3.20
`
`3.00
`
`2.80
`
`2.60
`
`2.40
`
`2.20
`
`2.00
`
`1.80
`
`1.60
`
`1.40
`
`1.20
`
`1.00
`
`0.80
`
`0.60
`
`0.40
`
`0.20
`
`0.00
`
`100.0
`
`97.6
`
`92.4
`
`87.3
`
`82.2
`
`77.0
`
`71.9
`
`66.8
`
`61.6
`
`56.5
`
`51.3
`
`46.2
`
`41.1
`
`35.9
`
`30.8
`
`25.7
`
`20.5
`
`15.4
`
`10.3
`
`5.1
`
`0.0
`
`molarity
`Initial
`
`saturation
`Percent
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`Curr Protoc Protein Sci. Author manuscript; available in PMC 2016 April 01.
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`Grams of Ammonium Sulfate to Add to 1 Liter of Solution at 0°C
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`
`0.00
`
`498
`
`994
`
`1489
`
`1981
`
`0.00
`
`332
`
`662
`
`991
`
`2472
`
`1319
`
`2961
`
`1645
`
`0.00
`
`248
`
`496
`
`742
`
`988
`
`3447
`
`1971
`
`1232
`
`3931
`
`2294
`
`1475
`
`4412
`
`2616
`
`1718
`
`4891
`
`2936
`
`1959
`
`5366
`
`3255
`
`2199
`
`5837
`
`3570
`
`2437
`
`6305
`
`3884
`
`2673
`
`6768
`
`4194
`
`2907
`
`7228
`
`4503
`
`3140
`
`7684
`
`4809
`
`3371
`
`8134
`
`5111
`
`3.40
`
`3.20
`
`Author Manuscript
`
`0.00
`
`198
`
`396
`
`593
`
`789
`
`984
`
`1179
`
`1372
`
`0.00
`
`165
`
`330
`
`494
`
`657
`
`819
`
`981
`
`1565
`
`1143
`
`1756
`
`1303
`
`0.00
`
`141
`
`282
`
`423
`
`562
`
`702
`
`840
`
`978
`
`0.00
`
`124
`
`247
`
`369
`
`492
`
`613
`
`1946
`
`1462
`
`1115
`
`2135
`
`1620
`
`1252
`
`2322
`
`1777
`
`1387
`
`2508
`
`1933
`
`1522
`
`3600
`
`2693
`
`2088
`
`1655
`
`3.00
`
`2.80
`
`2.60
`
`2.40
`
`Author Manuscript
`
`302
`
`377
`
`452
`
`0.00
`
`70.5
`
`141
`
`211
`
`281
`
`351
`
`0.00
`
`65.9
`
`132
`
`197
`
`263
`
`0.00
`
`61.9
`
`124
`
`185
`
`0.00
`
`58.4
`
`117
`
`1.20
`
`1.00
`
`0.80
`
`0.60
`
`0.40
`
`0.00
`
`55.3
`
`0.20
`
`0.00
`
`0.00
`
`3.40
`
`3.20
`
`3.00
`
`2.80
`
`2.60
`
`2.40
`
`2.20
`
`2.00
`
`1.80
`
`1.60
`
`1.40
`
`1.20
`
`1.00
`
`0.80
`
`0.60
`
`0.40
`
`0.20
`
`0.00
`
`molarity
`Initial
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`Curr Protoc Protein Sci. Author manuscript; available in PMC 2016 April 01.
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`Milliliters of a 3.8 M Ammonium Sulfate Solution to Add to 1 Liter of Solution at 0°C
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`Author Manuscript
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`
`735
`
`855
`
`975
`
`1094
`
`1213
`
`0.00
`
`110
`
`219
`
`328
`
`437
`
`545
`
`652
`
`760
`
`866
`
`972
`
`1330
`
`1077
`
`0.00
`
`98.7
`
`197
`
`295
`
`393
`
`490
`
`587
`
`683
`
`779
`
`875
`
`0.00
`
`89.7
`
`179
`
`268
`
`357
`
`446
`
`534
`
`621
`
`709
`
`0.00
`
`82.3
`
`164
`
`246
`
`327
`
`408
`
`489
`
`570
`
`0.00
`
`75.9
`
`152
`
`227
`
`2.20
`
`2.00
`
`1.80
`
`1.60
`
`1.40
`
`Final molarity
`
`Table A.3.F.3
`
`Page 8
`
`

`

`Wingfield
`
`Page 9
`
`1000
`
`1011
`
`1000
`
`1033
`
`1022
`
`1000
`
`1055
`
`1044
`
`1022
`
`1000
`
`1077
`
`1066
`
`1043
`
`1021
`
`1099
`
`1087
`
`1064
`
`1041
`
`1121
`
`1109
`
`1085
`
`1062
`
`1142
`
`1129
`
`1105
`
`1082
`
`1162
`
`1150
`
`1125
`
`1183
`
`1170
`
`1145
`
`1203
`
`1190
`
`1164
`
`1222
`
`1209
`
`1183
`
`1242
`
`1228
`
`1202
`
`1260
`
`1247
`
`1220
`
`1278
`
`1265
`
`1237
`
`1296
`
`1282
`
`1254
`
`1313
`
`1299
`
`1271
`
`1329
`
`1315
`
`1286
`
`1344
`
`1330
`
`1301
`
`1359
`
`1345
`
`1316
`
`1373
`
`1359
`
`1329
`
`3.90
`
`3.80
`
`3.60
`
`Author Manuscript
`
`1000
`
`1020
`
`1000
`
`1040
`
`1019
`
`1000
`
`1060
`
`1039
`
`1019
`
`1000
`
`1101
`
`1079
`
`1058
`
`1037
`
`1018
`
`1121
`
`1098
`
`1076
`
`1056
`
`1036
`
`1140
`
`1116
`
`1094
`
`1073
`
`1054
`
`1158
`
`1135
`
`1112
`
`1091
`
`1071
`
`1176
`
`1152
`
`1130
`
`1108
`
`1088
`
`1194
`
`1170
`
`1147
`
`1125
`
`1211
`
`1187
`
`1163
`
`1141
`
`1228
`
`1203
`
`1179
`
`1156
`
`1244
`
`1218
`
`1194
`
`1172
`
`1259
`
`1233
`
`1209
`
`1186
`
`1274
`
`1248
`
`1223
`
`1200
`
`1288
`
`1262
`
`1237
`
`1213
`
`1301
`
`1275
`
`1249
`
`1225
`
`3.40
`
`3.20
`
`3.00
`
`2.80
`
`1000
`
`1014
`
`1000
`
`1028
`
`1014
`
`1000
`
`1042
`
`1027
`
`1013
`
`1000
`
`1054
`
`1039
`
`1025
`
`1012
`
`1000
`
`1067
`
`1052
`
`1037
`
`1024
`
`1012
`
`1000
`
`1079
`
`1063
`
`1049
`
`1035
`
`1023
`
`1011
`
`1000
`
`1090
`
`1074
`
`1060
`
`1046
`
`1033
`
`1023
`
`1010
`
`1000
`
`1.60
`
`1.40
`
`1.20
`
`1.00
`
`0.80
`
`0.60
`
`0.40
`
`0.20
`
`0.00
`
`3.90
`
`3.80
`
`3.60
`
`3.40
`
`3.20
`
`3.00
`
`2.80
`
`2.60
`
`2.40
`
`2.20
`
`2.00
`
`1.80
`
`1.60
`
`1.40
`
`1.20
`
`1.00
`
`0.80
`
`0.60
`
`0.40
`
`0.20
`
`0.00
`
`molarity
`Initial
`
`Curr Protoc Protein Sci. Author manuscript; available in PMC 2016 April 01.
`
`Final Volume in Millimeters After Addition of Solid Ammonium Sulfate to 1 Liter of Solution at 0°C
`
`Author Manuscript
`
`Author Manuscript
`
`1000
`
`1018
`
`1000
`
`1035
`
`1017
`
`1000
`
`1052
`
`1033
`
`1016
`
`1000
`
`1068
`
`1050
`
`1032
`
`1016
`
`1000
`
`1104
`
`1084
`
`1065
`
`1048
`
`1031
`
`1015
`
`1120
`
`1100
`
`1081
`
`1063
`
`1046
`
`1030
`
`1135
`
`1115
`
`1096
`
`1077
`
`1060
`
`1044
`
`1150
`
`1129
`
`1110
`
`1091
`
`1074
`
`1057
`
`1164
`
`1143
`
`1124
`
`1105
`
`1087
`
`1070
`
`1178
`
`1157
`
`1137
`
`1118
`
`1100
`
`1083
`
`1191
`
`1169
`
`1149
`
`1130
`
`1112
`
`1095
`
`1203
`
`1181
`
`1161
`
`1142
`
`1123
`
`1106
`
`2.60
`
`2.40
`
`2.20
`
`2.00
`
`1.80
`
`Final molarity
`
`Table A.3.F.4
`
`Author Manuscript
`
`Page 9
`
`

`

`Wingfield
`
`Page 10
`
`1000
`
`1498
`
`1000
`
`1994
`
`1331
`
`1000
`
`2488
`
`1661
`
`1248
`
`2979
`
`1989
`
`1494
`
`3469
`
`2316
`
`1740
`
`3956
`
`2642
`
`1984
`
`4441
`
`2965
`
`2227
`
`4922
`
`3287
`
`2469
`
`5402
`
`3606
`
`2709
`
`5878
`
`3924
`
`2948
`
`6350
`
`4240
`
`3185
`
`6818
`
`4552
`
`3420
`
`7282
`
`4862
`
`3652
`
`7741
`
`5168
`
`3883
`
`8196
`
`5472
`
`4111
`
`8646
`
`5773
`
`4337
`
`9091
`
`6070
`
`3.40
`
`3.20
`
`Author Manuscript
`
`1000
`
`1198
`
`1000
`
`1394
`
`1164
`
`1000
`
`1590
`
`1328
`
`1141
`
`1000
`
`1785
`
`1491
`
`1280
`
`1122
`
`1979
`
`1652
`
`1419
`
`1244
`
`2171
`
`1813
`
`1557
`
`1365
`
`2363
`
`1973
`
`1694
`
`1486
`
`2553
`
`2131
`
`1831
`
`1605
`
`2741
`
`2289
`
`1966
`
`1723
`
`2927
`
`2444
`
`2099
`
`3112
`
`2598
`
`2232
`
`3294
`
`2751
`
`2363
`
`3476
`
`2902
`
`2493
`
`4560
`
`3654
`
`3051
`
`2621
`
`3.00
`
`2.80
`
`2.60
`
`2.40
`
`1000
`
`1068
`
`1000
`
`1135
`
`1063
`
`1000
`
`1291
`
`1202
`
`1126
`
`1059
`
`1000
`
`1362
`
`1268
`
`1187
`
`1117
`
`1055
`
`1000
`
`1432
`
`1333
`
`1248
`
`1174
`
`1109
`
`1051
`
`1000
`
`1.20
`
`1.00
`
`0.80
`
`0.60
`
`0.40
`
`0.20
`
`0.00
`
`3.40
`
`3.20
`
`3.00
`
`2.80
`
`2.60
`
`2.40
`
`2.20
`
`2.00
`
`1.80
`
`1.60
`
`1.40
`
`1.20
`
`1.00
`
`0.80
`
`0.60
`
`0.40
`
`0.20
`
`0.00
`
`Molarity
`Initial
`
`Curr Protoc Protein Sci. Author manuscript; available in PMC 2016 April 01.
`
`Final Volume in Millimeters After Addition of 3.8 M Ammonium Sulfate Solution to 1 Liter of Solution at 0°C
`
`Author Manuscript
`
`Author Manuscript
`
`1000
`
`1108
`
`1000
`
`1216
`
`1097
`
`1000
`
`1324
`
`1194
`
`1088
`
`1000
`
`1430
`
`1290
`
`1176
`
`1080
`
`1000
`
`1535
`
`1385
`
`1262
`
`1160
`
`1074
`
`1841
`
`1640
`
`1479
`
`1348
`
`1239
`
`1147
`
`1957
`
`1743
`
`1573
`
`1433
`
`1317
`
`1219
`
`2072
`
`1846
`
`1665
`
`1517
`
`1394
`
`2186
`
`1947
`
`1757
`
`1601
`
`1471
`
`2298
`
`2047
`
`1847
`
`1683
`
`1547
`
`2.20
`
`2.00
`
`1.80
`
`1.60
`
`1.40
`
`Final molarity
`
`Table A.3.F.5
`
`Author Manuscript
`
`Page 10
`
`