- Email: [email protected]
Ionic partial molar volumes of density gradient salts at finite concentrations
637 Biochimica et Biophysica Acta, 586 (1979) 637--640
© Elsevier/North-HollandBiomedicalPress
BBA Report BBA 21514 IONIC PARTIAL MOLAR VOLUMES OF DENSITY GRADIENT SALTS AT FINITE CONCENTRATIONS
RICHARD I. KELLEY Departments of Pathology and Pediatrics, University of Pennsylvania School of Medicine and Children's Hospital of Philadelphia, Philadelphia, PA 19104 (U.S.A.)
(Received April 17th, 1979) Key words: Partial molar volume; Density gradient; Isopycnic centrifugation
Summary A general method is presented for estimating concentration-dependent partial molar volumes for individual ions of heavy density gradient salts used in the isopycnic ultracentrifugation of charged macromolecules.
For many applications of density gradient sedimentation equilibrium to the study of macromolecules and their interactions, ion-binding has an important effect on experimentally determined partial molar volumes. Because density gradients of heavy salts are generated at high ionic strengths, the frequently employed, published values of ~ion, the partial molar volume at infinite dilution, are substantially smaller than the effective partial molar volumes under experimental conditions. Recognizing this problem, Ifft and Williams [ 1] proposed apportioning V for cesium chloride to the cesium and Chloride ions according to the cubes of their radii in crystalline cesium chloride. This approach assumes that solvation differences are small for two monovalent ions of similar size, 1.69 and 1.81 .~ for Cs* and CI-, respectively. Unfortunately, this method is useful only for CsC1, most other salts having ions of dissimilar sizes. This communication describes an alternate method for obtaining Vion at finite salt concentrations that is applicable to most of the commonly used density gradient salts. Table I lists the concentration-dependent partial molar volumes for eight salts as calculated by the method of intercepts [2] using density vs. weight fraction data from the International Critical Tables [3] and, for cesium sulfate, from Ludlum and Warner [4]. The values of Vsalt were replotted as the mostly linear function of the square root of the molarity and a smooth curve visually fitted to the points, as shown in Fig. 1. When extrapolated to infinite
638 TABLE
I
INTERPOLATED PARTIAL OF MOLARITY AT 25°C
MOLAR
VOLUMES
FOR EIGHT HEAVY SALTS AS A FUNCTION
Partial molar volume (cm 3/tool) c 1/2
RbCl
RbBr
RbI
CsC1
CsBr
CsI
Rb 2 SO 4
Cs 2 S O 4
0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.50
31.90 32.69 33.50 34.31 35.11 35.91 36.72 37.58 38.33 39.57
38.78 39.49 40.22 40.97 41.71 42.45 43.19 43.90 44.50
50.29 50.97 51.60 52.24 52.87 53.50 54.11 54.63 ---
39.17 39.96 40.77 41.57 42.38 43.20 44.00 44.78 45.42 46.49
46.05 46.80 47.55 48.29 49.01 49.76 50.43 51.03 51.52 --
57.56 58.20 58.82 59.42 60.02 60.55 60.98 ----
42.12 47.60 53.14 58.44 63.30 67.26
56.66 60.92 65.18 69.44 73.60 77.42
o
i
C1/2
F i g . 1. P a r t i a l m o l a r v o l u m e s f o r c e s i u m c h l o r i d e as a f u n c t i o n o f t h e s q u a r e r o o t o f m o l a r i t y .
dilution, V7° , the curves yield partial molar volumes that are within 0.5% of those given by Millero [ 5]. Assuming that for large, monovalent ions the electrostrictive and intrinsic volume components of --Vion are smooth, continuous_ functions of the ionic crystal radii, we can as a first approximation of Vion for a particular ion apportion the partial molar volumes of several of its salts to the ions according to the cubes of their crystalline radii, as did Ifft and Williams. If we then extrapolate a plot of, for example, Vcs. against the radii of its counterions, e.g. halides, to the point where the cesium and halide ions are the same radius, there, theoretically, the equal-sized ions_of the hypothetical salt have identical partial molar volumes and therefore Vcs÷ = l~YCsHalide, In effect, the extrapolation procedure brings into equivalence both the geometric and electrostrictive components of the partial molar volumes of the cation and anion. Fig. 2 illustrates this m e t h o d applied to the cesium ion for concentrations up to 6.25~'motar using Pauling's values [6] for the ionic crystal radii. The partial molar volumes for the rubidium ion are similarly obtained. Subtracting Yca_tion f~om Ysal_t at equivalent concentrations for the cesium and rubidium ions gave two values of V for each halide that were within 0.2 c m 3/mol of each Other over the entire concentration range, an indication of the validity
639
2~
~ -
I
125 ~
I
-5 E
to~ E I c~
75
I
)
o
I 03
0.4
05
Crystal Volume Fraction of Ca+
Fig. 2. G r a p h i c d e t e r m i n a t i o n o f V f o r t h e c e s i u m i o n at c o n c e n t r a t i o n s u p t o 2.5 M ½. T h e p a r t i a l m o l a r v o l u m e s f o r t h e c e s i u m halides listed in T a b l e I w e r e m u l t i p l i e d b y t h e a p p o r t i o n m e n t f a c t o r 3+ 3+ 3 . . . . . . r c . ~ / ( r c s + r ~ d e ) , w h e r e r Is t h e 1omc c r y s t a l r a d m s , t o give v o l u m e - b a s e d estLmates o f VCs+ f o r e a c h salt. T h e n , at e a c h c o n c e n t r a t i o n , t h e e s t i m a t e s o f VCs+ w e r e p l o t t e d against t h e v a l u e of t h e a p p o r t i o n m e n t f a c t o r a n d e x t r a p o l a t e d g r a p h i c a l l y ~ 0.5 as d e s c r i b e d in t h e t e x t . P o i n t s for t h e i o d i d e a t 2.0 a n d 2.5 M ½ a n d f o r t h e b r o m i d e a t 2.5 M VJare e x t r a p o l a t e d f r o m t h e d a t a in T a b l e I.
of the extrapolation procedure. Table II gives the average of the two. The agreement with the data of Iff~ and Williams for cesium chloride is, as expected, excellent. Partial molar volumes for the sulfate ion were calculated by subtracting Ycation from Vsalt at equivalent ionic strengths. This was based on the assumption that, for the weakly solvated cesium and rubidium ions, the concentration-dependent increase in the partial molar volume results from a simple decrease in electrostriction by the ionic-strength dependent dampening of electric potential. Although this method gives only an indirect estimate of the partial molar volume of the sulfate ion, the relatively fixed hydration shell and complex geometry of the sulfate ion preclude the use of the more direct extrapolation method. Because of a significant difference between the t w o derived values of the sulfate ion's partial molar volume at each concentration, both are listed in Table II. Similar discrepancies in the partial molar
640 T A B L E II I O N I C P A R T I A L M O L A R V O L U M E S AS A F U N C T I O N OF M O L A R I T Y A T 2 5 ° C Partial m o l a r v o l u m e ( c m a / m o l ) c
1/2
0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.50
Rb +
Cs ÷
CI-
Br-
I-
9.67 10.13 10.60 11.07 11.54 12.02 12.49 12.96 13.43 14.30
16.94 17.35 17.77 18.19 18.62 19.06 19.52 19.98 20.38 21.08
22.23 22.59 23.00 23.31 23.67 24.02 24.36 24.71 24.97 25.34
29.11 29.41 29.70 30.00 30.28 30.57 30.61 31.00 31.11 --
40.62 40.85 41.03 41.20 41.37 41.49 41.54 ----
so~ as so~ as Rb 2 SO 4
Cs 2 SO 4
22.78 26.64 30.54 34.20 37.44 39.76
22.98 25.62 28.36 31.10 33.76 36.14
volumes of the sulfate ions were also found by Zana and Yeager [ 7] using ultrasonic vibration potentials. Such differences may reflect real phenomena such as ion-pairing with a divalent anion. Overall, the values of ~ion obtained by extrapolation of the data of Table II to infinite dilution are in excellent agreement with conventional partial molar volumes [ 5] (~H ÷ = 0.0 cm 3/mol) and the best estimates of the actual partial molar volume of the hydrogen ion, as discussed by Millero [5, 9] and Mukerjee [8]. The partial molar volumes given here can be useful for the b u o y a n t density analysis of macromolecules. For example, by correcting for ion-binding, Ifft and Vinograd [10] were able to show that the equilibrium banding density of bovine mercaptalbumin was a monotonic function of the activity of water, although their use of -~ion introduced a systematic quantitative error. Isopycnic centrifugation has also been extensively used for calculating protein to DNA ratios of formaldehyde-fixed nucleoproteins [11, 12], but without consideration for changes in preferential hydration and ion-binding when protein, especially histone, binds to DNA. This has been shown to lead to errors of as much as 50% in estimating the histone content of nucleohistones [ 1 3 ] . Supported by United States Public Health Service grant CA-12686 to Dr. Charles Breedis, whose generous support is greatly appreciated.
References 1 2 3 4 5 6 7 8 9 10 11 12 13
I f f t , J.B. a n d Williams, A. ( 1 9 6 7 ) B i o c h i m . Biophys. A c t a 136, 151 Lewis, G.N. a n d R a n d a l l , K.S. ( 1 9 6 1 ) in T h e r m o d y n a m i c s (Pitzer, K.S. a n d B r e w e r , L., eds.), 3 r d e d n . , p. 2 0 7 , M c G r a w - H i l l , N e w Y o r k I n t e r n a t i o n a l Critical T a b l e s ( 1 9 2 6 ) Vol 3, p p . 9 3 - - 9 5 , M c G r a w - H i l l , N e w Y o r k L u d l u m , D.B. a n d W a r n e r , R.C. ( 1 9 6 5 ) J. Biol. C h e m . 2 4 0 , 2 9 6 1 M i n e r o , F.J. ( 1 9 7 1 ) C h e m . Rev. 71, 147 Pauling, L. ( 1 9 6 0 ) T h e N a t u r e o f t h e C h e m i c a l B o n d , 3 r d e d n . , p p . 514---523, Cornell U n i v e r s i t y Press, I t h a c a , N Y Z a n a , R. a n d Y e a g e r , E. ( 1 9 6 7 ) J. Phys. C h e m . 71, 521 M u k e r j e e , P. ( 1 9 6 6 ) J. Phys. C h e m . 70, 2 7 0 8 Millero, F.J. ( 1 9 7 1 ) J. Phys. C h e m . 75, 2 8 0 I f f t , J.B. a n d V i n o g r a d , J. ( 1 9 6 6 ) J. Phys. C h e m . 70, 2 8 1 4 Brutlag, D., S c h l e h u b e r , C. a n d B o n n e r , J. ( 1 9 6 9 ) B i o c h e m i s t r y 8, 3 2 1 4 Ilyin, Y.V. a n d G e o r g i e v , G.P. ( 1 9 6 9 ) J. Mol. Biol. 41, 299 Kelley, R.L (1978) Doctoral dissertation, University of Pennsylvania
© Elsevier/North-HollandBiomedicalPress
BBA Report BBA 21514 IONIC PARTIAL MOLAR VOLUMES OF DENSITY GRADIENT SALTS AT FINITE CONCENTRATIONS
RICHARD I. KELLEY Departments of Pathology and Pediatrics, University of Pennsylvania School of Medicine and Children's Hospital of Philadelphia, Philadelphia, PA 19104 (U.S.A.)
(Received April 17th, 1979) Key words: Partial molar volume; Density gradient; Isopycnic centrifugation
Summary A general method is presented for estimating concentration-dependent partial molar volumes for individual ions of heavy density gradient salts used in the isopycnic ultracentrifugation of charged macromolecules.
For many applications of density gradient sedimentation equilibrium to the study of macromolecules and their interactions, ion-binding has an important effect on experimentally determined partial molar volumes. Because density gradients of heavy salts are generated at high ionic strengths, the frequently employed, published values of ~ion, the partial molar volume at infinite dilution, are substantially smaller than the effective partial molar volumes under experimental conditions. Recognizing this problem, Ifft and Williams [ 1] proposed apportioning V for cesium chloride to the cesium and Chloride ions according to the cubes of their radii in crystalline cesium chloride. This approach assumes that solvation differences are small for two monovalent ions of similar size, 1.69 and 1.81 .~ for Cs* and CI-, respectively. Unfortunately, this method is useful only for CsC1, most other salts having ions of dissimilar sizes. This communication describes an alternate method for obtaining Vion at finite salt concentrations that is applicable to most of the commonly used density gradient salts. Table I lists the concentration-dependent partial molar volumes for eight salts as calculated by the method of intercepts [2] using density vs. weight fraction data from the International Critical Tables [3] and, for cesium sulfate, from Ludlum and Warner [4]. The values of Vsalt were replotted as the mostly linear function of the square root of the molarity and a smooth curve visually fitted to the points, as shown in Fig. 1. When extrapolated to infinite
638 TABLE
I
INTERPOLATED PARTIAL OF MOLARITY AT 25°C
MOLAR
VOLUMES
FOR EIGHT HEAVY SALTS AS A FUNCTION
Partial molar volume (cm 3/tool) c 1/2
RbCl
RbBr
RbI
CsC1
CsBr
CsI
Rb 2 SO 4
Cs 2 S O 4
0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.50
31.90 32.69 33.50 34.31 35.11 35.91 36.72 37.58 38.33 39.57
38.78 39.49 40.22 40.97 41.71 42.45 43.19 43.90 44.50
50.29 50.97 51.60 52.24 52.87 53.50 54.11 54.63 ---
39.17 39.96 40.77 41.57 42.38 43.20 44.00 44.78 45.42 46.49
46.05 46.80 47.55 48.29 49.01 49.76 50.43 51.03 51.52 --
57.56 58.20 58.82 59.42 60.02 60.55 60.98 ----
42.12 47.60 53.14 58.44 63.30 67.26
56.66 60.92 65.18 69.44 73.60 77.42
o
i
C1/2
F i g . 1. P a r t i a l m o l a r v o l u m e s f o r c e s i u m c h l o r i d e as a f u n c t i o n o f t h e s q u a r e r o o t o f m o l a r i t y .
dilution, V7° , the curves yield partial molar volumes that are within 0.5% of those given by Millero [ 5]. Assuming that for large, monovalent ions the electrostrictive and intrinsic volume components of --Vion are smooth, continuous_ functions of the ionic crystal radii, we can as a first approximation of Vion for a particular ion apportion the partial molar volumes of several of its salts to the ions according to the cubes of their crystalline radii, as did Ifft and Williams. If we then extrapolate a plot of, for example, Vcs. against the radii of its counterions, e.g. halides, to the point where the cesium and halide ions are the same radius, there, theoretically, the equal-sized ions_of the hypothetical salt have identical partial molar volumes and therefore Vcs÷ = l~YCsHalide, In effect, the extrapolation procedure brings into equivalence both the geometric and electrostrictive components of the partial molar volumes of the cation and anion. Fig. 2 illustrates this m e t h o d applied to the cesium ion for concentrations up to 6.25~'motar using Pauling's values [6] for the ionic crystal radii. The partial molar volumes for the rubidium ion are similarly obtained. Subtracting Yca_tion f~om Ysal_t at equivalent concentrations for the cesium and rubidium ions gave two values of V for each halide that were within 0.2 c m 3/mol of each Other over the entire concentration range, an indication of the validity
639
2~
~ -
I
125 ~
I
-5 E
to~ E I c~
75
I
)
o
I 03
0.4
05
Crystal Volume Fraction of Ca+
Fig. 2. G r a p h i c d e t e r m i n a t i o n o f V f o r t h e c e s i u m i o n at c o n c e n t r a t i o n s u p t o 2.5 M ½. T h e p a r t i a l m o l a r v o l u m e s f o r t h e c e s i u m halides listed in T a b l e I w e r e m u l t i p l i e d b y t h e a p p o r t i o n m e n t f a c t o r 3+ 3+ 3 . . . . . . r c . ~ / ( r c s + r ~ d e ) , w h e r e r Is t h e 1omc c r y s t a l r a d m s , t o give v o l u m e - b a s e d estLmates o f VCs+ f o r e a c h salt. T h e n , at e a c h c o n c e n t r a t i o n , t h e e s t i m a t e s o f VCs+ w e r e p l o t t e d against t h e v a l u e of t h e a p p o r t i o n m e n t f a c t o r a n d e x t r a p o l a t e d g r a p h i c a l l y ~ 0.5 as d e s c r i b e d in t h e t e x t . P o i n t s for t h e i o d i d e a t 2.0 a n d 2.5 M ½ a n d f o r t h e b r o m i d e a t 2.5 M VJare e x t r a p o l a t e d f r o m t h e d a t a in T a b l e I.
of the extrapolation procedure. Table II gives the average of the two. The agreement with the data of Iff~ and Williams for cesium chloride is, as expected, excellent. Partial molar volumes for the sulfate ion were calculated by subtracting Ycation from Vsalt at equivalent ionic strengths. This was based on the assumption that, for the weakly solvated cesium and rubidium ions, the concentration-dependent increase in the partial molar volume results from a simple decrease in electrostriction by the ionic-strength dependent dampening of electric potential. Although this method gives only an indirect estimate of the partial molar volume of the sulfate ion, the relatively fixed hydration shell and complex geometry of the sulfate ion preclude the use of the more direct extrapolation method. Because of a significant difference between the t w o derived values of the sulfate ion's partial molar volume at each concentration, both are listed in Table II. Similar discrepancies in the partial molar
640 T A B L E II I O N I C P A R T I A L M O L A R V O L U M E S AS A F U N C T I O N OF M O L A R I T Y A T 2 5 ° C Partial m o l a r v o l u m e ( c m a / m o l ) c
1/2
0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.50
Rb +
Cs ÷
CI-
Br-
I-
9.67 10.13 10.60 11.07 11.54 12.02 12.49 12.96 13.43 14.30
16.94 17.35 17.77 18.19 18.62 19.06 19.52 19.98 20.38 21.08
22.23 22.59 23.00 23.31 23.67 24.02 24.36 24.71 24.97 25.34
29.11 29.41 29.70 30.00 30.28 30.57 30.61 31.00 31.11 --
40.62 40.85 41.03 41.20 41.37 41.49 41.54 ----
so~ as so~ as Rb 2 SO 4
Cs 2 SO 4
22.78 26.64 30.54 34.20 37.44 39.76
22.98 25.62 28.36 31.10 33.76 36.14
volumes of the sulfate ions were also found by Zana and Yeager [ 7] using ultrasonic vibration potentials. Such differences may reflect real phenomena such as ion-pairing with a divalent anion. Overall, the values of ~ion obtained by extrapolation of the data of Table II to infinite dilution are in excellent agreement with conventional partial molar volumes [ 5] (~H ÷ = 0.0 cm 3/mol) and the best estimates of the actual partial molar volume of the hydrogen ion, as discussed by Millero [5, 9] and Mukerjee [8]. The partial molar volumes given here can be useful for the b u o y a n t density analysis of macromolecules. For example, by correcting for ion-binding, Ifft and Vinograd [10] were able to show that the equilibrium banding density of bovine mercaptalbumin was a monotonic function of the activity of water, although their use of -~ion introduced a systematic quantitative error. Isopycnic centrifugation has also been extensively used for calculating protein to DNA ratios of formaldehyde-fixed nucleoproteins [11, 12], but without consideration for changes in preferential hydration and ion-binding when protein, especially histone, binds to DNA. This has been shown to lead to errors of as much as 50% in estimating the histone content of nucleohistones [ 1 3 ] . Supported by United States Public Health Service grant CA-12686 to Dr. Charles Breedis, whose generous support is greatly appreciated.
References 1 2 3 4 5 6 7 8 9 10 11 12 13
I f f t , J.B. a n d Williams, A. ( 1 9 6 7 ) B i o c h i m . Biophys. A c t a 136, 151 Lewis, G.N. a n d R a n d a l l , K.S. ( 1 9 6 1 ) in T h e r m o d y n a m i c s (Pitzer, K.S. a n d B r e w e r , L., eds.), 3 r d e d n . , p. 2 0 7 , M c G r a w - H i l l , N e w Y o r k I n t e r n a t i o n a l Critical T a b l e s ( 1 9 2 6 ) Vol 3, p p . 9 3 - - 9 5 , M c G r a w - H i l l , N e w Y o r k L u d l u m , D.B. a n d W a r n e r , R.C. ( 1 9 6 5 ) J. Biol. C h e m . 2 4 0 , 2 9 6 1 M i n e r o , F.J. ( 1 9 7 1 ) C h e m . Rev. 71, 147 Pauling, L. ( 1 9 6 0 ) T h e N a t u r e o f t h e C h e m i c a l B o n d , 3 r d e d n . , p p . 514---523, Cornell U n i v e r s i t y Press, I t h a c a , N Y Z a n a , R. a n d Y e a g e r , E. ( 1 9 6 7 ) J. Phys. C h e m . 71, 521 M u k e r j e e , P. ( 1 9 6 6 ) J. Phys. C h e m . 70, 2 7 0 8 Millero, F.J. ( 1 9 7 1 ) J. Phys. C h e m . 75, 2 8 0 I f f t , J.B. a n d V i n o g r a d , J. ( 1 9 6 6 ) J. Phys. C h e m . 70, 2 8 1 4 Brutlag, D., S c h l e h u b e r , C. a n d B o n n e r , J. ( 1 9 6 9 ) B i o c h e m i s t r y 8, 3 2 1 4 Ilyin, Y.V. a n d G e o r g i e v , G.P. ( 1 9 6 9 ) J. Mol. Biol. 41, 299 Kelley, R.L (1978) Doctoral dissertation, University of Pennsylvania