Steady-state electrophoresis: A physical

Proc. Nati. Acad. Sci. USAVol. 86, pp. 4479-4483, June 1989Biophysics

Steady-state electrophoresis: A technique for measuring physicalproperties of macro-ions

(charge number/polydispersity/macro-ion-solvent ion interactions/diffusion)

JAMIE E. GODFREYBiology Department, The Johns Hopkins University, Baltimore, MD 21218

Communicated by William F. Harrington, March 3, 1989 (received for review January 17, 1989)

ABSTRACT The basic theory of a newly discovered phys-ical technique, steady-state electrophoresis, is described fol-lowed by analyses of several representative macro-ion systemswith the technique. This method measures apparent momentsof molar diminished charge (defined below) of solvated macro-ions from an analysis of a concentration gradient of themacro-ions stabilized against a semipermeable membrane bythe opposing forces of diffusion and an external electric field.The experimental results confirm that the theory adequatelydescribes the behavior of the macro-ion systems at electropho-retic steady state and suggest applications for the technique inaddition to measuring macro-ion-small ion interactions.

This paper introduces an analytical technique, steady-stateelectrophoresis, for measuring charge and other properties ofmacro-ions dissolved in aqueous solvent systems. (The the-ory presented here explains the operational basis of a devicefor making electrophoretic steady-state measurements de-scribed in ref. 1.) In essence, the method balances the forcesof diffusion and an imposed electrical field to establish astable concentration gradient of macro-ions (e.g., proteins)against a semipermeable membrane. I have designated thiscondition electrophoretic steady state.An analysis of the macro-ion gradient yields the apparent

number, weight, and Z-average moments (2) of molar dimin-ished charge throughout the gradient, which are applicable tothe composition of macro-ions at the point in the gradientwhere they are measured. The diminished charge may bedefined, somewhat loosely, as the effective net charge carriedby an ion in the presence of other ions or the net charge of theion-solvent-ion complex, which moves in response to anelectrostatic potential gradient. Until now, this quantitycould only be estimated by combining the results frommobility experiments and frictional coefficient determina-tions on macro-ions of interest (3). Because the techniquedescribed here determines this measurement of macro-ion-small ion interaction easily and directly, it should be ofparticular interest to polyelectrolyte chemists working in theareas of naturally occurring and synthetic polyelectrolytes.The theoretical bases of steady-state electrophoresis and

equilibrium ultracentrifugation share many parallels (2). Ac-cordingly, in addition to charge-related phenomena, thistechnique holds promise for addressing several problems inmacro-ion chemistry currently studied by the older method.

Methods and Materials

Electrophoretic steady-state experiments were carried out ina device of the author's design shown in schematic cross-section in Fig. 1. During experiments, the device (fabricatedprincipally from polymethylmethacrylate cast sheet) was

filled with an aqueous solvent, typically a pH-buffered saltsolution, introduced through two solvent ports (a and b). Aconstant-current power source [an LKB (Bromma) 2197power supply was used] connected to platinum electrodes (cand d) maintained a steady current within the device; anexternal ammeter (a 22-191 Micronta digital multimeter fromRadio Shack was used) wired in series with the device andpower supply monitored amperage levels. The current pathpassed through two double-chambered cells, (e and f) (fab-ricated from optical quartz) and a semipermeable membrane(g) (Spectrapor 1 dialysis membrane was used) sealed be-tween the two cells; the membrane was permeable to thesolvent ions. The chambers of the cells (width, 3 mm; height,9 mm; optical path length, 20 mm) were open at both top andbottom to allow the current to pass through the macro-ion cellchamber (h), the membrane, and the cell chamber below themembrane. The solvent cell chamber (i) was also filled withthe salt solution but was not an element in the electricalcircuit. The physical design of the device ensures that elec-trical fields maintained in the macro-ion cell chamber arelinear and perpendicular to the surface of the semipermeablemembrane.At the beginning of an experiment, the device and the

solvent cell chamber were filled with solvent. A macro-ionsample (typically 150-200 tkl of a 0.5-2 mg/ml solution)dialyzed to equilibrium against the solvent was then intro-duced into the macro-ion cell chamber by means of a syringefitted with a long needle. The needle was passed throughsample port (j) and the sample was layered on top of themembrane; because of its higher density, the macro-ionsample displaced the solvent and stabilized at the membranesurface. A current of the appropriate strength and polarity(see below) was applied to the electrodes and the system wasallowed to attain electrophoretic steady state in a constanttemperature environment (typically in 12-24 hr). In all ex-periments, macro-ion concentration gradients at electropho-retic steady state approached infinite dilution within 4 mm ofthe semipermeable membrane. With the macro-ion densitygradient directed downward and thereby stabilized by grav-ity, no detectable convection of the sample occurred unlessexcessively high wattage (out of useful experimental range)was applied. All experiments were conducted at room tem-perature (20'C-210C).The macro-ion and solvent chambers were monitored by a

Rayleigh interference optical system constructed from theoptical components of a Beckman model E analytical ultra-centrifuge (4). Rayleigh interference patterns of macro-iondistributions at electrophoretic steady state were recorded onglass photographic plates (Kodak spectroscopic type 2-G).To complete the experiment, a blank run was conducted withonly solvent in the macro-ion chamber under the sameconditions of temperature and electric field as the macro-ionrun. The Rayleigh interference patterns of the macro-ion and

Abbreviations: PSS, polystyrene sulfonate; GIDH, glutamate dehy-drogenase [NAD(P)+]; BSA, bovine serum albumin.

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FIG. 1. Schematic cross-section of the steady-state electropho-resis device, featuring solvent ports (a and b), electrodes (c and d),upper double-chambered optical quartz cell (e) containing macro-ioncell chamber (h) and solvent cell chamber (i), semipermeable mem-brane (g) sealed between upper cell (e) and lower double-chamberedcell (f), and sample port (j). Stippling above semipermeable mem-brane (g) represents a macro-ion sample at electrophoretic steadystate. (Inset) Perspective of the double-chambered cells (e and f).The two dashed arrows depict the paths of monitoring beams of aRayleigh interference optical system passing through the macro-ionand solvent cell chambers (h and i).

blank runs were digitally transcribed and analyzed by meth-ods reported elsewhere (5, 6) for the analysis of Rayleighpatterns from equilibrium sedimentation experiments. Thisprocess was aided by the use of the computer program ofRoark and Yphantis (5) for the analysis of equilibrium sedi-mentation data; the program had been appropriately modifiedto accommodate electrophoretic steady-state data (seebelow).

Solvent conductivities were estimated from values in theliterature (7).Meniscus depletion equilibrium sedimentation experiments

were conducted in a Beckman model E analytical ultracentri-fuge following procedures described previously (6, 8, 9).

Lyophilized bovine serum albumin monomer (BSA) waspurchased from Sigma (catalogue no. A-1900); glutamatedehydrogenase [NAD(P)+] [GIDH; L-glutamate:NAD(P)+oxidoreductase (deaminating), EC 1.4.1.3] was purchasedfrom Boehringer Mannheim. A narrow distribution fractionof the sodium salt of polystyrene sulfonate (PSS), weightaverage to number average molecular weight ratio = 1.1, wasfrom Polymer Laboratories (Church Stretton, U.K.).

Electrophoretic Steady-State Theory

With the device prepared for an electrophoretic steady-stateexperiment as outlined above, the applied electrical current(with the appropriate polarity) drives the macro-ions of thesample toward the semipermeable membrane. Because themacro-ions are stopped by the membrane, the concentrationof macro-ions at the membrane surface increases and theconcentration gradient thus formed produces a diffusion-driven back flow of macro-ions. In time, the macro-ionconcentration gradient stabilizes; at every point in the gra-dient, macro-ion flow due to the electrical field is countered,exactly, by macro-ion flow due to diffusion.Although the macro-ion concentration gradient is stable,

the smaller ions of the system continue to migrate. The very

modest electrical field required to establish and maintain themacro-ion gradient (typically <200 mV cm-l) is too weak togenerate experimentally significant concentration gradientsof solvent ions against the semipermeable membrane. More-over, the applied wattage is insufficient to generate poten-tially disruptive temperature gradients adjacent to the morehighly resistant semipermeable membrane (see Materials andMethods). Furthermore, the chemical decomposition thattakes place at the electrodes is insufficient to alter the solventcomposition within the macro-ion chamber during the timerequired to attain electrophoretic steady state. Thus, thesystem minimally encompassing the stabilized macro-ionconcentration gradient is essentially isothermal and of con-stant composition over time. Nevertheless, the system is notin thermodynamic equilibrium; the continuing migration ofthe solvent ions through the system generates an entropicflow, however negligible, to the environment. Rather, thesystem is in steady state and is appropriately described byirreversible thermodynamic theory (10, 11).Thus, for a monodisperse macro-ion system, the flow ofthe

macro-ion is

Jm = LmmFm +Lmhjj,J

[1]

where L is the phenomenological coefficient, F is the drivingforce, j indexes the diffusible (solvent) ions, and m refers tothe macro-ion. Water flow is assumed to be negligible (seebelow).The Nernst-Planck equation (11) describes the flow of a

charged species in an electrochemical gradient in the absenceof other ions and may be introduced into Eq. 1 to define theconjugate term

A(m (ax) NAG (al) +>LLmFj,[2]

where Cm is the molar concentration of the macro-ion; (m isthe frictional coefficient of the macro-ion at macro-ion con-centration Cm; F is Faraday's constant; NA is Avogadro'snumber; Zm is the net formal charge number carried by themacro-ion; x is the axis of ionic flows measured in centime-ters from the surface of the semipermeable membrane in thedirection of the electric field; and ao/ax and att/ax are theelectrostatic and chemical potential gradients, respectively.The presence of solvent ions even at modest concentra-

tions can substantially reduce the mobility of the macro-ion.Several mechanisms have been identified, notably the elec-trophoretic and relaxation effects, by which the flows ofdifferent ionic species interact to cause significant decreasesin the local electrical fields experienced by the individual ions(11). These effects on the macro-ion flow are expressed bythe cross terms of Eq. 2.When both electrophoretic and diffusion-driven macro-ion

transport cease (i.e., when electrophoretic steady state isachieved), Jm goes to zero, allowing Eq. 2 to be rearrangedto give

0 = FZm( ++ NA-mLmjFjkax ax Cm i

[3]

Because no pressure gradients are present and the system isisothermal, the chemical potential gradient reduces to thefamiliar expression for the diffusional force

alL - 11(8Cm(1 + Cma(lnfm)/aCm),ax cm \axl

[4]

where fm is the activity coefficient of the macro-ion (molarscale), R is the gas constant, and T is the absolute temper-

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Proc. Natl. Acad. Sci. USA 86 (1989) 4481

ature. Substituting Eq. 4 into Eq. 3, replacing the electricalfield with the equivalent quantity, -E/300 (the electricalfield, E, is measured in conventional V/cm) (11), and furtherrearranging yields

300RT dCm) =

ECm dx

may be written. For example, the apparent number andZ-average molar diminished charges can be measured by:

0Cm/a dCm -cma d(ln cm)/dxFzmbn

(1 + B'FZm,nCm + . . .)= mn app [9]

+ 300NA(mL. -)FzmECm j

[5]

(Because Cm is no longer time dependent, total differentialsare appropriate.) Eq. 5 measures the apparent molar formalcharge of the macro-ion plus a term expressing the effects ofsolvent ion-macro-ion interactions (this term will be nega-tive).A new quantity-the molar diminished charge of the mac-

ro-ion-is next introduced:

FtnF M(1 + 300NA(m ZLmjFi)-[6Fzm =Fzm( FzECm j~j~ [6]

(z' is then the diminished charge number of the macro-ion).Substituting Fz' into Eq. 5 and converting to units of massconcentration gives

0(d(ln cm))= Fzm Fz'

dx ~(1 + 2'z m+...pi

where cm is in mg/ml, dcm/cmdx is replaced by the equivalentexpression, d(ln Cm)/dX, 0 = 300RT/E, and the nonidealityterm is expressed as the familiar virial expansion in macro-ion concentration (12). B' is the second virial coefficient(comparable, but not equal, to the colligative second virialcoefficient).When Fz' is substituted into Eq. 2,

Jm = N [FzA(d ) +x] [8]

it can be seen that the molar diminished charge may beviewed as the net charge of the solvent ion-macro-ioncomplex which moves in response to the electrophoretic anddiffusional forces. Because of the significant retarding effectexerted by the solvent ions on the mobility of the macro-ion(see above), Fz' can be expected to be substantially lower inabsolute value than Fzm in most solvent systems used insteady-state electrophoresis analyses. More specifically, Fzmwill decrease linearly, to within a rough approximation, withan increase in the square root of the solvent ionic strength inaccord with Kohlrausch's empirical law and later theoreticaltreatments by Onsager and others concerning the mobilitiesof ions in the presence of other ions (11).

Eq. 7 is formally identical to the primary equation ofequilibrium ultracentrifugation theory (2), which measures

effective reduced molecular weights; accordingly, both equa-tions measure the apparent weight average moment. How-ever, because the centrifugal field is radially dependent, thelogarithm of the concentration is differentiated with respectto the square of the radial distance in the cell in analyses ofequilibrium sedimentation data; in the electrophoreticsteady-state equation, the logarithm of the concentration isdifferentiated with respect to the first power of x reflectingthe linearity of the electric field.

Following the mathematical treatment developed in equi-librium ultracentrifugation theory (2), other useful equations

( dcCmdxj) (1 + 2B'FzmnwCm + *)2

The integral in Eq. 9 is evaluated between limits of totalmacro-ion concentration at any point cm in the gradient anda point Cma on the x axis where the concentration of macro-ion is essentially zero. Thus, the number average momentmay be obtained only from those gradients that possess anexperimentally accessible region where the macro-ion con-centration approaches infinite dilution (8).

In addition, Eq. 7 may be rearranged and integrated withinappropriate limits to yield an expression relating the macro-ion concentration at any point in the macro-ion concentrationgradient to some reference concentration in the gradient. Fora monodisperse macro-ion system, the integrated form ofEq.7 is

Cm = cm,sexp -[01-Fzm(xs- x) - 2B'Fzm(cmss - cm)], [11]

where cm is the macro-ion concentration at point x, and cm,sis the macro-ion concentration at the membrane surface xs.For polydisperse systems, a single value ofB' is permitted

in Eqs. 7, 9, and 10 if it is assumed that the contribution tothe nonideality by any macro-ion species is proportional to itsmolar diminished charge (i.e., In yj = (Fz!/Fzj)ln Yi). Forsome polydisperse systems, the assumption is reasonable; forothers it may not be. This assumption is similar to the oneoften made in equilibrium ultracentrifugation-namely, thatthe contribution to the nonideality by any macromolecule ina polydisperse system is proportional to its molecular weight(5).

All quantities on the left side of Eqs. 7, 9, and 10 are eitherknown constants or can be independently measured. T is theenvironmental temperature of the device. The macro-ionconcentration gradient can be accurately measured by Ray-leigh interferometry (see Materials and Methods) or anothersuitable optical system. Ohm's law allows the electric field tobe expressed as the ratio of the total current density to theconductivity (3)

[12]/=.is Iss

i Y-Kj A>L-Kj

where the subscript ss refers to the quantity measured atelectrophoretic steady state, I is the current, >Kj is thesolvent conductivity, and A is the cross-sectional area of themacro-ion chamber (in cm2).The perturbations in solvent composition within the mac-

ro-ion gradient required to maintain electroneutrality and theretarding effect of the macro-ions on the flow of the solventions are considered to be experimentally insignificant whenmacro-ion/total diffusible ion charge concentration ratios are<0.02. Values of this ratio in electrophoretic steady-stateanalyses are typically well below this limit; thus, the elec-trical field within the macro-ion gradient can be accuratelyestimated from the conductivity of the solvent and theapplied current (Eq. 12).The presence of macro-ion at the upper surface of the

membrane before and after electrophoretic steady state isachieved generates an osmotic pressure. However, it has

Fzm (1(1 + Cma(Infm)IaCm)

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Proc. Natl. Acad. Sci. USA 86 (1989)

been found that the bulk solvent flow this condition promotesis much too slow to adversely affect the stability of themacro-ion gradients; thus water flow can be ignored in theflow equations presented earlier.

Experimental Results

The experimental results with BSA summarized in Fig. 2illustrate the behavior of a monodisperse ideal behavingmacro-ion brought to electrophoretic steady state. The sam-ple was exposed to two electric field strengths differing by=30%o. As predicted by Eq. 7, the plot of log macro-ionconcentration versus x at each value of E (Fig. 2A Inset) islinear, indicative of a constant value for the apparent weightaverage molar diminished charge throughout the concentra-tion gradient of the protein. Moreover, as expected, theapparent number and weight average molar diminishedcharge moments measured at both field strengths essentiallysuperimpose at a single value for the apparent molar dimin-ished charge at all protein concentrations (Fig. 2B). Theaverage value, Fz' = -1.15 x 1015 electrostatic units(ESU)-mol-1 (z' = -4.0), is considerably lower than the

molar formal charge reported for BSA, Fz = -3.1 x 1015ESU-mol-1 (z = -10.7) (13) reflecting strong macro-ion-solvent ion interactions.

Fig. 3 shows results obtained with a narrow fraction ofPSSanalyzed for degree of polydispersity by both steady-stateelectrophoresis and equilibrium ultracentrifugation (6, 14).The plots in Fig. 3 A and B extrapolated to infinite dilution-

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1, I.'J FIG. 3. Polydispersity analyses of a narrow distribution of PSSx, mm by steady-state electrophoresis (A) and equilibrium sedimentation

B (B) (6, 15). The reciprocal apparent number or weight averageAA2AAy AA8A A AA6 AA * *, moment of either molar diminished charge or molecular weight is0 o plotted against macro-ion concentration. Each data point on the four60 linear regression curves represents the analysis of a single sample of

PSS at a different cell-loading concentration; the plotted point is thereciprocal of the apparent number or weight average moment mea-sured at the midconcentration within the macro-ion distribution at

I | | sedimentation equilibrium or electrophoretic steady state. The mid-0 1.0 2.0 concentrations were one-half of the macro-ion concentrations at the

[BSA], mg/ml high end of the gradients estimated in each experiment by modestlinear extrapolation of the data to the known position of the gradient

2. BSA monomer brought to electrophoretic steady state at extremity. The ratio of the apparent weight average/number averageifferent electrical fields. The solvent was 0.1 M KCI/50 mM moment measured at infinite PSS dilution is given for each set ofpH 7.2. (A) BSA concentration gradients plotted versus x regression curves. (A) Apparent number (0) and apparent weight

ired from the semipermeable membrane (M); o, E = 114 average (o) Fz' of PSS dissolved in 30 mM KCI/3 mM potassiumn 1; 9, E = 153 mV cm-1. (Inset) The data in A with the BSA phosphate, pH 7.0; E = 18.1 mV-cm-1. (B) Apparent number (e) andntration plotted on a logarithmic scale. The straight lines are apparent weight average (o) molecular weights of PSS dissolved inits to the data points at the higher protein concentrations. (B) 0.2 M KCI/20mM potassium phosphate, pH 7.0; the rotor speed was-ent moments ofFz' calculated from the datainA plotted versus 15,000 rpm and the temperature was 190C. (C) Apparent number (e),concentration. Apparent number (o) and apparent weight apparent weight (o), and apparent Z-average (A) Fz' of the PSSge (A) Fz' (114 mV cm-l); apparent number (A) and apparent sample identified by an asterisk (*) in A plotted versus PSS concen-t average (A) Fz' (153 mV cm-1). tration.

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4482 Biophysics: Godfrey

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Proc. Natl. Acad. Sci. USA 86 (1989) 4483

required because of the pronounced nonideal behavior of themacro-ion (Fig. 3C)-yield reciprocal number and weightaverage moments of molar diminished charge and molecularweight, respectively, which are descriptive of the PSS sam-ple. It can be seen that the two techniques yield similar valuesfor the ratio of the two moments (ratios are shown in Fig. 3A and B).The results obtained with a reversibly self-associating

protein system brought to electrophoretic steady state areillustrated in Fig. 4. The number, weight, and Z-averageapparent molar diminished charges of two samples ofG1DH,which differed in total mass of protein, are plotted againstprotein concentration. All three moments are seen to increasewith macro-ion concentration, behavior consistent with theresults of Reisler et al. (15) based on equilibrium ultracen-trifugation and light scattering studies showing that theenzyme assembles isodesmically under the same solventconditions used in the present study. The overlap of the twosets of data points is characteristic of the behavior of areversibly assembling system (as opposed to a polydisperse,noninteracting mixture, such as the PSS sample character-ized above) (8).

Discussion

The experimental results strongly suggest that the behavior ofmacro-ions at electrophoretic steady state are quantitativelydescribed by the theory developed earlier. Moreover, be-cause the theoretical bases of steady-state electrophoresisand equilibrium ultracentrifugation are formally identical, itseems highly likely that the newer method will be used tocharacterize macro-ion systems in ways currently addressedby the older technique. The utility of this method in one suchapplicstrong

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Apart from applications in the study of macro-ion systems,which steady-state electrophoresis may share with analyticalultracentrifugation, it is clear on the basis of the preliminaryresults presented that the technique described here providesa powerful method for characterizing macro-ion charge prop-erties. For example, the molar diminished charge measuredby the technique is a direct experimental measure of theinteractions between macro-ions and small ions which De-bye-Huckel electrostatic potential theory attempts to model(3). One expression due to Henry (3) based on electrostaticpotential theory describes the flow of a spherical macro-ionicspecies

Jm = 3(mE [FZmX(KRm)1,300NA(m 1 + K¢Rm

[13]

where Rm is the radius of the macro-ionic species, X(KRm) isHenry's function (dimensionless and having a value between1.0 and 1.5), and K is the Debye-Huckel reciprocal ion-atmosphere radius. From Eq. 8, it can be seen that theapparent molar diminished charge is equal to the bracketedexpression in Eq. 13.

Note. During the preparation of this paper, I learned that DavidYphantis and Thomas Laue (personal communication) have con-structed a device that operates by the same physical principles as thedevice described here; in their device, however, the macro-iongradient is directed horizontally and is formed within a gel matrix toretard convective disturbances.

I wish to thank Dr. E. N. Moudrianakis for his support andgenerosity throughout this study. I also wish to thank Dr. MichaelRodgers for his competent direction and timely assistance in thecomputer analyses. This paper is publication no. 1432 from the JohnsHopkins University Biology Department.

cation, the characterization of polydispersity, iS 1. Godfrey, J. E., inventor; Apparatuses and Methods for Ana-;ly supported by the results summarized in Fig. 3. lyzing Macro-Ions at Electrophoretic Steady State, U.S. patent

4,801,366; date of issue, January 31, 1989.2. Fujita, H. (1975) Foundations of Ultracentrifugal Analysis

0 (Wiley, New York).a 3. Van Holde, K. E. (1985) Physical Biochemistry (Prentice-Hall,

0 0 Englewood Cliffs, NJ), 2nd Ed., pp. 138-142.)-o 4. Beckman Instruments, Inc. (1966) Beckman Model E Analyti-

*0 o ° cal Ultracentrifuge Instruction Manual (Beckman Instruments,0 * 0 Palo Alto, CA), Section 4, pp. 1-35.

°* 0° 5. Roark, D. E. & Yphantis, D. A. (199) Ann. N.Y. Acad. Sci._* 0 164, 245-278.

a.000 £ 6. Godfrey, J. E. (1976) Biophys. Chem. 5, 285-299.0 * A A A 7. Washburn, E. W., Klemenc, A. & Parker, C. H. (1926) in

so*° 0 A&A A International Critical Tables, ed. Washburn, E. W. (McGraw-*_.0 A Hill, New York), Vol. 6, pp. 229-255.*A..a* 8. Yphantis, D. A. (1964) Biochemistry 3, 297-317.

S- 9. Godfrey, J. E., Eickbush, T. H. & Moudrianakis, E. N. (1980)Biochemistry 19, 1339-1346.

10. Katchalsky, A. & Curran, P. F. (1965) Nonequilibrium Ther-o 1.0 2.0 modynamics in Biophysics (Harvard Univ. Press, Cambridge,

[GIDH], mg/ml MA).11. Bockris, J. O'M. & Reddy, A. K. N. (1970) Modern Electro-

i. 4. The apparent number, weight and Z-average molar chemistry (Plenum, New York), Vol. 1, pp. 363-443.;hed charges of two samples of GIDH containing different 12. Eisenberg, H. (1976) Biological Macromolecules and Polyelec-,of protein plotted versus GIDH concentration. The solvent trolytes in Solution (Oxford Univ. Press, London), pp. 17-19.2 M sodium phosphate/0.5 mM EDTA, pH 7.0; E = 60.2 13. Tanford, C., Swanson, S. A. & Shore, W. S. (1955) J. Am.

' for both samples. Solid symbols, sample contained 0.132 Chem. Soc. 77, 6414-6421.GIDH; open symbols, sample contained 0.290 mg of GIDH. 14. Fujita, H. (1969) J. Phys. Chem. 73, 1759-1761.es, apparent number average Fz'; circles, apparent weight 15. Reisler, E., Pouyet, J. & Eisenberg, H. (1970) Biochemistry 9,Fz'; squares, apparent Z-average Fz'. 3095-3102.

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