Anal. Chem. IDS?, 64, 2991-2997
299 1
Computer Simulation and Experimental Validation of the Electrophoretic Behavior of Proteins. 2. Model Improvement and Application to Isotachophoresis Richard A. Mosher Center for Separation Science, University of Arizona, Tucson, Arizona 85721
Petr Gebauer,?Jitka Caslavska, and Wolfgang Thormann. Department of Clinical Pharmacology, University of Berne, Murtenatrasse 35, CH-3010 Berne, Switzerland
Our model for the computer slmulatlon of the electrophoretlc behavlor of proteins has been modlfled wlth regard to the contribution of the protein to Ionic strength. The DebyeHiickeCHenryapproach, which treats a proteln llke any other polyvalent Ion (Le. the contrlbutlon contalns the square of the valence), was replaced by the Linderstrerm-Lang approxlmatlon, whlch assumes that a z-valent Ion behaves as a monovalent Ion wlth z-fold concentratlon. This produces a conslderabie difference in predictedproteln behavior because of the conslderatlon of the Impact of ionk strength on protein moblilty. The predictedlsotachophoretlc behavlor of several protelns is shown to compare much better wlth experlmental data when the LlnderstrermLang approach Is employed. The Influence of the Input proteln data on both quailtatlve and quantltatlveshnulath data Isdlscwsed, and the first computer slmuiations of lsotachophoretlc proteln fractionation are presented, uslng an lsotachophoretlc scheme whlch Includes low molecular mass spacers. Good agreement between slmulatlon and capillary lsotachophoretic data Is shown.
INTRODUCTION Computer simulation of electrophoresis has demonstrated considerable value as a research tool. Many examples of qualitative and even quantitative agreement between predictions and experimental results have confirmed the utility of simulations for prediction of separability, separation dynamics, zone characteristics, and boundary structure, as well as for the reproduction and explanation of some experimentally observed phenomena.lS2 Most of the simulation work performed thus far was limited to low molecular mass compound^,^^ and only three computer models have been created for the treatment of In comparison to low molecular mass compounds,the treatment of proteins is more complex, with one aspect of this being the consideration of the impact of ionic strength on protein mobility. t Permanent address: Institute of AnalyticalChemistry, Czechoslovak Academy of Sciences, CS-61142 Brno, Czechoslovakia. (1) Thormann, W.; Mosher, R. A. Adu. Electrophoresis 1988,2, 45. (2) Mosher, R. A.; Saville, D. A.; Thormann, W. The Dynamics of Electrophoresis; VCH Publishers: Weinheim, 1992. (3) Bier, M.; Palusinski, 0. A.; Mosher, R. A.; Saville, D. A. Science
1983,219, 1281. (4) Schafer-Nielaen,C. In Gel Electrophoresis of Proteins; D u n , M. J., Ed.; Wright: Bristol, 1986; p 1. (5) Gai, B.; Vacfk, J.; Zelenskfi, I. J. Chromatogr. 1991, 545, 225. (6) Dose, E. V.; Guiochon, G. A. Anal. Chem. 1991,63,1063. (7) Shimao, K. Electrophoresis 1986, 7, 297.
(8)Mosher, R. A.; Dewey, D.; Thormann, W.; Saville, D. A.; Bier, M. Anal. Chem. 1989, 61, 362. (9) Roberts, G. 0.;Rhodes, P. H.; Snyder, R. S. J . Chromatogr. 1989, 480, 35. 0003-2700/92/0364-2991$03.00/0
In part 1of this series of papers? utilization of the DebyeHiickel-Henry theory of protein mobilitylO was shown to provide predictions of the behavior of single proteins which were in qualitative agreement with experimental results for three electrophoretic modes, zone electrophoresis, isoelectric focusing, and isotachophoresis (ITP). However, predictions of protein net mobility and zone parameters, including concentration and conductivity, exhibited much greater discrepancieswith experimental data than did corresponding predictions for low molecular mass substances. This was particularly evident for the ITP behavior of serum albumin.11 It was clear that the model underestimated protein mobility, perhaps because of excessive contributions of the macroions to ionic strength, which modifies protein mobility in the DebyeHiickel-Henry theory. This resulted in an underestimation of the steady-state ITP protein zone concentrations by about a factor of 2. Investigation of multicomponent ITP systems revealed that qualitative disagreemente with experimentaldata were present as well. Simulationof ITP behavior provides the most vigorous test of an electrophoretic model because of the strong interaction of samples. Small changes in electrochemicalparameters may result in the formation of a different ITP zone pattern, e.g. a change in separability or even reversal of zone order. These observations prompted an investigation of the Linderstrom-Lang approximation for the contribution of a protein to ionic strength.I2 In this paper, we (i) show that w e of this approximationprovides predictions of protein behavior which are in much better agreement with experimental measurements, (ii) discuss the influence of the input protein electrochemical parameters on both qualitative and quantitative simulation data, (iii) demonstrate that ITP serves as an excellent method for the testing of the reliability of a protein electrophoresis model, and (iv) present the first computer simulations of the ITP separations of proteins with and without low molecular mass spacers.
THEORETICAL CONSIDERATIONS The protein model has been described in great detail previously.8 In the interest of clarity, the major points will be reviewed. The model is one dimensional and is based upon the principles of electroneutrality and conservation of mass and charge. Isothermal conditions are assumed, as is the absence of bulk flow. Relationships between the concentrations of the various speciesof a component are described by equilibrium constants. Proteins have a large number of dissociating groups, which generates a population of molecules (10) Henry, D. C. Proc. R . SOC.London A 1931,133,106. (11) Thormann, W.; Mosher, R. A. Electrophoresis 1990, 1 1 , 292. (12) Linderstrom-Lang, K. Trans. Faraday SOC.1935, 31, 324.
0 1992 Amerlcan Chemical Socbfy
2992
ANALYTICAL CHEMISTRY, VOL. 84, NO. 23, DECEMBER 1, 1992
Table I. Electrochemical Parameters of Smell Molecules Used in the Simulation mobility coefficient compd
PKi
acetic acid formic acid
4.76 3.75
PK~
K+ Tris EACA 8-alanine GAJ3A
8.3 4.43 3.6 4.23
TPA ammediol c1H+ OH-
8.6
10.75 10.19 10.43
x 109 ( " W e ) 42.4 56.4 79.1 24.1 31 36.3 32.0 18.1 40 79.1 362.7 198.7
which possesses an average net charge at any given pH. To describe the contribution of the protein to the current density and ionic strength, the mean square charge of this population is required. In order to make the protein mobility a function of ionic strength, the Debye-Htickel-Henrylo expression is used
where u is the electrophoretic mobility, q is the viscosity, e is the unit charge, r is the particle radius, and K is the Debye parameter defined by
with e being the dielectric constant of the fluid, eo the permittivity of free space, k the Boltzmann constant, T absolute temperature, nmthe ionic concentration, and zm equivalent to standard valence for small ions. The function f(Kr) varies sigmoidally from 1 to 1.5.1° While this approach, referred to as model I in the remainder of this paper, provided data which were in acceptable qualitative agreement with experimental data for simple configurations,8J1 discrepancies in multicomponent ITP systems were noted. In the above approach the protein is treated as any other ion and therefore makes a very large contribution to the ionic strength when there is a significant charge on the molecule. Linderstram-Lang12postulated that in cases where the distances between the charges on a macroion (such as in proteins), a z-valent are great compared with I / K ion behaves like a monovalent ion with z-fold concentration. The valence of the ion 2(), thus enters only with its first power and not with its square into eq 2. No other changes were made to the model. This approach was adopted for simulation and referred to as model I1 in this paper. To simulate the behavior of a protein and to calculate its net mobility (eq 11, two inputs are required, a diffusion coefficient (serving for calculation of the protein radius as well as diffusive mass transport) and a tabular representation of net charge vs pH (titration curve). Thus far data taken from the literature were employed,the table being extracted from experimentally determined titration curves. It is important to note that such titration data are strongly dependent on the ionic strength and are measured at a fiied ionic strength. Therefore, these data serve as a rough approximationonly, particularly for simulationsin which the proteins encounter regions of different ionic strengths. The results, however, may be quite good for media of low ionic strength, such as those employed in ITP. Nonrealistic results may occur also when operation is at pH values which are not very far from the isoelectric point of the protein. Here a small shift of the protein titration curve along the pH a x i s
Table 11. p H Dependence of the Ionization of the Proteins net charge PH
2.00 2.08 2.12 2.32 2.33 2.62 2.94 3.00 3.04 3.30 3.36 3.50 3.58 3.68 3.72 3.80 3.84 4.00 4.06 4.07 4.10 4.30 4.34 4.42 4.56 4.61 4.78 4.80 4.90 5.18 5.20 5.40 5.52 5.69 5.76 5.80 5.88 6.32 6.45 6.80 6.90 7.04 7.35 7.66 7.80 8.60 8.65 8.80 9.12 9.60 9.72 9.84 10.00 10.10 10.20 10.40 10.60 10.83 10.85 10.96 11.05 11.10 11.30 11.50 11.60 11.68
BSA
BLB
RNase 17.75
OVA 22
40 16.5 20 35 15 58.0
30 14.0
44.5 25 35.5
10 11.5 20 22.0 8 13.0 15 6 8.0 3.0 4 10 9.00 2
5
0.0
0 0 -2 -4.0
-a -5 6.50
-6.1 -6
-8 -10 -12.2 -10 4.00 -15 -12 -18.3 -14 -20 -24.4 1.50 0.00 -25 -1.00 -32.0 -16 -30 -3.50 -36 -40 -18
-6.00 -45 -48.0 -20 -64.0 -8.50 -22
causes a dramatic change in the protein's computed net mobility. It is thus very important to have the right zero point of this curve. As was shown by Longsw~rth,'~ one of the limitations of experimental titration curves is that the measured isoelectric point may be different from the true (13)Lowworth, L. G.Ann. N.Y.Acad. Sci. 1941,41, 267.
ANALYTICAL CHEMISTRY, VOL. 64, NO. 23,
DECEMBER 1, 1992 2988
Table 111. Simulation and Experimental Results for anionic ITP of BSA leader 10 mM HCVammediol
PHL
10 mM HCl/ammediol
9.5
10 mM formic acid/Tris
9.0
10 mM formic acid/a"ediol
9.0
modellexpa
8.0
I I1
expb I I1
expb I I1
expb I I1
expc
concn (mM)
cond (mS/m)
PH
net m o b i l i ~ X 108 (mz/Vs)
0.159 0.255 0.294 0.119 0.205 0.195 0.169 0.268 0.338 0.146 0.247 0.377
17.9 31.7 20.0 21.9 43.9 27.0 17.4 35.3 29.0 22.1 43.5 38.0
8.45 8.26 8.20 9.92 9.70 9.52 9.33 9.15 9.24 9.39 9.18 9.17
12.3 21.8 13.8 15.0 30.1 18.4 12.6 25.5 21.0 13.3 26.3 23.0
a Models I and I1 refer to the employment of Debye-Hiickel-Henry and Linderstrem-Lang approximations, respectively (for details see text). * Continuous flow ITP data as described in ref 11. Recycling ITP data as described in ref 23. These mobilities were calculated wing the mobility of the leading compound (TableI) multiplied by the ratio of the experimentallydetermined or computer-predictedconductivities of protein and leading zones."
Table IV. Input and Simulation Results for Cationic ITP of Various Proteins section 10"D no. protein PHL titration curve (reoa (ref) (m*/s) modelb concn (mM) I 0.237 7.48 (15) 1 BLB 4.75 Cannan et al. (14) 7.48 (15) I1 0.368 BLB 4.75 Cannan et al. (14) I 0.153 5.94 (17) BSA 4.75 Linderetrem-Lang (16) 2 5.94 (17) I1 0.270 BSA 4.75 Linderetrem-Lang (16) I 5.94 (17) 0.093 BSA 4.25 Linderstrem-Lang (16) 3 I1 0.220 5.94 (17) BSA 4.25 Linderetrem-Lang (16) I 13.6 (19) 0.549 RNase 4.75 Tanford et al. (18) 4 I1 13.6 (19) 0.686d RNase 4.75 Tanford et al. (18) I 0.271 7.76 (21) OVA 4.75 Cannan Z = 0.033 (20) 5 7.76 (21) I 0.274 OVA 4.75 Cannan Z 0 (20) 0.405 7.76 (21) I1 OVA 4.75 Cannan Z = 0.033 (20) 7.15 (22) I1 0.365 OVA 4.75 Cannan Z = 0.033 (20) I1 0.401 7.76 (21) OVA 4.75 Longsworth (13)' I1 0.406e 7.76 (21) OVA 4.75 Cannan z 0 (20) 7.76 (21) I1 0.296 OVA 4.25 Longsworth (13)' 6 I1 0.307 7.76 (21) OVA 4.25 Cannan z 0 (20)
-
-
cond x 102 (S/m)
pH
net protein mobility X 108 (mz/Vs)
1.93 2.58 1.53 1.74 2.39 3.18 3.33 4.47 1.74 1.48 2.13 2.01 1.55 1.65 2.39 2.45
4.19 4.34 3.98 4.07 3.65 3.86 4.45 4.54 4.11 3.93 4.23 4.20 3.99 4.06 3.65 3.68
12.9 17.4 10.3 11.7 15.8 21.1 22.3 30.0 11.6 9.9 14.3 13.5 10.4 11.0 15.8 16.2
Z denotes ionic strength. Model I refers to the Debye-Hiickel-Henryapproach and model I1 to the Linderetram-Langapproximation (for detailssee text). Z = 0.01; the z-values of the titration curve were multiplied by a factor of 0.603. Experimental value obtained with recycling ITP:0.91 mM, 0.031 S/m, pH 4.47.23e Experimental value obtained with recycling ITF': 0.58 mM, 0.017 S/m, pH 4.06.23
zero (or isoionic) point owing to binding of small ions from the solution. Therefore, for a given simulation, careful selection of the protein titration curve is essential. EXPERIMENTAL SECTION Chemicals. Chemicals used were of analytical or research grade. Ribonuclease A (RNase) from bovine pancreas was from Sigma (St. Louis, MO), ovalbumin (OVA) from chicken egg was from Serva (Heidelberg, FRG), bovine serum albumin (BSA) was from Fluka (Buchs, Switzerland), and b-lactoglobulii B (BLB)of bovine milk was from Koch-Light (Haverhill,England). Computer Simulations. The model of Mosher et al.B was extended to include the Linderstrolm-Lang approximation (see previous section) and adapted for use on a PC. A Mandax AT 286 computer (Panatronic AG, Zuerich, Switzerland) running at 12 MHz and featuring a mathematical coprocessor,a 40-Mbyte hard disk as well as 1-Mbyte RAM memory was employed throughout this work. Initial conditions which must be specified for a simulation include the distribution of all components, the diffuaion coefficients and net charge-pH relationships of the proteins, the pK and mobility values of the buffer constituenta, the current density, and the duration of the current flow. The program outputs concentration,pH, and conductivity profiles as functions of time. For making plots, these data were imported into SigmaPlot ScientificGraphing Softwareversion 4.01 (Jandel Scientific, Corte Madera, CA) and completed plota were printed on a HP Laserprinter IIP (Hewlett Packard, Widen, Switzerland). The used input data of low molecular mass components are summarized in Table I. The net charge-pH relationships (Table
11) and diffusion coefficienta for the proteins were taken from literature data, the corresponding references for BLB, BSA, RNase, and OVA being 14/16,16/17,18/19, and 20/21, respectively. Instrumentation and Experimental Procedure. The experiments were performed on a Tachophor 2127 isotachophoretic capillary analyzer (LKB AB, Bromma, Sweden) equipped with a 28-cm PTFE capillary of 0.5-mmi.d., as well as a conductivity and W detector (iodine lamp and 277-nm fiiter) at the column end. Zone patterns were recorded on a two-pen strip chart recorder as they migrated across the pointa of detection. The cationic electrolyte systems used consisted of 0.01 M potassium acetate and acetic acid (PHL4.75 or 4.25) as the leader and 0.01 M acetic acid as the terminator. Unless stated otherwise, all measurements were performed at a constant current of 150 pA (initial and fiial voltageswere about 2.5 and 8.5 kV, respectively) provided by the Tachophor 2127 power supply (600 pA max;30 kVmax). Samples (1-4 r L containing mg/mL and mM quantitiea of proteins and spacers, respectively)were injected with a 10-rL syringe (Hamilton,Bonaduz, Switzerland).
RESULTS AND DISCUSSION ITP Zone Characteristics. Comparison of the two protein models employed anionic and cationic simulations of the ITP behavior of selected model proteins. Anionic ITP of BSA using model I has been examined previously and experimentally validated by continuous-flow and capillary ITP.11 These systems were resimulated with model 11, and
2994
ANALYTICAL CHEMISTRY, VOL. 64, NO. 23, DECEMBER 1, ls92
0.6
1 4.5
h
I E
v
OVA/-
z
1
0
2!x
a
0.3
I I I
I2
w
0 2
R
3.0
0
t
0
Na
0.0
1
0
2
4
2
0
L
4
-
TIME Flgwo 1. Computer-simulated and experimental ITP of OVA in the cationic system with a pY of 4.75. The steady-state concmtrah profllee obtained with models I and I1 are shown in panel A, and corresponding pH and conducttvny dlstribuHons are presented in panel B. The data correspond to 100 min of electrophoresis time at a current density of 5 Aim2. An inltiaiO.4 mM protein pulse was applied between 0.4 and 0.8 cm of column length. The theoreticalWration curve by Cannan for I Om was usedas input (Table I I). CapHlaty I t P data of an electrophoreticelly purified OVA samplez4are depicted in panel C. The Na zone represents an imp-. L and T refer to leading and terminating electrolytes, respectively. I and I1 refer to modeis I and 11, respectively. COLUMN LENGTH (cm)
COLUMN LENGTH (cm)
-.
comparison of data of the protein zones is presented in Table 111. Two configurations comprised C1- as the leading, e-aminocaproic acid (EACA)as the terminating, and 2-amino2-methyl-l,3-propanediol(ammediol) as the counter component. These systems differ in the pH of the leading electrolyte (pHd. The third and fourth examples had formate as the leading compound and &alanine as the displacing component. Tris(hydroxymethy1)aminomethane (Tris) and ammediolwere employed as counter constituents respectively. Current density for all simulations was 20 A/m2. In all cases well-developed ITP zones with plateau concentrations were predicted, the steady-state concentrations obtained with model I1being higher than those calculated with model I and in much better agreement with experimental results. The pH values were somewhat smaller with the second approach and also more closely corresponding to experimental data. The predictions of protein zone conductivities obtained with model 11, however, did not agree as well with experimental data as those of model I. Table IV presents data of several aspects of the simulation of cationic protein ITP behavior using models I and 11. Predicted zone characteristics are compared for BLB, BSA, RNase,and OVA in sections 1, 2, 4, and 5, respectively. Potassium acetate (10 mM) adjusted with acetic acid to pH 4.75 waa used aa the leader, and acetic acid, as the terminator. (14) Cannan, R. K.; Palmer, A. H.; Kibrick, A. C.J . Biol. Chem. 1942, 142,803. (15) Lehninger, A. L.Biochemistry, 2nd ed.; Worth Publishers Inc.: New York, 1975; p 176. (16) Linderstrcam-Lag, K.; Nielsen, S. 0. In Electrophoresis; Bier, M., Ed.;Academic Press: New York, 1969; Vol. 1, p 85. (17) Mabler,H. R.; Cord-, E. H.Biological Chemistry,2nd ed.; Harper and Row: New York, 1971; p 87. (18) Tanford, C.; Hauenetain, J. D. J. Am. Chem. Soc. 1956,78,5287. (19) Greenberg, D. M. Aminoacids and Proteim; Charlea C.Thomas: Spdr&eld, IL,1951; p 394: (20) Cannan, R. K.; Kibnck, A.: Palmer, A. H. Ann. N . Y. Acad. Sci. 1941,41, 243. (21) Tiseliua, A.; Svenason, H. Trans. Faraday SOC.1940,36, 16. (22) Waltars, R. R.: Graham, J. F.: Moore. R. M.:Anderson. D. J. Anal. Biochem. 1984,.140, 190.
40 r
-40
1
5
10
PH
-
Flguro 2. Comparison of the three dlfferenttitratkn curves of OVA usedforsimulatlon(seeTableIV): (1)Cannan1 3 0.033;20(2)Cannan I QZo(3) Longsworth I = 0.01 (charge numbers muhiplied by
0.603).13
The model predicted the formation of an ITP zone for each protein. Again, simulation with model I produced d e r concentration and conductivity values compared to those obtainedwith model 11. This is depictad in Figure 1AJ3which represent the steady-state zone shape of OVA (A) and the corresponding conductivity and pH profiles (B)obtainedwith the two models. Experimental data are shown in Figure lC, representing the UV absorption (277nm)and conductivity (expressed as increasing resistance R) capillary ITP data across electrophoretically purified Due to a serial mounting of the two detectors at the capillary end, there is a small shift of detection time intervals, the UV absorbance response being recorded before the conductivity. Although the employed current densities differ by more than 2 orders of magnitude (experiment, 765 A/m2; simulation, 5 A/m2), there is great similarity between predicted and experimental protein zone shape and conductivity distribution with both (23) Caslawka, J.; Gebauer, P.; Odermatt, A.; Thormann, W. J. Chromatogr. 1991,545, 315. (24) Caslawka,J.; Gebauer, P.;Thormann, W. J. Chromatogr. 1991, 585,145.
ANALYTICAL CHEMISTRY, VOL. 64, NO. 23, DECEMBER 1, 1002
8 ,
150
I
5-
1991
0.12
v
-
6
I E v Z
"1 E
5
t
z W
3ol
0
L
150
z
0 0
2 z4-
T
21 23 TIME ( m i d
COLUMN LENGTH (cm)
Flgluo 3. Computer simulation (panels A and B) and experimental (panel C) data of the separation of OVA (5), BLB (3), and RNase (1) in the cationic system with pY 4.75 using model 11. For the simulation, the lnltlal c "Included pulses of OVA, BLB, and RNese at 0.5,0.5 and 0.7 mM, r m e l y , bcated between 0.6 and 1 cm of the d u m n length. The cwemt density was 10 A/m2. Panel A shows the concentratkn profiles of the three proteins at the Indicated time intervals between 0 and 150 mln. The conductMty and pH p r o m fxmqmding to 150 min of current f b w are depicted In the upper and lower halves, respectively, of panel B. Experimental data showing the steady-6tate absorbance at 277 nm (upper graph) and conductMty proflle expressed as Increasing redstance R (bwer graph) are presented In panel C. Whlk the experimental data were recorded, the current was reduced to 50 FA. Zone 6 and Na represent impurtties. Land T refer to leader and terminator, respecthrely.
models. Most ITP structures are charcterized by a steplike conductivity decrease between the leading the terminating zones. OVA represents an example in which the sample zone has a lower conductivity than either the terminator or the leading electrolyte. This so-called enforced migration is due to the substantial pH change (pH terminator = 3.20) across the rear OVA boundary. The net mobility of OVA (section 5 of Table IV) is also smaller than that of the leader and terminator (79.1 and 16.6 X 10"Jm2/(Vs),respectively). Table IV also presents datawith a leader pH of 4.25 on the predicted behavior of BSA (section 3) and OVA (section 6). Comparing data in sections 2 and 3 reveals that a 0.5 pH unit change in the leader produces different zone characteristics but does not change the predictions of models I and I1relative to each other. For example, the zone concentration predicted by model I1 is higher than that predicted by model I. OVA was chosen for further investigation of the impact of protein input data on predicted behavior (sections 5 and 6, Table IV) because its isoelectric point (4.920) is near the operating pH region of this cationic system and because a substantial amount of titration data can be found in the literature. Using model I1 and the titration data of Cannan (I= 0.033"), the plateau concentration was close to experimental measurements (see Table IV legend); however, the zone conductivities and protein net mobilities were higher. Improved agreement with experimental data was obtained with the theoretical curve by Canna@ which is extrapolated to zero ionic strength. These data (Table 11)were used for the simulations presented in Figure 1 and all subsequent figures including OVA simulation data. They were particularly important for reproduction of the experimental behavior of OVA in multicomponent systems. In addition to the titration curve8 of Cannan,20the use of the data by Longsworth13 which were (i)shiftedalong the pH axis in order to fit with the experimental mobility curve (PI= 4.58) and (ii) reduced by a factor of 0.603 for the same reason (an adjustment used by Longsworth to account for the binding
I E
v
z
2
2+ z W
u
z
0 V
1.35
0.00 0
10
20
COLUMN LENGTH (cm)
Flguro 4. Computer simulation of the ITP separation dynamics of BSA (fkst zone) and OVA with TPA as spacer In the catbnlc system with a p y of 4.25 wing model 11. The concentration profibs of the two proteins are shown at the indicated time Intervals from 0 to 400 nrln (current dendty of 10 A/&). The Initlei sample pulse (betweon 0.6 and 1 an)comprised 0.5 mM OVA, 0.4 mM BSA, and 7.5 mM TPA. The mow marks the bcation of the TPA zone.
of small ions by the protein, see Theoretical Considerations) were evaluated. Predicted zone properties were very close to those obtained using the zero ionic strength curve of Cannan (sections 5 and 6, Table IV). The three OVA titration curves are plotted in Figure 2. The data listed in section 5 of Table IV also reveal the impact of the protein diffusion coefficient on predicted zone properties. A smaller D value produces a lower plateau concentration as well as a reduced mobility. Conductivity and pH values are also decreased. Protein Separation. Model I1 has proven useful for predicting the ITP behavior of protein mixtures. Figure 3A presents the dynamics of the separation of RNase,BLB, and
2898
ANALYTICAL CHEMISTRY, VOL. 64, NO. 23, MEMBER 1, 1992
-
n
1
E v 2
2
2 Lz I-
5
0
t
I
4
2
z
0
u I
I o 0.12
1
lBSA
I
E
v
0.4
0
