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Molecular weight distributions of proteins by equilibrium ultracentrifugation and gel filtration chromatography Ma, Ching-Yung 1975

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MOLECULAR WEIGHT DISTRIBUTIONS OF PROTEINS BY EQUILIBRIUM ULTRACENTRIFUGATION AND GEL FILTRATION CHROMATOGRAPHY by CHING-YUNG MA B.Sc, University of Hong Kong, 1970 M.Sc, University of Hong Kong, 197^ A thesis submitted in partial fulfilment of the requirements for the degree of Master of Science i n the Department of FOOD SCIENCE Faculty of Agricultural Sciences We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1975 In present ing th is thes is in p a r t i a l fu l f i lment o f the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho la r ly purposes may be granted by the Head of my Department or by h is representa t ives . It is understood that copying or pub l i ca t ion of th is thes is fo r f i n a n c i a l gain sha l l not be allowed without my wri t ten permission. Department of Pood Science The Un ivers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date 6, Oct., 1975-i . ABSTRACT The molecular weight distributions (MWDs) of some proteins were determined by equilibrium ultracentrifugation and gel f i l t r a t i o n chromatography (GPC). A linear program-ming technique was used to compute MWDs from equilibrium data. The light-scattering second v i r i a l coefficient (B L S) of one protein, ovalbumin, was determined and was used to correct for the non-ideal behavior of the polymers. For unimodal systems, good MWDs were obtained from single experi-ment without correction for non-ideality. For more complex systems, combination of data from several experiments per-formed at different rotor speeds was required to give reason-able distributions; and correction for B L S brought about further improvement in the smoothness and accuracy of the MWDs. GFC was found to be a rapid and convenient method for MWD determination, having better resolving power than the linear programming technique. The advantages and l i m i t -ations of these two methods were discussed. i i TABLE OF CONTENTS PAGE INTRODUCTION 1 THEORY 8 A. EQUILIBRIUM SEDIMENTATION 8 1. Basic Equations 8 2. Scholte^ Method for Determining MWD 11 3. Correction for Non-ideality 14-B. GEL FILTRATION CHROMATOGRAPHY (GFC) 16 1. Basic Theory 16 2. Determination of MWD by GFC 17 MATERIALS AND METHODS 19 A. CHEMICALS 19 B. ULTRACENTRIFUGATION 19 1. Instrumentation 19 a. Centrifuge;, and optical system 19 b. Rotor and c e l l 21 2. Equilibrium Ultracentrifugation 21 C. GEL FILTRATION CHROMATOGRAPHY 23 RESULTS 27 A. B L S DETERMINATION BY THE METHOD OF ALBRIGHT AND WILLIAMS , 27 B. SCHOLTE'S METHOD FOR MWD DETERMINATION 27 1. Unimodal Systems 27 a. Ovalbumin 27 b. Other proteins 33 i i i PAGE 2. Bimodal Systems , 39 a. Ovalbumin/y-globulin 39 b. Ovalbumin/RNase 39 3. Trimodal Systems 39 a. Ovalbumin /y-globulin/apoferritin 39 b. Trypsin inhibitor/bovine serum albumin/ catalase 46 C. MWD DETERMINATION BY GFC 46 DISCUSSION 58 LITERATURE CITED 68 i v . LIST OF FIGURES FIGURE PAGE 1. Record of a UV trace from an equilibrium 2k experiment using double-sector c e l l . 2. Plot of A C / C n vs. A . 29 3. Plot of (AC/xG)'1 vs. A . 30 k. Plot of ( M ^ ) " 1 vs. C Q. 31 5. MWD of ovalbumin by Scholte's method, with 35 data from four A . 6. MWD of ovalbumin by Scholte's method, with 36 data from one A . 7. MWD of human y-globulin, RNase and trypsin 38 inhibitor by Scholte's method. 8. MWD of ovalburain/y-globulin mixture by kl Scholte's method. 9. MWD of ovalbumin/RNase mixture by Scholte^ kj method. 10. MWD of ovalbumin /y-globulin/apoferritin kS . mixture by Scholte's method. 11. MWD of trypsin inhibitor/bovine serum albumin/ kQ catalase mixture by Scholte's method. 12. Calibration curve of Sephadex G-200. k9 13. Elution pattern of trypsin inhibitor on 50 Sephadex G-200. v. FIGURE PAGE 14. Elution pattern of ovalburain/V-globulin 50 mixture on Sephadex .G-200. 15. Elution pattern of ovalbumin/RNase mixture 52 on Sephadex G-200\ 16. MWD of trypsin inhibitor, determined by GFC. 53 17. MWD of ovalbumin/y-globulin mixture, deter- 5^ mined by GFC. 18. MWD of ovalburain/RNase mixture, determined 55 by GFC. v i i LIST OF TABLES TABLE 1. Data for B^ s determination by the method of Albright and Williams. 2. Results of B L S determination by the method 32 of Albright and Williams. 3. Table for the calculation of MWD of ovalbumin 34 by Scholte*s method. 4. Average molecular weights of ovalbumin , 37 calculated from MWD data. 5. Data for calculation of MWD of ovalbumin/ 40 y-globulin/mixture by Scholte*s method. 6. Data for calculation of MWD of ovalbumin/ 42 RNase mixture by Scholte*s"method. 7. Data for calculation of MWD of ovalbumin/ 44 y-globulin/apoferritin mixture by Scholte*s method. 8. Data for calculation of MWD of trypsin 47 inhibitor/bovine serum albumin/catalaise mixture by Scholte*s method. 9. Average molecular weights and molecular weight 57 ratios of some proteins, determined from MWDs. PAGE 28 v i i . LIST OF SYMBOLS A c e l l area, ( 1 - V P ) W 2 / 2 R T B second v i r i a l coefficient (or B|,s light-scattering second v i r i a l coefficient C concentration on volume-based scales (g/l) C Q original concentration of solution concentration of the i-th species concentration at the c e l l bottom CL, concentration at the meniscus m (C)^ d ideal equilibrium concentration G(s) integral distribution function of sedimentation coefficient K a y fraction of gel volume available to the substance K d distribution coefficient M molecular weight molecular weight of the i - t h species Mapp apparent weight average molecular weight Mapp apparent weight average molecular weight at zero speed Mn true number average molecular weight true weight average molecular weight M true z-average molecular weight z P pressure R molar gas constant T absolute temperature V V elution volume e inner volume v i i i . V o void volume total bed volume U ( x , l ) C/Co f^ weight fraction of i-th species in an equilibrium mixture f:(W)) normalized differential distribution function of molecular weight g(s) normalized differential distribution function of sedimentation coefficient h c e l l depth, parallel to axis of revolution r radial distance from the centre of rotation r^ radial distance from the c e l l bottom r m radial distance from the meniscus m s sedimentation coefficient s Q limiting sedimentation coefficient v partial specific volume of solute, cm-Vg y^ activity coefficient of the i-th species A correction term for B L S determination s. experimental errors A ( l - v P ) o ) 2 ( r b 2 - r m 2 ) / 2 R T chemical potential of the i - t h species total potential of the i-th species reference chemical potential of the i - t h species ( r b 2 - r 2 : ) / ( r b 2 - r m 2 ) p density of solution, g/cm ul angular velocity, radians per second ACKNOWLEDGEMENTS I would like to express my deepest gratitude to Dr. S. Nakai for i n i t i a t i n g this project and his valuable advice and encouragement throughout the course of the study, and in the preparation of the thesis. I like to thank Dr. Th. G. Scholte for providing me the computer program used in this work. 1. INTRODUCTION Equilibrium ultracentrifugation has been considered a classical method for determining the molecular weight of macromolecules i n solution. At the establishment of sedi-mentation-diffusion equilibrium after prolonged rotation at moderate speed, the variation i n concentration (or concentr-ation gradient) along a solution column i n an ultracentrifuge c e l l can be measured optically. From these data, the molecular weight can be calculated from the following equationsi or Where M i s the molecular weight of the solute; R, the universal gas constant; T, the absolute temperature; v, the p a r t i a l specific volume of the solution; p, the density of the solv- ' ent; c, the concentration of the solution; co, the angular velocity of the rotor and r, the radial distance from the centre of rotation. A plot of the logarithm of concentration against the square of the radial distance should give a straight line , with the slope directly related to the molec-ular weight. High polymeric substances are mixtures of a large number of molecules which are chemically identical but are different i n molecular weight. Various average molecular 2. weights such as number-average (MJJ), weight-average (M^) end z-average (M_) molecular weights can be calculated from the sedimentation equilibrium data by either one of the several procedures available (1,2, 3t 4 0 • However, these molecular weight averages can only give ,limited information to the fractional distribution of the component molecules over the whole range of molecular weights. In principle, the entire molecular weight distribution(MWD) of a sample can also be determined from sedimentation equilibrium experiments. Shortly after the construction of the f i r s t u l t r a -centrifuge by Svedberg and his associates i n the early 1920*s (5i 6), Rinde (7) developed a method for determining the distribution of r a d i i of the colloidal gold sols from equi-librium data. He derived the following equationi Here, G Q i s the i n i t i a l concentration of the solution, A and £ are functions of the rotor speed and the radial distance respectively, and f(M) i s the differential MWD function. After this pioneering work, many attempts have been made to solve Rinde's equation for f(M). In some cases (1, 8, 9), specific models such as the most probable distribution were used. Wales and his co-workers (10, 11, 12, 13) avoided these models and used osmotic pressure second v i r i a l coeffic-ient, B__, to correct for non-ideality. Sundelbf (14), pro-OS-, posed a method which was based on Fourier convolution theorem. 3. Refinements of this method were reported by Provencher (15) who showed that the basic equation for MWD determination (Eq. 3) i s a Fredholm integral equation of the f i r s t kind. He recommended a method by which the equation can be solved by a combination of quadrature and least squares. A l l these methods were found to be unsatisfactory and experimental errors may lead to negative weight fractions for some of the polymeric components. Recently, some new and elegant methods have been devised to solve the problem. Donmelly (16, 17) showed that the concentration distribution of the polymeric solutes at sedimentation equilibrium i s i n the form of a Laplace trans-form. He substituted a function <A(M) for f(M) i n Eq. (3) i n such a way that the right-hand side of Eq, (3) yielded a Laplace transform which can be represented asi f ( C , l ) = f ^ (M)exp[-U(A,!)M]dM (4) Jo , where U (A , I ) i s a known function. The f i r s t step i s to evaluate the function <A(M) by finding the inverse Laplace transform of f(C,|). Once t(M) i s obtained, f(M) can be determined by the relationship established between them (16, 17). This method i s based on one equilibrium run and has been found to work well for unimodal distributions (18), but could be unsatisfactory i n dealing with multimodal d i s t r i b -utions . Scholte proposed a method by which Eq. (3) may be 4 . rewritten as a set of linear equations which can be solved by a modified linear programming technique (19, 2 0 ) . His method requires several experiments to be performed on the same solution at different rotor speeds. This i s equivalent to fractionation of the sample since at lower speeds, the concentration distribution of the low molecular weight solutes i s relatively slight, while at higher speeds, the high molec-ular weight solutes are sedimented to the c e l l bottom and the lower molecular weight components are redistributed through-out the c e l l . This method has been proved to work satisfactor-i l y on multimodal systems. More recently, Gehatia and Wiff (21-24) developed a sophisticated mathematical treatment for obtaining MWD from single equilibrium experiments. They showed that Rinde's equation i s an "improperly posed problem" i n the Hadamard sense. Small errors i n experimental data (C/CQ) can lead to severe oscillations i n the MWD when one trys to obtain f(M) from this integral equation. They applied Tikhonov's regular-ization functions (25) which dampened out the oscillation. Regularization;alone was not f u l l y adequate for more complex distributions and additional algorithms had to be used. Two procedures had been devised incorporating regularization into linear programming and quadratic prograinming. They claimed that these methods can handle up to pentamodal distributions. However, this technique demands advanced mathematical s k i l l and a l o t of computer time. Furthermore, the fact that a 5. large number of data points from a single equilibrium pattern are required for computation means that a long solution column has to be employed and consequently, i t w i l l take an inconveni-ently long time to reach sedimentation equilibrium. Apart from the above methods which have supporting experimental evidences, Magar (26) suggested some alternative techniques for computing MWD. These include the least square or L 2 norm approximation (27» 28), the method of steepest descent (27» 29» 30) and the Simplex method of Nelder and Mead (31). Most of these s t a t i s t i c a l methods have never been explored for MWD determination and may be used independently or i n connection with other established methods to yield a better solution for the problem. Most of the above methods were f i r s t developed for non-aggregrating polydisperse systems under ideal or pseudo-ideal (theta) conditions* These conditions can only be met by synthetic chemical polymers and some biological macro-molecules such as sheared DNA, glycogen and other high poly-mer carbohydrates. However, Wan (18) showed that such r e s t r i c -tions can be removed by introducing a correction term, the light-scattering second v i r i a l . coefficient, B L S. Originally, a l l these methods could only be used for ultracentri^uge cells with sector-shaped centerpieces. Wan (18) and Adams et a l . (32) wrote equations analogous to those used by Donnely, Scholte and Gehatia and Wiff that are applicable to nonsector-6. shaped centerpieces (Yphantis or multi-channel equilibrium centerpieces). Equilibrium ultracentrifugation i s not the only method for determining MWD. Williams and his associates (33, 34) developed a procedure by which MWD can be obtained from sedimentation velocity data. Velocity method dependtf'bn the application of a sufficently high gravitational f i e l d to cause the sedimentation of molecules at a rate that can be measured. Williams 1 method was based on finding the dif f e r e n t i a l distribution of sedimentation coefficient, g(s), which i s defined by e y s ) = I d G - dQ(s) , 0  s ^ s ; C ds ds o ; Here, s i s the sedimentation coefficient and G(s) i s the integral distribution of sedimentation coefficient. Both g(s) and G(s) can be determined from velocity experiments. In order to convert the sedimentation coefficient to MWD, an empirical relation has to be assumedJ s Q = KMd (6) where s Q i s the limiting sedimentation coefficient at zero concentration and K and <* are temperature-dependent parameters characteristic for each polymer-solvent system. For a contin-uous distribution, i t was shown that g(s 0)ds Q = f(M)dM (7) and , . , f(M) = g ( s j f f o =g(s ) KM (8) 0 dM 0 \ These relations make the conversion of g(s 0) to f(M) feasible. The sedimentation velocity method has the advantages of rapidity and higher sensitivity to polymer heterogeneity, and preliminary correction for non-ideality i s not required since i t would be accounted for i n the extrapolation of s to zero concentration. However, the technique suffers from the fact that the theory i s largely empirical and the experimental procedures are tedious, requiring 2-3 extrapolations which may easily lead to an erroneous f i n a l sedimentation c o e f f i c i -ent distribution. In addition to ultracentrifugation, gel permeation chromatography (GPC) developed by Moore (35) i s a well-established technique for finding the MWD of organophilic polymers. GPC employs semi-rigid cross-linked polystrene beads and non-polar solvents as eluents. Its application i s therefore limited to synthetic organic polymers. Recently, gel f i l t r a t i o n chromatography (GFC) using soft cross-linked hydrophilic gels has been applied to determine the MWD of some biological polymers such as dextrans (36,37)» collagen (38) and peptides produced by proteolysis (39)• In the present study, the MWDs of some proteins were computed by Scholte*s linear programming method. The B-^ g of ovalbumin was determined to make correction for the non-ideal behavior of the protein. The MWDs of these proteins were also computed from GFC data and compared to sedimentation results• 8. THEORY A. EQUILIBRIUM ULTRACENTRIFUGATION 1. Basic Equations According to classical thermodynamics, the total potential, ju^, of each component i i n a polymeric solute i s constant throughout the solution column in an ultracentrifuge c e l l at sedimentation equilibrium. This can be expressed mathematically ass — ? ? " M i  00 ' 2 = o o n s - t a n * (9) where ji^ = the chemical potential of component i which i s related to a volume-based concentration, C^, as follow: / i i = ;i? + RT In yL 0± (10) Here, p.? i s the reference chemical potential of the solute species i and y^ i s an activity coefficient. For an incompressible solution of q polymeric solutes, the c r i t e r i a for equilibrium are T = constant (11) g - /»w 2r = 0 (12) and dju. du. 9 - d f = - d F - M . ^ 2 r = 0 (13) At constant temperature, the chemical potential of any com-P ponent i s a function of pressure Aand concentration. Then, d r ~ \ a p / G d r VdC^/P dr (14) 9. and ( ^ ) c • M i 7 i ( 1 5 ) ^ a - W ^ r - - ^ ) * £ (1.1 4 , U6> Combining Eq. (12) through Eq. (15) gives Making use of Eq. (10) we have M l ( l - V ) ^ 2 r 1 1C ± a / a i n y i \ The logarithm of y\ i s expressed i n power of C^ i n the form l n y 1 = M i ^ B i k C k + (18) k=l and M. (l-i7. f>) toZrQ. dC. q dC. ~ fe i = -3F' + Mi ci|»ik-3? <W) B i k a r e v e r v complicated functions of M^  which appro-ache zero in dilute, ideal solution and Eq. (19) can be reduced to din C, ( 1 - i / ^ ) ^ 2 _ i = M . = AM. (20) d;(r ) 2RT or dC, f- = AC.M. (21) d(r 2) 1 1 According to Fujita's notations (2) , Eq. (20) can be written i n dimensionless quantities ass 10. where A = (l-\7/>)w2(r2 - r 2)/2RT ( 2 3 ) 3 , 1 4 |=(r 2 - r 2 ) / ( r 2 - r 2 ) (24) Here, r m and r v are the radial distances from the centre * m D of rotation to the meniscus and bottom of the c e l l respect-ively. Eq. (20) can be integrated between £ = 0 to | a $ to give l n . [ c i ( t ) / C i ( ^ = 0 ) ] = - A M j l ( 2 5 ) which can be converted to the exponential form C ^ l ) s ^(1=0) exp(-AM iO (26) In order to relate C^(£=0) to the i n i t i a l concentr-ation of component i , CQ^, the concept of-conservation of mass has to be employed, which states that i n a closed system (the solution column in the ultracentrifuge cell) the total amount of solute i s constant at a l l time. Since mass = concentration x volume, the dimension of the center-a piece has to be known. For Asector-shaped centerpiece, the conservation of mass equation can be expressed as» .r* 8hr*-:&±A(i*) = * h C o i ( r 2 - r 2 ) ( 2 7 ) m Here, e i s the sector angle ( 2 . 5 ° for a double-sector center-piece) and h i s the c e l l thickness, which can vary from 12mm to 3 0 mm. 11. Substitution of Eq. (26) to Eq. (28) gives C (*-<» - X ¥ ; < 4 . (29) u i u - u ; ~ l-expt-AM..) Substitution of Eq. (29) back to Eq. (26) leads to AMvC - exp(-AM.O l-exp^AM.) 1 (30) Summation of Eq. (30) over a l l solute components, followed by the division of C Q gives c m ^ AM.f.exp(-AM.O C Q - V l-exp(-AMi) u i ; Here, f^ i s the weight fraction of component i , 0 o^/C Q, Eq. (31) i s the basic equation for computing MWD. In a continuous distribution, Eq. (31) can be written i n integral form which i s identical to Eq. (3) . 2. Seholte*s Method for Determining MWD (19, 20) Seholte 1s method i s based on solving Eq. (31) which he wrote asi V(XyO = £ f i K i j + * j - (32) i n which U ( A » 0 - ^ (33) o and K s A^ex P(>A. 1M i O ( 3 ^ } l-exp(-A^Mi) and 6^ i s the experimental error. Seholte assumed a discrete 12. series of molecular weights M^ with, a range large enough to include the whole MWD. The best result was obtained when the molecular weights were spaced at equal intervals* on a , logarithmic scale. The interval factor determines the "resolving power" of the method but the lowest interval should be about 2 . The experiment; should be designed such that there are more U(Aj,£) data than the number of molecular weights. Once the molecular weight series has been chosen, the following set of linear equations can be written« U ( A , 0 2 - f x K 1 2 + f 2 K 2 2 + ..... + 8 2 . . (35) . . . . . . . . U ( A , O n = f 1 K l n + f 2 K 2 n + . . . . . + 8 n This set of linear equations i s then solved by a modified linear programming technique. Linear programming i s a perfect solution to such a problem because: (l) the program i s set to optimize a linear objective function and i n the present case i s to minimize the sum of the absolute value of the error terms, ; : ' ^ r ^ i ; (2) the program i s subjected to some linear constraints which are now Eq. (35) and f ^ > 0 : and (3) a further constraint can be added to specify 2^fv= i"V;: It should be noted that non-negative f^ and the unity of 2 ify. are essential features of a MWD. 13. The set of f^ obtained from the chosen set of i s not unique. Seholte suggested the use of four molecular x weight series spaced from each other "by a factor of 2*. Thus, f. (one series) =1 m i ^fjL (four series) = 4 l ^ f j A (four series) =1 Eq. (36c) i s therefore also a solution, but w i l l give a more smooth MWD since more points are included. After the f^ have been obtained, a continuous MWD can be constructed using Seholte*s procedures. Note that * a f i = 1 = j f f < M ) d M = CM<M) * A In M2 i[Mf(M)] ± (37) If the interval between successive molecular weights i s Jr. 2*, then A In M = £ln 2 = 0.693A (38) and ^[Btf (M)] ± = 4/0.693 (39) Since %. f. (four series) = k (Eq. 36c), i t follows that 1 1 f ./0.693 = 4/0.693 (40) •>l 1 Thus, [Mf (M)^ = f 5/0.693 (41) Hence, the MWD curve i s constructed by plotting Mf(M) vs. In M, and the area under the curve i s 1. (36a) (36b) (36c) 14. the various average from the following (42) (43) (44) 3» Correction for Non-ideality For monodisperse non-ideal solutions at sedimentation equilibrium, Williams and co-workers (34) derived the following 1 i equationsi "ap* 1 = V 1 + ( V 2 > (Cm + °b ) + < * 5 ) where M a p p i s defined by Mapp = (Cb-Cm)/XCo= A C / X C o < W Here, i s the apparent weight-average molecular weight app calculated from the concentrations at the meniscus (C„) and m c e l l bottom (C^). 1/^  i s the true weight-average molecular weight of the solute, B 1 i s the coefficient for the f i r s t power of the solute concentration C ( i n g/ml) which appears when the logarithm of the activity coefficient of the solute, y, i s expanded i n a Taylor series as* In y = B^C + BgMC2^ (47) An approximation was proposed by Fujita (40) for From the computed MWD functions, molecular weights can also be calculated relationsi M = f°°Mf (M)dM w •'O o 15 polydisperse non-ideal solutions which leads to ^ P P 1 = + ( B V 2 ) (Cm+ C b ) + ( W with B« = B(l+ A) (49) In these equations, B i s the non-ideality parameter essentially equal to the lightr-scattering second v i r i a l coefficient, B L S and A i s a small correction depending primarily on the poly-dispersity of the solute and experimental conditions chosen. It was shown that A generally remains as 0.1 or less when x M ^ l . Hence, i t i s preferrable to perform the experiment at low rotor speeds. The experimental procedures for evaluating B-^ g were developed by Albright and Williams (41). Sedimentation equilibrium experiments are performed on the same solution at different rotor speeds. M a p p i s estimated from Eq. (46), and a plot of M a p p values versus x w i l l give an intercept equals to M °, the apparent weight-average molecular weight at zero speed. Alternatively, M a T (° can be determined from the limiting slopes of plots of AC/C versus x . M ° i s app o • — app related to B L g by the following equations »app»" X " V 1 + BlS°o <50) In order to use Seholte's method for non-ideal systems, the observed values of C (UV or interference optics) or dC/dr (Schlieren optics) have to be converted to ideal values. Wan (18) showed that 16 — — 1 - 2 . = 1 ( 5 i ) dC/d(r 2) A [dC/d(r 2)] i d Here, the subscript i d means ideal and A i s defined in Eq. (20). The corresponding equation for the conversion of C to (C^d i s i - , ' a 8 . f ( 5 2 ) The values of ( G ) ^ D can then be used to calculate U ( A , | ) ^ for Scholte's method. B. GEL FILTRATION CHROMATOGRAPHY 1. Basic Theory Gel f i l t r a t i o n chromatography (GFC) employing hydro-p h i l i c gel matrices i s generally looked upon as a process of steric exclusion (42) or equilibrium partition in a three-dimensional network (43). Fractionation of solute molecules i s based on the dimensions of the particles and i s independent of adsorption, p r e f e r e n t i a l solubility or ion exchange. A gel column can-be characterized by some parameters, namely V., V , V and V. which are defined as * t e o l V e = Elution volume, the volume of effluent that/precedes elution of a specific solute in the sample. V Q = Void volume, the volume of space between gel particles. This can be estimated by measuring the V e of a large molecule incapable of entering the gel matrix. 17. = Total bed volume. This can be determined by prior water calibration of the column or by measuring the the V e of a small molecule. V^= Inner volume, the volume of liquid contained within the gel particles. The behavior of a solute within a gel matrix i s ideally represented by the distribution coefficient, K^, defined as V - Vrt x Since i s d i f f i c u l t to be determined accurately, an altern-ative formula was proposed (43) V e ~ V o K a v= (54) t o where K _ i s defined as the fraction of gel volume available av for the substance. 2. Determination of MWD by GFC To obtain the MWD of a polymeric solute by GFC, the column has to be f i r s t calibrated with a number of standard proteins with known molecular weights, prefer-rably with molecular geometry similar to the sample to be fractionated. The elution of these standards are determined, and a c a l i -bration curve can be constructed by plotting the logarithm of molecular weights (In M) as a function of either one of the elution parameters, the most common of which are V g, Ve/V"0 and K a v. The sample to be analyzed i s then applied 18. to the column and eluted with the appropriate solvent. The relative amount of polymers i n each fraction of effluent, f^, can be determined either optically or by other quantit-ative methods. Plotting of these f^ values versus ln^M yields a MWD for the sample. Alternatively, the weight fractions can be divided by the slope of the calibration curve (-din M/dV_) in the corresponding region to give Mf(M) and the MWD i s constructed by plotting these Mf(M) values versus In M. The various average molecular weights can be computed from the weight fractions and the relevant molecular weight, M l A ^ S ^ / M ^ M w = * i f i M i (55) (56) 2 (57) 19 MATERIALS AND METHODS A. CHEMICALS The proteins used in -this study and their sources weret ovalbumin (5 x crystalline) was a product of Calbiochem; apoferritin, cytochrome c (horse heart) and myoblobin (sperm whale) were from Schwartz/Mann; human y-globulin, ribonuclease A (bovine pancreas), trypsin inhibitor (soybean), insulin (bovine pancreas), a-chymotrypsin (bovine pancreas) ,/?-lacto-globulin (bovine), bovine serum albumin, aldolase (rabbit muscle) and catalase (bovine liver) were a l l products of Sigma Chemical Company. Reagents used i n this study were a l l of analytical grade. B. ULTRACENTRIFUGATION 1. Instrumentation a. Centrifuge and optical system The centrifuge used i n the present study was a Beckman L2-65B preparative ultracentrifuge equipped with a UV scanner. A high intensity UV light source i s provided by a mercury lamp and the light beam i s directed to pass through the e e l l i n the rotor. The light beam then passes through a UV f i l t e r which produces a light-source of 278 nm. It then strikes the photomultiplier mounted behind a s l i t assembly. The s l i t and photomultiplier are moved by a motor-driven carrier 20. towards the axis of rotation, scanning the composite image of the c e l l and counterbalance i n about 60 seconds. The signal picked up by the photomultiplier tube i s amplified by a logarithmic amplifier since absorbance i s defined as -log T (where T i s the light transmittance of the sample). A strip chart recorder (Beckman 10-inch recorder) i s used to provide a permanent record of the absorbance as a function of time, and the trace can be related to the dimension of the analytical c e l l . The scanner has multiplex circuits which can recognize different cells i n a four- or six-place rotor. The optical system measures the absorbance difference between the sample and solvent i n the c e l l which i s directly related to the solute concentration i n g / l . The scanner produces zero and one absorbance signals, and the recorded trace can be read out i n absorbance units. The temperature of the rotor i s controlled by the temperature control system composed of two independent servo systems. One system i s built around an infra-red radiometer mounted on the bottom of the rotor chamber. By detecting the amount of infra-red energy given off, the radiometer senses the temperature of the rotor. The radiometer then holds i t s e l f at that temperature by means of a thermoelectric module which either heats or cools the radiometer shield. The other servo system senses the temperature of the radio-meter shield and cycles the flow of refrigerant to keep the rotor at the chosen temperature. Rotor speed i s adjusted by ah electronic speed control and the actual rotor speed i s measured from the odometer readings during the run. b. Rotor and ce l l s Analytical rotors used are made of aluminum alloys and are black anodized (products, of Beckman Instruments Inc.). For single sample runs, a two-place rotor (model AN-D) was used which has two holes housing, one ce l l . and. a,counter-balance. For multisample runs, a four-place rotor (model AN-F) holding, three ce l l s and a counterbalance was employed. A coding ring on the base of the four-place rotor enables the UV scanner to recognize individual, c e l l s . The ultracentrige c e l l s used are double-sector c e l l s . The sector-shaped centerpieces are 12 mm thick and are made of carbon-filled exppxy, resin. Quartz windows were used to allow the passage of UV l i g h t . A counterbalance was used for balancing and to provide some reference marks from which the radial distances from the centre of rotation could be measured accurately through the optical system. 2. Equilibrium Ultracentrifugation The double-sector centerpiece was sandwiched between two window holders containing the quartz windows• The assembly was put inside a barrel housing and held i n place by a screw ring which was then tightened to 110 in-lbs by a torque wrench. 22. One side of the centerpiece was f i l l e d with solvent; 0.18 ml was generally used. The other side was f i l l e d with 0.12 ml of solution, followed toy 0.03 ml of fluorocarbon o i l . For the determination of the second v i r i a l coefficient, i n order to shorten the time to reach equilibrium, 0.08 ml of solution was used instead. Protein solutions were usually dialysed against the buffer before use and the dialysates were applied to the solvent channel. For most experiments, the buffer used was 0 .05 M phosphate buffer, pH 7*0. The protein concentrations selected were such that the absorbance at 280 nm, determined by spectrophotometry, was between 0.4-0.8. Sedimentation equilibrium runs were carried out at 25^±0.5°C. More than one rotor speed for each i n i t i a l solute concentration were sometimes chosen to collect the necessary data for the Seholte»s (19, 20) and Albright and Williams* (41) methods. The experiment was started by running the rotor at low speed (about 5»000 rpm) and making a scan to obtain the i n i t i a l solute concentration reading. The rotor was then overspeeded at If times the expected equilibrium speed for three hours before decelerated to the selected speed. The time required to reach equilibrium at a certain speed was estimated by the method of van Holde and Baldwin (44). When the equilibrium state was reached, several scans were made to record the concentration distribution pattern along the solution column. The rotor was then allowed to run at maximum 23 speed for two to three hours to deplete the upper portion of the c e l l of macromolecular solutes. The rotor was then decelerated to the original equilibrium speed and additional scans were immediately taken. The average position of the trace in the depleted region of the c e l l was assumed to i n -dicate the base line for the entire c e l l . A typical UV scan of a double-sector centerpiece i s shown in Fig. 1. C. GEL FILTRATION CHROMATOGRAPHY The gel used i n the present study was Sephadex G-200 (Pharmacia Fine Chemicals, Uppsala) , with particle diameter from 40-120 jumand a fractionation range (peptides and globular proteins) of 5,000-800,000 daltons. The appropriate amount of gel was weighted out and an allowed to swell in Aexcess of d i s t i l l e d water over a boiling-water bath for five hours• The swollen gel was washed with several changes of water and the finest particles were discarded. The gel was deaerated and packed into a glass chromato-graphic column (Sephadex column K25/100, Pharmacia Fine Chem-icals) with an internal diameter of 2.5 cm and a length of 100 cm. Packing, was done by attaching an extension funnel to the top of the column, such that the gel slurry could be packed i n one operation. The bottom of the column was f i t t e d with a flow adaptor and the outlet was opened five minutes 24. a b f Fig. 1. Record of a UV trace from an equilibrium experiment using double-sector c e l l . a-outer reference edge. b-top of c e l l , c-air base l i n e . air-solvent meniscus, e-solvent-solution meniscus. /.- UV pattern for solution. g- bottom of column. hr-bottom of c e l l . /- inner reference edge. j- 1.0 absorbance mark. k- zero absorbance mark. 25. after the gel was introduced. The flow was then adjusted to about that used during the experiments. The settled gel was stabilized with one bed volume of buffer (0.1 M phosphate buffer, pH 7.4, containing 0.02# sodium azide to prevent bacterial growth). Another flow adaptor was mounted to the top of the column. The packed column was then equilibrated with the elution buffer. The column was operated i n a upward flow system. The in l e t tubing was joined to a 3-way valve which was connected to a mariotte flask with eluent and a 5 nil syringe. Sample containing 10-30 mg protein i n 3»0 ml solution was added v i a the syringe into the column by opening the outlet tubing at about 10 cm below the, l i q u i d level i n the syringe. The valve was then turned to connect the eluent chamber to the column. Elution was carried out at a hydrostatic pressure head of 12 cm which yielded a flow rate of about 18 ml per hour. The eluent was collected i n 3 ml fractions by an Isco fraction collector equipped with a drop counter (products of Instrumentation Specialties Co., Inc.). The absorbance of the eluent was measured at 280 nm by a Beckman DB spectrophotometer. Quartz cuvettes of 1.0 cm ligh t path were used. The amount of protein i n each fraction under the absorbance peak was determined by the method of Lowry et aJL. (45), using a Technicon autoanalyz er. The column was calibrated with the following standard 26 proteinsi Protein standard Source Mol. Wt.* insulin bovine pancreas ' 6,000 cytochrome c horse heart 12,500 myoglobin sperm whale 17,500 «-chymotrypsin bivine pancreas 25,000 ft-lact oglobulin bovine pancreas? 35,000 albumin bovine serum 67,000 albumin, dimer bovine serum 134,000 aldolase rabbit muscle 158,000 catalase bovine l i v e r 220,000 Trglobulin, dimer human serum 310,000 * Values were obtained from the literature; (46, 47) . ** Dimers were present i n small amount i n some samples. The void volume of the column was determined by measur-ing the elution volume of Blue Dextran 2,000 (Pharmacia Fine Chemicals). The total bed volume was estimated by calculating the elution volume of tryptophan. 27 RESULTS A. B L S DETERMINATION BY THE METHOD OF ALBRIGHT AND WILLIAMS The light-scattering second v i r i a l coefficient of ovalbumin was determined by the method of Albright and Williams (4-1). Sedimentation equilibrium experiments were performed at 25° C, using five i n i t i a l solute concentrationst 0.30, 0.55» 0.65» 0.80 and 1.05 g / l . For each concentration, four rotor speeds were employed. From the equilibrium patterns, the values of 0 , - 0 / 0 or A C A: and (A C / A C„)~ 1 or (M„ ) ~ 1 D Hr O ' 0 v ' 0 aPP can be obtained. These data are l i s t e d in Table 1. The plots of AC/C Q vs. A and those of ( A C / A C ^ - 1 V S . A are presented i n Fig. 2 and Fig. 3 respectively. From these plots, quantities of l / M a p p were obtained and they were plotted against the corresponding C Q (Fig. 4 ) . The two lines i n Fig. 4 have slightly different intercepts, but the slopes are essentially the same. B^g can be measured from the slpoe of these two plots and the weight average molecular weight from the inter-cepts (Eq. 50). .These results are l i s t e d in Table 2. The —6 2 average value of the two slopes, 8.371 x 10~ mole-l/g or 1.415 x 10*^ mole/g-absorbance unit, was used as the B L S value of ovalbumin for later computations. B. SCHOLTE'S METHOD FOR MWD DETERMINATION 1. Unimodal Systems a. Ovalbumin Equilibrium experiments were carried out on a solution 28. Table 1. Data for B L g determination by the method of Albright and Williams. (Absorbance unit) Xx 10^ AC/C0 [AC/XC0]'1 x 1 0 5 0.186 0.570 0.324 1.761 0.186 1.038 0.570 1.821 0.186 1.974 1.020 1.935 0.186 3.259 1.385 2.353 0.340 0.590 0.312 1.893 0.340 1.021 0.520 1.964 0.340 1.942 0.970 2.002 0.340 3.098 1.338 2.315 0.400 0.578 0.270 2.141 0.400 1.010 0.460 2.196 0.400 1.921 0.860 2.234 0.400 3.118 1.280 2.436 0.500 0.559 0.250 2.236 0.500 1.012 0.451 2.249 0.500 2.004 0.853 2.358 0.500 3.156 1.245 2.535 0.626 0.542 0.229 2.366 0.626 0.986 0.399 2.469 0.626 1.872 0.753 2.484 0.626 3.051 1.137 2.683 29. d Data from Fig. 2 • Data from Fig. 3 1.01 / ° 0.2 0.4 0.6 C 0 (Absorbance unit) Fig. 4 Plot of (Mapp)"1 vs. C0. 32. Table 2. Results of B L S determination by the method of Albright and Williams. ° 0 Absorbance unit g/l From Fig. 2* From Fig. 3** 0.186 0.30 1.850 1.715 0.340 0.55 1.975 1.860 0.400 0.65 2.150 2.068 0.500 0.80 2.292 2.146 0.626 1.05 2.450 2.315 * The values of the limiting slopes were obtained manually. **The values of the intercepts were determined by linear regression analysis. For data from Fig. 2, 63,400; BLS 8.449x10"6 mole-l/g 2 or 1.428x10"^ mole/g*absorbance unit. For data-from Fig. 3, 69,200; 8.293xl0"6 mole-l/g 2 or 1.402X10"-3 mole/g-absorbance unit. 33. of ovalbumin i n 0.1 M phosphate buffer, pH 7.0, at an i n i t i a l concentration of 0.5 gm/l (A280nm ° 0«36)« Four rotor speeds were employed* 12,076, 15»957» 19»956 and 24,181 rpm,. From the equilibrium patterns, the values of U(A.j, £) were calculated (Eq. 33) . The ideal values, S )id» w e r e 3 1 8 0 obtained after correction for non-ideality (Eq. 52). These data are shown in Table 3. They were used for computing, the weight fractions, f», of the polymer at the corresponding molecular weight M^ , using four molecular weight series. The MWDs are presented i n Fig. 5* The MWDs computed from one ?v., before and after correction for B^g, are also shown i n Fig. 6a and Fig. 6b respectively. The various average molecular weights and molecular weight ratios were computed by the computer (Eq. 42-44) and are presented i n Table 4. b. Other proteins The MWDs of three other globular proteins, namely, human 7-globulin, trypsin inhibitor and RNase, were also determined. The protein concentrations employed werei T -globulin, 0.35 gm/li RNase,*0.75 gm/l and trypsin inhibitor, 0.50 gm/l. MWDs were computed from data obtained from one experiment. Since the B L g values of these polymers are not known, no correction for non-ideality was made. The results are presented as plots of Mf(M) vs. In M i n Figs. 7a,b and c. The average molecular weights of these proteins were calculated i n the same way as above and are l i s t e d i n Table 9 . 34 Table 3. Data for calculation of MWD of ovalbumin by Seholte*s method. A x 1 0 5 U ( A , I ) non-ideal - ideal 2 . 4 7 2 0.935 0.541 0 . 5 0 1 2.472 0.748 0.700 0.665 2.472 0.466 0.967 0.962 2.472 0.277 1.202 1.246 2 . 4 7 2 0.086 1.484 1.620 4.387 0.909 0 . 3 5 1 0.332 4.387 0 . 7 2 5 0.524 0 . 5 0 2 4.387 0.541 0.767 0.740 4.387 0.262 1.335 1.378 4.387 0.075 2 . 0 5 4 2 . 2 7 5 6.856 0 . 9 3 6 0.144 0 . 1 3 6 6.856 0.753 0 . 3 0 2 0.290 6.856 0.476 0.573 0.553 6.856 0.290 1.043 1 . 0 5 2 6.856 0.103 2.049 2.195 10.080 0.909 0.039 0.037 10.080 0 . 7 2 5 0.131 0.126 10.080 0.541 0.291 0.283 10.080 0.262 0 . 9 6 6 0 . 9 6 5 10.080 0.169 1 . 5 0 0 35. / © \ « V V. \ I I I I I . I •• H \ i: i : ': -b \\ }:' Vk o non-ideal • i d e a l 0' Q--V • i u——I * — i i .i I n '» i-ro 4 5 „ i o 5 F/'g. 5 MWD of ovalbumin by Scholtes method, with data from four A . Fig. 6 MWD of Ovalbumin by Seholte's method, with data from one \. 012,076 rpm; © 15,957 rpm: A 19,956 rpm. A 24,181 rpm. Table 4. Average molecular weights of ovalbumin calculated from MWD data*. B^xlO" •2 V 1 0 " -2 MzxlO" -2 non-ideal ideal non-ideal ideal non-ideal ideal , st 1 series 434 457 524 579 671 769 2 n d series 428 457 526 582 686 821 3 r d series 410 452 518 596 654 852 4 series 418 454 519 602 654 897 Average 423 455 522 592 666 835 * Results were obtained from the combined data of four experiments performed at different rotor speeds. 1.5 a. 38. 1.0 i.5 r 1.0 0.5 b. 05 \ / o I o f oLqL p 2d \ \ 10' \ o \ o / \ o 1.51 \ 06 8 TO4 3 1.0 0.5 i I O / / o / / o \ o 0 \ 8 10 4 Fig. 7 MWD of human y-gfobufin (a), RNase (b)r and trypsin inhibitor (cf by Schofte's method. 39 2. Bimodal System a) OvalbuminA-globulin / Experiments were performed on a mixture of ovalbumin and 7-globulin i n a ratio of 4«3 using four rotor speedst 8,650, 12,100, 18060 and 24,330 rpm. MWDs were computed from both original data and values corrected for non-ideality, assuming the B L S value of the mixture to be approximately equal to that of ovalbumin. The raw data are l i s t e d in Table 5 and the computed MWDs are presented in Fig. 8. b) Pralbuma.n/RNase The MWD of ovalbumin/RNase mixture (in a ratio of 2i3) was determined using U ( x , £ ) values from two experiments performed at different rotor speed (13,920 and 24,030 rpm). Correction for non-ideality was again carried out using the BLS v a l u e o f ovalbumin. The data are presented i n Table 6 and the MWDs are shown i n Fig. 9* 3* Trimpflal Systems a) Pra 1 ftwnin/r^loTmlln/apof e r r j t i n The MWD of the above three-components system i n a ratio of 3«4i5 (T-globulin t apoferritin i ovalbumin) was computed from sedimentation equilibrium data. Two rotor speeds, namely 7,816 and 11,000 rpm, were selected. No correction for non-ideality was attempted. The data and computed MWD are presented i n Table 7 and Fig. 10 respectively. Table 5. Data for calculation of MWD of ovalbumin/y-globulin mixture by Seholte*s method. Ax IO 5 U(A,|) non-ideal U(A,£) ideal 1.701 0.918 0.710 0.622 1.701 0.781 0.740 0.656 1.701 0.505 0.965 0.949 1.701 0.226 1.415 1.777 1.701 0.034 2.310 3.004 3.483 0.948 0.240 0.210 3.483 0.751 O.36O 0.321 3.483 0.485 0.640 0.599 3.483 0.284 1.110 1.134 3.483 0.014 2.675 2.709 7.672 0.941 0.110 0.103 7.672 0.744 0.190 0.179 7.672 0.478 0.450 0.431 7.672 0.277 1.010 1.011 7.672 0.143 2.000 2.171 13.970 0.816 0.010 0.010 13.970 0.751 0.020 0.019 13.970 0.485 0.165 0.159 13.970 0.284 0.560 0.550 13-970 0.082 2.250 2.374 Fig. 8 MWD of ovalbumin/y-g/obulin mixture by Scholte's method. Table 6. Data for calculation of MWD of ovalbumin/RNase mixture by Scholte 1s method. AX 1 0 5 U(A,I) non-ideal U(A,|) ideal 5.282 0.966 0.532 0.491 5.282 0.853 0.623 0.584 5.282 0.739 0.717 0.683 5.282 0.624 0.811 0.785 5.282 0.509 0.925 0.912 5.282 0.383 1.076 1.090 5.282 0.276 1.245 1.302 5.282 0.159 1.453 1.580 5.282 0.041 1.687 1.921 15-730 0.983 0.170 0.163 15.730 0.870 0.226 0.218 15.730 0.756 0.298 0.287 15.730 0.641 0.393 0.380 15.730 0.526 0.532 0.519 15.730 0.410 0.785 0.776 15.730 0.352 0.925 0.921 15.730 0.235 1.396 1.426 15.730 0.118 2.019 2.135 Fig. 9 MWD of ovalbumin/RNase mixture by Scholtes method. 44 Table 7 . Data for calculation of MWD of ovalbumin/y-globulin/ apoferritin mixture by Scholte's method. A x 1 0 5 U ( A , i ) 1 .625 0 .943 0 . 2 1 4 1 .625 0 . 8 2 7 0 . 2 4 3 1 .625 0 . 7 6 9 0 . 2 6 4 1 .625 0 . 6 5 2 0 . 3 2 1 1 .625 0 . 5 3 5 0.407 1 .625 0 . 4 1 7 0 . 5 1 4 1 .625 0 . 2 3 9 0 . 8 5 7 1.625 O . 1 2 0 1.450 1.625 0 . 0 6 0 2 . 3 5 7 3 .063 0.936 0 . 1 3 1 3 . 0 6 3 0 . 8 1 9 0 .168 3 .063 0 . 7 6 0 0 . 1 9 7 3 . 0 6 3 0 . 5 8 3 0 . 3 1 2 3 .063 0 . 4 6 4 0 . 4 2 6 3 .063 0 . 3 4 4 0 . 6 0 7 3.063 0 . 2 2 4 0 . 9 3 4 3.063 0.103 1.820 Fig. IO MWD of ovalbumin/y-globulin/apoferritin mixture Scholte's method. 46, b) Trypsin inhibitor/bovine serum albumin/catalase Sedimentation equilibrium experiments were performed on the above protein mixture. The relative amount of the polymers present was approximately l t l i l . Two rotor speeds, 7,835 and 11,000 rpm, were chosen. Since the B L g value of the mixture was not known, the data (see Table 8) were applied directly without correction and the MWD i s presnted i n F ig. 11. G. MWD DETERMINATION BY GFC The Sephadex G-200 column was calibrated with standard proteins as described i n Method. The calibration curves, i n both V a and V a/V« In M, were plotted (Fig. 12). The elution patterns of some proteins and protein mixtures were obtained and are shown i n Fig. 13 (trypsin inhibitor), Fig. 14 (ovalbumin/y-globulin) and Fig. 15 (ovalbumin/RNase). For trypsin inhibitor, only the absorbance at 280 nm was determined and was assumed to be proportional to the amount of protein present. For ovalbumin/7-globulin mixture, the amount of proteins added was approximately 20 mg i n a ratio of l i l . For ovalbumin/RNase mixture, the amount of proteins loaded was about 10 mg of ovalbumin and 15 mg of RNase. The MWDs were determined by the procedures described i n Theory. The results are presented i n Fig. 16 (trypsin inhibitor), Fig. 17 (ovalbumin/7-globulin) and Fig. 18 (ovalbumin/RNase). 47 Table 8. Data for calculation of MWD of trypsin inhibitor/ bovine serum albumin/catalase mixture by Seholte*s method Xx 1 0 5 U(A, 1 ) 3.087 0.948 0.432 3.087 0.827 0.474 3.087 0.775 0.510 3.087 0.658 0.573 3.087 0.482 0.729 3.087 0.364 0.880 3.087 0.245 1.125 3.087 0.066 1.969 1.579 0.982 0.563 1.579 0.865 0.615 1.579 0.747 0.667 1.579 0.628 0.740 1.579 0.509 0.828 1.579 0.389 1.010 1.579 0.268 1.182 1.579 0.146 1.484 Fig. I1 MWD of trypsin inhibitor/ bovine serum albumin/ catalase mixture by Scholte's method. CO 2.5 50. . 1 2 F .09 E c o 00 .06 .03 o i 90 / p 6 i I P I I 'o o d / 95 100 o 'o \ \ o \ \ 105 Fraction Mo. n o Fig. 13 Elution pattern of trypsin inhibitor on Sephadex G-200. Fraction No. Fig. 14 Elution pattern of ovalbmin/ y-globulin mixture on Sephadex G-200. 52. Fig. 75 Elution pattern of ovalbumin/RNase mixture on Sephadex G - 2 0 0 . 5 3 .8 .6 . 4 .2 0 I f f A 9 ' 1.5 I? 1 \ -O—J 2.5 3 3.5 Fig. 16 MWD of trypsin inhibitor, determined by GFC. 54 55. Fig. 78 MWD of ovalbumin/RNase mixture, determined by GFC. 5 6 . The average molecular weights of ovalbumin, trypsin inhibitor and y-globulin were determined from the MWDs (Eq. 55-57), and the molecular weight ratios were also calculated. These values, together with those determined from sedimentation equilibrium experiments, are shown i n Table 9. 57. Table 9« Average molecular weights and molecular weight r a t i o s of some proteins, determined from MWDs. Protein Method M n x l 0 " 2 M^IO" 2 M x l 0 ~ 2 Zi \ / \ \ / \ y-globulin Seholte 1,410 1>540 1.670 1.089 1.086 y - g l o b u l i n GFC 1,490 1,550 1,630 1.042 1.056 Trypsin i n h i b i t o r Seholte 184 199 214 1.080 1.079 Trypsin i n h i b i t o r GFC 212 220 227 1.039 1.035 Ovalbumin, non-ideal Seholte, 1 X* 433 489 580 1.129 1.186 Ovalbumin, i d e a l Seholte, 1 X* 459 521 630 1.135 1.209 Ovalbumin, non-ideal Seholte, k X 423 522 666 1.235 1.277 Ovalbumin, i d e a l Seholte, 4 X 455 592 835 1.301 1.410 Ovalbumin GFC 450 462 473 1.027 1.025 * Average of values obtained from 4 experiments performed at di f f e r e n t A. 58. DISCUSSION Foods are generally complex systems containing macro-molecular components such as proteins and polysaccharides. During processing, there may be profound structural changes in these constituents including alterations i n molecular size and MWD. These changes can affect the texture, nutritional quality and functional properties of the products. For example, the size of starch granules often governs the visco-s i t y of starch-containing liquid foods, and the enzymatic digestion of some food proteins to smaller peptides i s related to the nutritional quality of the product. Hence, the study of changes i n molecular weight and MWD of these food components during processing i s of great importance to both quality control and research and development. MWD determination also provides valuable information to the study of interaction between food constituents, for example ** gi~x-casein inter-action. Ideally, this determination can give an evaluation of -the size distribution and the relative quantity of the inter-acting molecules and the interaction product. The association constant can be readily computed from such information. The objective of this study was to find a reliable method for determining the MWD of proteins. Both ultracentri-fugation and GFC were employed. The f i r s t attempt i n the study was to evaluate the light-scattering second v i r i a l coefficient of ovalbumin. 59 Many high polymers are known to exhibit non-ideal "behaviors, such as self-aggregation and concentration dependence, when they are under a centrifugal f i e l d i n sedimentation experi-ments. One way to overcome this problem i s to perform the experiments at theta ( 0 ) temperature as defined by Flory (48) who demonstrated that the osmotic pressure or light-scattering second v i r i a l coefficient approaches zero at a certain temper-ature. However, this only applies to organic high polymers which are linear. For branched polymers, e.g., dextrans, and complex biopolymers such as proteins, there i s no general theta temperature ( 4 9 ) . The only solution when working with these solutes i s to find a reliable second v i r i a l coefficient at a selected temperature. Several methods are available for determining this coefficient with the ultracentrifuge. These include the approach to equilibrium method of Archibald (50), and the equilibrium methods of Fujita (2) and Albright and Williams (41 ). The last two methods have been shown to yield a reason-ably accurate B^g value for dextran ( 1 8 ) . Fujita's method, however, requires constant solution column length and rotor speed, and at least two A values which should be as low as possible. Such restrictions are not found in the Albright and Williams* method, although more experiments have to be performed with different rotor speeds and i n i t i a l solute concentrations which make this procedure jrvery time-consuming 60. even when multi-hole rotors axe used. The concentration range and rotor speed lim i t chosen for E^g determination i n this work were those used i n other experiments. It i s obvious that the plots of AC/CQ vs. x (Fig. 2) have slight curvature, especially towards higher solute concentrations. This probably indicates the effect of rotor speed on the non-ideal behavior of the solution. The steepness of the curves i n Fig. 4 leads to a relatively high average molecular weight (M^) of ovalbumin when compared to values (about 45,000 daltons) obtained from the literature (46, 47). i t should be noted that the workable protein concentration range for UV optical system i s low when compared to Schlieren or interference systems. If the concentration range i s increased, there may be a change i n the steepness of the slope for the same plots, with resulting changes i n B L S and M^ values. The MWDs of ovalbumin and some proteins were determined by Seholte 'a linear programming technique. Results indicate that the MWDs of ovalbumin computed from one x value were very similar to one another (Fig. 6a) except for the run at 19,600 rpm where a small peak was observed after the main peak. This could be either due to experimental errors or aggregation of the monomers. However, since the same solution was run under similar experimental conditions, i t i s unlikely that aggre-gation would occur at an intermediate rotor speed and not 61. at higher and lower speeds. When correction for non-ideality was done using the estimated B^g value, the shape of the resulting MWDs remained unchanged (Fig. 6b). However, the variation among different distributions became larger and the average molecular weights and molecular weight ratios were increased considerably. (Table 9 ) . When data from a l l runs were combined for computation, the shape of the resulting MWD (Fig. 5) was significantly a l -tered, with a broadening i n the distribution, especially at the higher molecular weight range where a small shoulder can be observed following the main peak. After B^g correction, this widening effect was even more pronouned (Fig. 5 ) , and the calculated molecular weight averages and ratios were much higher than those computed from one A. (Table 9 ) , indicating greater degree of polydispersity. The broadening of the distribution could be due to the accumulation of inaccurate data from the individual runs. This inaccuracy was magnified after correction for BLg.' As pointed out by Wan (18), errors or uncertainties are introduced into the values of dC(S)/d£ or C(£)/CQ when correction for non-ideality i s made. They are further amplified when carried over to;the solution of the linear simultaneous equations (Eq. 35)• The MWDs of human 7-globulin, bovine pancreasJ ribo-nuclease and soybean trypsin inhibitor were also studied 62. by Scholte*s method. The results were satisfactory (Fig. 7 ) although only one equilibrium experiment was performed and no correction for non-ideality was made. The MWDs of two bimodal systems were determined. For ovalbumin/y-globulin mixture, MWD was f i r s t computed from one x but was found to be erratic. Data from four experiments performed at different rotor speeds were then combined and used for calculation. A bimodal distribution was obtained (Fig. 8). Correction for non-ideality was made using the B L g value of ovalbumin and the resulting MWD was much smoother with improved resolution (Fig. 8). There was a shift i n the position of the two components towards higher molecular weight range, and the quantitative ratio between the two proteins, as indicated by the area under the peaks, was also changed after correction. A mixture of ovalbumin and RNase was also analyzed. The computed MWD showed two peaks at around 10,000 and 30,000 daltons respectively (Fig. 9). After correction for non-ideality using the B^g value of ovalbumin, there was a marked shif t in the position of the peaks to 14,000 and 48,000 daltons respectively which are more reasonable values for these two proteins. After B^g correction, the relative area of the two peaks was also significantly changed to a ratio more approaching the actual amount of proteins present in the mixture. 6 3 . Attempts were also made to study the MWDs of proteins i n trimodal systems. For a mixture of ovalbumin, y-globulin and apoferritin, computation using data from two experiments led to a bimodal distribution (Fig. 1 0 ) . The f i r s t peak was at a position of about 80 , 0 0 0 daltons and the second at 4 5 0 -5 0 0 , 0 0 0 daltons. Hence, ovalbumin and 7-globulin probably emerged as one peak. Similar result was obtained for the other mixture, trypsin inhibitor/bovine serum albumin/catalase, where two peaks were again observed (Fig. 1 1 ) . However, the f i r s t peak (lower molecular weight) had a shoulder indicating the presence of two components. The position of the second peak was at a molecular weight range of 1 3 0 , - 2 1 0 , 0 0 0 daltons which was considerably lower than the value obtained from the literature ( 2 2 0 , 0 0 0 daltons) (46, 4 7 ) , f o r catalase. The results of these equilibrium experiments suggest that Seholte*s linear programming technique can be used to give satisfactory MWDs of simple unimodal protein systems without the need to perform experiments at different rotor speeds. Correction for B L S may not be required depending on the magnitude of non-ideality of individual proteins. With inaccurate experimental data, B L S correction may even produce:' poorer distributions. For more complex polymodal systems, more rotor speeds and correction for non-ideality seemr; to be required to yield smooth, well-resolved MWDs. BTC, correction i n these cases can also bring about a 64 rearrangement of peak position and relative peak height (area) to more precise values. However, since the B-^ g values of different proteins may "be variable, one has to determine the average B^g of the mixture i n order to make appropriate corrections. For a complex system containing proteins vastly different i n B L g values, the corrected U( A , £ ) value at certain radial position based on an average B^g may be considerably different from that based on the B L g of the components distributed at that position. For multimodal systems, the calculation of A and U(A,£) was based on the assumption that the partial specific volume of a l l proteins i n the mixture i s the same. This i s not an unreasonable assumption since the t i values of most proteins have been found to be similar. The next attempt i n the project was to determine the MWDs of proteins by GFC. The gel column, Sephadex G-200, was calibrated with standard proteins. The calibration curves (Fig. 12) showed a characteristic sigmoid shape and a linear relation was observed at the molecular weight range 20-150,000 daltons. However, in order to cover the range of molecular weights of the proteins under study, the non-linear portions of the calibration curves had to used. The elution patterns and corresponding MWDs of trypsin inhibitor, ovalbumin/r-globulin and ovalbumin/RNase mixtures 65 were shown i n Fig. 13-18. The results indicate that the distributions of these proteins were considerably narrower than the MWDs computed from sedimentation data. This led to a better resolution between individual components i n a multimodal system. The average molecular weights of these proteins, as computed from GFC data, were compared to those determined 1 by ultracentrifugal analysis (Table 9). For y-globulin, the two sets of values were i n good agreement. The average molecular weights of trypsin inhibitor from GFC were slightly higher than those from equilibrium experiment. For both proteins, the two methods yielded low molecular weight ratios which might imply the monodisperse character of these two proteins. For ovalbumin, the average molecular weights computed from one \ were quite similar to those estimated by GFC method but Seholte*s method yielded higher molecular weight ratios, especially after B L S correction. With an increase i n polydispersity after combining data from different experiments and correcting for non-ideality, the resulting molecular weight averages and ratios were much higher than those determined by GFC. Since RNase had a MWD beyond the range of the calibration curve, average molecular weights of this protein were unable to be obtained from GFC results. Comparing the two methods for MWD determination, the following conclusions had been derived1 66. (1) GFC has a better resolving power than Scholtemethod. Similar results were reported for organic synthetic polymers (19). (2) GFC method i s more rapid and convenient to operate, and the computation i s much simpler than linear pro-gramming which requires the aid of a d i g i t a l computer. (3) GFC requires calibration using " p u b l i s h e d values for molecular .weights of standard proteins which may not always be reliable. (4) GFC i s affected by the molecular shape of the solute, e«g»» globular and fibrous proteins have different elution behaviors. Sedimentation equilibrium method i s not affected by the shape of the molecules. (5) The fractionation range for each gel type i s limited. Hence, i t i s not possible to work on a wide MWD with GFC. For example, the mixture ovalbumin/y-globulin/ apoferritin covers a molecular weight range wider than the fractionation range of Sephadex G-200, and for ovalbumin/RNase distribution, the molecular weights at the lower region can only be estimated with some uncertainties. In contrast, equilibrium sedimentation method can handle much wider range of molecular weight. (6) For GFC, MWD i s computed directly from the elution patterns which can be different under various operation 67 conditions such as gel type (fine or super-fine), column dimensions, sample size, flow rate, solvent and temper-ature . Hence, a sample may have different MWDs under different operation conditions. Therefore, although GFC seems to be a more convenient method for MWD determination, sedimentation equilibrium would be the method of choice. However, Seholte*s technique has certain limitations which can be l i s t e d as followst (1) Data obtained from linear programming cannot be analysed s t a t i s t i c a l l y and i t i s not known how close the assumed MWD i s to the true distribution. (2) The fact that several rotor speeds have to be employed makes i t d i f f i c u l t to work on self-associating protein systems since different rotor speeds w i l l produce d i f f e r -ent MWDs. (3) Although the MWD of a mixture computed by linear program-ming can give some evaluation of the relative proportions of individual molecules present, the quantitation of these components i s unreliable. Hence, further work has to be undertaken before a more versatile and precise method can be developed for the deter-mination of MWD of proteins and other non-ideal macromolecular systems. 68 LITERATURE CITED 1. Lansing, W.D. and Kraemer, E.O. (1935)• J . Amer. Chem. Soc, 5Zi 1369. 2. Fujita, H. (1962). "Mathematical Theory of Sedimentation Analysis", Academic Press, N.Y. 3. Osterhoudt, H.W. and-Williams,-J.W. (1965). J . Phys. Chem., 6£: 1Q50. 4. Scholte, Th. G. (1968). J. Polymer Sci. Part A-2, 61 91. 5. Svedberg, T. and Nichols, J.B. (1923). J . Amer. Chem. Soc, 4£i 2910. 6. 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In* "Handbook of Biochemistry -Selected Data for Molecular Biology", Sober, H.A. and Harte, R.A. eds. CRC, Ohio. 48. Flory, P.J. (1953). "Principles of Polymer Chemistry". Cornell Univ. Press, N.Y. 49. Candau, F., Rempp, P. and Benoit, H. (1972). Macromole-cules, 31 627. 50. Archibald, W.J. (19^7). J . Phys. Colloid Chem., i i * 1204. 

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