MOLECULAR WEIGHT DISTRIBUTIONS OF

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 i n p a r t i a l f u l f i l m e n t of the requirements f o r the degree of Master of Science i n the Department of FOOD SCIENCE Faculty of A g r i c u l t u r a l Sciences We accept t h i s thesis as conforming to the required standard

THE UNIVERSITY OF BRITISH COLUMBIA September 1975

In p r e s e n t i n g t h i s

thesis

an advanced degree at

further

for

freely

of

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requirements

B r i t i s h Columbia, I agree

available

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t h a t p e r m i s s i o n for e x t e n s i v e copying o f

this

representatives. thesis for

It

financial

The

of

g a i n s h a l l not

Pood Science

U n i v e r s i t y of B r i t i s h Columbia

2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5

Date

6, Oct., 1975-

that

this

thesis or

i s understood that copying or p u b l i c a t i o n

written permission.

Department

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i.

ABSTRACT The molecular weight d i s t r i b u t i o n s (MWDs) of some proteins were determined by equilibrium u l t r a c e n t r i f u g a t i o n and g e l f i l t r a t i o n chromatography

(GPC).

A l i n e a r program-

ming technique was used to compute MWDs from equilibrium data.

The l i g h t - s c a t t e r i n g second v i r i a l c o e f f i c i e n t ( B ) LS

of one protein, ovalbumin, was determined and was used to correct f o r the non-ideal behavior of the polymers. F o r unimodal systems, good MWDs were obtained from single experiment without correction f o r non-ideality.

For more complex

systems, combination of data from several experiments performed at d i f f e r e n t rotor speeds was required to give reasonable d i s t r i b u t i o n s ; and correction f o r B

L S

brought about

further improvement i n the smoothness and accuracy of the MWDs. GFC was found to be a rapid and convenient method f o r MWD determination, having better resolving power than the l i n e a r programming technique. The advantages and l i m i t ations of these two methods were discussed.

ii

TABLE OF CONTENTS PAGE INTRODUCTION

1

THEORY

8

A.

EQUILIBRIUM SEDIMENTATION

8

1. Basic Equations

8

2. S c h o l t e ^ Method f o r Determining MWD B.

11

3. Correction f o r Non-ideality

14-

GEL FILTRATION CHROMATOGRAPHY (GFC) 1. Basic Theory 2. Determination of MWD by GFC

16 16 17

MATERIALS AND METHODS

19

A.

CHEMICALS

19

B.

ULTRACENTRIFUGATION

19

1. Instrumentation a. Centrifuge;, and o p t i c a l system b. Rotor and c e l l 2. Equilibrium U l t r a c e n t r i f u g a t i o n

19 19 21 21

GEL FILTRATION CHROMATOGRAPHY

23

C.

27

RESULTS A.

B

L S

DETERMINATION BY THE METHOD OF ALBRIGHT

AND WILLIAMS , B. SCHOLTE'S METHOD FOR MWD DETERMINATION 1. Unimodal Systems a. Ovalbumin b. Other proteins

27 27 27 27 33

iii

PAGE 2. Bimodal Systems

,

39

a. Ovalbumin/y-globulin

39

b. Ovalbumin/RNase

39

3. Trimodal Systems a. Ovalbumin/y-globulin/apoferritin

39 39

b. Trypsin inhibitor/bovine serum albumin/ catalase C.

MWD DETERMINATION BY GFC

46 46

DISCUSSION

58

LITERATURE CITED

68

iv.

LIST OF FIGURES FIGURE

PAGE

1.

Record of a UV trace from an equilibrium experiment using double-sector c e l l .

2.

Plot of A C / C

3.

Plot of (AC/xG)'

k.

P l o t of ( M ^ ) "

vs. C .

31

5.

MWD of ovalbumin by Scholte's method, with data from four A .

35

6.

MWD of ovalbumin by Scholte's method, with data from one A .

36

7.

MWD

of human y - g l o b u l i n , RNase and t r y p s i n

38

vs. A .

n

29

vs.

1

1

2k

A.

Q

30

i n h i b i t o r by Scholte's method. 8.

MWD

of ovalburain/y-globulin mixture by

kl

Scholte's method. 9.

MWD

of ovalbumin/RNase mixture by S c h o l t e ^

kj

method. 10.

MWD

of ovalbumin/y-globulin/apoferritin

kS

. mixture by Scholte's method. 11.

MWD of t r y p s i n inhibitor/bovine serum albumin/ catalase mixture by Scholte's method.

kQ

12.

C a l i b r a t i o n curve of Sephadex G-200.

k9

13.

E l u t i o n pattern of t r y p s i n i n h i b i t o r on

50

Sephadex G-200.

v.

FIGURE 14.

PAGE E l u t i o n pattern of ovalburain/V-globulin

50

mixture on Sephadex .G-200. 15.

E l u t i o n pattern of ovalbumin/RNase mixture

52

on Sephadex G-200\ 16.

MWD of t r y p s i n i n h i b i t o r , determined by GFC.

53

17.

MWD of ovalbumin/y-globulin mixture, deter-

5^

mined by GFC. 18.

MWD of ovalburain/RNase mixture, determined by GFC.

55

vii

LIST

OF

TABLES PAGE

TABLE 1.

Data f o r B^

s

determination by the method of

28

Albright and Williams. 2.

Results of B

L S

determination by the method

32

of Albright and Williams. 3.

Table f o r the calculation of MWD of ovalbumin

34

by Scholte*s method. 4.

Average molecular weights of ovalbumin calculated from MWD data.

5.

Data f o r c a l c u l a t i o n of MWD of ovalbumin/ y-globulin/mixture

,

37

40

by Scholte*s method.

6.

Data f o r c a l c u l a t i o n of MWD of ovalbumin/ RNase mixture by Scholte*s"method.

42

7.

Data f o r c a l c u l a t i o n of MWD of ovalbumin/

44

y - g l o b u l i n / a p o f e r r i t i n mixture by Scholte*s method. 8.

Data f o r c a l c u l a t i o n of MWD of t r y p s i n inhibitor/bovine serum albumin/catalaise

47

mixture by Scholte*s method. 9.

Average molecular weights and molecular weight r a t i o s of some proteins, determined from MWDs.

57

vii.

LIST OF SYMBOLS A

c e l l area,

B

second v i r i a l c o e f f i c i e n t (or

B|,

(1-VP)W /2RT 2

l i g h t - s c a t t e r i n g second v i r i a l c o e f f i c i e n t

s

C

concentration on volume-based scales (g/l)

Q

o r i g i n a l concentration of solution

C

concentration of the i - t h species concentration at the c e l l bottom CL, m concentration at the meniscus (C)^

i d e a l equilibrium concentration

d

G(s) K

i n t e g r a l d i s t r i b u t i o n function of sedimentation coefficient

a y

K

f r a c t i o n of g e l volume available to the substance

d

distribution coefficient

M

molecular weight molecular weight of the i - t h species

M

app

apparent weight average molecular weight

M

app

apparent weight average molecular weight at zero speed

M

n

true number average molecular weight true weight average molecular weight

M

true z-average molecular weight z

P

pressure

R

molar gas constant

T VV e

absolute temperature elution volume inner volume

viii.

V

o

void volume t o t a l bed volume

U(x,l) f^

C/C

o

weight f r a c t i o n of i - t h species i n an equilibrium mixture

f:(W)) normalized d i f f e r e n t i a l d i s t r i b u t i o n function of molecular weight g(s)

normalized d i f f e r e n t i a l d i s t r i b u t i o n function of sedimentation c o e f f i c i e n t

h

c e l l depth, p a r a l l e l to axis of revolution

r

r a d i a l distance from the centre of r o t a t i o n

r^

r a d i a l distance from the c e l l bottom

rm m

r a d i a l distance from the meniscus

s

sedimentation c o e f f i c i e n t

Q

l i m i t i n g sedimentation c o e f f i c i e n t

s

v

p a r t i a l s p e c i f i c volume of solute, cm-Vg

y^

a c t i v i t y c o e f f i c i e n t of the i - t h species

s

A

correction term f o r B

.

experimental errors

A

(l-v )o) (r -r )/2RT 2

P

2

L S

determination

2

b

m

chemical potential of the i - t h species t o t a l potential of the i - t h species reference (r

2 b

-r

2 :

chemical potential of the i - t h species

)/(r

2 b

-r

2 m

)

p

density of solution,

g/cm

ul

angular v e l o c i t y , radians per second

ACKNOWLEDGEMENTS

I would l i k e to express my deepest gratitude to Dr. S. Nakai f o r i n i t i a t i n g t h i s project and h i s valuable advice and encouragement throughout the course of the study, and i n the preparation of the t h e s i s . I l i k e to thank Dr. Th. G. Scholte f o r providing me the computer program used i n t h i s work.

1.

INTRODUCTION Equilibrium u l t r a c e n t r i f u g a t i o n has been considered a c l a s s i c a l method f o r determining the molecular weight of macromolecules i n s o l u t i o n . mentation-diffusion

At the establishment of s e d i -

equilibrium a f t e r prolonged r o t a t i o n at

moderate speed, the v a r i a t i o n i n concentration (or concentration gradient) along a solution column i n an ultracentrifuge c e l l can be measured o p t i c a l l y .

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 s p e c i f i c volume of the solution; p,

the density of the solv- '

ent; c, the concentration of the solution; co, the angular v e l o c i t y of the rotor and r , the r a d i a l distance from the centre of r o t a t i o n .

A p l o t of the logarithm of concentration

against the square of the r a d i a l distance

should give a

s t r a i g h t l i n e , with the slope d i r e c t l y r e l a t e d to the molecu l a r weight. High polymeric substances are mixtures of a large number of molecules which are chemically i d e n t i c a l but d i f f e r e n t i n molecular weight.

are

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 t o the f r a c t i o n a l d i s t r i b u t i o n of the component molecules over the whole range of molecular weights.

In p r i n c i p l e , the entire

molecular weight distribution(MWD) of a sample can also be determined from sedimentation equilibrium experiments. Shortly a f t e r the construction of the f i r s t

ultra-

centrifuge by Svedberg and h i s associates i n the early 1920*s (5i 6 ) , Rinde (7) developed a method f o r determining the d i s t r i b u t i o n of r a d i i of the c o l l o i d a l gold sols from equil i b r i u m data. He derived the following equationi

Here, G

Q

i s the i n i t i a l concentration of the s o l u t i o n , A and

£ are functions of the rotor speed and the r a d i a l distance respectively, and f(M) i s the d i f f e r e n t i a l MWD function. A f t e r t h i s pioneering work, many attempts have been made to solve Rinde's equation f o r f(M).

In some cases (1,

8, 9 ) , s p e c i f i c models such as the most probable d i s t r i b u t i o n were used.

Wales and h i s co-workers (10, 11, 12, 13) avoided

these models and used osmotic pressure second v i r i a l i e n t , B__, to correct f o r non-ideality.

coeffic-

Sundelbf (14), pro-

OS-

, posed a method which was based on Fourier convolution theorem.

3.

Refinements of t h i s method were reported by Provencher (15) who showed that the basic equation f o r MWD

determination

(Eq. 3) i s a Fredholm i n t e g r a l 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 l e a s t squares.

A l l these

methods were found to be unsatisfactory and experimental errors may lead to negative weight f r a c t i o n s f o r 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 d i s t r i b u t i o n of the polymeric solutes at sedimentation equilibrium i s i n the form of a Laplace transform.

He substituted a function

Making use of Eq. (10) we have M

l-V)^ r

1C

2

l (

1

a/ain

±

y i

\

The logarithm of y\ i s expressed i n power of C^ i n the form l n y

1

=

M ^B k=l i

i k

C

(18)

k +

and M. (l-i7. f>) to rQ. Z

~

fe B

ache

ik

a

r

e

i

v

e

r

v

dC.

q

dC.

= -3F' i i|»ik-3? +M

c

0 : and (3) a further constraint can be added to s p e c i f y 2^fv= i"V;: It should be noted that non-negative f ^ and the unity of 2 fy. are e s s e n t i a l features of a i

MWD.

13.

The set of f ^ obtained from the chosen set of not unique.

is

Seholte suggested the use of four molecular

x weight series spaced from each other "by a factor of 2*. Thus, =1

(36a)

=4

(36b)

(four s e r i e s ) =1

(36c)

f. (one series)

m i ^ f j L (four series) l^fjA

Eq. ( 3 6 c ) i s therefore also a solution, but w i l l give a more smooth MWD

since more points are included.

A f t e r the f ^ have been obtained, a continuous can be constructed using Seholte*s procedures. *a i f

=

1

=

j f < f

M

)

d

M

MWD

Note that

C< M

=

*

M)

A In M2 [Mf(M)] i

±

(37)

I f the i n t e r v a l between successive molecular weights i s Jr.

2*, then A In M = £ln 2 = 0 . 6 9 3 A

and

Since

^[Btf (M)]

±

= 4/0.693

%. f . (four series) = k

1 1

(39)

(Eq. 3 6 c ) , i t follows that

f ./0.693 = 4/0.693

•>l

(38)

(40)

1

Thus, [Mf ( M ) ^

= f5/0.693

(41)

Hence, the MWD curve i s constructed by p l o t t i n g Mf(M) v s . In M, and the area under the curve i s 1.

14. From the computed MWD functions, the various average molecular weights can also be calculated from the following relationsi (42) M

= f°°Mf (M)dM w

(43)

•'O

(44)

o

3» Correction f o r Non-ideality For monodisperse non-ideal

solutions at sedimentation

equilibrium, Williams and co-workers (34) derived the following i

1

equationsi "ap* = V 1

where M

a p p

app

+

(

V

2

> m (C

°b

+

)

+