Isoenzymes of tetrameric proteins

BIOPOLYMEKS VOL. 11, PP. 110-126 (1072)

Isoenzymes of Tetrameric Proteins

Cs. FAJSZI and T. KELETI, Institute of Biochemistry, Hungarian Academy of Sciences, Budapest

Synopsis

A theory is presented concerning the possible arrangements of protomers in tetrameric molecules. Isoenzymes may exist even in the case of homotetramers if the asymmetry of the identical protomers is detectable. The number of tetrahedral isoenzymes that can be isolated depends on the nature of the intersubunit bonds and on the level of the asymmetry of the protomers. Five isoenzymes can be distinguished only if two different types of protomers form tetrahedral tetramers and the asymmetry of protomers is not detectable with the method used. If the two types of protomers can bind each other by any pairs of binding sets and the asymmetry of both protomer types reaches the level of detection with the method used, we obtain 117 isoenzymes: 15 individual ones, and 51 stereoisomeric pairs.

INTRODUCTION

After the discovery of the two different types of protomers in the 5 isoenzymes of lactic dehydrogenase i t was supposed that more than 5 isoenzymes could exist only in a few special cases. The finding t,hat 15 to 20 isoenzymes were demonstrated in lactic dehydrogenase of various organs was explained either in terms of differences in the coenzyme binding of tjhe two subunit,s1S2 or in terms of genetic variations resulting in more than two different types of subunit13 or assuming two different polypeptide chains in each ~ u b u n i t . ~ ~ * ~ ~ In the last years the existence of s e ~ e n , ~ . ~ nine,6-9 fif- teen to eighteen1l0-l2 or even of forty-five isoenzymes13 has been reported in case of different enzymes.

Several theories have been presented which considered the nature of binding sets (contacting surfaces, cf. Ref. 14) of protomers in different 01igomers'~~'~ and t'he possible arrangements of protomers in tetrameric molecules. 15*16 The best known oligomeric molecule is hemoglobin, in which even the atoms cont,acting each other have been pinpointed."

In this paper we present a theoretical treatment of arrangement of protomers in tetrameric molecules and of the number of isoenzymes,* con-

* We regard as isoenzymes the enzyme forms, occurring in a single species, having identical catalytic function but differing in a t least one property.

119

@ 1972 by John Wiley & Sons, Inc.

120 FAJSZI AND KELETI

sidering the nature of possible bonds and the symmetry** of subunits. This theory accounts for the existence of more than five isoenzymes in the case of both hetcro- and homotctramcrs without making any further as- sumptions.

RESULTS

The Possible Arrangements of Protomers in Tetrameric Molecules In tetrameric molecules, theoretically, there are 6 possible arrangements

of the protomers: the tetrahedral, the plane, the cyclic, the stirrup, the triangular, and the linear structures. Table I shows the different structures, the possible interactions between the protomers, the number of isoenzymes if two different types of approximately symmetric subunits are assumed.

Table I contains the dejinit im of the different structures in terms of the number and distribution of bonds between the protomers. No further differentiation is made according to the angle of binding (which could lend, for example, stirrup form to the linear arrangement :

P ,a

etc.). Similarly, we consider only the “pure” form of the different arrangements neglecting any transitory state, which may exist if there are more than 3 contacting surfaces in each subunit.

Among the 6 arrangements shown in Table I, only the tetrahedral and the cyclic ones can be closed, i.e., in each protomer the same (or equivalent) contsbcting surfaces take part in the binding of the other protomers. We suppose that, if structurally pcrrnitted, the tetrahedron is the most probable structure for a tetrameric enzyme, since this arrangement provides the largest number of contacts between the p r o t ~ m e r s . ~ ~ In this paper we deal only with the tetrahedral arrangement, despite the fact that in the case of lactic dehydrogenase the subunits are considered to be more in a planar arrangement.20

** The subunits are arbitrarily regarded as approximately symmetric or asymmetric. In fact, i t is not reasonable to assume the existence of protein molecules (subunits) which are strictly symmetric. However, some protein molecules may have an approximate symmetry, i.e., no asymmetry can be detected in them with methods used in a given ex- periment. Obviously, the approximate symmetry of a molecule is a relative term which changes with the development of methods. I n other words, we recognize isoenzymes if the asymmetry of subunits reaches the level of detection. I n this work “approximate symmetry” means that the asymmetry is not detectable with the method used. At the same time it follows that the number of isoenaymes as presented below is the lower and upper limit if approximately symmetric or asymmetric protomers are assumed, respectively.

TETRAMERIC PROTEINS 121

TABLE I The Possible Arrangements8 of Protomers in Tetramers

Tetra- Tri- Linear hedral Plane Cyclic Stirrup angular

Number of neces- sary binding setas 2 3 2 3 3

Number of differ- ferent types of protomersb and

Number of possible isoenzymes in the case of two different types of approximately symmetric subunits 10 5 9 6 12 8

.?

their proportion 2 (I : 1) I 2(1:1) I 3(1:2:1) 2 ( 3 : 1 )

As an example, the isoenzymes arb and a2br of the plane arrangement are the following:

The protomers are regarded as different if they are in contact with different num- bers of protomers.

Structure of Tetrahedral Homotetramers

In the case of a tetrahedral tetramer as defined in Table I, each protomer must have a t least 3 binding surfaces. Tetrahedrons in which the protomers contain more than 3 binding sets will not be dealt with here.

The contacting surfaces of a given protomer may be functionally equivalent, i.e., they contain approximately the same number of hydrophobic and/ or ionic amino acids in similar arrangement. In other cases some or all of the contacting surfaces of the given protomer may be different. In both cases the contacting surfaces, as binding sets between two protomers, are complementary to each other, i.e., a hydrophobic residue in one binding set is in contact with a similar one in the other, an acidic residue is in contact with a basic one and vice versa.

Let us denote the three different contacting surfaces on a subunit by A, B, and C. Then the binding of two protomers can be described in terms of a pair of binding sets, e.g., AB means that binding set A of one protomer is in contact with binding set B of the other protomer. Analogously, a homo- tetramer can be characterized by 6 pairs of intersubunit bonds, each pair

I 22 FAJSZI AND KELETI

TABLE I1 Geomet ricnlly Possible Homotet,rahedrons Contailring Asymmetric Sirbiuiits

-

The following types of It:( lahetli~otts :trc foi~rtictl NlrInl)cr I)ctt:c:t-

i c tile I , ~ ~ ~ ~ ~ I ~ s~lc~wl l -. ~ _ _ of isn- able iso- below are possible, i i bl bS (:1 c2 c3 d l d2 d:: enzymes enzymes"

AA,BB:CC,AB,AC,BC + + + + + + + + + 9 4 AA, BB,CC, AB, AC + - - - - + - - - 2 2 AA,BB,CC,AB, BC + - - - + - - - - 2 2 AA,BB,CC, AC,BC + - - + - - - - - 2 1

AA,BB,CC, AC + - - - - - - - -

+ - - - - - - - -

AA, BB,CC,AB

AA,BB,CC, BC

AA,BH,CC

1 I

1 1 AA,BB, AB,AC,BC - - - + - - + + - 3 2 AA, CC,AB,AC,BC - - - - + - + - + 3 3

BB,CC,AB,AC,BC - - - - - + - + + 3 3 AA,BB, AC,BC - - - + - - - - - 1 1 AA, CC,AB, BC - - - - + - - - - 1 1

+ - - - 1 1 AA, AB,AC,BC - - - - - - + - - 1 I

BB, AB,AC,BC - - - - - - - + - 1 1 CC,AB,AC,BC - - - - - - - - + 1 I

AB,AC,BC - - - - - - - - - 0 0

_ - - _ - BB,CC, AB, AC

a Isoenzymes which can be isolated by the current methods (electrophoresis, chroma- Mirror images are considered to be un- tography, gel filtration, ion exchange, etc.).

resolvable.

representing the contact between two protomers. Accordingly, the following homotetramers are geometrically possible which differ from onc another in their mode of binding:

a: 12(AA), 2(BB), 2(CC) b l and b2: AA, BB, CC, AB, AC, BC (mirror images)

cl: AA, BB, 2(AC), 2(BC) c2: AA, CC, 2(AB), 2(BC) c3: BB, CC, 2(AB), 2(AC) d l : AA, AB, AC, 3(BC)

where, e.g., 2(AA) means that there are two contacts of type AA. Theoretically there are 6 possible bonds (AA, BB, CC, AB, AC, and BC)

between 3 different binding sets. If each binding set may be in contact with any other, i.e., all the 6 bonds can be formed, then the tetramers a to d3 will exist. If, for example, only 4 pairs of binding srts may be formed (only the AA, BB, AC, BC bonds are possible or only the BB, CC, AB, AC bonds, etc.), then the tetramers cl, c2, and c3 will exist, respectively, but no others. The cases when the possible tetrahedrons occur are shown in Table 11.

We can add that tetrahedron a corresponds to an isologous tetramer of Monod et al. ,I4 whereas an heterologous tetrahedral tetramer (i.e., where on& rontacts AB, AC, and BC are present) does not exist.

d2: BB, AB, BC, 3(AC) d3: CC, AC, BC, 3(AB)

TETRAMER.IC PROTEINS 123

If the subunits are approximately symmetric, i.e., the asymmetry due t,o tlic different binding scts is not detectable cithrr, w may find cxpcrimcn- tally a single rnzgme form in the case of homotc4mmcrs. However, if thc iden t id subunits :Lrc :tsymmc.tric- (gc.omc.tric.:LIly, in charge distributio~i, etc.) the riumber of isoc~nzgint~s that can bc isolatcd will be 4, 3, 2, or 1, as shown in Tablc 11. These forms will bc distinguishnble since, eg., the enzymic activity of an oljgomer having a substrate with positive charge will change depending on whether somc asymmetrically distributed nega- tive charges are directed in parallel, perpendicular, or opposite manner in the protomers. In this case the asymmetry is due to the active center. One subunit contains one active center and this endows the protomer with an inherent asymmetry. The question is, however, whether this asymmetry is reflected in the change of enzymic activity or whether it is detectable by any other mcthods.

Table I1 cnumerates the possible isocnzymes. We may also calculate the number of isocnzymcs which can be isolated by the current methods. For example b l and b2 are mirror images, so they cannot be isolated by common methods. We cannot dctcct the differences in the mode of binding either (if the asymmetry of the molecule is due only to differences in the contacting surfaces), so from the point of view of isolation ( I ) a and cl, (2) bl , b2, d l , and d2, and (3) c2 and c3 are also “mirror images” and thus inseparable from one another. Howevcr, if the subunits have, in addition, any other kind of detectable asymmetry, thc above 3 groups are distinguish- able from one another and from d3.

If the tetramers can dissociate, it is reasonable to assume that the identical (or equivalent) contacts will be broken simultaneously. * Accordingly, from a and cl, c2, c3 only dimcrs and monomers can be formed, but from bl, b2, and d l , d2, d3 trimers too. Since there is no experimental evidence for the existence of stable trimeric forms, WC may assume that the steps leading to trimers are oppressed, or the trimer dissociates very rapidly or that thermodynamically only forms a and cl, c2, c3 are probable, where at least two pairs of identical contacts function, e.g., 2(AC) and 2(RC) in c l , etc.

Structure of Tetrahedral Heterotetramers

The existence of isoenzymes is commonly explained by the presence of more than one kind of subunit. Thus 5 isoenzymes can be formed from two different kinds of subunit, a and b, from which tetramers a4, a3b, aZb2, abo, and bq can be built up. The two subunits may differ chemically but they may only be conformers of each other. Similarly, the existence of 15 isoenzymes can be explained by assuming 3 different subunits and accordingly,

* This assumption implies that the breakage of one bond does not affect the others in the same tetramer. If this is not the case, interactions exist between the subunits. However, in this paper we do not deal with allosteric enzymes or with enzymes whoye asymmetry is due to a regulatory center.

TA

BL

E I11

Poss

ible

Iso

enzy

mes

of

Het

erot

etra

hedr

ons

Num

ber

of iso

- a

b Po

ssib

le b

onds

a4

ah

at

bz

aba

br

enzy

mes

Subu

nit

Sym

met

ric

or

Sym

met

ric

or

AA

,BB

,CC

, 1

1

3b

1

1

7 q

c as

ymm

etri

c as

ymm

etri

c D

D,E

E,F

F,

m

AD

,BE

,CF

E

Sym

met

ric

Sym

met

ric

all b

onds

are

pos

sibl

e 1

1

1

1

1

5 Sy

mm

etric

8 as

ymm

etri

c al

l bon

ds a

re p

ossi

ble

1 1

2 3

3 10

Asy

mm

etric

. A

sym

met

ric

all b

onds

are

pos

sibl

e 3

3 3

3 3

1 3

+9

x2

R

h

+.il

X 2

F

-

rn

+2

X2

+

4X

2

+3

X2

+3

x2

+

12

x2

+

21

x2

+

12

x2

+

3x

2

8 T

he n

otat

ion

2 3

+a

x2

m

eans

tha

t the

re a

re 3

sin

gle

isoe

nzym

es a

nd 3

ste

reoi

som

eric

pai

rs.

Thi

s do

es n

ot n

eces

saril

y m

ean

that

the

re a

re 6

iso

enzy

mes

tha

t ca

n be

iso

- la

ted,

sin

ce, e

.g.,

in t

he c

ase

of a4

and

br, o

nly

4 is

oenz

ymes

are

det

ecta

ble

(cf.

the

sect

ion

on S

truc

ture

of

Tet

,rah

edra

l Kom

otet

ram

ers

and

Tab

le 1

1).

If on

e of

the

subu

nits

is a

sym

met

,ric

ther

e ar

e 2

dete

ctab

le

isoe

nzym

es (

1 +

1 X

2) a

nd w

e ha

ve 3

det

ecta

ble

isoe

nzym

es if

bot

h su

buni

ts a

re a

sym

met

ric.

If

both

sub

units

are

app

roxi

mat

ely

sym

met

ric,

the

isoe

nzym

es o

f az

b2 a

re u

nres

olva

ble.

TETRAMERIC PROTEINS 125

if there are k different types of subunit the number of possible tetramers in the general case (when no restrictions are made) will be:

However, we may have more than 5 isoenzymes from two different typcs of subunit in certain cases. Let us denote the binding sets of protomer a with A, B, and C and those of protomer b with D, E, and F. The number of possible contacts between identical and different protomers is too high and therefore we will consider only two extreme cases.

(a) Two protomers of type a or type b can be connected only by identical binding sets (i.e., AA, BB, and CC, or DD, EE, and FF, respectively), whereas protomers of type a and b can be connected only by the correspond- ing contacting surfaces (AD, BE, and FC). In this case tetramers a4, aQb, ab3, and bd can be built up in a single way, whereas azbz can be built up in 3 different ways, due to the intrinsic asymmetry of the contacting surfaces. If both subunits a and b are approximately symmetric, the isoenzymes of azbz cannot be isolated; howvcr, there arc two or three isoenzymes that can be isolated if the asymmetry of either or both of the subunits is detectable, respectively (Table 111).

(b) Two protomers, whether different or identical, can be connected by any pairs of binding sets. If the asymmetry of one of the two different subunits is detectable we can isolate 19 isoenzymes (10 individual ones and 9 stereoisomeric pairs). If the asymmetry of both subunits is detectable we obtain 66 isoenzymes, 15 individual oues and 51 stereoisomeric pairs, the latter not being separable by the methods known so far (Table 111).

Five isoenzymes can be isolated i f two diflerent protomers f o r m tetrahedra1 tetramers and the asymmetry of subunits i s not detectable by the method used.

Mr. I. Simon and Dr. L. Polg6.r are gratefully acknowledged for the very valuable criticism and suggestions during the preparation of the manuscript.

References

1. P. J. Fritz and K. B. Jacobson, Science, 140,64 (1963). 2. P. J. Fritz and K. B. Jacobson, Biochem., 4, 282 (1965). 3. J. H. Wilkinson, Isoenzymes, E. and F. N. Spon Ltd., London, 1965. 4. D. A. Thurman, C. Palin, and M. V. Laycock, Nature, 207, 193 (1965). 6. B. hlooreland and I). C. Watts, Nature, 215, 1092 (1967). 6. E. Goldberg, Science, 151, 1091 (1966). 7. C. L. Markert and I . Faulhaber, J. Exptl. Zool., 159,319 (1963). 8. C. L. Markert and W. J. L. Sladen, Nature, 210,948 ,(19,66). 9. R. Pietrusnko, 13. J. Itingold, T. K. Li, B. I,. Vallee, A. Akeson, and H. Theorell,

Nature, 221, 440 (1969). 10. P. W. Hochachka, Conip. Biocheni. Physiol., 18, 261 (1966). 11. A. L. Koen, Biochem. Biophys. Acta, 140,487, 496 (1967). 12. M. Valenta, J. Hyldgaard-Jensen, and J . AIonstgaard, Nature, 216, 506 (1967). 13. A. P. Kraus, and C. L. Neely, Jr., Science, 145, 595 (1964). 14. J. Xlonod, J. Wyman, and J. P. Changeux, J. MoZ. Biol., 12, 88 (1965).

126 FAJSZI AND KELETI

15. I. M. Klotz, N. R. Langerman, and D. W. Darnall, Ann. Reu. Biochem., 39, 25

16. D. E. Koshland, Jr., G. NBrnethy, and D. Filrner, Biochem., 5,365 (1966). 17. M. F. Perutz, H. Muirhead, J. M. Cox, and L. C. G. Goaman, Nature, 219, 131

18. R. Stambaugh and J. Buckley, J . Biol. Chem., 242,4033 (1967). 19. D. B. Millar, V. Frattali, and G. E. Willick, Bwchem., 8 , 2416 (1969). 30. hf. J. Adams, D. J. Haas, B. A. Jeffery, A. McPherson, Jr., H. L. Mermall, M. G.

Rossmann, R. W. Schevitz, and A. J. Wonacott, J . Mol. Bwl., 41, 159 (1969).

(1970).

(1967).

Received March 12, 1971 Revised June 1, 1971

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Isoenzymes of tetrameric proteins