Pure & Appi. Chem., Vol. 51, pp. 1409-4420.Pergamon Press Ltd. 1979. Printed in Great Britain.

THERMODYNAMICS AND KINETICS OF THE INTERACTION OF SYNThETIC• AND SEMI—SYNThETIC POLYMERS WiTH ENZYMES DURINU THEIR iO

BILIZAT1ON AND MODiFICATION

G.V.Sawsonov, R .B.Ponomareva and A.T.Melenevsky

institute of Maoromolecular Uompounds, Academy of Sciences ofthe USSR, Leningrad, USSR

Abstract — The interaction of enzymes and polyelectrolytesleads to modification of the enzymes, changing not only their

catalytioal properties but also their stability. Garboxylic

heterogenic exchangers "Biooarb" were synthesized from metha—

crylic acid and hexahydro—l,3,5—triaoryloyltriazine. Proteins

are sorbed on these exchangers with high selectivity and good

kinetics (diffusion coefficient B LO 10 cm2.seo ).

The sorption of QL—amyiass on Bioearb leads to its acid sta-

bilization. Urease is sorbed on Biocarb with gieat capacity

and on covalent immobilization completely retains its activi-

ty after repeated use in the conditions of a flow reactor.

A ohromatographic method for determination of the equili-

brium and kinetic constants of interaction between enzymes

and soluble polyelectrolytes was developed. The kinetic con-

stants of the formation (k1 (84)IO seo) and dissociati-on (k1= (42)io' sec) of the KNase—dextran=sulfate comp-lex were determined. The thermodynamic analysis of the inter-

action showed that the inhibition of the enzyme in the coup—

lex is characterized by high energy intermolecular interacti-

on and low specificity, whereas the activation of the enzyme

is a more specific process accompanied by an increase in en-

tropy.

The immobilization or modification of enzymes by synthetic poly-

mers, in particular by polyelectrolytes, can be carried out either in the

solid phase, or swollen gel or in the solution. Urosslinked polyelectroltes are used in the former case, while linear or branched polyelectrolytes

in the latter. Ths immobilized or modified enzymes acquire new properties,e.g. an increasing stability of th structure, resistance to inhibitors and

some times higher activity. Although the modifoation of enzymes by crosi—

linked and soluble polyelectrolytes gives different new fOrms (insoluble or

soluble), they still have many properties in common.

To immobilize enzymes, Only those crosslinked polyslectrolytes should bs

used which do not cause structural deformation of the sorbed macromolecules

and exhibit high sorption capacity with respect to enzymes. New oarboxylio

biosorbents Biocarb5 (1) satisfy these requirements. They are obtained bythe copolymerization of aethacrylic acid (MAA) with h.xabydro—l,3,5-'triaory—

1409

1410 G. V. SANSONOV, R. B. PONOMAREVA and A.. T. MELENEVSKY

loyltriazine (T) in low concentration acetic acid solutions containing large

amount of the trivinyl component. These highly permeable ion exchangers ex-

hibit a stable steno structure and their catalytic effect on enzymes is neg—

ligible; they iomobilze native macromolecules in the voids filled with the

solveut. The structure of the networks of macroreticular carboxylic MDM ca-

tion exchangers (copolymers of M&A and N, ' alkylene dimethacrylamides) isslightly less rigid. We mean by a macroreticular exchanger the exchangers,

whose structure contains orosslinking agents with remotely spaced vinyl

groups. Their synthesis is carried out in the presence of a good solvent.

Biosorbente of the Biocarb type exhibit little change in the degree of swell-

ing during titration (Fig.l). The most rigid network structure is aisplayed

8

60)

01 4>0

2

I0I.r8Ca)C.)

a)0C-)

(I) 2C—I 2 345 678Crosslinking agent, mole %

Fig.l. Swelling coefficients

Xsw (g H20/g of dry sorbent)of oarboxylio cation exohang-'

ers Biooarb (1 and 1'), KMDU—2(2 and 2') and IMDM-6 (3 and3'); Hfora (1,2,3) and H±Naform (l',2',3').

by the Biocarb cation exchangers containing a large percentage (6—7 aols) of* orosslinking agent and by macroretioular cation exchangers containing aethy"

lone dimethaorylaaide. The thermodynamic mobility 01 crasslinked structures

can be followed by potentiometnic titration of copolymer micrograms (l—5,,Q.m)obtained by dispersing the crosslinked polyelectrolyt•s. in this cams the ki-netic difficulties of the titration are eliminated. The sobility of oligomerslocated between the knots can be observed froni the conformational transition

characteristic of polymethacrylic acId (Puu) for which, in contrast to poly-'

acrylic acid (PA&) the hydrophobic internal interaction decreases when the

ionization rate increases (2). This is shown by the plateau region on the tit-ration curve (Fig.2). The comparison of the aobilty of oligomer chains shows

\

f x\ \ X.\ \\ \. \'.40+I0.

a

Fig.2. Potentiometnic tit-'

ration of Biooarb (1) and

ktIM—2 (2) polyelectroly—tes.

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cpeuss expip peeLoeu•orie boLo8T; bLoçspJe BL• qe;LTpnQq lu zjie.PTUCS BT0C9LP PTOB0LP.*8 euq O9LPOXt7G 171J7 0VOU 92

BTOCVLP

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iT' c'.o'.bpe 0 çpe BTOCLP Ttt' Maf14pr!ou ot AOL—

10 1000

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qnoeq ouq pe eabTe *08 poqeueq oL *O gBR 01 °o BCO4US 1*01

p e;pvuoj ouq elpeL• v.i. 4pe vu eboxqe OOmbORTTOIIb 1*08 puLO-LeR• yoL wa bn'.boae flJe *B4CL 711 RAOflOU ROLPCUIR 1408 8riCCd88TAST Leb700.q1091 1P R7C O Je LSOIJR O vuq 70* dU97 O OL088J1JG RlLffClfl—CRLp pJoeoLpeu4,P L01JO LO1 $0 0 7 RIOCILOD m7CL0L0bp 78 r!8dT 10 •A0.11077 0IJJe X.4.B 8C044OL71I RpOMd( 494 41d L9(ITT O L047OD tOL 4JS flO-.oug 7014 qeu1T4 MØ TUAGR47047O0 0 4J16 boLoR74) O BAO77eU boj)weLe ppoov'.p PTOROLP9IJ9 OLd pe4eL0eUeorT8 W94Y6L7078 CO049TU71Jf LSTOU8 MI,!I T1PØLGAft 1LB4dL p pornq MS4SLgnc;ou o; 7008 u çpe excpvneL jea o boI.47v7 '.ebjciceiieuç ot pe

vj b'.eaen'.e O AB4dL ABbOfiLR OLd AdL qie'.eu 1JT79 8110148 1T1 476 7041.0—

;pe ewonua o aopeq *ve'. MeLdVB pe CrlI.Ad0 oL ,*v,eL RoLb4,7011 AdLBfJ8 be'....

epo*eq *IJBI 1116 8Ad7771J 0 flTdTL -— vuq 404.40LW8 91.9 OOTIJbOLBp7e 08 L90L8

4700 O 1116 *4146 0 AB4eL 70 4JJC fl7oCOL XCT19D9L8 p pe 780b798ç70 meioq0047011 O1 4P6 ROLp6( SUIXICI BJJq 40 C0IJ876LBP79 71J0C47A04YO0' T6 70AG84T0-411 10P77T* O tIICTL UA4*OLJ( 78 LdB1 *PTC 76(T1 0 7LL9ASLR7p7S 7W10p77Tbe'.iiepje LOL UJ9CL01D07OtflJC8 OUJ) 14 01077 OWOflIJ41 0 *119 CLO8*TT1J1T1Jf V9U*411111 IBCLOLA4?701170L •XO0IJCLR OL I3T009LP 8OLpdIJ4 COInUIALCTST dXC11vU*9Ll 11.9

.L1 0p40700q 1474p q7A71Jt7p6IJoeu6 18 0 CL0R07TU1T1J 161J4 01.9 7988 99C4TA6

•X00UdL ()• 74 *ponq pe UO4d *1101 flOIUIN9LCTI7 C9LPOXTT0 C14700 ecpvu

pv; pe BIOCOLP IOLPGD* 70 1110)1 101.6 *PBU 4)10 WOCLOLO47CIT7OL 014100

iucrou ot JJIJJEcTC uq 2GWT— UJJO1TG boj?w50L2

a,

C,

>.Ua0UC04-0.0

U)

Fig.6. Differential enthalpies (A) and

sorption isotheras (B) of. baenioglobinfor k)M—2 (1) and nADM—2 (11) exchang-ers, a is sorption capacity, ilg. ueqis equilibrium concentration of protein

in solution.

Protein MM Sorbent

Aver age

sorbentgrain,

1)

2 —1om • sea

—--Terri]ytin(protease)

Lysosyrne

26,000

17,500

Biooarb

Biocarb

urn360

600

7.A00

6.o'9Serum alburnine 68,000 Biocarb 450 2.100o(,—aaylase

(Baa. subt.) 40,ooo 1c&WM 360

1412 C. V. SANSONOV, R. B. PONOMAREVA and A. T. MELENEVSKY

cooled. Their aicrosections were dyed with Amidosohwarz, The degree of prote-in penetration into Biooarb grain depends on the molecular mass (MM) of the

biopolymer, its morphology and electroohemical properties of its macromolecu-

les as well as on the pM of the solution. Thus, for cytochrome G the penetra'-

tion depth of macromolecules was half of the grain radius and for haeaoglobin

the protein distribution was uniform. The dispersion of the Biocarb biosor—bents to the size of several microns makes it possible to carry out uniformsorption of very great amounts of protein throughout the grain Fig.5 shows

that the amount of bound serum albumin is 5 g per gram of sorbent. Thus, a

gel microcapsule is formed, which consists of a network filled with the pro-

tein and the solvent; the weight fraction of the copolymer is only 20.

0)0E

0UI1

Na+_ concentration, mgequiv/mt.

m

Fig.5. Serption ca-

pacities, a (ilg),of KMDM—2 cationexchanger for serum

albumin. Grain dia-meter: I , 100pm;2,

.L—5p.m./

The linear dependence of the extent of the protein sorption on the square

root of time permits the calculation of the df fusion coefficient D(Table 1)

from the law of diffusion into the sphere taking into account the relative

radius of unsorbing grain.Table 1

Protein diffusion into sorbents.

Interaction of synthetic and semi—synthetic polymers 1413

Investigation of the temperature dependence of the initial linear parts ofsorption isotherms permits the calculation of the sorption enthalpy from the

•quation of isobars, wich in combination with the thermodynic potentialgives the entropy of interaction. Data in Table 2 show that the entropy is

the main reason for the selective sorption of protein. by Biocarb. Apart from

the hydrophobic interaction, other mechanisms also determine the increase in

the entropy during sorption. The impossibility of interpreting all the sorp-

tion phenomena from the hydrophobic properties was shown by an increase in

the positive entropy on passing to aqueous—alcohol solutions. We advance an

alternative conception of polyfunctional interaction (4), wich is based on

the sorption model of organic ions capable of forming both electrovalent and

weak bonds with the sorben;. This gives rise to a set of aicrostates of the

sorbent—organic counterion system or to increasing entropy in sorption. In

some cases the increased entropy can be accounted for by the degradation of

associates when the protein passes from solution into the sorbent.

Analysis of differential functions of sorption can be made by microcalori—

aetry. Differential enthalpies of sorption and isothersas of haemoglobin sorp-tion on macroreticular sorbents MDU—2 and AADM-2 (in the latter liLA is re—

replaced by AA) shown in Pig.6 indicate that positive IL and S correspond

to the cooperative effect of sorption on the first sorbent whereas the sta-

tistical sorption corresponding to the Langmuir isotherm is revealed by the

usual decrease in enthalpy.

Table 2

Thermodynamic functions of protein sorption by Biocarb (25°)

Protein(enzyme)

GkcaVmole

4Hkoal/mole

4Skcal/aole.de—

gree —

Bibonucleass —3.5 —2.0 + 4.4

Terrilytin —5.5 0 + 17

Thermolysine —5.4 —12.9 — 24

PepsIn —4.5 *4.9 +32Serum albumin(bovine)

— 4.0 + 5.4'

32

insulin — 5.3 — 4.4 +. 5.0

Persumably, the cooperative effect favours the polyfuntionality and increas-es the number of microstates of the protein—sorbent system. The competing se-

lectivity of protein sorption by biosorbents is extremely high and depends onthe volume oncentration of uarboxylio groups in the sorbent. 1ig.7 shows

that the selectivity coefficient of proteins in crosslinked copolymers inclu-

ding liLA, P and hydroxypropyl methacrylamide (liPliat) increases on passing to

Biocarb from the eopolymers that contain a lower amount of carboxylic groupsbut exhibit high hydrophilic properties and high permeability for macromole-

cules. Fig.8 shows the pH dependence of he selectivity of insulin sorption

by Biocarb and a uroeslinked copolymer of MAA and iiIMA (M—3o). Biocarbsorbs a much greater quantity of insulin than does M—30.

The i*anobilization of enzymes by Biooarb was carried out for two purposes:to stabilize enzymes, in particular with respect to acid denaturation, and to

1414 C. V. SAMSONOV, R. B. PONOMAREVA and A. T. MELENEVSKY

prepare an insoluble term of enzyme suitable for pz'o1oned perlorniance. Thi

first approach .&8 of eonsiderable interest, especially, for the o1ution ot a

medical problem; the preparation of a modified form of hydrolytic enzyme ca-pable of passing through the stomach without inactivation, it is alio nece-ssary to prepare a modified enzyme form that would be uapable of catalyzingthe hydrolysis of macromolesular substrates in tue intestine. Both the stabi-lization and tue maintenance of the oatalytic activity of enzymes to mauroiso—

0

Fig.7. Selectivity coefficient

lof protein sorption vs N—vs—lame concentration of carboxy—lic groups in the copolymers ofMAA—IIPMA containing I, 30; 11,50; III, 75 and IV, ioo% MAA.

(0) pepsin; (Lt) ohymotrypsi—nogene, ( • ) papain.

lecular substrates were achieved for cL—amylase and terrilytin proteass on

the basis of enzyme sorption by Biocarb. The stabilization of Biooarb—sorbed

,(,—amylase (p11 5.5), isolated from the ac..subtil. culture liquid, was in-vestigated by incubation of the sorption complex in 0.1 N solution of hydro-

chloric acid at 25 and 37°V (5). After the incubation, o(,—amylase was deaorb—ed by a 0.4 N borate buffer solution at p11 7.5, in which the activity to so-

luble starch was determined. A comparison of the degree of acid inactivation

of free o—amylaae and the polymer sorption complex is shown in Pig.9. 0(—amylase is completely inactivated in a few minutes, whereas the amylolytic ac-tivity in the complex decreases by 50% for about an hour. The inactivation ofsorbed amylase depends on several parameters, including the amount of boundenzyme. When an edditional amounts of —amylaee is introduced into Rio'carb, the degree of stabilization decreases. This phenomenon may be accountedfor by the cooperative mechanism of interaction between the enzyme and the sor—bent, which is revealed in the S—shaped sorption isotherm. .Ln this case thecooperative interaction leads to destabilization of polyeleotrolyte—bound en-

zyme, like in the case stabilization by soluble polyelectro]ytes to be consi-dered below. The acid-resistant polymer complex of oc-amylase is dissociated

at p11 6.5 (Fig.lo) and the active enzyme passes into solution. Acid stabili-

zation is also observed when the terrilytin is sorbed by Biocarb.

The belective interaction of Biocarb with enzymes retains their native

-0.3

log N

Fig.8. Selectivity coeffici-ent, K,, of insulin sorptionby Biocarb (I) and MM—30 (2)from 0,1 N buffer solutionsvs p11.

Literaction of synthetic and semi—synthetic polymers 1415

structure, which permits to prepare reversibly dissociating insoluble comple-xes and to immobilize the enzyme on the sorbent by covalent bonding. This

too

4->•1-C)0

50

0

-20 40 60

Time, minutes

Fig.9. inactivation of d—amy— Fig.l0. Dissiciation of thelase (3) and its sorption corn— sorbed complex o,—amylaae —

plexea with Biocarb (1 and 2) Biocarb. N is the portion of

at pH2.0 enzyme in sorbed state.1, 2400 act. units/g, 2, 10000

act. units/g.approach is bimilar to the incorporation of enzymes into gels in the cross—linking polymerization in the enzyme solution. however, the sorption method

followed by chemical immobilization on highly permeable Biocarb sorbent with

very stable structure permits the Immobilization of greater amounts of enzyme

per unit volurn of the swollen copolyrner and also favours substrate diffusion

to the enzyme. The immobilization of urease on Biocarb was carried out by its

sorption from solution and chemical immobilization in the presence of a 0.3J4solution of glutaric aldehyde (6). The sorption capacity of Biocarb for urea—

seg*'eatly depends on the ph of the solution and reaches a maximum at the

isoelectricpoint of the enzyme (Fig.ll). Lirease tompletely retains its acti—Vity on Immobilization. The activity of the immobilized urease with respectto urea was studied in a column under dynamic conditions (1'ig.L2). Stationary

Fig.lI. Urease sorption byBiocarb (0) and its acti—ity after ohómioal immo-bilization (A) vs ph ofsolution.

Volume, ml

Fig.L2. hydrolytic cycles of 3urea in column 0.7 x 0.8 cm with

immobilized ureaae, ph 7.0,25 m]/br.

1416 G. V. SANSONOV, R. B. PONOMAREVA and A. T. MELENEVSKY

conditions were attained in iO—30 mm. tfter the process was finished andthe column was washed with a buffer solution, the dynamic cycle o enzymaticactivity was made repeatedly, which indicates a long—term use o the lisisobi—

lized urease in the column process.

The interaction of enzymes with oluble synthetic and natural polymer

electrolytes opens up new possibilities to modify the properties of biocata—lysts. nzymes in soluble polymer complexes can be stabilized and even acti-vated (4). it becomes possible also o inhib.t the enzymes by soluble poly—electrolytes and to uhange their enzymatic specificity. Finally, soluble po-lymeric complexes can interact readily with substrates of high molecular mass.it should be noted that thrombi dissolve faster under the action of trypsin—polyvinylimidazole (pYl) complex (7) than due to trypsin alone. Nucleases areactivated or inhibited by dextran—sulphates (DS) and changs their specificity.Fig.13 shows that the introduction of bS into the hNase solution can increaseor decrease the transf erase activity, but the hydrolytic activity is low in

all cases. As a rule, the modification of enzymes by synthetic or natural p0—

lyelectrolytes is a result of the action of the polymer—carrier on the enzymemacromolecular structure. The stabilization of trypsin is carried on by WI

but not by its analogues of low molecular mass (Fig.14). The polymer effect

>% >.4- 4-

•4 4-U Uo 0a) a)>

4-.9 0a) a)a: a:

100-

50 -

4 6 pH pHI 2

Time, hours

Fig.13. Transferase (A)

and hydrolytic (B) activa—

ties of pancreatic RNaae

and its complexes with L)S.

I, ENase; 2,RNase — DS

.(MM6500o, nu.8); 3.ILNase — DS (iIM 500000,n

Fig.14. 4utolysis oX trypsin (I)

and its complexes with imidazo].

(2), poly—N—ethylimidazol (3) and

poly'N'—vinylimidazol (4), ph 6.i,rOdl .

consists in the polyfunotional interaction of synthetic polyelectrolyte andis revealed in the fixation of the enzyme native conformation in case of sta-bilization or its disterbanee in the .aae of inhibition. uantitative methodsfor the estimation and analysis of thermodynamic and kinetic constants ofoomplexation should be used to determine the mechanism of molecular coaplexe

formation in polymer systems. The equilibrium characteristics of the formati-

on of polymer complexes in solution are usually determined by dynamic me-thods, such as sedimentation, chromatography (9) along with other physical

a is degree of substitution, number of ulfate groups per monomer unit.

. Interaction of synthetic and semi—synthetic polymers 1417

and physico-cheaical methods (iO). The ohromatographio diutlon ana1yis OX

the polymer complex against the background of constant concentration of one

of the components, e.g. synthetic polymer electrolyte (Ii), is a suitableapproach to the solution of these problems. The simplest problem is the chro—

matogi'aphic analysis of the system of reversible complexation when one enzyme

molecule ( .) interacts with synthetic polyelectrolyte (F):

I 1 P = IF (i)

If component concentrations C>> C, it is possible to introduce the insta-

bility constant of the polymer complex in the IoTa:

=

The analysis of the chromatographic problem has shown that under conditions

of equilibrium chromatography the elution curve for the protein is oliaracte—

rize4 by one maximum, although both the protein and its polymer complex co-

exist in the solution. This phenomenon is associated with quasi—equilibrium

and occurs at law rates of solution flow. the analysis of the chrumatographic

process of reversibly dissociating oystem migration under the constancy of

coefficients for the distribution of substances between the mobile and the

stationary phases (ii) leads to the following expression for the constants

of the complex instability:

(vu— v') / (V1 —v5)

where V' is the elution volume of the complex for the protein at the unimodal

shape of the tlution curve.V1

is the elution volume of protein obtained in

an independent experiment with only one component, and V is the elution

volume of the etable complex. The value of V1 can be determined, for examp-

le, in a gel chromatographic experiment when the complex moves without pene-

trating the porous gel structure and is cluted with the free volume of the

column. The calculation of the instability constant for a polymer complex of

pancreatic ENaae — DS (MM 500 000, sulphur content I6) at the US/ItNaseweight £atio of & : 2 according o eq. (3) yields the value of 5.I02. Thedissociation constants for the complexation of ItNase with copolymers of vinyl

sulpbonate and vinyl pyrrolidone are shown in F3g.15.

Fig.a5. Dissociation con-

stants of the complexes

RNase—compolyiners of vinylpyrrolidone and vinyl sul—

phonate (vs). 1, i8VS;2, 27% VS;. 3, 50% VS.

0.1 0.2 0.3 0.4

Na+_concentration, N

The thermodynamic analysis of the interaction of kNase with US of differentmolecular masses was carried out for he initial (linear)parts of th.e iso—therms describing the ratio of bound RNaae to free RNase. Data in Table 3

4-.CC)

a,00C00C)0(I)Inb

2

I —

I—.

0.6

1418 G. V. SANSONOV, R. B. PONONAREVA and A. T. NELENEVSKY

show that the inhibition of the enzyme uOee n at all mean that the interac-

tion between the tnzyme and the polymer—carrier is very specific, since the

thermodynamic potential of complexation is not very great. kiowever, in this

process the enthalpy decreases, i.e., the intermolecular interaction energy

is high. in contrast, the complexation with activation is a highly specific

process accompanied by a greater decrease in the thermodynamic potential. Tile

increase in entropy is a still more interesting feature of this process,which

can be interpreted as the appeareance of a set of microstates of the bound

enzyme owing to the polyfunctional nature of intermolecular interaction. Asystem of weak bonds with the energy close to that of the thermal motion

leads to the coexistence of a whole set of states differing in the levels of

interaction energies. Table 3

Thermodynamic functions of the formation of polymer complexes

of ribonuolease

Polymer

Jiextran—

MM.i0' Deflreeofub—stitu—tion, n

ionicstrength

-

AGcal,!mole

4HCal,'mole

AScal,'mole

degree

sulphate 500 1.4 u.C56 —400 -6QOt) —2u

Dextran—

sulphate 500

.

1.4 0.316 —500 —4o00 —11

Dextran—sulphate

c60 0.8 o.o56 —1100 t25oo i-l3

Suiphoethyl . : :

cellulose 150 0.45 0.u56 —1500 i2øOO -t12

We determined the kinetic constants of the formation and aissociation of com-

plexes by using chromatographi* analysis of the systems with rapidly eatab—lished quilibrium between the mobileand the stationary phases for allthree interacting components (g, i, iip). in contrast to the chromatographic

procss uescribed above, here we consider a system in which the cquilibriumin the process of complexation itself is absent. This problem is solved (12)

for the elution chromatographic process of the movement of a narrow zone of

interacting components.

in this case the equation of material balance can be represented by a system

of equations for all three components:

iç (1 JCL =..U 1 1-f1 k.1 ) (4)

where =k1Cgp

— k1 CECp, fg = f — fpx is the coordinate corresponding to the distance from the upper layer of the

sorbent, t is the time, are the concentrations of components, k is therate constant of complexation, k.1 is the rate constant of the reverse re-

action, o( s the relative porosity of the column and is the coefficient

of substance distribution between the phases. The initial1and boundary condi-

tions were determined as follows:

fconst (0<x x )C1 (x,O)

0 ( z> c (o,t) 0 (t > (5)is th.. height of the zone at the column inlet.

Interaction of synthetic and semi—synthetic polymers 1419

The numerical solution of this problem leads to a system of cbromatograms

shown in Fig.&6. it can be seen that as the elution rate of the solution in-

creases, the height and the area of the first maximum corresponding to the

complex zone also increase. For any selected rate pair we introduce the func-

tion: i ii ii= (.c / CU ) / (c / CU ) (6)1 1 2 2

where CL is the maximum concentration of protein in the zirst zone (L) andi Uis its maximum concentration in the second zone (II) at the ulution

rates of the solution U (U1 and U2), The numerical calculation makes it poe—Bible to plot a family of curves f va.—log k1 (Fig.7) giving the values of

and the pairs of elution rates U1 and U2.

This method of evaluation of kinetic constants was used to btudy the ratus of

the formation and dissociation of he polymer complex in the interaction of

pancreatic RNase and DS. The ehromatogx'apbic process was carried out on a

column (I x 90 cm) packed with Sepharose. A 0.05 M phosphate buffer at p11 7.4

0

C

I(p

Elution volume, V

Figa6. Theoretical elution Fig.17. Plots of j vs.—logk,.,1

curves for a two—component re— (a) U1 i8 al/br, U2= 36 mI/bracting bystea at -l 5.10. (b) U = 9 mI/br, U i8 al/br;(a) U4 .5 al/br; (b) U9 al/br; (o) u— 4 •s al/br, U 9 mI/br.(o) U= 18 mI/br; (d) u36 mI/hr. 1 2

was used. icach of he ueaponents gave a symmetrical elution uurve. For liNase

96 ml, for DS V, 57 ml. in the complexation experiment the molar ratioof DS to RNaee was I : 8. The elution curves are shown in Fig.l8. The calcu-

lated values of P for chromatograma (1), (2) and (2), (3) wereY'1,2 =0.77

and P2.3 = 0.68. This permitted the determination of the formation and disso-

ciation constants from the theoretical curves in Fig.L7. For this system

K,.,1 = (4+2).1o seo' and k1 (8+4).io' sec'1 These data show that the

4iomplexation time of liNase with US is eeveral hours. Presumably, the probabi-

lity of the formation and dissociation of the complex is limited by thestrict bteric complementarity between the polymer omponeuts and by the •iP.A.A.C. 51/7—c

-tog k_1

1420 G. V. SANSONOV, R. B. PONOMAREVA and A. T. MELENEVSKY

: pJk°40 80 120

C' 40 80 120 Fig.18. lution curvesc C for the reacting system

.2 RNase—dextran—sulyhate

0.8 • (ns) (M&& 60000, n 0.8).(a) U4.5 4/hr,

0.4 (b) U 9 ml/hr;I I I (c) U181/br.40 80 20

Elution volume, m

multaneous break of several Intermolecular bonds during dissooiati-on.

Acknowledgement: The authors are greatly indebted to N.V.Glazova, 0.V.Orli—

evekaya, L.A.Shataeva, NJ .1uznetsova, N .N .1uznetsova, 0 .A .Pisarev, V .S ,Yurohenko and R.N,Miahaeva for their contribution to this work.

ReferencesI • N,NJuznetsova, At.M.Uozltetskaya, 1.B.Moskviokiev, L..Shataeva, A .A.Selez—

neva, .M.0gorodnikova and G.V.Samsonov, Vysokomol.Soedin. Ser. L8A, 355,(1976).

2. T.N.Nekraaova, .V.Anutrieva, A.M.Ilyaskievich and O.B.Ptitsyn, Yysokomo1Soedin. 1' 913 (1965).

3 • N,P.10znetsova, R .N.Mishaeva, L.R.tiudkin, N.N.huznetsova, 1.M4tozhetskaya,T.D.Muravieva and G.V.Samsonov, Vysokomol, Soedin. ser. 20 A 629 (1978).

4. G.V.Samsonov. Pure and Applied Chem., , .51 (1974).

5. G.P.Lvanova, 0.A.Mirgorodskaya, B.V.Moskvichev and (a.V.Samsonov, kriklad"nays biokhimiya and mikrobiologiya., 886 (i976).

6. 0.V.Orlievskaya, .N.Morozova, It.13.Ponomareva and Ii.V.Samaonov, Aollo1d., 1182 (1976).

7. .V.1oltsova, G.V.Samsonov, G.U.Rudkovskaya and T.A.Sokolova, Author'scertificate in 422418, Bull. Izobretenli N 13 (1974).

8. O.V.Samsonov, N.V.Glazova, 0.AJisarev, V.N.Gomolitsky and R.B.Ponomare—va, ppkl.Akad.Nauk SSSR, 985 (1976).

9. G.Gi]bert, Disc. Faraday Soc. 20, 68 (1955).10. A.IJ.Antipina, .s.M.Papisov and V.A.1abanov, Vysokornol.Soedin. Bi2, 329

(1970).

11. G.V.Sameonov, P.B.Ponomareva, Studia Biophysics 24/25, 399 (1970).12. A.T.Melenevsky, G.B.Elkin and G.V.Samsonov, Jzvest. Akad.Nauk SSSR. Ser.

ithini., in prusa (1978).