Turn Allows This Particular Enzyme to Degrade a Polynucleotide in a Continuous Manner

A NEW KINETIC MODEL FOR POLYNUCLEOTIDE METABOLISM BY HARRISON M. LAZARUS,* MICHAEL B. SPORN,t AND DAN F. BRADLEY:

NATIONAL CANCER INSTITUTE, AND NATIONAL INSTITUTE OF MENTAL HEALTH, BETHESDA, MARYLAND Communicated by C. B. Anfinsen, May 22, 1968 Several exonucleases, such as the exoribonuclease from Ehrlich ascites tumor cells, I Escherichia coli ribonuclease 11,2 and bacterial polynucleotide phosphorylase,3, 4 have recently been shown to remain complexed with an individual polynucleotide molecule while the enzyme continuously and almost completely degrades the polymer to mononucleotides. The behavior of these exonucleases is in marked contrast to that of the exonuclease from snake venom2' 3 and exonuclease I from E. coli.5 When snake venom exonuclease hydrolyzes polynucleotides, the enzyme-substrate complex dissociates into separate entities between successive hydrolytic steps, and the next phosphodiester bond hydrolyzed comes from a polynucleotide molecule taken at random from the molecules in the vicin- ity of the enzyme. However, when Ehrlich ascites tumor cell exoribonuclease, E. coli ribonuclease II, and bacterial polynucleotide phosphorylase degrade polynucleotides, the polynucleotide apparently does not dissociate from the enzyme after cleavage of the terminal mononucleotide, but rather the enzyme and shortened polynucleotide move relative to each other so as to bring the next phosphodiester bond into position for cleavage. By means of such procession, an entire polynucleotide molecule may be degraded without ever leaving the sur- face of the enzyme. The presumption of a processive step implies that after a hydrolytic step, the enzyme and shortened polynucleotide are still held to- gether by one or more bonds. We wish to point out that the processes of dissociation and procession of the polynucleotide should not be considered as mutually exclusive; after the first cleavage step, there will in general be a probability for dissociation and a probability for procession, the values for which are related to the rate constants for the two processes. We would like to present a formal kinetic model of exonucleolytic action that includes both classes of exonucleases as special cases for limiting values of the k6inetic constants. This model has been used to design kinetic experiments witl the exoribonuclease from Ehrlich ascites tumor cells. The data yield information about: (1) the number of bonds between the enzyme and the polynucleotide being degraded; (2) the energetic contribution of each bond; and (3) the free- energy drop causing procession of the polynucleotide on the enzyme, which in turn allows this particular enzyme to degrade a polynucleotide in a continuous manner. Although the kinetic model is applicable to both random and continuous exo- niucleolytic degradation, it will be presented and illustrated (Fig. 1) with emphasis on the special case of continuous degradation: The enzyme is assumed to bind a substrate, such as polyadenylic acid (Poly A), of chain length n (step 1, Fig. 1). The binding is assumed to be between m filled binding places on the enzyme and m places on the polymer. The chain length, n, of the polymer is greater than the number of binding places, m. The hydrolysis of the terminal 1503 Downloaded by guest on September 27, 2021 1504 BIOCHEMISTRY: LAZARUS ET AL. PROC. N. A. S.

Enzyme FIG. l.-Schematic representation k and kinetic model of an exonuclease 1 E+Ani EmAn Pydeyc i degrading a polymer. E represents k-i an exonuclease, A. is a polynu- Polyodenylic Acid cleotide (such as Poly A) of chain length n, EmAn is the enzyme- Enzyme polynucleotide complex in a con- k2 figuration capable of liberating 2 EmAn )EmiAn+Ai the terminal nucleotide, with m 'lip-??....?+AMP as the number of enzyme-poly- Polyodenylic Acid nucleotide bonds. Em-iAn-i is Enzyme the enzyme-polynucleotide com- A; plex, with the terminal nucleotide k3 3 l-mAn- liberated as A1. Em.-An-i repre- Em-imn k-3 sents a complex no longer capable Polyodenylic Acid of releasing another mononucleotide until it returns to the confor- Enzyme mation of EAn,1 == E,3A.. Ir k4 is an oligonucleotide of chain 4 E+Ir'EmIr length r, which is not hydrolyzed. k-4 0....ie Emar represents the enzyme-oligo- 01ligonucleotide nucleotide complex. mononucleotide is not kinetically reversible (step 2, Fig. 1). The polynucleotide can now move over one unit to fill up all the enzyme binding points (step 3, Fig. 1). An oligonucleotide of chain length r that is not degraded by the exonuclease can be bound reversibly to the enzymatic site and act as an inhibitor (step 4, Fig. 1). Thus, the over-all reaction for substrates is ki k2 E E,-1A + Al. + An EmAnk3l n4- k-a In setting down the kinetic model, we have assumed that the hydrolytic step is kinetically irreversible and that the polymers are sufficiently long so that EmAni- has the same kinetic behavior as EmAn; i.e., EmAn = EmAni. The differential rate equations for this model are as follows: d [A1 I= dt k2[EmAn] =V, (1)

d[EmAn] = ] dt ki[E][An] -k-i[EmAn] -k2[EmAn] -k-3[EmAn-l +k3[EmlAnj] (2) d[Em-iAn-1] = k2 dt [EmAn] +k-3[EmAnI] -k3[EmiAn..], (3)

d[EmIr] = dt k4[E][Ir] -k.4[EmIrI]. (4) Mlaking the steady-state assumption that the concentration of all intermediate species (EmAn, EmiAn-i, EmIr, with EmAn EmAn-) are time-independent from (3), [Em-iAn-i] = [(k2 + k4)/k3] [EmAn]; from (2) and (3), [E] = (k-1 [EmAnI)/ Downloaded by guest on September 27, 2021 VOL. 60, 1968 BIOCHEMISTRY: LAZARUS ET AL. 1505

(k1 [An]); and from (4) and above, [EmIr] = (k-1 k4 [EmAn] [Ir])/(k1 k4 [An]) Substituting into the conservation equation [Eo] = [E] + [EmIr] + [EmAn] + [Em-iAnj], [Eo] = [EmAnI (1 + k4A I + k2+k3 + k1k4A ]) From (1), 1 1 1 (1 + k-1 + k2+k-3 + k-1k4[Ir] V k2[EmAn] k2[Eo] \ k[An] k3 kik4[An]J/' therefore, 1( + k2 + ()+ V (+ KI 1A

where Vmax = k2 [Eo], Keq = k-l/ki, Ki = k4/k4. The model does not require the enzyme to degrade an individual polynucleotide molecule continuously, but allows it to do so. However, after step (3), the EmAn complex can dissociate to Em and An by reversing step (1). In contrast, if step (2) were replaced by EmAn -- E + An-1 + A1, then the enzymatic degradation would have to be random. However, in the present model, whether or not the enzyme is continuously degrading the same polymer molecule depends only on the ratio of k2/k-1. A plot of 1/v versus 1/An with Ir = 0 gives a Lineweaver-Burk6 plot (Fig. 2A). In plotting 1/v versus Ir, as done by Dixon7 (Fig. 2B), at two different concentrations of An the same 1/v will be obtained at the same Ir concentration when Ir = -Ki. Ki can also be determined, for Ki = -Ir at 1/v = 1/Vmax [1 + A B Keq A Slope- I/v Vmax I/v

I/Vmx (I+ I/Vmax(I+ k 3

0 ° I/An Ir -Kj FIG. 2.-Graphic representation of kinetic constants. (A) A Lineweaver-Burk plot. An is the concentration of a polymer of chain length n, v is the velocity. The derivation of the slope and y intercept are given in the text. (B) A Dixon plot. Ir is the concentration of inhibitor of chain length r, and the derivation of Ki is in the text. An' and An2 represent two different concentrations of polyitucleotide of chain length n. Downloaded by guest on September 27, 2021 1506 BIOCHEMISTRY: LAZARUS ET AL. PROc. N. A. S.

(k2 + k-3)/k3] (Fig. 2B). The Ks's of a set of I,'s can be used to find the maxi- mum number of monomer units (r) necessary to saturate the principal binding

of an exonuclease; i.e., an r is sought such that r + q, q _ 1, will give no greater inhibition of the enzyme than r as reflected in the Ki. In the present work, the model is used to evaluate the number of principal binding points, as well as the energetic contribution of each bond, for the exoribonuclease from Ehrlich ascites tumor cells.' This enzyme attacks polynucleotides, such as Poly A, from the 3'-OH end, liberating 5'-mononucleotides. Oligo- nucleotides terminated by a 2', 3'-cyclic phosphate, such as (Ap)r-,A-cyclic-p, are not degraded by this exoribonuclease and are competitive inhibitors, as well as analogues, of the substrate Poly A. The K/'s for a set of these oligonucleotides, I, (r, chain length, from 1 to 8), were determined with Poly A as substrate for exoribonuclease. Experimental Procedure.-Materials: Poly A-H3 and oligonucleotides were obtained from Miles Laboratories, Elkhart, Indiana. The exoribonuclease was prepared from Ehrlich ascites tumor nuclei.' Analytical methods: (a) Enzymatic assays: The standard assay mixture (0.5 ml) was as follows: 0.1 M Tris-HCl, pH 7.7; 5mM MgCl2; 400,ug/ml BSA; 0.4mM dithio- threitol; 0.84mM or 1.68mM or2a52mM Poly A-H3 (mononucleotide equivalent), spec. act. 0.25 Ac/,uM; 0.0-0.048 M (Ap),_-A-cyclic-p, varying with the chain length; exoribonuclease 0.1-0.3 units/ml. A unit of enzyme is defined as that amount which forms 1 gmole of AMP per hr with 3mM Poly A as substrate.' After 30 min at 370, the reaction was stopped by the addition of 0.5 ml ice-cold 0.8 M perchloric acid. The tubes were centrifuged for 30 min at 1900 X g, and the radioactivity of 0.4 ml of the clear supernatant was measured. The homogeneity of all inhibitors was verified by thin-layer chromatography before use. The solvent systems used werez 1 11 ammonium acetate, pH 7.0-7.3, 95% ethanol, 70:30 (v/v) in solvent 1, and 80:20 (v/v) in solvent 2. (b) Data analysis: The best fit for each 1)lot of 1/v versus I and 1/v versus 1/An, as well as forintersection points, was determined by a least-squares analysis with an IBM 1620 computer. (c) Other methods: The coiiceiitratioii of Poly A (mononucleotide equivalent) was determined by usingop (257m,) = 9.9 X 103.9 The concentration of the oligonucleotides was determined by incubation at 370 in 0.31l1 NaOH for 18 hr, followed by neutralization to pH 7.1, withs- (260mIA) = 15 X 103.10 All concentrations of oligonucleotides reported are expressed as the molarity of the oligonucleotide itself, rather than of the mononucleotide equivalent. Results.-Equilibrium constants for (Ap)r,_A-cyclic-p: The equilibrium co'istants (K/'s) for (Ap) rA-cyclic-p were determined by utilizing the plot of 1/v versus I shown in Figure 3 for (Ap)3A-cyclic-p. The binding energy of exoribonuclease with the Poly A analogues can be derived from the Ki values; if AFV is the standard free energy of forming a complex between enzyme and oligollucleotlide, theii AF' =URT'lnK. Table1 shows that there is an appreci- able increase in the stability of the complex between enzyme and oligonucleotide as the chain length increases to 6. The Ki values are graphically represented by a semilogarithmic plot of Ki versus the chain length of (Ap)r-,A-cyclic-p in Figure 4. From Table 1 and Figure 4, there appears to be a break at chain length 6, with little increase in the binding affinity of the enzyme for the oligonucleotide as the chain length is increased to 7 and 8. Therefore, the complex between Ehrlich tumor exoribonuclease and a Poly A analogue is stabilized by 7.6 Downloaded by guest on September 27, 2021 VOL. 60, 1968 BIOCHEMISTRY: LAZARUS ET AL. 1507

FIG. 3.-Typical procedure used for experi- 40 _ 00\Ul mental determination of K1. The value of I lAA (the molar concentration of the oligonucleotide l/v 0. (Ap)aA-cyclic-p) has been multiplied by 5.9 X 30 104; v is velocity in j.moles of Poly A (mononucleotide equivalent) made acid-soluble in 30 Molor min at 370. The value for 1/Vmax [1 + (k2 + 2lA52 k-3)/k3] was determined from a l/v versus 1/An 20 _ A plot and found to be 13.2 moles-1-30 min (see Fig. 2A). K, for this oligonucleotide was taken k2+k_3 as the intersection of the l/v versus I plots for I/VmfQ(I+ Ik) Poly A = 0.84 mM and for Poly A = 2.52 mM, averaged with the intersection value of each of these lines with 13.2 moles-130 min. The amount of enzyme used in all measurements was 0.14 unit per ml. -4 -3 -2 -@ 0 2 3 4 I kcal/mole (the average of the values for (Ap)5_7A-cyclic-p). This entire set of values of Ki versus (Ap),-1A-cyclic-p was repeated with an entirely different preparation of enzyme and with a different lot of (Ap)TlA-cyclic-p, and the same results were obtained. Main contribution of the polymer to complex formation: -Most of the enzymatic binding is apparently electrostatic to the phosphate monoanion. Using the same method employed in Figure 3, we found approximately equal Kg's for A-cyclic-p and ApA (which is hydrolyzed extremely slowly), as well as for ApA- cyclic-p and ApApA (which is hydrolyzed at less than 2 per cent of the rate of Poly A at equivalent monomeric concentration). This also showed that there are similar binding contributions whether the terminal phosphodiester bond is a 2', 3'- or a 5', 3'-linkage. Discussion.-Exonucleases that degrade a polynucleotide continuously to completion must be thought of as being bound to the polymer in an operational sense.3 This is in marked contrast to the classical Miichaelis-MNlentenll model of enzyme action, which postulates that the enzyme should release its products, remaining polymer and mononucleotide, and free enzyme after each catalytic step. Several possible mechanisms for this continuous degradation have been suggested by Klee and Singer:' ... on dissociation from the enzyme, a substrate molecule has a very high probability of becoming reattached (to the same enzyme molecule) compared to other chains in the population. Alternatively, TABLE 1. Equilibrium constants and free energy of enzyme-oligonucleotide complexes. Chain length* of AF0 = RT In Ki oligonucleotide Ki (M) t (cal/mole) 1 2.7 X 10-2 -2200 2 1.3 X 10-8 -4100 3 2.4 X 10-4 -5100 4 5.5 X 105 -6000 5 1.5 X 105 -6900 6 5.4 X 106 -7500 7 3.2 X 106 -7800 8 5.0 X 10- -7500 * Chain length refers to the value of r for (Ap),-A-cycli-p. t Molarity of oligonucleotide. Downloaded by guest on September 27, 2021 1.508 BIOCHEMISTRY: LAZARUFS ET AL. PROC. N. A. S. IXIO'°I

-1~~~~~~~~~~~~~~~ liIXI0-4\IXIO-5-

Iflo-6 2 3 4 5 6 7 8 CHAIN LENGTH OF OL/GONUCLEOT/DE

FIG. 4.-Semilogarithmic plot of Ki versus increasing chain length of oligoribo- nucleotide. The values of Ki for (Ap)r_-A-cyclic-p for r from 1 to 8 were determined as shown for (Ap'A-cyclic-p in Fig. 3.

attachment of the substrate to the enzyme by a relatively strong bond at a point remote from the site of cleavage or physical entrapment of the substrate within the enzyme structure are possible mechanisms." This continuous mechanism contrasts with the random mechanism of exonucleases that dissociate from the polynucleotide following hydrolysis of the terminal mononucleotide and then hydrolyze the next phosphodiester bond more or less randomly from the molecules in solution. We have attempted to point out that the two modes of action should not be considered as mutually exclusive; after the first hydrolytic step, there will in general be a probability for dissociation and a probability for procession, the values for which are related to the rate constants for the two processes. Since rate constants can be manipulated by varying the environment, we might expect that with a particular enzyme-polymer system, under some conditions dissociation would be favored, whereas in other situations procession would be favored. The Ehrlich exoribonuclease is just such a case in point. It degrades Poly A to pA in a continuous manner, whereas it degrades ApApA to ApA and pAl in a random manner. (The hydrolysis of ApApA must be considered random since the rate of further hydrolysis of ApA is negligible when compared to the rate of hydrolysis of ApApA.) Similar results have been obtained with polynucleotide Downloaded by guest on September 27, 2021 VOL.. 60, 1969 BIOCHEMISTRY: LAZARUS ET AL. 1.509

phosphorylase and E. coli ribonuclease II when degradation of polymers and oligonucleotides has been compared.2' 3 Thus there must be conditions in which the enzyme-polymer system would exist with the probability of procession being equal to that of dissociation. We have developed a model that covers both of these cases. An important feature of the continuous case is the manner by which the polymer is encouraged to move and to move in the correct direction on the enzyme. When the polymer binds to the enzyme, m of its nucleotides in a row form m bonds with the enzyme. After hydrolysis of the last nucleotide, the number of links is reduced to m -1. Since the formation of the linkages is favored thermodynamically by a decrease in free energy, hydrolysis automatically sets up a free energy gradient favoring the movement of the polymer in the correct direction to return the number of bonds to m. Movement in the opposite direction would involve an unfavorable motion against the free energy gradient to form m -2 bonds. For the Ehrlich tumor exonuclease, the data obtained can be interpreted in terms of the above thermodynamic explanation for continuous degradation of a polymer. When a polymer is degraded by this enzyme, there is an initial binding energy of 7.6 kcal/mole (assuming for Poly A, Keq = Ki for (Ap)j_7A-cyclic-p). This represents the sum of the binding energies of each of the six enzyme-polymer bonds (i.e., the energy bond of the first nucleotide unit at the 3'-OH end is equal to that found for A-cyclic-p and that of the second nucleotide unit is equal to the additional binding energy of ApA-cyclic-p over A-cyclic-p, etc.). Thus, after hydrolysis of the 3'-OH terminal nucleotide, the enzyme-polynucleotide complex would still be stabilized by 5.4 kcal/mole and the drive to fill the terminal binding site would be 2.2 kcal/mole. The curvature of the plot of log Ki versus r (Fig. 4) leads to the hypothesis that the enzyme-polymer bonds are stronger at the right- hand side of the binding region (Fig. 1), so that there exists a thermodynamic gradient that tends to give alignment of the terminal nucleotide of the substrate with the hydrolytic center even when n < m. Thus, thermodynamic criteria have been established for an exoribonuclease to bind a polynucleotide and keep it bound while continuously degrading it with proper alignment. In contrast, data have previously been reported12 for snake venom exonuclease (an enzyme that degrades polynucleotides by a random mechanism) that enable one to calculate the binding energy between a polynucleotide and this enzyme; in this case, the terminal phosphodiester bond and the enzyme have a greater binding energy than the contribution from additional binding places on the polymer. The model described here should also find application in the derivation of an analogous kinetic model describing the synthesis of polynucleotides promoted by template or primer. Kinetic analysis of polynucleotide synthesis can be used to determine the random or continuous nature of this process under particular reaction conditions. Summnary.-A kinetic model has been derived from steady-state theory for exonucleolytic degradation of polynucleotides, with specific emphasis on a mechanism whereby an exonuclease is continuously bound to a polynucleotide molecule while completely degrading it to mononucleotides. The model has been used experimentally to study the nuclear exoribonuclease isolated from Ehrlich Downloaded by guest on September 27, 2021 1510 BIOCHEMISTRY: LAZARUS ET AL. PROc. N. A. S.

ascites tumor cells. The data show that this enzyme binds to six anionic places on a polynucleotide molecule with a total energy of 7.6 kcal/mole. The binding energy between enzyme and polynucleotide is estimated to diminish by 2.2 kcal/ mole upon hydrolysis of the terminal mononucleotide. It is suggested that the remaining binding energy is adequate to keep the polynucleotide bound to the enzyme during and after each hydrolytic step. The restoration of the full binding energy by reorientation of the remaining polynucleotide and enzyme then allows another cycle of hydrolysis of a terminal mononucleotide, eventually re- sulting in total conversion of polynucleotide to mononucleotides. Random degradation of polynucleotides by exonucleases is also discussed. We thank Dr. F. K. Millar for writing the program utilized in the IBM 1620 computer and for assisting in its execution. The abbreviations used are: Tris, tris(hydroxymethyl)aminomethane; BSA, bovine serum albumin; AMP, adenosine 5'-phosphate. Abbreviations for nucleotides and polynucleotides are those used in J. Biol. Chem. Thus, ApA-cyclic-p stands for adenylyl-(3',5')-adenosine 2',3'- cyclic phosphate; (Ap)r,-A-cyclic-p stands for an adenylate oligonucleotide of chain length r, with r - 1 repeating mononucleotide units, terminated with a mononucleotide bearing a 2',3'- cyclic phosphate on its 3'-OH-end group. * Present address: Department of Surgery, University Hospital, Boston University, Boston, Massachusetts 02118. t To whom requests for reprints should be sent, at the National Cancer Institute. $ Present address: Department of Chemistry, Polytechnic Institute of Brooklyn, Brooklyn, New York 11201. l Lazarus, H. M., and M. B. Sporn, these PROCEEDINGS, 57, 1386 (1967). 2 Nossal, N. G., and M. F. Singer, J. Biol. Chem., 243, 913 (1968). 3 Klee, C. B., and M. F. Singer, J. Biol. Chem., 243, 923 (1968). 4Thang, M. N., W. Guschlbauer, H. G. Zachau, and M. Grunberg-Manago, J. Mol. Biol., 26, 403 (1967). 5 Lehman, I. R., J. Biol. Chem., 235, 1479 (1960). 6 Lineweaver, H. and D. Burk, J. Am. Chem. Soc., 56, 658 (1934). 7Dixon, M., Biochem. J., 55, 170 (1953). 8Thach, R. E., in Procedures in Nucleic Acid Research, ed. G. L. Cantoni and D. R. Davies (New York: Harper & Row, 1966), p. 520. 9Sarkar, P. K., and J. T. Yang, Biochemistry, 4, 1238 (1965). '0Beaven, G. H., E. R. Holiday, and E. A. Johnson, in The Nucleic Acids, ed. E. Chargaff and J. N. Davidson (New York: Academic Press, 1955), vol. 1, p. 513. Michaelis, L., and M. L. Menten, Biochem. Z., 49, 333 (1913). 12 Razzell, W. E., and H. G. Khorana, J. Biol. Chem., 234, 2105 (1959). Downloaded by guest on September 27, 2021