A Practical Introduction to Structure, Mechanism, and Data Analysis - Part 10 doc

11.2 Bi Bi REACTION MECHANISMS11.2.1 Random Ordered Bi Bi Reactions In the random ordered bi bi mechanism, either substrate can bind first to theenzyme, and either product can leave first.

calmodulin and subsequent photolysis led to a covalent peptide—calmodulin

complex that could be separated from free calmodulin by SDS-PAGE orreversed phase HPLC The same peptide was also synthesized with a H-containing acetyl cap on the N-terminal lysine to impart a radiolabel to thepeptide and photolysis product Cleavage of the photoproduct with cyanogen

bromide or S aureus V8 proteinase led to selective cleavage of amide bonds

within the calmodulin polypeptide without any cleavage of the peptide ligand.The tritium-containing cleavage product was separated by reversed phaseHPLC and subjected to N-terminal amino acid sequence analysis From thesestudies DeGrado and coworkers were able to identify Met 144 and Met 71 asthe primary sites of photolabeling These results allowed the researchers tobuild a model of the three-dimensional structure of the peptide binding pocket

in calmodulin

Affinity labeling of enzymes is a common and powerful tool for studyingenzyme structure and mechanism We have barely scratched the surface in ourbrief description of these methods Fortunately there are several excellentin-depth reviews of these methods in the literature General affinity labeling is

covered in a dedicated volume of Methods in Enzymology (Jakoby andWilchek, 1977) General chemical modification of proteins is covered well inthe texts by Lundblad(1991) and Glazer et al (1975) Photoaffinity labeling is

covered in the Methods in Enzymology volume edited by Jakoby and Wilchek

(1977) and also in review articles by Dorman and Prestwich (1994) and byChowdhry(1979) These references should serve as good starting points for thereader who wishes to explore these tools in greater detail

10.6 SUMMARY

In this chapter we have described the behavior of enzyme inhibitors that elicittheir inhibitory effects slowly on the time scale of enzyme turnover These slowbinding, or time-dependent, inhibitors can operate by any of several distinctmechanisms of interaction with the enzyme Some of these inhibitors bindreversibly to the enzyme, while others irreversibly inactivate the enzymemolecule Irreversible enzyme inactivators that function as affinity labels ormechanism-based inactivators can provide useful structural and mechanisticinformation concerning the types of amino acid residue that are critical forligand binding and catalysis

We discussed kinetic methods for properly evaluating slow binding enzymeinhibitors, and data analysis methods for determining the relevant rate con-stants and dissociation constants for these inhibition processes Finally, wepresented examples of slow binding inhibitors and irreversible inactivators toillustrate the importance of this class of inhibitors in enzymology

REFERENCES AND FURTHER READING

Anderton, B H., and Rabin, B R.(1970) Eur J Biochem 15, 568.

Chowdhry, V.(1979) Annu Rev Biochem 48, 293.

Copeland, R A.(1994) Methods for Protein Analysis: A Practical Guide to L aboratory Protocols, Chapman & Hall, New York, pp 151— 160.

Copeland, R A., Williams, J M., Giannaras, J., Nurnberg, S., Covington, M., Pinto, D., Pick, S., and Trzaskos, J M.(1994) Proc Natl Acad Sci USA, 91, 11202.

Copeland, R A., Williams, J M., Rider, N L., Van Dyk, D E., Giannaras, J., Nurnberg, S., Covington, M., Pinto, D., Magolda, R L., and Trzaskos, J M.(1995) Med Chem Res 5, 384.

Dorman, G., and Prestwich, G D.(1994) Biochemistry, 33, 5661.

Glazer, A N., Delange, R J., and Sigman, D S.(1975) Chemical Modification of Proteins, Elsevier,

Kettner, C., and Shervi, A.(1984) J Biol Chem 259, 15106.

Kitz, R., Wilson, I B.(1962) J Biol Chem 237, 3245.

Lundblad, R.(1991) Chemical Reagents for Protein Modification, CRC Press, Boca Raton, FL.

Malcolm, A D B., and Radda, G K.(1970) Eur J Biochem 15, 555.

Morrison, J F.(1982) Trends Biochem Sci 7, 102.

Morrison, J F., and Walsh, C T.(1988) Adv Enzymol 61, 201.

Norris, R., and Brocklehurst, K.(1976) Biochem J 159, 245.

O’Neil, K T., Erickson-Viitanen, S., and DeGrado, W F.(1989) J Biol Chem 264, 14571.

Paterson, A K., and Knowles, J R.(1972) Eur J Biochem 31, 510.

Picot, D., Loll, P J., and Garavito, M R.(1994) Nature, 367, 243.

Rome, L H., and Lands, W E M.(1975) Proc Natl Acad Sci USA, 72, 4863.

Silverman, R B.(1988a) Mechanism-Based Enzyme Inactivation: Chemistry and Enzymology, Vols.

I and II, CRC Press, Boca Raton, FL.

Silverman, R B.(1988b) J Enzyme Inhib 2, 73.

Tang, M S., Askonas, L J., and Penning, T M.(1995) Biochemistry, 34, 808.

Tian, W.-X., and Tsou, C.-L.(1982) Biochemistry, 21, 1028.

Tipton, K F.(1973) Biochem Pharmacol 22, 2933.

Trzaskos, J M., Fischer, R T., Ko, S S., Magolda, R L., Stam, S., Johnson, P., and Gaylor, J L.

(1995) Biochemistry, 34, 9677.

Tsou, C.-L.(1962) Sci Sin Ser B (English ed.) 11, 1536.

Vane, J R.(1971) Nature New Biol 231, 232.

Weissman, G.(1991) Sci Am January, p 84.

REFERENCES AND FURTHER READING 349

us look back at some of the enzymatic reactions we have used as examples.Many of them are multisubstrate and/or multiproduct reactions For example,the serine proteases selected to illustrate different concepts in earlier chaptersuse two substrates to form two products The first, and most obvious, substrate

is the peptide that is hydrolyzed to form the two peptide fragment products.The second, less obvious, substrate is a water molecule that indirectly suppliesthe proton and hydroxyl groups required to complete the hydrolysis Likewise,when we discussed the phosphorylation of proteins by kinases, we needed asource of phosphate for the reaction, and this phosphate source itself is asubstrate of the enzyme An ATP-dependent kinase, for example, requires theprotein and ATP as its two substrates, and it yields the phosphoprotein andADP as the two products A bit of reflection will show that many of theenzymatic reactions in biochemistry proceed with the use of multiple substratesand/or produce multiple products In this chapter we explicitly deal with thesteady state kinetic approach to studying enzyme reactions of this type

Table 11.1 General nomenclature for enzymatic

at the active site of the enzyme, or does the reaction proceed by transfer of thegroup from the donor molecule, A, to a site on the enzyme, whereupon there

is a second transfer of the group from the enzyme site to the acceptor molecule

B(i.e., a reaction that proceeds through formation of an E—X intermediate)?

These questions raise the potential for at least three distinct mechanisms forthe generalized scheme; these are referred to as random ordered, compulsoryordered, and double-displacement or ‘‘Ping-Pong’’ bi bi mechanisms Often amajor goal of steady state kinetic measurements is to differentiate betweenthese varied mechanisms We shall therefore present a description of each anddescribe graphical methods for distinguishing among them

In the treatments that follow we shall use the general steady state rateequations of Alberty(1953), which cast multisubstrate reactions in terms of the

equilibrium constants that are familiar from our discussions of the Henri— Michaelis—Menten equation This approach works well for enzymes that

utilize one or two substrates and produce one or two products For morecomplex reaction schemes, it is often more informative to view the enzymaticreactions instead in terms of the rate constants for individual steps (Dalziel,1975) At the end of this chapter we shall briefly introduce the method of Kingand Altman (1956) by which relevant rate constants for complex reactionschemes can be determined diagrammatically

REACTION NOMENCLATURE 351

11.2 Bi Bi REACTION MECHANISMS

11.2.1 Random Ordered Bi Bi Reactions

In the random ordered bi bi mechanism, either substrate can bind first to theenzyme, and either product can leave first Regardless of which substrate bindsfirst, the reaction goes through an intermediate ternary complex(E · AX · B), asillustrated:

Here the binding of AX to the free enzyme(E) is described by the dissociation

constant K 6, and the binding of B to E is likewise described by K Note that

the binding of one substrate may very well affect the affinity of the enzyme forthe second substrate Hence, we may find that the binding of AX to thepreformed E · B complex is described by the constantK6 Likewise, since the

overall equilibrium between E · AX · B and E must be path independent, thebinding of B to the preformed E · AX complex is described byK When B is

saturating, the value of K6 is equal to the Michaelis constant for AX (i.e.,

K6) Likewise, when AX is saturating,

enzymatic reaction is given by Equation 11.1:

v : k [E·AX·B]:[E]; [E · AX] ; [E · B] ; [E · AX · B]k [E][E·AX· B] (11.1)

If we express the concentrations of the various species in terms of the freeenzyme concentration [E], we obtain:

v:K6K ; K [AX] ; K6[B] ; [AX][B] (11.2)

If we fix the concentration of one of the substrates, we can rearrange andsimplify Equation 11.2 significantly For example, when [B] is fixed and [AX]varies, we obtain:

v:

K6
1;K

[B]; [AX]
1;K

Figure 11.1 Double-reciprocal plot for a random ordered bi bi enzymatic reaction.

At high, fixed concentrations of B, the terms K /[B] and K /[B] go to zero.

Thus, at saturating concentrations of B we find:

that converge to the left of the y axis, as illustrated in Figure 11.1 The data

from Figure 11.1 can be replotted as the slopes of the lines as a function of

1/[B], and the y intercepts (i.e., 1/V ) as a function of 1/[B] (Figure 11.2)

The y intercept of the plot of slope versus 1/[B] yields an estimate of

y and x intercepts of the plot of 1/V 

and 91/K , respectively Thus from the data contained in the two replots, one can calculate the values of K

Bi Bi REACTION MECHANISMS 353

Figure 11.2 (A) Slope and (B) y-intercept replots of the data from Figure 11.1, illustrating the graphical determination of K

11.2.2 Compulsory Ordered Bi Bi Reactions

In compulsory ordered bi bi reactions, one substrate, say AX, must bind to theenzyme before the other substrate (B) can bind As with random orderedreactions, the mechanism proceeds through formation of a ternary intermedi-

ate In this case the reaction scheme is as follows:

E; AX & E · AX& E · AX · B & E · A · BXB E · A& E ; A

If conversion of the E · AX · B complex to E · A · BX is the rate-limiting step incatalysis, then E, AX, B, and E · AX · B are all in equilibrium, and the velocity

of the reaction will be given by:

v:

If, however, the conversion of E · AX · B to E · A · BX is as rapid as the othersteps in catalysis, steady state assumptions must be used in the derivation ofthe velocity equation For a compulsory ordered bi bi reaction, the steady statetreatment yields Equation 11.7:

v:

As we have described before, the term K6 in Equation 11.7 is the dissocation

constant for the E · AX complex, and K6is the concentration of AX that yieldsThe pattern of reciprocal plots observed for varied [AX] at different fixedvalues of [B] is identical to that seen in Figure 11.1 for a random ordered bi

bi reaction(note the similarity between Equations 11.2 and 11.7) Hence, one

cannot distinguish between random and compulsory ordered bi bi mechanisms on the basis of reciprocal plots alone It is necessary to resort to the use of isotope

incorporation studies, or studies using product-based inhibitors

11.2.3 Double Displacement or Ping-Pong Bi Bi Reactions

The double displacement, or Ping-Pong, reaction mechanism involves binding

of AX to the enzyme and transfer of the group, X, to some site on the enzyme

The product, A, can then leave and the second substrate, B, binds to the E—X

form of the enzyme(in this mechanism, B cannot bind to the free enzyme form).The group, X, is then transferred(i.e., the second displacement reaction) to thebound substrate, B, prior to the release from the enzyme of the final product,

BX This mechanism is diagrammed as follows:

E; AX & E · AX & EX · A EX& EX · B & E · BX & E ; BXB

Bi Bi REACTION MECHANISMS 355

Figure 11.3 Double-reciprocal plot for a double-displacement (Ping-Pong) bi bi enzymatic reaction.

Using steady state assumptions, the velocity equation for a ment reaction can be obtained:

B will yield a nest of parallel lines, as seen in Figure 11.3 For each

concentration of substrate B, the values of 1/V  and 91/K6  can be

determined from the y and x intercepts, respectively, of the double-reciprocal plot The data contained in Figure 11.3 can be replotted in terms of 1/V as

a function of 1/[B], and 1/K6 as illustrated in Figure 11.4 The value of

versus 1/[B] replot) and 1/K6 (for the 1/K versus 1/[B] replot) for thereaction, as seen in Figure 11.4

Figure 11.4 Replots of the data from Figure 11.3 as (A) 1/Vapp

maxversus 1/[B] and (B) 1/KAX,app

Table 11.2 Patterns of dead-end inhibition observed for the Bi Bi reaction

E; AX ; B ; E ; A ; BX for differing reaction mechanisms

Inhibitor for

involving ternary complex formation But again, it is not possible to furtherdistinguish between random and compulsory ordered mechanisms on the basis

of reciprocal plots alone If, however, there is available an inhibitor that binds

to the same site on the enzyme as one of the substrates (i.e., is a competitiveinhibitor with respect to one of the substrates), addition of this compound willslow the overall forward rate of the enzymatic reaction and can allow one tokinetically distinguish between random and compulsory ordered reactionmechanisms Because of their structural relationship to the substrate, theproduct molecules of enzymatic reactions themselves are often competitive

inhibitors of the substrate binding site; this situation is referred to as product

inhibition.

Recall from Chaepter 8 that competitive inhibition is observed when theinhibitor binds to the same enzyme form as the substrate that is being varied

in the experiment, or alternatively, binds to an enzyme form that is connected

by reversible steps to the form that binds the varied substrate The pattern ofreciprocal lines observed with different inhibitor concentrations is a nest of

lines that converge at the y intercept (see Chapter 8) For an enzyme thatrequires two substrates, a competitive inhibitor of one of the substrate bindingsites will display the behavior of a competitive, noncompetitive, or evenuncompetitive inhibitor, depending on which substrate is varied, whether theinhibitor is a reversible dead-end (i.e., an inhibitor that does not permitproduct formation to occur when it is bound to the enzyme, corresponding to

Table 11.3 Pattern of product inhibition observed for the Bi Bi reaction

E; AX ; B ; E ; A ; BX for differing reaction mechanisms

Inhibitor Pattern Observed?

For Varied [AX] For Varied [B]

Used As Unsaturated Saturated Unsaturated Saturated

?C, competitive; N, noncompetitive; U, uncompetitive; —, no inhibition.

 : 0 for the scheme in Figure 8.1) or product inhibitor, and the mechanism

of substrate interaction with the enzyme For a bi bi reaction, one observesspecific inhibitor patterns for the different mechanisms we have discussed when

a competitive dead-end inhibitor or a product of the reaction is used as theinhibitor The patterns for both dead-end and product inhibition addition-ally depend on whether the fixed substrate is at a saturating or non-saturating(typically at [S]

The relationships leading to these differing patterns of dead-end and productinhibition for bi bi reactions have been derived elsewhere(see, e.g., Segel, 1975).Rather than rederiving these relationships, we present them as diagnostic toolsfor determining the mechanism of reaction The patterns are summarized inTables 11.2 and 11.3 for dead-end and product inhibition, respectively Bymeasuring the initial velocity of the reaction in the presence of severalconcentrations of inhibitor, and varying separately the concentrations of AXand B, one can identify the reaction mechanism from the pattern of double-reciprocal plots and reference to these tables

DISTINGUISHING BETWEEN RANDOM AND COMPULSORY ORDERED MECHANISMS 359

11.4 ISOTOPE EXCHANGE STUDIES FOR DISTINGUISHING

REACTION MECHANISMS

An alternative means of distinguishing among reaction mechanisms is to look

at the rate of exchange between a radiolabeled substrate and a productmolecule under equilibrium conditions(Boyer, 1959; Segel, 1975)

The first, and simplest mechanistic test using isotope exchange is to askwhether exchange of label can occur between a substrate and product in thepresence of enzyme, but in the absence of the second substrate Looking overthe various reaction schemes presented in this chapter, it became obvious thatsuch an exchange could take place only for a double-displacement reaction:

E;A*X & E·A*X & EX · A*

—A*

EX& EX·B & E · BX & E;BXBFor random or compulsory ordered reactions, the need to proceed through theternary complex before initial product release would prevent the incorporation

of radiolabel into one product in the absence of the second substrate

Next, let us consider what happens when the rate of isotope exchange ismeasured under equilibrium conditions for a general group transfer reaction:

AX; B & A ; BXUnder these conditions the forward and reverse reaction rates are equivalent,and the equilibrium constant is given by:

If under these conditions radiolabeled substrate B is introduced in an amount

so small that it is insufficient to significantly perturb the equilibrium, the rate

of formation of labeled BX can be measured The measurement is repeated atincreasing concentrations of A and AX, to keep the ratio [A]/[AX] constant(i.e., to avoid a shift in the position of the equilibrium) As the amounts of Aand AX are changed, the rate of radiolabel incorporation into BX will beaffected

Suppose that the reaction proceeds through a compulsory ordered ism in which B is the first substrate to bind to the enzyme and BX is the lastproduct to be released If this is the case, the rate of radiolabel incorporationinto BX will initially increase as the concentrations of A and AX are increased

mechan-As the concentrations of A and AX increase further, however, the formation ofthe ternary complexes E · AX · B and E · A · BX will be favored, while dissocia-tion of the EB and EBX complexes will be disfavored This will have the effect

Figure 11.5 Plots of the equilibrium rate of radioisotope exchange between B and BX as a function of [AX] for (A) a compulsory ordered bi bi reaction in which B is the first substrate to bind to the enzyme and BX is the last product to be released, and (B) either a compulsory ordered bi bi reaction in which AX binds first or a random ordered bi bi reaction.

of lowering the rate of isotope exchange between B and BX Hence, a plot ofthe rate of isotope exchange as a function of [AX] will display substrateinhibition at high [AX], as illustrated in Figure 11.5A

The effect of increasing [AX] and [A] on the rate of radiolabel exchangebetween B and BX will be quite different, however, in a compulsory orderedreaction that requires initial binding of AX to the enzyme In this case,increasing concentrations of AX and A will disfavor the free enzyme in favorISOTOPE EXCHANGE STUDIES FOR DISTINGUISHING REACTION MECHANISMS 361

of the EAX and EA forms The EAX form will react with B, leading toformation of BX, while the EA form will not Hence, the rate of radiolabelincorporation into BX will increase with increasing [AX] as a hyperbolicfunction (Figure 11.5B) The same hyperbolic relationship would also beobserved for a reaction that proceeded through a random ordered mechanism.

In this latter case, however, the hyperbolic relationship also would be seen forexperiments performed with labeled AX and varying [B]

Thus isotope exchange in the absence of the second substrate is diagnostic

of a double-displacement reaction, while compulsory ordered and randomordered reactions can be distinguished on the basis of the relation of the rate

of radiolabel exchange between one substrate and product of the reaction tothe concentration of the other substrate and product under equilibriumconditions (See Segel, 1975, for a more comprehensive treatment of isotopeexchange studies for multisubstrate enzymes.)

11.5 USING THE KING ALTMAN METHOD TO DETERMINE

VELOCITY EQUATIONS

The velocity equations for bi bi reactions can be easily related to the

Henri—Michaelis—Menten equation described in Chapter 5 However, for more

complex reaction schemes, such as those involving multiple intermediatespecies, it is often difficult to derive the velocity equation in simple terms Analternative method, devised by King and Altman(1956), allows the derivation

of a velocity equation for essentially any enzyme mechanism in terms of theindividual rate constants of the various steps in catalysis On the basis of themethods of matrix algebra, King and Altman derived empirical rules forwriting down the functional forms of these rate constant relationships Weprovide a couple of illustrative examples of their use and encourage interestedreaders to explore this method further

To begin with, we shall consider a simple uni uni reaction as first tered in Chapter 5:

encoun-E; S & ES - E ; P

In the King and Altman approach we consider the reaction to be a cyclicprocess and illustrate it in a way that displays all the interconversions amongthe various enzyme forms involved:

For each step in the reaction we can define a term  (kappa) which is theproduct of the rate constant for that step and the concentration of freesubstrate involved in the step Next, we determine every pathway by which aparticular enzyme species might be formed in the reaction scheme For thesimple uni uni reaction under consideration we have:

Enzyme Form Pathways to That Form  of Kappa Products

Inspecting Equation 11.15, we immediately see that k is equivalent to k , and

results in the same velocity equation we had derived as Equation 5.24.Now let us consider the more complex case of a double-displacement bi bi

reaction using the King—Altman approach Note here that the initial

concen-trations of the two products A and BX are zero, and the release of these

USING THE KING-ALTMAN METHOD TO DETERMINE VELOCITY EQUATIONS 363

products from the enzyme is essentially irreversible Hence, the cyclic form

of the reaction scheme is:

Consideration of this reaction yields the relationships given in Table 11.4 Theoverall rate equation for a double-displacement reaction is:

With similar considerations, the velocity equations for random ordered andcompulsory ordered bi bi mechanisms can likewise be derived With somepractice, this seemingly cumbersome approach provides a clear and intuitivemeans of deriving the appropriate velocity equation for complex enzymatic

systems A more thorough treatment of the King—Altman approach can be

found in the text by Segel(1975) as well as in the original contribution by Kingand Altman(1956)

11.6 SUMMARY

In this chapter we have briefly introduced the concept of multisubstrateenzyme reactions and have presented steady state equations to describe the

velocities for these reactions We have seen that enzyme reactions involvingtwo substrates and two products can proceed by at least three distinctmechanisms: random ordered, compulsory ordered, and double-displacementreactions Experimental methods were presented to allow the investigator todistinguish among these mechanisms on the basis of kinetic measurements,product inhibition studies, and radioisotope exchange studies We brieflydescribed the method of King and Altman for deriving the velocity equation

of complex enzymatic reaction, such as those involving multiple substrates.The importance of multisubstrate enzymatic reactions can hardly be over-stated In fact, the vast majority of enzymatic reactions in nature proceedthrough the utilization of more than one substrate to yield more than oneproduct

REFERENCES AND FURTHER READING

Alberty, R A.(1953) J Am Chem Soc 75, 1928.

Boyer, P D.(1959) Arch Biochem Biophys 82, 387.

Cleland, W W.(1963) Biochim Biophys Acta, 67, 188.

Cornish-Bowden, A., and Wharton, C W.(1988) Enzyme Kinetics, IRL Press, Oxford, pp 25—33.

Dalziel, K (1975) Kinetics and mechanism of nicotinamide-dinucleotide-linked dehydrogenases, in

T he Enzymes, 3rd ed., P D Boyer, Ed., Academic Press, San Diego, CA, pp 1—60.

King, E L., and Altman, C.(1956) J Phys Chem 60, 1375.

Palmer, T.(1981) UnderstandingEnzymes, Wiley, New York, pp 170—189.

Segel, I H.(1975) Enzyme Kinetics, Wiley, New York, pp 506— 883.

COOPERATIVITY IN ENZYME CATALYSIS

As we described in Chapter 3, some enzymes function as oligomeric complexes

of multiple protein subunits, each subunit being composed of copies of thesame or different polypeptide chains In some oligomeric enzymes, each subunitcontains an active site center for ligand binding and catalysis In the simplestcase, the active sites on these different subunits act independently, as if eachrepresented a separate catalytic unit In other cases, however, the binding ofligands at one active site of the enzyme can increase or decrease the affinity ofthe active sites on other subunits for ligand binding When the ligand bindingaffinity of one active site is affected by ligand occupancy at another active site,

the active sites are said to be acting cooperatively In positive cooperativity ligand binding at one site increases the affinity of the other sites, and in negative

cooperativity the affinity of other sites is decreased by ligand binding to the first

site

For cooperative interaction to occur between two active sites some distanceapart(e.g., on separate subunits of the enzyme complex), ligand binding at onesite must induce a structural change in the surrounding protein that istransmitted, via the polypeptide chain, to the distal active site(s) This concept

of transmitted structural changes in the protein, resulting in long-distancecommunication between sites, has been termed ‘‘allostery,’’ and enzymes that

display these effects are known as allosteric enzymes. (The word ‘‘allosteric,’’

which derives from two Greek words — allos meaning different, and stereos,

meaning structure or solid — was coined to emphasize that the structural

change within the protein mediates the cooperative interactions among