Enzyme Kinetics 3

• Many enzymes catalyze reactions with 2 substrates.
  • There are 2 different types of bisubstrate kinetic mechanisms:

    • sequential (single displacement) reactions, which can be
      
      • ordered sequential
      • random sequential
    • "ping-pong" (double displacement) reactions
      
      
• Bisubstrate kinetic mechanisms can be written in a "shorthand" notation as originally suggested by Cleland.
  
  
• Sequential and ping-pong kinetic mechanisms can be distinguished by double reciprocal plots of 1/v_o vs. 1/[S₁] at a series of different fixed concentrations of [S₂].
  
  
• Enzyme inhibition (and many other biochemical phenomena, including effect of binding of one ligand to a protein on the binding of another ligand to that protein) can be understood in the context of a "linked function" diagram, a thermodynamic box.
  
  
• Enzyme inhibitors are compounds that REDUCE VELOCITY OF ENZYME-CATALYZED REACTIONS
  • 2 types: reversible and irreversible
    
    
  • reversible inhibition:
    • competitive: I increases K_m by a factor of {1 + ([I]/K_I)}; no effect on V_max
    • uncompetitive: I decreases BOTH K_m and V_max by the same factor, {1 + ([I]/K_I')}
    • mixed (noncompetitive): I decreases V_max by a factor of {1 + ([I]/K_I')}; "pure" noncompetitive inhibitors have no effect on K_m.
      
      
  • The 3 types of reversible inhibitors can be distinguished on the basis of double reciprocal plots (1/v_o vs. 1/[S]) in the absence of I and in the presence of different concentrations of I. Such plots also permit calculation of K_I (or K'_I), the dissociation constant for the enzyme-inhibitor complex.
    
    
• Irreversible inhibitors cause irreversible (generally covalent) modification of the enzyme, inactivating it.
  • Such inhibitors can be group-specific chemical modifying reagents that would react with certain types of functional groups on a variety of enzymes,
  • substrate analogs with a reactive group on them (so more specific for one enzyme), or
  • "suicide" substrates (mechanism-based inhibitors) that aren't reactive until the specific chemical mechanism of their target enzyme makes them "kill" (covalently modify) the active site they're in.
    
    
• Both reversible and irreversible inhibitors can be very helpful in
  • providing information about shape of active site and types of amino acid side chains there
  • working out enzyme mechanisms
  • providing info about control of metabolic pathways
  • design of drugs
    
    
• pH can have a major effect on enzyme activity, due to ionizable groups on either enzyme or substrate.
  • Note: protons are ligands that bind to and dissociate from enzymes, and can affect substrate binding and/or k_cat.
  • Determination (or even estimates) of pK_a of group whose state of ionization affects activity can help in formulation of hypotheses about what groups are in enzyme active site, chemical mechanism, etc.
    
    

REACTIONS INVOLVING 2 SUBSTRATES (Bisubstrate Reactions)

• ~ 60% of enzyme-catalyzed reactions have 2 substrates & 2 products
• bisubstrate reaction:
  S₁ + S₂ <==> P₁ + P₂
• Kinetics can be complex, but can be very informative about the mechanism.
• objectives:
  • to understand the 2 different types of bisubstrate kinetic mechanisms:
    • sequential (single displacement) reactions, which can be of either of 2 subtypes:
      
      • ordered sequential
      • random sequential
    • "ping-pong" (double displacement) reactions
  • to understand and be able to write kinetic mechanisms for different types of bisubstrate reactions using Cleland (W.W. "Mo" Cleland) terminology ("shorthand" diagrams for kinetic mechanisms)
    • Cleland terminology:
      • Reaction coordinate (progress of reaction) indicated by a line
      • Reactants and products are indicated by arrows "coming" and "going" from the reaction above the line.
      • Stable enzyme forms (designated E, E', etc. if there are different stable enzyme forms in the reaction) are written below the line ("stable enzyme form" = a form that can't convert to another stable enzyme form by itself)
      • Number of reactants and number of products in reaction indicated as "uni" (1), "bi" (2), "ter" (3), and "quad" (4). For example, A + B --> C would be "bi uni", and A + B --> C + D would be "bi bi".
  • to be able to distinguish between sequential and ping-pong kinetic mechanisms based on the patterns observed on double reciprocal (Lineweaver-Burk) plots
    
    
• Types of kinetic mechanisms for bisubstrate reactions, with examples -- SEQUENTIAL vs. PING-PONG
  • Sequential kinetic mechanisms (single displacement reactions):
    • All substrates must bind to enzyme before any product is released.
    • A ternary complex (3 components: E, S₁ and S₂, all bound in same E•S₁ •S₂ complex) must form before any chemistry can occur.
    • 2 sub-types, depending on whether the substrates can bind randomly or must bind in a required order:
      • ordered sequential: substrate binding has to occur in a certain order to form the ternary complex
      • random sequential: the substrates can bind randomly -- doesn't matter which one binds first on the way to forming the ternary complex
        
        
• Ordered sequential kinetic mechanisms (single displacement reactions)
  • Second substrate's binding site isn't there or isn't available until first substrate binds.
  • e.g., many enzymes that use the coenzyme (cosubstrate) NAD+/NADH, such as lactate dehydrogenase, which catalyzes a redox reaction (so it's an oxidoreductase)
    • the coenzyme (cosubstrate) has to bind first, and the other substrate then can bind
    • product release is also ordered: the other product is released first, and other form of the coenzyme is released last.
      
  • EXAMPLE: the lactate dehydrogenase reaction
    • a very important enzyme in glucose metabolism -- reversible reaction in which pyruvate (an a-keto acid) is reduced to lactate (the corresponding a-hydroxy acid); the 2-electron donor is the coenzyme NADH; the products are the reduced product (lactate) and the oxidized coenzyme, NAD⁺
    • an ordered bi bi reaction

• Kinetic mechanism of the LDH reaction (modified Cleland notation):
  • Is a ternary complex formed?

• Random sequential kinetic mechanisms
• Both substrates' binding sites are available on the free enzyme.
• EXAMPLE: the creatine kinase reaction (phosphoryl group transfer from ATP to creatine, or from phosphocreatine to ADP)
  • a random bi bi reaction

• Kinetic mechanism of the creatine kinase reaction (modified Cleland notation):
• Is a ternary complex formed?
• Either creatine can bind first and then ATP, or vice versa; likewise, the order of product release is random.

• Ping pong kinetic mechanisms (double displacement reactions)
  • NO ternary complex is formed.
  • One or more products are released before all substrates have been added.
  • Substrates don't react directly with each other in active site of enzyme.
    • 1st substrate binds and reacts with enzyme, converting enzyme to another stable enzyme form (E'), a CHEMICALLY modified form of the enzyme
    • 1st product (the "remains" of first substrate) is released
    • 2nd substrate binds to E' and reacts with E', forming 2nd product and regenerating original stable enzyme form (E)
    • 2nd product is released
  • There are thus 2 HALF REACTIONS in the kinetic mechanism.
    
  • Example: the aspartate aminotransferase reaction (one of a number of metabolically very important aminotransferase reactions (enzymes sometimes called transaminases), that all use the coenzyme pyridoxal phosphate (PLP)

   

• a ping pong bi bi reaction
• The amino group donor substrate (an a-AMINO acid) transfers its amino group to PLP and the resulting product, an a-KETO acid, dissociates from the "modified enzyme"
• The second substrate, a different a-keto acid, which is to receive the amino group, binds to the modified enzyme, and the coenzyme transfers the amino group to the recipient a-keto acid, generating the second product of the reaction, a different a-amino acid.
  
  
• kinetic mechanism of aspartate aminotransferase
  • Is a ternary complex formed?
  • Identify the 2 half reactions, connected by the modified enzyme form, E-NH₃ (the amino group is actually "attached" to the pyridoxal cofactor on the enzyme.)
• Double reciprocal plots for bisubstrate reactions (S₁ + S₂ --> product(s))
  • Concentration of substrate 1 is varied while the concentration of S₂ is held constant and velocities are measured.
  • This is repeated for several concentrations of S₂.
  • 1/velocity as a function of 1/S₁ is plotted as a straight line (Lineweaver-Burk/double reciprocal plot) for each concentration of S₂, generating several separate lines.
  • Pattern of those lines, specifically whether or not they intersect permits identification of the kinetic mechanism as sequential or ping-pong.
    
  • Intersecting lines (1/v_o vs. 1/S₁, with a different line for each concentration of S₂) are diagnostic of a sequential kinetic mechanism.
    • Fig. 8-14a (Nelson & Cox, Lehninger Principles of Biochemistry, 3rd ed., 2000) Intersecting lines indicate that a ternary complex is formed in the reaction. (Lines always intersect to left of the 1/v_o axis.)
    • What is the overall order of this reaction?
    • Start at line for the lowest [S₂] value. At a higher [S₂], are the velocities HIGHER or LOWER? Does higher [S₂] make the values of 1/v higher or lower?
    • cannot distinguish random from ordered by double reciprocal plots
      • One way to make that distinction is by product inhibition studies, not discussed here.

• Parallel lines (1/v_o vs. 1/S₁, with a different line for each concentration of S₂) are diagnostic of a ping-pong kinetic mechanism.
  • Fig. 8-14b (Nelson & Cox, Lehninger Principles of Biochemistry, 3rd ed., 2000) Parallel lines indicate a ping-pong (double displacement) pathway. (No ternary complex is formed in the reaction.)
  • What is the overall order of this reaction?
  • Start at line for the lowest [S₂] value. At a higher [S₂], are the velocities HIGHER or LOWER? Does higher [S₂] make the values of 1/v higher or lower?

• True V_max for bisubstrate reactions is observed only at SATURATING concentrations of BOTH S₁ and S₂, and the true Km value for one substrate is that required to give 1/2 V_max when the other substrate is saturating.
  
  
• What steady-state kinetics DO and DON'T tell you:
• You CAN determine whether a particular kinetic mechanism is consistent with the data (so you can eliminate mechanisms that aren't consistent with the data).
• There can be many kinetic mechanisms all consistent with the data, so you canNOT "PROVE" a specific mechanism is correct by steady-state kinetic studies.
• CanNOT determine
  • individual rate constants for different steps (need PRE-STEADY STATE analysis, RAPID kinetic measurements before steady state is reached.
  • number or chemical nature of intermediates in the pathway (need other types of analysis, e.g. spectroscopic characterization of intermediates).

Linked Functions (thermodynamic "boxes"):

• Suppose that S can be converted to P by either of 2 pathways, via an intermediate X or via an intermediate Y:

What is the overall free energy change for the S --> P reaction (DG(S-P)) in terms of the component DG values going by way of "X"? What is the overall free energy change for the S --> P reaction (DG(S-P)) in terms of the component DG values going by way of "Y"?

• DG_(S-P) is independent of the reaction pathway, and DG values for coupled reactions in a reaction pathway are additive.
  That means that
  DG_(S-P) = DG₁ + DG₂ = DG₃ + DG₄
  

• What is the overall equilibrium constant for the S --> P reaction (K_(S-P)) in terms of the component K_eq values going by way of "X"?
• What is the overall equilibrium constant for the S --> P reaction (K_(S-P)) in terms of the component K_eq values going by way of "Y"?
  
  
• K_S-P is independent of the reaction pathway, and K_eq values for coupled reactions in a reaction pathway are multiplicative.
  That means that
  K_(S-P) = K₁• K₂= K₃ • K₄
  
  (On your own, try writing out the expressions for the various K_eq values in this "linked function" box in terms of the eq. concentrations of S, P, X and Y, and show that indeed the overall K_eqS-P value is the product of the 2 "component" equilibrium constants.)

• What if K₂ differs from K₃ by a factor of "a" (a constant)?
  i.e., K₂ = aK₃
  THEN (to maintain the equality of K₁ • K₂ = K₃ • K₄, i.e., the fact that K_(S-P) is what it is irrespective of the pathway),
  K₄ = aK₁

The equilibria are LINKED -- if you change Keq for one reaction, you'll change another one by the same factor: K1• K2= K3 • K4 becomes K1•aK3 = K3•aK1 Obviously, you have to pay attention to what the overall reaction is, so you're maintaining equalities that make sense!

• ENZYME INHIBITION
  • Inhibitor: any compound that reduces the velocity of an enzyme-catalyzed reaction when present in the reaction mixture
  • Use of enzyme inhibitors can often provide valuable information about the catalytic mechanism of an mechanism. 
  • Many drugs (some discussed below) are based on the use of enzyme inhibitors, e.g.,
    • Penicillin irreversibly (covalently) inhibits an enzyme involved in bacterial cell wall synthesis.
    • Ibuprofen and many other nonsteroidal antiinflammatory drugs (NSAIDs) are reversible competitive inhibitors of the cyclooxygenase activity of prostaglandin H₂ synthase; they bind to the channel leading to the active site, preventing substrate binding. (See cox2 if you're interested in some structural information about cyclooxygenase and inhibitor binding.)
      
      
• Inhibitors can be either reversible or irreversible.
  • Irreversible inhibitors bind very tightly (usually covalently) to the enzyme they inhibit.
  • Reversible inhibitors bind to and dissociate from the enzyme (with a measurable dissociation equilibrium constant, K_I).
    • E•I <==> E + I
• 3 types of reversible inhibition, distinguishable by steady-state kinetics:
  • competitive inhibition
  • uncompetitive inhibition
  • noncompetitive inhibition (also called mixed inhibition)
  • Reversible inhibition can be thought of in the context of a linked function diagram (thermodynamic box), as follows:

If binding of inhibitor alters the dissociation constant for the substrate from enzyme by a factor C (so K'ES = CKES), then binding of substrate must alter the dissociation constant for inhibitor from the enzyme by the same factor C (so K'I = CKI).

In the following discussion, it is assumed that the rate of formation of P from ESI (ES with inhibitor also bound) is "zero" (operationally, so slow as to be negligible).

• Competitive Inhibition:
  • E can bind S OR it can bind competitive I, but not both at the same time.
  • a has such a large value that there is no measurable binding of both substrate and inhibitor at the same time. That doesn't prove that they can't bind at the same time, only that no simultaneous binding is detectible experimentally.
  • The K_dissoc value for I from ESI (K_I') and the K_dissoc value for S from ESI (K_ES') are both too high to measure (C is a very large number), so we say that the binding of substrate and the binding of inhibitor are mutually exclusive as far as we can measure.
  • From your knowledge of protein structure and ligand binding, what ways can you think of that might explain how binding of one ligand could prevent binding of another?
  • Fig. 8-15a (Nelson & Cox, Lehninger Principles of Biochemistry, 3rd ed., 2000): competitive inhibition
    

• Competitive inhibitor reduces velocity by effectively reducing the number of available active sites (the effective concentration of free [E]) -- some of the [E] is tied up in the (inactive) form, EI, thus increasing K_m to K_m^app by a factor of a
  

(from J. D. Rawn, Biochemistry, 1989) Figs. 7-32 and 7-33, v_o vs. [S] (hyperbolic) and 1/v_o vs. 1/[S] in the absence and in the presence of a competitive inhibitor.

• On a Lineweaver-Burk (double reciprocal) plot in the presence of a competitive inhibitor (on right below):
  • x-intercepts give – 1/K_m^app (= – 1/aK_m because K_m^app = aK_m)
  • y-intercept gives 1/V_max^app (but V_max^app = V_max for a competitive inhibitor)
  • slope is K_m^app/V_max = aK_m/V_max
    

• Steady state kinetics for competitive inhibitor:
  • effect of competitive inhibitor = increase in apparent K_m in presence of inhibitor.
  • The higher the inhibitor concentration, the greater the increase in K_m.

Apparent Km (Km app) in the presence of a given concentration of inhibitor [I] is greater than the Km in the absence of inhibitor by a factor a: so

Is a greater than, or less than, 1?
Thus, is K_m^app greater than, or less than K_m?
What happens to the velocity in the presence of a competitive inhibitor as [S] gets very high (approaches infinity, i.e., 1/[S] approaches zero)?

• High [S] overcomes the effect of the inhibitor, so V_max is unaffected by a competitive inhibitor. (Note that the 1/v intercept, 1/V_max, is unchanged by the competitive inhibitor.)
• Examples:
  • succinate dehydrogenase:
    
• alcohol dehydrogenase:
  
• Often (but not always), inability to bind both ligands at once is due to inhibitor binding at same site as substrate -- both ligands obviously cannot occupy the same site at the same time! Such examples often involve inhibitors that are structural analogs of the substrate.
• However, there are examples of competitive inhibitors that bind to a different site, preventing substrate binding by another means, such as a conformational change.
  • To cite an example of competitive ligand binding with which you're already familiar:
    Hemoglobin is of course not an enzyme, but 2,3-bisphosphoglycerate binds in central cavity of tetramer in T state, effectively preventing oxygen binding to all 4 hemes on that tetramer, so it behaves as a competitive inhibitor of oxygen binding, but binds to an entirely different site from the oxygen binding sites.
• Uncompetitive inhibition
  • Uncompetitive I binds only to the ES complex, and cannot bind (detectibly) to the free enzyme E.
    • NOTE: a ligand (I) that binds only to the ES complex will have the effect of increasing the apparent binding affinity of E for S (shifting the E + S binding equilibrium toward ES), which results in a decrease in the apparent K_m for substrate.
    • K_I' is the dissociation equilibrium constant for the ESI complex, ESI <==> ES + I, so
      
      
    • Fig. 8-15b (Nelson & Cox, Lehninger Principles of Biochemistry, 3rd ed., 2000): uncompetitive inhibition
  • Uncompetitive inhibitors affect the "uninhibited" V_max and K_m by exactly the same factor (a'), where
    
    
    • V_max is decreased to V_max^app and
    • also K_m is decreased to K_m^app (by the same factor), so
    • the slope of a Lineweaver-Burk plot, K_m/V_max, is unaffected by the presence of the inhibitor.
  • Thus in the presence of increasing concentrations of inhibitor, a Lineweaver-Burk plot shows a family of parallel lines.

(from J. D. Rawn, Biochemistry, 1989) Figs. 7-34 and 7-35, v_o vs. [S] (hyperbolic) and 1/v_o vs. 1/[S] (linear) in the absence and in the presence of an uncompetitive inhibitor.

• On Lineweaver-Burk (double reciprocal) plot in the presence of an uncompetitive inhibitor (on right below):
• x-intercepts give – 1/K_m^app (where K_m^app = K_m/a')
• y-intercepts give 1/V_max^app (where V_max^app = V_max/a')
• slopes are the same in presence and absence of inhibitor because slope = K_m/V_max = K_m^app/V_max^app (a' cancels out in expression for slope)

• Steady state kinetics for uncompetitive inhibitor:
• Uncompetitive inhibitor reduces velocity by making the ESI complex catalytically inactive,
• thus effectively reducing the concentration of the active [ES] (some of the [ES] is tied up in the (inactive) form, ESI),
• decreasing K_m by a factor of a' to K_m^app, AND ALSO decreasing V_max by a factor of a' to V_max^app.

Apparent Km (Kmapp) and apparent Vmax (Vmaxapp) in the presence of a given concentration of inhibitor [I] are BOTH less than the Km in the absence of inhibitor by a factor a': so

• Is a' greater than, or less than, 1?     Thus, is K_m^app greater than, or less than K_m?

Apparent Vmax (Vmaxapp) in the presence of a given concentration of uncompetitive inhibitor [I] is less than the Vmax in the absence of inhibitor by the factor a', so uninhibited Vmax must be divided by a'. Increasing the substrate concentration does not overcome the effect of the uncompetitive inhibitor.

• What happens to the velocity in the presence of an uncompetitive inhibitor as [S] gets very high (approaches infinity, i.e., 1/[S] approaches zero)?
  Is V_max^app greater than, or less than V_max?

 

• Mixed inhibition (special case: pure noncompetitive inhibition)

• A mixed inhibitor
  • binds to a site other than the active site, and
  • reduces the rate of product formation, and
  • can bind to either E or to ES, not necessarily with the same affinity
  • Note: In real life, mixed inhibitors usually affect BOTH K_m and V_max.
  • Fig. 8-15c (Nelson & Cox, Lehninger Principles of Biochemistry, 3rd ed., 2000): mixed inhibition

• Steady state kinetics for mixed inhibition

  • A mixed inhibitor reduces velocity by both tieing up enzyme active sites in the forms of both EI and ESI, and also making the ESI complex catalytically inactive,
  • thus changing K_m by a factor of a/a' to K_m^app, and decreasing V_max by a factor of a' to V_max^app .
  • "pure" noncompetitive inhibition
    • a special case of mixed inhibition in which E and ES both bind I with the same affinity, so
      • a = a', so
      • K_I = K_I' and K_ES = K_ES'
      • Km is not affected by I.
    • "pure"noncompetitive inhibition (shown on plots below)
      • rarely encountered in real life
    • does not affect K_m (K_m^app = K_m) because a = a'.
    • reduces the velocity of the reaction by reducing the concentrations of both E_free and ES by equivalent fractions, so V_max is reduced by a factor a' .

(from J. D. Rawn, Biochemistry, 1989) Figs. 7-36 and 7-37, v_o vs. [S] (hyperbolic) and 1/v_o vs. 1/[S] (linear) in the absence and in the presence of a pure noncompetitive (mixed) inhibitor.

• On Lineweaver-Burk (double reciprocal) plot in the presence of a pure noncompetitive inhibitor (on right below):
• x-intercept gives – 1/K_m^app (where K_m^app = K_{m because} a = a')
• y-intercepts give 1/V_max^app (where V_max^app = V_max/a')
• Mixed inhibition slopes are actually Kmapp/Vmaxapp, which = (aKm/a')/(Vmax/a'); the a' values cancel so slopes = aK_m/V_max;
  because a = a' for pure noncompetitive inhibition, slopes for pure noncompetitive inhibition = K_m/V_max^app

Apparent Vmax (Vmaxapp) in the presence of a given concentration of uncompetitive inhibitor [I] is less than the Vmax in the absence of inhibitor by the factor a', so uninhibited Vmax must be divided by a'. Increasing the substrate concentration does not overcome the effect of the noncompetitive inhibitor.

• SUMMARY OF EFFECTS OF REVERSIBLE INHIBITORS ON V_max AND K_m
  

Type of Inhibition	Vmaxapp	Kmapp
None	Vmax	Km
Competitive	Vmax	aKm
Uncompetitive	Vmax / a'	Km / a'
Mixed PURE noncompetitive (special case of Mixed)	Vmax / a' Vmax / a'	aKm / a' Km (a = a')

• Irreversible or covalent inhibition
  • involves chemical modification of the protein 

Example 1: irreversible inhibition of enzymes that have active site Ser residues (required in the catalytic mechanism) reagent diisopropyl fluorophosphate, DIFP, also known as diisopropyl phosphofluoridate reaction shown at right DIFP inhibits the digestive proteases chymotrypsin and trypsin (was useful in identifying the active site Ser in the structure and chemical mechanism) also a potent nerve toxin -- it covalently inhibits acetylcholine esterase, an enzyme with an active site Ser that's required for the breakdown of the neurotransmitter acetylcholine at synapses.

• Example 2: irreversible inhibition of the cyclooxygenase activity of prostaglandin H₂ synthase by aspirin
  • acetylates a Ser residue that is NOT catalytically required; the covalent modification blocks access of the substrate arachidonate to the active site.
• See Chime routine cox2 for some structural information about cyclooxygenase and inhibitor binding.
• Other nonsteroidal antiinflammatory drugs (e.g., ibuprofen) bind noncovalently in the same channel into the cyclooxygenase active site, so also block substrate binding, but aren't covalent inhibitors.
  
  
• MECHANISM-BASED INHIBITORS ("suicide substrates")
  • inhibitor not especially reactive until it binds to enzyme active site
  • Enzyme treats inhibitor as a substrate, but chemical structure of inhibitor results in covalent inactivation of enzyme by an intermediate generated in the mechanism of catalysis, so active site ends up irreversibly modified.
  • (Enzyme "commits suicide" by trying to catalyze the reaction with the inhibitor as substrate.)
  • Mechanism-based inhibitors are very useful as drugs, because they're specific for only the enzyme with the unique catalytic capability to generate the reactive species in its active site, so few side effects
  • Examples:
    • Penicillin:
      • blocks formation of peptide crosslinks in peptidoglycan component of bacterial cell walls (so no equivalent enzyme in eukaryotes, minimizing side effects)
      • targets an enzyme required for bacterial cell wall synthesis, a transpeptidase
      • enzyme binds penicillin (or an analogous b-lactam antibiotic) and catalytic mechanism generates a covalent penicilloyl-enzyme derivative that can't break down to form product and regenerate free enzyme the way the normal intermediate would. (See Nelson & Cox, Lehninger Principles of Biochemistry, 3rd ed., 2000, Box 20-1, pp. 746-747 if you want more details.)
    • drugs for African sleeping sickness (African trypanosomiasis, caused by a trypanosome, a single-celled eukaryote)
      • target enzyme = ornithine decarboxylase (ODC) , enzyme required for first step in biosynthesis of polyamines needed for DNA packaging
      • mammalian cells degrade ODC and make new enzyme rapidly and continuously, so inhibiting host enzyme isn't much of a problem; trypanosomes make a stable enzyme that isn't rapidly degraded and replaced, so covalent inhibition affects the parasite much more than the host cells.
      • Drugs (substrate analogs like difluoromethylornithine) form a covalent bond to the pyridoxal phosphate cofactor in the enzyme active site the way the normal substrate ornithine does, but as the drug is decarboxylated, a fluorine (excellent leaving group) departs as a F^- ion, generating a highly reactive fluoromethylornithine derivative of the cofactor that can be attacked by a nucleophilic group on the enzyme to displace a 2nd F^-, so the drug derivative ends up irreversibly attached to both the enzyme and the cofactor. (See Nelson & Cox, Lehninger Principles of Biochemistry, 3rd ed., 2000, Box 22-2, pp. 846-847 if you want more details.)
      • Development of such drugs requires understanding the microbiology of the pathogen, an understanding of metabolic pathways in order to choose a target enzyme (and in this case, also understanding the difference in turnover rate of the target enzyme itself between host and pathogen), and of course an understanding of enzymology, the chemical mechanism of the enzyme. (It also helps to know the structure of the enzyme, in particular the structure of its active site, to design a drug that's a good "fit".)
        

• Effect of pH on enzyme-catalyzed reactions
  • Alteration in pH is not usually an important regulatory mechanism in biological systems, but the effect of pH can be highly informative about the mechanism -- see linked function diagram below..
  • Changing pH can increase or decrease rate of an enzyme-catalyzed reaction by changing state of ionization (protonation/deprotonation) of one or more specific functional groups, which can be either on the enzyme:
    • pH can affect catalytic activity (k_cat).
    • pH can affect substrate binding (K_ES).
    • pH can affect the structure or stability of the enzyme in a less specific way (usually only a problem at extremes of pH)
  • or on the substrate: state of ionization of substrate can have an effect either on k_cat or on K_ES.
  
  
  • (Analogous linked functions diagram could be drawn to illustrate effect of state of ionization of substrate on pKa values.)
    
    
  • "pH-rate profile" = plot of velocity vs. pH (but one could also look at effect of pH on K_m, or explicitly on V_max, or V_max / K_m, rather than just velocity at a fixed substrate concentration)
    • Bell-shaped pH-rate profile below: there must be 2 ionizable groups whose state of ionization affects velocity.
    • Be sure to look at problem #17, p. 292, in Nelson & Cox, Lehninger Principles of Biochemistry, for another example.

Hard to get accurate estimate of pKa values from this plot because on a bell-shaped curve the 2 groups' titrations are overlapping so the "maximal" rate isn't really reached (Plots of log Vmax or log Vmax / Km can be extrapolated for much more accurate estimates of pKa values.) pH optimum for this enzyme seems to be about pH 7, with one ionizable group whose pK seems to be between 5.5 and 7, and another whose pK seems to be between 7.5 and 9.5. can't PROVE by pKa values (even if they were more accurate) what ionizable groups are implicated, but IF these were both groups on the enzyme, as opposed to substrate ionizations, what protein ionizable groups can you suggest with pKa values in those two ranges, to develop a hypothesis as to the identities of the two ionizable groups, and state whether each group needs to be in its protonated or deprotonated form for the enzyme to be active?
Note: since we haven't looked explicitly at Vmax (making sure the velocities plotted are with saturating substrate at each pH) or Km, we can't tell what kinetic parameter is affected by pH. Think about the two ionizable groups separately -- Lower pH "arm" of pH-rate profile shows that a deprotonated group is required for activity. It could be the conjugate base form of the imidazole group of a His residue, but of course it could be something else, e.g., a Glu g-carboxyl group with an abnormally high pKa; His is just the likeliest first suggestion.
Higher pH "arm" of pH-rate profile shows that another group, in its protonated form, is required for activity. It could be the conjugate acid form of the e-amino group of a Lys residue, or a protonated Tyr-OH, or a protonated Cys-SH, or even the protonated form of the a-amino group of the polypeptide. A more accurately determined pKa would be useful, but still wouldn't prove the identity of the functional group. More sophisticated analysis is required to obtain an accurate estimation of the pKa in the enzyme. Other experiments required to identify specific residues, e.g., covalent modification that inactivates the enzyme, with identification of the chemically modified residue, or modification of the pH curve or of the activity by mutational change in a residue you think may be involved.

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Biochemistry 462a
http://www.biochem.arizona.edu/classes/bioc462/462a/462a.html
Department of Biochemistry and Molecular Biophysics
The University of Arizona
zieglerm@u.arizona.edu
All contents copyright © 1998-2003. All rights reserved.
Last revision fall 2003