ENZYME KINETICS

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ENZYME KINETICS

• Medical Biochemistry, Lecture 24

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Lecture 24, Outline

• Michaelis-Menten kinetics
• Interpretations and uses of the Michaelis-Menten
  equation
• Enzyme inhibitors types and kinetics

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Enzyme Kinetics Equation
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Michaelis-Menten Equation
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Initial Velocity (vo) and S

• The concentration of substrate S present will
  greatly influence the rate of product formation,
  termed the velocity (v) of a reaction. Studying
  the effects of S on the velocity of a reaction
  is complicated by the reversibility of enzyme
  reactions, e.g. conversion of product back to
  substrate. To overcome this problem, the use of
  initial velocity (vo) measurements are used. At
  the start of a reaction, S is in large excess
  of P, thus the initial velocity of the reaction
  will be dependent on substrate concentration

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Michaelis-Menten Curve
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Initial Velocity (vo) and S (cont)

• When initial velocity is plotted against S, a
  hyperbolic curve results, where Vmax represents
  the maximum reaction velocity. At this point in
  the reaction, if S gtgt E, all available enzyme
  is "saturated" with bound substrate, meaning only
  the ES complex is present.

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Michaelis-Menten Curve
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Substrate Saturation of an Enzyme
A. Low S B. 50 S or Km C. High,
saturating S
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Steady State Assumption

• The M-M equation was derived in part by making
  several assumptions. An important one was the
  concentration of substrate must be much greater
  than the enzyme concentration. In the situation
  where S gtgt E and at initial velocity rates,
  it is assumed that the changes in the
  concentration of the intermediate ES complex are
  very small over time (vo). This condition is
  termed a steady-state rate, and is referred to as
  steady-state kinetics. Therefore, it follows
  that the rate of ES formation will be equal to
  the rate ES breakdown.

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Michaelis-Menten Equation Derivation

• Rate of ES formation k1(ET - ES)S (where
  ET is total concentration of enzyme E and k-2
  is considered neglible)
• Rate of ES breakdown to product k-1ES k2ES

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Michaelis-Menten Equation Derivation (cont)

• Thus for the steady state assumption
• k1(ET - ES)S k-1ES k2ES
• This equation is the basis for the final
  Michaelis-Menten following algebraic
  rearrangement and substitution of Km and Vmax
  terms.

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Meaning of Km

• An important relationship that can be derived
  from the Michaelis-Menten equation is the
  following If vo is set equal to 1/2 Vmax, then
  the relation Vmax /2 VmaxS/Km S can
  be simplied to Km S 2S, or Km S.
  This means that at one half of the maximal
  velocity, the substrate concentration at this
  velocity will be equal to the Km. This
  relationship has been shown experimentally to be
  valid for many enzymes much more complex in
  regards to the number of substrates and catalytic
  steps than the simple single substrate model used
  to derive it.

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Meaning of Km (cont)

• The significance of Km will change based on the
  different rate constants and which step is the
  slowest (also called the rate-limiting step). In
  the simplest assumption, the rate of ES breakdown
  to product (k2) is the rate-determining step of
  the reaction, so k-1 gtgt k2 and Km k-1/k1. This
  relation is also called a dissociation constant
  for the ES complex and can be used as a relative
  measure of the affinity of a substrate for an
  enzyme (identical to Kd). However if k2 gtgt k-1
  or k2 and k-1 are similar, then Km remains more
  complex and cannot be used as a measure of
  substrate affinity.

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Uses of Km

• Experimentally, Km is a useful parameter for
  characterizing the number and/or types of
  substrates that a particular enzyme will utilize
  (an example will be discussed). It is also useful
  for comparing similar enzymes from different
  tissues or different organisms. Also, it is the
  Km of the rate-limiting enzyme in many of the
  biochemical metabolic pathways that determines
  the amount of product and overall regulation of a
  given pathway. Clinically, Km comparisons are
  useful for evaluating the effects mutations have
  on protein function for some inherited genetic
  diseases.

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Meaning of Vmax

• The values of Vmax will vary widely for different
  enzymes and can be used as an indicator of an
  enzymes catalytic efficiency. It does not find
  much clinical use.
• There are some enzymes that have been shown to
  have the following reaction sequence
• In this situation, the formation of product is
  dependent on the breakdown of an enzyme-product
  complex, and is thus the rate-limiting step
  defined by k3.

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Derivation of kcat

• A more general term has been defined, termed
  kcat, to describe enzymes in which there are
  multiple catalytic steps and possible multiple
  rate-limiting steps. The Michaelis-Menten
  equation can be substituted with kcat

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Definition and Use of kcat

• The constant, kcat (units of sec-1), is also
  called the turnover number because under
  saturating substrate conditions, it represents
  the number of substrate molecules converted to
  product in a given unit of time on a single
  enzyme molecule. In practice, kcat values (not
  Vmax) are most often used for comparing the
  catalytic efficiencies of related enzyme classes
  or among different mutant forms of an enzyme.

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Two Substrate Reactions

• Many enzyme reactions involve two or more
  substrates. Though the Michaelis-Menten equation
  was derived from a single substrate to product
  reaction, it still can be used successfully for
  more complex reactions (by using kcat).

Random
Ordered
Ping-pong
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Two Substrate Reactions (cont)

• In random order reactions, the two substrates do
  not bind to the enzyme in any given order it
  does not matter which binds first or second.
• In ordered reactions, the substrates bind in a
  defined sequence, S1 first and S2 second.
• These two reactions share a common feature termed
  a ternary complex, formed between E, ES1, ES2
  and ES1S2. In this situation, no product is
  formed before both substrates bind to form ES1S2.

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Two Substrate Reactions (cont)

• Another possibility is that no ternary complex is
  formed and the first substrate S1 is converted to
  product P1 before S2 binds. These types of
  reactions are termed ping-pong or double
  displacement reactions.

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Km and kcat ExampleHSV-1 Thymidine Kinase

• A phosphorylation kinase reaction T (thymidine)
  ATP is converted to TMP (thymidine
  monophosphate) ADP
• In herpesvirus infected cells, this viral encoded
  TK phosphorylates the antiviral drug acyclovir
  this is the pharmacological basis of most
  herpesvirus treatments
• In the last 10 years, this approach has been
  applied to cancer gene therapies with HSV-TK and
  ganciclovir

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Thymidine Kinetic Constants for HSV-1 Thymidine
Kinase (ONLY AN EXAMPLE!!)
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Ganciclovir Kinetic Constants for HSV-1 Thymidine
Kinase (ONLY AN EXAMPLE!)
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Lineweaver-Burk (double reciprocal plot)

• If the reciprocal (1/X) of the Michaelis-Menten
  equation is done, after algebraic simplification
  the following equation results
• This relation is written in the format of the
  equation for a straight line, y mx b, where
  y 1/vo, m (slope) Km/Vmax, x 1/S and the
  y-intercept, b 1/Vmax. When this relation is
  plotted,the result is a straight line graph

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Lineweaver-Burk (double reciprocal plot) (cont)
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Uses of double reciprocal plot

• The x intercept value is equal to -1/Km. The
  biggest advantage to using the double reciprocal
  plot is a more accurate determination of Vmax,
  and hence Km. It is also useful in
  characterizing the effects of enzyme inhibitors
  and distinguishing between different enzyme
  mechanisms.

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Enzyme Inhibitor Types

• Inhibitors of enzymes are generally molecules
  which resemble or mimic a particular enzymes
  substrate(s). Therefore, it is not surprising
  that many therapeutic drugs are some type of
  enzyme inhibitor. The modes and types of
  inhibitors have been classified by their kinetic
  activities and sites of actions. These include
  Reversible Competitive Inhibitors, Reversible
  Non-Competitive Inhibitors, and Irreversible
  Inhibitors

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Definition of Ki

• For reversible inhibitors, a term Ki can be
  determined.
• For competitive inhibitors, the following
  relation can be used Km I Km (1 I / Ki
  ) (where Km I is the determined Km in the
  presence of I).
• Determining the Ki for other inhibitor types is
  related but much more complex and not within the
  scope of this lecture or course

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Uses of Ki

• Ki values are used to characterize and compare
  the effectiveness of inhibitors relative to Km.
  This parameter is especially useful and important
  in evaluating the potential therapeutic value of
  inhibitors (drugs) of a given enzyme reaction.
  For example, Ki values are used for comparison of
  the different types of HIV protease inhibitors.
  In general, the lower the Ki value, the tighter
  the binding, and hence the more effective an
  inhibitor is.

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Competitive Inhibition
Vmax - No change Km INCREASES - indicates a
direct interaction of the inhibitor in the active
site
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Reversible Competitive Inhibition

• Competitive inhibitors compete with the substrate
  for binding at the active site (as E I). In the
  double reciprocal plot for a competitive
  inhibitor acting at the substrate site for the
  following reasons, notice with increasing
  concentration of inhibitor, the Vmax does not
  change however, the Km of the substrate is
  increased. This also reflects the reversible
  nature of the inhibitor there is always some
  concentration of substrate which can displace the
  inhibitor.

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Non-Competitive Inhibition
Vmax DECREASES - inhibitor affects rate of
reaction by binding to site other than substrate
active-site Km - No change
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Reversible Non-Competitive Inhibition

• Non-competitive inhibitors combine with both the
  enzyme (E I) and the enzyme-substrate (EI S)
  complex. The inhibitor binds to a site other that
  the substrate site, and is thus independent of
  the presence or absence of substrate. This action
  results in a conformational change in the protein
  that affects a catalytic step and hence decreases
  or eliminates enzyme activity (formation of P).
  Notice in the reciprocal plot, a non-competitive
  inhibitor does not affect the binding of the
  substrate (Km), but it does result in a decrease
  in Vmax. This can be explained by the fact that
  since inhibitor bound to an enzyme inactivates
  it, the more EI formed will lower ES and thus
  lower the overall rate of the reaction Vmax.

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Irreversible Inhibitors

• Irreversible inhibitors generally result in the
  destruction or modification of an essential amino
  acid required for enzyme activity. Frequently,
  this is due to some type of covalent link between
  enzyme and inhibitor. These types of inhibitors
  range from fairly simple, broadly reacting
  chemical modifying reagents (like iodoacetamide
  that reacts with cysteines) to complex inhibitors
  that interact specifically and irreversibly with
  active site amino acids. (termed suicide
  inhibitors). These inhibitors are designed to
  mimic the natural substrate in recognition and
  binding to an enzyme active site. Upon binding
  and some catalytic modification, a highly
  reactive inhibitor product is formed that binds
  irreversibly and inactivates the enzyme. Use of
  suicide inhibitors have proven to be very
  clinically effective

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Irreversible Inhibitor Allopurinol
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Irreversible Inhibitor Penicillin (Ex)
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Diisopropyl Phosphofluoridate Irreversible
Acetylcholinesterase Inhibitor (Example)
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Inhibitor Summary

• REMEMBER - The types of enzyme inhibitors
  described have been for relatively simple, single
  substrate-product reactions that obey
  Michaelis-Menten kinetics. However, not all
  enzyme inhibitors will necessarily be one type of
  inhibitor. Especially for some multi-substrate
  reactions, a particular inhibitor can be
  competitive for one substrate and non-competitive
  with a second or third substrate. Also, suicide
  inhibitors by design are generally competitive
  inhibitors of a substrate, and therefore must
  first bind in the active site.