06523 Kinetics' Lecture 6 Kinetics and Mechanism III' Enzyme Kinetics Catalysis Enzymes Enzyme kinet

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06523 Kinetics. Lecture 6Kinetics and
Mechanism III. Enzyme KineticsCatalysisEnzymes
Enzyme kinetics Michaelis-Menten
equationPlotting enzyme kinetic dataInhibition

• Dr John J. Birtill

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Catalysis

• The reaction rate of simple reactions can be
  increased by increasing the temperature.
• The rate constant follows the Arrhenius law where
  Ea activation energy.

• An alternative approach is to use a catalyst
• Catalyst substance that increases the rate of a
  chemical reaction but is not changed itself at
  the end of the reaction.
• The catalyst provides an alternative mechanism
  via a transition state with lower Ea

• Catalysts can be heterogeneous (different phase
  to the reactants) or homogeneous ( same phase as
  the reactants).

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Enzyme catalysis

• Enyzmes biochemical catalysts, based on proteins.

• Protein unbranched polymer of 10s to 100s of
  a-amino acid units with amide linkages.
  General formula

• Enzymes may be entirely protein or may use other
  groups (co-enzymes).
• An enzyme may be highly specific in its catalytic
  action.
• It will catalyse the reaction of a specific
  molecule (the substrate).
• The conformation (shape) of the complex enzyme
  molecule allows it to bind to the target
  substrate to form an intermediate.
• The enzyme is then restored in the final reaction
  step.
• Hydrolytic enzymes catalyse hydrolysis reactions,
  e.g., of esters and sugars
• commonly acid-base catalysts that assist H
  transfer
• Oxidative enzymes catalyse electron-transfer
  steps in redox processes
• Transferring enzymes promote the interchange of
  groups, e.g., amino- or keto-groups.

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X-ray structure of human sigma alcohol
dehydrogenase

• Source Homo sapiens.
• Organ stomach.
• Expressed in escherichia coli.

Ref D.Hurley, P.Xie, www.biochem.ucl.ac.uk/bsm/p
dbsum/1agn/main.html
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Enzyme catalysis continued
Example conversion of fumarate to (-)-malate
Initial rate vs S

• Enzyme reactions may be reversible or
  irreversible.
• The initial rate increases with enzyme
  concentration E.
• The initial rate increases with substrate
  concentration S but levels off to a maximum
  value ?max.

Constant E

• Note that the symbol ? is generally used for
  reaction rate in enzyme kinetics.

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Enzyme catalysis Michaelis-Menten kinetics

• A simple rate law might follow 2nd order kinetics

• The empirical (experimentally observed) kinetics
  of enzyme catalysis are more complex.
• The initial rate depends on the concentrations of
  both enzyme E and substrate S
• The initial rate does not increase indefinitely
  with S but tails off to a maximum.

• The rate can be expressed in the form ..
• The maximum rate ?max (when S gtgt KM) is then
  given by
• By rearrangement the rate at any value of S is
  related to the maximum rate by the
  Michaelis-Menten equation .where KM is the
  Michaelis constant (units of concentration)
• Note that ? ?max /2 when S KM

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Enzyme catalytic mechanisms I

• Proposed mechanism (irreversible reaction in this
  case but could be reversible).
• The enzyme molecule E causes it to bind to the
  substrate S to form an intermediate ES in a
  reversible reaction.
• The intermediate ES decomposes irreversibly to
  yield the product P and the enzyme E.
• The enzyme is not changed in the overall reaction.

• The overall mechanism consists of two consecutive
  reactions with a reversible 1st step. We met
  this type of mechanism in lecture 5 (slide 5) but
  there are some important differences
• in this case there are two reactants E and S
• the enzyme E is a catalyst and is restored in the
  final reaction step
• the enzyme E is present in very small quantity
  compared to substrate S, E ltltS
• the enzyme is present mainly in the form of the
  intermediate ES
• The solution for enzyme kinetics is therefore a
  little different to the previous case.

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Enzyme catalytic mechanisms II

• The initial rate equations for each step at the
  steady state are given by (1) to (3)with the
  steady state approximation applied to the 2nd
  step.
• E is ltlt S and so ES ltlt S and so SS0
  and is therefore known.
• Rearrange (2) and solve for ES in (4)-(6).
• We dont know E but we do know E0.and E
  E0- ES. Substitute for E in (6) and then
  rearrange (7) to resolve out ES in (8).
• Hence we can express ES in (8) in terms of
  known concentrations E0 and S .
• Hence we can express the rate law to match
  Michaelis-Menten kinetics.
• Note KM is not an equilibrium constant

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Enzyme catalytic mechanisms III

• As has already been seen, the rate law can be
  expressed in terms of the maximum rate ?max
• This is the normal form of the Michaelis-Menten
  equation.
• The vaues ?max and KM can be determined by
  least-squares fitting of initial rate data to
  this equation.
• This equation can also be expressed in reciprocal
  form and ?max and KM can then be determined
  graphically.
• The plot of 1/ ? vs 1/S has the formy mx
  cand is known as the Lineweaver-Burk plot

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Lineweaver-Burk plot
Gradient KM/?max

• The extrapolated intercept at 1/S 0 is equal to
  -1/?max
• Use gradient plus intercept on y-axis or
  intercept on x-axis to determine KM.
• Disadvantage plot dominated by points at low
  S, high 1/S

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Alternative graphical methods I

• The Michaelis-Menten equation can be rearranged
  in different ways for alternative plots

• Eadie or Hofstee plot.
• Plot ? against ? /S. Linear plot
• Gradient KM
• Intercept on y-axis ?max
• Errors in ? can lead to deviation from linearity

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Alternative graphical methods II

• Hanes or Dixon plotPlot S/? against S.
  Linear plot
• Gradient 1/ ?max
• Intercept on y-axis KM/?max

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Enzyme inhibition
Competitive inhibition

• The action of an enzyme may be suppressed by an
  inhibitor.
• This could be a substance that is naturally
  present as part of the regulatory mechanism of
  the cell.
• A poison is a strongly-binding substance that is
  not meant to be present.
• Example cytochrome oxidase (a key enzyme in
  aerobic oxidation) is poisoned by cyanide.
• Competitive inhibition inhibitor competes for
  active sites.
• Leads to modified Michaelis-Menten equation
• Effect of increasing I on Lineweaver-Burk plot
• gradient increases
• intercept on x-axis changes but intercept on
  y-axis does not change (1/?max)

• Non-competitive inhibition inhibitor does not
  compete for active sites but modifies the
  structure and hence activity of the enzyme.

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Summary

• The kinetics of reactions with complex mechanisms
  can be simplified using suitable approximations
• Steady state approximation
• Quasi-equilibrium approximation
• Rate-determining step
• These methods can be applied to the kinetics of
• liquid phase reactions
• gas phase reactions
• enzyme catalysis.