06: Protein Catalysis
Carbonic Anhydrase
Early Enzyme Studies
• Biological systems do not follow ordinary laws
of chemical thermodynamics
• Biological processes caused by the action of
‘unknown’ chemical substances
• Fermentation:
– C6H12O6  2CH3CH2OH + 2CO2
– Ex vivo reaction: “enzyme”
• Greek: en= in, zyme=yeast
Reaction Catalyst
• Catalyst: General term to describe an entity
that can participate in a reaction to increase
the overall rate of product formation, without
being consumed in the process itself
• COORDINATION: brings reactants into close
proximity to increase the probability of a
reaction
• Enzyme Activity:
– Active Site: chemical catalysis
– Allosteric Site: rate regulation
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Catalysts:
General Catalyst:
mineral crystal surface
Specialized Catalyst:
Carbonic Anhydrase
Enzymes as Catalysts
• Highly specialized to facilitate a chemical activity
How do you distinguish
• 1. Higher reaction rates
between concentration
– 106-1012 for enzymes
and coordination effects?
– 103-106 for general catalysts
• 2. Mild reaction conditions
– Low temp (<100 oC)
– Neutral pH
– Low pressure (1 atm)
• 3. Greater reaction specificity for reactants
• 4. Direct mechanism for regulating reaction rates
Enzymes increase reaction rates
• Reaction Rates are determined by two factors:
• Concentration: probability of a successful
encounter between reactants (do the math . . . )
• Coordination: orientation of a successful
encounter between reactants (lock and load . . .)
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It is the electrons that are the reaction participants in
biochemical reactions, not the nucleus
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Carbonic Anhydrase
• HCO3- + H+  H2O + CO2
Model FN: “Carbonic Anhydrase.html”
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CA
mechanism
VMD state model
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Enzyme Kinetics:
Transition State Theory
intermediate
transition
state
free energy
of activation
• Model for simple proton exchange reaction
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Transition State Theory
• Bi-Bi reaction model
Molecular Free Energy
population average
free energy state
• A population of any molecule will possess a
wide range of free energies
Kinetic Energy
frequency
average
Free energy
Activation
reactants
molecular energy
• A fraction of reactants will always have a free energy in
excess of the activation energy
• Enzymes do not change the free energy of the reactants
• Enzymes alter the level of the activation energy
• Is AE constant in an enzyme population?
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Reaction Rates
• Concentration: probability of a successful encounter
between a protein’s active site and a reactant
• Increasing the concentration of reactants will increase
the proportion of those reactants with sufficient free
energy to overcome the activation energy
• Coordination: proximity and destabilization to reduce the
free-energy barrier for a reaction to occur
• A reduction in the activation energy can be achieved by
destabilizing the reaction intermediates and thus lowering
the free energy of those states
• In comparing the reaction rates of two enzymes, does a
higher or lower energy of activation increase the reaction
rate?
Catalyzed Transition States
Kinetics
rate constant
• The rate of an elementary reaction is proportional to the
frequency with which the reacting molecules come together
• The reaction velocity at any time is proportional to the
concentration of the reactant
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First order kinetics
• Rate equation to describe the reaction
progress as a function of time
First order kinetics
• Integral where [A]o is the concentration at t=0
Linearized function
• First order reaction will evidence a proportional decrease
in ln[A] as a function of time
• Exponential decrease in the probability of an adequate
collision between a protein and reactants
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Enzyme Kinetics
rate of glucose
formation
Brown, 1902, β-fructofuranosidase
[sucrose]
At high [S], the rate
of the reaction was
independent of the
concentration of
sucrose
E:S Intermediates
• Brown proposed an intermediate complex between
sucrose and a protein enzyme
• At saturation [S], all the available enzymes are
associated with sucrose and the reaction rate cannot
increase
• At this point the dissociation of the ES complex
becomes the rate limiting step
– K1: selective pressure to recognize reactants
– K2: selective pressure to release products
Reaction Mechanism
• 1. Equilibrium Assumption
• 2. Steady State Assumption
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Assumptions
Steady-State:
Equilibrium:
• Km we define as the association constant
when k-1 << k2
• Ks we define as the dissociation constant
when k -1 >> k2
Michaelis Menton Equation
Reaction velocity at time = 0 . . . .
• The fundamental rate equation in enzyme kinetics
• Vmax and Km can be experimentally measured,
so one can calculate the rate of a reaction under
steady-state conditions
Reaction Velocity
“physiological” [S]
Km
• Km is the substrate concentration at which the reaction
velocity is exactly ½ the maximum possible rate
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Substrate Affinity
Low Km = high affinity
• Enzyme affinity establishes the responsiveness of a
pathway to changes in the concentration of a metabolite
Analyzing Kinetic Data
Lineweaver-Burke, double-reciprocal plots
Equation has a linear form: y = mx + b
• From a simple series of reaction rate measurements,
one can easily calculate the substrate-enzyme affinity
Calculating enzyme kinetics
• X-intercept
– Km
• Y-intercept
– Vmax
• Slope
– Ratio
Km/Vmax
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Enzyme Catalysis
• Enzyme catalysis IS what we mean when we say
“protein function”
• Structure is integral to function
• Measuring the kinetics of enzymatically catalyzed
reactions is important for understanding the
selective pressures on metabolic rate functions
• Reaction Rates are determined by two factors:
• Concentration: probability of a successful encounter
between a protein’s active site and a reactant
• Coordination: proximity and destabilization to reduce the
free-energy barrier for a reaction to occur
Selective Forces
RuBP
• This is the slowest metabolic enzyme known . . . .
• Is that a bad thing? . . . . .
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