Molecular Cell Biology

Kinetics: Enzymology

Cooper

Kinetic analysis

• How cells change over long time periods (development, long term adaptive changes; hours - years)

• Movement of proteins and membranes within cells - dynamics of cellular events (sec - hrs)– Pulse chase analyses– Real time imaging: GFP and other fluorophores allow

measurement of trafficking, diffusion, etc. (time-lapse, fluorescence recovery after photobleaching (FRAP), etc.)

• Kinetics of molecular interactions, enzyme reactions (msec - min)

Catalyst (enzyme): increases rate of a reactionSubstrate: molecule on which enzyme acts to form product

S ------> P enzyme Free energy of reaction not changed by enzyme. For a favored reaction (ΔG negative), enzymeaccelerates reaction.

Graph:ΔG* = activation energyΔG negative overall for forward reaction

Enzymes are catalysts for chemical reactions in cells

Active Site: Region of the enzyme that does the work. Amino acid residues in this site assume certain 3D conformation, which promotes the desired reaction.

What does the Enzyme do to cause catalysis?

•High affinity for substrate in its transition state, facilitating transition to product•Increased probability of proper orientation of substrates•Increased local concentration of substrates•Has atoms in places that push the reaction forward•Change hydration sphere of substrates

Enzymes as Catalysts

Phases of Enzyme Reactions• Transient phase

– Accelerating Velocity– Short (<1s)– Formation Enzyme-Substrate

Intermediates• Steady-state phase

– May Not Occur– Constant Velocity– Duration up to Several Minutes– Little Change Levels of Enzyme– Small Fraction Substrate Consumed– Small Levels Product Formed

• Exhaustion phase– Decreasing Velocity– Depletion of Substrate– Accumulation of Product– Inactivation of Unstable Enzyme

What Can You Learn from What Happens at Steady State?

• Turnover number => catalytic efficiency of enzyme

• Affinity of enzyme for substrates• Lower bounds for rate constants• Inhibitors and pH variations to probe active site• Details of mechanism require transient (pre-

steady state) kinetic analysis

Need an assay that measures the product of the chemical reaction. For example...

Enzyme β-galactosidase catalyzes this reaction: lactose --------------------> glucose + galactose

Measure the amount of glucose or galactose over time.

Trick - use a substrate that produces a reaction product that absorbs light (creates color). Measure absorbance.

How to Measure Enzyme Activity at Steady State

ONPG = ONP-galactose (ONP = o-nitro-phenol) ONPG --------------> galactose + ONP

(colorless) (colorless) (yellow)

X-gal = X-galactose (X = 4-chloro-3-bromo indole) X-gal ---------------> galactose + 4-Cl-3-Br-indigo (colorless) (colorless) (deep blue)

Measure absorbance with a spectrophotometer•Beer’s law - concentration proportional to absorbance•96-well format instruments

Color-Producing Substrates for β-galactosidase

Optimizing assay

• No Enzyme -> No Product• Optimize pH, salt, other buffer conditions• Optimize temperature• Choose set of conditions to be kept

constant• Amount of enzyme

– Linear range of assay– More is better

One Single Experiment at One Substrate Concentration•Plot product vs time•Determine rate during initial linear phase

Equilibrium?

Steady-state?

Measure Velocity of Reaction

Run the Assay at Different Substrate Concentrations

Plot initial rate (v0)vsConcentration of Substrate [S]

Michaelis-Menten Plot

• What’s interesting or useful about this plot?

• Can we use this plot to compare results for different enzymes or conditions?

• Can we derive an equation for the curve?

Consider time zero•We measure the initial velocity of the reaction)•No product present: Back reaction is neglible, i.e. no k-2.

The initial velocity, v0, is therefore simply:

v0 = k2[ES]

(k2 often called “kcat” - catalysis rate constant)

Deriving an Equation for the Curve

Problem - [ES] cannot be measured

• However...• [S0] (the initial concentration of substrate) is known• [P] (product produced) can be measured• [ETotal] (the amount of enzyme added to the reaction) is

known• The individual rate equations allow us to solve, using

algebra, for [ES] in terms of these known values

At steady state, d[ES]/dt is zero.So...

Solving for [ES]...

To simply, let’s define a constant, Km, theMichaelis constant as...

This simplifies the equation:

But... we don’t know [E].

We do know that the total amount of Enzyme is the sum of E and ES...

[E0] = [E] + [ES]

thus..

[E] = [E0] − [ES]

Substituting for [E]...

Rearrange to solve for [ES]...

From before, the rate (or velocity) of the reaction is...

Substituting for [ES]...

V, the velocity (rate) of the reaction is...

How does v depend on (vary with) S?

Km is the “Michaelis-Menten constant” - the substrate concentration at which reaction velocity is half-maximal.

Km = (k-1 + k2)/k1

Typical values? nM to mM

Vmax = k2 [E]total = kcat [E]total Typical kcat values? 1-1000 per second

V0

Consider three situations...

1. [S] very large, much greater than Km The enzyme will be saturated with substrate. [S] + Km = ~ [S], so the rate equation simplifies to... v0 = Vmax

2. [S] very small, much less than Km[S] + Km = ~ Km , so the equation simplifies to ...

v0 linearly proportional to [S]

3. [S]=Kmv0 = 50% of Vmax

V0

How Km values affect metabolism

• Glucose + ATP --> glucose-6-P + ADP + H+

• Typical cell [glucose] = 5 mM• Two enzymes catalyze above reaction

– Hexokinase• Km (glucose) = 0.1 mM

• Km << [S], so velocity independent of [glucose]

• Reaction is inhibited by product--regulated by product utilization

– Glucokinase• Km (glucose) = 10 mM

• Km > [S], promotes glucose utilization only when [glucose] is high

• Reaction not inhibited by product--regulated by substrate availability

Determining Km and Vmax

• Estimate Vmax from asymptote, Km from conc. at Vmax/2

• Curve fitting w/ computer programs, inc Excel• Visual inspection (Graph paper)

Lineweaver-Burke plot and others

Michaelis-Menten equation can be rearranged into “Lineweaver-Burke” equation

From this graph, visually estimate Km and Vmax.

Regulating enzyme activity

• Allosteric regulation• Reversible covalent modifications• Enzyme availability (synthesis, degradation, localization)• Substrate availability (synthesis, degradation,

localization)• Inhibition

– By specific metabolites within the cell– By drugs, toxins, etc.– By specific analogues in study of reaction mechanism

Competitive inhibitor ...

• binds to free enzyme

• prevents simultaneous binding of substrate

- i.e. competes with substrate

• Apparent Km of the substrate is therefore increased

• High substrate concentration:

- substrate overcomes inhibition by mass action

- v0 approaches Vmax (which does not change)

Competitive Inhibition

Example of Competitive Inhibition

• EtOH Rx for MeOH poisoning• Methanol (ingested from solid alcohol, paint strippers,

windshield washer fluid, etc.) is metabolized by alcohol dehydrogenase to formaldehyde and formic acid. Leads to metabolic acidosis and optic neuritis (from formate) that can cause blindness.

• Treatment: Infuse EtOH to keep blood concentration at 100-200 mg/dL (legally intoxicated) for long enough to excrete the MeOH.

• EtOH serves as a competitive inhibitor. Ethylene glycol poisoning is treated in the same way.

Noncompetitive Inhibition

• Noncompetitive inhibitor ...• Binds to a site on the enzyme (E or ES) that

inactivates the enzyme• Decreases total amount of enzyme

available for catalysis, decreasing Vmax• Remaining active enzyme molecules are

unaffected, so Km is unchanged

Uncompetitive Inhibition

• Uncompetitive inhibitor...• Binds specifically to the [ES] complex (and

inactivates it• Fraction of enzyme inhibited increases as

[S] increases• So both Km and Vmax are affected

Summary: Types of Inhibitors• Competitive

– Binds Free Enzyme Only– Km Increased

• Noncompetitive– Binds E and ES– Vmax Decreased

• Uncompetitive– Binds ES only– Vmax Decreased– Km Decreased

Plots to Distinguish Types of Inhibitors

• Competitive

• Uncompetitive

• Noncompetitive

No inhibitor

No inhibitor

No inhibitor

Plots show curves with no inhibitor vs. presence of two different concentrations of inhibitor

Reading and Homework for Kinetics

• Alberts (5th edition) pp. 159-166• Lodish (6th edition) pp. 79-85• See handout or website for homework