Molecular)Cell)Biologymcb5068.wustl.edu/MCB/Lecturers/Cooper/s/4... · Catalyst (enzyme): increases...

Molecular Cell Biology

Kine1cs: Enzymology

Cooper

Wednesday, August 29, 2012

Kine1c analysis

• How cells change over long 1me periods (development, long term adap1ve changes; hours -‐ years)

• Movement of proteins and membranes within cells -‐ dynamics of cellular events (sec -‐ hrs)

– Pulse chase analyses

– Real 1me imaging: GFP and other fluorophores allow measurement of trafficking, diffusion, etc. (1me-‐lapse, fluorescence recovery aPer photobleaching (FRAP), etc.)

• Kine1cs of molecular interac1ons, enzyme reac1ons (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 Reac1ons• Transient phase

– Accelera1ng Velocity– Short (<1s)– Forma1on Enzyme-‐Substrate

Intermediates

• Steady-‐state phase– May Not Occur– Constant Velocity– Dura1on up to Several Minutes– Li\le Change Levels of Enzyme– Small Frac1on Substrate Consumed– Small Levels Product Formed

• Exhaus1on phase– Decreasing Velocity– Deple1on of Substrate– Accumula1on of Product– Inac1va1on of Unstable Enzyme


What Can You Learn from What Happens at Steady State?

• Turnover number => cataly1c efficiency of enzyme

• Affinity of enzyme for substrates

• Lower bounds for rate constants

• Inhibitors and pH varia1ons to probe ac1ve site

• Details of mechanism require transient (pre-‐steady state) kine1c 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 Ac1vity 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


Op1mizing assay

• No Enzyme -‐> No Product

• Op1mize pH, salt, other buffer condi1ons

• Op1mize temperature

• Choose set of condi1ons to be kept constant

• Amount of enzyme – Linear range of assay

– More is be\er


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

Equilibrium?

Steady-state?

Measure Velocity of Reac1on


Run the Assay at Different Substrate Concentra1ons

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


Michaelis-‐Menten Plot

• What’s interes1ng or useful about this plot?

• Can we use this plot to compare results for different enzymes or condi1ons?

• Can we derive an equa1on for the curve?Wednesday, August 29, 2012

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 Equa1on for the Curve


Problem -‐ [ES] cannot be measured

• However...

• [S0] (the ini1al concentra1on of substrate) is known

• [P] (product produced) can be measured

• [ETotal] (the amount of enzyme added to the reac1on) is known

• The individual rate equa1ons 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)/k1Typical 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]=Km v0 = 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 reac1on– Hexokinase

• Km (glucose) = 0.1 mM

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

• Reac1on is inhibited by product-‐-‐regulated by product u1liza1on

– Glucokinase• Km (glucose) = 10 mM

• Km > [S], promotes glucose u1liza1on only when [glucose] is high

• Reac1on not inhibited by product-‐-‐regulated by substrate availability


Determining Km and Vmax

• Es1mate Vmax from asymptote, Km from conc. at Vmax/2

• Curve fiong w/ computer programs, inc Excel

• Visual inspec1on (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.


Regula1ng enzyme ac1vity

• Allosteric regula1on

• Reversible covalent modifica1ons

• Enzyme availability (synthesis, degrada1on, localiza1on)

• Substrate availability (synthesis, degrada1on, localiza1on)

• Inhibi1on– By specific metabolites within the cell

– By drugs, toxins, etc.

– By specific analogues in study of reac1on 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)

Compe11ve Inhibi1on


Example of Compe11ve Inhibi1on

• 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 op1c neuri1s (from formate) that can cause blindness.

• Treatment: Infuse EtOH to keep blood concentra1on at 100-‐200 mg/dL (legally intoxicated) for long enough to excrete the MeOH.

• EtOH serves as a compe11ve inhibitor. Ethylene glycol poisoning is treated in the same way.


Noncompe11ve Inhibi1on

• Noncompe11ve inhibitor ...

• Binds to a site on the enzyme (E or ES) that inac1vates the enzyme

• Decreases total amount of enzyme available for catalysis, decreasing Vmax

• Remaining ac1ve enzyme molecules are unaffected, so Km is unchanged


Uncompe11ve Inhibi1on

• Uncompe11ve inhibitor...

• Binds specifically to the [ES] complex (and inac1vates it

• Frac1on of enzyme inhibited increases as [S] increases

• So both Km and Vmax are affected


Summary: Types of Inhibitors• Compe11ve

– Binds Free Enzyme Only

– Km Increased

• Noncompe11ve– Binds E and ES

– Vmax Decreased

• Uncompe11ve– Binds ES only

– Vmax Decreased

– Km Decreased


Plots to Dis1nguish Types of Inhibitors

• Compe11ve

• Uncompe11ve

• Noncompe11ve

No inhibitor

No inhibitor

No inhibitor

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


Reading and Homework for Kine1cs

• Alberts (5th edi1on) pp. 159-‐166

• Lodish (6th edi1on) pp. 79-‐85

• See handout or website for homework


Molecular)Cell)Biologymcb5068.wustl.edu/MCB/Lecturers/Cooper/s/4... · Catalyst (enzyme): increases...

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