Enzyme Kinetics Flashcards
Michaelis Menton Assumptions
- No K-2 (helps simplify the model)
- Assume steady state kinetics for [ES]
- rate of formation = rate of breakdown - [S] = [S total] (More substrate than enzyme)
Irreversible inhibition
Covalently modify active site and inactivate the enzyme
* irreversible inhibitor forms a covalent bond with the enzyme.
* Ex. DIPF & Serine proteases; iodoacetamide & cysteine protease
DIPF & Serine Protease
- Irreversible inhibition
- F in DIPF is a good leaving group and reacts with serine
- Serine attacks P–F bind and kicks out F
- Covalent bond between serine and phosphate
Iodoacetamide & Cysteine Proteases
- Iodine is a good leaving group
- Cysteine sulfhydryl group (nucleophile) attacks the carbon, removing iodine
Penicillin
- Irreverisble inhibitor
- Inhibits bacterial cell wall formation
- Has a highly reactive peptide bond
- Bond breaks, carbon then covalently binds to the serine of enzyme to inhibit
Reversible Inhibition
usually non covalent inhibitors
three main types
* Competitive - binds active site
* Uncompetitive - typically binds away from active site
* Mixed - has elements of both types
Competitive Inhibition
E + I ⇌ EI + S
* Reversible inhibition
* Binds active site
* Vmax is unchanged
* km is different
* can be overcome by increased S concentration
Uncompetitive Inhibition
E + S ⇌ ES + I ⇌ ESI
* Reversible inhibition
* Binds away from active site
* both Vmax and Km change
* Increasing the substrate concentration does not overcome inhibition
* has a different lineweaver burke
Lineweaver burke
y = mx +b
Km/Vmax = the slope (or m).
1/[S] = x
1/Vmax = y-intercept (or b).
1/V0 = Km/Vmax * 1/[S] + 1/vmax
- Works for no inhibition
α in lineweaver burke
α = 1 + [I]/Ki
related to how much inhibitor
α = 1 (no inhibitor), increased concentration = higher α
Lineweaver Burke for
Competitive Inhibition
y = mx +b
αKm/Vmax = the slope (or m).
1/[S] = x
1/Vmax = y-intercept (or b).
1/V0 = αKm/Vmax * 1/[S] + 1/vmax
Effect of Inhibition:
* Increases Km
Lineweaver Burke for Uncompetitive Inhibition
y = mx +b
Km/Vmax = the slope (or m).
1/[S] = x
α/Vmax = y-intercept (or b).
1/V0 = Km/Vmax * 1/[S] + α/vmax
Effect of inhibition
* decreases Vmax and Km
Kcat
Kcat = Vmax/[ES]
Catalytic constant (the same as K2)
* reflects the turnover number and enzyme efficiency in catalyzing reactions
Km
Michaelis constant
* the substrate concentration at which the reaction rate is 50% of the Vmax
* Km is a measure of the affinity an enzyme has for its substrate
* Low Km = STRONG substrate binding
* High Km = WEAK substrate binding
Km = K-1 +K2/K1
Kd
Dissociation constant
* Kd reports the extent of binding that occurs naturally between the ligand and receptor
Kd = koff/kon (surface plasmon resonance)
Kd = K-1/K1
Kd = [R][L]/[R * L] (equilibrium dialysis)
Ki
inhibitor constant, Ki, is an indication of how potent an inhibitor is
* concentration required to produce half maximum inhibition
* Ki = [E][I]/[EI]
Coenzymes
- Enzymes that need to bind additional molecules in order for them to function
Cofactors
- The additional molecules needed for coenzymes to function
ex. - Inorganic ions (e.g. Zn2+, Fe2+, Mg2+)
- Prosthetic groups (e.g. heme)
Apo-enzyme
enzyme that needs a cofactor
Holoenzyme
- enzyme with a cofactor
- Apo-enzyme + cofactor = holoenzyme
Yeast Alcohol Dehydrogensase & NAD+
Coenzyme = Yeast Alcohol Dehydrogenase
Cofactor = NAD+
* NAD+ hydrate transfer to oxidse ethanol to acetaldehyde
Acids
Proton donors
Bases
Proton acceptors
RNases
Degrades RNA using general acid and base catalysis
Breaking RNA
1. His12 deprotonates 2’ Oxygen (acting like a base)
2. 2’ oxygen becomes a nucleophile and attacks the phosphate (forming cyclic intermediate
3. His119 acts like an acid and protonates an oxygen to break different O–P bond
- His 119 is now a base, and His12 is an acid
Intermediate
1. Water enters system, His119 deprotonates H2O to regenerate into acid. H2O is now -OH
2. -OH is strongly nucleophilic & attacks electrophilic phosphate causing cyclic bond to break
3. His12 protonates o- to regenerate the base
Covalent Catalysis/Nucleophilic catalysis
Substrate forms a bond with the enzyme
Metal Ion Catalysis
- Metal ions are cofactors that can bind to enzymes and catalyze reactions
- metalloenzymes are tightly bound metal ions
- Metal is bound & groups will reversibly bind to metals to become activated. Those groups them carry out catalysis
- Ex. Carbonic Anhydrase and Zn2+
Carbonic Anhydrase and Zn2+
Carbonic Anhydrase (metalloenzymes) helps break down carbonic acid
1. Zinc is bound to 3 his residues and 1 H2O
2. When carbonic anhydrase is active a nearby His deprotonates the H2O to make it a nucleophile
Metalloenzyme catalysis
3. The nucleophilic -OH (deprotonated by basic His) attacks CO2 – results in negatively charged O
4. Addition of H2O regenerates -OH bound to zinc
Proximity & Orientation effects
- Productive if orientated and in proximity (more likely to react)
- Unproductive if not orientated well, proximity isnt helpful if they are not orientated. Vice versa
Enzymes orient and increase proximity
Perfect Enzyme Theory
When S < Km then most of the enzyme is uncomplexed; E = Etotal
V = Kcat/Km [Etotal][S]
Kcat/Km == K2/Km == K2K1/K-1+K2
A perfect ennzyme has a Kcat/Km = 10^8 – 10^9 m-1s-1
Mechanisms of Lysozyme
Acid catalysis
Asp52 and Glu35 = catalytic residues that carry out cleavage of β (1->4) glycosidic bond
Cleavage occurs between sugar ring D & E
Glu35 is protonated and acidic but in hydrophobic environment it is neutral
Asp52 - deprotonated, basic, and nucleophilic, in a polar environment which makes it more likely to ionize
Binding substrate to the lysozyme
1. Glu35 protonates glycosidic bond – losing its proton. (allows it to be protonated later)
2. Asp52 is protonated by water
Two different catalytic mechanisms understood
- Phillips Mechanism
- Withers mechanism
Phillips mechanism
- Lysozyme attaches to bacteria cell wall by binding to a hexasaccharide unit (Lysozyme causes D saccharide ring to distort into half-chair formation to make it more catalytically reactive
- Acidic Glu35 transfers its proton to O1 of the D ring (GENERAL ACID CATALYSIS). The C1-O1 bond is cleaved - generating an oxonium ion at C1 (which now has a positive charge)
- Asp52 stabilizes the oxonium ion through charge-charge interactions
- the distances between Asp52 and oxonium ion are too great to bond but STABILIZES CHARGE - The E saccharide is released from the enzyme; water adds to the reverse chemistry and reprotonates Glu35
Withers Mechanism
- Asp52 is involved in a direct attack on D site carbonium atom
- Results in a covalent E-S bond which is then broken down by attacking water (covalent catalysis)
Serine Proteases Catalytic Triad
- Serine - nucleophile that drives rxn
- Histidine - deprotonates serine to stabilize
- Aspartate - provides charge stabilization to the histidine
Specificity Pocket
- Serine -OH side chain is deprotonated by histidine to become a stronger nucleophile
- Asp provides charge stabilization to the protonated his
The substrate lays across the enzyme and catalytic Ser cleaves bond. Next to the cleaved bond is a long chain that is positively charged. There is a specificity pocket in trypsin with an negatively charged Arg residue which stabilizes the charge
Catalytic Mechanism of Serine Proteases
- Nucleophili attack of Ser on carbonyl of sscissle bond forming a tetrahedral intermediate (which the oxyanion hole stabilizes)
- Ser = NUCLEOPHILE; His = general BASE; Asp: electrostatic stabilization - Decomposition of the tetrahydral intermediate through general acid catalysis by his, polarized by Asp, and followed by the loss of amine product and replacement by H2O
- Reversal of step 2 to form tetrahedral intermediate –> binding of O-C reforming peptide (N–> O subsitution)
- Reversal of step 1 to yield carboxyl product and active enzyme – serine breaks bond with substrate and his reprotonates the serine
Oxyanion Hole
The tetrahedral intermediate is complementary to the oxyanion hole
- forms two hydrogen bonds with the tetrahedral intermediate to stabilize
Zymogens
Enzyme precursors
- Ex. trypsinogen – zymogen of trypsin. needs first 15 N-terminal residues to be cleaved to become active
- Trypsin is also autocatalytic so trypsin can cleave the bond of trypsinogen. meaning a small amount of trypsin will lead to more activation
- Have disordered active states which are able to move once cleaved to form proper binding sites for substrate.
- Some terminal tails can also bind to the active site, acting as inhibitors. Once cleaved the active site is exposed
Hill Plot
Shows cooperativity of allosteric enzymes
n = 1 (noncooperative)
n > 1 (cooperative)
The max value of n is the number of binding sites in theory – n will approach the number
MWC Model
Symmetric
2 active states
* T = tense, low activity
* R = relaxed, high activity
ALL OR NOTHING! either T or R
* Keq = L = (T)/(R)
* Higher L = More cooperative
* Lower L = Less cooperative
Substrate binds active site & stabilizes the R. The other active states are affected and stabilized into R so symmetry is maintained
* The intial binding is difficult b/c of the energy barrier. Induced fit from the first site causes a change in the second active site.
- Can me affected by homotropic and heterotropic allosteric affectors
Homotropic Allosteric Effectors
When effector directly binds the active site to induce change in other active sites. The allosteric effector is often the substrate.
Heterotropic Allosteric Effectors
The binding of the heterotropic effector induces a change in a different site that binds a different type of molecule
* Allosteric inhibitor or activator binds to allosteric site. Effects the binding of the substrate at the active site.
Allosteric inhibitor: stabilizes conformation with less binding affinity for the substrate
Allosteric activator: stabilizes the conformation with more affinity for the substrate
KNF model
Asymmetric
* Two states (T & R) but are independent of each other
* Hybrid states!
* No T,R equilibrium exists.
* Homo and hetero effectors exist
ATCase
- Aspartate is a homotropic effector
- ATP (+) and CTP (-) heterotropic effectors
- ATCase catalyzes the first step to make CTP - negative feedback loop
ATCase homotropic allosteric transition
When homotropic effector binds:
* the C3 trimer opens by 12Å
* C3 untwists by 10Å
* R chain twists by 15
240s loop rotates inward to bind PALA
= global change occurs in the prescense of substrate
Addition of inhibitor to ATCase
- activity will shoot up and the gradually decrease
- When one PALA is bound the entire enzyme moves into R state which removes the barrier to binding. This allows more PALA to bind. Once those active sites are full (~3 PALA) then the activity will decrease
Allosteric Enzyme Vs. Allosteric Site
Allosteric enzyme: Classic multi-subunit enzymes w/ multi-active sites
Allosteric site: Site away from active site that effects the binding of substrate to active site. A monomeric enzyme can have an allosteric site.
