Enzyme Kinetics and Inhibition Flashcards
Irreversible Reactions
A –> P
Rate of P formation equals rate of A disappearance
Rate of P formation is directly proportional to the concentration of reactant
V= dp/dt= k[A]
V= -dA/dt= k[A]
Characteristics of 1st order reactions
Exponent is 1
Units: s^-1
Bimolecular irreversible reaction
A + B –> P
Rate of P formation equals rate of disappearance of A OR B
Rate of P formation (or A/B disappearance) is directly proportional to concentration of reactants
V= dp/dt = k [A] [B]
Unimolecular reversible reaction
A P
V= dp/dt = k1[A] - k2[P]
^rate of P formation and rate of A disappearance
Rate gained = rate loss AT EQUILIBRIUM
Equilibrium constant: Keq
K1/k2 = [P]/ [A]
Steady state Assumption for Michaelis Menten
[ES] assumed to be unchanging
Michaelis Constant=
Km= (k2 +k3)/k1 > [E] and ES formation has negligible effect on S… [S]= constant = [S]t
Formula for [ES] under steady state
[ES]= [E][S]/ Km = ([E]t [S])/ (Km + [S])
Maximal Velocity
When E is saturate with S
[ES] = [E]t
Vo= k3 [ES] = k3 [E]t = Vm
Michaelis Menten equation
V = Vm [S]/ (Km + [S])
~ hyperbolic curve ~
of active sites are filled
[ES]/ [E]t = v/Vm = [S]/ (Km + [S])
Michaelis Menten Assumptions
- Formation of ES complex between enzyme and substrate
- no back reaction from product buildup (k4=0)
- initial velocities used for analysis (t=0)
- steady state for [ES]
- negligible depletion of substrate [S]»_space; [E]
Michaelis constant
Km= (k2 + k3)/ k1
Larger Km
Has a smaller v at the same [S]
Graph levels off at the same Vm but reaches it slower
Weak binding of the [ES] –> low affinity
Vm=k3[E]t
Maximum rate when [ES] = [E]t
Proportional to k3
Turnover number= k3=kcat
- Catalytic ability
- Typical values: 1-10^4 s^-1
- Number of S molecules converted to P by one E molecule in unit time under saturation conditions
- larger kcat –> larger v –> faster reaction
Catalytic Efficiency- what happens when [S]
Typical physiological conditions
Plot of v versus [S] is learn with an apparent second order rate constant: k3/Km = kcat/Km –> proportional to that initial slope Vm/Km
What is catalytic efficiency?
Kcat/Km –> how well an enzyme reacts with dilute amounts of substrate
Kcat/Km
Combines attributes of kcat and Km (characteristics of E-S interaction)
Perfect enzymes
Have the highest kcat/Km values
Limited only by the rate of diffusion of substrate to enzyme
10^8 - 10^9
Slowest step of the enzyme reaction
Diffusion of substrate to enzyme
However overall reaction is fast
Ideal substrate range
1/3 [KM] 2 [KM]
Line-weaver Burke
Take double reciprocal of the MM equation
1/v = Km/Vm (1/[S] + 1/Vm
Slope= Km/Vm = Km/(kcat [E]t)
Y-intercept= 1/Vm
X-intercept= -1/Km
Low slope has a better catalytic efficiency
Dis-advantages to the Lineweaver Burk Plot
Distorts errors at low [S]
Compresses data at high [S]
Sequential Mechanism
Substrate bind to form a ternary complex with the enzyme before product is release
Order sequential
Specific order for substrate binding and product leaving
“A has to go in first”
Random sequential
Random order for substrate binding and product leaving
“Either A or B can go into the reaction first”
Ping-Pong Mechanism (double replacement)
One substrate binds and release product before second substrate binds and release product
A goes in P comes out * enzyme intermediate* B goes in and Q comes out
Reversible inhibition
Bind the enzyme with noncovalent interactions
Dissociate rapidly
Allow the enzyme to recover its original activity
Irreversible Inhibitors
Bind the enzyme with covalent interactions targeting a critical residue for catalysis
Permanent inactivation of the enzyme
Competitive Inhibition
Binds to only the free enzyme
Compete with substrate for active site
Usually resembles shape and structure of substrate (or transition state) –> lacks functionality for reaction
Hinders reaction by interfering with substrate binding and reducing amount of ES complex
Analysis of Competitive Inhibitors
reduced rate is same as noncompetitive inhibitor at very low [S]
Degree of inhibition decreases with increasing [S] –> low substrate concentration is the best place for the inhibitor to work
Km decreases
Vm stays the same
Kcat/Km decreases
Substrate analogs
Have key structural features that mimic the substrate
Transition state analogs
Stable compounds that resemble the transition state in structure and polarity or charge
Uncompetitive Inhibitor
Binds only to ES Complex (substrate must be bound to enzyme) at a site different from active site but created by substrate-enzyme interaction
Lacks structural resemblance to substrate
How does a uncompetitive inhibitor work?
Hinders reaction by distorting active site and making catalytically inactive
^^catalytic residues cannot line up properly
Km decreases by the same factor of Vm
Vm decreases by the same factor of Km
Catalytically efficiency stays the same (same slope)
Do the rate constants change during inhibition for uncompetitive inhibitors?
Rate constants don’t change, we’re looking at them when the inhibitors are present –> called apparent changes
How does the degree of inhibition change with uncompetitive inhibition?
Doesn’t do much as low [S] (rate is same as control) but inhibition increases with increasing [S]
Noncompetitive Inhibition
Binds with same Ki to free enzyme or ES complex at site different from active site
Lacks structural resemblance to substrate
How does noncompetitive inhibition work?
Hinders reaction by distorting enzyme structure and preventing alignment of catalytic center
Kinetics of Noncompetitive Inhibitors
Vm –> decrease
Km –> no change
Catalytic efficiency –> decrease
increasing [S] cannot overcome effects
Degree of inhibition for noncompetitive inhibition?
Degrees of inhibition is constant with increasing [S]
% Inhibition
(1-voi/vo) X 100
Relative Rate
Voi/Vo
Relative rate- Competitive Inhibition
[S]
1/(1+ [I]/Ki)
Relative rate- Competitive Inhibition
[S]»_space; Km
1
Relative rate- Uncompetitive Inhibition
[S]
1
Relative rate- Uncompetitive Inhibition
[S]»_space; Km
1/(1+[I]/Ki)
Relative Rate- Noncompetitive Inhibition
[S]
1/(1+[I]/Ki)
Relative Rate- Noncompetitive Inhibition
[S]»_space; Km
1/(1+[I]/Ki)
Irreversible Inhibitors
Result in permanent inactivation by forming stable covalent bonds with functional groups involved in enzyme activity
What happens to [E]t and Vm with irreversible inhibitors?
[E]t decreases Vm decreases but no change in Km
^this is because inhibitors remove free enzymes from the reaction
Operate within the active site
Irreversible Inhibitors- Group Specific Reagents
Group specific reagents covalently interact with specific side chains of enzyme residues
Irreversible Inhibitors- Affinity Labels
Structurally similar to substrate and covalently bind with active-site residues
More specific than group specific reagents
Irreversible Inhibitors: Suicide Inhibitors
Also called mechanism-based inhibitors or suicide in activators
Bind at the active site and “trick” the enzyme into activating the catalytic mechanism
A chemically reactive intermediate is produced which covalently modifies the enzyme and results in permanent inactivation
^^permanent inactivation of the enzyme is a result of the enzyme’s own participation
Doe Allosteric Control obey Michaelis Menten model?
Does not obey Michaelis-Menten Kinetics
Shows a sigmoidal dependence of reaction velocity on substrate concentration
When would you use allosteric control?
These enzymes are typically rate-determining enzymes in metabolic pathways or at a junction where the substrate can be used for more than one pathway
How does Allosteric regulation work?
Involves noncovalent binding of a ligand (effector) to a site other than the active site (Regulatory or allosteric site) –> this binding affects the activity of the active site
Allosteric enzymes are generally oligomers (>1 subunit) such that interaction on one subunit affects the others (+ or - cooperativity)
Homotropic effector
Effector is same as substrate
Site is usually adjacent to active site (adjoining subunit)
Interaction almost always increases activity (sigmoidal curve)
Heterotrophic Effector
Effector is different from substrate
Site is “true” allosteric site
Interaction increases or decreases activity
How is allosteric control different from inhibition?
Allosteric control actually changes the rate constants instead of the apparent change
What can allosteric control change?
Effector-induced conformational changes in the enzyme can alter activity by changing Km (k class) and Vm (v class) or both
Positive Effector (A)
Binds to activator site and increases activity –> decreases Km
Negative effector
Binds to inhibitory site and decreases activity –> increases Km
How can allosteric enzymes by controlled?
Thru feedback inhibition
Regulatory Proteins
Proteins that either have Stimulatory or inhibitory reversible interactions with enzymes
Calmodulin
Regulatory protein that stimulates activity
Senses intracellular Ca2+ concentration and activates proteins when calcium levels rise
Antihemophilic factor (factor VIII)
Regulatory protein that stimulates activity
Enhances activity of a serine protease to accelerate the blood clotting cascade
PKA
Regulatory protein that inhibits activity
Inhibitors PKA catalytic subunits until binding of cAMP causes dissociation of regulatory and catalytic subunits
How does reversible covalent modifications work?
Catalytic properties of enzymes are modified by adding/removing charged groups (phosphate, sulfate, acetate) –> that causes conformational change and alter their function
most common: the phosphorylation/dephosphorylation cycle of specific serine, threonine, and tyrosine residues
Rate depends on the concentration of kinases (phosphate example)
Proteolytic Activation
Many enzymes are synthesized as an inactive precursor called a pro enzyme or zymogen
