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Michaelis-Menten kinetics
Vmax approachedasymptotically
V0 = Vmax x[S]/([S] + Km)
V0 is moles of productformed per sec. when [P]is low (close to zero time)
Michaelis-Menten Equation
E + SESE + P
Michaelis-Menten Model
V0 varies with [S]
Steady-state & pre-steady-state conditions
At equilibrium, no net change of [S] & [P]or of [ES] & [E]
At pre-steady-state,[P] is low (close to zerotime), hence, V0 for initial reaction velocity
At pre-steady state, we can ignore the back reactions
Michaelis-Menten kinetics (summary)Enzyme kinetics (Michaelis-Menten Graph) :
At fixed concentration of enzyme, V0 is almost linearly proportionalto [S] when [S] is small, but is nearly independent of [S] when [S]is large
Proposed Model: E + S ES E + P k2
ES complex is a necessary intermediate
Objective: find an expression that relates rate of catalysis to the concentrations of S & E, and the rates of individual steps
k1
Michaelis-Menten kinetics (summary)
Start with: V0 = k2[ES], and derive,
V0 = Vmax x[S]/([S] + Km)
At low [S] ([S] < Km), V0 = (Vmax/Km)[S]
At high [S] ([S] > Km), V0 = Vmax
When [S] = Km, V0 = Vmax/2. Thus, Km = substrate concentration at which the reaction rate (V0) is half max.
Allosteric enzyme kinetics
Sigmoidal dependence of V0 on [S], not Michaelis-Menten
Enzymes have multiple subunitsand multiple active sites
Substrate binding may be cooperative
MethotrexateA competitive inhibitor of dihydrofolate reductase - role in purine& pyrimidine biosynthesis
Used to treat cancer
Kinetics of competitive inhibitor
Increase [S] toovercomeinhibition
Vmax attainable,Km is increased
Ki =dissociationconstant forinhibitor
Kinetics of non-competitive inhibitor
Increasing [S] cannotovercome inhibition
Less E available,Vmax is lower,Km remains the samefor available E
Enzyme inhibition by DIPFGroup - specific reagents react with R groups of amino acids
diisopropylphosphofluoridate
DIPF (nerve gas) reacts with Ser in acetylcholinesterase
Catalytic strategies commonly employed
1.Covalent catalysis. The active site contains a reactive group, usually a nucleophile that becomes temporarily covalently modified in the course of catalysis
2. General acid-base catalysis. A chemical reaction is catalyzed by an acid or a base. The acid is often the proton and the base is often a hydroxyl ion. A molecule other than H2O may play the role of a proton donor or acceptor.
3. Metal ion catalysis. Metal ion can function in several ways;
• can serve as an electrophile, stabilizing a negative charge on a reaction intermediate. • can generate a nucleophile by increasing the acidity of a nearby molecule, such as H2O in the hydration of CO2 by carbonic anhydrase. • can bind to substrate, increasing the number of interactions with the enzyme.
4. Catalysis by approximation. Bringing two substrates together along a single binding surface on an enzyme
Enzyme specificity: chymotrypsinCleaves proteins on carboxyl side of aromatic, or large hydrophobic amino acid
Bonds cleaved, indicated in red
The enzyme needs to generate a powerful nucleophile to cleave the bond
A highly reactive serine (#195) in chymotrypsin
27 other serines not reactive to DIPF,Ser 195 is a powerful nucleophile
DIPF: di-isopropylphosphofluoridate, only reacts with Ser 195
Covalent catalysis
Hydrolysis in two stages
Acylation to form acyl-enzyme intermediate
Deacylation to regeneratefree enzyme
Ser 195 OH groupattacks the carbonyl group
Acyl-enzyme intermediateis hydrolysed
Chymotrypsin in 3D3 chains; orange,blue, & green
Catalytic triad ofresidues, includingSer 195
2 interstrand, &2 intrastranddisulfide bonds
See Structural Insights
Synthesized as chymotrypsinogenProteolytic cleavage to 3 chains
The catalytic triad (constellation of residues)
Ser 195 converted into a potent nucleophile, an alkoxide ion
Imidazole N asbase catalyst,accepts H ion,positions &polarizes Ser
Asp 102orientsHis 57
H ion withdrawal from Ser 195 generatesalkoxide ion
1. Allosteric control. Proteins contain distinct regulatory sites and multiple functional sites. Binding of regulatory molecules triggers conformational changes that affect the active sites.
Display cooperativity: small [S] changes - major activity changes. Information transducers: signal changes activity or information shared by sites
2. Multiple forms of enzymes (isozymes). Used at distinct locations or times. Differ slightly in structure, in Km & Vmax values, and in regulatory properties
3. Reversible covalent modification. Activities altered by covalent attachment of modifying group, mostly a phosphoryl group
4. Protleolytic activation. Irreversible conversion of an inactive form (zymogen) to an active enzyme
Regulatory Strategies: Enzymes & Hemoglobin
Aspartate transcarbamoylase reaction
Committed step in pyrimidine synthesis: inhibited by end productCTP
ATCase displays sigmoidal kineticsSubstrate binding to one active site converts enzyme to R stateincreasing their activity: active sites show cooperativity
Oxygen delivery by hemoglobin, cooperativity enhanced
Partial pressure of oxygen
98 - 32 = 66%
63 - 25 = 38%
Cooperativityenhances delivery 1.7 fold
Heme group structure
4 linked pyrrole ringsform a tetrapyrrolering with a centraliron atom.side chains attached
Position of iron in deoxyhemoglobin
Iron slightly outsideporphyrin plane
His (imidazole ring)binds 5thcoordination site
6th site for O2 binding
Transition from T-to-R state in hemoglobin
As O2 binds, top pair rotate 15o with respect to bottom pair
Interface most affected
Oxygen affinity of fetal v maternal red blood cells
Fetal Hgl does notbind 2,3-BPG,higher O2 affinity
Fetal hemoglobintetramer has2 alpha & 2 gamachains,
Gene duplication
Isozymes of lactate dehydrogenase: glucose metabolism
Rat heart LDH isozyme profile changes with development
H(heart) isozyme (chain)= square, M(muscle) isozyme = circle
Tissue content of LDHFunctional LDH is tetrameric, with different combinations of subunits possible. H4 (heart) has higher affinity for substrates than does M4 isozyme, different allosteric inhibition by pyruvate
H4
H3M
H2M2
HM3
M4Some isozymes in blood indicative of tissue damage, used for clinical diagnosisIncrease in serum levels of H4 relative to H3M, indicative of myocardial infraction (heart attack)
Protein phosphotases
Reverse the effects of kinases, catalyze hydrolytic removal ofphosphoryl groups attached to proteins
Secretion of zymogens by acinar cell of pancreas
Pancreas, one of the mostactive organs insynthesizing & secretingproteins
Acinar cell stimulated byhormonal signal ornerve impulse, granulecontent released intoduct to duodenum
Proteolytic activation of chymotrypsinogen
Active enzyme generatedby cleavage of a singlespecific peptide bond
3 chains linked by 2interchain disulfidebonds, (A-B & B-C)
Conformations of chymotrypsinogen & chymotrypsin
Electrostatic interactionbetween Asp 194carboxylate & Ile 16-amino group possibleonly in chymotrypsin,
essential for activity
Zymogen activation by proteolytic cleavage
Digestive proteins of duodenum
Secreted by cells that line duodenum
Zymogens orange, active enzymes yellow