Lecture 12 - How fast is that enzyme? continued Flashcards
Michaelis-Menton equation
Vmax [S]
V = –––––––––
KM + [S]
= [ES]
\_\_\_\_\_\_\_\_
[E] totalLineweaver-Burk Plot
Fitting a curve to the Michaelis-Menten equation requires a computer.
Vmax [S]
V = –––––––––
KM + [S]
The double reciprocal plot can be fit to a line.
1 = KM ́ 1 +. 1
— — x — + —
V Vmax [S] Vmax
Interpretation of Km
Characterises one enzyme-substrate pair (if an enzyme can act on different substrates, it will have different KM values for each).
Is the substrate concentration needed to reach half Vmax - Units are units of concentration, e.g. mmol/ L
k -1 + k 2
Formally, KM = –––––––
k1
For many enzymes k 2 «_space;k -1 , so approximation neglects k 2 :
k -1
KM = –––– (i.e. the ES dissociation constant)
K1
Low KM = high affinity between E and S; high KM = low affinity.
Km is the ratio of rate constants
Physiological significance of Km
In the cell, for a particular enzyme-substrate interaction, [S] is often below the KM.
• This means rate will rise to accommodate more substrate, tending to maintain steady state.
Km : substrate preference and response
Hexokinase generates energy in muscle and brain. Glucose + ATP → glucose-6-phosphate + ADP
KM for each isozyme and substrate is different.
Isozyme glucokinase stores energy as glycogen in the liver.
Kcat
Is the number of substrate molecules converted to product, per enzyme, per unit of time, when E is saturated with substrate.
Therefore helps to define the activity of one enzyme molecule – a measure of catalytic activity.
If the Michaelis-Menten model fits , kcat = k2
Thus, kcat describes the ‘rate limiting’ step.
Vmax = kcat [E]T
K2 = Vmax/ [E]T = Kcat
Kcat, Km and catalytic efficiency
The most effective enzymes should have…
• A high kcat (ability to turnover a lot of substrate into product, per second). Higher rate constant therefore can run fast
• A low KM (low substrate concentration required to achieve near Vmax; high affinity for the substrate under the Michaelis-Menten assumptions).
So kcat / KM is an overall measure of enzyme efficiency; the higher the better.
Kcat, Km and “catalytic perfection”
The upper limit for kcat / KM is the diffusion- controlled limit; i.e. the rate at which enzyme and substrate diffuse together.
Viscosity of water sets an absolute upper limit at ~109 s-1 M-1.
Enzymes with kcat / KM above 108 s-1 M-1 are referred to as ‘perfect’ catalysts.
Enzymes are optimised for …..
Specific roles
Enzyme inhibitors
Inhibitor: a compound that binds to an enzyme and reduces its activity.
Important because:
o Natural inhibitors regulate metabolism.
o Many drugs, poisons & toxins are enzyme inhibitors. o Used to study enzyme mechanisms.
o Used to study metabolic pathways.
Two classes of inhibitors
Irreversible inhibitor – binds covalently to the enzyme.
Reversible inhibitor – not covalently bound to the enzyme.
Irreversible inhibitor
binds covalently to the enzyme.
Binds and ‘kills’ the enzyme and main effect you measure is that the amount of enzyme drops
Inhibitor binds to the enzyme and permanently inactivates it.
Inhibitor reacts with a specific amino acid side chain, usually in the active site, and forms a covalent bond
Irreversible inhibition
Inhibitors bind covalently to E, thereby inactivating them irreversibly (e.g. natural toxins)
Note: They can be competitive (most common) or non-competitive (less common) but in either way their binding will result in changing the enzyme’s structure so that it no longer works. Irreversible inhibitors bind permanently to their target enzyme, often via a covalent bond that influences catalysis. “Permanently” here means over a time-scale that is long compared to the functional lifetime of the enzyme itself (and that timescale may be minutes for some bacterial enzymes, and months or years for enzymes found in stationary populations of cells in eukaryotes). So, irreversible inhibition is brought about by covalent bonds, however, normal enzymatic reactions can also include convalent bonds. The covalent bonds in normal enzymatic reactions are however easily broken simply due to the enzymes being equipped to deal with that covalent bond. Phophorylation being one example and you’ve also been told about covalent catalysis (which includes a covalent bond being formed, but also broken).
Reversible inhibitor
not covalently bound to the enzyme.
A reversible inhibitor binds to the enzyme but can subsequently be released, leaving the enzyme in its original condition.
Inhibitor binds with non-covalent bonds therefore can let go of the enzyme
A reversible inhibitor may be either ….
Competitive or non-competitive
Covalent inhibitors often react with catalytic residues
Addition of the bulky tosyl-L-phenylalanine methylketone to the histidine disables the catalytic triad and fills the active site, blocking substrate binding.
Competitive inhibition
Inhibitor competes with the substrate for binding in the active site.
Michaelis-Menten Plot - No change in Vmax (looks like it is getting to the same asymptote but it just takes longer to get there (one of them takes longer), this is what happens with a competitive inhibitor because the inhibitor and substrate are wanting to bind in the same place): High [S] outcompetes the inhibitor. (if you have more substrate then there is going to be a majority more ES complexes
Lineweaver-Burk Plot - Increases KM (because of more substrate): More substrate is needed to get to V= Vmax /2.
- Inhibitor (I) competes with the S for the active site on E
- No reaction when I bound as S cannot access the active site - I binding does affect S binding - I is usually structurally AND chemically very similar to S and forms an EI complex - Inhibition can be overcome by increasing [S]
- Vmax is unchanged and Km increases which means that the enzyme can’t bind so well anymore
Transition state analogues as drugs
Enzymes are often targets for drugs. Transition state analogues can make ideal enzyme inhibitors. Enalapril and Aliskiren lower blood pressure. Statins lower serum cholesterol. Protease inhibitors are AIDS drugs. Juvenile hormone esterase is a pesticide target. Tamiflu is an inhibitor of influenza neuraminidase.
Transition state analogs make tight binding inhibitors
Adenosine deaminase uses a tetrahedral intermediate.
A non-reactive analog, 1,6-dihydroinosine, effectively inhibits the enzyme.
Substrate analogue inhibitors of HIV protease
The inhibitor (shown as solid balls) fills the active site. Two catalytic aspartic acid residues are shown as pink rods below.
