29 - Basic Enzymology Flashcards
Michaelis Menten Model
“E”+”S” ⇌ “E”∙”S” → “E”+”P”
1st step is REVERSIBLE
2nd step is irreversible
(unidirectional)
“E”+”S” ⇌ “E”∙”S” → “E”+”P”
Enzyme contacts substrate by diffusion to form the
E-S Intermediate
Which then passes over the activation barrier to yield:
Product = P
OR
E-S can FALL APART & the enzyme / substrate diffuse away
What is k+1
- *BI-molecular** rate constant
- (involves BOTH E & S, SEPERATELY)*
for FORMING E-S
L/mole-sec = molarity-1sec-1 = M-1-sec-1
What is k-1
- *uni-molecular** rate constant
- (starts with just ONE MOLECULE = E-S complex combined)*
for DISSOCIATION of E-S
sec-1
What is k+2
- *uni-molecular** rate constant
- (starts with just ONE MOLECULE = E-S complex combined)*
for BREAKDOWN of E-S into E + P
sec-1
What is this?
RATE LAW for the M-M Model
Km = Michaelis Constant
[E0] = original enzyme concentration
NO simple interpretation of MOLECULARITY or ORDER
What is Km
Michaelis Constant
it can be RELATED to a dissociation constant (Ks)
but is NOT quite the same
just the SAME UNITS
of micromolar
What is k+2 or kcat
TURNOVER Number
the MAXIMUM # of
substrate molecules converted / turned over into product
per unit time, per active site
What is the Maximal Rate of Reaction?
Rxn rate is maximixed when ALL of the active sites
on ALL of the enzyme molecules are Filled w/ substrate
Rate equation simplifies to:
Vmax = kcat [E0]
this occurs ONLY if the enzyme is SATURATED with substrate
- generally requires that* [S] >>> Km
- If [S] is not high enough to saturate the enzyme*, you can’t use this simple expression, but must instead use the original rate law
When can this rate equation NOT be used?
Vmax = kcat [E0]
if the [S] is NOT high enough to saturate the enzyme
we can not use that expression,
we MUST use the Original Rate law
Traditional Unit = U
vs
katal = kat
- *U** of enzyme activity is the
- *amount of ENZYME** that can convert ONE micromole of substrate into products in ONE MINUTE
- *kat** = SI unit of activity, the amount of ACTIVITY that converts
- *ONE** mole of substrate into products in one SECOND
Equivilance of U to kat
1 microkat = 60 (traditional) Units of activity
Since:
kat=1mole vs U=1micromole
1 second vs 1 minute
What does this indicate? Km vs kcat
Km = micromolar
Takes A LOT of CO2 to saturate the enzyme
kcat = per second
there is a VERY FAST TURNOVER
What does this indicate? Km vs kcat
Km = micromolar
does NOT take a lot of substrate to saturate the enzyme
kcat = per second
there is a VERY FAST TURNOVER –> produce pyruvate quickly
What does this indicate? Km vs kcat
elastase chews up on AA’s
Km = micromolar
Takes A LOT of substrate to saturate the enzyme
kcat = per second
there is a SLOW turnover
What does this indicate? Km vs kcat
fumarase is in the TCA cycle
Km = micromolar
does NOT take a lot of substrate to saturate the enzyme
kcat = per second
there is a VERY FAST TURNOVER
When can Km be APPROXIMATED by Ks for the E-S complex?
Km = Michaelis Constant
Ks = dissociation constant
Km =~ Ks
ONLY IF
k+2 / k+1 <<< Ks
rate of catalysis is MUCH SLOWER*** than ***rate of dissociation
_k<sub>+2</sub>_ = _rate of **breakdown** of E-S --\> E + P_ k<sub>+1</sub> = rate of ***dissocation*** of E + S \<-- E-S
What is Ks
_k<sub>-1</sub> = rate of ***dissociation*** of **E + S** \<-- E-S_ k<sub>+1</sub> = rate of **formation** of E + S --\> **E-S**
- *RATE of Dissociation**
- only approximates Km if the rate catalysis is MUCH SLOWER than the rate at which E-S dissociates back to E + S*
How to determine the INITIAL RATE of an enzyme reaction?
and [Eo]
Set up the rxn with measured # of enzyme & substrate
then follow the progress by measuring appearance of PRODUCT
then PLOT = [Product] vs [time]
SLOPE = Rate of Rxn
(use the slope in the LINEAR REGION of the plot)
then TRACE BACK TO T=1 for [E0]
Initial Rate Determination
GRAPH
use the slope in the LINEAR REGION of the plot
How to find Half-Maximal Velocity = 1/2 Vmax
When [S] = Km , then v = 1/2 Vmax
the numerical value for [S0] = Km
First find the maximum (plateau) for the initial rate = v
then drop back in concentration of substrate = [S] to where v is
half the maximal value
then find the corresponding initial concentration of S
What is the Lineweaver-Burk Plot?
Double-Reciprocal Plot
1/v vs 1/[S]
(min/um) vs (M-1)
Km / Vmax = Slope
should be a STRAIGHT LINE
ONLY IF the enzyme obeys the Michaelis-Menten model
x-intercept @ -1 / Km
y-intercept @ 1 / Vmax
What type of plot is this?
Double Reciprocal
LINEWEAVER-BURK
only a STRAIGHT LINE slope if enzyme obeys M-M model
Where is the X-Axis Intercept in the
Lineweaver-Burk (Double Reciprocal) Plot?
-1 / Km
(micromolar-1)
slope = Km / Vmax
Where is the Y-Axis Intercept in the
Lineweaver-Burk (Double Reciprocal) Plot?
1 / Vmax
slope = Km / Vmax
(min / micromole)
What plot is this?
Lineweaver-Burk
What plot is this?
- *Eadie - Hofstee Plot**
- not very useful*
What plot is this?
Hanes - Wolf Plot
Technically superior > lineweaver burk
because there is least distortion to experimental ERRORS
When do we see a Non-Linear / CURVED Plot?
and WHY?
When the enzyme is NOT following that model
2 common possibilities of curvature:
may be MORE Kinetic STEPS in the mechanism that the M-M model allows
ENZYME may have MULTIPLE ACTIVE SITES
which may be interacting with one another
= cooperativity (pos / neg)
What do we do with CURVED PLOTS?
compare to “linear” type plots to diagnose deviations
from the M-M model
USE Curve-Fitting SOFTWARE** + **full non-linear rate law
to get accurate estimates of the kinetic parameters
kcat and Km
k+2= kcat = turnover number
Basic ways to measure the # of enzyme (concentration)
Assays
IMMUNOASSAY
needs specific AB’s, does NOT measure _inactive_ enzymes
ELECTROPHORESIS
stain -> scan slow also does NOT measure active enzyme
STANDARDIZED RXN
FAST, but may call for _coupling_ of 2+ sucessive rxns in order to measure the product spectrophotometrically
Immunoassay
Positives & Negatives
(basic ways to measure enzyme concentration)
Need SPECIFIC ANTIBODIES to the enzyme
does NOT measure INACTIVE enzyme
only measures the ACTIVE enzyme
think immunoAssay = measures ACTIVE
Electrophoresis
Positives & Negatives
(basic ways to measure enzyme concentration)
Electrophoresis -> stain -> scan
SLOW
NOT for measuring ACTIVE enzyme
only measures the inactive enzyme
Stantardized Reaction
Positives & Negatives
(basic ways to measure enzyme concentration)
Measures the ACTIVITY of enzyme
FAST
but may call for COUPLING of two or more successive rxns in order to measure the product
SPECTROPHOTOMETRICALLY
How do we monitor an enzyme that
does NOT use a substrate or form a product?
ENZYME COUPLED ASSAY
UV ABSORBANCE** or **FLUORESENCE
done DIRECTLY by coupling it to a second INDICATOR REACTION that itself, does NOT give a useful signal
need to add EXCESS SUBSTRATE & Secondary ENZYME
to ensure that the
rate limiting factor is the #enzyme in the first rxn
Coupled Assay Time Course
Lag Phase -> up to Incubation time
time BEFORE products are being made
To ensure that the:
Overall Rate-limiting Factor = Amount of Enzyme 1
(1st enzyme that is or diagnostic quanitity)
we need:
EXCESS SUBSTRATES for BOTH reactions to reach SS
EXCESS ENZYME #2 the one for the indicator reaction
Aspartate Amino Transferase (AST)
as an Example of Coupled Enzyme Assay
AST catalyzes this rxn:
Aspartate + a-Ketoglutarate ↔ Glutamate + Oxaloacetate
The indicator rxn #2 uses malate dehydrogenase for:
Oxaloacetate + NADH + H+ ↔ Malate + NAD+
We then follow the PRODUCTION OF NAD+ using
FLUORESCENCE** or **UV ABSORBANCE
we need excess:
reactants & 2ndary enzyme (malate dehydrogenase)
What type of Inhibition is this?
Reversible COMPETITIVE inhibition
Competitive Inhibition
- *inhibitor** blocks S from binding in the active site
- various ways to block / different points of contacts*
Formation of E-S complex is Reduced, new complex, E-I is formed
unlike Km,
Ki(inhibitory constant) isreally a EQ dissociation constant (Ks)
- Competitive Inhibitor** has *_NO EFFECT_ on the catalytic step
- *kcat = k+2** is THE SAME & Vmax is also THE SAME
In Reversible Competitive Inhibtion
Can the addition of MORE substrate OVERCOME the inhibition?
(restore the OG rate of rxn)
YES
apparent Michaelis constant is numerically LARGER than Km
so it INCREASES as the concentration of INHIBITOR RISES
takes MORE substrate to HALF-SATURATE the enzyme when a competitive inhibitor is present
Competitive Inhibition’s effects on:
kcat & Vmax & Km
(k+2) turnover rate / maximum velocity
kcat & Vmax STAY THE SAME
Km decreases
MORE substrate can OVERCOME inhibition
What type of Inhibition Graph?
Reversible COMPETITIVE inhibition
Increasing [I] = more inhibitor leads to:
Slope = Steaper Slope
Y-axis (vertical) = Same Y-Intercept
Vmax does NOT change
X-axis = Different X-intercepts
Km decreases
What type of Inhibition Graph?
UN-COMPETITIVE inhibition
Increasing [I] = more inhibitor concentration leads to:
Slope = No Change (Parallel Plot)
Y-axis (vertical) = Increase Y-Intercept
Vmax is progressively reduced
X-axis = Increase X-intercept
Km is progressively reduced
What type of Inhibition Graph?
NON-COMPETITIVE inhibition
Increasing [I] = more inhibitor concentration leads to:
Slope = Increasing Slope
Y-axis (vertical) = Increase Y-Intercept
Vmax is reduced
X-axis = SAME X-Intercept
Km does NOT change
UN-Competitive Inhibition’s effects on:
kcat & Vmax & Km
(k+2) turnover rate / maximum velocity
kcat idk
REDUCE BOTH Vmax & Km
NOT POSSIBLE TO OVERCOME INHIBITION
NONCompetitive Inhibition’s effects on:
kcat & Vmax & Km
(k+2) turnover rate / maximum velocity
kcat ?
Vmax INCREASES
Km stays the SAME
NOT able to OVERCOME INHIBITION with more substrate
What type of Inhibition is this?
NONCompetitive / MIXED Inhibition
NONCompetitive = special case of mixed
inhibitor has SAME AFFINITY for either E or E-S complex
Ki = Ki‘
MIXED
Ki & Ki’ are allowed to be different
What type of Inhibition is this?
UN-Competitive Inhibition
parallel graph, vmax &km get smaller
UN-Competitive Inhibition
relatively UNCOMMON, Parallel Plots
- *Inhibitor –> E-S complex**
- does NOT bind to the FREE ENZYME*
NO E-I complex is formed
E-S-I complex is catalytically inert
still reversible
NOT POSSIBLE to
OVERCOME INHIBITION w/ MORE SUBSTRATE
Mixed / NON-Competitive Inhibition
converge to the same X-intercept (-1/km), same Km
Inhibitor –> complex with BOTH: E & E-S
E-I & E-S-I complexes are Both INACTIVE
ADDING MORE SUBSTRATE WILL NOT OVERCOME INHIBITION
since inhibition can STILL OCCUR when the substrate binds
alcohol dehydrogenase inhibition
by 3-butylthiolane 1-oxide
Example of
UN-Competitive Inhibition
PARALLEL PLOTS
NAMPT inhibtion by NAD / NADH
NON-Competitive Inhibition
all converge to same X-Intercept
(-1/Km)
What is the difference between
Mixed** & **Noncompetitive Inhibition?
NON-Competitive Inhibition
a SPECIAL CASE of Mixed Inhibition where
inhibitor has the SAME affinity for BOTH E & E-S complex
numerically, Ki = Ki‘
- *Mixed Inhibition**
- *Ki & Ki‘** are allowed to be DIFFERENT
